DOCSLIB.ORG

Risk Parity an Alternative Approach to Asset Allocation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Risk Parity an Alternative Approach to Asset Allocation FEATURE Risk Parity An Alternative Approach to Asset Allocation Alexander Pekker, PhD, CFA®, ASA, Meghan P. Elwell, JD, AIFA®, and Robert G. Smith III, CIMC®, AIF® ollowing the financial crisis of tors, traditional RP strategies fall short respectively, but a rather high Sharpe 2008, many members of the of required return targets and leveraged ratio, 0.86. In other words, while the investment management com- RP strategies do not provide enough portfolio is unlikely to meet the expected F munity, including Sage,intensified their potential benefits to outweigh their return target of many institutional inves- scrutiny of mean-variance optimization risks. Instead we advocate a liability- tors (say, 7 percent or higher), its effi- (MVO) and modern portfolio theory based approach that incorporates risk ciency, or “bang for the buck” (i.e., return (MPT) as the bedrock of asset alloca- budgeting, a key theme of RP, as well as per unit of risk, in excess of the risk-free tion (Elwell and Pekker 2010). Among tactical asset allocation. rate), is quite strong. various alternative approaches to asset How does this sample RP portfo- What is Risk Parity? allocation, risk parity (RP) has been in the lio compare with a sample MVO port- news lately (e.g., Nauman 2012; Summers As noted above, an RP portfolio is one folio? A sample MVO portfolio with a 2012), especially as some hedge funds, where risk, defined as standard deviation return target of 7 percent is shown in such as AQR, and large plan sponsors, of returns, is distributed evenly among table 2. Unlike the sample RP portfolio, such as the San Diego County Employees all potential asset classes;1 table 1 shows the MVO portfolio is heavily allocated Retirement Association, have advocated a sample (unleveraged) RP portfolio toward equities, and it has much higher its adoption. based on sample adjusted historical cap- risk and a much lower Sharpe ratio. In The traditional MVO approach con- ital market assumptions.2 Heavily tilted addition, unlike in the sample RP port- structs a portfolio that minimizes total toward fixed income, this portfolio has folio where each asset class is allocated expected risk, defined as standard devi- modest expected return and standard 25 percent of the risk, here, U.S. equities ation of returns, subject to a desired deviation, 5 percent and 5.2 percent, make up the largest portion of the assets return target. Because equities typi- cally have much higher expected returns TABLE 1: SAMPLE (UNLEVERAGED) RISK PARITY PORTFOLIO than other asset classes, they make up Contribution to Contribution to Weight (%) Return (%) Risk (%) the largest portion of an MVO portfolio; as a result (and because they also typi- U.S. Fixed Income 69% 55% 25% cally have higher risk than many other Global Equities 10% 15% 25% asset classes), equities also contribute U.S. Equities 12% 20% 25% the largest share of portfolio risk, often Alternatives 10% 11% 25% more than 80 percent. In contrast, RP Total 100% 100% 100% constructs a portfolio such that all asset Return 5.0% classes contribute equally to portfolio Risk 5.2% risk, with the return determined by this Sharpe Ratio 0.86 allocation. As a result, RP portfolios have a much larger allocation to fixed income TABLE 2: SAMPLE MEAN-VARIANCE OPTIMIZATION PORTFOLIO and a much lower allocation to equities Contribution to Contribution to than MVO portfolios. Not surprisingly, Weight (%) Return (%) Risk (%) then, RP portfolios generally have lower U.S. Fixed Income 28% 16% 1% risk and lower return than MVO portfo- Global Equities 10% 11% 14% lios, unless leverage is allowed. U.S. Equities 57% 69% 81% In this article, we address some of the Alternatives 5% 4% 4% key issues associated with RP strategies, Total 100% 100% 100% including efficiency, leverage, imple- Return 7.0% mentation, past performance, and the Risk 10.5% impact of rising interest rates. We con- clude that, for most institutional inves- Sharpe Ratio 0.62 July/August 2013 23 © 2013 Investment Management Consultants Association. Reprint with permission only. FEATURE Practical Considerations and constitute 81 percent of the risk. depends on a key assumption, namely Thus, the sample MVO portfolio, while that funds can be consistently borrowed The first consideration in implementing achieving the desired return target, is at a relatively stable low rate. If this RP is the same one that befalls MVO: more risky and less efficient than the assumption is violated to a high enough its reliance on asset risk and correla- sample RP portfolio. degree, RP is no longer as appealing. tions estimates, either ex post or ex ante, As noted above, despite its high Indeed, in reality the cost of leverage which may or may not be at all indica- Sharpe ratio, the sample RP portfolio is varies. Market volatility, the