BOND MATH: The Theory Behind the Formulas

Interest Rate Forwards and Futures

There is a very important difference between interest rate forwards and futures that matters for bond math. This has to do with the timing of the gains and losses on the contracts. Suppose that in June 2011 a hedge fund asks a commercial bank for pricing on a 60 × 63 OTC forward contract on 3-month LIBOR—these exist and are called forward rate agreements (FRAs). That FRA is essentially a bet on the level of 3-month LIBOR in June 2016. The bank in turn observes that June 2016 Eurodollar futures are trading at price index of 94.00, implying a futures rate of 6.00%. (In this market, the price index is 100 minus the rate.) If the bank sets the cost and risk of hedging the OTC forward over the five years at 4 basis ...