DOCSLIB.ORG

The Market Risk Premium: Expectational Estimates Using Analysts' Forecasts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

The Market Risk Premium: Expectational Estimates Using Analysts' Forecasts Robert S. Harris and Felicia C. Marston Us ing expectatwnal data from f711a11cial a 11 a~r.11s. we e~ t ima t e a market risk premium for US stocks. Using the S&P 500 a.1 a pro1·1•.fin· the market portfolio. the Lll'erage market risk premium i.lfound to be 7. 14% abo1·e yields on /o11g-ter111 US go1·ern 111 e11t honds m·er the period I 982-l 99X. This ri~k premium 1•aries over time; much oft his 1·aria1io11 can he explained by either I he /e1 1el ofi11teres1 mies or readily availahle fonrard-looking proxies for ri.~k . Th e marke1 ri.1k p remium appears to 111 onz inversely with gol'ern111 e11 t interes1 ra/es .rngges1i11g Iha/ required rerurns 011 .~locks are more stable than interest rates themse!Pes. {JEL: GJI. G l 2] Sfhc notion of a market ri sk premium (th e spread choice has some appealing chara cteri sti cs but is between in vestor required returns on safe and average subject to many arb itrary assumptions such as the ri sk assets) has long played a central rol e in finance. 11 releva nt period for tak in g an average. Compound ing is a key factor in asset allocation decisions to determine the difficulty or usi ng historical returns is the we ll the portfolio mi x of debt and equity instruments. noted fa ct that stand ard model s or consum er choice Moreover, the market ri sk premium plays a critica l ro le would predi ct much lower spreads between equity and in th e Capital Asset Pricing Model (CAPM ), the most debt returns than have occurred in US markets- the widely used means of estimating equity hurdle rates by so ca lled equity risk premium puzzle (sec Welch, 2000 practitioners. In recent years, the practical signifi ca nce and Siegel and Thaler, 1997). ln addition. theory call s of estimating such a market premium has increased as fo r a forward-l ook in g risk pre mium th at could well firms, financi al analysts. and in vestors empl oy fin ancial change over time. fram eworks to analyze corporate and in vestment This paper takes an alternate approach by usin g pe rform ance. For in s tance. th e increased use of expectational data to estimate the market risk premium. Economi c Value Added (EVA') to assess corp orate The a pproach has two major advantages for prac titioners. First, it provides a n independ ent performance has provided a new impetus for estimating estimate that can be compared to historical averages. capital costs. Al a minimum. this can help in understanding likely The most prevalent approach to estimating the market ranges for risk premi a. ccond, expectati onal data al low ri sk premium relies on some average of the historical in vestigation of changes in risk premia over time. uch spread between returns on stocks and bonds. 1 This time variations in risk premia serve as important signal s from investors th at should affect a host of financia l ·Robcn S. lla rr i ~ is 1he C. Ste\\ an Sheppard Professor of Business decisions. Th is paper provides new te ts of whether Administration and l·chcia C. Ma rston 1, an Associate l'mfcs,or changes in ri k premia over time are li nked 10 forward­ a1 1hc Uni' crsi1y of Vi rg in ia. Charlo1tcsv11lc. VA 22906. looking measures of ri sk. Specifica ll y, we look at the The a uthors tha nk Eri k Bcnrud. a n ano nymous re\ icwcr. and ,cmin a r participants a l the Universi ty or Vi rgi n ia. th e 113 run.:r. Ea des. Ha rris. a nd Higgins ( 1998) pro1 idc suncy University of Con nec tic ut and a 1 the SEC for co m ment~. c1 idene.: on hoth te\thuo1' advice and prac11110ncr 111c1hods T ha n!..;, to Darden Sponsors. TVA. the Walker Family Fund, for es11n1:11111g c.:a1lital eos1s. As tcs1:1n11.:n1 10 1hc market for and Mcintire A~'ociatco, for sup port t•I' this research and 10 cost of c;1p11al estimmc'. lbho1,on Assm:1a1cs ( 1998) publishes IBF.S, Inc. fo r s upplying data. a "( 0,1 of Capital Quarterly.'' 