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TRENDS IN PORTFOLIO MANAGEMENT

The State of the Art in Portfolio Modeling

by Charles W. Smithson and Gregory Hayt his is the second of a series of five excerpts from a forth- coming book Managing Credit : Toward a Portfolio T Approach to Management by Charles Smithson and Gregory Hayt of Rutter Associates. Future articles will appear in the May, July/August, and October 2001 issues. quity investors have given level of return or increase an investor might wish to include enthusiastically embraced for a given level a “loser” in the portfolio, as long Ethe concepts of diversifica- of risk. In marked contrast to the as that asset has a very low (or tion and asset allocation. Modern pick-winners philosophy that negative) correlation with other portfolio theory (MPT) has trans- dominated equity investing assets in the portfolio. formed equity portfolio manage- through the 1960s, this means that ment from a philosophy of “pick- ing winners” to one where Figure 1 investors strive to hold an “effi- cient portfolio.” The central fea- The Efficient Frontier—The portfolios that ture of MPT is an efficient portfo- simultaneously maximize expected return for a given level of risk and minimize risk for a lio that simultaneously maximizes given level of expected return expected return for a given level of risk and minimizes risk for a given level of return. Expected Return Recognition of correlation is The “Feasible Set”—All the key to the benefits of holding possible portfolios of securities a well-diversified portfolio. If the returns of two assets are less than perfectly positively correlated, an investor can reduce the risk for a Risk (Standard Deviation) © 2001 by RMA and Rutter Associates. Smithson is managing partner and Hayt is principal at Rutter Associates, a New York-based consultancy. Smithson and Hayt have both presented at RMA conferences and have co- authored other articles in The RMA Journal.

34 The RMA Journal March 2001 The State of the Art in Credit Portfolio Modeling

Challenges to the credit assets have more dimen- to consolidate into a workable cen- Implementation of MPT for sions than equity as well, includ- tral database reflects the tradition- Portfolios of Credit Assets ing uncertain usage of credit lines, al originate-and-hold strategy at While MPT has driven equity uncertain losses in the event of most financial institutions in portfolio management for more , , and the ability which loans are viewed in isolation than 30 years, it is still not widely to restructure assets by changing rather than as part of a portfolio. applied to credit assets. The norm the terms of the lending agree- Another problem area for loans and other credit assets is ment. involves estimates of expected still for a financial institution to In addition, credit portfolio return, risk, and correlation. For originate the asset and then hold it management requires more than a credit assets, these parameters until it matures or defaults. One mean/variance view of the world. are, themselves, determined by reason for this is that portfolios of The credit portfolio manager the (down- credit assets present more chal- places much more emphasis on grade), the volatility of the proba- lenges to the implementation of extreme outcomes—“tail” bility of default (downgrade), loss MPT than do portfolios of equities. events—to determine economic in the event of default, and the capital and . correlation of defaults (or down- Distribution of losses. The grades). As noted earlier, there is mean-variance (that is, normally Data limitations. Arguably, limited data on the historical per- distributed) environment assumed the largest obstacle to the applica- formance of credit assets from by MPT is less justifiable for port- tion of portfolio theory in is which to estimate these parame- folios of credit assets than for the lack of clean, consistent data. ters. However, in the case of portfolios of equities. As is illus- One problem area involves stand-alone measures of the risk trated in Figure 2, the loss distri- the data on existing and new and return of individual , butions for loans and other credit loans. Financial institutions are there is an increasing array of assets are not normally distributed making significant investments in choices. and are not even symmetric. And order to locate data (often still in Figure 3 (next page) provides a there is limited data on the histor- original loan documents), to recon- listing of sources of information on ical performance of credit assets cile different systems, clean and probabilities of default for public from which the appropriate shape validate data, and develop an and private firms. Each of the of the loss distribution could be infrastructure to maintain the data default models uses proprietary estimated. Credit has strong going forward. The fact that data analytics with inputs ranging from -like characteristics, and on credit portfolios is so difficult financial statements alone, to finan- cial statements plus equity market Figure 1 data, and to systems based entirely Losses from Loans and Other Credit Assets on spreads on traded assets. Are Not Normally Distributed Figure 4 summarizes sources for (LGD) and Observed Distribution of Losses usage of committed facilities by defaulting firms. Of course, large financial institutions have consid- erable internal data, if they can Normal Distribution organize it, on these variables. There also are important industry, academic, and commercial studies that have added to our knowledge through the pooling or collecting -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 of data across institutions. Promised Return 100% (No Loss) Loss

