Question

ASSETS :A=$100m

Liabilities: L=$90m E= $10m

a. Assume that the average duration of assets is 5 while the average duration of liabilities is 3 years. You are the liability manager of the bank and your boss is unhappy about the interest rate risk. How should you change the duration of the liability side to eliminate all interest rate risk? Provide your answer by calculating the new liability duration with two decimals.

b. Assume that the average duration of assets is 9 while the average duration of liabilities is 3 years. You are the liability manager of the bank and your boss is unhappy about the interest rate risk. How should you change the duration of the liability side to eliminate all interest rate risk? Provide your answer by calculating the new liability duration with two decimals.  

Answer 1

a.

Interest risk is risk of change in yield-interest rate. Assets consist future cash inflows and Liabilities consist future cash outflows.

Duration is measure of price sensitivity with change in yield-interest rate. In other words, duration measures how price of assets or liability change if interest rate change by 1%.

Interest rate and value of assets or liabilities inversely related.

So, Duration of Assets is more than duration of liabilities then, if interest rate rise - value of assets reduces more than liabilities and thus value of equity would reduce and vice versa.

Therefore, Bank manager need to match the duration of assets and liabilities to immunize the interest risk. For this, Bank manager should analysis the Duration gap of assets and liabilities.

To immunize or eliminate the interest risk, the duration gap of assets and liabilities must be zero.

$Duration Gap = Duration of Assets - Duration of Liabilities *\frac{liability}{assets}$

Computation of New duration of liabilities for Zero duration Gap

Assets = $ 100m

Liabilities = $ 90

Equity = $ 10

Duration of Assets = 5

Duration of Liabilities = 3

New Duration of Liabilities (DUR_L) to eliminate interest risk = ?

Duration Gap for immunization = 0

putting the values in above formula -

0 = 5 - DUR_L (90/100)

DUR_L (90/100) = 5

DUR_L = (5*100)/90

DUR_L = 5.56

Thus, New liability duration to eliminate interest risk is 5.56 years.

b.

Computation of New duration of liabilities for Zero duration Gap

Assets = $ 100m

Liabilities = $ 90

Equity = $ 10

Duration of Assets = 9

New Duration of Liabilities (DUR_L) to eliminate interest risk = ?

Duration Gap for immunization = 0

putting the values in above formula -

0 = 9 - DUR_L (90/100)

DUR_L (90/100) = 9

DUR_L = (9*100)/90

DUR_L = 10

Thus, New liability duration to eliminate interest risk is 10 years.