Risk Management View of Global Best Practices in ERM for Insurers and Financial Supervision Reinsurers Webcast by Stephen W

R ISK M ANAGEMENT S ECTION

“A JOINT SECTION OF SOCIETY OF ACTUARIES, CASUALTY ACTUARIAL

SOCIETY AND CANADIAN INSTITUTE OF ACTUARIES”

August 2008, Issue No. 13 Risk Published in Schaumburg, Ill. Management by the Society of Actuaries

Table of Contents

Diversity is the Spice of Life International Survey of Emerging Risks by Ronald J. Harasym______2 by Max J. Rudolph ______33

ERM Perspectives Summary of “Variance of the CTE Estimator” by Wayne H. Fisher______4 by John Manistre and Geoffrey Hancock______37

An Enterprise Risk Management View of Global Best Practices in ERM for Insurers and Financial Supervision Reinsurers Webcast by Stephen W. Hiemstra______9 by Tsana Nobles______43

Increasing the usefulness of ERM to ERM Symposium: Notes on a Conference insurance companies by Stephen W. Hiemstra and Valentina Isakina _ 50 Jean-Pierre Berliet______18 Third Year a Charm for ERM Symposium Risk Identification: A Critical First Step in Scientific Papers Track Enterprise Risk Management by Steven C. Siegel ______55 by Sim Segal______29 Risk Management w August 2008 Chairman’sChairperson’s Corner Corner Diversity is the Spice of Life! Ronald J. Harasym

fabulous thing about Looking at some of the articles in this issue enterprise risk man- of the newsletter, there is a wide and exciting A agement (ERM) is range of topics. Wayne Fisher discusses what it the diversity of issues that takes to successfully embed ERM in a firm, the one can become involved in. development of models and setting parameters, Timing is everything! There and the importance of research. As discussed is no question that the operat- in the article by Stephen Hiemstra, supervisory ing environment keeps in- ERM differs from firm ERM because loss ex- creasing in complexity over posures and consequences differ. However, in time. Add to this a few emerg- order to be effective and efficient, the two need ing risks in concert with some to work and evolve in harmony with each other. systemic risks and you have ERM provides a company’s management the the ideal setting for the call to opportunity to inform and communicate with action of ERM professionals. supervisors. Without this window, supervisors must make risk assessments at a distance and It is the diversity of ERM issues that as actuar- with a lag—clearly not a good situation. ies, we have the opportunity to apply our training, skills, and knowledge to many different Jean-Pierre Berliet’s article discusses how types of issues well beyond what we could have the application and integration of ERM into imagined just a few years ago. The basic train- the decision making process has faced many ing to become an actuary provides a great foun- challenges and how ERM will be more effective dation and solid grounding for an ERM role, but in companies that identify and correct design it is important to recognize that our training not weaknesses in their approach. Sim Segal’s only prepares us with the specific issues that article highlights that even common practice are part of our education, but also to apply those in risk identification is suboptimal in several principles to new, non-traditional areas. aspects and how companies can better execute the risk identification phase of the ERM process As is true for anyone who wants to do well in any cycle. As the results from a survey of emergings role, a critical element of success is to stay cur- risks for financial services by Max Rudolph rent and educated on the latest thinking, trends, show, any given group will have differing views practices, and experiences. From an ERM per- and bias based on their knowledge, location spective, an easy way to do this is to volunteer and experience. and get involved in the Joint Risk Management Section’s activities. Over the past several years, All in all, there is still much we can learn with the section has been actively involved in educa- respect to ERM. We have a strong foothold on tion, meetings, webcasts, networking sessions, ERM positions in the insurance industry and and research. The Joint Risk Management we have a basis for competing for ERM positions Section has been reaching further out into the outside of the insurance industry. The Section international risk management arena with Ronald J. Harasym, FSA, Council has acknowledged that acquiring and the translation of the section’s newsletter into CERA, FCIA, MAAA, is vice improving our skills is a critical part of the equa- French, Spanish, and Chinese. There are areas president and actuary at tion. Together, we can succeed. So get involved New York Life Insurance Co for all interests and opportunities for everyone in the section. Volunteer! F in New York, NY. He can be to actively participate, contribute, and share reached at experiences. ronald_j_harasym@ newyorklife.com

w Page 2 Chairman’s Corner Risk Management w August 2008 Chairman’sERM Perspectives Corner ERM Perspectives Wayne H. Fisher

Fortunately, CROs have now typically made it to the “C” suite, which is critically important for access to information and the ability to ensure remedial actions are actually implemented. But the challenge now, in these times, is staying in the “C” suite and balancing personal risk management with the enterprise’s risk management.

Personal experiences always influence our perspective and in my case I was fortunate to see just how an engaged CEO and board, with a real commitment to risk management, can build real value. Zurich Financial Services (ZFS) went through a “near death experience” in 2002 with financial guarantees emerging from the woodwork, reserve inadequacies, little data Note: A truncated version of this article on risk accumulations on the underwriting and originally appeared in the February investment side, subsidiaries operating very in- 2008 issue of the Casualty Actuarial dependently, and on and on. Jim Schiro entered Society’s Actuarial Review. Reprinted with as CEO and immediately launched a large num- permission. ber of critical improvement actions, including raising capital, selling assets, implementing iming is everything and these are expense measures, and putting a focus on core exciting times for chief risk offi- businesses and systems. And one of these T cers. The subprime phenomena has critical initiatives was a solid mandate to build led to such visibility that you can’t open a a state-of-the-art risk management program newspaper these days without mention of a and embed it in the organization. Thereafter, firm’s ability or, all too frequently, its inin every move we made, we always knew we ability to manage its risk. And that’s where had the full backing and support of our CEO. we can step in. We’re the risk people! That’s unquestionably the single most important key to success in implementing a risk man- And as always, risk creates opportunity. agement framework. Personal risk is high as boards and regulators probe the adequacy of risk measures and In June 2007, five years later, S&P returned controls. Even CEOs have been fired. But ZFS to “double A” status, and in its press re- the opportunity to contribute to a firm’s value lease particularly noted improvements in risk is greater than ever with all of the focus on controls and management. Then in October identifying and quantifying risk, whether in 2007, it was announced that Jim Schiro would appropriately valuing assets and liabilities for receive an award from St. Johns University extreme scenarios, managing limits for a firm’s as “Insurance Leader of the Year,” which risk profile to minimize the next problem, and singularly noted that he was an “exceptional bridging the various risk elements to create a leader with a comprehensive view of risk taking truly enterprise view. and risk management.” This showed me that

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during all that time, when we had our meetings The board sets the tolerances at the highest and he was looking at his Blackberry, he really level. The risk framework then extends this was listening! tolerance to units at the operating level, with the intent of providing transparency and an This article will address three themes: internally consistent framework. Generally The lesson you always this leads to a risk policy with internal limits on learn is your defini- 1. Successfully embedding ERM in the firm almost everything, at unit and divisional levels, 2. Developing models and setting parameters and that allows such limits to be actionable tion of extreme is not 3. Incorporating and supporting the latest and monitored at the lowest levels. It’s the risk extreme enough. You ERM research modeling and the risk management function need the leadership that ensures and reports that the actionable 1. Embedding ERM in the Firm limits, when aggregated across the firm, reason- and involvement from ably meet the risk expectations implicit in the Most critical to embedding ERM in the firm the top to try to iden- board’s high-level tolerances. It’s also impor- is the interest and involvement of the board of tant for the board to review and agree on the tify Donald Rumsfeld’s directors. Today that might not be an issue, but internal operating risk limits, again, to engage today’s risk failure headlines won’t always be at “unknown unknowns”… the limits, but also to provide an element of clout the top of the mind. the risks “we don’t know within the firm to ensure adherence. we don’t know.” Risk tolerances, and how the firm monitors Another measure to engage the board is what compliance with the agreed tolerances, are a we call total risk profiling. This is a structured good starting point as they are at the heart of exercise with a senior management group that the board’s governance responsibilities and, as develops and evaluates scenarios for risk impli- a practical matter, the discussions quickly be- cations and reviews remedial plans and the sta- come engaging. Basic questions should address tus of agreed-upon follow-up actions. Including what the board wants for maximum volatility, the board and senior management provides for quarterly or annually, in an agreed period of the broadest views on stress scenarios and is a time (e.g., one in ten years), in the following solid way to get real involvement and ownership. areas: net income (posting a loss, for example), This is key to considering bold scenarios, as the ability to maintain dividends, solvency and CFO of Goldman Sachs recently remarked, rating agency capital at levels not impacting “The lesson you always learn is that your defi- operations or strategic initiatives, and franchise nition of extreme is not extreme enough.” You value (performance vs. peers). need the leadership and involvement from the top to try to identify Donald Rumsfeld’s “un- These are followed by more intriguing ques- known unknowns”…the risks “we don’t know tions, such as how to balance a maximum loss we don’t know.” on a hurricane vs. an operational risk loss. Or consider foreign exchange trading vs. non- Discussions of emerging risks are an important investment grade bonds. All affect the balance element. We must consider not just which ones sheet the same way but the perceptions from the might in fact emerge (e.g., nanotechnology, investors may well be vastly different. Thinking climate change, pandemics, cell mutations) through the New York Times test, with the goal but also why they might be relevant to our of avoiding the “whatever were they thinking” firm. We must also consider major changes in questions, also makes for good engagement with foreign exchange or the credit markets—how the board. continued on page 6 w

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might they be relevant? The CRO needs to do oversight in the specific risk area. Why? It is im- the homework, of course, on the stress scenarios portant to assign ownership within the area and and relevant exposure numbers, but such an then risk management can be the “auditor” and exercise is a good way to embed risk manage- keep its primary focus on correlations, aggrega- ment in the organization. If the “top dogs” at the tions, modeling, and scenarios at the enterprise board level do it, you can quite effectively get the level, which are at the heart of an ERM program businesses to emulate the exercise at their levels and where the real value is added. and to stiffen up the scenarios they consider. Then you can really harness the creative power Operational risk (including business continuity of the organization. management) is another way to increase awareness and involve local management. Subtleties With the board involved and demanding infor- such as allocation to line and geographical mation, the mandate is there to establish risk unit help to strengthen the reliability of data committees at all levels in the organization. collection, for example, and ensure other fol- Designated CROs, too, even if not full time, low-through actions are implemented. More should organize the risk activities, including the important than the rigor, though, is the idea risk profiling, reviewing risk exposures vs. risk that you are doing allocations and that makes it policy limits, measuring progress on remedial important, and so actions follow. If there are no actions, and providing relevant information up- consequences, then it becomes a “nice to-do.” wards. The breadth provides an important com- Operational risk losses can have greater conse- fort to management and the board, but it’s also quences than, say, a hurricane loss—one is our valuable in embedding the risk culture in the business and the other is a sign of weak controls organization. The enterprise view necessarily and management. This sends a tough signal to requires bridging the silos in an organization. My the markets. experience is that it is best if the CRO allows each functional area to carry out its own risk manage- Collectively, actions like these engage the ment. While risk management coordinates these board and drive ERM into the organization. risk management activities, ensuring rigor and Nirvana is when the audit committee (or finance that the limits fit the overall risk profile, I advise committee) gets so engaged with risk issues that leaving responsibility for the day-to-day risk the board decides to create a risk committee… which ZFS did in 2006.

2. Develop Models Collecting relevant data is critical. A mantra of Zurich’s Jim Schiro is: “What gets measured gets done” (and paid attention to). This requires addressing system incompatibilities, standardiz- ing definitions, and the like, so that measures of risk exposure can be aggregated on a consistent and meaningful basis.

The models, of course, are what provide the overall framework to aggregate the firm’s risk tolerance to specific risk limits by segment (e.g., credit risk, investment risk, ALM risk,

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underwriting risk, F/X) while incorporating Ben Bernanke describes as the all too frequent assumptions on correlations and distributions. “misunderstanding of financing models among The models are unquestionably important but senior management, or a failure to recognize and almost more important than the models and their cover limitations of the models.” “results” is the discipline in setting the myriad internal risk limits, monitoring compliance, and A typical scenario that would provide valuable aggregating relevant accumulations across the discussion with the management group would be organization. That’s where real risk management how interconnected global markets should make value gets added. the world economy more stable, with risk spread more widely. But, Richard Bookstaber writes Assessing aggregate credit exposure is a good that “It’s not happening.” What’s different now example of the complexity and need for data is how closely international markets are cor- capture across the firm: Reinsurance assets, related with one another. Bookstaber continues, exposure in the UPR, bonds, equities, security “Everyone tends to invest in the same assets lending, performance guarantees, and surety and employ the same strategies…As markets bonds, E&O and D&O all have the potential to become more linked, diversification doesn’t aggregate into a loss in a stress situation for a work as well.” firm. Examples in the insurance arena include group life, workers compensation, property Bookstaber further points out that “global mar- on the building, D&O, E&O, equities, bonds, kets may actually be more risky than in the past, guarantees of various types, etc. All present as the same types of investors are taking on the complicated data capture issues, especially in same type of risky bets and then simultaneously an international organization, not to mention heading for the exits when trouble comes,” mak- referring and acting on incidents of excess ac- ing the hedging fail or become unavailable. cumulation. Later, I’ll address some research Stress scenarios we need to consider for their im- that Enterprise Risk Management Institute pact on a particular enterprise need to contem- International (ERMII) members are conducting plate such unfolding economic relationships. in this area. The models are also necessary for capital al- Collective input on correlations is important, location (but again much of the value isn’t in particularly correlations for stress scenarios. the allocation, but in the understanding that Valuing underwriting exposures and assets and capital is being allocated and if one effectively liabilities in stress situations are important, too. and transparently manages risk it leads to less Richard Bookstaber the author of A Demon of capital—an important outcome). our Own Design, observed, “We must move from the technicalities to judgment.” The “KISS” This is much more important than the nuances principle (Keep it Simple, Stupid) is alive and on the allocation. It’s the same for the operational well. In identifying the key parameters, espe- risk allocation. Too often, we don’t allocate such cially correlations, we need to get outside and expenses because we can’t provide sufficient inside views and create a transparent process “accuracy” but it’s the idea that it is being al- for the final selections and related probabilities, located that lines up the “hearts and minds.” both for buy-in from senior management and the Another aspect of the models and relevant data board and for the explanations when and if an is to question values under extreme stress sce- incident arises. We must balance the sophisti- narios. The subprime meltdown is, of course, a cated with the practical if one is to avoid what recent glaring example. But as a general rule,

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and going back to Shiro’s “What gets measured Heriot-Watt University in Scotland, explained gets done,” perhaps it should be expanded to how mixture models for random vectors may be “Don’t do what you won’t be able to measure.” You useful in risk modeling. Steve Kou, of Columbia don’t want to go to your management with a quote University, tackled the question of what is a like Ben Bernanke’s on collateralized debt obli- good risk measure. Gary Venter had an excellent gations, when he said: “I’d like to know what these presentation on pricing the “option” a subsidiary damn things are worth.” And in this vein, we have has on the firm’s capital. All of the presentations preliminary plans in place for ERMII to develop were interesting, with practical insights. The a joint workshop in the spring with Columbia on presentations are on the ERMII Web site. Please valuing illiquid assets. In addition, the research visit the site to see which ones might be relevant track at the ERM Symposium will include work on to your organization. certain aspects of quantifying credit risk. Broadly, the subjects are extremely relevant 3. Incorporate and Support now. The real internal value is in discussing the Latest Research relevance to a firm’s risks and the discussion of Why is research important? It’s partly defen- parameters, stress scenarios, etc.—getting the sive—if adverse circumstances develop, you risks identified and getting senior management want to be able to demonstrate an appreciation involved in determining them. Also, participa- and work toward “state of the art.” And there tion in such research work on correlation factors is some good research work going on now. The might well provide some “safe harbors” for the task is to determine which best practices could modeling and firm if and when a stress incident meaningfully and reasonably be incorporated occurs. And since the Lyon workshop we’ve held in the risk models, impacting stress scenarios, a workshop with Columbia University on valuing correlation parameters, and so forth. illiquid assets, a timely subject for sure. We’ve also worked with the PRMIA Institute on the ERMII members are one good source for such re- research track for the ERM Symposium in April. search. The CAS and SOA are sponsors of ERMII, as is the Institute of Actuaries in Australia. ERMII Plans are under way for a research conference has a clear research focus. Academic institu- November 12 on commodity risk, which we tions are the members, and include Columbia will co-sponsor with S&P. The venue will be University, University of Lyon, Carnegie Mellon, New York. Details will follow. University of New South Wales, Georgia State, Wuhan University in China, and others. If anyone is interested in participating with one or more of the ERMII research groups on top- ERMII has held a research workshop in Lyon, ics such as the treatment of risks with different Wayne H. Fisher is executive France on evaluating diversification at the time horizons in a market-consistent way, or the director of the Enterprise group level, which was typical of a number of interplays between liquidity, market value and Risk Management Institute such research activities. The presentations long-term value, and how one might value a se- International. He can be ries of deposits (as in a life policy), please contact reached at [email protected]. included one by Shaun Wang of Georgia State on “Correlation Modeling and Correlation me. This would be another way to ensure that you Parameters for Economic Capital Calculations,” are incorporating state-of-the-art research and which examines various drivers of correlation, techniques. My final thought is that the ERM along with their diversification benefits or techniques described here readily apply to non- contagion effects. Wang’s project also included financial services industries. Longer term, using some tail correlation models, including correla- our quantitative risk skills to expand into these tion between risk factors, business lines, and other industries presents strong growth opportu- geographic regions. Alexander McNeil, from nities for actuaries. F

w Page 8 August 2008 w Risk Management Chairman’s Corner An Enterprise Risk Management View of Financial Supervision

Dr. Stephen W. Hiemstra

This research report has been reprinted with permission from ERM-II. Due to space considerations, only the introduction and the first section of the research report appear here. To view the complete report, please visit www.ermii.org.

Introduction

inancial supervision refers genetically to the many activities used by govern- F ment financial regulators to promote safe and sound firmmanagement, including:

• Recommending that Congress pass laws and promulgating regulations and policies to implement those laws that enhance firm safety and soundness. • Monitoring firm activities through on and off- SAFETY AND SOUNDNESS site risk analysis, including examination. SUPERVISORS FOCUS ON • Requiring firms publish financial FIRM SOLVENCY statements and supporting information on Financial firms play a key role in assuring a their operations. healthy economy through the expansion of cred- • Legal and regulatory sanctions imposed on it. They are able to play this role in a safe and firm staff and management and corporate sound manner, however, only if the firm is prof- entities. itable and remains solvent. If a financial firm • Administration of deposit and other insurance is not profitable, it cannot expand credit and funds. credit could contract as underwriting standards • Requiring firms maintain adequate levels of are tightened and loanable funds are no longer reserves and capital. available. When it becomes insolvent, then • Verbal and written public comments about its creditors cannot be compensated for their firm operations. investment, borrowers cannot be served, employees cannot be paid, and management has an Traditionally, the definition of safety and sound- incentive to make imprudent investments. For ness has been kept vague to preclude regulated these reasons, governments frequently tie the firms from undermining regulatory and legal privileges of operating a financial firm to the re- requirements through honoring the letter, but quirement that they remain solvent and submit not the spirit of the law. to financial supervision.

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1 I have quoted occasionally from presentations at the 2006 Enterprise Risk Management Symposium in Chicago. The slides and recordings of the presentations can be found at: www.ERMSymposium.org/handouts.php. Look for General Session 3: The Role of ERM in Regulation and Concurrent Sessions 4: Case Studies of ERM in Financial Regulation.This problem is starting to be noticed. See, for example: (Altman, 2006).

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Virtually every decision made by supervisors is and stake in the firm. Because of limited li- predicated on concern about future firm solvency. ability, stock and bond investors will only lose A formal statement of this concern is to measure the amount of their investment. Counterparties the impact of a decision on the chance that a firm will lose only the amount of their contractual will become insolvent over a period of time into obligation. Managers and employees may only the future. We define the risk of a future loss lose their jobs. resulting insolvency as the probability (a percent between zero and one) of insolvency over the next The view of losses taken by supervisors may X years. also differ depending on the mix of activities— chartering authority, insurance fund manage- Because insolvency is usually a rare event, ment, and policy responsibilities—bundled with supervisors typically disaggregate and analyze the safety and soundness mandate. Chartering the firm’s losses. In doing so, they are implicitly supervisors will loose the revenue associated arguing that likely losses associated with partic- with their fees. Indirect (spillover) costs may be ular activities or investments are correlated with extensive and may include: the risk of insolvency. This implicit argument is normally weak because firms offset their day-to- • Loss of reputation, charter value, and relation- day losses with insurance, reserves, and formal ship with any financier; hedging activities. In fact, the argument for fo- • Market transmission of lower prices for collat- cusing on disaggregated losses is only materially eral, inputs, products, and securities; and significant when insolvency risk is high because • Higher risk premiums. only then does hedging not offset disaggregated losses. Understanding the nature and timing of Supervisors managing insurance funds may ad- threats to solvency therefore validates the focus ditionally lose resolution costs.2 on disaggregated losses and provides the supervisor with appropriately weighted priorities in all Supervisors with program responsibilities may aspects of normal operations. additionally fail to meet program objectives. Insolvencies of large firms can even have ter- The conditions that lead to insolvency are ac- tiary effects like undermining local economies, cordingly the focus of financial supervisors and, reducing the local tax base, and exacerbating by implication, the focus of supervisory ERM. social tensions. For all these reasons, supervisors are likely to define ERM much more broadly STAKEHOLDERS SHARE than private managers who focus mostly on PROBABILITY NOT LOSS shareholder losses.3 The supervisory focus on insolvency risk is not necessarily shared by other stakeholders and For all these reasons, while firm managers are may vary between supervisors. Short term pres- likely to define ERM differently than supervi- sures on supervisors from staff, firms, and others sors, supervisors need the firm to execute ERM. make it hard to maintain focus. ERM provides senior managers a window into firm risk taking that also informs superviso Dr. Stephen W. Hiemstra Without this window, supervisors must make is financial engineer and Supervisory ERM differs from firm ERM because is also an ERM Symposium loss exposures differ. The losses associated with risk assessments at a distance and with a lag. program committee member. insolvency depend on one’s relationship with He can be reached at [email protected]. 2Resolution costs are the costs of closing a depository institution. 3A good text discussing the conventional view of ERM is provided by: (Lam, 2003).

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Analytical Framework • Improve market transparency by publishing for Supervision financial statements, reporting price and loss The theory of the firm, as articulated by Coase,4 data, and encouraging objective underwriting says that the firm will sell a product when its cost standards and collateral appraisal; of production is below the market price and buy • Discourage vertical arrangement among firms a product when its cost of production is above that limit competition or market transparency; the market price. In other words, the efficiency • Strengthen corporate governance regula- of the firm’s operations determines whether it is tions to encourage director independence and a buyer or seller. provide compensation incentives to promote prudent risk taking and a risk management This theory suggests that the value of ERM to culture; and firm managements is a function of market com- • Reduce barriers to market entry by competing petition. If the firm is inefficient in managing firms. operations, it will be forced to buy more products—limiting its future prospects. Likewise, if While supervisors can improve competition and the firm improves its efficiency in management, are in some instances legally obligated to pro- it will be able to sell more products. Over time, mote competition, government regulation more it is likely then that competitive markets will en- frequently serves as a barrier to market entry courage better management. Likewise, oligopo- protecting established firms from competition. listic markets are likely over time to encourage or at least tolerate weak management. They may DEFINING THE also lead to inefficient operations. SUPERVISORY PROBLEM Because financial supervisors focus on provid- What this theory implies for supervisors is that ing information, supervisors need a theory of because the value of ERM rises with market learning behavior. A key impediment to super- competition, supervisors encourage ERM when visory learning about safe and sound operations they promote market competition. In like man- is the peak-load problem that characterizes and ner, allowing oligopolistic practices to evolve dominates financial losses. discourages ERM. Learning Is a Problem Supervisors can encourage competition in a Solving Process number of ways, including: How do government agencies learn and how do they act on lessons learned? They learn by the • Permit new firms to enter the market either process of solving problems. through issuing new charters or by permitting acquisition of existing market participants, A process is a sequence of related actions that or both; bring about a result. Learning is the acquisition • Remove excess market capacity by tak- of ability through experience or study.5 Johnson ing weak firms into receivership promptly; (1986) outlines 8 steps in the learning process,

including:

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4Coarse, Ronald. 1937. The Nature of the Firm. Economica. 4 No. 4. November. pp. 386-405. 5Process: 1. A series of actions, changes, or functions bringing about a result: the process of digestion; the process of obtaining a driver’s license. 2. A series of operations performed in the making or treatment of a product: a manufacturing process; leather dyed during the tanning process. Learn: 1. To gain knowledge, comprehension, or mastery of through experience or study. 2. To fix in the mind or memory; memorize: learned the speech in a few hours. 3. To acquire experience of or an ability or a skill in: learn tolerance; learned how to whistle. (see: www.answers.com).

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• Articulate a felt need; be unclear, significant organizational problems • Define the problem; require a multiyear effort to resolve and lead- • Assemble observations and data; ership changes occur frequently (the average • Analyze the data and observations; federal appointee serves about 24 months), it is • Decide on a plan; obvious that progress in solving problems can • Execute the plan; and be difficult. • Bear responsibility for the decision and execution of the plan. Although steps can be taken out of sequence, if steps are the likelihood of success is reduced as As shown in chart 1, these steps are informed knowledge gaps become obvious and credibility by both objective (positivistic knowledge) and suffers. The easiest way for a new manager to subjective (normative knowledge) information. loose face with staff, for example, is to make a Steps may be taken out of sequence and may be decision without checking to see whether it has repeated as new information becomes available. been tried before and what was the outcome. Another favorite path to failure is to infer that The repeating of steps in the supervisory learning an action be taken based on a felt need that process should be anticipated. New subjective is not obviously linked to the proposal. The information, such as what might arise from an process of problem solving implicitly provides a election, can easily motivate an agency to rethink vehicle for developing a consensus for proposed its decisions and come out with new research or solutions and for joint responsibility sharing new programs. New objective information, such should problems arise with the execution of the as the results of a recent study, can likewise lead proposal. Taking steps even perceived out of policy makers to rethink their preferences. sequence can accordingly be perilous for those making the attempt. Given this framework, it is easy to see why supervisory agencies have trouble making course Interestingly, the learning process plays a key corrections. If one assumes that objectives may role in risk-management for the U.S. military. A recent study reported that making information available to all members of the military—irre- spective of rank—plays a key role in responding to the threat of terrorism. In other words, the military’s information needs to be more decentralized, in part, because it is hard for a topdown management culture to respond to a threat from a decentralized opponent (Cartwright, 2006). Peak-Load Problem Complicates Loss Measurement and Management.

Chart 2, on page 13, shows annual corporate bond issuer default counts from 1920 through 2004. The characteristic of these data that jumps out at you is that most of the bonds defaults are bunched up in time. This bunching up of losses in particular periods is known among engineers as a peak-load problem. The peak-load

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problem in the financial markets has generally mechanism, however, is contagion within the associated with market contagion. This problem market itself. has important implications for regulation, risk management, and long-term planning which are Supervisors need to resolve troubled financial not well understood. institutions quickly to avoid financial contagion. For banks, the Federal Deposit Insurance Special Problem Posed Corporation (FDIC) is responsible for resolving by Contagion insolvent banks. A resolution normally involves finding a strong bank to purchase or merge with Contagion is a medical term that refers to the the insolvent bank. The new, larger bank pre- rapid diffusion of a disease among a host popula- sumably has sufficient capital to mitigate the tion. One person with the disease exposes anoth- need for rapid liquidation of the weak bank’s er person who quickly becomes sick and infects assets which can undermine the pricing of finan- still other people. An important characteristic cial assets in other firms. of contagion is the observation that the health of the patient prior to infection does not inoculate When trouble financial firms are not dealt with the patient against the disease—resistance is a promptly by supervisors, these firms can under- function of previous exposure and the presence mine asset pricing in several ways, including: of antibodies, not general health.