6 OPC 002716 FPL RC-16 HARRIS & MARSTON-THE MARKET RISK PREMIUM 7 relationship between the risk premium and four ex­ et al. ( 1998) point out, few respondents cited use of ante measures of ri sk: the spread between yields on expectational data to supplement or replace hi storical corporate and government bonds, consumer sentiment ret urns in estimating the market premium. about future economic conditions, the average leve l Survey evidence also shows substantial variation or dispersion across analysts as they forecast in empirical es tim ates. When respondents gave a corporate earnings. and the implied volatility on the precise estimate of th e market premium, they cited S& P500 In dex derived from options data. figures from 4% to over 7% (Bruner et al., 1998). A Section I provides background on the estimation of quote from a survey respondent highl ights the range equity required returns and a brief di sc ussion of in practice. " In 1993, we polled various investment current practice in estimating the market ri sk premium. banks and academic studies on the issue as to th e In Section II , models and data are discussed. Following appropriate rate and got anywhere between 2 and 8%, a comparison of the results to historical returns in but mos t we re between 6% and 7.4%." (Bruner et al.. Secti on 111. we examine the time-series characteristics I 998 ). An informal sampling of current practice also of the estimated market premium in Section IV. Finally, reveals la rge differences in assumptions about an conclusions are offered in Section V. appropriate market premium. For instance, in a 1999 application o f EVA analysis, Goldman Sachs I. Background In vestment Research specifics a market risk premium of"3% from 1994-1997 and 3.5% from I 998- l 999E for The notion of a ··market" required rate of return is a the S&P lndustrials" (Goldman Sachs, 1999). At the conveni ent and widely used construct. Such a rate (k) same time, an April 1999 phone call to Stern Stewart is the minimum level of expected return necessary to re vea led that their own applicati on of EVA typically compensate investors for bearing the average risk of employed a market risk premium of6%. In its application equity investments and receiving dollars in the future of the CAPM. Ibbotson Associates ( 1998) uses a market rather than in the present. In general. k wi ll depend on risk premium of7.8%. Nol surprisingly, academics do not returns available on a lternative investments (e.g., agree on the ri sk premium either. Welch (2000) surveyed bonds). To isolate the effects of ri sk, it is useful to leadin g financial economists at major universiti es. For a work in terms of a market risk premium (rp), defined as J O-year horizon, he found a mean ri sk premium of 7. I% but a range from 1.5% to 15% with an interquartile range Ip = k - i, ( I ) of2.4% (based on 226 responses). To provide additional insight on estimates of the where i = required return fo r a zero ri sk in ve tment. market premium , we use publicly avail able Lacking a superior alternati ve, in vestigators often expectational data. This expectational approach use averages of hi storical reali za tio ns to estimate a employs the di vidend growth model (hereafter referred market risk premium. Bruner. Eades. Harris, and Higgins to as the discounted cash now (DCF) model) in which ( 1998) provide recent_s urvey results on best practices a consensus measure of financial analysts' forecasts by corporati ons and financial advisors. While almost (FAF) of earnings is used as a proxy for in vestor all respondents used some average of past data in expectations. Earlier work has used FAF in DCF mode l s ~ estimatinu a market risk premium. a wide range of but generall y has covered a span of only a few years approaches emerged. "While most of our 27 sample due to data avai la bi lity. compan ies appear to use a 60+ year hi stori cal peri od to estimate returns, one cited a window of less than II. Models and Data ten years, two cited windows of about ten years, one began averaging with 1960, and another with 1952 data" The simplest and most commonl y used version of (p. 22). Some used arithmetic averages. and some used the DCF model is employed to estimate shareholders' geometric. Thi s hi stori cal approach requires the required rate of return, k, as shown in Equation (2): assumptions that past reali zati ons are a good surrogate for future expectations and, as typically app li ed. that th e risk premium is constant over tim e. Carl eton and :sec Malkicl ( 1982), Orighum, V in ~o n. an d Shorn.: ( 1985), Lakoni shok ( 1985) demonstrate empirica lly some of the Harris ( 1986), a nd Ha rris and Ma rston ( 1992). The DCF problems wit h such historical premia when th ey are approach w ith analysis· forecasts has been used frequently in disaggregated fo r different time periods or groups of reg ulator) settings.
Recommended publications
  • Basel III: Post-Crisis Reforms

