Question
In: Finance
7. Consider a F/I with the following balance sheet: Assets consisting of Cash of $150M; Loans...
7. Consider a F/I with the following balance sheet: Assets consisting of Cash of $150M; Loans of $1,500M at 12% with a duration of 1.75 years; and, Treasuries of $350M at 9% with a 7.00 year duration. Liabilities consisting of time deposits of $700M at 7% with a 1.75 year duration; CDs of $1,150M at 8% with a duration of 2.50 years; and, equity of $150M. Calculate the duration gap and state the F/I's interest rate risk exposure.
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+1.03 years; exposed to interest rate increases. |
||
|
+0.32 years; exposed to interest rate increases. |
||
|
+0.86 years; exposed to interest rate increases. |
||
|
+0.49 years; exposed to interest rate increases. |
||
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-1.32 years; exposed to interest rate decreases. |
Solutions
Expert Solution
Solution: CORRECT ANSWER is D) +0.49 years; exposed to interest rate increases.
| Assets | Market Value | Yield | Duration(Years) |
| Cash | 150 | ||
| Loans | 1500 | 12.00% | 1.75 |
| Treasuries | 350 | 9.00% | 7 |
| Total assets | 2000 | ||
| Liabilities | Market Value | Rate | Duration Years |
| Time Deposits | 700 | 7.00% | 1.75 |
| CDs | 1150 | 8.00% | 2.5 |
| Total liabilities | 1850 | ||
| Equity | 150 | ||
| Total | 2000 |
| Weighted Average Duration of Bank assets (Da) = Summation of the product of weights of individual assets and their respective Duration years. Where, weight of individual asset = Market value of that asset divided by the market value of all bank assets | (1500/2000)*1.75 + (350/2000)*7 = 2.5375 |
| Weighted Average Duration of Bank Liabilities (Dl) = Summation of the product of weights of individual liabilities and their respective Duration years. Where, weight of individual liability = Market value of that liability divided by the market value of all bank liabilities | (700/1850)*1.75 + (1150/1850)*2.5 = 2.216 |
| Duration Gap = Weighted average duration of assets -(Market value of liabilities/Market value of assets)*(Weighted average duration of liabilities) = (2.5375) - ((1850/2000)*2.216) = 0.4875 | +0.49 |
The duration gap is +0.49 and positive duration gap means that the market value of equity of F/I will fall when interest rates rise. So, F/I is exposed to interest rate increases.
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