• Selling assets to raise capital; In financial markets, contagion arises when • Placing imprudent bets in asset markets; and financial weakness in one firm spreads to other • Under-pricing assets in their transactions. firms in the same market. Supervisors usually think of contagion as having two transmission Asset pricing is important because financial mechanisms—bank runs and bank correspon- viable firms need to earn a rate of return greater dent relationships—reflecting the treatment than their cost of funds plus administrative costs. oft contagion in the academic research on com- If they cannot earn a reasonable rate of return in mercial banks. The more general transmission continued on page 14

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The existence of a peak-load problem complicates both risk analysis and decisions under uncertainty. Risk is the probability of a future loss. Managers do not possess perfect knowledge of their businesses or the future. Regulators possess even less knowledge than managers. A peak-load problem further limits the usefulness of averages of financial indicators and exacer- bates volatility in the measurement of losses. Let their usual markets, then they compete more ag- me address these two problems briefly. gressively in new markets where they may drive down pricing in those markets as well causing The peak-load problem makes average loss data the problem to spread further. This problem misleading. Holding a capital against an aver- is especially severe for large firms with low age loss is like building a levy against an aver- per-unit mark-ups because any loss in output age flood: half the time your average levy will be volume raises per-unit costs pressuring the firm inadequate and your losses will be catastrophic. to maintain volume precisely when the lost prof- Levies are typically built based on the highwa- itability signals a need to pull back from—not termark flood adding in a margin for error that 7 expand into—that particular market. depends mostly on financial capacity.

Falling market prices can drive sound financial The peak-load problem leads to volatility in institutions towards insolvency, if they operate measured risk. The probability of future losses at a loss. Contagion accordingly leads to a clus- changes dramatically over time. Model error, tering of financial losses in particular locations, for example, that is inconsequential in normal industries, and time periods that may be hard market periods can threaten firm survival dur- to contain. ing peak periods. Managers and supervisors accordingly provide their largest value added Implications for Decisions by recognizing early on when market conditions under Uncertainty have changed and acting on that knowledge. The peak-load problem in financial losses poses Losses are Correlated, Not a challenge for regulator learning because aver- Random age losses are a poor proxy for peak losses. Most Concentrating losses, like bond defaults and of the losses during the credit cycle are concen- credit losses, in short time periods by itself trated in a very short period of time, in specific suggests that losses are correlated and are locations, and in specific industries. This shows not randomly or uniformly distributed in up statistically as a very large difference be- time as assumed by most loss models.8 This tween the mean and mode6 of the distribution of problem implies that loss models are likely to losses (table 1).

6The mode of a distribution is the most frequent observation. It differs from the mean and the median of the distribution. 7The economic capital approach takes this problem into account by assuming that average losses are accounted for in product pricing. Capital is held against the difference between expected loss (the mean) and unexpected loss (the mean plus X number of standard deviations). The key problem with the economic capital approach is the practical problem of getting access to data sufficient to account for the historical peak load periods. 8Most modelers use logit models to estimate these equations. Logit model explicitly assume independence because they use maximum likelihood estimation (MLE). MLE works by assuming you know a distribution and fitting your data to it. Because MLE assumes that independent observations are multiplied by one another in the likelihood estimator, covariance among the observations leads to an exponential increase in error and a much more complex functional form than is typically assumed. For this reason, econometricians will argue for hours that their observations are independent rather than account for the covariance. This problem is starting to be noticed. See, for example: (Altman, 2006).

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underestimate losses just when the models are short-run profitability and maintaining long- most needed. run solvency.

Chart 2 makes the concentration of losses in Economists distinguish two kinds of costs in time fairly obvious. There is, however, a second the theory of the firm: variable and fixed costs. Operational risks that source of correlation in the chart. Note that loss- Variable costs vary in the short term with the es on investment grade bonds typically peak level of output. Fixed costs associate with long threaten firm solvency at close to the time when the sub-investment term investment. Risk is the probability of a tend to be long run and grade bonds default. Sub-investment grade future cost to the firm. Credit and market risks tied to firm structure. bond losses are greater, but they are correlated tend to be short run and tied to current business to the investment grade losses. This observa- decisions like variable costs. Operational risks This gives them fixed tion implies contagion both within and across that threaten firm solvency tend to be long run cost characteristics. industries. Because these are national figures, and tied to firm structure. This gives them fixed this observation also implies contagion across cost characteristics. geographic regions of the country. In a competitive market, economic theory sug- At least during peak periods, losses are not gests that prices should be set close to variable normally distribution. The statement that loss costs. Competition has this effect because the events are normally distributed implies that: pricing of fixed costs is arbitrary and large firms are able to lower their per-unit fixed costs by ex- • The mean values provide useful information panding their output up to a point of diminishing about typical losses and • The tail values are well-behaved and can be marginal returns. The implication for financial accurately estimated. regulators is that in competitive markets firms will pass on the costs of prudentially managed If losses are concentrated in time (that is, are credit and market risks, but not the costs associ- not normally distributed), both observations are ated with operational risks. Firms are less likely misleading. The mean values provide little in- to be able to pass on the costs of operational sight into the distribution as a whole and tail val- risks because of the fixed cost characteristics ues are highly volatile and cannot be measured of operational risks. Pricing operational risks, with any degree of precision. This is another way like the peak load losses associated with sys- of saying that historical events are unique.9 temic risk, is likely to invite new entrants, customer substitution away from products, and Conflict between Short Run regulatory arbitrage.10 Profitability and Long Run Solvency Firms May Not Anticipate Ratings Downgrades Accounting for the peak-load problem in financial losses over time draws attention to a Chart 2 provides some insight into the effect of conflict in incentives between managing for a systemic event. In a systemic event, counter continued on page 16

9 Central tendency—the law are large numbers—which statisticians use to draw many common inferences does not apply when historical events are unique and do not tend to show regularity. 10 Parenthetically, when fixed costs need to imposed, they need to be imposed on the entire industry and all competitors within the industry. A classic example is the imposition of labor contracts on the meat industry during the Second World War. The federal government created a wartime labor relations board to maintain production to support the war effort. Master labor agreements were imposed on the entire meat industry to preclude strikes and competition that would lead to strike behavior. This raised the cost of meat, but labor got a higher standard of living not undermined by industry competition. These master agreements amount to government sponsored collusion and were only eliminated in the 1980s when structural changes in the meat industry introduced.

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parties fail resulting in loss of credit enhance- can hide significant loss surprises in firms that ment. Investment grade firms may accordingly do not anticipate them. be downgraded to sub-investment grade status. The probability of default accordingly follows The downgrade effect noted here is really a the path of the sub-investment grade firm—not proxy for the problem of firm revaluation. When investment grade firms—where default levels firms are revalued, the risk premium associated are substantially higher. with a firm’s securities rises and the value of the firm falls from market towards liquidation The downgrade effect can mask true risk mea- value. Private rating companies may or may surement efforts in several ways, including: not anticipate this revaluation. Depending on the quality of the analysis done, ratings can be • Firm planning may assume investment grade downgraded before or after these changes in market valuation, depending on the quality of status when sub-investment grade status is the analysis done. the more appropriate assumption. • Capital is typically allocated after credit enhancement. If credit enhancement fails, RISK MANAGEMENT IS ATTACHING capital is by definition inadequate. INCENTIVES TO INFORMATION • Defaults are typically recorded by those Managers work with directors to define clear that bear the cost. If counterparties typically firm strategic objectives, translate those absorb normal defaults, the defaults are re- objectives into a plan, communicate the plan to corded by the counterparties, not the firm. staff, and execute the plan in daily operations (chart 1). Because managers cannot do every- Estimating loan defaults based only on firm thing themselves, the most critical elements in records may accordingly understate the true their work are information processing, commu- risk of default because the observed loss data is nication, and incentives. An effective supervi- really the residual loss, not total loss.11 sory program targets these critical elements.

The downgrade effect accordingly suggests that Problem Definition, Observation, and Analysis. In risk management, timing is everything. the assumptions about firm losses in a systemic Taking advantage of market opportunities and event can be much higher than anticipated by avoiding catastrophic losses both require time- typical worse case scenarios. ly responses. The higher portfolio turnover rates that have evolved in recent years exacerbate the These effects can be illustrated with a numerical timing problem. For risk management, monitor- example from table 1. If risk managers mitigate ing loss data is key. against an annual bond default event with only a one percent probability and assume losses are nor- Two pieces of loss information drive risk mally distributed, investment grade bond losses analysis: are likely not to exceed 10.6 bond defaults (3.4 + 2.33*3.1). This estimate is too low to offset • Identifying trends that suggest losses are even average losses of 48.3 for sub-investment rising; and grade bonds. This observation suggests that loss • Recognizing changes in product loss co- mitigation efforts, such as credit enhancement, variances that may undermine the efficiency

11 The technical term for this problem used by statisticians is data censuring.

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of hedging relationships (basis risk) and Incentives Matter. Even when people agree indicate rising model risk.12 that a problem exists, fixing the problem must become a priority. In an administrative context, Both signal the transition between normal priorities are communicated through the perfor- markets and peak-load periods. mance management system—what does boss think is important enough to evaluate staff on? A peak-load problem potentially leads to Risk management information, once created, under-investment in prudential measures for need to be communicated and to be attached to two reasons: incentives communicated through performance management imperatives. F • A principal agent problem13 arises because the term of office of managers and regulators does not typically extend long enough to account for the next peak load period; and • Because future losses are potentially separated by decades of prosperity, losses are discounted over several decades and their present value may approximate zero.

All forecasts are subject to uncertainty. Until everyone agrees a problem exists nothing gets done. If no one has an incentive to account fully for the risks borne, both firm and supervisor are likely to under-invest in prudential measures.

Communication. Once a problem has been defined, information gathered, and analysis undertaken, people must be informed and then convinced to act on it. The first part of this process is providing information. Articulating risk analysis information accurately to directors, managers, and staff in time to take corrective action requires effective written and oral communication.

12 The standard guideline used to undertake model risk examinations is available online. See: (Brown and Dick, 2000). Also see: (Derman, 1996). 13 The idea of a principal agent problem is at least in part analogous to the asset-liability mismatch problem in interest rate management. Also see previous footnote.

Page 17 w Risk Management w August 2008 Chairman’sIncreasing Corner Usefulness of ERM Increasing the Usefulness of ERM to Insurance Companies Jean-Pierre Berliet

I am indebted to Robert Stein of Ernst & weaknesses can have a significant impact. This Young, Robert Rosholt, of Nationwide Group, generates much organizational heat and can cre- Thomas Rogers, of Zurich Financial Services, ate a dysfunctional decision environment. Stephen Steinig of New York Life and Valentina Isakina of Bain & Company for insightful Discussions with senior executives suggested and stimulating comments on this paper. I am responsible for errors and ambiguities that decision signals from ERM would be more that remain. credible and that ERM would be a more effective management process if ERM framework Background and Overview were shown to: lthough many independent studies sug- • Reconcile the risk concerns of policyholders gest that Enterprise Risk Management and shareholders. (ERM) may be coming of age in the A • Support management of operational risk. insurance industry—efforts to integrate risk • Produce credible and useful risk adjusted considerations into daily decisions appear to performance measures. progress slowly and meet resistance. As a re- • Align performance metrics with sult, it is far from clear whether ERM is a factor management’s performance measurement in actual decisions and is having a beneficial philosophy. impact on the financial performance of com- • Integrate ERM into daily management panies. In many companies, executives have activities. also been wondering whether costs incurred to establish ERM have produced commensurate The following five sections discuss these issues benefits. and suggest action steps that insurance companies should take to establish ERM as a more This article is based on discussions I had with robust and valuable management process. many executives of insurance companies regarding the challenges they are encountering to establish ERM and in preparing for discussions Reconciling Risk Concerns of with rating agencies or regulators. Observations Creditors and Shareholders Jean-Pierre Berliet, is they shared suggest that, in many companies, Creditors—including policyholders and rating the founder of Berliet the effectiveness of ERM and related risk ad- Associates, LLC, a New agencies or regulators whose mission it is to York area-based advisory justed performance measurement frameworks protect creditors—and shareholders are all in- firm on strategy and risk is impeded by design weaknesses, especially terested in the financial health of an insurer, but management. He can be the absence of a mechanism to reconcile the sol- in different ways. Creditors want to be assured contacted at jpberliet@ vency concerns of policyholders and the value that an insurance company will be able to honor att.net. concerns of shareholders. its obligations fully and in a timely manner. For creditors, the main risk question is: what is the Design weaknesses are an important source of re- risk of the business? This is another way to ask sistance to ERM implementation. Some are subtle whether the company will remain solvent. and thus often remain unrecognized. However, seasoned business executives recognize readily Shareholders, however, are interested in the that decision signals from ERM can be mislead- value of the business as a going concern—in ing in particular situations in which these design how much this value might increase and by how

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much it might decline. For shareholders, the atility of financial outcomes. Stochastic model- main risk question is: what is the risk to the busi- ing is being used more broadly by companies to ness? Shareholders are interested in what ERM understand how such risks accumulate, interact can do to increase and protect the value of their and develop over time and to evaluate strategies investment in a company. While both creditors that enhance the stability of outcomes. Capital Methodologies used and shareholders are interested in the tail of the adequacy is the ultimate defense against severe distribution of financial results—as an indica- risk “surprises” from insurance and investment by rating agencies tor of solvency risk—shareholders are also very activities. It is of interest to policyholders who on behalf of creditors interested in the mean of these financial results want to be certain to collect on their claims, but describe in detail how and their volatility, which could have an adverse also to shareholders who want assurance that a impact on the value of their investment. company can be viewed as a going concern that the rating process deals will write profitable business in the future. with the three main Policyholders’ and shareholders’ views are different but not incompatible: a company could Methodologies used by rating agencies on drivers of a company’s not stay in business if it were not able to per- behalf of creditors describe in detail how financial position and suade regulators that it will remain solvent and the rating process deals with the three main should be allowed to keep its license, or obtain drivers (insurance risk, inverstment risk and of the volatility (risk) of from rating agencies a rating suitable for the operational risk) of a company’s financial this position. business it writes. Its value to investors would position and of the volatility (risk) of this be significantly impaired. position. In response to rating agency concerns, insurance companies focus Insurers recognize that the main drivers of their on determining how much “economic risk profile are financial risks, including insur- capital” they need to remain solvent, as a ance risk accumulations and concentrations, first step toward demonstrating the adequacy and the related market risk associated with their of their capital. Analyses they perform involve investment activities. They understand that calculation of the losses they can suffer resulting risks are best controlled at the point of under scenarios that combine the impact of origination through appropriate controls on un- all the risks to which they are exposed. This derwriting and pricing and through reinsurance “total risk” approach and the related focus and asset allocation strategies that limit the vol- on extreme loss scenarios (“high severity/low frequency” scenarios) are central to addressing creditors’ concerns.

To address the solvency concerns of creditors, rating agencies and regulators and the value risk of shareholders, insurance companies need to know their complete risk profile and to develop separate risk metrics for each group of constituents. Knowledge of this risk profile enables them to identify the

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distinct risk management strategies that they concern basis (e.g., over the next three or five need to maintain high ratings while also protect- years). ing the value of their shareholders’ investment. • Integrate insights from risk modeling Leading ERM companies have become well and analysis into strategic and tactical aware of this requirement and no longer focus decisions, including capacity and capital solely on tail scenarios to develop their risk deployment across business lines or segments, management strategies. underwriting/pricing, risk retention and risk transfer, asset allocation. ERM frameworks must also recognize that • Seek formal approval from the Board of tools and processes required to address value Directors on proposed strategies, expected risk concerns of shareholders are differ- returns and the related confidence level. ent from those required to address solvency • Establish processes to identify and manage risk concerns of policyholders. Measuring exposures to material operational risks— and managing shareholders’ value risks re- including recovery programs and appropriate quires tools and processes capable of ad- oversight and compliance mechanisms—and dressing risk issues on a “going concern” strategic risks that can inflict severe value basis, including explicit consideration of losses to shareholders. operational risk, with special focus on its strategic component. Managing Operational Risk Operational risk comprises two different types To reflect these critical considerations, of risks: execution risk and strategic risk. companies need to: These two categories of operational risk are • Create a risk measurement capability important to policyholders and shareholders (e.g., a stochastic risk analysis model) for because they can reduce both the insurance their business, at an appropriate level of strength and the value of insurance companies. granularity, to analyze the combined effects Strategic risk stems from external changes that of underwriting and investment strategies on can undermine the profitability and growth the company’s ability to withstand plausible expectations of a company’s business model stress scenarios and the volatility of its and strategy, and therefore have a significant earnings. impact on its value. Execution risk originates • Seek agreement on the level of earnings

volatility acceptable to investors, relative to the volatility of results evinced by companies of similar capitalization. • Assess the impact of alternative underwriting, investment, reinsurance strategies on the volatility of their financial results and capital positions and their ability to carry out their strategy on a going

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in internal failures to manage the operations of value. Company management has fiduciary a company competently, with the needed level obligations to set in place processes designed of foresight, prudence, risk awareness, and pre- to avoid executions risks, establish post event paredness. Execution and strategic risks impact recovery procedures and to ensure compliance. insurance companies differently and, as a result, call for distinct mitigation strategies. Both policyholders and shareholders need to note that Execution Risks • Execution risks can impact financial Although financial risks are the primary deter- performance significantly in the year or minant of the volatility of financial results of period of occurrence but may have a more insurance companies, execution risks can also or less pronounced impact on performance cause material adverse deviations from expected in subsequent periods and company financial results. valuation, depending on the availability of recovery strategies and the preparedness of Execution risks include, for example, economic a company. losses resulting from • The impact of execution risks on a company’s market value can be derived from estimated • Delays in alleviating adverse consequences adjustments to free cash-flow projections. This of changes in the volume of activity is particularly significant in connection with (mismanagement). risk events that erode a company’s competitive • Events that can interrupt business operations advantage or damage its reputation. Such events whether man made or natural (lack of can reduce the market value of a company preparedness). significantly by reducing its volume of business • Failures in controls that cause economic losses, or its pricing flexibility. create liabilities or damage the company’s reputation (market conduct, regulatory Management processes and management action compliance, bad faith in claim management, —not capital—are the natural remedy for fraud, IT security, etc.). execution risks. Board of Directors or Audit Committees of such boards have become Execution risks reduce current financial increasingly involved in exercising oversight performance and company valuation. Company of execution risks and their management by valuation is reduced investors because operating executives. • Often view negative earnings deviations as predictors of future decline in profitability and Strategic Risks • also performance volatilitycan derail the execution of a company’s growth strategy. Strategic risks can undermine the economic viability of the business model and future Execution risks are relatively easy to identify, financial performance of insurance companies. if not to mitigate for company management. They can have a significant adverse effect on Although stochastic modeling tools and event a company’s insurance ratings and the credit databases could be used to simulate the impact worthiness of its debt and also its market of execution risks on financial performance capitalization. Strategic risks can cause other- and fine tune mitigation strategies, undertaking wise solvent companies to lose a substantial such modeling is very costly and may be of limited share of their market value in a short time,

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provoke legal action by disgruntled shareholders, capabilities, redeployment of capacity, inflict serious economic losses to Directors, change in composition and level of service senior executives and other employees, and provided, industry level lobbying of law- induce potential raiders to attempt a take over. makers and regulators, sponsorship of and participation in industry associations, etc. Strategic risks are also very important to • Communicate reasons for and objectives policyholders, (especially those who have of needed changes to both customers and bought protection against slowly emerging shareholders. liabilities or policies that provide • Integrate the planned strategic response indemnification benefits in the form of into action plans, budgets and objectives of annuity payments), because strategic risks business units. that undermine the ability of companies to earn formerly expected returns also reduce Insurance companies need to include in ERM a the credit worthiness of these companies. process that provides consistent and updatable Strategic risks stem from external changes in insights into strategic risks to which they are ex- the regulations, institutional arrangements, posed. Because the insurance industry has been competition, technology or demand that highly regulated, many insurance companies can erode the competitive advantage of an have not developed deep strategy development insurance company and its ability to operate and assessment skills. It will be a challenge at credibly and profitably as a going concern in first for such companies to establish strategic the future. risk assessment frameworks powerful enough to yield robust insights but simple enough to be Strategic risks do not receive as much attention user friendly. as they should because they are difficult to identify and assess, and are often viewed as “uncon- Conducting systematic reviews of strategic trollable.” At any point in time, it can be very risks is important to all constituents. A number difficult to assess whether a quantum change of companies that have already implemented in any element of strategic risks is close to comprehensive risk management frameworks happening. When such a change occurs, how- have begun addressing strategic risks more ever, its impact on future performance can formally. In one company, the CEO stated to me cause a swift decline in the market values of that he bore ultimate responsibility to share- a company. holders for being both his company’s Chief Risk Officer and Chief Return Officer. To identify and manage strategic risks, companies need to: Producing Credible and Useful Risk Adjusted • Conduct and challenge a periodic Performance Measures defensibility analysis of their business model Risk adjusted performance measures (RAPM) and competitive advantage. such as Risk Adjusted Return On Capital • Monitor market developments for emerging (RAROC), first developed in banking institu- trends with potential adverse effects (loss tions, or Risk Adjusted Economic Value Added of business to competitors, emergence of (RAEVA) have been heralded as significant new risk transfer technologies or product breakthroughs in performance measurement innovations, regulatory developments, etc.). for insurance companies. They were seen as • Develop appropriate responses to adverse offering a way for risk bearing enterprises to developments through adjustment in relate financial performance to capital con-

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sumption in relation to risks assumed and thus to tively more challenging to develop and validate value creation. than RAROC/RAEVA measures, risk adjusted performance measures are not typically capable Many insurance companies have attempted to of relating financial performance to return on establish RAROC/RAEVA performance mea- value considerations that are of critical impor- surement frameworks to assess their economic tance to shareholders. performance and develop value enhancing business and risk management strategies. To provide information that is credible and A number of leading companies, mostly in useful to management and shareholders, insur- Europe where regulators are demanding it, have ance companies need to establish risk adjusted continued to invest in refining and using these performance measures based on: frameworks. Even those that have persevered, however, understand that framework weak- • A (paid up or economic) capital attribution nesses create management challenges that method, with explicit allowance for devia- cannot be ignored. tions in special situations, that is approved by directors; Experienced executives recognize that the at- • Period income measures aligned with tribution of capital to business units or lines pricing and expense decisions, with explicit provides a necessary foundation for aligning the separation of in-force/run-off, renewals, and perspectives of policyholders and shareholders. new business; • Supplemental statements relating period or Many company executives recognize, however, projected economic performance/ changes in that risk adjusted performance measures can value to the value of the underlying business; be highly sensitive to methodologies that de- • Reconciliation of risk adjusted performance termine the attribution of income and capital metrics to reported financial results and that earnings reported for a period do not under accounting principles used in their adequately represent changes in the value of jurisdictions (GAAP, IFRS, etc.); insurance businesses. As a result, these senior • Establishment and maintenance of executives believe that decision signals pro- appropriate controls, formally certified by vided by risk adjusted performance measures management, reviewed and approved by the need to be evaluated with great caution, lest Audit Committee of the Board of Directors. they might mislead. Except for Return on Embedded Value measures that are compara- In many instances, limitations and weaknesses in performance measures create serious differences of view between a company’s central ERM staff and business executives. Capital Attribution To be useful, a RAROC framework must be based on a credible and robust method of attributing a company’s

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capital to its individual lines of business or Comparing RAROC to a company’s cost of capi- business segments. tal is problematic when attributed economic capital is used for calculating RAROC. Since Many calculation methods, often based on economic capital is derived from consideration stochastic corporate models of insurance, have of the company’s total risk and represents an been developed for the purpose of attributing amount of assets available to pay obligations to capital. Unfortunately, these methods have creditors, return on economic capital cannot be been shown to produce results that are sen- compared to the company’s cost of capital. The sitive to the methodology selected and to company’s cost of capital represents expecta- changes in risk measures and tolerance tions of return by investors in compensation for targets, correlations assumptions, the rela- systematic risk assumed for owning shares of tive growth and performance of individual the company, not for being exposed to total risk, segments and the applicable risk assump- a part of which can be diversified away. Further, tion horizon. Instability of capital attribution this cost of capital performance benchmark results undermines the confidence that senior should be used to assess returns on the value executives can place in RAROC as a guidepost of investors’ ownership positions rather than for decisions. returns on the nominal amount of economic capital supporting a business segment or a com- Meanwhile, investors and directors insist on pany. Adjusting a RAROC measure to reflect understanding how management “allocates” the impact of these complexities and make the capital across activities. From their vantage resulting adjusted RAROC comparable to a point, capital “allocation” refers to how capital cost of capital estimate derived from observa- (as a proxy for “insurance capacity”) has been tions in the capital market would not be straight- or will be deployed across lines and business forward, and appears to involve resolution of segments as a result of explicit decisions to methodology issues for which no approach has seek particular exposures or types of business. yet been developed. Much caution is needed They correctly see that management moves to use a calculated RAROC to assess finan- (i.e., “allocates”) capital across lines and cial performance and drive business and risk business segments whenever underwriting management decisions. activities are redirected. As a result, they seek to hold management accountable and demand Comparing RAROC to a company’s ROE target that executives be able to demonstrate that can also be misleading when the company’s capital is or will be deployed toward uses in available capital measured under GAAP rules which realized returns are commensurate with is used to calculate RAROC. The potential for risks assumed. misleading signals exists because there is no direct and simple relationship between Performance Benchmarks measures of ROE under GAAP, measures of economic returns (such as GAAP income return It is customary to compare RAROC perfor- on economic capital; economic income on the mance to a company’s cost of capital or to its “fair value” of net assets; and return on embed- return on equity target, depending on whether ded value), and a company’s cost of capital. the capital attributed to business segments is Accounting adjustments needed to reconcile the company’s “economic capital” or the com- risk adjusted return metrics with reported pany’s available capital measured under GAAP statements are neither simple nor easy to grasp accounting rules. Both ways can be misleading, intuitively. Although it would be possible to for different but important reasons. develop a mapping of GAAP ROE into corre-

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sponding measures of economic performance, • Matching of the structure of the financial I am not aware that any company has actually management reports to the boundaries of attempted to do this to calibrate its perform- business segment, ance benchmarks. In any case, relating such • Accurate attribution of capital, premium benchmarks to a company’s cost of capital revenues, investment income and expenses with confidence would remain problematic for to business segments, and reasons explained in the preceding paragraph. • Segregation in financial reports of the results associated with the current period from It is important to note that methodology issues the impact of business written in prior years. discussed above in connection with the calculation and interpretation of RAROC would This alignment ensures appropriate distinctions also apply to other measures of risk adjusted between results of current and past decisions performance, such as RAEVA. They would and a sharp focus on differences in drivers of not, however, apply to return on embedded performance. value metrics (or the more recently developed Comparing RAROC to a return on European Embedded Value metric), In practice, leading companies are making based on a framework that aligns the calcula- explicit decisions about the design and features company’s ROE target tion of returns with the change in value orienta- of the financial performance measures they can also be mislead- tion of calculations made by investors in the develop by developing customized answers to ing when the compa- capital market. questions such as the following: ny’s available capital In a number of leading companies, difficul- • Are business segments to be evaluated on measured under GAAP ties involved in calculating and interpreting a stand alone basis or in a portfolio context correctly RAROC or other measures of risk (i.e., after attribution of a capital credit rules is used to calcu- adjusted performance such as RAEVA are for diversification)? late RAROC. leading management to fall back on traditional • Are business segments to be evaluated as performance measures, such as loss ratios and if assets they earned risk free, duration combined ratios or investment spreads, cali- matched investment income? Or the average brated to reflect differences in risk levels, and rate of return on the investment portfolio? to explore the feasibility of adopting additional • Are business segments to be evaluated in performance metrics such as earnings at risk or relation to their “consumption” of economic embedded value at risk. capital? Regulatory capital? Rating agency capital? Aligning Performance • Should individual business segments bear Metrics with Management’s the cost of “excess” or “stranded” capital? Performance Measurement • Should performance benchmarks vary across Philosophy business segments, in line with differences in To provide useful guideposts for business the volatility of their total risk? Or differences decisions, the risk adjusted performance in exposure/premium leverage across lines? measurement framework supporting ERM Or contribution to corporate debt capacity? needs to reflect senior management’s views • How granular does such reporting need regarding alignment of responsibilities and to be? performance metrics. Alignment is ensured by • Should performance metrics be developed in a policy/underwriting year framework?