35 The State of the Art in Credit Portfolio Modeling

First Generation Credit Portfolio released its CreditMetricsTM 1998. During the same period, Models methodology (and the Credit- many firms had or were develop- The public release of credit ManagerTM software package) in ing internal models for credit portfolio models began in the mid 1997. Also in 1997, Credit Suisse portfolio management. Many of 1990s. KMV released Portfolio First Boston introduced its the internal models addressed ManagerTM in 1993. The CreditRisk+TM . McKinsey intro- assets that were not covered by RiskMetrics Group (RMG) duced CreditPortfolioViewTM in the initial releases of the public models, including middle market Figure 3 corporate lending and consumer lending. Sources of Standalone Risk Estimates for Credit Assets These four models are imple- mentations of three broad Vendor Product Description approaches: KMV Credit Expected Default FrequencyTM Monitor᭨/ (EDF TM ) credit measures for public 1. Asset volatility CreditEdgeTM firms updated monthly/daily. Private approach. The risk of default or ᭨ Firm Model also available. downgrade is modeled in terms of Kamakura KRM—crTM Default probability derived from credit the value of a firm’s assets relative spreads to its liabilities. These models are also called structural models be- Loan Pricing Corporation Risk Rater TM Default probability and expected loss for cause the risk of default/down- commercial loans grade is derived from a formal Moody’s RiskCalcTM Default probabilities for public or private model of credit risk at the firm firms level.

TM Standard & Poor’s CreditPro Historical marginal and cumulative 2. Actuarial approach. The default rates by industry and geography risk of default and the loss given Standard & Poor’s CreditModel TM Implied credit ratings for public or default are assumed to fit certain private firms distributions. This assumption EnronCredit.com Enron Cost of Default probability estimates coupled makes it possible to calculate the Credit TM with historical recovery data distribution of portfolio losses analytically. In some ways, this Figure 4 approach is closest to the original mean/variance approach of Sources of Data on Loss Given Default and Usage of Markowitz, which assumes nor- Committed Lines mally distributed asset returns and yields closed form results for Study or portfolio risk and risk Source Database? Description of Data Altman & Kishore (96) Recovery study Recovery on bonds organized by seniority (Beta). and industry 3. Factor model approach. Carty & Lieberman (96) Default and Recovery data by seniority; Post default The probability of default is (Moody’s) recovery study default secondary market prices assumed to depend on the state of Loan Pricing Corporation Loan Loss Historical loss data for a large sample of such user-defined factors as GDP, credit assets unemployment, commodity S&P/Portfolio Loss/Recovery Historical data for a large sample of prices, and so forth. These models Management Data Database credit assets are quite general in that no under- Asarnow & Marker (95) Study of usage Usage by credit rating and loss given lying theory determines which of committed default factors are most appropriate or credit lines what weights should apply to