amount bor- tive of the future. Each provider of not very attractive to most institutional rowed, the low quality of the underlying a RP strategy will use different methods investors—its expected return is just collateral, and rising overall levels to determine these parameters too low. However, by introducing lever- of interest rates are all factors that are (e.g., indexes corresponding to asset age, RP can be adjusted to reach the likely to increase borrowing costs. In par- classes, observation-period length, required return target, making it more ticular, the impact of market volatility on observation frequency, potential incor- competitive with an MVO portfolio. leveraged RP portfolios cannot be under- poration of correlations, forward-look- estimated. In times of extreme market ing adjustments, etc.), leading to some Leverage and Its Risks stress (such as the financial crisis of nontrivial variations in asset allocations To bring the sample RP portfolio to a 2008), the cost of borrowing rises sharply between RP strategies. Indeed, it’s gen- return target of 7 percent while main- while liquidity generally plummets. In erally well-known that small variations taining the same equal risk decomposi- such an environment, asset returns fall in risk assumptions, including correla- tion among asset classes, leverage must far below borrowing costs, and the fund tions, probably the most elusive MPT be employed. Assuming that the cost of may have to sell assets (if it can, given assumption to estimate, can lead to borrowing is fixed at 1 percent (or 0.5 the illiquidity of the markets) at inoppor- large variations in optimal asset alloca- percent above cash), the required lever- tune prices to meet margin and collateral tion (e.g., Elwell and Pekker 2010). This age is 49 percent (1.49 × 5.2% – 0.49 × requirements. This lose-lose proposition, unfortunate and inescapable variation in 1.0% = 7.0%). As table 3 shows, relative while seemingly remote, is an important parameters is at the root of all asset to the sample unleveraged RP portfolio, risk to keep in mind whenever borrowing allocations based on MPT. the Sharpe ratio is slightly lower, 0.83 vs. is involved, especially at such a high level The second consideration in imple- 0.86, but it is still much higher than that (almost half of the assets). menting RP is rebalancing. Typically RP of the sample MVO portfolio; in addi- Leverage often comes with other portfolios are rebalanced monthly or tion, the volatility of the sample lever- risks and costs as well. For example, quarterly based on risk parameters aged RP portfolio, 7.8 percent, is much while government bonds can be lev- computed over rolling time periods lower than that of the MVO portfolio. eraged through bond futures (which (e.g., rolling three-year periods). Thus Clearly, with its return equal to are traded on an exchange and con- RP rebalancing is typically more fre- that of the MVO portfolio and a lower sequently have virtually no counter- quent and involves greater dollar risk and greater efficiency (i.e., higher party risk and little basis risk), leverag- amounts than traditional strategies, Sharpe ratio) than the sample MVO ing other asset classes potentially would leading to higher transaction costs. portfolio, the sample leveraged RP port- require some kind of swap, introducing Occasionally, rebalancing may be folio becomes more appealing to insti- counterparty risk, basis risk, and addi- impossible due to lack of liquidity asso- tutional investors. All this analysis tional implementation costs. ciated with some alternative assets (e.g., hedge funds with lock-up peri- TABLE 3: SAMPLE LEVERAGED RISK PARITY PORTFOLIO ods or illiquid real estate), thus unravel- Contribution to Contribution to ing (at least in part) the whole premise Weight (%) Return (%) Risk (%) of RP. Moreover, if RP involves multiple U.S. Fixed Income 102% 4.1% 25% asset managers (e.g., specialists by asset Global Equities 15% 1.1% 25% class), the coordination of leverage and U.S. Equities 18% 1.5% 25% rebalancing across asset classes may be Alternatives 15% 0.8% 25% particularly cumbersome. Leverage –49% –0.5% 0% Finally, in today’s low-interest-rate Total 100% 7.0% 100% environment, RP requires extra scrutiny because of its high allocation to fixed Return 7.0% income and, in the case of leveraged Risk 7.8% RP, borrowing costs, both of which are Sharpe Ratio 0.83 closely tied to interest rates. This consid- 24 Investments&Wealth MONITOR © 2013 Investment Management Consultants Association. Reprint with permission only. FEATURE eration once again reveals the key draw- FIGURE 1: RANGE OF 1-YEAR RETURNS FOR UNLEVERAGED RP, LEVERAGED back of using MPT to construct asset RP, AND MVO PORTFOLIOS, ASSUMING INTEREST RATES RISE BY 1 PERCENT allocations: It is based on long-term 25% risk/return assumptions, not on current market conditions, economic outlook, or expectations for interest-rate shifts (and their impacts on asset returns).