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Would such metrics need to be reconciled In my experience, success in establishing with metrics based on fiscal year GAAP ERM is highly dependent on the level of effort reported numbers? that companies devote to designing a reporting • How should the period performance of the in- framework that the organization can understand force (or liabilities run-off) be measured and and embrace intuitively, without having to be separated from the performance of the “new trained in advanced financial or risk topics. In business?” To what extent and how should this area, setting out to develop the most rigorous the performance of “renewal” policies be and actuarially correct framework is likely to separated from that of policies written for new result in poor acceptance and much resistance customers in property, casualty companies? on the part of decision makers who run the busi- • Should the performance reporting framework ness day by day. provide only period measures of performance or should it be extended to capture the longer Integrating ERM into Daily term economic value of insurance contracts, Management Activities such as the change in the embedded value of the business? Many senior executives recognize that establish- • Should the performance reporting framework ing an ERM process is an obligation that cannot be extended to incorporate stochastic be avoided in today’s environment. They also performance metrics such as Earnings@Risk have a strong intuitive sense that the science of or Embedded Value@Risk? risk measurement and analysis offered by the actuarial profession and other specialists in risk Leading ERM practitioners, especially in does not yet provide robust answers to many im- Europe, have found that the usefulness, but also portant questions that are asked by people who the complexity and cost of risk adjusted perfor- manage the operations of insurance companies mance metrics are determined by the desired day by day. Differences in perspectives between level of granularity in reporting, and design deci- executives in the corporate center and the man- sions in risk measurement, capital measurement agers of business units hamper the effectiveness and, financial reporting. The availability and of ERM. Bridging these differences is a major quality of risk and financial data determine to a challenge to the establishment of ERM. This significant degree the level of granularity that challenge is rooted in fundamental differences can be built to support ERM. in the roles and responsibilities of these actors.

Corporate center executives who operate under oversight of the Board of Directors are highly sensitive to risk concerns of shareholders. It is natural for these executives to take an aggregate view of risk, across the business portfolio. They contribute to corporate performance by making strategic risk management decisions in connection with capacity deployment, reinsurance and asset allocation, and also operational risk management decisions principally in connection with the management of shared services. Their most important risk decisions, related to capital allocation, involve significant strategic risks.

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By contrast, business unit managers have a dif- Consistent with these considerations, ERM ferent outlook. They are typically more focused appears to work best in companies in which on meeting the needs of policyholders. They are operating managers have “bought in” ERM and more likely to view risk as stemming from prod- embraced the perspective it provides. In many ucts and customers. From their point of view, of these companies, one observes that: risk management starts with product design, underwriting and pricing decisions, control • Risk management responsibility is owned by of risk accumulations and concentrations, operating managers. product mix and customer mix. With regards to • Product definitions and investment operational risk, their activity places them on boundaries are clear and matched to explicit the front line to control the “execution risk” ele- risk limits. ments of operational risk. Business unit manag- • Policies and procedures have been co- ers tend to view requests for support of ERM developed with operating personnel. as distractions from serving policyholders and • Product approval and risk accumulation are accomplishing their goals. They believe that subject to oversight by the central ERM unit. they help protect shareholders from value loss • Risk and value governance are integrated by focusing on establishing and maintaining a through a committee with authority competitive advantage. to adjudicate decisions about trade-offs between risks and returns. The CFO of a very large insurance group • Compliance and exceptions are subject to confided to me recently that aligning the review by senior management. perspectives of executives at the corporate center with that of business managers was a Note that none of these requirements are about challenge of great importance. He expressed the technical components of risk management. the view that results from risk models cannot Rather, they define a context for empowerment be used simplistically and that experience and appropriate limitations on the activities of and business judgment are needed to guide people who run day to day operations. decisions. Caution and prudence are especially important in interpreting decision signals Conclusion when model results appear unstable or when In earlier times, when markets were both less complexity makes it difficult to recognize competitive and less turbulent, experienced possible biases. He had become interested in insurance executives could rely on insights using a combination of approaches to develop from experience to manage their companies reliable insights into strategy and risk dynamics successfully. This is no longer the case. Some of in his company. He was particularly focused on the most successful companies in this country finding ways to bring these insights to bear on and in Europe have set out to move from a focus the daily activities of employees who manage on managing individual risk silos to establish- risk accumulation, risk mitigation and risk ing frameworks and processes that can deal transfer activities, on both sides of the balance with the interaction of risks on an “integrated” sheet. In his judgment, borne out by other basis. The companies that have made more discussions and my experience with clients, progress have recognized that methodology ERM comes to life and creates value best weaknesses can be overcome by practical “work when a top down framework initiated by senior arounds” that keep ERM credible and relevant management is embraced bottom up through- out the organization. continued on page 28

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Increasing the Usefulness of ERM … w continued from page 27

to people who run their businesses day by day. costly risk capture, measurement, and analyti- They establish structures and processes that cal infrastructure if the data collected is not used combine actuarially based risk measurement to produce insights that executives believe to with linkages to operations and strategy. be credible and relevant. Rather, it matters a great deal to design and establish an approach In practice, the integration of ERM into op- that can reconcile the perspectives of the most erations of an insurance company is easier to critical constituents, policyholders and share- accomplish in areas that are managed centrally holders, and produce results that managers can (e.g., investments, ceded reinsurance) and for understand and find useful. With a proper focus which financial modeling can provide strong on the data elements that illumine key mate- analytical insights. This integration is harder to rial risks, simpler, better designed frameworks accomplish with regards to capital redeployment will help management identify and resolve issues and activities conducted to generate rev- important risk issues more effectively and enues and manage resulting risk accumulations more rapidly. and concentrations. These decisions can have a direct impact on the status and compensation of ERM professionals and executives of insurance executives and can generate much resistance. companies need to engage in a constructive de- bate about the limits of risk management meth- It is time for executives of insurance companies odologies, to reach agreement on what we do not and ERM professionals to recognize that ERM know and determine how best to reach the next frameworks are not developed enough, and level of effectiveness in ERM. F may never be developed enough, to address and resolve conclusively all the risk issues that insurance companies need to address. In spite of the initial claims, this was never a realistic expectation. Many senior executives seem now ready to support less ambitious but practical approaches to ERM. ERM would be institution- alized in areas where well tested methodologies are clearly advantageous (e.g., financial risks), but would be introduced very gradually in other areas where available methodologies just do not fit well (e.g., strategic risks). In these areas, “work around” based on other disciplines would be created to provide the insights needed to support decision making.

ERM will be more effective in companies that identify and correct weaknesses in their approach. In final analysis, it is unproductive to insist upon the development of a complex and

Page 28 w August 2008 w Risk Management EditorialChairman’s , Chairman’s Corner Corner or Blank Risk Identification: A Critical First Step in Enterprise Risk Management

Sim Segal

nterprise Risk Management (ERM) is 4. Gather data appropriately often defined as a process to identify, 5. Define frequency-severity clearly E measure, manage and disclose all key risks to increase value to stakeholders. ERM is Defining Risks by Source still an emerging concept, and those companies Risks are often defined by their outcome rather adopting it are in varying stages of implementa- than their source. For example, “reputation tion. The first phase in the ERM process cycle, risk” is a risk commonly found on a company’s after developing the initial ERM framework and key risk list. However, this is not a source plan, is risk identification. of risk, but rather an outcome of other risks. There are several risks—such as poor product Risk identification typically involves three quality, poor service, fraud, etc.—that might types of activities: rise to a level whereby reputation is negatively impacted. • Defining and categorizing risks; • Conducting internal qualitative surveys on Another example is “ratings downgrade.” the frequency and severity of each risk; and Again, this is not a source of risk, but an out- • Scanning the external environment for emerg- come that can result from several different risk ing risks. sources, e.g., strategy risk, execution risk, etc. A poor strategy, for example, might result in a Since risk identification is the first phase in rating agency downgrading the company. the ERM cycle, some assume that by now the approach must have matured, and that com- This is a common practice, yet defining risks by mon practice is essentially “best practice.” their outcome, rather than their source, results However, through our research and client work, in several suboptimal ERM steps. It degrades we have found that common practice in risk the qualitative survey results; survey par- identification is suboptimal in several aspects, ticipants have an inconsistent understanding and produces misleading information not only of the risk they are assessing, since each person in risk identification, but also in all downstream may be considering a different risk source and ERM phases: risk quantification, risk manage- scenario triggering the event. This also makes ment and risk disclosure. Relying upon this risk quantification more challenging and un- Sim Segal, FSA, CERA, MAAA, flawed information puts management at risk of: even; risk experts have difficulty constructing is US Leader of ERM Services specific risk scenarios for quantification, since at Watson Wyatt in New York. • Focusing on the wrong priorities; He can be reached at sim. the risk is defined so ambiguously. Finally, • Making poor decisions; and [email protected]. management struggles to identify and evaluate • Producing improper risk disclosures. mitigation alternatives, since risks are generally mitigated at the source rather than the outcome. To have a successful ERM risk identification For example, it’s easier to consider mitigation phase and avoid these problems, companies of potential sources of reputation risk (e.g., poor must: product quality, poor service, internal fraud) than it is to mitigate an amorphous concept like 1. Define risks by source reputation damage in the abstract. 2. Categorize risks with consistent granularity 3. Identify risks prospectively

continued on page 30

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Risk Identification … w continued from page 29

To avoid these difficulties, management must impacts from each originating source. Finally, define risks by their source. In our prior ex- management can clearly identify and evaluate ample of “reputation risk,” we listed three both pre-event and post-event mitigation al- examples of risk sources that might involve ternatives, since both the source of risk and the reputation damage in an extreme scenario. downstream events are apparent. Chart A shows these risks along with a partial illustration of the relationship of risk sources to Categorizing Risks with intermediate impact(s) and to outcomes. In the Consistent Granularity chart, the arrows show how each risk can trigger Risks are often categorized with inconsistent media coverage, resulting in reputation dam- levels of granularity—either at too high a level age, followed by financial repercussions. or too low a level.

It is common to find a risk list that includes some risks defined at too high a level of abstraction— the risk is really a category of risks that should be refined into a set of smaller, individual component risks. For example, “talent management” —a type of human resources risk— should be broken down into its individual risks, such as “ability to recruit/retain,” “succession planning,” etc.

Defining risks at too high a level, results in suboptimal internal qualitative surveys. It leads With risks defined by their source, the ERM to uneven scoring by survey participants, since steps flow well. There is data integrity in the the larger category obscures its several compo- qualitative survey; since each risk is clearly nent risks. However, when risks are consistently defined by its source, survey participants defined at the individual risk level, the assess- have a consistent understanding of each risk, ment is more meaningful, since participants can resulting in a coherent assessment. This also consider and assess each risk individually. makes risk quantification easier. Since risks are defined so clearly—each with its own specific It is even more common to find risks defined at source—risk experts can more easily develop too low a level of abstraction—the risk is really risk scenarios, following logical downstream only one of a larger category of risks. For example, “lack of innovative products” is only one specific risk in a larger category. This should be elevated to a higher level of abstraction, and included in the category of “strategy execution.”

Defining risks at too low a level, threatens the environmental scanning activity. It can cause a failure to identify all related types of risk in the larger category. In our example, management may not have considered other risks to strategy execution, for example, “inability to achieve planned growth,” “failure to expand into key new markets,” etc.

w Page 30 August 2008 w Risk Management Chairman’s Corner

A partial example of how to categorize risks at a gation in place; planned mitigation; anecdotal consistent level of granularity is shown in Chart experience at competitors, etc. B for human resources risks. However, it is counter-productive to gather all Identifying Risks Prospectively this data during the risk identification phase. Too much data is gathered. Most of this data is Risks are often identified retrospectively. Some only needed for the key risks, rather than the risks are on the key risk list merely because long list of risks provided to survey participants. they occurred recently and management wants The primary purpose of the risk identification to see them there. This is called “fighting the phase is to prioritize—to narrow down a list last battle” syndrome. In addition, these risks of (potentially hundreds of) risks to those key are often defined at too low a level of granular- risks that will go to the next ERM phases: risk ity, since they are descriptive of the recent quantification, risk management and risk dis- specific event. closure. All that is needed for prioritization is the frequency-severity scoring. Including these on the risk list, in this way, can skew the qualitative survey results. These risks In addition, the data is collected too early. are often over-weighted; participants are more The data that is needed—the data for the key sensitized to them and are not fully aware of the risks—is not needed until the risk quantifica- mitigation that has likely been put in place fol- tion phase because it is used to develop and lowing the recent occurrence. Retrospectively quantify risk scenarios. Since the data is col- defining risks also negatively impacts envi- lected too early, it is often deposited in a data- ronmental scanning; it is a distraction from base where it languishes and as time passes, the identifying the next risk event (as opposed to the quality decreases. last risk event).

Finally, the burden of the shear volume of data Identifying risks prospectively can help avoid requested results in survey fatigue. this over- these difficulties. It reduces some of the bias whelms survey participants and decreases the in the risk assessment, by not confusing recent quality of the critical input—frequency and experience with future likelihood and impact. severity assessment. It also focuses management away from the past, and concentrates attention on what might These difficulties can be resolved by gathering impact the company’s ability to deliver on its the appropriate data at the proper stage in the strategic objectives going forward. This enables ERM process. In the risk identification phase, a robust, untainted examination of where the the qualitative survey should focus participants company is, where it’s headed and what could primarily on assessing frequency and severity. get in the way. At the risk quantification phase, data should be gathered for developing and quantifying risk Gathering Data Appropriately scenarios for the key risks. This avoids gather- In the risk identification phase, qualitative ing too much data, since the larger data request survey participants are usually asked to assess is not unnecessarily performed for those risks the frequency and severity of a large list of risks. that are not key risks. In addition, data is more However, in most cases, there is also an attempt current, since it is gathered closer to the time it to gather a large amount of additional data at this is needed. Finally, survey participants can do stage: key risk indicators; exposure metrics; a better job, since they are not overwhelmed by historical frequency and severity; current miti- excessive volume.

continued on page 32

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Risk Identification … w continued from page 31 Defining Frequency- worst case”—not an (extremely unlikely) end- Chart C: Severity Clearly of-the-world event and not an event that occurs Illustrative Scoring Criteria When survey participants are asked to quali- with moderate frequency. Frequency Severity tatively assess a list of potential risks, the most 5 = Very High 5 = Impact of $100M+ common approach is to ask them to score each To more clearly define severity, more specific- ity should be provided on the metric(s) intend- 4 = High 4 = Impact of $50M - $100M risk on both a frequency and severity scale. ed. A leading practice is to express the scoring 3 =Moderate 3 = Impact of $25M - $50M Guidance is usually provided in terms of scoring criteria. A simplified example is shown in criteria in terms of a single metric that can cap- 2 = Low 4 = Impact of $10M - $25M Chart C. ture all potential impacts—impacts to income 1 = Very low 5 = Impact of less than $10M statement, balance sheet, required capital and However, this approach often results in dispa- cost of capital. The only metric that captures rate impressions among survey participants as all of these impacts appropriately is enterprise to how to score both frequency and severity, value—the present value of projected cash and negatively impacting survey results. capital flows into the future, where the projec- tion is consistent with the strategic plan. This is To score frequency, participants must consider not market capitalization. Rather, it is the value a specific risk scenario. Is it an end-of-the world an investor should pay today, if the company scenario? Is it a most likely scenario? The for- were to perfectly execute its strategic plan and mer would solicit a lower frequency score than everything go precisely as expected. the latter. However, such guidance is rarely provided. As a result, each participant tends to The enterprise value metric is initially less tan- imagine a different scenario, and collectively gible to some, since it’s a complex calculation. they are essentially not scoring frequency for However, it is intuitive—the value of the firm the same risk event. is a concept everyone understands. In addition, simple illustrations of selected risk events To score severity, participants must understand and their relative impact on enterprise value the metric impacted. Is it an earnings hit? Is it provide survey participants with a general feel one-time or cumulative hit (and for how many for this metric that is sufficient for qualitative years)? Is it a capital hit? Is it a hit to market cap- assessment purposes. italization? While guidance usually includes magnitude, as in our example, sufficient detail Though risk identification is the first step in the regarding the impact is often omitted. Again, ERM process cycle, appears to be the simplest, participants have an inconsistent understand- and is the most traveled, common practices are ing and are not assessing on the same basis. fraught with issues that can damage an ERM program. To avoid this, management must: To resolve this, it is important to more clearly define risks by source; categorize risks with define frequency and severity prior to the quali- consistent granularity; identify risks prospec- tative risk assessment. tively; gather data appropriately; and define frequency-severity clearly. Companies adopting To define frequency clearly, participants must these “better practices” have found that the risk be given guidance as to the type of risk scenario identification phase is quicker, easier, more to consider. One example of how to do this is to widely understood and produces higher quality focus participants on a particular type of risk results, paying dividends as well in downstream event, as shown in Chart D. A range of data ERM phases. Those continuing with common points is shown in the chart, each representing a practices may find themselves more at risk—of potential risk event. The ellipse illustrates that focusing on the wrong priorities, making poor survey participants should consider a “credible mitigation decisions, and ultimately improper risk disclosures. F

Page 32 w August 2008 w Risk Management EditorialChairman’s , Chairman’s Corner Corner or Blank International Survey of Emerging Risks

Max J. Rudolph

Editor’s note: This article also appears in the charts do not add up to 100 percent due to round- August 2008 issue of International News. ing). As the survey evolves, information such as primary practice area also may be included. merging risks surprise us, they sneak up on us, and after they occur everyone The survey asked for the top five emerging risks E wonders why we didn’t anticipate them from the list, and 369 responses were made in the first place. Hindsight is, indeed, 20/20. using the core risks listed. An additional 18 re- Try to recall how often you thought about the sponses fell in the “other” category. The domi- likelihood of the most recent financial bubble or a nant response, with 57 percent, was oil shock/ recent natural disaster prior to its occurrence. energy supply interruptions. Given the timing of Even if you were aware of it and wanted to take the survey, in May 2008, it will be interesting to action, the markets were unlikely to recognize the risk. see how this risk stands up in less hostile energy environments. For more detail about the 23 core Recently, a group was asked to complete a risks, see the attached glossary of risks. survey of emerging risks for financial services firms. The International Network of Actuarial Four of the top five responses reflected eco- Risk Managers (INARM) is a loosely organized nomic risks. In addition to oil, they were: group of actuaries who work to share best practices across the six continents where they • Climate change (environmental risk): reside. A total of 86 responses were received 40 percent during this inaugural survey. The project is • Blow up in asset prices/excessive indebted- likely to be repeated periodically and should ness: 40 percent receive broader exposure. • U.S. current account deficit/fall in U.S. dollar: 38 percent Rather than ask responders to create their own • Fiscal crises caused by demographic shift: list of risks, an existing set was chosen. The 29 percent World Economic Forum report on global risks, completed in January 2007, listed 23 core risks The most interesting response is the last one, for the next decade. Respondents were asked which pertains to looking at the trends caused to choose their top five emerging risks from by an aging population and their potential ef- this list, and could select other risks in addi- fect on the financial landscape. The business Max J. Rudolph, FSA, CERA, is tion. General categories included economic, press reports on the other topics on a daily the owner of Rudolph Financial environmental, geopolitical, societal and tech- basis. Demographic shifts take longer to reach Consulting LLC in Omaha, nological risks. Not surprisingly, this group critical mass. Neb. He can be reached at primarily chose economic risks as the highest max.rudolph@rudolphfinan- priority. One might hypothesize that the risks of The next most popular responses are more diverse. cialconsulting.com. most importance to a group of actuaries would differ from a list compiled by farmers, military • Pandemics (societal risk): 26 percent officers or technology experts. • Chinese economic hard landing (economic risk): 23 percent The responders were more diverse than the typi- • Breakdown of critical information infrastruc- cal actuarial crowd, with 47 percent from outside ture (technological risk): 22 percent North America (Chart 1) and 40 percent employed • Middle East instability (geopolitical risk): outside the insurance industry (Chart 2. The 20 percent continued on page 34

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International Survey … w continued from page 33

Chart 1 • Chronic diseases in the developed world (societal risk): 10 percent • Liability regimes (societal risk): 10 percent • Emergence of risks associated with nanotechnology (technological risk): 8 percent • Interstate and civil wars (geopolitical risk): 8 percent • Natural catastrophe: inland flooding (environmental risk): 7 percent • Proliferation of weapons of mass destruction (geopolitical risk): 7 percent • Transnational crime and corruption Chart 2 (geopolitical risk): 7 percent • Natural catastrophe: earthquakes (environmental risk): 5 percent • Failed and failing states (geopolitical risk): 5 percent

With even the 23rd-highest response rate at 5 percent, the core risks provide a solid group with which to work. The response rates at another point in time would likely yield a different answer. It will be interesting to trend this survey over time. The current focus has been on energy • International terrorism (geopolitical risk): imbalances and the subprime crisis, and that is 17 percent reflected in the responses. Recent events, such as if a major metropolitan area like Tokyo had These are the highest-ranking geopolitical risks. been hit by an earthquake or if a nuclear war- It is hard to classify these as emerging risks but head had gone off somewhere in the world, will instability caused by nation-states and orga- drive responses to some unknown extent. This nizations not tethered to physical geographic is the opposite of the old saying, “Out of sight, boundaries will continue to change history and out of mind.” be high-priority risks for world leaders. Those who decided that these 23 trends were Sorted by response rate, here are the remaining not broad enough tended to look at societal 13 risks: and economic risks, sometimes combining • Retrenchment from globalization (geopoliti- them. An example of this is the combination of cal risk): 15 percent depleted resources and a shift in the balance • Natural catastrophe: tropical storms (environ- of power from developed countries with stable mental risk): 14 percent populations to developing countries with grow- • Loss of freshwater services (environmental ing populations. Other examples focused on risk): 10 percent food shortages, bioengineering developments • Infectious diseases in the developing world and several who expressed concern about (societal risk): 10 percent

Page 34 w August 2008 w Risk Management EditorialChairman’s , Chairman’s Corner Corner or Blank

the unintended consequences of accounting • Chinese economic hard landing—China’s requirement changes. economic growth slows, potentially as a result of protectionism, internal political or eco- Learnings nomic difficulties. • Fiscal crises caused by demographics shift— Any survey is limited by its size and participant Aging populations in developed economies expertise, but this group of INARM actuaries drive economic stagnation by forcing govern- has provided a first look at what risk managers ments to raise taxes or increase borrowing. are worried about internationally as they gaze • Blow up in asset prices/excessive indebted- into their crystal balls. It also shows the bias ness—Personal assets, such as housing, col- that any given group will have based on their lapse in the United States and Europe, fueling knowledge, location and experience. This sur- a recession. vey can help other risk professionals, especially actuaries, improve their thought processes regarding emerging risks to provide better in- Environmental Risks sights on the topic. • Climate change—Climate change generates both extreme events and gradual changes, af- Functioning risk areas can include this type fecting infrastructure, agricultural yields and of information to help their efforts evolve. No human lives. matter which industry you are involved in, these • Loss of freshwater services—Water risks have the potential to affect your com- shortages. pany’s results. This survey can help prioritize • Affect agriculture, businesses and human risk-education efforts. One way is to facilitate lives. a workshop to prioritize current risks. By start- • Natural catastrophe: tropical storms— ing off talking about future risks, it puts some Hurricane or typhoon passes over a heavily perspective on previous prioritizations and populated area, leading to catastrophic eco- reminds participants that the list must evolve nomic losses and/or high human death tolls. over time and not simply be copied from the • Natural catastrophe: earthquakes— last pass. Strong earthquake(s) occur in heavily populated areas. Glossary of Risks • Natural catastrophe: inland flooding— Flooding associated with rivers causes The following 23 core risks were defined in significant economic losses, fatalities and “Global Risks 2007: A Global Risk Network disruption. Report,” and can be found at www.weforum.org/ pdf/CSI/Long_Global_Risk_Report_2007.pdf. What follows is a summary of these risks. Geopolitical Risks • International terrorism—Attacks disrupt Economic Risks economic activity, causing major human and economic losses. Indirectly, attacks aid re- • Oil price shock/energy supply interruption trenchment from globalization. —Oil prices rise steeply due to major supply • Proliferation of weapons of mass destruction disruption. —Trend fatally weakens the Nuclear Non- • U.S. current account deficit/fall in U.S. dollar

—U.S. current account deficit triggers a major

fall in the dollar’s value. continued on page 36

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International Survey … w continued from page 35

Proliferation Treaty and leads to the spread of Technological Risks nuclear technologies. • Breakdown of Critical Information • Interstate and civil wars—Major interstate or Infrastructure (CII)—A major disruption of civil war breaks out. the availability, reliability and resilience of • Failed and failing states—Trend of widening CII caused by cyber crime, a terrorist attack gap between order and disorder. or technical failure. Results are felt in major • Trans-national crime and corruption— infrastructure: power distribution, water Corruption continues to be endemic and supply, transportation, telecommunication, organized crime successfully penetrates the emergency services and finance. global economy. • Emergence of risks associated with nanotech- • Middle East instability — The Israel-Palestine nology—Studies indicate health impairment conflict and Iraqi civil war continue. due to under regulated exposure to a class of • Retrenchment from globalization—Rising commonly used nanoparticles (used in paint, concerns about cheap imports and immigra- nano-coated clothing, cosmetics or health tion sharpen protectionism in developed care), exhibiting unexpected, novel proper- countries. Emerging economies become more ties and easily entering the human body. F nationalist and state-oriented.

