Question

Assume that the market value assets and liabilities of a bank are $520 million and $260 million, respectively, and the duration of assets is 3. Find the duration of liability that eliminates the interest-risk of this bank.

Answer 1

The duration of liabilities required to eliminate interest rate risk for a bank with assets of $520 million, liabilities of $260 million, and asset duration of 3 is 6 years. To calculate this, the weighted average duration of the liabilities is set equal to the duration of the assets.

Step-by-step explanation:

The student's question pertains to managing interest rate risk by matching the duration of assets and liabilities for a bank. To eliminate interest rate risk, the bank would need to set the weighted average duration of its liabilities equal to the duration of its assets. With a market value of assets of $520 million and liabilities of $260 million, and given the duration of assets is 3, we can use the formula:

Duration of Assets (DA) × Market Value of Assets (A) = Duration of Liabilities (DL) × Market Value of Liabilities (L)

Plugging in the given values:

3 × $520 million = DL × $260 million

To find the Duration of Liabilities (DL), we solve for DL:

DL = (3 × $520 million) / $260 million

DL = 6

Therefore, the duration of liabilities needed to eliminate the bank's interest-rate risk would be 6.