Market Risk

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

Market Risk Measurement

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

JP Morgan RiskMetrics Model

Determine the daily earnings at risk (DEAR):

DEAR = dollar value of position × price sensitivity × potential adverse move in yield

Or DEAR = Dollar market value of position × Price volatility

For fixed income securities:

Daily price volatility=[-D/(1+R)] × adverse daily yield move

Assume that changes in the daily yield are normally distributed, 90% (95%, 99%)of the time the changes in the daily yield will be within 1.65 (1.96, 2.33) standard deviations of the mean.

Example 10-1: calculate DEAR for a position of $1 million of 7-year zero-coupon bonds with a yield of 7.243%.Assume that the mean of standard deviation of the daily yield change is 0 and 10 basis points, respectively.

Given 90% confidence interval:

Market value of position = $1,000,000/(1+7.243%)^7=$612,900

Price volatility = [-D/(1+R)] (Potential adverse change in yield)

= (-7/1.07243) (1.65x0.0010) = -1.077%

DEAR = Market value of position  (Price volatility)

= ($612,900) (.01077) = $6,600

Question: Calculate DEARs given 95% and 99% confidence interval.

To calculate the potential loss for more than one day:

Market value at risk (VAR) = DEAR × N

Example: For a five-day period

VAR = $6,600 × 5 = $14,758

For foreign exchange & equities:

In the case of foreign exchange, DEAR is computed in the same fashion we employed for interest rate risk.

Example

Export Bank has a trading position in Japanese Yen and Swiss Francs. At the close of business on February 4, the bank had ¥300,000,000 and Swf10,000,000. The exchange rates for the most recent six days are given below:

Exchange Rates per U.S. Dollar at the Close of Business

2/4 2/3 2/2 2/1 1/29 1/28

Japanese Yen112.13112.84112.14115.05116.35116.32

Swiss Francs1.41401.41751.41331.42171.41571.4123

a.Calculate the foreign exchange (FX) position in dollar equivalents using the FX rates on February 4.

Japanese Yen:¥300,000,000/¥112.13 = $2,675,465.98

Swiss Francs:Swf10,000,000/Swf1.414 = $7,072,135.78

b.Calculate the volatility of change in exchange rates for each currency over the five-day period.

DayJapanese Yen:Swiss Franc

2/4-0.62921%-0.24691%% Change = (Ratet/Ratet-1) - 1 * 100

2/30.62422%0.29718%

2/2-2.52934%-0.59084%

2/1-1.11732%0.42382%

1/290.02579%0.24074%

 0.01205 0.00428

c. Determine the bank’s DEAR for both currencies by using 90% confidence level.

Japanese Yen:$2,675,465.98 * 1.65*0.01205 = $53,194.95

Swiss Francs:$7,072,135.78 * 1.65*0.00428 = $49,943.42

 For equities, if the portfolio is well diversified then

DEAR = dollar value of position × βx1.65xM.

In order to aggregate the DEARs from individual exposures, we cannot simply sum up individual DEARs. Instead, it requires the correlation matrix.

 Three-asset case:

DEAR portfolio = [DEARa2 + DEARb2 + DEARc2 + 2ab × DEARa × DEARb + 2ac × DEARa × DEARc + 2bc × DEARb × DEARc]1/2

Example:

Calculate the DEAR for the following portfolio with and without the correlation coefficients.

Estimated

Assets DEAR S,FXS,BFX,B

Stocks (S)$300,000-0.100.750.20

Foreign Exchange (FX)$200,000

Bonds (B)$250,000

What is the amount of risk reduction resulting from the lack of perfect positive correlation between the various assets groups?

The DEAR for a portfolio with perfect correlation would be $750,000. Therefore the risk reduction is $750,000 - $559,464 = $190,536.

Historic 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

Advantages:

Simplicity

Does not require normal distribution of returns

Does not need correlations or standard deviations of individual asset returns

Disadvantage:

500 observations is not very many from statistical standpoint

Increasing number of observations by going back further in time is not desirable.

Monte Carlo simulation

To overcome problem of limited number of observations

Employ historic covariance matrix and random number generator to generate observations.

Objective is to replicate the distribution of observed outcomes with synthetic data

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