Chapter 10 Market Risk Financial Institutions Risk Management Saunders and Cornett

1. 1 Sk�vde University, Risk Management Chapter 10 Market RiskFinancial Institutions Risk Management Saunders and Cornett

2. 2 Sk�vde University, Risk Management Overview This chapter discusses the nature of market risk and market risk measures, including: Dollar exposure RiskMetrics Historic or back simulation Monte Carlo simulation Links between market risk and capital requirements

3. 3 Sk�vde University, Risk Management Trading Risks Trading exposes banks to risks 1995 Barings Bank 1996 Sumitomo Corp. lost $2.6 billion in commodity futures trading AllFirst/ Allied Irish $691 million loss Allfirst eventually sold to Buffalo based M&T Bank due to dissatisfaction among stockholders of Allied Irish

4. 4 Sk�vde University, Risk Management Concepts: Market Risk Market risk (or Value at Risk) is the uncertainty of a FI�s earnings resulting from changes in market conditions, e.g. interest rate, market volatility, etc.) It can be measured over periods as short as one day. DEAR: daily earnings at risk Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark.

5. 5 Sk�vde University, Risk Management Market Risk Measurement 5 reasons why risk measurement is important: Management information Setting limits, position limits per trader. Resource allocation (higher return per risk) Performance evaluation (risk/return tradeoff) Regulation BIS and Fed regulate market risk via capital requirements leading to potential overpricing of risks Allow for use of internal models to calculate capital requirements

6. 6 Sk�vde University, Risk Management Calculating Market Risk Exposure Generally concerned with estimated potential loss under adverse circumstances. Three major approaches of risk measurement (JPM) RiskMetrics (or variance/covariance approach) Historic or Back Simulation Monte Carlo Simulation

7. 7 Sk�vde University, Risk Management JP Morgan RiskMetrics Model Market risk= estimated potential loss under adverse circumstances Daily earnings at risk = (dollar market value of position) � (price sensitivity) � (potential adverse move in yield) DEAR = (Dollar market value of position) � (Daily price volatility). Daily price volatility = (MD) � (adverse daily yield move) where, MD = Modified duration = D/(1+R)

8. 8 Sk�vde University, Risk Management Formula

9. 9 Sk�vde University, Risk Management 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. (5% of the extreme values greater than +1.65 standard deviations and 5% of the extreme values less than -1.65 standard deviations)

10. Sk�vde University, Risk Management 10 Adverse 7-Year Rate Move

11. 11 Sk�vde University, Risk Management Confidence Intervals: Example Suppose that we are long in 7-year zero-coupon bonds, $1M, yield on the bonds is 7.243%. We define �bad� yield changes as: there is only 5% chance of the yield change will exceed in either direction. Assuming normality, 90% of the time yield changes will be within 1.65 standard deviations of the mean. If one 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%.

12. 12 Sk�vde University, Risk Management Confidence Intervals: Example Price volatility = (MD) ? (Potential adverse change in yield) = (7/1.07243) ? (0.00165) = 1.077% DEAR = (Market value of position) ? (Price volatility) = ($1,000,000) ? (0.01077) = $10,770 Note: 1 basis point =0.0001

13. Sk�vde University, Risk Management 13 Confidence Intervals: Example To calculate the potential loss for more than one day, for N days: Market Value At Risk (VARN) = DEAR � Example: For a five-day period, VAR5 = $10,770 � = $24,082

14. 14 Sk�vde University, Risk Management Foreign Exchange In the case of Foreign Exchange, DEAR is computed in the same fashion as we do for interest rate risk. DEAR = dollar value of position � FX rate volatility where the FX rate volatility is taken as 1.65 sFX, Only 5% of the time exceeds the interval.

15. 15 Sk�vde University, Risk Management FX example: dollar position 1 M

16. 16 Sk�vde University, Risk Management Equities 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 sM. 5% of the time it exceed the interval.

17. 17 Sk�vde University, Risk Management Aggregating DEAR Estimates Portfolio aggregation 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 = [DEARa2 + DEARb2 + DEARc2 + 2rab � DEARa � DEARb + 2rac � DEARa � DEARc + 2rbc � DEARb � DEARc]1/2

18. 18 Sk�vde University, Risk Management 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.

19. 19 Sk�vde University, Risk Management 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 (25th lowest value of 500 days) outcomes. Only 5% of the outcomes were lower.

20. 20 Sk�vde University, Risk Management 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.

21. 21 Sk�vde University, Risk Management 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.

22. 22 Sk�vde University, Risk Management 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.

23. 23 Sk�vde University, Risk Management 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.

24. 24 Sk�vde University, Risk Management 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

25. 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 )*. Capital charge will be higher of: Previous day�s VAR (or DEAR ? ) 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. Large Banks: BIS versus RiskMetrics