Recall the FRA problem presented as Example 11.2. Show how the bank can alternatively use a position in Three-Month SOFR futures contracts to hedge the interest rate risk created by the maturity mismatch it has with the $3,000,000 six-month Eurodollar deposit and rollover Eurocredit position indexed to three-month CME Term SOFR. Assume that the bank can take a position in Three-Month SOFR futures contracts that mature in three months and have a futures price of 94.00.

As an example of using an FRA to hedge interest rate risk due to a maturity mismatch, consider a bank that has made a three-month Eurodollar loan of \$3,000,000 against an offsetting six-month Eurodollar deposit. The bank's concern is that three-month CME Term SOFR will fall below expectations and the Eurocredit is rolled over at the new lower base rate, making the six-month deposit unprofitable. 6 To protect itself, the bank could sell a $3,000,000 "three against six" FRA. The FRA will be priced such that the agreement rate is the expected three-month dollar LIBOR in three months. From the graph in Exhibit 11.7, it is clear that the short position the bank establishes will protect it if interest rates fall below the AR. Assume AR is 3 percent and the actual number of days in the three-month FRA period is 91 . Thus, the bank expects to receive $22,750(=$3,000,000.0391/360) as the base amount of interest when the Eurodollar loan is rolled over for a second three-month period. If SR (i.e., three-month CME Term SOFR) is 2.125 percent, the bank will receive only $16,114.58 in base interest, or a shortfall of $6,635.42. Since SR is less than AR, the bank will profit from the FRA it sold. It will receive from the buyer in three months a cash settlement at the beginning of the 91-day FRA period equaling the present value of the absolute value of [$3,000,000(.02125.03)91/360]=$6,635.42 This absolute present value is: 1+(.0212591/360)$3,000,000.02125.0391/360=1.0054$6,635.42=$6,599.78 The sum, $6,599.78, equals the present value as of the beginning of the 91-day FRA period of the $6,635.42 shortfall from the expected Eurodollar loan proceeds that are needed to meet the interest on the Eurodollar deposit. Had SR been greater than AR, the bank would have paid the buyer the present value of the excess amount of interest above what was expected from rolling over the Eurodollar credit. In this event, the bank would have effectively received the agreement rate on its three-month Eurodollar loan, which would have made the loan a profitable transaction