Question

Lia bilities Duration 7 years $120 Duration 5 years $108 Average interest rate 6.00% $12 Al What is the bank's duration Ga 1 What is the bank's interest rate risk exposure? Why? (Hint: this is a qualitative question: exposure if interest rate increase or decrease? Justify your answer C) How can the bank use futures ajd forward contracts to put on a macro-hedge Hint: this is a qualitative question) what is the impact on the bank's equity if the interest rate increases by 1%? r) E) Suppose that the bank's macro-hedges using Treasury bond futures that are currently priced at 97 what is the impact per futures contract of the bank's futures position if the interest rate increase by 1% Assume that the Treasuty bond has a duration of 8.5 years. (Hint: per contract implies Nf= 1. F) If the bank wants to micro-hedge, how many Treasury bond futures contract dies it need?

Answer 1

a) Duration Gap = Duration of assets - Duration of liabilities * (Liabilities / Assets)

= 7 - 5 *(108 / 120)

Duration Gap = 2.5

b) Exposure of interest rate exposure:

If the interest rate increase and since Duration Gap is positive number, then value of bank's asset will fall more than the value of bank's liabilities.Hence decreasing the bank's equity value.

On the other way, if the interest rate decreases and since Duration Gap is positive number, then assets will gain more than the liabilities. Hence will increase the bank's equity value.

c) Use of future or forward interest rate future:

Since bank positive has positive duration gap, it is more concern about increase in interest rate and resulting more impact on the assets than liabilities. Hence bank should take short position in futures /forward market. So increase in interest rates will results in gain from the future market which will somewhat offset the losses

d) Interest rate increases by 1%

Impact on the equity = -Duration gap * change in interest rates / (1+ current interest rates)

= -2.5 * 1% / (1+6%)

= -2.36%

Absolute impact on equity = -2.36% * 12

Absolute impact on equity =-$0.28 million

e) for 1% increase in interest rate, value of Treasury bond future value will decrease by = -1% *duration of future

= -1% * 8.5

=-8.5%