Tree Row Bank has assets of $150 million, liabilities of $135 million, and equit

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? 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 c. 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 T- bill futures contracts?

Explanation / Answer

Solution:

a). The Bank should go Short on Futures Contract. Reason for this being, as the Interest Rate will increase, the value of equity as well the as the value of futures contract will decrease. Thus as a result of short position in Futures, bank can buy the Futures to establish an Gain.

b). The no of contracts to fully hedge the banks is calculate as:

N = - (Da-kDL)A / DF x PF

Here, Da - Duration of Assets (6) , k= Liabilities/ Assets= 0.9, DL-Duration of Liabilities (4), A-Assets, DF=Duration, PF=Price

N = - (6- (0.9)4) $150mn / 10.3725 x $ 95,000

N = 365 contracts

So, shorting 365 contracts will be required to hedge the bank.

c) Calucalte the effect of increase in rates by100 bps:

Change of Cash B/s Postion:

Expected E = -DGAP[R/(1 + R)]A = -2.4(0.01/1.10) $150m = -$3,272,727.27.

Calculate change of Bond Value = -10.3725(0.01/1.085295) $95,000 = -$9,079.41,

Change in 365 contracts is simply multiplication of above by 365= - $9,079.41 x -365 = $3,313,986.25.

Futures can be repurchased due to short position which results in gain of $3,313,986.25.

Calculate the sum of two above = Gain of $41,259.

Calculate the effect of decrease in rates of 50 bps:

Change of Cash B/s Postion:

E = -DGAP[R/(1 + R)]A = -2.4(-0.005/1.10)$150m = $1,636,363.64.

Change of bond = -10.37255(-0.005/1.085295)$95,000 = $4,539.71

Change in 365 contracts is simply multiplication of above by 365= $4,539.71 x -365 = -$1,656,993.13.

Futures can be repurchased due to short position which results a loss of $1,656,993.13.

Calculate the sum of two above =Loss of $20,629.

d) In this case, No of contracts required to hedging of bank is calculated as:

N = -(Da-(k)DL) A / DF x PF

N = -(6-0.9x4)$150mn / 0.25 x $980,000

N = -1469 contracts

e) For all the cases, when no of Treasury Bonds required for Hedging is a large number, then the bank should consider that large number of Treasury Bonds may not be easily available, as the Treasury bond market is less in depth as compared to Treasury Bills market. So, in case of T-Bills, if large no of contracts are required to hedge, then there is no such problem of availability of contracts.

Hope it helps !

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