Question

Refer to the following information about ABC Bank for the questions 1-3.

The starting average interest rate (on assets and liabilities): 5%

	Market Value (million)	Duration
Total Assets	$50	9.0
Total Liabilities	$40	3.0

1. If interest rates grow by 1 percentage point, what is the resulting percentage change in assets’ value for ABC Bank?

1. 8.57%
2. -8.57%
3. 5.71%
4. -5.71%
5. None of the above

2. The duration gap adjusted to leverage equals:
   1. -6.6
   2. 6.0
   3. 7.7
   4. 10
   5. None of the above

3. If interest rates grow by 1 percentage point, what is the resulting market value change in the bank's equity?
   1. -6.27
   2. -6.58
   3. 6.58
   4. 7.67
   5. 7.30
   6. None of the above

Answer 1

1) Percentage Change in Value of Assets

Assets Duration = 9 | Liabilities Duration = 3 | Interest rate = 5%

Change in Interest rate = 1%

Change in Value / Value = - Duration * (Change in interest rate / (1 + Interest rate)

The Change in Value to Value ratio is Percentage change in Value

Putting all the values of Assets and change in interest rate

% Change in Assets' Value = - 9 *(1% / (1 + 5%)) = - 0.08571 or - 8.57%

Hence, answer is Option B (- 8.57%)

2) Leverage Adjusted Duration Gap

Formula for Leverage Adjusted Duration Gap = Duration of Assets - Duration of Liabilities * Liabilities / Assets

Assets = 50 | Liabilities = 40

Leverage Adjusted Duration Gap = 9 - 3 * 40 / 50 = 9 - 2.4 = 6.6

Hence, answer is Option E (None of the above) as none of the options are 6.6 which is the Leverage Adjusted Duration Gap

3) Change in Bank's market value of Equity

Change in interest rate = 1%

As Equity = Assets - Liabilitites, similarly, Change in Equity = Change in Assets - Change in Liabilities

Using this concept with Durations:

Change in Equity = (A * Duration of Assets - L * Duration of Liabilities)*Change in interest rate / (1 + Interest rate)

Multiplying and dividing the right hand side with Assets

Change in Equity = (Duration of Assets - Duration of Liabilities * L/A) * A * Change in interest rate / (1 + Interest rate)

As (Duration of Assets - Duration of Liabilities * L/A) = Leverage Adjusted Duration Gap which is = 6.6

Since interest rate has grown which has inverse effect on the Value of equity, therefore, we will put a negative sign at the front the equation

Change in Equity = - Leverage Adjusted Duration Gap * Assets * Change in interest rate / (1 + Interest rate)

Change in Equity = - 6.6 * 50 * 1% / (1 + 5%) = -3.143

Hence, answer is Option F (None of the above) as none of the options are -3.14 which is the change in equity's market value with increase in interest rate by 1%