Chapter

1. Chapter 10 Market Risk

2. 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

3. Market Risk: • Market risk is the uncertainty resulting from changes in market prices . 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.

4. Market Risk Measurement • Important in terms of: • Management information • Setting limits • Resource allocation (risk/return tradeoff) • Performance evaluation • Regulation

5. 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

6. 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)

7. 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.

8. 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%.

9. Confidence Intervals: Example • Price volatility = (-MD)  (Potential adverse change in yield) = (-6.527)  (0.00165) = -1.077% DEAR = Market value of position  (Price volatility) = ($1,000,000)  (.01077) = $10,770

10. Confidence Intervals: Example • To calculate the potential loss for more than one day: Market value at risk (VAR) = DEAR × N • Example: For a five-day period, VAR = $10,770 × 5 = $24,082

11. 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 sM.

12. 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 = [DEARa2 + DEARb2 + DEARc2 + 2rab × DEARa × DEARb + 2rac × DEARa × DEARc + 2rbc × DEARb × DEARc]1/2

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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

20. Web Resources • For information on the BIS framework, visit: Bank for International Settlement www.bis.org Federal Reserve Bank www.federalreserve.gov Web Surf

21. 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.

22. Pertinent Websites Bank for International Settlements www.bis.org Federal Reserve www.federalreserve.gov Citigroup www.citigroup.com J.P.Morgan/Chase www.jpmorganchase.com Merrill Lynch www.merrilllynch.com RiskMetrics www.riskmetrics.com Web Surf