Societal Risks • Pandemics — A pandemic emerges with high mortality among economically productive segments of the population. • Infectious disease in the developing world —HIV/AIDS continues to spread geographi- cally. Other diseases could develop. • Chronic disease in the developed world— Obesity, diabetes and cardiovascular diseases become widespread. • Liability regimes—U.S. liability costs rise by multiples of gross domestic product (GDP) growth, with litigiousness spreading to Europe and Asia.

w Page 36 Summary of ERM paper John Manistre Summary of ERM paper The purpose of this article is to provide a high level summary of the paper “Variance of the CTE John Manistre Estimator” by B. John Manistre and Geoffrey H. Hancock that appeared in the North American Actuarial Journal in 2005. We also expand on some of the results. The purpose of this article is to provide a high level summary of the paper “Variance of the CTE Estimator” by B. John Manistre and Geoffrey H. Hancock that appeared in the North American An actuary who is responsible for estimating reserves and capital using stochastic methods must Actuarial Journal in 2005. We also expand on some of the results. deal with a wide range of issues. Not only must the actuary worry about the underlying stochastic model, it’s parameterization, data, assumptions and calculation formulae but he/she An actuary who is responsible for estimating reserves and capital using stochastic methods must now has (or should have) the new issue of trying to quantify the precision of the estimated risk deal with a wide range of issues. Not only must the actuary worry about the underlying measure. Summary of ERM paper stochastic model, it’s parameterization, data, assumptions and calculation formulae but he/she SummaryJohn Manistre of ERM paper now has (or should have) the new issue of trying to quantify the precision of the estimated risk The Value-at-Risk (VaR) estimator (i.e., percentile or quantile value) is still often used as a risk John Manistre measure. measure. However,The purpose the C ofonditional this article Tail is to Expectationprovide a high (levelCTE summ, alsoary called of the Expected paper “Variance Shortfall of the or CTE Tail-VaR) is ThebecomingEstimator purpose ”increasinglyof by this B. articleJohn Manistre is prevalent to provi andde Geoffreyadue high to level its H. desirablesummHancockary thatof properties the appeared paper “ Varianceandin the ease North of of the American CTE The Value-at-Risk (VaR) estimator (i.e., percentile or quantile value) is stillAugust often 2008 used w Riskas a riskManagement interpretation.Estimator Actuarial A tool” thatby Journal B. can John inquantify Manistre2005. We theand also statisticalGeoffrey expand H. on precision Hancock some of thatthe of results.appearedan estimated in the CTENorth isAmerican therefore measure. However, the Conditional Tail Expectation (CTE, also called Expected Shortfall or Chairman’s Corner important. ThatActuarial is, the Journal sampling in 2005. error We in also the expand estimate on some can ofbe the placed results. in perspective with other An actuary who is responsibleTail-VaR) for estimating is reservesbecoming and increasinglycapital using stochastic prevalent methods due to must its desirable properties and ease of modeling issues, including parameter, model and assumption risk. Andeal actuary with whoa wide is responsible range of issues. forinterpretation. estimating Not only reserves must A the tooland actuary capital that worry can using quantify about stochastic the theunderlying methods statistical must precision of an estimated CTE is therefore stochastic model, it’s parameterization, data, assumptions and calculation formulae but he/she deal with a wide range of issues. important. Not only m ust That the actuaryis, the worrysampling about error the underlying in the es timate can be placed in perspective with other If all we werestochastic interestednow has model, (or inshould wasit’s parameterization, have)a regular the new mean issue data, then of assumptionstrying we would to quantify and know calculati the what precisionon toformulae do. of the W butestimatede draw he/she a risk modeling issues, including parameter, model and assumption risk. Summarynow measure.of has (or should “Variance have) the new issue of trying to quantifyof thethe precision of Cthe estimatedTE1 riskEstimator” sample x 1 x measure.2 ,...,, x n of size n from our model and calculate the sample average Pˆ ¦ xi . n John Manistre and Geoffrey HancockThe Value-at-Risk (VaR) estimIfator all (i.e.,we werepercentile interested or quantile in wasvalue) a isregular still often mean used theni as a werisk would know what to do. We draw a Statistical theoryThemeasure. Value-at-Risk tells us However, three (VaR things the) estim Conditional ator (i.e., Tail percentile Expectation or quantile (CTE ,value) also called is still Expected often used Shortfall as a risk or 1 measure.Tail-VaR) However, is becoming the C onditionalincreasinglysample Tail prevalent Expectation x 1 x 2 due,...,, tox (CTEn its ofdesirable, also size called n propertiesfrom Expected our and model Shortfall ease andof or calculate the sample average Pˆ ¦ xi . interpretation. A tool that can quantify the statistical precision of an estimated CTE is therefore n i 1. The samTail-VaR)ple average is becoming is an increasingly unbiased estimatorprevalent due i.e. to Eits[ Pdesirableˆ] P the properties true mean. and ease We of expect to interpretation.important. That A tool is, thethat sampling can quantifyStatistical error the in statistical the theory estimate precisiontells can us be threeof placed an estimatedthings in perspective CTE is withtherefore other get the modelingright answer. issues, including parameter, model and assumption risk. he purpose of thisimportant. article That is to is, provide the sampling error2. in The the esvariancetimate can ofbe placedthe sample in perspective average with otheris modeling issues, including parameter,1. modelThe and sam assumptionple average risk. is an unbiased estimator i.e. E[Pˆ] P the true mean. We expect to a high level2. The summary varianIf allce we of ofwere the the interestedsample paper average in was a regularis VAR m[eanˆ thenVP 2 we/] n wouldwhere know V 2 whatis thethe to true do.true Wvariance. variance.e draw a If all we were interested in was a regular mgetean the then right we would answer. know what to do. We draw1 a sample x 1 x 2 ,...,, x n of size n from our model and calculate the sample average Pˆ ¦ xi . “Variance of the CTE Estimator” by 1 n sample x x ,...,, x of size n from our model and calculate the sample average Pˆ x i . T 3. If the sample 1 size2 is largen enough, and a few other technical conditions are satisfied,¦ i the 2 2 B. John Manistre and GeoffreyStatistical H. theory Hancock tells us three things3.2. If The the variansamplece ofsize the is sample large average enough, isn andVARi [aˆ few VP /] n where V is the true variance. estimatorStatistical Pˆ has theory an approximate tells us three things normal distribution. that appeared in the North American1. The sam Actuarialple average is an unbiasedother estimator technical i.e. E [conditionsPˆ] P the true are mean. satisfied, We expect the to 3. If the2 sample1 size is large2 enough, and a few other technical conditions are satisfied, the The distribution’s1. varianceTheget sam theple rightcan average beanswer. estimated is an unbiased from estimator Vˆ i.e. E¦[Pˆ]( xiP thePˆ) trueand mean. the actuaryWe expect would to Journal in 2005. We also expand on some of estimatorn P 1 has an approximate normal dis- get the right answer. estimator ˆ hasi an approximate normal distribution. 2 2 the results. 2. The variance of the sampleVˆ averagetribution. is VAR[ ˆ VP /] n where V is the true variance.2 1 2 then report the result of the work as Pˆ rThe distribution’s giving any potential variance2 user can a be sense2 estimated of how from large V ˆthe (x Pˆ) and the actuary would 2. The variance of the sample average is VAR[ ˆ VP /] n where V is the true variance. ¦ i n n 1 i sampling error (i.e.,3. statisticalIf the sample unc sizeertainty) is large mightenough, be. and Usersa few other can technicalthen judge conditi whetherons Vareˆ this satisfied, is large the An actuary who is responsible3. If theestimatorfor sam estimatingple P ˆsizehas is an large approximate then enough,The report andnormal distribution’s athe few distribution.result other oftechnical the work variance conditi asons Pˆ rare can satisfied, giving be the esti any - potential user a sense of how large the or small relative to estimatorother model Pˆ has se annsitivities, approximate such normal as distribution.a change in lapse assumptions for example, 2 1 2 n reserves and capitaland react using appropriatel Thestochastic distribution’sy. In methodsparticular, variance can users bemated estimated can judge from from wh Vetherˆ the precision(xi Pˆ) ofand and the the estimatetheactuary actuary would is 2 1 ¦ 2 sampling error V(i.e., statisticaln 1 i uncP ertainty) might be. Users can then judge whether this is large high enough Thefor distribution’sthe intended variance application. can be estimated from ˆ ¦(xi ˆ) and the actuary would must deal with a wide range of issues. Not only or smallwould relativeV ˆ then to report othern 1 imodel the result sensitivities, of the such work as a aschange in lapse assumptions for example, Pˆ r then report the result of the workand as react Vˆ appropriatel giving anyy. potential In particular, user a sense users of how can large judge the whether the precision of the estimate is must the actuaryHow worrydoes this aboutthen process report the thechange underlyingresult ofwhen the work we start as P ˆ estimatingr givingngiving Conditionalany any potential potential userTail a Expectations?sense user of ahow sense large ofthe how sampling error (i.e., statistical highuncertainty) enoughn might for thebe. intendedUsers can thapplication.en judge whether this is large stochastic model, it’s parameterization,samplingor small error relative (i.e., to statistical otherdata, model uncertainty) selargensitivities, mightthe such samplingbe. asUsers a change can error th inen lapse judge (i.e., assumptions whether statistical this for is large example,uncer - First, the bad news. There is no general set of formulas that are guaranteed to work in all assumptions and calculationor andsmall formulaereact relative appropriatel to otherbut y.modelhe/ In particular, seHownsitivities,tainty) does users suchthismight can asprocess judge a be.change wh Userschangeether in lapse the canwhen precisionassumptions then we ofstartjudge thefor estimating estimateexample, whether is Conditional Tail Expectations? circumstances.andhigh Thereact enough distributionappropriatel for they. intended of In a particular, CTE application. estimator users can depends judge wh onether a widethe precision range of thevariables estimate suchis as sample size, highthe actual enough distribution for the intended you application. are sampling from and the method of estimation itself. she now has (or should have) the new issue of First,this the is bad large news. or small There relative is no general to other set ofmodel formulas sen -that are guaranteed to work in all Summary of ERM paper How does this process change when we start estimating Conditional Tail Expectations? trying to quantify the precisionHow does of thisthe process estimated change whencircum sitivities,we startstances. estimating such The Conditional asdistribution a change Tail of in Expectations? a lapse CTE estimatorassumptions depends on a wide range of variables such as John Manistre Summary of ERM paper risk measure. First, the bad news. There is nosample generalfor example,size, set of the formulas actual and that distribution react are guaranteed appropriately. you to are work sampling in allIn par from-1 and the method of estimationJohn Manistre, itself. FSA, FCIA, is First,circum the stances.bad news. The There distribution is no general of a CTE set of estimator formulas depends that are onguaranteed a wide range to work of variablesin all such as John Manistre circumsamplestances. size, the The actual distribution distribution of aticular, CTE you estimatorare sa usersmpling depends canfrom onjudgeand a widethe methodwhether range of variablesestimation the precision such itself. as vice president, group risk, The purpose of this articlesample is tosize, provi the actualde adistribution high level you are summ samplingary from of andthe the paper method “ ofVariance estimation itself.of the CTE TheEstimator Value-at-Risk” by B. John (VaR Manistre) estimator and (i.e., Geoffrey per- H. ofHancock the estimate that appearedis high enough in the for North the intendedAmerican at AEGON NV in Baltimore,1 The purpose of this article is to provide a high level summary of the paper “Variance of the CTE 1 Md. He can be reached at centileActuarial or Journalquantile in value) 2005. is We still also often expand used on someapplication. of the results. 1 Estimator” by B. John Manistre and Geoffrey H. Hancock that appeared in the North American [email protected]. Actuarial Journal in 2005. We also expand on someas a riskof the measure. results. However, the Conditional An actuary who is responsible for estimating reserves and capital using stochastic methods must Summary of ERM paper Tail Expectation (CTE, also called Expected How does this process change when we start deal with a wide range of issues. Not only must the actuary worry about the underlying An actuaryJohn whoManistre is responsible for estimating reserves and capital using stochastic methods must Shortfallstochastic or model,Tail-VaR) it’s is parameterization, becoming increasingly data, assumptionsestimating and Conditional calculation Tail formulae Expectations? but he/she deal with a wide range of issues. Not only must the actuary worry about the underlying The purpose of this article is to provide a high levelprevalentnow summ hasary (or due of shouldthe to paper its have)desirable “Variance the new ofproperties the issue CTE of and trying to quantify the precision of the estimated risk stochastic model, it’s parameterization, data, assumptions and calculation formulae but he/she Estimator” by B. John Manistre and Geoffrey H. easemeasure.Hancock of interpretation. that appeared in theA tool North that American can quantify First, the bad news. There is no general set now hasActuarial (or should Journal have) in 2005. the new We alsoissue expand of trying on some to quantifyof the results. the precision of the estimated risk measure. the statistical precision of an estimated CTE is of formulas that are guaranteed to work in all An actuary who is responsible for estimating reservesthereforeThe andValue-at-Risk capital important. using stochastic ( ThatVaR )is, estim themethods samplingator must (i.e., error percentile circumstances. or quantile value) The distributionis still often of used a CTE as a esrisk- deal with a wide range of issues. Not only must themeasure. actuary worry However, about the the underlying Conditional Tail Expectation (CTE, also called Expected Shortfall or The Value-at-Risk (VaR) estimator (i.e., percentilein theor quantile estimate value) can be is placedstill often in usedperspective as a risk timator depends on a wide range of variables stochastic model, it’s parameterization, data, assumptionsTail-VaR) and calculatiis becomingon formulae increasingly but he/she prevalent due to its desirable properties and ease of measure. However, the Conditional Tail Expectation (CTE, also called Expected Shortfall or now has (or should have) the new issue of trying withtointerpretation. quantify other the modeling precision A tool issues,of that the estimated can including quantify risk param the statistical- such precision as sample of size,an estimated the actual CTE distribution is therefore Tail-VaR)measure. is becoming increasingly prevalent due to its desirable properties and ease of eter,important. model and That assumption is, the sampling risk. error in the estimateyou arecan besampling placed infrom perspective and the withmethod other of interpretation. A tool that can quantify the statistical precision of an estimated CTE is therefore modeling issues, including parameter, model and estimationassumption itself. risk. important.The Value-at-RiskThat is, the sampling(VaR) estim errorator (i.e., in thepercentile estimate or quantile can be value) placed is still in perspectiveoften used as awith risk other measure. However, the Conditional Tail ExpectationIf all ( CTEwe were, also calledinterested Expected in was Shortfall a regular or mean Geoffrey Hancock, FSA, CERA, modeling issues, including parameter, model and assumption risk. FCIA, is a director at Oliver Tail-VaR) is becoming increasingly prevalent duethenIf to all its we wedesirable wouldwere properties interestedknow what and in easeto was do. of a regularWe draw m eana thenNow, we the would (really) know good what news. to do. We draw a interpretation. A tool that can quantify the statistical precision of an estimated CTE is therefore 1 Wyman in Toronto, ON. He If all weimportant. were interested That is, the in samplingwas a regular error in m theean estimate thensample wecan bewould x placed x know,...,, in perspectivex what of size to with do.n from other W eour draw model a Pˆ x sample 1 2 n of size n from our model and calculate the sample average ¦ i . can be reached at geoffrey. modeling issues, including parameter, model and assumption risk. 1 n i and calculate the sample average P 1. If the sample size being used is large enough, [email protected]. sample x 1 x 2 ,...,, x n of size n from our model andStatistical calculate theory the sample tells us average three thingsˆ ¦ xi . If all we were interested in was a regular mean then we would know what to do. We draw a n i then there are approximate formulas analo- Statistical theory tells us three things Statistical theory tells us three things1 gous to those that apply for an ordinary mean. sample x 1 x 2 ,...,, x n of size n from our model and calculate1. The the sam sampleple average averagePˆ is an¦ unbiasedxi . estimator i.e. E[Pˆ] P the true mean. We expect to n i It is therefore possible to quantify the statisti- Statistical theory tells us three things get Pthe rightP answer. 1. The sample average is an unbiased estimator1. The i.e. sample E[ ˆ] average the is true an unbiasedmean. We estimator expect to cal precision of an estimated CTE. get the right answer. 1. The sample average is an unbiased estimatori.e., i.e.2. E The [ P ˆ ] varian P thethe truetruece of mean. mean. the sampleWe We expect expect average to to get is VAR[ ˆ VP 2 /] n where V 2 is the true variance. get the right answer. the right answer. 2. There is a practical process, called a “vari- 2. The variance of the sample average is VAR[ ˆ VP 2 /] n where V 2 is the true variance. 2 2 ance verification” exercise in this article, 2. The variance of the sample average is VAR[ ˆ 3. VP If/] nthewhere samVple is size the true is large variance. enough, and a few other technical conditions are satisfied, the estimator Pˆ has an approximate normal distribution. 3. If the sample size is large enough, and a few other technical conditions are satisfied, the 3. If the sample size is large enough, and a few other technical conditions are satisfied, the 1 estimator Pˆ has an approximate normal distribution. 2 2 continued on page 38 estimator Pˆ has an approximate normal distribution.The distribution’s variance can be estimated from Vˆ ¦(xi Pˆ) and the actuary would n 1 i 2 1 2 2 1 2 The distribution’sThe distribution’s variance variance can can be be estimated estimated from V ˆVˆ (x (xPˆi) andPˆ) theand actuary the actuarywould would ¦ ¦i Vˆ then reportn n1 i1thei result of the work as Pˆ r giving any potential user a sense of how large the Vˆ n then report the result of the work as Pˆ r Vˆ giving any potential user a sense of how large the then report the result of the work as Pˆ r givingsampling any potential error (i.e., user statistical a sense ofunc howertainty) large mightthe be. Users can then judge whether this is large nn sampling error (i.e., statistical uncertainty) might orbe. small Users relativecan then judgeto other whether model this seis nsitivities,large such as a change in lapse assumptions for example, Page 37 w sampling error (i.e., statistical uncertainty) might be. Users can then judge whether this is large or small relative to other model sensitivities, suchand as a reactchange appropriatel in lapse assumptionsy. In particular,for example, users can judge whether the precision of the estimate is or small relative to other model sensitivities, such as a change in lapse assumptions for example, and react appropriately. In particular, users can judgehigh whenoughether the for precision the intended of the estimate application. is and reacthigh appropriatel enough for they. intended In particular, application. users can judge whether the precision of the estimate is high enough for the intended application. How does this process change when we start estimatingHow doesConditional this process Tail Expectations? change when we start estimating Conditional Tail Expectations? How does this process change when we start estimating Conditional Tail Expectations? First, the bad news. There is no general set of formulasFirst, thatthe arebad guaranteed news. There to work is inno all general set of formulas that are guaranteed to work in all circumstances. The distribution of a CTE estimatorcircum dependsstances. on a wide The range distribution of variables of such a CTE as estimator depends on a wide range of variables such as First, thesample bad news.size, the There actual distributionis no general you areset saofmpling formulas from thatand the are method guaranteed of estimation to work itself. in all sample size, the actual distribution you are sampling from and the method of estimation itself. circumstances. The distribution of a CTE estimator depends on a wide range of variables such as sample size, the actual distribution you are sampling from and the method of estimation1 itself. 1

1 Now, the (really) good news.

1. If the sample size being used is large enough, then there are approximate formulas analogous to those that apply for an ordinary mean. It is therefore possible to quantify the statistical precision of an estimated CTE.

2. There is a practical process, called a “variance verification” exercise in this article, that one can execute to test (and confirm) the validity of the approximate formulas for any particular application. An example is given at the end this article.

3. Some standard variance reduction tools such as importance sampling and control variate methods can be adapted to the CTE problem to improve, sometimes dramatically, the precision of a CTE estimator for a given computational cost. These techniques will be the topic of a second article on CTE variance.

So what are the approximate formulas? First, we need some notation. Suppose we want to estimate the Conditional Tail Expectation of a random variable X, with cumulative distribution Pr^` X d x F x )( at the level DThus, we want to calculate the conditional expectation

( D ) > | ! qXXECTE D @

where qD is the D-quantile, defined as the smallest value satisfying

Pr^ X ! q D ` 1D

The D-quantile is often called Value-at-Risk (VaR) and is used extensively in the financial management of trading risk over a fixed (usually short) time horizon.

Risk Management w August 2008 The standard approach to this problem is to start with a random sample x 1 x 2 ,...,, x n of size n Chairman’sVariance of Corner the CTE Estimatorfrom the model and then sort the sample in descending order to obtain the order statistics

x ( 1 ) t x ( 2 ) t ... t x n)( . We can then calculate the plug-in estimators for the required parameters k CTE Estimator … by looking at the observed empirical distribution. Let D 1 so that practical expressions for w continued from page 37 n the plug-in estimators are k ˆ 1 ETC n D ¦ x i)( , Now, the (really) good news. that one can execute to test (and confirm) the In terms of this notation statistical theory hask i 1