Load more

Recommended publications
  • Hedge Performance: Insurer Market Penetration and Basis Risk
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Research Papers in Economics This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: The Financing of Catastrophe Risk Volume Author/Editor: Kenneth A. Froot, editor Volume Publisher: University of Chicago Press Volume ISBN: 0-226-26623-0 Volume URL: http://www.nber.org/books/froo99-1 Publication Date: January 1999 Chapter Title: Index Hedge Performance: Insurer Market Penetration and Basis Risk Chapter Author: John Major Chapter URL: http://www.nber.org/chapters/c7956 Chapter pages in book: (p. 391 - 432) 10 Index Hedge Performance: Insurer Market Penetration and Basis Risk John A. Major Index-based financial instruments bring transparency and efficiency to both sides of risk transfer, to investor and hedger alike. Unfortunately, to the extent that an index is anonymous and commoditized, it cannot correlate perfectly with a specific portfolio. Thus, hedging with index-based financial instruments brings with it basis risk. The result is “significant practical and philosophical barriers” to the financing of propertykasualty catastrophe risks by means of catastrophe derivatives (Foppert 1993). This study explores the basis risk be- tween catastrophe futures and portfolios of insured homeowners’ building risks subject to the hurricane peril.’ A concrete example of the influence of market penetration on basis risk can be seen in figures 10.1-10.3. Figure 10.1 is a map of the Miami, Florida, vicin- John A. Major is senior vice president at Guy Carpenter and Company, Inc. He is an Associate of the Society of Actuaries.
    [Show full text]
  • ABSTRACT LUCY, ZACHARY MARC. Analysis of Fixed Volume Swaps For
    ABSTRACT LUCY, ZACHARY MARC. Analysis of Fixed Volume Swaps for Hedging Financial Risk at Large-Scale Wind Projects (Under the direction of Dr. Jordan Kern). Large scale wind power projects are increasingly selling power directly into wholesale electricity markets without the benefits of stable (fixed price) off-take agreements. As a result, many wind power producers are incentivized to use financial hedging contracts to mitigate exposure to price risk. One particular hedging contract - the “fixed volume price swap” - has gained prevalence, but it poses several liabilities for wind power producers that reduce its effectiveness. In this paper, we explore problems associated with fixed volume swaps and examine two different interventions to improve contract performance for wind power producers. Using a hypothetical wind power project in the Southwest Power Pool (SPP) market as a case study, we first look at how “shape risk” (an imbalance between actual wind power production and hourly production targets specified by contract terms) negatively impacts contract performance and whether this could be remedied through improved contract design. Using a multi-objective optimization algorithm, we find examples of alternative contract parameters (hourly wind power production targets) that are more effective at increasing revenues during low performing months and do so at a lower cost than conventional fixed volume swaps. Then we examine how “basis risk” (a discrepancy in market prices between the “node” where the wind project injects power into the grid, and the regional hub price) can negatively impact contract performance. We statistically manipulate basis risk as a proxy for the effects of increased transmission and its effect on contract performance.
    [Show full text]
  • CAIA Member Contribution Long Term Investors, Tail Risk Hedging, And
    CAIA Member Contribution Long Term Investors, Tail Risk Hedging, and the Role of Global Macro in Institutional Andrew Rozanov, CAIA Portfolios Managing Director, Head of Permal Sovereign Advisory 24 Alternative Investment Analyst Review Long Term Investors 1. Introduction This paper focuses on two related topics: the tension between the fundamental premise of long-term investing and the post-crisis pressure to mitigate tail risks; and new approaches to asset allocation and the potential role of global macro strategies in institutional portfolios. To really understand why these issues are increasingly coming to the fore, it is important to recall the sheer magnitude of losses suffered by sovereign wealth funds and other long-term investors at the peak of the recent financial crisis and to appreciate how shocked they were to see large double-digit percentage drops, not only in their own portfolios, but also in portfolios of institutions that many of them were looking to as potential role models, namely the likes of Yale and Harvard university endowments. Losses for many broadly diversified, multi-asset class portfolios ranged anywhere from 20% to 30% in the course of just a few months. In one of the better publicized cases, Norway’s sovereign fund lost more than 23%, or in dollar equivalent more than $96 billion, an amount that at the time constituted their entire accumulated investment returns since inception in 1996. Some of the longer standing sovereign wealth funds in Asia and the Middle East, which had long invested in a wide range of alternative asset classes such as private equity, real estate and hedge funds, are rumoured to have done even worse in that infamous year.
