158 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY
4.7 Appendix: The Forward Forward and the Forward Rate Agreement
Rate Agreement
4.7.1 Forward Contracts on Interest Rates
You may know that loans often contain options on interest rates (caps and floors;
see Chapter 16). Besides interest-rate options, there are also forward contracts on
interest rates. Such forward contracts come under two guises: the Forward Forward
contract (FF), and the Forward Rate Agreement (FRA).
AForward Forward contractis just a forward deposit or loan: it fixes an interest
rate today (=t) for a deposit or loan starting at a future timeT 1 (>t) and expiring
atT 2 (>T 1 ).
Example 4.28
Consider a six-to-nine-month Forward Forward contract for 10m Brazilian Real at
10 percentp.a. (simple interest). This contract guarantees that the return on a
three-month deposit ofbrl10m, to be made six months from now, will be 10%/4
= 2.5%. At timeT 1 (six months from now), thebrl10m will be deposited, and
the principal plus the agreed-upon interest of 2.5 percent will be received at time
T 2 (nine months from now).
A more recent, and more popular, variant is theForward Rate Agreement. Under
anFRA, the deposit isnotional—that is, the contract is about a hypothetical deposit
rather than an actual deposit. Instead of effectively making the deposit, the holder
of the contract will settle the gain or loss in cash, and pay or receive the present
value of the difference between the contracted forward interest rate and market rate
that is actually prevailing at timeT 1.
Example 4.29
Consider a nine-to-twelve-monthcad5m notional deposit at a forward interest rate
of 4 percentp.a.(that is, a forward return of 1 percent effective). If the Interbank
Offer Rate after nine months (T 1 ) turns out to be 3.6 percentp.a. (implying a
return of 0.9 percent), theFRAhas a positive value equal to the difference between
the promised interest (1 percent oncad5m) and the interest in the absence of the
FRA, 0.9 percent oncad5m. Thus, the investor will receive the present value of
this contract, which amounts to:
market valueFRA=
5 m×(0. 01 − 0 .009)
1. 009= 4955. 40. (4.44)
In practice, the reference interest rate on which the cash settlement is based is
computed as an average of many banks’ quotes, two days beforeT 1. The contract
stipulates how many banks will be called, from what list, and how the averaging
is done. In the early eighties, FRAs were quoted for short-term maturities only.
Currently, quotes extend up to ten years.