Enfoque adoptado para la evaluación de la eficiencia

If an FRA involves only an exchange of the difference in interest rates, how does it allow borrowers and lenders to hedge interest-rate risk, i.e., to lock-in rates for borrowing/lending in the future?

Consider a corporation that can borrow at Libor and that anticipates a borrowing need for the period [T1, T2]. Suppose the corporation (a) enters into a long FRA today with a fixed

rate k, and then (b) borrows the required amount at time T1at the then-prevailing Libor rate . Under this strategy, the corporation pays the interest rate  on the borrowed amount but

receives the difference − k from the FRA. The net rate paid is  − ( − k) = k, which is the fixed rate in the FRA.

Similarly, consider an investor who wishes to lock in an interest rate for lending over the period [T1, T2] in the future. The investor can enter into a short FRA today and then lend

at T1at the then-prevailing Libor rate. The investor receives  from the lending but pays  − k on the FRA, so receives a net rate of k, the fixed rate in the FRA.

Thus, by combining a position in an FRA with borrowing or lending at the Libor rate at time T1, borrowers and investors effectively lock in the fixed rate in the FRA. The following

example provides an illustration.

Example 6.4

Hedging with FRAs

We build on Example 6.1 above. On March 15, a corporation anticipates a need to borrow $5,000,000 for the three-month period from July 15 to October 15. The corporation enters

into a long 4× 7 FRA on March 15 and borrows the $5 million at Libor on July 15. The fixed rate in the FRA is k= 5.00%.

We consider two possibilities for the Libor rate on July 15, = 5.40% and  = 4.70%,

and show that the corporation’s net cash flows are the same in either case. Of course, these two Libor rates are only illustrative; as the reader may check, the net cash flows are the same whatever the Libor rate on July 15. For the calculations, note that there are 92 days in the three-month period between July 15 and October 15.

Case 1: Libor on July 15 Is 5.40%

In this case, as we saw in Example 6.1, the long position (here, the corporation) receives $5,041.54 on July 15 in settlement from the FRA. Investing these receipts at the prevailing Libor rate of 5.40% for three months, the corporation receives the following cash inflow on October 15: 5,041.54×  1+ (0.054) 92 360  = 5,111.11 (6.21)

The corporation must also pay interest on the $5,000,000 loan taken on July 15 at Libor. This interest amounts to

5,000,000× (0.054) 92

360 = 69,000.00 (6.22)

Thus, the net cash outflow facing the corporation is

69,000− 5,111.11 = 63,888.89 (6.23)

Case 2: Libor on July 15 Is 4.70%

As we saw in Example 6.1, the long position must now pay the short position an amount of 3,787.83 on July 15. Suppose the corporation borrows this amount on July 15 for three months at the Libor rate of 4.70%. The resulting cash outflow in three months is

3,787.83×  1+ (0.047) 92 360  = 3,833.33 (6.24)

In addition, the corporation also owes interest on the $5,000,000 loan taken at Libor on July 15. This interest is

5,000,000× (0.047) 92

360 = 60,055.56 (6.25)

Thus, the net interest cost the corporation incurs is

60,055.56+ 3,833.33 = 63,888.89 (6.26)

which is identical to (6.23). Remark

In practice, such perfect hedges are infeasible since companies may not be able to borrow or invest at Libor flat for odd cash flows. The actual hedge will be very good but involve some slippage. This raises an interesting question: why are FRAs settled in discounted form rather than at maturity, when the latter would allow companies to obtain better hedges? One reason, suggested by Flavell (2002), is that discounted settlement is preferred by banks

6.4

Eurodollar Futures

Eurodollar futures are the exchange-traded counterparts of FRAs in that they too are instru- ments designed to enable investors to lock-in Libor rates for future investment or borrowing. But while they are similar to FRAs in many ways, there are also important differences that stem from their standardization.

For practical purposes, a eurodollar futures contract may be thought of as an instrument that enables investors to lock in a Libor rate for a three-month period beginning on the expiry

date of the contract. (Precise definitions of the contract and its payoffs are offered further

below.) So, for example, for a futures contract expiring in September, the locked-in Libor rate applies to the three-month period from September to December. At any point in time, the CME and SGX (the two dominant exchanges in eurodollar futures trading) offer 44 expiry dates on eurodollar futures contracts: contracts expiring in March, June, September, and December for each of the next 10 years plus contracts in the four nearest serial expiry months outside the quarterly cycle. This means investors can lock in three-month rates as much as 10 years out in the future.

Note the contrast with FRAs here. In an FRA, the investment/borrowing period can be specified as the counterparties wish; for example, a 4× 10 FRA locks in an invest- ment/borrowing rate for a six-month period beginning in four months. In the eurodollar futures contract, this period is standardized both in terms of length (three months) and in terms of its starting date (one of the 44 standard expiry dates of the futures contract). Other differences with FRAs will be pointed out as we go along.

A more detailed description of the contract and its use in hedging interest-rate risk follows. But first, some remarks to put the contract into perspective.