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
  • Expected shortfall

You will us the RiskMetrics model approach to measure Daily Earnings at Risk (DEAR) and Value at Risk (VAR) for individual securities and a portfolio.

For fixed income securities, DEAR can be stated as:

DEAR = (Dollar market value of position) (MD) (potential adverse move in yield)

where MD = D/(1+R)

MD = Modified duration

D = Macaulay duration

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 remain in either tail of the distribution).

Adverse Rate Move, Seven-Year Rates

Confidence Intervals: An Example

To calculate potential loss for more than 1 day: N-day market value at risk (VAR):

(VAR_N) = DEAR N^1/2

• VAR₅= 10,770 *5^1/2 = $24,082 Aggregating DEAR estimates: In order to aggregate the DEARs from individual exposures, we require the correlation matrix. Three-asset case (assets or portfolios a, b and c.

DEAR portfolio = [DEAR_a² + DEAR_b² +

DEAR_c² + 2r_ab DEAR_a DEAR_b + 2r_ac

DEAR_a DEAR_c + 2r_bc DEAR_b DEAR_c]^1/2 To get VAR for the portfolio, multiply the DEAR portfolio by the square root of the number of days to be analyzed.

Do the following problem: Compute the portfolio VAR for 10 days from the DEARs for the portfolio below for assets and liabilities separately and for the banks entire portfolio.

Consider the following bank balance sheet (fixed rates and pure discount securities unless indicated otherwise). Interest rates on liabilities are 4 percent and on assets are 6 percent.

Duration

DEAR $billions (years)

Assets

PrimeRate Loans (rates set monthly) 10.3 325 1.0

2Year Car Loans 9.5 275 2.0

30Year Mortgages 15.5 400 7.0

Total Assets (A) 1,000 ?

Liabilities and Equity

Super Now Checking Accounts (rates set monthly) 5.0 350 1.0

6Month Certificates of Deposit 4.0 250 .5

3Year Certificates of Deposit 4.0 300 3.0

Total Liabilities (L) 900 ?

Equity (E) 100

Total Liabilities (L) and Equity (E) 1,000

Assume the correlations between the liability and asset items are zero and the asset correlations are between 5% and 80%. Correlations among liabilities are 75% each.

a. Compute the DEAR for each asset and liability item in this banks portfolio assuming interest rates increase by 200 basis point. Recall that Modified Duration is Macaulays Duration/(1+R).

b. Try a low correlation for assets of 10% and a high correlation of 80%. Report each for assets and the portfolio.

c. Compute the VAR for each of your assumptions of low and high correlations for assets and the portfolio for a 10 day period.

d. For each set of correlations consider the minimum level of capital the bank should hold.