# Overview. We will discuss the nature of market risk and appropriate measures

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1 Market Risk

2 Overview We will discuss the nature of market risk and appropriate measures RiskMetrics Historic (back stimulation) approach Monte Carlo simulation approach Link between market risk and required capital levels

3 Market Risk Market risk is the earnings uncertainty resulting from changes in market prices Affected by other risks such as interest rate risk and FX risk Can be measured over periods as short as one day or as long as a year 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 Provides regulators with information regarding how to protect banks and the financial system against failure due to extreme market risk

5 Calculating Market Risk Exposure Generally concerned with estimating potential loss under adverse circumstances Three major approaches of measurement: JPM RiskMetrics (or variance/covariance approach) Historic or back simulation Monte Carlo simulation

6 RiskMetrics Model Daily earnings at risk = (dollar market value of the position) (Price sensitivity of the position) (Potential adverse move in the yield) DEAR= dollar market value of position Price volatility where, price volatility = price sensitivity of position potential adverse move in yield

7 RiskMetrics For fixed income securities, DEAR can be stated as: DEAR = Dollar market value of position x MD x potential adverse move in yield where MD=D/(1+R) MD= Modified duration D = Macaulay duration

8 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% (95% and 99%) of the time the disturbance will be within 1.65 (1.96 and 2.33) standard deviations of the mean (5% of the extreme values remain in either tail of the distribution)

9 Adverse Rate Move, Seven-Year Rates

10 The Potential Loss for More Than One Day To calculate the potential loss for more than one day: N day market value at VAR DEAR N N risk (VAR) :

11 Foreign Exchange In the case of foreign exchange, DEAR is computed in the following manner: DEAR = dollar value of position FX rate volatility

12 Equities For equities, total risk = systematic risk + unsystematic risk If the portfolio is well diversified, then DEAR = dollar value of position stock market return volatility, where market volatility taken as 2.33σ m If not well diversified, a degree of error will be built into the DEAR calculation

13 Aggregating DEAR Estimates Cannot simply sum up individual DEARs to find aggregate portfolio risk In order to aggregate the DEARs from individual exposures, we require the correlation matrix. Three-asset case: DEAR portfolio DEAR DEAR 2 a a DEAR DEAR b 2 b DEAR 2ρ ac 2 c 2ρ DEAR a ab DEAR c 2ρ bc DEAR b DEAR c 1 2

14 DEAR: Large US Commercial Banks 2005, 2011, and 2014 (1 of 3) Name Average DEAR for the Year Minimum DEAR during the Year Maximum DEAR during the Year 2014: Bank of America \$65 \$44 \$120 Citigroup J.P. Morgan Chase KeyCorp Wells Fargo Sun Trust 2 1 3

15 DEAR: Large US Commercial Banks 2005, 2011, and 2014 (2 of 3) Name Average DEAR for the Year Minimum DEAR during the Year Maximum DEAR during the Year 2011: Bank of America \$167 \$75 \$319 Citigroup J.P. Morgan Chase KeyCorp Wells Fargo Sun Trust 5 3 7

16 DEAR: Large US Commercial Banks 2005, 2011, and 2014 (3 of 3) Name Average DEAR for the Year Minimum DEAR during the Year Maximum DEAR during the Year 2005: Bank of America \$62 \$38 \$92 Citigroup J.P. Morgan Chase KeyCorp Wells Fargo Sun Trust *The figures are based on these banks internal models, i.e., they may be based on methodologies other than RiskMetrics.

17 Historic (Back Simulation) Approach Basic idea: Revalue current market portfolio based on actual prices (returns) on the assets as of yesterday, the day before that, etc. (usually previous 500 days) Then, calculate 1% worst case (portfolio value that has 5th lowest value out of 500)

18 Historic or Back Simulation Advantages: Simplicity Does not require the calculations of correlations or standard deviations of individual asset returns Does not require normal distribution of asset returns Directly provides a worst-case scenario number RiskMetrics does not!

19 Weaknesses Key disadvantage: Degree of confidence is based on 500 observations; not very many from a statistical standpoint Potential solution: increasing number of observations by going back more than 500 days Not desirable Could weight recent past observations more heavily and go further back

20 Monte Carlo Simulation To overcome problem of limited number of observations, simulate additional observations Perhaps 10,000 real and synthetic observations Employ historic variance-covariance matrix and random number generator to simulate observations Objective is to replicate the distribution of observed outcomes with synthetic data

21 Regulatory Models BIS (including Federal Reserve) approach: Simple standardized framework: Subject to regulatory approval, large banks may be allowed to use their internal models as the basis for determining capital requirements

22 Large Banks: Using Internal Models In calculating DEAR, adverse change in rates defined as 99th percentile Minimum holding period is 10 days (means that daily DEAR must be 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

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