validity of the approximate formulas for any the following three things to say V a ˆ R n D x k )( . 1.Now,If the the sample (really) sizegood beingnews. usedparticular is large application. enough, An then example there is givenare approxim In terms ofate this formulas notation statistical theory has the following three things to say analogous to those that applyat the foendr thisan ordinaryarticle. mean. It is therefore1. Ifpossible the sample to sizequantify is large enough, and a few Now, the (really) good news. the1. statisticalIf the sample precision size being of anused estimated is large enough, CTE. then there are approxim1. otherateIf the formulas very sam pletechnical size is conditionsl arge enough, hold, and then a few other very technical conditions hold, then analogous to those thatNow, apply the (really) for an good ordinary news. mean. It is therefore possible to quantifyˆ 3. Some standard1. If the variance sample size reduction being used tools is such large enough,thethe then pair pair there ( C are n ,approxim VET a ˆR n ) hashasate an an formulas approximate approximate multivariate normal distribution. the statistical precision of an estimatedanalogous CTE to those. that apply for an ordinary mean. It is therefore possible to quantify 2. There is a practical process,as1. importance calIf theled sample a “variancesampling size being and verification” used control is large variate enough, exer cisethenmultivariate therein this are article,approxim normal distribution.atethat formulas the statistical precision of an estimated CTE. one can execute to test (andmethods confirm)analogous can be the toadapted those validity that to the apply ofCTE thefo rproblem an approxima ordinary mean.te formulas It is therefore for possible any to quantify 2. There is a practical process, called a “variance verification” exercise in this article, that particular application. 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( VaRCTE ) n ( 1 D) one can execute toprecision test (and confirm)of a CTEthe topicthe estimator va lidityofprecision a second ( forofD the VaRfn aof given approxima aarticle )]([ CTE> comput estimator|) onte CTE! formulas(ationaqXXECTE forˆvariance.ETCVAR @ a)l given| cost.for n any comput n These ationatechniquesl cost. Thesewill be techniques ( 1 DD ) ,will be X ( D ) > | ! qXXECTE DD@ n ( D ) > | !precisionXqXXECTE DVaRnf @ )( ( ˆ ofRaVVAR )a| CTE estimator, for a given computational cost. These techniques will be particular application.the topic An example of a second is given article atthe the topicon end CTE of this a variance.second article. article on CTE variance. n ( 1 D) n VaRfn )]([ 2 ( 1 DD ) whereD(qDTheis th notationeVaRCTE D-quantile,) VaRf defined)( refers as tothe the smallest probability valuethe topic density satisfying of a f second x )( ofX the article random onˆ variableCTE| variance. X at the So what are the approximate formulas?ˆ First, we need some notation. SupposeX we want to X ( RaVVAR n ) 2 , So what( are n , ˆ theRaVETCCoV n ) approxim| ate formulas?. First, we need ( 1 DD some) 2. notation.The estimator SupposeD( pair weVaRCTE is) want asym toptotically unbiased. For any finite sample size the CTE plug-in 3. Some standard variance reduction tools such as importance sampling and control variate ˆ ˆ | X VaRfn )]([ estimate the Conditional Tail Expectation wherewofhere a random q D is th variable e point XD -quantile, VaRnf X x , = )( with VaR. definedcumulative ( as asˆ RaVVAR distrthe then ) |smallestibution small- value satisfying(, n , RaVETCCoV n ) . methodswhere Socan q whatbeD is adaptedD th aree D -quantile, thetoestimate the approxim CTE the definedproblemSo ateCond what formulas? as itionalto are improve,the the smallestTail approxim First, sometimesExp valueectationate we formulas? need dramatically,satisfying of some a random First, notation. the we variable need Suppose2 some X, with notation. we cumulative want Suppose to distr we ibution want to ˆ o f where qD is the -quantile, defined as the smallest value satisfying ^ VaRfn ! )]([ ` D estimator isX negativelyVaRnf )( biasedD i.e. [ ] CTEETCE , but the bias goes to 0 as n . Pr^` X d The x F notationx )( at the levelVaRf DThus,)( refers we esttowant thevalue to probabilitycalculate satisfying the conditional density f expectationx )( of the randomPr SoX what variableq D are1 X the at approxim the ate formulas?ˆ First,( we needVaRCTE ) some notation. Suppose we want to precisionestimate of a CTE theestimatorX CondPr^` X itionalfor d a x given estimate Tail F comput x Exp)( attheectation theationa Cond levelitionall cost.of D a randomTailTheseThus, ExpX techniqueswe ectationvariable wantThe notation toof willX calculatea, randomwith be VaRf cumulative thevariable)( refers conditional toX , distr thewith probabilityibution cumulativeexpectation ( density distr n , ibutionˆ f RaVETCCoV n )x )( | of the random variable. X at the Several comments are in order D( estimateX VaRCTE the) CondPracticalitional experience Tail Expectation suggestsX of the a random biasVaRnf is us)( variableually much X, with smaller cumulative than the distr samplingibution error. the topic of a second article on CTE variance.Pr^` X d x F x )( at the level Dˆ Thus, wePr^ want X ! q toD `calculate 1D the conditional expectation X pointPr^`x X = d VaR. x F x )( at the level DThus, we want to( calculate n , pointˆRaVETCCoV n the) |x conditional= VaR. expectation. D The D!-quantilePr^ X ! isq Doften` 1calledD Value-at-RiskPr (^`VaR X d ) x and is F usedx )( atextensi the levelvely inD theThus, financial we want to calculate the conditional expectation ( ) > | PrqXXECTE ^D @ !x qX CTED ` is 1clearlyD ( D ) easier > to work| ! XwithqXXECTE VaRnf TheThe @than)( notationnotation VaR. If we XwereVaRf using)( refers VaR to as to the a the risk probability probabilitymeasure then density f X x )( of the random variable X at the So what are the approximate formulas? First, wema nagement need some of notation.trading risk Suppose over a fixed we want (usually toD short) time horizon. The D-quantile is oftenwe ca wouldlled Value-at-Risk haveSeveral to find ( D ) commentsa (wayVaR> to)| andestimate are! is qXXECTE in used @order 3.the extensi probabilityThe followingvely densityin the approximate financial VaRf )( in ordervariance/covariance to formulas are also asymptotically valid estimate the CondSeveralitional comments Tail Exp areectation in order ofThe a random notation variable XDVaRf X , with)( refers cumulative ! to the probabilitydistributionpoint densityD x = f VaR.X x )( of the the random randomX variable variable X atX the at the management of trading ( ) risk> over| a fixedqXXECTE D @ (usually short) time horizon. ^` d where TheqD is thDe-quantile D-quantile, is Ddefined often as ca thelled smallest Value-at-Risk value satisfying (VaR apply) and the asymptoticis used extensi formula.vely This in can the be financial very difficult in practice, especially ( D ) in the> tails| ! qXXECTE D @ Pr X x F x )( at the level wThus,here weqD iswantpointThe the toDThe -quantile,xcalculate = standard VaR. the definedis approach conditionaloften calledas tothe thisexpectation smallestValue-at-Risk problem value is to satisfying starpointt with x a= randomVaR. sample x x ,...,, x of size n 2 The Dm-quantileanagementx CTE is is oftenof clearly trading ca easierlled risk toValue-at-Risk over work a withfixed than (usually (VaRVaRof. Ifthe)short) weand distribution. were istime used using horizon. x extensiVaRCTE asis clearlyavely risk measureeasierin the to workfinancial then with than VaR 1 . If2 we weren using VaR as ( a | risk t measureVaRXXVAR ) thenD( VaRCTE ) w(VaRhere) qandD is thise used D-quantile, extensively defined in as the the financial smallest valueSeveral satisfying comments are in order ( ÊTCVAR ) | , The standardfrom the approach model and to this then problem sort the is sampleweto starwouldt inwith have descending a torandom find a way ordersample to estimate to x obtain x the,...,, theprobabilityx order of size statisticsdensityn n X VaRf )( in order to managementwhere weof qwouldtradingD is th havee D risk-quantile, to findover a definedwaya fixed to estimate as (usually the smallest the probabilityshort) value time satisfying density horizon. VaRf )( in order to 1 2 n ( PrD^ ) X ! q >D ` | 1!DqXXECTE D @ X n ( 1 D) Severalmanagement x comments t x of trading t x... aret x risk in .order over WePr a ^can X fixed !thenq (usuallyD àpplycalculate 1w the Dhere asymptotictheSeveralq plug-inD is th commentsformula.e estimatorsD-quantile, This are for can indefined the orderbe veryrequired as difficult the param smallest in practice,eters value especially satisfying in the tails from the ( 1 ) model ( 2 ) and The thenn)( VaR sort and the CTE sample estimators in descending are positively order correlated. to obtain This the makes order intuitive statistics sense. The standardapply theapproach asymptotic to thisformula. problem This iscan to be star veryt with difficult a random inPr practice,^ X of !sample theq èsdistribution. pecially1 x D 1 x x 2 in CTE,...,, thex ntailsis clearlyof size easier n to work with than VaR ( 1 DD . If) we were using VaR as a risk measure then short) x t time x t horizon.... t x . We can then calculate Dthe plug-in estimatorsk for the required param( êtersRaVVAR ) | , where qD is the D-quantile,of the defineddistribution. as the smallest ( 1 ) byvalue ( looking 2 ) satisfyingPr at^x X nthe)( ! observedq ` 1 emD pirical distribution. Let D 1 so that practical expressionsn for 2 TheThe standardD-quantile is oftenapproach called Value-at-Risk toD this problem (VaRx ) andCTE isis usedis to clearly extensistarThet vely easierDwith variance in the toa financialworkofrandom the CTEwith estimatorsample than VaR has . x If two wewe terms.21 were,...,, would xx Theusingn have firstof VaR to sizeterm find as isn athea risk way “obvious” measure to estimate then theVaRfn probability)]([ density X VaRf )( in order to from the model andThe then-quantile sort is the often sample called in Value-at-Risk descending ( orderVaR) and to obtainis used• CTE extensi the isorder clearlyvelyn statisticsin easier the financial to work with Prthan^ X VaR.! q D If` X 1D management of trading risk over a fixed (usually short) time horizon.extension of what wasx The happeningVaR and in CTE the firstestimatorsk (D 0 are) case. positively The origin correlated. of the This second makes term intuitive sense. t t t managementTheby oflookingD trading-quantilewe atwould riskthe is oftenobserved over have ca a lledto fixed emfind Value-at-Riskpirical (usually a way distribution. to short) estimate(VaR )time andLet the ishorizon.D used probability 1 apply extensi so the velythat density asymptotic practicalin the financialX expressionsVaRf formula.)( in order forThis to can be very difficult in practice, especially in the tails from the x ( 1 ) x model x The ( 2 ) VaR...and and x thenn )( CTE . We sortestimators^ canThe! the then`standardthe are sample plug-in calculate positivelyD approach estimators in canthe descendingcorrelated. beplug-into are seenthis by Thisproblem estimators conditioning order makes is tointuitiveto foron obtain thethe observation wesense.required were the usingorder ofparam the VaR estimated statisticseters as a risk V a ˆ R measure. We can then then Dwe write( VaRCTE ) Pr X maq nagementD 1 of trading risk over a fixed (usually short) time horizon.n ( ˆ , ˆRaVETCCoV ) | . The D-quantile is often called Value-at-Riskapply the asymptotic (VaR) and formula. is usedx extensi ThisThe variance canvely be in ofvery1 the thek offinancialCTEdifficult the estimator distribution. in practice, has two terms. especially n The first n in termthe tails is the “obvious” x The ( 1 standard () 2 ) tt approach... t xx ton this)( . problem We can is tostartthe thenstar plug-in witht with calculate a arandomestimators random sample thesample are plug-in x 1 x 2 ,...,, estimatorsx n kofof sizeˆ nThen forD D -quantilethewould required have is often to find param ca alled wayeters Value-at-Risk to estimate the ( probVaR-) andX VaRnf is used)( extensively in the financial The standard approach to this problem is to start extensionwithETC na random of what¦ wassamplex i)( ,happening x 1 x in2 ,...,, the firstx n (ofD size0 ) case. n The origin of the second term by lookingmx anagement at the of observed trading risk em piricalover ofa fixed distribution.the distribution. (usually Letshort) D time 1 ˆhorizon. so that practicalk ˆ ˆ expressions forˆ ˆ The D-quantile is oftenThe ca lledvariance Value-at-Risk of the CTE (VaR estimator) and is hasused two extensi terms.vely The in the first[ financial termn is thema1 nagement“obvious”[{] kn i| 1 ofn } trading risk[{] overn | aRaVETCEVARRaVETCVAREETCVAR fixedn ]}. (usually short) time horizon. from the model and then sort the sampleThefrom in standard descending the model approach order and to then to obtain this sort problem the theorder sample is n statistics ˆtocan star beint withseen bya Theability randomxconditioning The notation density sampleVaR on and the X x 1 observationCTEVaRf x 2 ,...,, )( estimatorsrefersx inn order ofof sizethe to to theestimated applyaren probabilitypositively the V a ˆR . We correlated. density can then f write XThisx )( ofmakes the randomintuitive variablesense. X at the management of tradingextension risk over of froma whatfixed the was(usually model happening short)and time in then the horizon. first sort ( theD sample0 ) case. in The k descendingETC norigin D of¦ the orderx isecond)( , to obtainterm the order statistics V a ˆ R n D x k )( . by x looking ( 1 ) t x ( 2 ) t ... att x then)( . observedWe can then calculateempiricaldescending the plug-in distribution. order estimators to obtain for Let the the requiredD order 1 param statistics etersso that k i 1practicalasymptotic expressions formula. This forcan be very difficult the plug-inThe standard estimators approach x ( 1 ) are t x ( 2 to) from t this...x t theproblemx The n model)( . VaR We isand andtocan thenstar CTEthent sortwith estimatorscalculate the a random sample the are plug-in in samplepositively descending estimators x pointcorrelated. x order,...,, x x for= to VaR. obtaintheThisof sizerequired makes the n order intuitiveparam statisticseters sense. can be seen by conditioning on the observationIntuitively, of the weestimated can sayn that V a ˆR when. We we can 1 estimate ˆ2 then write then CTE weˆ are estimating both theˆ CTE t In terms t oft this notationk statistical V theory a ˆ R D hasThe x the standard. following[x n approach three things[{] to this nto| say ˆproblemn } is to[{] starn |t withˆRaVETCEVARRaVETCVAREETCVAR n ]}. a random sample x 1 x 2 ,...,, x n of size n The standard approach to this problem is to star x ( 1 ) t with x ( 2 ) a ...randomx k n)( . andsample We We 1the can can VaR then x then 1 and x 2 calculate ,...,, calculate uncertaintyx n n of the size inplug-in thenk )( VaRin kestimators practice, estimateThe variance for increasesespecially the requiredof the the in uncertainty CTEthe param tails estimatoreters of the CTE dishas- two terms. The first term is the “obvious” by looking atfrom the observed the model embypirical andlooking distribution. then at sortthe Let observed the D sample1ÊTC em D so inpirical that descending practical distribution.x expressions, order Let tofor D obtain 1 the so order that practical statistics expressions for fromthe the plug-in model and estimators then sort theare sample ˆ plug-inIn in terms descendingx The estimatorsof this ˆvariance notation ordernn for estimate. toofthe statistical obtainthe required¦ CTE This i the)( theory estimatoris parametersorder theˆ hasorigin statistics the has fromof following thetwo second the terms.Severaltribution. model three extensionkterm. The commentsthings and first of thento term saywhat are sort is wasin the theorder happening“obvious” sample in in descendingthe first (D order0 ) case. to obtain The origin the order of the statisticssecond term x t x t ... t x [ . n We can then[{] calculaten | ˆ n thek plug-ini 1 [{]} estimatorsn |Intuitively,ˆRaVETCEVARRaVETCVAREETCVAR nfor]}. the Dwe nrequiredcan say that param when eterswe estimate the CTE we are estimating both the CTE x t x t ... t x ( 1 ) . We ( 2 ) can then calculaten)( by thelooking plug-in1. at If theestimators the observed sample for emsizek thepirical is required l arge distribution. enough, parameters Letand t a few1 t othercan sot be verythat seen practicaltechnical by conditioning expressions conditions onforhold, the then observation of the estimated V a ˆR . We can then write ( 1 ) the ( 2 ) plug-in estimatorsn)( are the plug-in byestimators lookingextension atare the observedof what1 wasempirical happening distribuand in the -the x ( VaR 1 ) first and x ( 2 ( ) Duncertaintyn ...0 ) x case.n in)( .the TheWe VaR canorigin estimate then of increases calculatethe second the the uncertaintyterm plug-in ofestimators the CTE for the required parameters k ˆ D V theETC a ˆ R n pair nDk ( C T ˆx E k,)( V . a ˆxR i)( ),has ank approximatek multivariate normal distribution. by looking at theby observed looking em atpirical the observed distribution.ˆ thet i oem nplug-in1. . pirical Let 1 If can theD estimators be distribution. sam 1 seen ple so byaresize thatthat conditioning is n ¦ Letpractical practical l arge Dn enough,1 expressions expressions on estimate.the1 soand thatobservation a forfew practicalThis • other The is the xofVaRvery expressionsorigin theCTE andtechnical estimated of is theCTE clearly second for conditioestimators V a easier ˆterm.R .ns We hold, toare workcan positivelythen then with write than VaR. If kwe were using VaR as a risk measure then Intuitively, we can sayETC n that D whenx wei)( , Simple estimate Example kthei CTE1 –ˆ Thewe areEuropean estimating Put both the CTE ¦ n ETC n D n ¦byx i )( lookingk, at the observed emˆpirical distribution.ˆ Let D 1 so thatˆ practical expressions for In terms of this notation statisticalk theorythei 1 pair has( C T ˆ E the, V following a ˆR ) has an three approximate things1 multivariateto say normalwe would distribution. have[ ton find a way[{] to estimaten | ˆ nthe probability[{]} densityn | ˆ RaVETCEVARRaVETCVAREETCVAR n ]}.VaRf )( in order to and the VaR and uncertaintyfor the in plug-in the VaR estimators estimate n are n increases theÊTC uncertaintyk D i 1 x ofcorrelated. ,the CTE This makes intuitive sense. n X the plug-in estimators are V a ˆ D xR . n ¦ i)( the plug-in estimators V are a ˆ R D x . Onen way to[ testkˆ)( the formulas pres[{] êntedk | aboveˆ is to pick an[{]} exampleˆ | thatˆRaVETCEVARRaVETCVAREETCVAR is]}. simple enough that we estimate. This is the originn of kthek)( second term. n V a ˆ R Simple D x Example.then iplug-in 1– The n European estimatorsapply Put the are asymptotic n n formula. This can be very difficult in practice, especially in the tails ˆ 1 can get closed formk expressionsn k for)( all the relevant risk measures. We can then perform ETC n D x i)( , 1 Intuitively,of the distribution. we can say that when we estimate2 k the CTE we are estimating both the CTE In terms of this notation statistical theory has the following¦ threeˆ thingsD to say V a ˆ R n D x k )( . In terms of1. thisIf the notation sampleIn termsstatistical size ofis thisl arge theory notationk enough,i 1 has simulationsstatistical ETC andthen afollowing few theoryon ¦the other xmodel hasi)( , three verythe to seefollowing technicalthings how well tothree • theconditio Thesay vari things varianceancens estimatorsto hold, say of the then perform. CTE estimator In the ˆformal has papertwo1 k One way to test the formulasand pres theented VaR above and1 is uncertainty to pick an example inETC nthe D that VaR is simpleestimatex i)( ,enough increases that we the uncertainty of the CTE ˆ V a ˆ R InD terms x Intuitively,of. thiswe notation chose we statisticalthe can example sayi 1 thattheory of whenan has “in-the-money” thewe following estimate European threethe CTE things Put we tooption aresay estim at theating D 0 both . 9 5 confidence the2 CTE ¦ Simplethe Example pair ( – The n , VETC European a ˆR nn ) has Putank )( approximate multivariatecan getnormal closed distribution.form expressionsterms. The for first all the term relevant is the risk “obvious” measures. exten We can-k ithen 1 perform and the V level. a ˆVaR R HereD and isuncertaintyx an. edited excerpt in the from VaR the estimate paper. xestimate. increasesThe VaR This the and uncertainty is CTE the origin estimators of of the the CTEare second positively term. correlated. This makes intuitive sense. In terms of1. thisIf thenotation sample statistical size is l arge theory 1.enough, Ifhas the andthe sam afollowing fewple other size threevery is n l technical argethings enough, to kconditio )( say simulationsandns hold, a few then onother the model verysion to technicalof see what how was well conditio happening the varinsance hold, in estimators the then firstˆ (perform.D = 0) In the formal paper If the sample size is l arge enough,estimate. and This a fewis the other origin very of the technicalsecond term. conditio ns hold, then V a R n 1 x k )( . 1. ˆ 1 we chose the example of an “in-the-money” European Put option at the D 0 . 9 5 confidence the pair ( C T n , VE a ˆR n ) has an approximatethe pair1. ( multivariateIf ˆthe ,sam VETC a ÂR plenormalEuropean) hassize distribution. an isput l approximate argeoption enough, gives the holder andmultivariate a the few right other to sellnormal very the underlying technical distribution. asset conditio on the maturityns hold, date then for the specified OneIn way terms to test of thisthe formulasnotation statisticalpresented abovetheory n is hasn to pickthe following an example three that things is simple to say enough x thatThe we variance of the CTE estimator has two terms. The first term is the “obvious” 1. If the cansamthe getple pair closedsize ( is formlˆ arge, expressionsenough,ˆRaVETC ) hasand for aan few all theapproximate the otherpair re levant(very C strikeˆ price.technical, VET risk a ˆmultivariateR measures.) has conditio an level.approximate Wens normal Here hold,can isthenIn thenmultivariatean termsdistribution. edited perform of excerpt this normal notation from distribution. the paper.statistical theory has the following three things to say nn n n Simple Example extension – The of what European was happening Put in the first (D 0 ) case. The origin of the second term ˆ 1 2 the pairsimulations ( C n , VET a ˆ R onn ) thehas model an approximate to see how multivariate well the vari normalance estimatorsdistribution. Aperform. European put In option the formal gives the paperholder the right to sell the underlying asset on the maturity date for the specified 1. If the sample sizeSimple is l arge Example enough, –and The a fewEuropean other1 very Put technical conditionscan hold, be seen then by conditioning on the observation3 of the estimated V a ˆR . We can then write we chose the example of an “in-the-money” European Put option strike at the price. D 0 . 1.9 5 confidenceIf the sam ple size is l arge enough, and a few other very technical conditions hold, then ˆ 2 One way to test the formulas presented2 above is to pick an example that is simple enough that we level. Herethe is an pair edited ( excerpt n , VETC a ˆR fromn ) has the an paper. approximate multivariate normal distribution. ˆ One way to test the formulas presented above is canto thepick get pair closedan example( form n , VETC that a expressionsˆR n )ishas simpleˆ an approximatefor enough all2 the that relevant ˆmultivariate we risk measures. normal 3 distribution. Weˆ can then perform w Page 38 2 [ n [{] n | ˆ n [{]} n | ˆRaVETCEVARRaVETCVAREETCVAR n ]}. 1 can get closed form expressions for all the relevantsimulations risk measures. on the modelWe can to then see2 howperform well the variance estimators perform. In the formal paper A European put option gives the holder the right to sell the underlying asset on the maturity date for the specified 1 strike price. simulations on the model to see how well the variweance chose estimators the example perform. of an In“in-the-money” the formal paper European Put option at the D 0 . 9 5 confidence Intuitively, we can say that when we estimate the CTE we are estimating both the CTE we chose the example of an “in-the-money” Europeanlevel. HerePut option is an 1edited at the2 excerpt D 0 . 9 from 5 confidence the paper. and the VaR and uncertainty in the VaR estimate increases the uncertainty of the CTE2 level. Here is an edited excerpt from the paper. 3 1 A Europeanestimate. put option Thisgives theis the holder origin the rightof the to sellsecond the underlying term. asset on the maturity date for the specified

1 strike price. A European put option gives the holder the right to sell the underlying asset on the maturity date for the specified strike price. Simple Example – The European Put 3 3 One way to test the formulas presented above is to pick an example that is simple enough that we can get closed form expressions for all the relevant risk measures. We can then perform simulations on the model to see how well the variance estimators perform. In the formal paper we chose the example of an “in-the-money” European Put option1 at the D 0 . 9 5 confidence level. Here is an edited excerpt from the paper.

1 A European put option gives the holder the right to sell the underlying asset on the maturity date for the specified strike price.

3 2. The estimator pair is asymptotically unbiased. For any finite sample size the CTE plug-in estimator is negatively biased i.e. [ ˆ ] CTEETCE , but the bias goes to 0 as n o f . Practical experience suggests the bias is usually much smaller than the sampling error.

3. The following approximate variance/covariance formulas are also asymptotically valid Now, the (really) good news. ˆ 2 ˆ ˆRaVFSE ˆ ,VaRCTEvoC ˆ ( | t VaRXXVAR ) ETC D( %)95( VaRCTE ) ETCFSE V ˆRa VaRf ˆ | To be more( specific,ETCVAR n ) assume the option matures, in T 10 years with a strike price of X 110 . 1. If the sample size being usedn ( 1 isD large) enough, then there are approximate formulas Closed Form 13.80 n/a 4.39 n/a 2.37 n/a The currentanalogous stock to those price ( 1 that DD is) applyS 100 for an and ordinary assumed mean. to followIt is therefore a lognormal possible returnto quantify process with ( ˆRaVVAR ) | To be, more specific, assume the option matures in T 10 years with a strike price of X 110 . P V n FirstVaRfn Trial)]([ 2 13.67 1.54 5.09 1.40 1.65 0.49% the%8 statistical and precision 5 %1 X The. That of current an is, estimated the stock stock priceCTE price. is S at To 100maturity be moreand assumed specific,is given toassu by: followme the a optionlognormal matures return in Tprocess 10 years with with a strike price of X 110 . ˆ D( VaRCTE ) 14.93 1.95The current3.33 stock price is3.07 S 100 and assumed4.91 to follow 0.22%a lognormal return process with ( n , ˆRaVETCCoV n ) | Last PTrial 8 % . and V 1 5 % . That is, the stock price at maturity is given by: VaRnf )( 2. There is a practical Xpˆrocess, called a “varianceˆ verification”ˆ P 8 % and exer Vcise 1ˆ 5 in% this. 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These S techniques T S e will be Using a continuousMinimum discount7.72 rateMinimum of1.01 GX %6 ,7.72 the0 random0.191.01 variable whose0 0.22 CTE0.19 we wish0.09% to 0.22 0.09% apply the asymptoticthe topic formula. of a secondThis canUsing bearticle very difficult aon continuous CTE in practice,variance. discountespeciallyUsing in ratethe tails a of continuous G 6 % , discount the random rate ofvariable G 6 % whose, the randomCTE we variable wish to whose CTE we wish to of thecalculate distribution. is thenS omethe present key1 3.70takeaways value payoff from1.63 thisfunction table13.704.5 :are:0 1.911.63 4.50 2.42 1.91 0.40% 2.42 0.40% Average calculate is thenwhereAverage theZ ispresent a standard valuecalculate Normal payoff variateis then function with the presentmean: zero value and unitpayoff variance. function : x TheSoVaR what and CTE are estimators theMaximum approxim are positivelyate18.89 formulas? correlated. MThis aximum First, makes2.27 weintuitive need18.89 sense.9.17 some notation.7.312.27 Suppose 9.17 we 13.05 want to 7.31 3.65% 13.05 3.65% estimate thecase. Cond Theitional originAny Tail of given theExp secondectation trial providesUsingterm of Ga Tcan arandom continuous abe reasonable variableUsing discount spreadsheet estimateX, ratewith VP of cumulative ZTT ofG software, what 6 % , would the distrwe random canibution happen generate variable if the whose simulation CTE we wishwere to x eC >@,0max SX e G T VP ZTT G T VP ZTT The variance of Stdseenthe CTEDeviation by estimator conditioning has two1.63 terms.on the Std The observation Deviationfirstcalculate term0.18 is is the thenof “obvious” the1.63n1.76 present = C 1000 e value samples payoff0.770.18 >@ offunction,0max X this S variable.:1.76 e C 1.06 e From 0.77 this >@0.19%,0max X S e 1.06 0.19% extensionPr^` X of d what x was F x happening)( at therepeated, inlevel the first D ( DThus,but 0 )with case. we wantThea sample origin to calculate of sizethe second of the nterm conditional 1000 there expectation is considerable variability, especially for can be seen by conditioningthe estimated on the observation aV ˆR . We can of the then estimated write V a ˆR . We cansample, then write we can calculate the plug-in estima- G T VP ZTT Using S spreadsheetome key takeaways softwaUsing re,from spreadsheetS ome wethis cankeytable takeaways generate softwaare: re, torsUsing nfrom we for1000 can spreadsheetthisthe C generateCTEtable samples e andare: softwa VaR n of>@ ,0max X 1000re, thisusing S we variable.e samplesthe can formulas generate of From this n variable. this1000 samples From of this this variable. From this ˆ ˆ ˆ ( D ) ˆ >ˆ | ! qXXECTE D @ [ n [{] n | n } [{] n | RaVETCEVARRaVETCVAREETCVAR n ]}. sample, we can calculateThesample,CTE plug-in the we plug-in can estimator calculate estimators is biased thedevelopedsample, plug-in for below wethe earlier. estimatorscantheCTE true calculateTo and estimateclosed forVaR the theform the plug-in using CTEprobability value and theestimators of VaR formulas13.80 using for(i.e., the average the CTE formulas and VaR using the formulas ˆ developed earlier. To estimate the probability density VaRf )( use the estimator: Intuitively,developed we canIntuitively, sayAny earlier. that givenwhen we we canTo trial estimateETC developed sayestimate is provides that13.70). the CTEwhen theearlier. Any weHoweveraUsing we reasonableprobabilityare estimategiven estim spreadsheet Toating the estimatetrial bothbiasestimate density providesdensity softwathe is CTEthe muchre, ofprobability a wewhatVaRf smallerreasonable can )( would use generateuse densitythan the the happenestimateestimator: the nestimator: sampling1000VaRf if of the samples)( what use simulation error. thewould of thisestimator: variable. happenwere if From the thissimulation were where qD is the D-quantile, defined as the smallest value satisfying and the VaR andthe uncertainty repeated,CTE we in arethe but VaRestimating with estimate a increasessamplebothrepeated, sample,the the sizeCTE uncertainty we of andbut cann withof calculate 1000the CTEa sample there the plug-inis size considerable of estimators n 1000 forva riability,there the CTE is considerable andespecially VaR using for va theriability, formulas especially for estimate. This is the origin of theThe second asymptotic term. variancedeveloped earlier.formula To for estimate the CTE the probability estimator density performs VaRf quite)( use thewell estimator: on [average (i.e., the VaR aV ˆR . and uncertainty in the VaR aV ˆR . estimate [ ˆ VaRf )( Prˆ^ X ! q D ` 1D [ˆ ˆ 1 1 average ˆ ETCFSE empirical standardVaRf deviation)( of ETC ). ˆ )( FF ˆ [DD )( increases the uncertainty of the CTEVaRf estimate.)( 1 1 ˆ 1 ˆ 1[ n n Simple Example – The European Put ˆ ˆ ˆ n )( FF n [DD )( )( FF VaRf [DD )( )( 1 1 ThisThe is theCTE origin plug-in of the secondestimator term.The isCTE biased plug-in nbelow estimator the ntrue isclosed biased formˆ below value)( FF theˆ of true 13.80 [DD )( closed (i.e., form average value of 13.80 (i.e., average The D-quantile is often caThelledVaR Value-at-Risk plug-in estimator (VaR) and is biasedis used highextensi (averagevely in the isn 4.50),financial butn again the bias is much smaller One way to test the formulas presÊTC ented is 13.70).above is to However pick an example theÊTC thatbias is is 13.70). simpleis much enough Howeverwith smaller that [ we 1thethan bias .the issampling much smaller error. than the sampling error. can get closedmanagement form expressions of trading for all the riskthan relevant overwith the risk samplinga[ fixed measures. 1 (usually error. .We can short) then perform time horizon.100 simulations onwith the model [Simple to1 see how Example. well the vari—ance estimators100with perform. [ 1 In the. formal paper we chose the example of anThe “in-the-money”100 asymptotic European variance Put optionThe formula1 at asymptotic the D for100 0 . 9the 5 confidence varianceCTE estimator formula performs for the CTEquite estimator well on average performs (i.e., quite well on average (i.e., The standardThe approachEuropean to this Put problem is to start with a randomWe can samplethen calculate x x ,...,, thex Formula of size Standard n level. Here is an edited excerpt from theThe paper. sam ˆ ple covariance for all 1000ˆWe can pairs then of calculate estimˆ 1 ators2 the Formulaisn 2.37, Standardwhich îs Error higher (FSE (lower)) of each than estim ator as average ETCFSE empiricalaverage standard deviationErrorETCFSE empirical(FSE) of of each standardETC ).estimator deviation as of ETC ). 1 from the model and thenthe sortestimatedWe can the then sample covariance Wecalculate can in descendingthen fromthe calculate Formula the orderthe first Formula Standard to(last) obtain Standard trials, Error the Error bu(orderFSEt (closeFSE) of statistics) eachofto each the estim estim meanatorator of as all covariance A European putWe option can givesOne then the way holder calculateto the test right theto sell theformulas the underlying Formula presented asset onStandard the maturity above date Error for the (specifiedFSE) of each estimator as strike price. x t x t ... t x . We can then calculate the plug-in estimators for the required parameters ˆ 2 ( 1 ) ( 2 is) to pickThe anVaRn)( example estimators.plug-in that estimator is simple The enoughis VaRbiased thatplug-in high (averageestimator is is 4.50), biased but high again (average the bias is 4.50),is much ( but 1 ) smaller againXXVAR ( k ) theD bias(),...,( is muchXETC k )( ) smaller D ˆ 2 3 ( 1 XXVAR CTEFSE () k ) )( (),...,( ˆ XETC k )( ) 2 , we canthan get the closed sampling form expressions error. than for the all sampling the error.k CTEFSE )( ( 1 ) XXVAR ( k ) D (),...,( XETC k )( ) , n ( 1 D) by looking at the observed empirical distribution. Let D CTEFSE 1 )( so that practical expressionsn2 ( 1 D for) , relevant risk measures. We can then perform XXVAR n D (),...,( ˆ XETC ) A number of more realistic examples ( 1 ) are ( kdoc) umented in then kpaper)( ( 1 D ) using1 the same 1 methodology DD The sample covarianceCTEFSE forThe)( all sam 1000ple pairscovariance of estim forators all 1000is 12.37, pairs which of 1VaRFSE estimDD is,)( higherators is(lower) 2.37, thanwhich , is higher (lower) than the plug-insimulations estimatorsas on aredescribed the model above. to see how In eachwell thecase the asymptoticn ( VaRFSE )( D theory)1 worked as expected., ˆ The examples were k 1 ˆ 1 DD VaRf )( n variancethe estimatedestimators covarianceperform. Inthe from the estimated formalthe1 first covariance (last) trials, from bu t thecloseVaRf first)( to (last)then mean trials, of bu allt closecovariance to the mean of all covariance chosen to test a wideÊTC range D of possiblex ,VaRFSE beha)( viours and practical pr, oblems facing insurers. n 1 ¦ i)( 1 DD ˆ VaRf D)( ( ˆ nXETC ) D ( ˆ XETC ) paperestimators. we chose the exampleVaRFSE ofestimators.)( an “in-the-k i 1 ˆ VaRCTEvoC , ),( ˆ k )( VaRCTEvoC . ),( k )( . ˆ money” European Put option1 at V a ˆthe R D ˆ = VaRf 0.95x )( . n D ( ˆ n XETC f ( V a ˆR ) ) n f ˆ( V a ˆR ) n ˆ k )( VaRCTEvoC ),( k )( . confidenceA number level. of more Here isrealistic an editedA number examples excerpt of from moreareˆ doc realisticumented examples in theˆ paper are doc usingumented the same in the methodology paper using the same methodology In terms of this notation statistical theory has Dthe (following XETC Table threek )( ) 1 things shows n tothef say( results V a ˆ R ) of two trials (first and theas paper.described above.ˆ In eachVaRCTEvoC as described case),( Table the 1 shows asymptoticabove. the resultsTableIn each theory .of1 showstwocase workedtrials the the (first asymptoticresults as and expected. oflast) two andtheory trials also The workedthe(first examples results and as oflast) expected. repeatingwere and also the The theentire resultsexamples of repeating were the entire simulation 1000ˆ times.last) and The also table the also results shows of therepeating exact values the entire of the CTE and VaR for this chosen toA test More a wide Practical rangechosen of Example possible to test – abehafn Variancewide( V a ˆvioursR sim range) ulation Verificationand of practicalpossible 1000 times. behaproblems viours The tablefacing and also practical insurers. shows pr theoblems exact facing values insurers. of the CTE and VaR for this 1. If the sample size isTable l arge enough,1 showsproblem, andthe aresults whichfew other canofsimulation betwo very calculated trials technical 1000 (first from times. andclosedconditio last)The formns table and expressionshold, alsoalso then shows the that results the are given of inrepeating the paper. the entire To be moreˆ specific, assume the option matures problem, which can be calculated from closed form expressions that are given in the paper. the pair ( n , VETC a ˆR n ) has an approximate multivariateexact normal values ofdistribution. the CTE and VaR for this prob- in T = 10 yearsSuppose withsim ayou strikeulation have price a 1000 modelof X times. = that110. takes The all table night also to showsrun n = the 1,000 exact scenarios. values ofIt would the CTE be andimpractical VaR for this To be more specific, assumeTable the 1option shows maturestothe repeat resultsproblem, the in of runT two processwhich10 trialsTable years can hundreds 1:(first Montebe with calculated and Carlo of lem, alast) timstrike Simulati which efrom andin orderprice canclosedonalso without be to the ofcalculated formtest X resultsVariance the expressions 110 valid from of Reduction. ity repeatingclosed of that the form are variance the given entire in formulas the paper. as The current stock price is S = 100CTE(95%) and as for- a 10-year European Put Option (1000 Trials), X=$110, S=$100 sim ulationTo be more 1000 specific,described times. assu above. me The the tableoption matures also shows in T 10expressionsTable the years exact 1: with Monte that valuesa strike are Carlo givenprice of Simulati the ofin Xthe CTE paper.110on . andwithout VaR Variance for this Reduction The currentTo stock be more price specific, is S assu100mesumed the and tooption follow assumed matures a log normal to in followT return 10 process yearsa lognormal with with a strikeCTE(95%) return price ofprocess forX a110 10-year with. European Put Option (1000 Trials), X=$110, S=$100 problem,The current which stock can price be calculated is S 100 and from assumed closed to follow form a expressionslognormal return that process are withgiven in the2 paper. P %8 andThe V current 5 %1 stock. That price isis, P S Athe More 8 100% stock and and Practical V assumed price 1 5 % Table . atExampleThatThat to maturity followis,1:A theMonte More –stock a Variance lognormal is Practical Carlo priceprice given at at Simulati maturity Verification return by: Example isprocesson given without – by:Variance with Variance Verification Reduction To be more Aspecific, more assu practicalme the option process matures for in confirming T 10 years withthe asymptotica strike price of varianceX 110 . formula, which we call Table 1: 4 P 8 % and V 1 5 % . ThatmaturityThe is, current the is givenstockVariancestock price by:priceCTE(95%) isVerification, atS maturity100 and for assumed is is agiven as10-year follows:to followby: Europe a lognormalan Put return Option process with(1000 Trials), X=$110, S=$100 Suppose you have a modelSuppose that takes you allhave night> VP a modelMonte ZTT to@ run thatC narlo= takes1,000 Simulation all scenarios. night without to Itrun would Variancen = 1,000 be impractical Reduction scenarios. C TE(95%)It would for be aimpractical 10-year Table P1: Monte 8 % and V Carlo 1 5 % . Simulati That is, the onstock S without price T at S maturitye Variance is given Reduction by: 4 to repeat the run process > tohundredsVP repeat TT Z @ the of timrune process in orderEuropean hundreds to test Put the Oofption valid time (1000ity in oforder theTrials), tovariance test X=$110, the formulas valid S=$100ity ofas the variance formulas as CTE(95%) for S a 10-year ST e Europe> VP ZTT an@ Put Option (1000 Trials), X=$110, S=$100 S T S e > VP ZTT @ described above. described S T above. S e 5 wherewhereZ Z is is a a standard standard No Normalrmal variate variate with with mean mean zero and unit variance. 4 zero and unit variance. ÊTC %)95( ÊTCFSE V a ˆR ˆRaVFSE ˆ ,VaRCTEvoC ˆ VaRf where Z is wherea standardZ is a standard Normal No variatermalAwhere more variateZ withis practicala standardwith mean mean Noprocess rmalzero zero variateA forand more confirmingwith unit unit practicalmean variance. variance. zero the andprocess asymptoticunit variance. for confirming variance formula,the asymptotic which variancewe call formula, which we call Using a continuous discount rate of G 6 % , the randomClosed variable Form whose13.80 CTE we n/a wish to 4.39 n/a 2.37 n/a calculateVariance is then Verification, the present valueis Varianceas payofffollows: function Verification, : is as follows: 4 Using a continuous discount rate of G the First Trial 13.67 1.54 5.09 1.40 1.65 0.49% Using a continuous discountUsing rate a continuous of G 6 discount% , the rate random of 6 variable% , the random whose variable CTE whose we wish CTE towe wish to randomcalculate variable is then the whose present CTE value we payoff wish function to calcu: - Last Trial 14.93 1.95 3.33 3.07 4.91 0.22% Using a continuous discount rate of G %6 , the random G T variable whose VP ZTT CTE we wish to calculate is then the present value payoff function: C e ,0max X S e 5 5 late is then the present value payoff function:>@Minimum 7.72 1.01 0 0.19 0.22 0.09% calculate is then the present value payoff function: G T VP ZTT C e >@,0max X S e Average 13.70 1.63 4.50 1.91 2.42 0.40% Using spreadsheet G T software, we can generateVP ZTT n 1000 samples of this variable. From this C e >@,0max X S e Maximum 18.89 2.27 9.17 7.31 13.05 3.65% sample, we can calculate the plug-in estimators for the CTE and VaR using the formulas Using spreadsheetG T software, we can generateVP TT Z n 1000 samplesStd Deviation of this variable.1.63 From 0.18 this 1.76 0.77 1.06 0.19% developedsample, eC we earlier. can calculate To> estimate,0max the plug-in SX the probabilitye estimators density @ for the VaRf CTE)( and use VaRthe estimator: using the formulas Using spreadsheet software, we can generate n 1000 samples of this variable. From this developed earlier. To estimate the probability density VaRf Some)( use key the takeaways estimator: from this table are: [ sample, we can calculate the plug-in estimators forˆ VaRf the )( CTE and VaR using the formulas ˆ 1 [ ˆ 1 continued on page 40 Using spreadsheetdeveloped earlier. softwa re,To estimate we can the probability generate densityn 1000ˆ VaRf VaRf )( samples)( nuse the)( FF estimator: ofn this Any[DD )( given variable. trial provides From a reasonable this estimate of what would happen if the simulation were ˆ 1 ˆ 1 [DD 1 n )( FF n )( sample, we can calculate the A plug-in European put estimators option gives the holder for the the right toCTE sell the underlying and VaR repeated,asset on using the but maturity with the a date sample formulasfor the size specified of n strike1000 price. there is considerable variability, especially for with [ 1 . [ V a ˆR . developed earlier. To estimate thewith [probability ˆ 1100VaRf .)( density VaRf )( use the estimator: 100 ˆ 1 ˆ 1 The CTE plug-in estimator is biased below the true closed form value of 13.80 (i.e., average n )( FF n [DD )( ˆ We can then calculate the Formula Standard Error (FSE) of eachETC estim is 13.70).ator asHowever the bias is much smaller than the sampling error. We can then calculate the Formula[ Standard Error (FSE) of each estimator as [ 1 ˆ The asymptotic variance formula for the CTE estimator performs quite well on average (i.e., with . VaRf )( 2 Page 39 w 100 1 1 D ˆ 2 ˆ ˆ ˆ ˆ ( 1 XXVAR XXVAR k )() D (),...,( averageˆ(),...,( XETC XETC ) k )( ) ETCFSE empirical standard deviation of ETC ). n )( CTEFSE FF )( n DD [ ( 1 )( () k ) k )( , CTEFSE )( n ( 1 D) , n ( 1 D) We can then calculate the Formula Standard Error (FSE) of each estimator as The VaR plug-in estimator is biased high (average is 4.50), but again the bias is much smaller 1 1 1 1DD DD than the sampling error. VaRFSE VaRFSE )( )( , , with [ 1 . ˆ ˆVaRf VaRf )( )( n n 2 The sample covariance for all 1000 pairs of estimators is 2.37, which is higher (lower) than 100 XXVAR D ˆ(),...,( ˆ ˆ XETC ) ( 1 ) ( k ) DD ( ( XETC XETC k )( )k )( ) k )( the estimated covariance from the first (last) trials, but close to the mean of all covariance CTEFSE )( ˆ VaRCTEvoC VaRCTEvoC ),( ),( . . , n ( 1 n D n ) f ˆ ( f V ˆ( a ˆ V R a ˆ)R ) estimators. We can then calculate the Formula Standard Error (FSE) of each estimator as 1 1 DD A number of more realistic examples are documented in the paper using the same methodology TableTableVaRFSE 1 1 shows shows)( thethe results ofof twotwo trials trials ,(first (first and and last) last) and and also also the theresults results of repeating of repeating the entire the entire ˆ VaRf )( n as described above. In each case the asymptotic theory worked as expected. The examples were simsimulationulation 1000 1000 times. The The table table also also shows shows the the exact exact values values of the of theCTE CTE and andVaR VaR for this for this problem, which can be calculated from closed form expressionschosen that to 2are test given a wide in therange paper. of possible behaviours and practical problems facing insurers. problem, whichD can( beˆ calculated XETC XXVAR ) from closedD (),...,( form C T ˆ expressions XE ) that are given in the paper. ˆ VaRCTEvoC ),( ( 1 k )( . () k ) k )( CTEFSE )( ˆ , Table 1: Monte n Carlo f ( V Simulati a ˆR ) onn without ( D Variance)1 Reduction TableCTE(95%) 1: Monte for aCarlo 10-year Simulati Europeonan without Put Option Variance (1000 Trials), Reduction X=$110, S=$100 CTE(95%) for a 10-year European Put Option (1000 Trials), X=$110, S=$100 1 1 DD A More Practical Example – Variance Verification Table 1 shows the resultsVaRFSE of )( two trials (first and last) and also, the results of repeating the entire simulation 1000 times. The tableˆ VaRf also shows)( the n exact values of the CTESuppose and you VaR have fora model this that takes4 all night to run n = 1,000 scenarios. It would be impractical problem, which can be calculated from closed form expressions that are givento repeat in the the paper. run process hundreds of time 4in order to test the validity of the variance formulas as D ( C T ˆ XE ) described above. ˆ VaRCTEvoC ),( k )( . ˆ A more practical process for confirming the asymptotic variance formula, which we call Table 1: Monte Carlo Simulation without ( Vfn Variance a ˆR ) Reduction Variance Verification, is as follows: CTE(95%) for a 10-year European Put Option (1000 Trials), X=$110, S=$100