    [Show full text]
  • Hedging in the Portfolio Theory Framework: a Note
    UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN 330K3TA.CK3 Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/hedginginportfol1331park BEBR FACULTY WORKING PAPER NO. 1331 u.\, Hedging in the Portfolio Theory Framework: A Note Hun Y. Park College of Commerce and Business Administration Bureau of Economic and Business Research University of Illinois, Urbana-Champaign BEBR FACULTY WORKING PAPER NO. 1331 College of Commerce and Business Administration University of Illinois at Urbana-Champaign February 1987 Hedging in the Portfolio Theory Framework: A Note Hun Y. Park, Professor Department of Finance Hedging in the Portfolio Theory Framework: A Note Howard and D T Antonio (1984) developed the hedge ratio and the measure of hedging effectiveness of futures contracts in the framework. of what they called the modern portfolio theory. This note shows that the H-D analysis is misleading and not consistent with the portfolio theory. For the comparison purpose, an alternative and simpler hedge ratio and measure of hedging effectiveness of futures is developed which is consistent with the portfolio theory. Hedging in the Portfolio Theory Framework: A Note Hun Y. Park I. Introduction The key to any hedging strategy using futures contracts is a knowl- edge of the hedge ratio, i.e., the number of futures per spot position. The most common method to estimate the hedge ratio using futures contracts is the regression approach relating changes in cash prices to changes in futures prices. Inherent in the regression is the assumption that the optimal combination of cash position with futures is the one whose variance is minimized.
    [Show full text]
  • Economic Aspects of Securitization of Risk
    ECONOMIC ASPECTS OF SECURITIZATION OF RISK BY SAMUEL H. COX, JOSEPH R. FAIRCHILD AND HAL W. PEDERSEN ABSTRACT This paper explains securitization of insurance risk by describing its essential components and its economic rationale. We use examples and describe recent securitization transactions. We explore the key ideas without abstract mathematics. Insurance-based securitizations improve opportunities for all investors. Relative to traditional reinsurance, securitizations provide larger amounts of coverage and more innovative contract terms. KEYWORDS Securitization, catastrophe risk bonds, reinsurance, retention, incomplete markets. 1. INTRODUCTION This paper explains securitization of risk with an emphasis on risks that are usually considered insurable risks. We discuss the economic rationale for securitization of assets and liabilities and we provide examples of each type of securitization. We also provide economic axguments for continued future insurance-risk securitization activity. An appendix indicates some of the issues involved in pricing insurance risk securitizations. We do not develop specific pricing results. Pricing techniques are complicated by the fact that, in general, insurance-risk based securities do not have unique prices based on axbitrage-free pricing considerations alone. The technical reason for this is that the most interesting insurance risk securitizations reside in incomplete markets. A market is said to be complete if every pattern of cash flows can be replicated by some portfolio of securities that are traded in the market. The payoffs from insurance-based securities, whose cash flows may depend on Please address all correspondence to Hal Pedersen. ASTIN BULLETIN. Vol. 30. No L 2000, pp 157-193 158 SAMUEL H. COX, JOSEPH R. FAIRCHILD AND HAL W.