    Basel III: Post-Crisis Reforms

    Basel III: Post-Crisis Reforms Implementation Timeline Focus: Capital Definitions, Capital Focus: Capital Requirements Buffers and Liquidity Requirements Basel lll 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 1 January 2022 Full implementation of: 1. Revised standardised approach for credit risk; 2. Revised IRB framework; 1 January 3. Revised CVA framework; 1 January 1 January 1 January 1 January 1 January 2018 4. Revised operational risk framework; 2027 5. Revised market risk framework (Fundamental Review of 2023 2024 2025 2026 Full implementation of Leverage Trading Book); and Output 6. Leverage Ratio (revised exposure definition). Output Output Output Output Ratio (Existing exposure floor: Transitional implementation floor: 55% floor: 60% floor: 65% floor: 70% definition) Output floor: 50% 72.5% Capital Ratios 0% - 2.5% 0% - 2.5% Countercyclical 0% - 2.5% 2.5% Buffer 2.5% Conservation 2.5% Buffer 8% 6% Minimum Capital 4.5% Requirement Core Equity Tier 1 (CET 1) Tier 1 (T1) Total Capital (Tier 1 + Tier 2) Standardised Approach for Credit Risk New Categories of Revisions to the Existing Standardised Approach Exposures • Exposures to Banks • Exposure to Covered Bonds Bank exposures will be risk-weighted based on either the External Credit Risk Assessment Approach (ECRA) or Standardised Credit Risk Rated covered bonds will be risk Assessment Approach (SCRA). Banks are to apply ECRA where regulators do allow the use of external ratings for regulatory purposes and weighted based on issue SCRA for regulators that don’t. specific rating while risk weights for unrated covered bonds will • Exposures to Multilateral Development Banks (MDBs) be inferred from the issuer’s For exposures that do not fulfil the eligibility criteria, risk weights are to be determined by either SCRA or ECRA.
  • Revised Standards for Minimum Capital Requirements for Market Risk by the Basel Committee on Banking Supervision (“The Committee”)

    Revised Standards for Minimum Capital Requirements for Market Risk by the Basel Committee on Banking Supervision (“The Committee”)

    A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Basel Committee on Banking Supervision STANDARDS Minimum capital requirements for market risk January 2016 A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf This publication is available on the BIS website (www.bis.org). © Bank for International Settlements 2015. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISBN 978-92-9197-399-6 (print) ISBN 978-92-9197-416-0 (online) A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Minimum capital requirements for Market Risk Contents Preamble ............................................................................................................................................................................................... 5 Minimum capital requirements for market risk ..................................................................................................................... 5 A. The boundary between the trading book and banking book and the scope of application of the minimum capital requirements for market risk ........................................................................................................... 5 1. Scope of application and methods of measuring market risk ...................................................................... 5 2. Definition of the trading book ..................................................................................................................................
  • Capital Adequacy Requirements (CAR)

    Capital Adequacy Requirements (CAR)

    Guideline Subject: Capital Adequacy Requirements (CAR) Chapter 3 – Credit Risk – Standardized Approach Effective Date: November 2017 / January 20181 The Capital Adequacy Requirements (CAR) for banks (including federal credit unions), bank holding companies, federally regulated trust companies, federally regulated loan companies and cooperative retail associations are set out in nine chapters, each of which has been issued as a separate document. This document, Chapter 3 – Credit Risk – Standardized Approach, should be read in conjunction with the other CAR chapters which include: Chapter 1 Overview Chapter 2 Definition of Capital Chapter 3 Credit Risk – Standardized Approach Chapter 4 Settlement and Counterparty Risk Chapter 5 Credit Risk Mitigation Chapter 6 Credit Risk- Internal Ratings Based Approach Chapter 7 Structured Credit Products Chapter 8 Operational Risk Chapter 9 Market Risk 1 For institutions with a fiscal year ending October 31 or December 31, respectively Banks/BHC/T&L/CRA Credit Risk-Standardized Approach November 2017 Chapter 3 - Page 1 Table of Contents 3.1. Risk Weight Categories ............................................................................................. 4 3.1.1. Claims on sovereigns ............................................................................... 4 3.1.2. Claims on unrated sovereigns ................................................................. 5 3.1.3. Claims on non-central government public sector entities (PSEs) ........... 5 3.1.4. Claims on multilateral development banks (MDBs)
  • Legal Risk Section 2070.1