5 Table 1 shows the results of two trials (first and last) and also the results of repeating the entire simulation 1000 times. The table also shows the exact values of the CTE and VaR4 for this problem, which can be calculated from closed form expressions that are given in the paper.

Table 1: Monte Carlo Simulation without Variance Reduction CTE(95%) for a 10-year European Put Option (1000 Trials), X=$110, S=$100

4 ˆ ˆ ˆ ÊTC %)95( ETC ÊTCFSE %)95( V ˆRa ETCFSE V ˆˆRaVFSE Ra ˆ ˆ,RaVFSE VaRCTEvoC ˆ ˆ VaRf ,VaRCTEvoC VaRf ÊTC %)95( ÊTCFSE V a ˆR ˆRaVFSE ˆ ,VaRCTEvoC ˆ VaRf ˆ ˆ ˆRaVFSE ˆ ,VaRCTEvoC ˆ Closed Form ETC Closed13.80%)95( Form ETCFSE 13.80n/a V ˆRa 4.39 n/a n/a4.39 n/a2.37 VaRf 2.37n/a n/a Risk ManagementClosed wForm August 2008 13.80 n/a 4.39 n/a 2.37 n/a Closed FirstForm Trial 13.8013.67First Trial n/a113.67.54 4.395.091.54 n/a1.405.09 2.371.401.65 n/a0.49%1.65 0.49% First Trial 13.67 1Chairman’s.54Variance5.09 of Corner the CTE1.40 Estimator1.65 0.49% FirstLast Trial Trial 13.6714.93Last Trial 1.541.9514.93 5.093.331.95 1.403.073.33 1.653.074.91 0.49%0.22%4.91 0.22% Last Trial 14.93 1.95 3.33 3.07 4.91 0.22% Last Trial 14.93MinimumÊTC 1.95%)95( 7.72 3.33ÊTCFSE 1.01 V 3.07ˆRa 0 ˆRaVFSE 4.91 0.19 ˆ 0.22%,VaRCTEvoC 0.22 ˆ VaRf 0.09% Minimum 7.72 CTE1.01 EstimatorMinimum 0… 7.720.19 1.01 0.22 0 0.09%0.19 0.22 0.09% ˆ ˆ ˆ ETC %)95( ETCFSE V ˆRa w continuedAverage ˆfrom RaVFSE page13.70ˆ 39 ,VaRCTEvoC 1.63 VaRf 4.50 1.91 2.42 0.40% Average 13.70 Minimum1.63 AverageClosed4.5 Form07.721 3.701.9113.801.011.63 2.42n/a04.50 4.390.40%0.191.91 n/a 0.222.42 2.370.09%0.40% n/a Maximum 18.89 2.27 9.17 7.31 13.05 3.65% Closed MFormaximum 13.8018.89 n/a2.27AverageMaximum 4.39First9.171 Trial3.7018.89 7.31n/a13.671.632.27 13.052.371.544.509.17 5.093.65%1.91n/a7.31 1.40 2.4213.05 1.650.40%3.65% 0.49% Std Deviation 1.63 0.18 1.76 0.77 1.06 0.19% FirstStd Deviation Trial 13.671.63 1Some.54MStd0.18aximum keyDeviation takeaways5.09Last1.76 18.89 Trial from 1.63 this1.400.77 table14.932.27 are:0.18 1.651.061.959.17A1.76 more 3.33practical0.19%0.49%7.310.77 process3.07 for13.05 confirming1.06 4.91 the3.65% 0.19% 0.22% Last Trial 14.93 Std1.95 Deviation 3.33Minimum1.63 3.077.720.18 4.911.011.76asymptotic0.22%0.77 0variance formula,0.19 1.06 which we0.22 call0.19% 0.09% Some key takeaways from this •table SAnyome are:given key takeawaystrial Sprovidesome fromkey a takeaways reasonablethis table are:fromes- thisVariance table are: Verification, is as follows: Minimum 7.72 1.01 Average0 0.1913.70 0.221.63 4.50.09%0 1.91 2.42 0.40% Sometimate key takeawaysof what would from happen this table if the are: simu - Average 13.70 1.63 4.5Maximum0 1.9118.89 2.422.27 9.170.40% 7.31 13.05 3.65% Any given trial provides a reasonablelationAny were given estimate repeated, trial of Anyprovides what but given would with a trialreasonable a happen sample provides if estimatethe 1.a simulationAsreasonable part of ofwhat modelwere estimate would development, happenof what ifwouldor the in ansimulation happen off if werethe simulation were Maximum 18.89 2.27 Std9.17 Deviation 7.311.63 13.050.18 1.763.65% 0.77 1.06 0.19% repeated, but with a sample Anysize repeated, of given n 1000trial but provides therewithrepeated, isisa considerable sample considerablea reasonable but sizewith vari ofva aestimate -riability,samplen 1000peak ofsizeespecially therewhat time, of isnwouldgenerate considerablefor1000 happen (once) there a if islargerva theconsiderableriability, simulationsample especially of va wereriability, for especially for Std Deviation V a ˆR . 1.63 0.18ability, especially1.76 for aV ˆR 0.77. 1.06 say N = 5,0000.19% scenarios. Let CTE be the es- repeated, aV ˆR . but with a sample size of n 1000 there is considerable variability,N especially for • The CTESome plug-in key estimator takeaways is biasedfrom this below table are:timated CTE based on this large sample and The CTE plug-in estimator is aV biasedˆR . below the trueThe closedCTE plug-inform value estimator of 13.80 is (i.e.,biased average below the true closed form value of 13.80 (i.e., average Some key takeaways from this tablethe are: trueThe closedCTE plug-inform value estimator of 13.80 (i.e.,is biased aver- belowFSE the truethe formula closed standardform value error of for 13.80 a given (i.e., average ÊTC is 13.70). However the bias is much smaller thanˆ the sampling error. N Theage CTEÊTC isisplug-inAny 13.70). 13.70). given estimatorHowever However trialETC is theprovides 13.70).is biasthe biased biasis muchHowever a belowisreasonable much the the smallerconfidence true bias estimate closed is than much level of theform whatαsmaller sampling. value would than of error. happen 13.80the sampling (i.e., if the average simulationerror. were smallerˆ than the sampling error. 2. From the large sample of size N, draw m=100 Any The given asymptotic trial provides variance a reasonableformulaETC for is estimate13.70).therepeated, CTE However ofestimator The whatbut asymptoticwith wouldthe performs biasa sample happen is variance quitemuch size if well smallerthe offormula on simulationn average than1000 for the the there(i.e.,were sampling CTE is considerableestimator error. performs variability, quite especially well on average for (i.e., • The Theasymptotic asymptotic variance variance formula formula for the CTE for the CTErandom estimator sub-samples performs of size quite n=1,000 well without on average (i.e., repeated,average but with aÊTCFSE sample empirical size ofstandard n 1000 deviation aV ˆR .there ofis considerableÊTC ). ˆ variability, especially for ˆ Theaverage asymptotic variance averageÊTCFSE formulaempirical for standardETCFSE the empiricalCTE deviation estimator standard of performs ˆdeviationETC ). quite of wellETC on). average (i.e., aV ˆR . estimator performs quite well on average (i.e., replacement. The VaR plug-in estimator isaverageaverage biased highThe (average1. CTEÂsETCFSE part plug-inisempirical 4.50), of model estimator but standard standard againdevelopmen isthe deviationbiased bias3.t, orForis below muchin each ofan off smaller theofˆ ETC peakthe true). m tim closedsub-samplese, genera formte valuecalculate(once) of a larger13.80a sample (i.e., average of The VaR plug-in The estimatorVaR plug-in is biased estimator high (average is biased is high 4.50), (average but again is 4.50), the bias but is again much the smaller bias is much smaller ThethanCTE the plug-in sampling estimator error. is biaseddeviation below of theÊTC ).sayistrue 13.70).N closed= 5,000 However form scenarios. value the biasofLet 13.80 CTEis CTEmuchN (i.e., beestimate smallerthe average estimated and than an theCTE FSE sampling based estimate. on error. this Also large sample and ThethanVaR the plug-in sampling estimatorthan error. the is sampling biased high error. (average is 4.50), but again the biasD is much smaller ÊTC is 13.70). However the bias• The is VaR much plug-in smaller FSEestimator thanN the the formula is sampling biased standard high error. error check for a givento see confidencewhether our level best answer. CTEN The sample covariance for allthan(average 1000 the pairs issampling 4.50),The of asymptotic estimbut error. againators the isvariance 2.37,bias is which much formula is higher forlies the (lower) in CTE the thanestimatorapproximate performs 95% confidence quite well on average (i.e., The sample covarianceThe sam forple allcovariance 1000 pairs for of all estim 1000ators pairs is of 2.37, estim whichators isis higher2.37, which (lower) is thanhigher (lower) than Thethe asymptotic estimated variance covariance formula fromsmaller thefor firstthe than CTEaverage (last)the2. sampling estimator Fromtrials, the buerror. tlargeperforms ˆcloseETCFSE sample empiricalto thequite of mean sizewell standard N,of oninterval drawall average covariancedeviationm CTE=100 (i.e.,+ 2xrandom of FSE. ˆ IfETC sub-sample it). does wes setof sizethe n=1,000 Thethe sam estimatedple covariancewithout covariancethe estimated forreplacement. all from 1000 covariance the pairs first of (last) estimfrom trials,atorsthe first isbu 2.37, t(last) close which trials, to the is bu meanhighert close of (lower) toall the covariance thanmean of all covariance averageestimators. ÊTCFSE empirical• The standard sample deviation covariance of for allˆ 1000ETC ). pairs of es- CI (Confidence Interval) count to 1 and 0 the estimators.estimated The covariance VaRestimators. plug-in from estimator the first is biased(last) trials,high (average but close is to4.50), the meanbut again of all the covariance bias is much smaller timators is 2.37,3. whichFor each is higher of the (lower) m sub-s thanamples calculateotherwise. a CTE estimate and an FSE estimate. Also A number of more realistic examplesestimators. are doc umented in the paper using the same methodology The VaR plug-in estimator is biasedthe estimated high (averagethan covariance thecheck samplingis 4.50),to from see the butwhethererror. first again (last) our the best bias 4.answer Useis much the CTE standard smallerlies in deviation the approximate of the CTE 95% esti confidence- as described above. In each case the asymptotic Atheory number worked of more as expected. realistic The examples examples are Nwere documented in the paper using the same methodology than the sampling error. Atrials, number but close of more to intervalthe realisticmean CTE of allexamples r covariance2u FSE are. If doc it doesumentedmates we from set in theStep the CI 3paper (Confto check idenceusing the validity theInterval) same of the countmethodology to 1 and 0 The samas describedple covariance above. for In alleach 1000 case pairs the asymptoticof estimators theory is 2.37, worked which as isexpected. higher (lower) The examples than were chosen to test a wide range ofA possiblenumberasestimators. described behaof moreviours above. realisticotherwise. and Inpractical each examples case problems the are asymptotic doc facingumented insurers.asymptotic theory in the worked formula. paper as usingAs expected. we thewill samesee Theshortly methodology examples a were The sample covariance for all 1000 pairsthe of estimestimatedchosenators to covarianceistest 2.37, a wide which fromrange is thehigherof possiblefirst (lower) (last) beha trials, thanviours bu andt close practical to the pr meanoblems of facingall covariance insurers. as describedchosen to above. test a wide In each range case of thepossible asymptotic behaviours theorysimple and worked adjustment practical as expected. needsproblems to be facingThe made examples toinsurers. this were estimators.4. Use the standard deviation of the CTE estimates from Step 3 to check the validity of the the estimated covariance fromchosenA numberthe to first test of (last)morea wide realistictrials, range bu examples oft closepossible areto docubehathe mean-viours of numberand all practicalcovariance before prcomparingoblems facing it to the insurers. formula asymptotic formula. As we will see shortly a simple adjustment needs to be made to this estimators. mented in the paper using the same method- estimates. A numbernumber of more before realistic comparing examples it to arethe formuladocumented estimates. in the paper using the same methodology A More Practical Example – ologyVariance as described Verification above. In each case the A number of more realistic examplesasymptotic areas doc theorydescribedumented worked above. in asthe expected. paperIn each using case The the the same Theasymptotic table methodology below theory shows worked the results as expected. of applying The examples were A More PracticalThe tabAle More Examplebelow Practical shows – Variance the Example results Verification of applying– Variance the aboveVerification process to an inforce portfolio of U.S. as describedSuppose youabove. have In a modeleach case that examples thetakes asymptotic allchosen nightwerevariable chosento theoryto run test annuities nto a= workedtest wide1,000 a with widerange scenarios.as GMDB, expected.range of possible ofIt GMAB would Thethe beha andbeaboveexamples impracticalviours GMWB process andwere featur to practical anes. inforce The pr portfolio oblemsbook is of slightlyfacing U.S. insurers. out of the A More Practical Example – Variance Verification chosento repeat to test the a widerun process range ofhundreds possiblepossible of behatim behaviourse vioursinmoney. order Sand uppose to5000and testpractical practicalreal theyou worldvalid havepr oblemsproblemsity (P a ofmeasure)model the facing variance that variablescenarios insurers. takes formulas annuitiesall we nightre asgenerated towith run GMDB, n and= 1,000 for GMAB each scenarios. scenario and Itthe would presen bet impractical described above. Suppose you have a model that takes all night to run n = 1,000 scenarios. It would be impractical facing insurers.value ofto guaranteerepeat the benefits run process (claims) hundreds lessGMWB the of presentfeatures. time in value The order bookof torelated istest slightly the fees valid outwas of itycaptured. the of the variance formulas as Supposeto repeat you thehave run a modelprocess that hundreds takes all of night time into orderrun n to= 1,000test the scenarios. validity ofIt wouldthe variance be impractical formulas as described above. A more practical process forto confirming repeatdescribed the the run Theabove. asymptotic process claims havehundreds variance been normalizedofformula, time in which orderso themoney. we to mean calltest 5000 CTEthe real valid(0) worldisity 1,000. of(P themeasure) The variance fees scenarios were formulas scaled so as t hat

Variance Verification, is as follows:describedA More above.A PracticalMoreCTE (75) Practical of Example—the net Example (PV claims – Variance – PV fees) Verification is zero. The example itself is for CTE(90). VarianceA more practical VerificationA processmore practical for confirming process thefor asymptoticconfirming variancethe asymptotic formula, variance which formula,we call which we call A More Practical Example – Variance Verification Variance Verification,Variance is Verification,as follows: Table is as 2: follows: Variance Verification A moreSuppose practical Syouuppose have process youa model have for that confirminga model that the takes asymptotic all night variance to run n5 formula,= 1,000 scenarios.which we Itcall would be impractical Variance Verification,to repeat the is run as processfollows: hundreds of time in order to test the validity of the variance formulas as Suppose you have a model that takestakes all all night night to runrun n = 1,000 scenarios. It wouldD be90% impractical N = 5,000 Samples 5 to repeat the run process hundredsscenarios. of timedescribed inIt wouldorder be to above. impracticaltest the valid ity of the CTEvarianceN = 2214 formulas as FSE N = 159 5 described above. to repeat the run process hundreds m = 100 Random Sub Samples of Size n = 1,000 5 of time in orderA more to test practical the validity process of for confirming the asymptotic variance formula, which we call Variance Verification, is as follows: A more practical process for confirmingthe variance the formulasasymptotic as described variance formula, which we call CTE FSE CI Count Variance Verification, is as follows: Mean 2,111 346 94% above. First 2,004 355 1 Last 2,242 353 1 5 Min 1,558 5 262 0 Max 3,120 376 0 Std Dev'n 316 30 2%

Adjusted Std Dev'n 354 =Std Dev'n/ (1-n/N)^1/2

The first thing we note is that if the FSE based on the sample of size 5,000 is correct then we expect an FSE of about | 3555159 when dealing with a sample size of 1,000. The FSE w Page 40 estimates are clearly consistent with this, but the standard deviation of 316 (of the 100 CTE estimates) is not. One possible explanation for this discrepancy is sampling error, but more testing shows this is not the case.

The standard deviation of the m=100 sub-samples is a biased estimate of the sampling error and it is not hard to understand why. The various sub-samples (each of size n=1,000) were all drawn

6 1. As part of model development, or in an off peak time, generate (once) a larger sample of say N = 5,000 scenarios. Let CTEN be the estimated CTE based on this large sample and FSEN the formula standard error for a given confidence level D.

2. From the large sample of size N, draw m=100 random sub-samples of size n=1,000 without replacement.

3. For each of the m sub-samples calculate a CTE estimate and an FSE estimate. Also check to see whether our best answer CTEN lies in the approximate 95% confidence interval CTE r 2u FSE . If it does we set the CI (Confidence Interval) count to 1 and 0 otherwise.

4. Use the standard deviation of the CTE estimates from Step 3 to check the validity of the asymptotic formula. As we will see shortly a simple adjustment needs to be made to this number before comparing it to the formula estimates.

The table below shows the results of applying the above process to an inforce portfolio of U.S. variable annuities with GMDB, GMAB and GMWB features. The book is slightly out of the August 2008 w Risk Management Chairman’sVariance of Corner the CTE Estimator money. 5000 real world (P measure) scenarios were generated and for each scenario the present value of guarantee benefits (claims) less the present value of related fees was captured.

The claims have been normalized so the mean CTE(0) is 1,000. The fees were scaled so that CTE(75) of the net (PV claims – PV fees) is zero. The example itself is for CTE(90).

