buying the FRA, "borrowed" money at the FRA rate, which subsequently rose. This is a gain, exactly like a short position in an interest rate futures contract, where if the price goes down (that is, interest rates go up), the trader realizes a gain. Conversely, a "short" position in a FRA which is accomplished by selling a FRA realizes a gain if on the fixing date the reference rate is less than the FRA rate.   FRA Pricing FRAs are forward rate instruments and are priced using standard for- ward rate principles.3 Consider an investor who has two alternatives, either a 6-month investment at 5% or a 1-year investment at 6%. If the investor wishes to invest for six months and then rollover the invest- ment for a further six months, what rate is required for the rollover period such that the final return equals the 6% available from the 1-year investment? If we view a FRA rate as the break-even forward rate between the two periods, we simply solve for this forward rate and that is our approximate FRA rate. In practice, FRAs are priced off the exchange-traded short-term interest rate futures for that currency. For this reason, the contract rates (FRA rates) for FRAs are possibly the most liquid and transparent of any non-exchange-traded derivative instrument. To illustrate the pricing ofFRAs,wewillassumethat         3For a discussion of these principles, see Frank J. Fabozzi and Steven V. Mann, In- troduction to Fixed-Income Analytics (New Hope, PA: Frank J. Fabozzi Associates, 2001)     ■ the FRAs start today, January 1 of year 1 (FRA settlement date) ■ the reference rate is LIBOR ■ today 3-month LIBOR is 4.05%   Exhibit 11.10 presents the information that we will utilize in the FRA pricing. We will in an analogous manner as when we determined the future floating-rate payments in a swap contract in the next chapter. Shown in Column (1) is when the quarter begins and in Column (2) when the quarter ends in year 1. Column (3) lists the number of days in each quarter. Column (4) shows the current value of 3-month LIBOR. Column (5) contains the prices of 3-month Eurodollar CD futures contracts used to determine the implied 3-LIBOR forward rates in Column (6). Lastly, Column (7) contains the forward rate for the period that we will refer to as the period forward rate. The period forward rate is computed using the