36 The RMA Journal March 2001 The State of the Art in Credit Portfolio Modeling changes in each factor. This lack simulated macro factors. In all of default rate volatility. of formal structure makes them the models, the user supplies the The segment allocation and very flexible and extremely trans- expected loss given default to the default rate volatility imply a cor- parent, since the risk of default is model. relation between default rates for linked explicitly to systematic Not surprisingly, the models any pair of obligors. In Credit- variables and a firm-specific com- differ in the way that they deal PortfolioView, default (down- ponent. with the correlation of defaults grade) correlation enters the Figure 5 provides an overview (downgrades). Correlation in model through the correlation of of the four widely-discussed credit Portfolio Manager is obtained by a the chosen macro factors and esti- portfolio models. The first row factor model of asset returns, mated factor weights. For this identifies the approach which, in turn, drives changes in purpose, obligors are grouped into employed—both Portfolio the EDF measures (default prob- industry and geographic segments Manager and CreditManager are abilities) of the obligors. Credit- that share common factors and asset volatility models, Credit- Manager uses a similar idea. weights. Risk+ is an actuarial approach, and Obligors are allocated to different CreditPortfolioView is a factor equity indexes based on geogra- Second Generation Credit model approach. CreditRisk+ is phy and industry. These alloca- Portfolio Models the only credit portfolio model that tions, together with the correla- This year, significant new deals only with default; the others tion of the equity indexes, drive releases of the CreditManager consider both default and down- the correlation of implied asset product from RMG and the grades. The user supplies probabil- values and, ultimately, the correla- Portfolio Manager and Credit ities of default (downgrade) to tion of defaults and downgrades. Monitor products from KMV are CreditManager and CreditRisk+. In CreditRisk+, default correla- expected. In addition to those While Portfolio Manager could use tion is created via two effects: early entrants, credit risk is the any probabilities of default, it is 1. Obligors can be allocated to focus of relatively new products most likely that they would come different segments, with the from and from KMV’s Credit Monitor. In segments themselves being Algorithmics. CreditPortfolioView, the probabili- independent of one another. Web and server-based appli- ties of default are determined by 2. Each obligor is also assigned a cations. The first generations of Figure 5 credit portfolio models were Overview of Four Credit Portfolio Models designed to reside on PCs or worksta- KMV RMG CSFB McKinsey Portfolio CreditMetrics CreditRisk+ CreditPortfolioView tions as stand- Manager (CreditManager) alone applications. While centralized Approach Asset Volatility Asset Volatility Actuarial Model Factor Model applications are Considers effects Both Both Default Only Both still the norm, of default and more products will downgrades? be available either Probability of Endogenous (from Exogenous Exogenous Endogenous over the web or default Credit Monitor) through a or Exogenous client/server link. Loss given default Exogenous Exogenous Exogenous Exogenous KMV’s Credit Correlation Asset Correlation Equity (index) Default correlation Default/migration EdgeTM is accessed via a factor model correlation via a via segments and correlated via macro over the Web and factor model default volatility factor model is targeted at the 37 The State of the Art in Credit Portfolio Modeling active portfolio manager. Users ing assets and the overall distribu- Correlated severity. First- receive EDF and stock price tion of losses. As such, they can generation credit portfolio models information that is updated daily. be used to compare collateral in have treated the uncertainty in The interactive format allows different CDOs and to model the the recovery, or the loss given users to track company-specific . What the first genera- default, as a random variable, but news, set EDF-driven alerts on tion models don’t do well is one that is uncorrelated with the companies in their portfolio, cap- model the risk and return of indi- default rate. However, historical ture current financial data, and be vidual tranches, which depend on data on default rates and recover- informed of corporate filings. the specific rules governing the ies suggests that the distribution RMG’s CreditManager will priority of cashflows, asset tests, of recoveries is different in high be available as a server application hedges, and so forth. default years than it is in low this year. The idea is that First released in 2000, RMG’s default years. It is possible to cap- CreditManager users may, them - CDO Model is specifically ture the dependence between selves, have clients who could designed for originators and default rates and recoveries evi- access the CreditManager model investors in CDOs. To evaluate denced in the data with a credit for their portfolios through the the risk and pricing of specific portfolio model, and it is likely server model. tranches, users describe a transac- that this will become a feature of These Web and server-based tion’s structure (for example, the commercial and proprietary mod- applications reflect, in part, the rules for cash flow allocation and els in the future. Ë increased use of credit models by asset tests) as well as the assets funds and institutional comprising the collateral. The References investors. These clients are more CDO Model departs from the Basel Committee on Banking Supervision, Credit active managers with smaller port- CreditManager approach, because Risk Modeling: Current Practices and Applications, April 1999 (available through folios than banks for which the it models time-to-default over www.bis.org). speed of updates and other inter- multiple periods rather than Frye, John, “Depressing Recoveries,” Risk, active features are likely to have default (or rating change) up to a November 2000. increased value. fixed horizon. KMV has not . Gordy, Michael, “A Comparative Anatomy of released a stand-alone CDO prod- CDOs. Although CDOs are Credit Risk Models,” Journal of Banking & uct but works with clients on a Finance, 24 (2000) 119-149. portfolios of credit assets, they consulting basis to model the spe- have proved difficult to model in Merton, Robert, “On the Pricing of Corporate cific structure of CDO cash flows ,” Journal of Finance, 29 (1974) the first generation of credit mod- using analytic tools developed els. Those models provide relative Saunders, Anthony, Credit Risk Measurement around its Portfolio Manager (Wiley, 1999) risk contributions for the underly- product.

Contribute to the Journal Share your expertise—articles need not focus on the month’s theme.

May 2001: Vindication for Syndiation? September: Rising Stars on the Consumer Front (articles due March 9) (articles due July 6)

June 2001: Risk: Where Is It Hiding Now? Contact Beverly Foster at 215-446-4096 or (articles due April 6) [email protected] July/August 2001: Hire’em, Train’em, Keep’em (articles due May 4)

38 The RMA Journal March 2001