6. The following balance sheet information is available (amounts in thousands of

Question

6. The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution: Amount Duration T-bills T-notes T-bonds Loans Deposits Federal funds 0.50 0.90 9 7.00 1.00 0.01 2,724 238 715 Treasury bonds are five-year maturities paying 6 percent semiannually and sell ing at par 8 a. What is the duration of the T-bond portfolio b. What is the average duration of all the assets? c. What is the average duration of all the liabilities? d. What is the leverage adjusted duration gap? What is the interest rate risk exposure? e. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 0.5 percent [ie., If the yield curve shifts downward 0.25 percent [Le, A/(1 + R) =-0.0029 g. What variables are available to the financial institution to immunize the balance AR/(1 R) 0.005o)? f. what is the forecasted impact on the market value of equity? sheet? How much would each variable need to change to get DGAP to equal o? a. What is the change in the value of the firm's assets for a relative upward shift b. What is the change in the value of the firm's liabilities for a relative upward atory agencies of financial institutions is to immu- 7. Refer again to the financial institutions in problem 26. 2 in the entire yield curve of 0.5 percent shift in the entire yield curve of 0.4 percent? c. What is the resulting change in the value of equity for the firm?

Explanation / Answer

Since, there are 2 questions and each question has multiple sub-parts, I have answered all the parts of Question 6 (from Part a to Part f).

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Part a)

The duration of T-Bond portfolio is determined as below:

Duration of T-Bond Portfolio = Total of Cash Flow*PVIF*Time/Current Value of Treasury Bonds = 773.18/176 = 4.3931 or 4.39 years

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Notes:

1) PVIF indicates Present Value Interest Factor for $1. It can be dervied from the Present Value Tables.

2) When the bond is selling at par, the coupon rate and YTM is same. Therefore, coupon rate and YTM will be same at 6%. We will take 3% (6%/2) as the rate (YTM) because the bond is semi-annual.

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Part b)

The value of average duration of all assets is determined as below:

Average Duration of All Assets = (Duration of T-Bills*Amount of T-Bills + Duration of T-Notes*Amount of T-Notes + Duration of T-Notes*Amount of T-Notes + Duration of Loans*Amount of Loans)/Total Value of Assets

Substituting values in the above formula, we get,

Average Duration of All Assets = (.50*90 + .90*55 + 4.3931*176 + 7*2,724)/(90 + 55 + 176 + 2,724) = 6.5470 or 6.55 Years

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Part c)

The value of average duration of all liabilities is calculated as follows:

Average Duration of All Liabilities = (Duration of Deposits*Amount of Deposits + Duration of Federal Funds*Amount of Federal Funds)/Total Value of Liabilities

Substituting values in the above formula, we get,

Average Duration of All Liabilities = (1*2,092 + .01*238)/(2,092 + 238) = .8989 or .90 Years

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Part d)

The leverage adjusted duration gap is calculated as below:

Leverage Adjusted Duration Gap = Average Duration of All Assets - (Total Value of Liabilities/Total Value of Assets)*Average Duration of Liabilities = 6.5470 - (2,092 + 238)/(90 + 55 + 176 + 2,724)*.8989 = 5.8592 or 5.96Years

There is an inverse relationship between interest rate and value of equity. Since, duration gap is positive, any increase in interest rate will result in a decline in the market value of equity.

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Part e)

The forecasted impact on the market value of equity is determined as below:

Change in the Market Value of Equity = -Leverage Adjusted Duration Gap*(Total Value of All Assets)*?R/(1+R)

Substituting Values in the above formula, we get,

Change in Market Value of Equity = -5.8592*(90 + 55 + 176 + 2,724)*.0050 = -$89.207

The total market value of equity will decrease from $715,000 to $625,793 (715,000 - 89.207*1,000).

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Part f)

The forecasted impact on the market value of equity is determined as below:

Change in the Market Value of Equity = -Leverage Adjusted Duration Gap*(Total Value of All Assets)*?R/(1+R)

Substituting Values in the above formula, we get,

Change in Market Value of Equity = -5.8592*(90 + 55 + 176 + 2,724)*-.0025 = $44.603

The total market value of equity will increase from $715,000 to $759,603 (715,000 + 44.603*1,000).

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Part g)

To achieve immunization, the financial institution is required to have DGAP of 0. This can be accomplished by reducing the asset duration or increasing the liability duration. The duration of assets can be reduced with the use of more T-Bills and loans. With the use of these assets, the financial institution will be able to reduce the duration of its assets to .6878 years. Another option would be to increase the duration of deposits with the use of fixed-rate certificate of deposits having a maturity period of 3 to 4 Years. However, the current DGAP is very high. Therefore, it is not practically possible to bring it down to 0 by making some adjustments to the value of assets/liabilities available in the balance sheet.

Time [A] Cash Flow [B] PVIF (at 6%/2 = 3%) [C] Cash Flow*PVIF*Time [A*B*C] 0.5 5.28 0.9709 2.56 1 5.28 0.9426 4.98 1.5 5.28 0.9151 7.25 2 5.28 0.8885 9.38 2.5 5.28 0.8626 11.39 3 5.28 0.8375 13.27 3.5 5.28 0.8131 15.03 4 5.28 0.7894 16.67 4.5 5.28 0.7664 18.21 5 181.28 0.7441 674.45 Total $773.18

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