 # APPLICATION. Hedging with Financial Futures

First National Bank can also use financial futures contracts to hedge the interest rate risk on its holdings of \$5 million of the 6s of 2023. To see how, suppose that in March 2007, the 6s of 2023 are the long-term bonds that would be delivered in the Chicago Board of Trade's T-bond futures contract expiring one year in the future, in March 2008. Also suppose that the interest rate on these bonds is expected to remain at 6% over the next year, so that both the 6s of 2023 and the futures contract are selling at par (i.e., the \$5 million of bonds is selling for \$5 million and the \$100,000 futures contract is selling for \$100,000). The basic principle of hedging indicates that you need to offset the long position in these bonds with a short position, so you have to sell the futures contract. But how many contracts should you sell? The number of contracts required to hedge the interest-rate risk is found by dividing the amount of the asset to be hedged by the dollar value of each contract, as is shown in Equation 1:

NC = VA/ VC (1)

where NC = number of contracts for the hedge

VA = value of the asset VC = value of each contract

Given that the 6s of 2023 are the long-term bonds that would be delivered in the CBT T-bond futures contract expiring one year in the future and that the interest rate on these bonds is expected to remain at 6% over the next year, so that both the 6s of 2023 and the futures contract are selling at par, how many contracts must First National sell to remove its interest-rate exposure from its \$5 million holdings of the 6s of 2023? Since VA = \$5 million and VC = \$100,000,

NC = \$5 million/\$100,000 = 50

You therefore hedge the interest-rate risk by selling 50 of the Treasury Bond futures contracts.

Now suppose that over the next year, interest rates increase to 8% due to an increased threat of inflation. The value of the 6s of 2023 that the First National Bank is holding will then fall to \$4,039,640 in March 2008. Thus the loss from the long position in these bonds is \$960,360:

Value on March 2008 @ 8% interest rate \$4,144,052

Value on March 2007 @ 6% interest rate -\$5,000,000

Loss -\$ \$\$5,948

However, the short position in the 50 futures contracts that obligate you to deliver \$5 million of the 6s of 2023 on March 2007 has a value equal to \$4,144,052, the value of the \$5 million of bonds after the interest rate has risen to 8%, as we have seen before. Yet when you sold the futures contract, the buyer was obligated to pay you \$5 million on the maturity date. Thus the gain from the short position on these contracts is also \$855,948:

Amount paid to you on March 2008, agreed upon in March 2007 \$5,000,000 Value of bonds delivered on March 2008

@ 8% interest rate -\$4,144,052

Gain \$ 85\$,\$\$8

Therefore the net gain for the First National Bank is zero, indicating that the hedge has been conducted successfully.

The hedge just described is called a micro hedge because the financial institution is hedging the interest-rate risk for a specific asset it is holding. A second type of hedge that financial institutions engage in is called a macro hedge, in which the hedge is for the institution's entire portfolio. For example, if a bank has more rate-sensitive liabilities than assets, we have seen in Chapter 9 that a rise in interest rates will cause the value of the bank's net worth to decline. By selling interest-rate future contracts that will yield a profit when interest rates rise, the bank can offset the losses on its overall portfolio from an interest-rate rise and thereby hedge its interest-rate risk.

•  In the real world, designing a hedge is somewhat more complicated than the example here, because the bond that is most likely to be delivered might not be a 6s of 2023.
•  The value of the bonds can be calculated using a financial calculator as follows: FV = \$5,000,000, PMT = \$300,000, I = 8%, N = 15, PV = \$4,144,052. 