    [Show full text]
  • Two Harbors Investment Corp
    Two Harbors Investment Corp. Webinar Series October 2013 Fundamental Concepts in Hedging Welcoming Remarks William Roth Chief Investment Officer July Hugen Director of Investor Relations 2 Safe Harbor Statement Forward-Looking Statements This presentation includes “forward-looking statements” within the meaning of the safe harbor provisions of the United States Private Securities Litigation Reform Act of 1995. Actual results may differ from expectations, estimates and projections and, consequently, readers should not rely on these forward-looking statements as predictions of future events. Words such as “expect,” “target,” “assume,” “estimate,” “project,” “budget,” “forecast,” “anticipate,” “intend,” “plan,” “may,” “will,” “could,” “should,” “believe,” “predicts,” “potential,” “continue,” and similar expressions are intended to identify such forward-looking statements. These forward-looking statements involve significant risks and uncertainties that could cause actual results to differ materially from expected results. Factors that could cause actual results to differ include, but are not limited to, higher than expected operating costs, changes in prepayment speeds of mortgages underlying our residential mortgage-backed securities, the rates of default or decreased recovery on the mortgages underlying our non-Agency securities, failure to recover certain losses that are expected to be temporary, changes in interest rates or the availability of financing, the impact of new legislation or regulatory changes on our operations, the impact
    [Show full text]
  • Value at Risk: Philippe Jorion
    VALUE AT RISK: The New Benchmark for Managing Financial Risk THIRD EDITION Answer Key to End-of-Chapter Exercises PHILIPPE JORION McGraw-Hill c 2006 Philippe Jorion ° VAR: Answer Key to End-of-Chapter Exercises c P.Jorion 1 ° Chapter 1: The Need for Risk Management 1. A depreciation of the exchange rate, scenario (a), is an example of financial market risk, which can be hedged. Scenario (2) is an example of a business risk, because it could have been avoided by better business decisions. Scenario (3) is a broader type of risk, which is strategic. 2. This is incorrect. Financial risks are related. An increase in oil prices could push down the stock prices of companies that are hurt by higher oil costs. 3. This is incorrect. Casinos create risk. Financial markets do not create risk. Instead, market prices fluctuations are coming from a variety of sources, including effects of company policies, government policies, or other events. In fact, financial markets can be used to hedge, transfer, or manage risks. 4. A derivative contract is a private contract deriving its value from some underlying asset price, reference rate, or index, such as stock, bond, currency, or commodity. For example, a forward contract on a foreign currency is a form of a derivative. Derivatives are instruments designed to manage financial risks efficiently. 5. Exchange-traded instruments include interest rate futures and options, currency fu- tures and options, and stock index futures and options. OTC instruments include interest rate swaps, currency swaps, caps, collars, floors and swaptions. 6. Derivatives are typically leveraged instruments.
    [Show full text]
  • Electricity Derivatives and Risk Management S.J
    Energy 31 (2006) 940–953 www.elsevier.com/locate/energy Electricity derivatives and risk management S.J. Denga,*, S.S. Orenb aSchool of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA bDepartment of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA Abstract Electricity spot prices in the emerging power markets are volatile, a consequence of the unique physical attributes of electricity production and distribution. Uncontrolled exposure to market price risks can lead to devastating consequences for market participants in the restructured electricity industry. Lessons learned from the financial markets suggest that financial derivatives, when well understood and properly utilized, are beneficial to the sharing and controlling of undesired risks through properly structured hedging strategies. We review different types of electricity financial instruments and the general methodology for utilizing and pricing such instruments. In particular, we highlight the roles of these electricity derivatives in mitigating market risks and structuring hedging strategies for generators, load serving entities, and power marketers in various risk management applications. Finally, we conclude by pointing out the existing challenges in current electricity markets for increasing the breadth, liquidity and use of electricity derivatives for achieving economic efficiency. q 2005 Elsevier Ltd. All rights reserved. 1. Introduction Electricity spot prices are volatile due to the unique physical attributes of electricity such as non- storability, uncertain and inelastic demand and a steep supply function. Uncontrolled exposure to market price risks could lead to devastating consequences. During the summer of 1998, wholesale power prices in the Midwest of US surged to a stunning $7000 per MWh from the ormal price range of $30–$60 per MWh, causing the defaults of two power marketers in the east coast.