    Legal Risk Section 2070.1

    Legal Risk Section 2070.1 An institution’s trading and capital-markets will prove unenforceable. Many trading activi- activities can lead to significant legal risks. ties, such as securities trading, commonly take Failure to correctly document transactions can place without a signed agreement, as each indi- result in legal disputes with counterparties over vidual transaction generally settles within a very the terms of the agreement. Even if adequately short time after the trade. The trade confirma- documented, agreements may prove to be unen- tions generally provide sufficient documentation forceable if the counterparty does not have the for these transactions, which settle in accor- authority to enter into the transaction or if the dance with market conventions. Other trading terms of the agreement are not in accordance activities involving longer-term, more complex with applicable law. Alternatively, the agree- transactions may necessitate more comprehen- ment may be challenged on the grounds that the sive and detailed documentation. Such documen- transaction is not suitable for the counterparty, tation ensures that the institution and its coun- given its level of financial sophistication, finan- terparty agree on the terms applicable to the cial condition, or investment objectives, or on transaction. In addition, documentation satisfies the grounds that the risks of the transaction were other legal requirements, such as the ‘‘statutes of not accurately and completely disclosed to the frauds’’ that may apply in many jurisdictions. investor. Statutes of frauds generally require signed, writ- As part of sound risk management, institu- ten agreements for certain classes of contracts, tions should take steps to guard themselves such as agreements with a duration of more than against legal risk.
  • Minimum Capital Requirements for Market Risk

    Minimum Capital Requirements for Market Risk

    This standard has been integrated into the consolidated Basel Framework: https://www.bis.org/basel_framework/ Basel Committee on Banking Supervision Minimum capital requirements for market risk January 2019 (rev. February 2019) This publication is available on the BIS website (www.bis.org). © Bank for International Settlements 2019. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISBN 978-92-9259-237-0 (online) Contents Minimum capital requirements for market risk ..................................................................................................................... 1 Introduction ......................................................................................................................................................................................... 1 RBC25 Boundary between the banking book and the trading book ....................................................................... 3 Scope of the trading book .......................................................................................................................................... 3 Standards for assigning instruments to the regulatory books ..................................................................... 3 Supervisory powers ........................................................................................................................................................ 5 Documentation of instrument designation .........................................................................................................
  • Economic Aspects of Securitization of Risk

    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.
  • Xvii. Sensitivity to Market Risk

    Xvii. Sensitivity to Market Risk

    Sensitivity to Market Risk XVII. SENSITIVITY TO MARKET RISK Sensitivity to market risk is generally described as the degree to which changes in interest rates, foreign exchange rates, commodity prices, or equity prices can adversely affect earnings and/or capital. Market risk for a bank involved in credit card lending frequently reflects capital and earnings exposures that stem from changes in interest rates. These lenders sometimes exhibit rapid loan growth, a lessening or low reliance on core deposits, or high volumes of residual interests in credit card securitizations, any of which often signal potential elevation of the interest rate risk (IRR) profile. Management is responsible for understanding the nature and level of IRR being taken by the bank, including from credit card lending activities, and how that risk fits within the bank’s overall business strategies. The adequacy and effectiveness of the IRR management process and the level of IRR exposure are also critical factors in evaluating capital and earnings. A well-managed bank considers both earnings and economic perspectives when assessing the full scope of IRR exposure. Changes in interest rates affect earnings by changing net interest income and the level of other interest-sensitive income and operating expenses. The impact on earnings is important because reduced earnings or outright losses can adversely affect a bank’s liquidity and capital adequacy. Changes in interest rates also affect the underlying economic value of the bank’s assets, liabilities, and off-balance sheet instruments because the present value of future cash flows and in some cases, the cash flows themselves, change when interest rates change.
  • Operational Risk Management: an Evolving Discipline