Table 2: Variance Verification

were generated and for each scenarioD 90%the pres- OurN variance= 5,000 Samples verification test is therefore to CTE N = 2214 FSE N = 159 ent value of guarantee benefits (claims) less the compare the empirical error estimate 354 with m = 100 Random Sub Samples offrom Size then = same1,000 universe of N=5,000 so they are not independent. Because the various CTE present value of related fees was captured. theestimates mean formula are using estimate some 346. of the We same conclude data they are positively correlated and so the set of CTE thatestimates the FSE asymptotic CI isCount more theory tightly appears clustered to be workingthan if they were truly independent. This intuitive result is Mean 2,111 346 94% o The claims have been normalized so the mean for verythis model.easy to That understand is, the asymptotic as nN variance. First 2,004 from 355 the same 1 universe of N=5,000 so they are not independent. Because the various CTE CTE(0) is 1,000. The feesLast were scaled so 2,242that of the 353 CTE Estimator 1 agrees with “experiment,” 2 estimatesIt is possible are using to use some the of meth theods same in dataour paperthey are to positivelyshow that, correlated in the large and sample so the limit, set of the CTE(75) of the net (PV claimsMin – PV fees) is zero. 1,558 after 262 adjusting 0for the non-independence of the Max 3,120 estimates c orrelation 376 is more 0of two tightly sub-sample clustered estimates than if they is just were U truly n / N independent.. A better estimateThis intuitive for the result sampling is from the same universe of N=5,000 so they are not independent. Because the various CTE The example itself is for CTEStd Dev'n(90). 316 verysub-samples. easy 30 to understand 2% as nNo . 316 316 estimates are using some of errorthe same when data using they a sampleare positively size of correlated1,000 is therefore and so the not set 316, of but3 |354 . Adjustedestimates Std Dev'n is more tightly 354 =Std clustered Dev'n/ (1-n/N)^1/2 than if they were truly independent.2 This intuitive result is n 1000 The first thing we note is that if the FSE based ItThe is possibleCI Count to resultuse the is meth alsoods consistent in our paper with to show that, in the large11 sample limit, the o very easy to understand ascorrelation nN. of two sub-sample estimates is just U n / N . A better estimateN for the 5000sampling Theon first the thing sample we of note size is 5,000 that if is the correct FSE thenbased we on ex the- sampletheOur ideaof sizevariance that 5,000 the verificationis formula correct thenstandard test we is thereforeerrors are to compare the empirical error estimate 354 with the 2 316 316 expectpect an an FSE FSE of of about about It is| 3555159 possible whenwhen to dealingdealing use the with metherrorworking. a samplemeanods when in formulaThesize o urusing ofactualpaper 1,000. estimatea sample count to The show 346ofFSEsize 94that, . of isWe 1,000invery conclude the close islarge therefore thatsample th note limit,asymptotic 316, the but 3 theory appears to be working|354 . for estimates are clearly consistent with this, but the standard deviation of 316 (of theU 100 CTE n 1000 with a sample size of 1,000.correlation The FSE ofestimates two sub-sample to expectedthis estimates model. value Thatis ofjust 95 is, (i.e.,the n asymptotic a/ 95%N . confidenceA better variance estimate of the for CTE the Estimatorsampling11 agrees with “experiment”, estimates) is not. One possible explanation for this discrepancy is sampling error,from butthe samemore universe of N=5,000 so they are not independent. Because the various CTE are clearly consistent with this, but the standard interval).after adjusting for the non-independence3 316of the sub-samples. 316 N 5000 testing shows this is not the case.error when using a sampleOur size variance of 1,000 verification is thereforeestimates test arenot usingis 316, therefore some but of the to same compare data th eythe are empirical positively|354 correlated erro . r estimate and so the 354 set of with the deviation of 316 (of the 100 CTE estimates) is estimates is more tightly clustered thann if they were1000 truly independent. This intuitive result is meanThe formula CI Count estimate resultvery easyis346 also to . understand Weconsis concludetent as nN witho 11that .the th ideae asymptotic that the formtheoryula appears standard to errors be working are working. for from the same universeThe of not.N =5,000standard One so they possibledeviation are not indepe explanation of thendent. m =10 Because for0 sub-sam thisthe various discrepples CTE is- a biasedFinally, estimate it might of the samplingappear from error Tableand 2 that N 5000 estimates are using some of the same data they are positively correlated and so the set of thisT model.he actual That count is, ofthe 94 asymptotic is very close variance to expected of the valueCTE Estimator of 95 (i.e., agrees a 95% with confidence “experiment”, interval). it isancy not hard is sampling to understand error, why. but more The varioustesting showssub-samples there (each is of evidence size n=1,000) of material were all drawnsmall sample 2 estimates is more tightly clustered than if they were truly independent.Our variance This intuitive verification result is after test isadjusting therefore for to the compareIt is non-indepe possible the to use empiricalndence the meth odsof erro thein orur sub-samples.estimate paper to show354 that,with in the the large sample limit, the correlation of two sub-sample estimates is just U n / N . A better estimate for the sampling very easy to understand as thisnNo is. not the case. mean formula estimate 346bias Finally,. Wesince conclude itthe m ightmean that appear of th thee asymptoticfrom 100 Tabl sub-samplee theory2 that thereappears is evidenceto be working of ma forterial small sample bias since from the same universe of N=5,000 so they are not independent. Because the various CTE 6 3 316 316 2 this model. That is, the asymptoticestimates is variance 2,111, with errorof the whenan CTEapparent usingEstimator a sample precision size agrees of 1,000 with is therefore “experiment”, not 316, but |354 . estimatesIt is possible are using to use some the meth of theods same in o urdata paper they toare show positively that, in correlated the large andsample so the limit, set theof Theth CIe mean Count of result the 100 is alsosub-sample consistent estimates with the is idea 2,111, that with the anform apparentula standard precisionn errors 1000of are working. estimatescorrelation is more of two tightly sub-sample clustered estimates than if isthey just were U truly n / N independent.. A afterbetter estimateadjusting This intuitive for the for sampling result the is non-independence of the sub-samples. 11 The standard deviation of the m=100 sub-sam- Tofhe actual count| 32100/316 of ,94 which which is very is is much muchclose lesstoless expected thanthan the value value of 2,214 95 (i.e., obtained a 95% from confidenceN the sample5000 interval). of size very easy to understand as nNo . 316 316 error when using a sample size of 1,000 is therefore not 316, but3 |354 . Our variance verification test is therefore to compare the empirical error estimate 354 with the ples is a biased2 estimate of the samplingn 1000 error the5,000. value 2,214However, obtained this analysis from the is sample misleading, of again due to the non-independence of the sub- It is possible to use the methods in our paper to show that, in theThe large 11CI sample Count limit, result the is alsoFinally, consis ittent might with appear themean idea formulafrom that Tabl estimatethe eform 2 346thatul . a Wethere standard conclude is evidence errorsthat the asymptoticare of maworking.terial theory small appears sample to be working bias since for correlation of two sub-sampleand estimates it is not is just hard U n to/ N understand. A betterThe estimateactual why.N for count The the5000 sampling vari of -94 is sizeverysam 5,000. closeples. toHowever, expectedthis this model. value analysis Thatof 95 is, is the(i.e., mislead asymptotic a 95%- variance confidence of the CTEinterval).Estimator agrees with “experiment”, Our variance verification test is therefore to compare the empirical3 erro316r estimate 316 354 with the the mean of the 100after sub-sample adjusting for estimates the non-indepe is 2,111,ndence of with the sub-samples. an apparent precision of error when using a sample sizeous of sub-samples 1,000 is therefore (each not 316, of but size n=1,000) were| all354 . ing, again due to the non-independence of the mean formula estimate 346 . We conclude that the asymptotic theory appearsn to 1000be working for | this model. That is, the asymptotic variance of the CTE Estimator agrees11 with “experiment”, When samples32100/316 , arewhich positively is much correlated less than the variancevalue 2,214 of theobtained sample from mean the is sample larger of size drawn from the same universeFinally, Nof it N m=5,000ight5000 appear so fromsub-samples. Table 2 that2 thereThe isCI evidenceCount result ofis alsoma terialconsistent small with samplethe idea that bias the sinceformula standard errors are working. Ourafter variance adjusting verification for the non-indepe test is thereforendence toof compare the sub-samples. the empirical error estimate 354 with the 5,000.VAR However,x this analysis UUV m is]/)1([)( misleading, than it would again otherwise due to be.the non-independenceA better estimate for of the precisionsub- of they are not independent.th Becausee mean ofthe the various 100 sub-sample estimates is T2,111,he actual with count an of 94apparent is very close precision to expected of value of 95 (i.e., a 95% confidence interval). mean formula estimate 346 . We conclude that the asymptotic theory appears to be working for samples. thisThe model. CI Count That result is, the is asymptoticalsoCTE consis tent estimatesvariance with theof theidea are CTE that using Estimatorthe form someul agreesa standard of thewith errors same“experiment”,| 32100/316 are data, working. which Whenis much samples less than aretheFinally, value positively it m2,214ight appear obtained correlated1000 from Tabl from e1000 2 thatthe there sample is evidence of size of material small sample bias since The actual count of 94 is very close to expected value of 95 (i.e., a 95% confidence interval). the 2,111 number is then 346 ( 1 | 158100/) which is not materially different after adjusting for the non-independence of the sub-samples. the mean of the 100 sub-sample estimates is 2,111, with an apparent precision of they are positively correlated5,000. and However, so the set this of analysisWhenthe variance is sam misleading,ples of are the positively againsample due correlatedmean to the5000 is non-independence larger the variance 5000 of theof the sample sub- mean is larger The CI Count result is also consistent with the idea that the formula standard errors are working. | 32100/316 , which is much less than the value 2,214 obtained from the sample of size Finally, it might appear from Table 2 that there is evidence ofsam materialples. small sample bias since from the sampling2 error in the 2,214 value. Thus, while there is some evidence of small sample The actual count of 94 is veryestimates close to expected is more value tightly of 95 (i.e., clustered a 95% confidence than ifinterval). they VAR x 5,000. UUV However,m]/)1([)( than this itanalysis would would is misleading,otherwise again be. due A tobetter the non-independence estimate for theof the precision sub- of the mean of the 100 sub-sample estimates is 2,111, with an apparent precision of bias in that 2,111 < 2,214, there is not enough data here to quantify it. The bias is lost in the | 32100/316 , which iswere much lesstruly than independent. the value 2,214 obtained This fromintuitive the sample result of size is otherwise be. A bettersamples. estimate for the Finally, it might appear from Table 2 that there is evidence of maWhenterial smallsam sampleples arebias sincepositivelysampling correlated error. the varianceThis is usually of the1000 samplethe case. mean1000 is larger from the same universe ofth5,000.e Nmean=5,000 However,of the 100so this sub-samplethey analysis are isestimates notmisleading, indepe is 2,111, againndent. with due toan theapparent Because non-independence precision the ofvarious of the sub- CTEthe 2,111 number is then 346 ( 1 | 158100/) which is not materially different very easy to understand as n → N. 2 precision of the When 2,111 sam numberples are positively is then correlated the variance of the sample mean is larger samples. | VAR x UUV m]/)1([)( than it would otherwise be.5000 A better 5000estimate for the precision of estimates are using some of the same32100/316 , which data is th muchey lessare than positively the value 2,214 correlated obtained from and the sosample the of set size of 2 5,000. However, this analysis is misleading, again due to the non-independence of the sub- VAR x UUV )1([)( m]/ than it would otherwise be. A better estimate for the precision of When samples are positively correlated the variance of the sample mean is larger fromAfter the goingsampling through error a in variance the 2,214 ve rificatiovalue. Thus,n exercise while a therfewe time is somes a practicing evidence actuaryof small will sample know estimates is more tightly samclusteredples. than if they were truly independent. This intuitive result2 is 1000 1000 from the same universe of N=5,000 so they are not indepe2 ndent. Because the various CTE | 1000 1000 very easy to understand asV ARnNox . UUV )1([)( Itm]/ is than possible it would otherwise to use be.the A methods thebetter 2,111 estimate in number forour the paper precision is then of bias346w hetherin that the2,111 ( 1 asymptotic < the2,214, 2,111 thereformulasnumber158100/) is is notthen described which enough346 is notdatahere ( 1 materially hereare working to quantify different| 158100/) for which his/herit. Th is note particularbias materially is lost different situation. in the When samples are positively correlated the variance of the sample mean is larger 5000 5000 5000 5000 estimates are using some of the same data they are positively correlatedto show1000 that, 1000and in so the the large set ofsample limit, the sampling error. This is usually the case. VARthe 2,111x number2 is thenUUV )1([)( m346]/ than it would ( 1 otherwise be.| 158100/) A better fromwhich estimate isthe not materiallysampling for the precision different error of in the 2,214 value. Thus,from the while sampling ther errore is in somethe 2,214 evidence value. Thus, of smallwhile ther samplee is some evidence of small sample estimates is more tightly clustered than if they were truly independent.2 5000 This5000 intuitive result is bias in that 2,111 < 2,214, there is not enough data here to quantify it. The bias is lost in the It is possible to use the methods in our papercorrelation1000 to show1000 that,of two in sub-samplethe large sample estimates limit, isthe which is not materially different from the sam- very easy to understand as nNo . thefrom 2,111 the number sampling is errorthen 346in the 2,214 value. ( 1 Thus, while| 158100/) ther e whichbias is some isin notevidence that materially 2,111 of small different < sample 2,214, After thereConclusions going is not through enoughsampling a data variance here error. tove This quantifyrificatio is usuallyn it. theexercise Thcase.e bias a few is lost time ins thea practicing actuary will know correlation of two sub-samplebias in estimatesthat 2,111 < 2,214, is just justthere5000 isU not enough n /5000N data. A Ahere better better to quantify samplingestimate estimate it. The forbiaserror. for theis lostthe samThis in samplingthe- is usuallypling error the case.in the 2,214 value. Thus, while there from the sampling error in the 2,214 value. Thus, while there is some evidence of small sample whether the asymptotic formulas described here are working for his/her particular situation. sampling error. This is usually the case. After going through a variance verification exercise a few times a practicing actuary will know bias2 in that 2,111 < 2,214, therepling is not error enough when data usinghere to quantifya3 sample316 it. Th sizee bias of is 1,000 lost 316 in the is is someIn the evidence authors’ ofexperience, small sample so far, bias we in havethat yet to see a practical situation where the theory It is possible to use theerror meth whenods usingin our a papersamplesampling tosize show error.of 1,000 that,This is isusuallyin therefore the the large case. not sample 316, butlimit,3 the |354 . whether the asymptotic formulas described here are working for his/her particular situation. After going through a variancetherefore verificatio notn exercise 316, buta few timeAfters a practicing ngoing actuary through 1000will know a variance 2,111outlined

Conclusions 2 This result is not in the original paper. 3 If we have m identically distributed, but correlated, samples from a distribution with finite In the authors’ experience, so far, we have yet to see a practical x x )( 2 situation where the theory outlined here fails in amean material and variance way. Hence, V 2 then we Ebelieve[¦ i that practitioners ] 2 ( 1 UV ) canwhere use Utheis asymptoticthe correlation between i m 1 samples. 2 This result is not in the original paper. 3 If we have m identically distributed, but correlated, samples from a distribution with finite 7 x x )( 2 mean and variance V 2 then E[¦ i ] 2 ( 1 UV ) where U is the correlation between i m 1 samples.

7 Risk Management w August 2008 Chairman’sVariance of Corner the CTE Estimator

CTE Estimator … w continued from page 41

After going through a variance verification ex- If simply increasing the run size is impractical ercise a few times a practicing actuary will know then there are other tools that can be used to im- whether the asymptotic formulas described here prove the precision of the CTE estimator without are working for his/her particular situation. significantly increasing the computational cost. That will be the subject of our next article. F Conclusions In the authors’ experience, so far, we have yet to see a practical situation where the theory outlined here fails in a material way. Hence, we believe that practitioners can use the asymptotic formulas presented here to understand the sampling error in a given CTE estimate. A practitioner can go through a variance verification exercise if they want to prove to themselves, or others, that the asymptotic formulas are working in their particular situation. formulas presented here to understand the sampling error in a given CTE estimate. A practitioner can go through a variance verification exercise if they want to prove to themselves, Finally, we note that if a practitioner were or others, that the asymptotic formulas are working in their particular situation. using this tool then, on the basis of the first run of 1,000Finally, scenarios, we note they that would if a reportpractiti aoner CTE were using this tool then, on the basis of the first run of estimate1,000 of 2,004 scenarios,+355. theyIs a relativewould reportsampling a CTE estimate of 2 , 004 r 355. Is a relative sampling error formulas presented here to understand the sampling error in a given CTE estimate. A errorpractitioner ofof roughly roughly can go through a variance| %18004,2/355 acceptable?verificationaccept- exercise The answer if they want to that to prove question to themselves, depends on the able?or Theothers,circumstances. answer that the to asymptotic that question formulas depends are working on in their particular situation. the circumstances. Finally,If 18% we isnote not that an if a acceptable practitioner error were then using what this tool are then,the alternatives?on the basis of th Onee first option run of is to increase the 1,000 scenarios, they would report a CTE estimate of 2 , 004 r 355. Is a relative sampling error number of scenarios. If we increase the number of scenarios by a factor of K then the sampling If 18%of roughly is not an acceptable| error%18004,2/355 acceptable? then what The are answer to that question depends on the the alternatives?circumstances.error scales One by optiona factor is of to 1 increase/ K . Cuttingthe the sampling error by a factor of 4 would require us to run 16,000 scenarios. number of scenarios. If we increase the number If 18% is not an acceptable error then what are the alternatives? One option is to increase the of scenariosnumberIf simply of by scenarios. a increasingfactor ofIf weK ththen increasee r unthe size thesampling number is impractical of scenarios then by there a factor are of otherK then tools the samplingthat can be used to errorerror scalesim scalesprove by by athe afactor factor precision ofof 1 / ofK the. CuttingCutting CTE estimator thethe sampling without error by significantly a factor of 4 would increasing require the us tocomputational samplingruncost. 16,000 error That scenarios. by willa factor be theof 4 subject would require of our usnext article. to runIf simply16,000 increasing scenarios. the run size is impractical then there are other tools that can be used to improve the precision of the CTE estimator without significantly increasing the computational cost. That will be the subject of our next article.

w Page 42

8 August 2008 w Risk Management Chairman’sVariance of Corner the CTE Estimator Global Best Practices in ERM for Insurers and Reinsurers Webcast

Tsana Nobles

n January 2008, the International Network of Actuarial Risk Managers (INARM), I which is an international ad hoc group formed by the Joint Risk Management Section of the North American actuarial profession, hosted the webcast “Global Best Practices in ERM for Insurers and Reinsurers.” The purpose of this webcast was “… to promote awareness of a global actuarial community by involving actuaries globally in one event, allowing people to share emerging and new risk management practices across different geographical regions ...” The program consisted of two tracks of sessions: one pre-recorded and one live.

The pre-recorded sessions included a basic introduction to ERM and covered:

• Emerging Risks • Embedding ERM in the DNA of an Enterprise The SOA, the Joint Risk Management Section, (Introduction) the Actuarial Profession (U.K.), and the Institute • Economic Capital of Actuaries of Australia were all underwriters • Risk Appetite of the webcast. Milliman and Standard & Poor’s were commercial sponsors, and their sponsor- The live sessions took place on January 16 and ship funds covered many of the fixed expenses covered: so the webcast was offered at a nominal fee.

• Stakeholder Views: Regulators, Rating Viewers of the webcast volunteered to Agencies, and Investors summarize some of the pre-recorded and live sessions to offer insight into the topics and • Embedding ERM in the DNA of an Tsana W. Nobles, FSA, MAAA, specific material covered. Those summaries are Enterprise is AVP and quantitative analyst listed below. • Economic Capital: A Passing Fad or a Brave with Dwight Asset Management New World? Co. in Burlington, Vt. • Active Risk Controls Emerging Risks She can be reached at tnobles@ Pre-recorded Session dwight.com. The webcast participation was fantastic. There Summarized by Clifford Angstman, FSA were 530 registratrants from 47 countries AIG Life Insurance Company resulting in approximately 1600 viewers. The live sessions ran over three time zones: Asia/ This session included a large number of pre- Pacific, Europe and Americas. Presenters in sentations on different aspects of analyzing and each time zone were from the region and the responding to emerging risks. Tony Campbell presentation material had specific application provided moderation and introductory mate- to that region. rial. continued on page 44

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The presentations are summarized below. can see how it is important to consider a risk in light of all of the other societal developments Nassim Taleb and Black Swan that will influence its resolution. Understanding Nassim Taleb discussed the concept of robust- the correlations and connections with other key ness of financial institutions to variations or risk drivers is important to a thorough analysis modeling errors in tail-distributions for unusual of emerging risks. but infrequent events. He also contrasted the differences in impact for those companies Zweimuller mentioned a number of current working in an “Extremistan” environment, as trends, including improving longevity and obe- opposed to those whose risk work is more in the sity, globalization, communication changes, “Mediocrastan” realm. climate change, complexity, and regulatory initiatives. Dr. Achim Regenauer (Munich) and Obesity. Robert W. Wilson (Sun Life Financial) Dr. Regenauer used graphical techniques to and Scenario Analysis. provide a fascinating description of the in- Robert W. Wilson discussed the use of scenario crease in obesity rates (BMI >30) in the U.S. analysis at Sun Life Financial. This process was and Europe from 1991 to 2005. He followed used extensively by Royal Dutch/Shell (see also this with similar graphs on the development of “The Art of the Long View,” by Peter Schwartz.) diabetes rates. After discussing the impact of for the strategic management of risks. For those diabetes on health, he concluded that increased interested in utilizing this “war game” type of obesity leads to increased diabetes about 10-20 approach to improve management response to years later, followed by increasing heart disease risks, this session provided a number of tips. incidence and with potential higher mortality. Jeff Smith (IAG) went through a similar sce- Dr. Peter Hoeppe (Munich Re) nario analysis example related to the Avian and Geographical Risk. Flu. He described the organizational process Dr. Hoeppe reviewed evidence that rising sea for dealing with risk events, and how scenario temperatures have led to the doubling of the risk analysis has allowed his organization to identify from heat waves, and increases of 50 percent in potential problems and improve their response the intensity of hurricanes. plans. The Avian Flu scenario brings out issues of staffing, changes in business distribution, Manuela Zweimuller (Munich Re) dealing with the media, and making operational and Environmental Scanning changes in a period of stress. Manuela Zweimuller looked for major trends in the global environment to develop an early Camilio Salazar (Milliman) warning system for risks as they develop. She and Disaster Recovery. provided an asbestos related example to explain Camilio Salazar provided his real life experi- the need for this process. The first asbestos ence in recovering from Hurricane Katrina, related death occurred in 1900, and it took the mostly from an operations point of view. It is next 100 years for society to fully develop its very interesting to get the prospective of some- view of this risk issue, including how to prevent one who has lived through such a significant exposure, who was responsible for its impact, event. He discussed many important issues in and how to compensate and treat those that were a recovery plan including dealing with the po- exposed. Thinking through this example, one tential loss of intellectual and human capital as

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employees may look to relocate elsewhere. He solely using ERM to meet an external stake- also discussed the significant communication holder’s requirements and suggested that best issues they faced with a loss of phone, mail and practice occurs when ERM is integrated into e-mail for a time. This could have resulted in strategic planning and the firm moves toward the loss of suppliers and producers. To ensure and better understands their optimal result. that these relationships remained intact, many personal visits were made with producers and The driver of ERM has been the regulator in suppliers to demonstrate their commitment to Europe, while in the United States, rating agen- the business. His insights and practical experi- cies have taken the lead. The speakers warn ence on recovering from a disaster situation are against a false sense of security that sophisti- useful to risk management professionals. cated models can provide, suggesting that the firm’s culture is the true long-term competitive Mike Metzger (Genworth) and the Event advantage. Risk Management Process Mike Metzger discussed the use of a formal Enterprise risk management has gone by a vari- process to manage and resolve risk incidents ety of names. Among these are: enterprise wide, that starts with indentifying and assessing the holistic, integrated, strategic, and global risk risk and ends with a post event debriefing stage. management. He also explained the management structure used to develop a coordinated response to risk The person acting as Chief Risk Officer (CRO) events. He discussed the value of having an of the firm should have direct access to the Emergency Preparedness Guide provided to Board of Directors or risk being buried in bu- every employee so that they understand their reaucracy. role in a crisis. There are many metrics being used by ERM Dave Ingram (S&P) and Rating Agency practitioners. The common feature of the best Consideration of Emerging Risks ones is that they look at a distribution of results Dave Ingram provided a rating agency view of and focus on sections of it, often the tail. No one company’s ability to manage emerging risks, metric provides all the information, so it is im- and how this evaluation is used in the rating portant to consider several. process. Reports should be tailored to the audience, with Embedding ERM in the DNA more graphics at the board level and more detail of an Enterprise (Intro)Pre- at lower levels. The owner of a risk, whose bonus recorded Session depends on the result, should not also be the Summarized by Max J. Rudolph, person measuring the risk. FSA, CFA, CERA Rudolph Financial Consulting, LLC Best practice ERM considers the major risks Presenters: Samuel Sender and Steve D’Arcy, through a prioritization process, involves the PhD, FCAS, MAAA board of directors, and is strategic in that it looks to optimize the risk/return relationship by mak- This session, lasting just over an hour, provided ing decisions that improve the firm’s position. background on Enterprise Risk Management This will give a company a leg up on its competi- (ERM) and how we got to today’s best practices. tors as future events unfold. The presenters warned against the practice of

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Economic Capital: Life/Non-Life Steve Lowe pointed out that there is no right or Prerecorded Session wrong approach to building an economic capi- Summarized by Tsana W. Nobles, FSA, MAAA tal model and that the chosen approach should Quantitative Analyst, Insurance Asset reflect the company and management’s objec- Management tives. He stated that the approach will address Dwight Asset Management Co. six key decisions: the risk horizon, the defini- Presenters: John F. Brierley, FSA, FCIA, tion of capital, the measure of security risk, the Gary Finkelstein, FIA, and Steve Lowe, risks included, the quantification methodology, FCAS, MAAA and the aggregation method. Currently there are two divergent views on the appropriate risk ho- These two sessions offered high level informa- rizon for economic capital, one-year or run-off. tion on the components of economic capital with Steve believes that all approaches to economic some specific numerical examples. capital modeling present a spectrum of systems requirements and sophistication and feels that John Brierley defined economic capital and any criteria should be used in the selection of stressed that all risks should be included in an appropriate model for general insurance the calculation, not just those stressed by risk such as data requirements, ease of imple- regulators. He stated that economic capital is mentation, type of risk measured, and whether used for pricing, is a fair and consistent way it is amenable to a one-year risk horizon. Steve to allocate capital, and is a method to compare described in detail several well-known methods profit margins for dissimilar lines of business of modeling. Steve concluded with the idea that on a level playing field. He contends that the it is worth building an internal model in order to key risks captured in economic capital calcula- earn rating agency credit and to compete effec- tions are credit, operational, business, interest tively. He added that eventually the economic rate, fixed asset, goodwill, and insurance. John capital modeling results will act as a spring- highlighted several challenges of calculating board to economic performance measurement. economic capital such as incorporating multiyear guarantees into a one-year time horizon as Stakeholder Views: Regulators, well as appropriately reflecting partial correla- Rating Agencies, Sell-Side tions and diversification. Analysts/Investors (Americas Focus) Live Session Gary Finkelstein stressed that economic capi- Summarized by Ashley Goorachurn, FSA, FCIA tal can be viewed from two different perspec- Director, Risk Management tives: the capital required to meet risk as well AEGON Institutional Markets as the capital available. Capital management Presenters: Max J. Rudolph, FSA, CFA, CERA, is “the marrying of these two” perspectives. David Ingram, FSA, CERA, and Risk-adjusted performance measures were David Sandberg, FSA, CERA. introduced. Hepresented specific numerical examples that highlight the difficulty in setting In this session, presenters discussed Enterprise an appropriate correlation matrix and capturing Risk Management (ERM) from the perspec- diversification benefits. Gary cautioned that tive of investors and sell-side analysts (Max “correlations in the tail may not be the same as Rudolph), rating agencies (David Ingram), and correlations at the mean.” regulators (David Sandberg).

