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), R is the rate of interest; and MD = Modified duration D = Macaulay duration. For three-asset case (assets or portfolios a, b and c. DEAR portfolio = [DEARaa2 + DEARbb2 + DEARcc2 + 2Þabab × DEARaa × DEARbb + 2Þacac × DEARaa × DEARcc + 2Þbcbc × DEARbb × DEARcc]1/2 , where Þab is the correlation coefficient between returns for assets a and b. To get VaR (Value at Risk) for the portfolio, multiply the DEAR portfolio by the square root of the number of days to be analyzed, say 30 days.

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.

 

1. For the balance sheet values is Problem 6 compute the portfolio VaR for 30 days and the DEARs for the asset portfolio separately and for the bank’s entire asset portfolio for an interest rates increase of 200 basis points.
2. Compute the VaR assuming the correlations between the liability and asset items are zero and the asset correlations are 20%, 1.5%, and 90%, respectively. Correlations among liabilities are 75% each. Is the asset VaR higher or lower at greater or lesser correlation among the asset returns?
3. If capital requirements are established using asset VaR and return correlations are higher during the recession and crisis periods, should banks be required to hold more capital as return correlations rise?

Assets Prime-Rate Loans (rates set daily) 1-Year Discount Loans 30-Year Mortgages Total Assets Liabilities and Equity Super Now Checking Accounts (rates set daily) 6-Month Certificates of Deposit 3-Year Certificates of Deposit Total Liabilities Equity (E) Duration Sbillion (years) 400 360 500 1260 1160 500 380 280 100 ? 1.0 1.0 7.0 ? 1.0 .5 3.0