    Operational Risk Management: an Evolving Discipline

    Operational Risk Management: An Evolving Discipline Operational risk is not a new concept in scope. Before attempting to define the the banking industry. Risks associated term, it is essential to understand that with operational failures stemming from operational risk is present in all activities events such as processing errors, internal of an organization. As a result, some of and external fraud, legal claims, and the earliest practitioners defined opera- business disruptions have existed at tional risk as every risk source that lies financial institutions since the inception outside the areas covered by market risk of banking. As this article will discuss, and credit risk. But this definition of one of the great challenges in systemati- operational risk includes several other cally managing these types of risks is risks (such as interest rate, liquidity, and that operational losses can be quite strategic risk) that banks manage and diverse in their nature and highly unpre- does not lend itself to the management dictable in their overall financial impact. of operational risk per se. As part of the revised Basel framework,1 the Basel Banks have traditionally relied on Committee on Banking Supervision set appropriate internal processes, audit forth the following definition: programs, insurance protection, and other risk management tools to counter- Operational risk is defined as the act various aspects of operational risk. risk of loss resulting from inadequate These tools remain of paramount impor- or failed internal processes, people, tance; however, growing complexity in and systems or from external events. the banking industry, several large and This definition includes legal risk, but widely publicized operational losses in excludes strategic and reputational recent years, and a changing regulatory risk.
  • Modern Portfolio Theory

    Modern Portfolio Theory

    Modern portfolio theory “Portfolio analysis” redirects here. For theorems about where Rp is the return on the port- the mean-variance efficient frontier, see Mutual fund folio, Ri is the return on asset i and separation theorem. For non-mean-variance portfolio wi is the weighting of component analysis, see Marginal conditional stochastic dominance. asset i (that is, the proportion of as- set “i” in the portfolio). Modern portfolio theory (MPT), or mean-variance • Portfolio return variance: analysis, is a mathematical framework for assembling a P σ2 = w2σ2 + portfolio of assets such that the expected return is maxi- Pp P i i i w w σ σ ρ , mized for a given level of risk, defined as variance. Its key i j=6 i i j i j ij insight is that an asset’s risk and return should not be as- where σ is the (sample) standard sessed by itself, but by how it contributes to a portfolio’s deviation of the periodic returns on overall risk and return. an asset, and ρij is the correlation coefficient between the returns on Economist Harry Markowitz introduced MPT in a 1952 [1] assets i and j. Alternatively the ex- essay, for which he was later awarded a Nobel Prize in pression can be written as: economics. P P 2 σp = i j wiwjσiσjρij , where ρij = 1 for i = j , or P P 1 Mathematical model 2 σp = i j wiwjσij , where σij = σiσjρij is the (sam- 1.1 Risk and expected return ple) covariance of the periodic re- turns on the two assets, or alterna- MPT assumes that investors are risk averse, meaning that tively denoted as σ(i; j) , covij or given two portfolios that offer the same expected return, cov(i; j) .
  • Basel III: Comparison of Standardized and Advanced Approaches