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Max Rudolph discussed how investors (specifi- management culture and strategic risk manage- cally private investors) can look to the areas of ment. While the first four categories largely compliance, culture, knowledge and value focus on limiting losses, the assessment of stra- added, to better understand a company’s strat- tegic risk management focuses on the potential egy and risks. upside. An effective ERM framework will not only measure risk capital but also utilize this Compliance can add value to a company when information to optimize the company’s risk ad- structured properly, but an investor must be justed returns. S&P looks at whether a company skeptical of companies where compliance is the is incorporating risk adjusted returns into their focus of their ERM framework. corporate strategic decision making processes such as product design, risk budgeting etc. Investors should look for a culture that supports proactive risk management at all levels of the Finally David Sandberg discussed how ERM organization. Also look for alignment between can add value for regulators. risk management and internal programs (incentive comp, etc.) Companies have adopted ERM because they believe it adds shareholder value. ERM can Investors should examine whether companies also add value to regulators by transforming are accepting risk where they have a competi- the focus of the regulatory review process from tive advantage and avoiding or mitigating risk verifying calculations and keeping of rules to where they do not. Investors will also want to ensuring that the reporting process enhances determine whether a company is accurately the learning of the regulator and the industry. communicating its risk profile to stakeholders, To accomplish this, changes to the regulatory and whether senior management understands functions and processes must be made which the risks the company is taking. enhance the effectiveness and comfort of the regulatory function. Exactly what these changes Next David Ingram covered ERM from a rating should be have not yet been clearly articulated. agency perspective with his review of the ERM evaluation process at S&P. Regulators (and industry) don’t need complex models to understand every risk. While sophis- In 2005, S&P created a framework to systemati- ticated risks typically require sophisticated cally evaluate firms’ ERM practices. This ERM risk management practices, some risks are bet- evaluation has become the eighth category of ter handled through other processes. S&P’s full ratings review process (the other seven are capital adequacy, management strat- Economic Capital - Passing Fad egy, investments, financial flexibility, earnings, or Brave New World (Americas) liquidity and market position). The weighting Summarized by Hubert Mueller, FSA, CERA on the ERM evaluation varies by company and Principle depends on the insurer’s risk profile and its Towers Perrin capacity to absorb losses. Presenters: Mike Angelina, FCAS, Ellen Cooper, FSA, CFA, Guogiang Li, CFA, S&P’s ERM evaluation considers a company’s Jeff Mohrenweiser, FSA. risk control processes, emerging risk manage- Moderator: Steve Lowe, FCAS ment, risk and economic capital models, risk continued on page 48

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The presenters discussed different perspec- European Focus Live Sessions tives on economic capital (EC). Summarized by Jules Constantinou, ASA, FFA Head of Marketing Jeff Mohrenweiser (Fitch Ratings) provided Gen Re Life Health a rating agency perspective, by illustrating Fitch’s Global EC Model, Prism, and its unique The Stakeholder’s views session was moderated attributes. He also discussed some of the chal- by Nikos Katrakis: lenges for a rating agency in assessing an insurer’s capital adequacy from the outside. • Paul Brenchley (FSA) specified ERM as a holistic process resulting in a framework re- Ellen Cooper (Aegon) discussed the use of EC sponsive to changes to the firms’ risk profile, for market-consistent pricing by illustrating regularly incorporating new risks and infor- a Term product example. In particular, EC mation. Sophistication should depend on the provides a new tool to assess how new products size and complexity of the enterprise. add value on a market-consistent basis, using • Keith Bevan (S&P) explained that ERM is a a stress testing technique consistent with the key part of the rating process. S&P has four European Solvency II regulation. She also dis- ERM classifications for insurers, Excellent, cussed the link from EC to a market-consistent Strong, Adequate and Weak. The evaluation framework. includes risk controls, emerging risks management and models of risk and economic Guo Li (AIG) discussed the governance as- capital. pects of EC, and its global applications and • William Allen (Bear Investments) was criti- challenges for insurers and reinsurers. In his cal of the current risk frameworks, in par- view, EC helps drive better decision-making by ticular citing exposure to recent events and providing a tool for the various applications. He the inability of firms to “foresee” these risks then described AIG’s process for ERM and EC through their ERM platforms. in greater detail. The Embedding ERM in the DNA of the Finally, Mike Angelina (Endurance) focused on Enterprise session was moderated by Lain the use of EC for optimal capital management Brown: and better management of earnings volatility. He mentioned several key principles for ERM • Alister Esam (eShare Limited) outlined how and EC: optimal management of capital, elimi- important a role IT plays in the management of nating risks that threaten solvency, managing risk information; earnings volatility, shaping the business by only • Roger Dix (HBOS) and David Dullaway taking risks that can be quantified, and creating (Tillinghast) jointly focused on risk-based behaviors that reinforce an ERM culture as the pricing and the potential benefits of diversify- key objectives for ERM and the implementation ing risk across different business units. of Economic Value. He also discussed several • Lukas Ziewer (Oliver Wyman) concluded implementation issues and challenges for EC. by covering the need to having a clear and robust process in place to manage the sheer volume of risk information that enterprises are

faced with.

w Page 48 August 2008 w Risk Management Chairman’s Corner INARM on the Web David Ingram

The session on Economic Capital was moder- WHAT IS INARM??? ated by Alessa Quane: You may have heard about it, but here is what the group is really about.

• Bernhard Bergman (Munich Re) questioned INARM is the International Network of Actuarial Risk Managers. It is a very informal group of folks who are interested in learning and sharing Enterprise Risk Management the relevance of economic capital to firms (ERM) practices across borders to enhance the actuarial ERM practice in all parts today. of the globe. • Colin Wilson (Barrie & Hibbert) discussed INARM is mainly a virtual group. We communicate via several modes and initiatives: the challenges of using economic scenario generators within the modelling. 1. INARM Listserv • Steven Vanduffel (X-Act Consulting) The SOA has provided an email listserv facility to get us started. This has been used by the continued the discussion on capital over 200 listserv members to share articles, questions, answers, opinions, and program modelling, focusing on current practices and information. There are now about 280 people who get irregular and mostly topical emails why they perhaps should not be considered from the listserv participants. Those emails have ranged from five to 15 per month. Topics ranging from subprime, to model risk, to historical risk management failures. Open to all. best practices. Sign up at link below: • To end, Eric Paire and Eddy Vanbeneden (Guy Carpenter) spoke on the management of http://www.soa.org/news-and-publications/listservs/list-public-listservs.aspx the capital through the use of reinsurance and 2. INARM Blog allocation to various parts of the business. As an alternative to the Listserv, an INARM Blog has been created. Discussions of Sub Prime, the 2008 ERM Symposium, Fair Value, Limitations to Modeling, and The final session on Risk Control Hot Topics Mortgage Lending in Asia have been copied there from the Listserv emails in was moderated by Steve Nuttall: March and April 2008. You can add your comments there without joining anything. http://riskviews.wordpress.com/ Neil Allan (University of Bath, who dialed in 3. INARM Emerging Risks from Brisbane) and Neil Cantle (Milliman) In January 2008, INARM helped to create the Global ERM Best Practices for Insurers and argued that a structured approach to strategic Reinsurers Webinar. This program ran for 16 hours and drew an audience of 1,600 people risk can help to avoid missing the big risks and from 47 countries. One of the programs was on the topic of Emerging Risks. Materials from identify hidden opportunities. that program plus new sources on the topic are now available in an open platform that allows users to add more materials as they see fit. This is accomplished with a Google Group called INARM Emerging Risks. Anyone can make comments. To add significant postings, Nick Silver (Parhelion) discussed the challenge you need to join the group. Instructions are there on the website. http://groups.google.com/ faced by insurers on managing climate change group/inarm-emerging-risks/web risk, including a summary of recent research 4. INARM LinkedIn Group amongst the profession on views on the impact of climate change to our current business and While the listserv is not anonymous, it does not provide for members to easily learn each other’s identities. LinkedIn is a professional networking Web site that allows the formation professional models. F of special groups. We have formed an INARM group. As of this writing, the INARM group on LinkedIn has over 80 members from more than 15 countries. To use this facility, you must join LinkedIn (please note that this should not constitute marketing for or against LinkedIn). There is a level of service on LinkedIn that is free and that you may find to be sufficient to make connections with other INARM members if you are interested in that. To join the INARM group http://www.linkedin.com/e/gis/83735/3270834C5E91 5. Other INARM citings on the Web. For more information about INARM, look at http://www.actuaries.asn.au/NR/rdonlyres/1C5D0157-1B4E-4059-B75E- 32F751723D99/2700/INARMKit.pdf http://www.soa.org/professional-interests/joint-risk-management/jrm-inarm.aspx

If INARM sounds of interest to you, please join us in the discussions!

Page 49 w Risk Management w August 2008 Chairman’sEnterprise CornerRisk Management Symposium Enterprise Risk Management Symposium: Notes on a Conference

Dr. Stephen W. Hiemstra and Valentina Isakina

nother year, another terrific event. led, for example, to the failure of Northern And this year, it was timelier than Rock Bank in the United Kingdom after loans A ever. We hope that the remarks below were made that could not be resold. will give those unable to attend a good overview of the insightful discussions that occurred at • The model risk contribution to the sub this year’s ERM Symposium. prime crisis is still not understood. Numerous speakers reported no problem with Executive Summary modeling in the crisis in spite of not anticipat- ing valuation problems (see HPI chart on next • The quality of conversation about page). Actuaries understand the issues in risk management among directors and the inadequate housing loss data and model managers is still below par. Tough ques- specification problems and follow the impli- tions about project proposals and business cations. But often, their managers cannot. operations are hard to ask particularly when Before the crisis, weaknesses in the subprime profits are strong. A weak risk management lending and marketing channels were not culture and lack of organizational power anticipated. After the crisis, some managers for Chief Risk Officers (CROs) exacerbate reported that stressing existing models with Dr. Stephen W. Hiemstra this outcome.1 Significant numbers of ERM standard scenarios would have allowed them is financial engineer and Symposium participants reported that they to anticipate the problems that emerged. is also an ERM Symposium experienced problems communicating risk program committee member. management principles between different He can be reached at • Other observations: professional groups and levels of manage- [email protected]. ment within the firm. 4Insurance firms experienced relatively few losses in the subprime crisis relative to • Risk appetite adjusts to the quality of banks, investment firms, and hedge funds. risk management. Studies show that people 4Reputation risk was a significant factor in driving safe cars drive faster and have similar the failure of Bear Stearns. The firm was numbers of accidents and injuries to other not liked on Wall Street and it refused to drivers. This outcome implies two things participate in previous bailouts, such as that are not necessarily intuitive. First, loss Long-Term Capital Management. outcomes are not a direct measure of the qual- 4The broken glass theory: crime is con- ity of risk management. Second, temporary tagious. Allowing small crimes to go un- lapses in risk management or changes in the Valentina Isakina, ASA, checked may signal it is okay to commit big CFA, MAAA, manager risk environment can have disastrous effects crimes.2 A similar principle may be at work at Bain & Company, Inc. as managers practice brinkmanship with in corporate cultures. Participants com- in Atlanta, GA. She can their perceptions of the state of firm risk man- mented that broken corporate cultures, be reached at valentina. agement and actual practice changes without such as that at Bear Stearns, are a signifi- [email protected]. their knowledge. Pipeline risk apparently cant factor in operational risk and are asso-

1They are not invited to director planning retreats, they are underpaid relative to business line officers, and risk management is frequently not a viable career path in the firm. 2James Emory White. 2004. Serious Times: Making Your Life Matter in an Urgent Day. InterVarsity Press. pp. 158.

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ciated with the rogue trader problem. This problem also affects nation states.3 4Focus on policy issues was small. Recognition of sub prime losses, financial policy, and liquidity concerns, which were the focus of a recent Basle study4 and other recent conversations in Washington, were not discussed in depth. Is this an opportunity to enhance the event discussions next year? 4The gold standard for crisis management certification: Standard on Disaster/ Anurag Saksena: Emergency Management and Business • Two basic CRO operating strategies exist: Continuity Programs 2007 Edition.5 4Partnership approach—where you have skin in the game. Are you respected enough This year was a year of a record attendance to participate in decisions and have access (circa 600). Good Chief Risk Officer (CRO) to the Board? participation and successful roll out of a new 4Watcher approach—where you observe director’s workshop suggest that the conference those with “skin in the game.” was an organizational success. However, • Can you communicate the risk story without an increasing non-insurance body of the resorting to jargon? What is the quality of the participants cited a greater need for presenter returns being earned? and topic diversification. • Everyone wants the same talent, but does not pay the same (e.g., market risk is less critical Below we provide highlights from some of the from a failure standpoint than credit risk, but selected sessions. the market risk managers get paid more). • Is risk management a career track in your General Session: firm? Is ERM Still Relevant—a Chief 4One firm required that all senior vice Risk Officer Perspective presidents spend at least two years in a risk Tuesday, April 15, 2008, 8:10 a.m. management position. Speakers: Marcello Cruz, AVIVA Randy Frietag, • Observations: CRO, Lincoln Financial Tim Patria, Vice President 4Regulators now want more detail than they and Director, Hartford Financial Services wanted 14 months ago. Group Anurag Saksena, CERO, Freddie Mac 4The CRO’s job is to reduce friction in the Moderator: Paul L. Horgan, Partner, system. PricewaterhouseCoopers 4Freddie Mac tracks nine categories of risks.

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3See, for example, Asharf Ghani and Clare Lockhart. 2008. Fixing Failed States: A Framework for Rebuilding a Fractured World. Oxford University Press. 4Senior Supervisors Group, Observations on Risk newsevents/news/banking/2008/SSG_Risk_Mgt_doc_final.pdf. Basle, Switzerland. March 6, 2008. Management Practices during the RecentMarcello Market Cruz:Turbulence. www.newyorkfed.org/ newsevents/news/banking/2008/SSG_Risk_Mgt_doc_final.pdf. Basle, Switzerland. March 6, 2008. 5www.nfpa.org/assets/files/PDF/NFPA1600.pdf

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•Current sub prime crisis has its roots in corpo- • Comments on the U.S. regulations rate governance problems. 4They are too cumbersome. 4Board of directors may be too far removed 4When too many groups are overseeing the from the best practice risk principles economy, things are bound to “fall through partially because of a generational lag. the cracks.” Consequently, they may be unable to ask 4Simplification of the regulations could be a the right questions and understand the sig- positive change. nificance of the reports they hear. Director education is one solution to this problem. General Session: In the Pursuit 4Who do CROs report to? They need a double of Return, Have We Lost Sight reporting line to allow them access both to of Risk? senior management (e.g., CEO, CFO) and Tuesday, April 15, 2008, 2:15 p.m. the Board. Speakers: James C. Allison, Regional Risk Manager NA, Conoco Phillips Leo Tilman, Luncheon Speaker: Lord John Eatwell, Chief Institutional Strategist, Bear Stearns President, Queens’ College, Cambridge Larry Moews, Vice President and Chief Risk Officer, Allstate Insurance Company EU Regulatory Changes in the Moderator: Jorge Montepeque, Global Light of Recent Events Director, Marketing Reporting McGraw- Tuesday, April 15, 2008, 1:00 – 2:15 p.m. Hill Platts

• Lord John Eatwell was one of the best present- Jorge Montepeque: ers at the Symposium. He was clear, precise • Life styles are converging worldwide. An and very insightful. This presentation alone inflationary environment is evolving out of the was worth the Symposium attendance. Federal Reserve actions. • Much of the discussion focused on the recent • Problems with rogue traders may arise when credit crisis and how it should be shaping the high-energy individuals make mistakes and regulatory activities. prevent oversight due to their force of per- • He proposed a new role of the regulator: sonality. 4Assure that the firm has incentives to management risk properly. James C. Allison: 4Enforce best practices management. • What went wrong? 4Focus specifically on systemic risk. 4Risk appetite adjusts to the quality of 4Develop countercyclical bank regulatory risk management. Losses were higher incentives, such as a required capital cush- because of our successes in risk manage- ion during economic booms that could be ment, not our failures. People with safe cars dipped into during the downtimes. drive faster. 4Make sure financial firms have “skin in 4Risk transference created couplings not the game”—no off-balance transactions previously observed. Tension exists be- should be allowed. tween product innovation (product differ- •Northern Rock bank in the United Kingdom entiation) and market transparency. Firms failed because of market gridlock—the make money being different, not uniform. chain of counterparties froze. Loans were 4Stress testing—everyone talks about it; no made that could not be sold. one does it properly.

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• Risk managers, directors, and buyers have an Moderator: Matt Feldman, EVP, Operations, obligation to ask tougher questions about the Chicago FHLB business. We need to make sure that all disciplines and professions are talking the same Matt Feldman: language and engaged in decisions. • A bad corporate culture can kill a firm. Risk • Nearly all of the largest bankruptcies were officers used to be lone wolves. due to preventable management failures— • What we are frequently missing is good in- integrity problems and competencies. teraction between the company, the regulator Source: www.bankruptcydata.com/ and the customer. In that sense, the CRO Research/15_Largest.htm plays a role like that of Henry Kissinger in the Nixon administration, getting everyone to talk Larry Moews: constructively even when they do not get along • Segmentation of duties makes it unlikely that on all issues. there is such a thing as a rogue trader—too many (30+) people have to be involved. When Dennis Chookaszian: bad news is disclosed, managers pile on all • National Fire Protection Association (NFPA) the bad news they know about so as to purge 1600—the gold standard for crisis manage- the system. ment certification: Standard on Disaster/ Emergency Management and Business Leo Tilman: Continuity Programs 2007 Edition.6 SOX re- • Nothing focuses your attention like the failure quires a risk review: an out of the box process of a firm (LTCM) just like your own (Bear for out of the box risks. Stearns, for example). • After 80 years of playing the “bad boy” • What went wrong? on Wall Street, Bear Stearns ended up 4If firm risk appetite adjusts and is a friendless. problem, then hire more policemen. • CRO role: If you cannot change things, what In the case of the autobahn road deaths, are you doing here? fatalities were reduced through driver • The big corporate failures could mostly have education. been prevented. 4We did not ask the right questions. Risk managers continue to be called after John Wengler: decisions are made and are not invited • What is frequently missing in risk manage- to participate in planning retreats. ment is cultural competence. Risk needs 4Risk management did not fail. Nor was to be examined from a multidisciplinary there a modeling failure. perspective. We cannot be married to our numbers or use a lot of jargon. Phrases, like General Session: “six sigma losses,” do not communicate to View from the Top most audiences. Wednesday, April 16, 2008, 7:45 a.m. • The model for avoiding turf wars is to Speakers: Dennis Chookaszian, Director, require that managers concur (not ap- CME Holdings Branko Terzic, Global & prove) that each proposal adequately de- U.S. Regulatory Policy Leader in Energy & scribes risk management implications. By Resources, Deloitte Services LP John Wengler, requiring only concurrence, concerns can be Chief Risk Officer, Entergy Services, Inc. (ESI)

continued on page 54 6 www.nfpa.org/assets/files/PDF/NFPA1600.pdf

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expressed without offering a direct challenge 4“Of the many introductions that I have re- to the proposing manager. Illustration is given ceived, this one was the most recent!” of not looking a child in the eye (simian male 4“As Henry the Eighth told his wives—I challenge)—a sideways glance is preferred won’t keep you long!” and less threatening. 4“An economist is someone who can make •Does your secondary staff feel secondary? love 16 ways, but doesn’t know a girl.” (They should not). 4“Greenspan: constructive ambiguity. •Question: Did Bear Stearns executives Congressman, if you understood what I just know they were rolling the dice or was it said, I misspoke.” an honest mistake that led to their failure? 4“Will Rogers: If the world comes to an end, We may never know. I want to be in Cincinnati, Ohio because everything happens in Cincinnati 10 years Branko Terzic: later.” • Does the CRO ask the right questions and 4“Winston Churchill: In the end, Americans have the support from senior management to always do the right thing—after exhausting do so? all the other alternatives.” • Reputational risk examples: 4Schlitz Brewing Company failed from repu- General Session: Strategic tational problems after introducing a new Risk—Making Models Relevant brewing process that cut costs dramatically in Executiv e Decisions but left the beer maker with a dramatically Wednesday, April 16, 2008, 1:50 p.m. reduced employee head count. Customers Speakers: Scott M. Polakoff, Senior Deputy fled when the story was leaked because the Director and Chief Operating Officer, Office of company tried to position itself as a “tradi- Thrift Supervision, Myron S. Scholes, Chairman, tional” brewer. Platinum Grove Asset Management, L.P., 4Arthur Andersen failed after playing a Charlie Shamieh, Executive Vice President, AIG brinkmanship game with federal prosecu- Moderator: Thomas S. Y. Ho, President and tors who failed to realize that even filling Founder, Thomas Ho Company an indictment of the firm would ruin their reputation and drive them out of business. Myron S. Scholes: 4Tylenol enhanced the reputation of their • Is there a difference between good manage- firm by acting promptly and prudently when ment and good luck? faced with a problem of poisoned product. 4Good management is a marriage between good theory, experience, and luck. Luncheon Speaker: Dr. William Freund, • Was Bear Stearns insolvent or illiquid? We Chief Economist Emeritus, The New York may never know. Stock Exchange • More information does not necessarily provide more value. Sometime we need to use What Is Ahead for Business mushware (our brains). and Investors? Wednesday, April 16, 12:30 p.m. See you in Chicago in 2009! F • Overall summary—great jokes, great insights. Some samples:

w Page 54 August 2008 w Risk Management Chairman’s Corner Third Year a Charm for ERM Symposium Scientific Papers Track

Steven C. Siegel

n 2006, the ERM Symposium established Foundation ERM Research Excellence Award its first-ever annual call for ERM-related for Best Overall Paper; the PRMIA Institute I research papers to present the very latest New Frontiers in Risk Management Award; and in ERM thinking and move forward principle- the Joint Risk Management Section Award for based research. Originally the brainchild of Practical Risk Management Applications. Max Rudolph, the 2006 ERM Symposium Call for Papers set into motion high expectations for The award winners along with the paper ab- succeeding years in the quest for expanding the stracts are shown below. Awards were pre- repository of ERM knowledge. Building on the sented at the ERM Symposium Opening session successes of 2006 and 2007, I am pleased to held on April 15th. report that the 2008 ERM Symposium Scientific Paper Track continues to push the envelope in 2008 Actuarial Foundation ERM Research terms of both quantity and quality of papers. Excellence Award for Best Overall Paper: “A Practical Concept of Tail Correlation,” by John Manistre.

Max Rudolph, chair of the ERM Symposium Call for Papers

John Manistre (right) accepts the third annual Actuarial With 65 abstracts submitted for review--a Foundation award from Gary Josephson. 40 percent increase over 2007—the level of response again confirms the cross-industry ABSTRACT interest in this topic. The papers review com- This paper shows how the results of copula mittee, chaired by Rudolph, included returning based capital aggregation models can always be members Mark Abbott, Maria Coronado, Sam locally approximated by relatively simple for- Cox, Steve Craighead, Krzysztof Jajuga, Jeanne mulas. The paper defines the concepts of diver- Nallon, Dan Oprescu, Nawal Roy, Matthieu sification factor and tail correlation matrix and Royer, Richard Targett, Fred Tavan and Al describes methods for estimating these quanti- Weller as well as newcomers John Birge, Dan ties from simulated data. We show how these Rosen, Greg Slone, and Robert Wolf. Choosing ideas can be put into practice as both compu- from among the 65 abstracts for nine presenta- tational short cuts and presentation tools. Some tion slots at the symposium required a great deal examples are then developed which suggest of review and careful consideration. Given the that, when copula based models are used to ag- quality and number of abstracts, as in previous gregate capital, two new phenomena emerge a) years, the committee wished there were more diversification benefits are reduced because of speaking slots available. additional tail dependence in the copula and b) diversification benefits are increased when ag- The final task of the committee was to select gregating risks that have finite variance and the the prize winning papers. The three prizes model does not have too much symmetry. Since awarded at the symposium are: the Actuarial continued on page 56

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few of the risks held by a life insurer are so heavy Empirical Investigation of the Characteristics of tailed that they have infinite variance, the paper Firms Adopting Enterprise Risk Management.” concludes by arguing that simple, correlation matrix based, capital aggregation formulas are more defensible than previously thought.

2008 PRMIA Institute Award for New Frontiers in Risk Management: Klaus Bocker and Martin Hillebrand for “Interaction of Market and Credit Risk: An Analysis of Inter-Risk Correlation and Risk Aggregation.” Don Pagach (left) and Richard Warr (center) accept Joint Risk Management Section award from Fred Tavan

ABSTRACT We use a hazard model to examine the factors that influence firm level adoption of enterprise risk management (ERM). We find that firms that are more levered, have more volatile earnings and have exhibited poorer stock market performance are more likely to initiate an ERM program. When the value of the CEO’s option Klaus Bocker (right) accepts PRMIA Institute award from and stock portfolio is increasing in stock volatil- John Birge ity, the firm is also more likely to adopt ERM. ABSTRACT Our results suggest that ERM is being used for In this paper we investigate the interaction reasons beyond basic risk management. These between a credit portfolio and another risk other reasons include offsetting CEO risk tak- type, which can be thought of as market risk. ing incentives and seeking improved operating Combining Merton-like factor models for credit performance. risk with linear factor models for market risk, we analytically calculate their inter-risk cor- As of this writing, an online monograph is relation and show how inter-risk correlation being created to house the papers. A link to the bounds can be derived. Moreover, we elaborate monograph, when completed, will be found on how our model naturally leads to a Gaussian the ERM Symposium Web site at www.erm- copula approach for describing dependence symposium.org. Papers that were not presented between both risk types. In particular, we sug- at the symposium will also be included in the gest estimators for the correlation parameter of monograph. the Gaussian copula that can be used for general credit portfolios. Finally, we use our findings to We wish to thank all the organizations and com- calculate aggregated risk capital of a sample mittee members for their support and for mak- portfolio both by numerical and analytical ing this year’s Symposium a success. Planning techniques. for the 2009 ERM Symposium call for papers has already begun and I invite you to contact me 2008 Joint Risk Management Section Award if you have ideas or feedback for next year. Until for Practical Risk Management Applications: then, watch the ERM Symposium site for up-to- Donald Pagach and Richard Warr for “An date information about next year’s event. F

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Risk Management Articles Needed for Risk Management Issue No. 13 August 2008 Your help and participation is needed and welcomed. All articles will include a byline to give you full credit for your effort. If you would like to submit an article, please contact Valentina Published by the Society of Actuaries Isakina, editor, at [email protected] or Steve Craighead, co-editor, at 475 N. Martingale Road, Suite 600 Schaumburg, IL 60173-2226 [email protected]. phone: 847.706.3500 fax: 847.706.3599 The next issue of Risk Management will be published: www.soa.org This newsletter is free to section members. Publication Date Submission Deadline Current-year issues are available from the December 2008 September 1, 2008 Communications Department. Back issues of section newsletters have been placed in the SOA library and on the SOA Web site: (www.soa.org). Preferred Format Photocopies of back issues may be requested for a nominal fee. In order to efficiently handle articles, please use the following format when submitting articles: 2007-2008 SECTION LEADERSHIP

Please e-mail your articles as attachments in either MS Word (.doc) or Simple Text (.txt) Editor files. We are able to convert most PC-compatible software packages. Headlines are typed Valentina Isakina upper and lower case. Please use a 10-point Times New Roman font for the body text. e: [email protected] Carriage returns are put in only at the end of paragraphs. The right-hand margin is not Co-Editor justified. Steven Craighead e: [email protected]

If you must submit articles in another manner, please call Kathryn Wiener, (847) 706-3501, Council Members at the Society of Actuaries for help. Ronald Harasym, FSA, CERA, FCIA, MAAA David Gilliland, FSA, FCIA, MAAA Donald Mango, FCAS, MAAA Please send an electronic copy of the article to: Todd Henderson, FSA, CERA, MAAA Steven Craighead, ASA, MAAA Matthew Clark, FSA, MAAA Kevin Dickson, FCAS, MAAA Valentina Isakina, ASA, MAAA Henry M. McMillan, FSA, CERA, MAAA John Nigh, FSA, MAAA Larry H. Rubin, FSA, FCA, MAAA Barbara Snyder, FSA, FCA, MAAA

Society Staff Contacts Robert Wolf, Staff Partner Valentina Isakina, ASA, CFA, MAAA Steven Craighead, ASA, MAAA e: [email protected] Manager Actuarial Consultant Meg Weber, Director, Section Services Bain & Company Towers Perrin e: [email protected] 3280 Peachtree Road NE TSS One Alliance Center 3500 Lenox Road Kathryn Wiener, Staff Editor Atlanta, GA 30305 e: [email protected] phone: 404.846.5206 Suite 900 e-mail: [email protected] Atlanta, GA 30326-4238 Sue Martz, Project Support Specialist phone: 404.365.1287 e: [email protected] e-mail: [email protected] Newsletter Design Judi Riley, Graphic Designer e: [email protected]

Facts and opinions contained herein are the sole responsibility of the persons expressing them and should not be attributed to the Society of Actuaries, its committees, the Risk Management Section 475 N. Martingale Rd., Suite 600 or the employers of the authors. We will promptly correct errors brought to our Schaumburg, IL 60173 attention.