Market Risk Chapter 10 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. K. R. Stanton

McGraw-Hill/Irwin 10-2 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Overview  This chapter discusses the nature of market risk and appropriate measures Dollar exposure RiskMetrics Historic or back simulation Monte Carlo simulation Links between market risk and capital requirements

McGraw-Hill/Irwin 10-3 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Trading Risks  Trading exposes banks to risks 1995 Barings Bank 1996 Sumitomo Corp. lost $2.6 billion in commodity futures trading 1997 market volatility in Eastern Europe and Asia 1998 continuation with Russian bonds AllFirst/ Allied Irish $691 million loss  Partly preventable with software  Rusnak currently serving 7 ½ year sentence for fraud  Allfirst sold to Buffalo based M&T Bank

McGraw-Hill/Irwin 10-4 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Implications  Emphasizes importance of: Measurement of exposure Control mechanisms for direct market risk—and employee created risks Hedging mechanisms

McGraw-Hill/Irwin 10-5 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Market Risk  Market risk is the uncertainty resulting from changes in market prices. Affected by other risks such as interest rate risk and FX risk It can be measured over periods as short as one day. Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark.

McGraw-Hill/Irwin 10-6 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Market Risk Measurement  Important in terms of: Management information Setting limits Resource allocation (risk/return tradeoff) Performance evaluation Regulation  BIS and Fed regulate market risk via capital requirements leading to potential for overpricing of risks  Allowances for use of internal models to calculate capital requirements

McGraw-Hill/Irwin 10-7 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculating Market Risk Exposure  Generally concerned with estimated potential loss under adverse circumstances.  Three major approaches of measurement JPM RiskMetrics (or variance/covariance approach) Historic or Back Simulation Monte Carlo Simulation

McGraw-Hill/Irwin 10-8 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. JP Morgan RiskMetrics Model Idea is to determine the daily earnings at risk = dollar value of position × price sensitivity × potential adverse move in yield or, DEAR = Dollar market value of position × Price volatility. Can be stated as (-MD) × adverse daily yield move where, MD = D/(1+R) Modified duration = MacAulay duration/(1+R)

McGraw-Hill/Irwin 10-9 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Confidence Intervals If we assume that changes in the yield are normally distributed, we can construct confidence intervals around the projected DEAR. (Other distributions can be accommodated but normal is generally sufficient). Assuming normality, 90% of the time the disturbance will be within 1.65 standard deviations of the mean.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Confidence Intervals: Example Suppose that we are long in 7-year zero-coupon bonds and we define “bad” yield changes such that there is only 5% chance of the yield change being exceeded in either direction. Assuming normality, 90% of the time yield changes will be within 1.65 standard deviations of the mean. If the standard deviation is 10 basis points, this corresponds to 16.5 basis points. Concern is that yields will rise. Probability of yield increases greater than 16.5 basis points is 5%.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Confidence Intervals: Example  Price volatility = (-MD)  (Potential adverse change in yield) = (-6.527)  ( ) = % DEAR = Market value of position  (Price volatility) = ($1,000,000)  (.01077) = $10,770

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Confidence Intervals: Example  To calculate the potential loss for more than one day: Market value at risk (VAR N ) = DEAR ×  N  Example: For a five-day period, VAR 5 = $10,770 ×  5 = $24,082

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Foreign Exchange & Equities  In the case of Foreign Exchange, DEAR is computed in the same fashion we employed for interest rate risk.  For equities, if the portfolio is well diversified then DEAR = dollar value of position × stock market return volatility where the market return volatility is taken as 1.65  M.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Aggregating DEAR Estimates  Cannot simply sum up individual DEARs.  In order to aggregate the DEARs from individual exposures we require the correlation matrix.  Three-asset case: DEAR portfolio = [DEAR a 2 + DEAR b 2 + DEAR c  ab × DEAR a × DEAR b + 2  ac × DEAR a × DEAR c + 2  bc × DEAR b × DEAR c ] 1/2

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Historic or Back Simulation  Advantages: Simplicity Does not require normal distribution of returns (which is a critical assumption for RiskMetrics) Does not need correlations or standard deviations of individual asset returns.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Historic or Back Simulation  Basic idea: Revalue portfolio based on actual prices (returns) on the assets that existed yesterday, the day before, etc. (usually previous 500 days).  Then calculate 5% worst-case (25 th lowest value of 500 days) outcomes.  Only 5% of the outcomes were lower.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Estimation of VAR: Example  Convert today’s FX positions into dollar equivalents at today’s FX rates.  Measure sensitivity of each position Calculate its delta.  Measure risk Actual percentage changes in FX rates for each of past 500 days.  Rank days by risk from worst to best.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Weaknesses  Disadvantage: 500 observations is not very many from statistical standpoint.  Increasing number of observations by going back further in time is not desirable.  Could weight recent observations more heavily and go further back.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Monte Carlo Simulation  To overcome problem of limited number of observations, synthesize additional observations. Perhaps 10,000 real and synthetic observations.  Employ historic covariance matrix and random number generator to synthesize observations. Objective is to replicate the distribution of observed outcomes with synthetic data.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Regulatory Models  BIS (including Federal Reserve) approach: Market risk may be calculated using standard BIS model.  Specific risk charge.  General market risk charge.  Offsets. Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for determining capital requirements.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. BIS Model Specific risk charge:  Risk weights × absolute dollar values of long and short positions General market risk charge:  reflect modified durations  expected interest rate shocks for each maturity Vertical offsets:  Adjust for basis risk Horizontal offsets within/between time zones

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Web Resources  For information on the BIS framework, visit: Bank for International Settlement Federal Reserve Bank

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Large Banks: BIS versus RiskMetrics In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics) Minimum holding period is 10 days (means that RiskMetrics’ daily DEAR multiplied by  10)*. Capital charge will be higher of:  Previous day’s VAR (or DEAR   10)  Average Daily VAR over previous 60 days times a multiplication factor  3. *Proposal to change to minimum period of 5 days under Basel II, end of 2006.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Pertinent Websites American Banker Bank of America Bank for International Settlements Federal Reserve J.P.Morgan/Chase RiskMetrics