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)  BANK'S DURATION GAP :

The difference between duration of assets and the liabilities held by financial entity is called duration gap. the formula for duration gap is :

Banks's Duration gap = duration of earning assets - duration of paying liabilities *paying liabilities / earning assets

= 7 - 5 * $108 / $120

= 7 - 5*0.9

= 7 - 4.5

= 2.5

B) BANK'S INTEREST RISK EXPOSURE :

Here in this case, duration of assets ( 7years ) is larger than the duration of liabilities (5 years), therefore the duration gap is POSITIVE. In such situation, if INTEREST RATES RISE, assets will lose more value than liabilities, thus reducing the value of firm's equity.

If INTEREST RATES FALL , assets will gain more value than liabilities, thus increasing the value of firm's equity.

C) FUTURE AND FORWARD CONTRACTS:

The bank can HEDGE its INTEREST RATE RISK by SELLING future or forward contracts.

D) IMPACT ON BANKS EQUITY IF INTEREST RATE RISES BY 1% :

When interest rates are rising,both businesses and consumers will cut back on spending. There is said to be an INVERSE CORRELATION between banks equity and interest rates. Higher the interest rates, lower will be equity valuations. Suppose the interest rate rises by 1% , change in equity will be :

change in equity = - 6* $12 *0.01 = - 0.72 %