    Basel III: Comparison of Standardized and Advanced Approaches

    Risk & Compliance the way we see it Basel III: Comparison of Standardized and Advanced Approaches Implementation and RWA Calculation Timelines Table of Contents 1. Executive Summary 3 2. Introduction 4 3. Applicability & Timeline 5 3.1. Standardized Approach 5 3.2. Advanced Approaches 5 3.3. Market Risk Rule 5 4. Risk-Weighted Asset Calculations 6 4.1. General Formula 6 4.2. Credit Risk 6 4.3. Market Risk 12 4.4. Operational Risk 13 5. Conclusion 14 The information contained in this document is proprietary. ©2014 Capgemini. All rights reserved. Rightshore® is a trademark belonging to Capgemini. the way we see it 1. Executive Summary In an effort to continue to strengthen the risk management frameworks of banking organizations and foster stability in the financial sector, the Basel Committee for Banking Supervision (BCBS) introduced, in December 2010, Basel III: A global regulatory framework for more resilient banks and banking systems. Subsequently, in July 2013, US regulators introduced their version of the BCBS framework, the Basel III US Final Rule1. The Final Rule, which outlines the US Basel III framework, details two implementation approaches: • The standardized approach • The advanced approaches To help banking clients understand what this means to their businesses, Capgemini has compared and evaluated both approaches, based on: • Implementation timelines as mandated by regulation • Risk-weighted asset (RWA) calculations for credit • Market and operational risks • Applicability to banks of all sizes—large or small A Glass Half Full While the standardized approach of Basel III introduces a more risk-sensitive treatment for various exposure categories than that of Basel II, the advanced approaches add another layer of complexity, by requiring that applicable banks employ more robust and accurate internal models for risk quantification.
  • The Market Risk Framework in Brief

    The Market Risk Framework in Brief

    Basel Committee BIS on Banking Supervision The market risk framework In brief January 2019 Revised market risk framework The failure to prudently What is market risk and why is its measurement being measure risks associated updated? with traded instruments caused major losses for Many banks have portfolios of traded instruments for some banks during the short-term profits. These portfolios – referred to as global financial crisis. trading books – are exposed to market risk, or the risk of The Basel Committee’s losses resulting from changes in the prices of instruments revised framework such as bonds, shares and currencies. Banks are required marks a significant to maintain a minimum amount of capital to account for improvement to the this risk. pre-crisis regulatory framework by addressing The significant trading book losses that banks incurred major fault lines. during the 2008 global financial crisis highlighted the need for the Basel Committee to improve the global market risk framework. As a stop-gap response, in July 2009 the Committee introduced the Basel 2.5 framework to help improve the framework’s risk coverage in certain areas and increase the overall level of capital requirements, with a particular focus on trading instruments exposed to credit risk (including securitisations). The main drivers of market risk nterest “Market rates risk: the risk uity redit of losses prices spreads arising from ommodity Foreign movements in prices echange market prices.” 1 2016 revised framework and review Following up on the What changes were proposed? Basel 2.5 framework, the Committee initiated From 2012, the Committee initiated a fundamental review of a fundamental review the trading book.
  • Market Risk with Interdependent Choice*

    Market Risk with Interdependent Choice*

    Market Risk with Interdependent ChoiceÆ Stephen Morris Cowles Foundation, Yale University, P.O.Box 208281, New Haven CT 06520, U. S. A. [email protected] Hyun Song Shin Nuf¿eld College, Oxford University, Oxford, OX1 1NF, U. K. [email protected] May 2000 Abstract Risks faced by traders from price movements are sometimes magni¿ed by the actions of other traders. Risk management systems which neglect this feature may give a seriously misleading picture of the true risks. The hazards arising from this potential blindspot are at their most dangerous when the prevailing conventional wisdom lulls traders into a false sense of security on the attractivenss of a trad- ing position. The efforts of one trader to reverse his trade makes more acute the ÆPaper prepared for the conference on liquidity risk, Frankfurt, 30 June - 1st July 2000. A non- technical version of this paper entitled “Risk Management with Interdependent Choice” appeared in the Oxford Review of Economic Policy (Autumn 1999) and reprinted in the Bank of England Financial Stability Review, November 1999. need to follow suit on the part of others. For markets dominated by traders with short time horizons, such interdependence leads to exaggerated price movements. Estimates of ‘value at risk’ which recognize such interdependence of actions can diverge substantially from those given by conventional techniques. 2 1. Introduction The summer and autumn of 1998 were exceptionally turbulent times for ¿nancial mar- kets and the risk management systems of ¿nancial institutions engaged in proprietary trading went through a searching examination. Although the ¿nancial system pulled back from the brink and the feared ¿nancial meltdown did not materialize, many insti- tutions suffered signi¿cant losses on their trading activities.