Irwin/McGraw-Hill 1 Market Risk Chapter 10 Financial Institutions Management, 3/e By Anthony Saunders

Irwin/McGraw-Hill 2 Market Risk: n Market risk is the uncertainty resulting from changes in market prices. It can be measured over periods as short as one day. n Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark.

Irwin/McGraw-Hill 3 Market Risk Measurement n Important in terms of: Management information Setting limits Resource allocation (risk/return tradeoff) Performance evaluation Regulation

Irwin/McGraw-Hill 4 Calculating Market Risk Exposure n Generally concerned with estimated potential loss under adverse circumstances. n Three major approaches of measurement JPM RiskMetrics Historic or Back Simulation Monte Carlo Simulation

Irwin/McGraw-Hill 5 JP Morgan RiskMetrics Model Idea is to determine the daily earnings at risk = dollar value of position × price sensitivity × potential adverse move in yield. Can be stated as (-MD) × adverse daily yield move where, MD = D/(1+R).

Irwin/McGraw-Hill 6 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.

Irwin/McGraw-Hill 7 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.

Irwin/McGraw-Hill 8 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

Irwin/McGraw-Hill 9 Historic or Back Simulation Approach n Advantages Simplicity Does not require normal distribution of returns Does not need correlations or standard deviations of individual asset returns.

Irwin/McGraw-Hill 10 Historic or Back Simulation n Basic idea: Revalue portfolio based on actual prices (returns) on the assets that existed yesterday, the day before, etc. (usually previous 500 days). n Then calculate 5% worst-case (25 th lowest value of 500 days) outcomes. n Only 5% of the outcomes were lower.

Irwin/McGraw-Hill 11 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.

Irwin/McGraw-Hill 12 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.

Irwin/McGraw-Hill 13 Monte Carlo Simulation n To overcome problem of limited number of observations, synthesize additional observations. Perhaps 10,000 real and synthetic observations. n Employ historic covariance matrix and random number generator to synthesize observations.

Irwin/McGraw-Hill 14 Regulatory Models n BIS (including Federal Reserve) approach: Market risk may be calculated using standard BIS model. »Specific risk charge. »General market risk charge. Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for the purpose of determining capital requirements.

Irwin/McGraw-Hill 15 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.