Question

Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15 million. The asset duration is six years and the duration of the liabilities is four years. Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20-year, 8 percent coupon bond underlying the contract, a market yield of 8.5295 percent, and a duration of 10.3725 years.

a. Should the bank go short or long on the futures contracts to establish the correct macrohedge?

b. How many contracts are necessary to fully hedge the bank?

c. Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points.

d. If the bank had hedged with Treasury bill futures contracts that had a market value of $98 per $100 of face value and a duration of 0.25 years, how many futures contracts would have been necessary to fully hedge the balance sheet?

e. What additional issues should be considered by the bank in choosing between T-bond or Tbill futures contracts?

Answer 1

a. Should the bank go short or long on the futures contracts to establish the correct macrohedge?
Macro-hedge is a strategy which hedges the duration gap of the entire balance sheet. The bank should go short on the futures contracts to establish the correct macro-hedge because an increase in interest rates will decrease the value of the equity and the futures contracts. The bank can buy the futures contracts again to make a profit to offset the decreased value of the equity.
b. How many contracts are necessary to fully hedge the bank?
Formula to calculate the number of contracts to necessary to fully hedge the bank
= (Duration Of Assets – 0.9 * Duration of liabilities) * value of assets / (duration of bonds * Value of contract)
= {6 – (0.9) *4} *$150 million / (10.3725 * $95,000)
= - $360,000,000 million / 985,387.5= -365.34 Contract
Therefore selling of 365.34 contracts are necessary to fully hedge the bank.
c) For an Increase in 100 Basis point, the change in cash Balance sheet position is
Expected ?E= -DGAP( ?R/((1+R))A
=-2.4(0.01/1.10)X150 Million= -$3272727.54
The Change in Bond Value= -10.05 (0.01/1.08525)X 95000= -8797.51
and the change in 377 Contract s is = -8797.51X377= -3316662.06
Since the future Contract are sold, they could be repurchased for a gain 3316662.06 . The difference bwetween two value is a net gain of = $43934.79
Working note
No. of Contract= ( DA-K(DL))A/ (DF X PF)
=((6-(0.9X4)) $150million)/(10.05X95000)= 377.06 Contract
For a decrease of 50 basis point , the change in Cash balance sheet position is :-
Expected ?E= -DGAP( ?R/((1+R))A
=-2.4(-0.005/1.10)X$150=$1636363.64
The Change in Bond Value= (-10.05X(-0.005/1.08526)X95000= 4398.76
Change in 377 Contract is ( 4398.76X 377 Contract)= 1658331.03
The difference between the two value is loss of $21967.39
d) No. of Contract necessary to hedge the bank is
NF= ((DA-KDL)X A)/(DFXPF)
=((6-(0.9X4)X $150 Million)/(0.25X980000)= $360000000/$245000=1469.39 Contract