    [Show full text]
  • Regulatory Capital Requirements for European Banks
    Regulatory Capital Requirements for European Banks Implications of Changing Markets and a New Regulatory Environment July 2009 Table of Contents Chapter 1 – Basics Key Concepts 8 Introduction 10 Basel I Capital Charges 11 Basel II Overview 12 Scope of Application 12 Types of Banks 13 Implementation and Timing 14 IRB Transition Period 15 Basel II – Three Pillars 16 Components of Regulatory Capital 17 Types of Eligible Capital and Provisions 18 Criteria for Recognition of External Ratings 19 Chapter 2 – Capital charges (Pillar 1) Sample Bank 21 Sovereign Exposures 22 Bank Exposures 25 2 Table of Contents (cont’d) Chapter 2 – Capital charges (cont’d) Corporate Exposures 28 Retail Exposures 36 Real Estate Exposures 39 Covered Bonds 43 Specialised Lending 45 Equity 46 Funds 48 Off-Balance Sheet Items 54 Securitisation Exposures 56 Operational Requirements 57 Proposed CRD Amendment – “Significant Credit Risk Transfer” 59 Standardised Banks 61 Ratings Based Approach 61 Most Senior Exposures; second loss positions or better 61 Liquidity Facilities 62 Overlapping Exposures 64 3 Table of Contents (cont’d) Chapter 2 – Capital charges (cont’d) Securitisation Exposures (cont’d) IRB Banks 65 Ratings Based Approach 65 Hierarchy 65 Internal Assessments Approach 67 Supervisory Formula Approach 70 Liquidity Facilities 74 Top-Down Approach 75 Rules for Purchased Corporate Receivables 76 Inferred Ratings 79 BIS Re-securitisation Proposals 80 CRD Retention Rules 83 BIS Other Securitisation Proposals 88 Credit Risk
    [Show full text]
  • Optimal Hedging with Basis Risk Under Mean-Variance Criterion
    Optimal Hedging with Basis Risk under Mean-Variance Criterion Jingong Zhang, Ken Seng Tan, Chengguo Weng∗ Department of Statistics and Actuarial Science University of Waterloo Abstract Basis risk occurs naturally in a number of financial and insurance risk management problems. A notable example is in the context of hedging a derivative when the underlying security is either non-tradable or not sufficiently liquid. Other examples include hedg- ing longevity risk using index-based longevity instrument and hedging crop yields using weather derivatives. These applications give rise to basis risk and it is imperative that such a risk needs to be taken into consideration for the adopted hedging strategy. In this paper, we consider the problem of hedging a European option using another correlated and liq- uidly traded asset and we investigate an optimal construction of hedging portfolio involving such an asset. The mean-variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure tech- nique. A closed-form optimal control process is obtained under a general diffusion model. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general European options with basis risk under the mean-variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk. ∗Corresponding author.
    [Show full text]
  • Option Pricing and Hedging in the Presence of Basis Risk
    EDHEC-Risk Institute 393-400 promenade des Anglais 06202 Nice Cedex 3 Tel.: +33 (0)4 93 18 32 53 E-mail: [email protected] Web: www.edhec-risk.com Option Pricing and Hedging in the Presence of Basis Risk February 2011 Lionel Martellini Professor of finance, EDHEC Business School and scientific director, EDHEC-Risk Institute Vincent Milhau Research engineer, EDHEC-Risk Institute with the support of Abstract This paper addresses the problem of option hedging and pricing when a futures contract, written either on the underlying asset or on some imperfectly correlated substitute for the underlying asset, is used in the dynamic replication of the option payoff. In the presence of unspanned basis risk modeled as a Brownian bridge process, which explicitly accounts for the convergence of the basis to zero as the futures contract approaches maturity, we are able to obtain an analytical expression for the optimal hedging strategy and corresponding option price. Empirical analysis suggests that the hedging demand against basis risk is an important ingredient of the hedging strategy. For reasonable parameter values, we also find the replication error implied by the optimal strategy to be substantially lower than that implied by heuristic strategies routinely used in practice. JEL code: G13. This research has benefited from the support of the Chair “Produits Structurés et Produits Dérivés", Fédération Bancaire Française. It is a pleasure to thank Michel Crouhy, Stephen Figlewski, Terry Marsh, Mark Rubinstein, Stephane Tyc and Branko Urosevic for very useful comments, Romain Deguest and Andrea Tarelli for excellent research assistance, and Hilary Till for her help in collecting index futures return data.
    [Show full text]
  • The Application of Basel II to Trading Activities and the Treatment of Double Default Effects
    Basel Committee on Banking Supervision The Application of Basel II to Trading Activities and the Treatment of Double Default Effects July 2005 Requests for copies of publications, or for additions/changes to the mailing list, should be sent to: Bank for International Settlements Press & Communications CH-4002 Basel, Switzerland E-mail: [email protected] Fax: +41 61 280 9100 and +41 61 280 8100 © Bank for International Settlements 2005. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISBN print: 92-9131-682-2 ISBN web: 92-9197-682-2 Table of Contents Introduction...............................................................................................................................1 I. Introduction......................................................................................................................3 II. Common aspects of the three measures of exposure for CCR.......................................4 A. Characteristics of instruments subject to a CCR-related capital charge ................4 B. Measures of CCR: Expected Positive Exposure, Expected Exposure, and Potential Future Exposure......................................................................................4 C. Relationship with the Revised Framework text on credit risk mitigation ................5 D. Netting sets ............................................................................................................5 E. Cross-product netting.............................................................................................6
    [Show full text]