4.7. APPENDIX: THE FORWARD FORWARD AND THE FORWARD RATE AGREEMENT 159
4.7.2 WhyFRAs Exist
Like any forward contract, anFRAcan be used either for hedging or for speculation
purposes. Hedging may be desirable in order to facilitate budget projections in an
enterprise or to reduce uncertainty and the associated costs of financial distress.
Banks, for example, useFRAs, along with T-bill futures and bond futures, to reduce
maturity mismatches between their assets and liabilities. For instance, a bank with
average duration of three months on the liability side and twelve months on the
asset side, can use a three-to-twelve monthFRAto eliminate most of the interest
risk. AnFRAcan, of course, serve as a speculative instrument too.
As we shall show in the next paragraph,FFs (orFRAs) can be replicated from
term deposits and loans. For financial institutions, and even for other firms,FRAs
and interest futures are preferred over such syntheticFRAs in the sense that they do
not inflate the balance sheet.
Example 4.30
Suppose that you need a three-to-six month forward loan forjpy1b. Replication
would mean that you borrow (somewhat less than)jpy1b for six months and invest
the proceeds for three months, until you actually need the money. Thus, your
balance sheet would have increased byjpy1b, without any increase in profits or
cash flows compared to the case where you used a Forward Forward or anFRA.
The drawback of using anFForFRAis that there is no organized secondary market.
However, as in the case of forward contracts on foreign currency, long-termFRA
contracts are sometimes collateralized or periodically recontracted. This reduces
credit risk. Thus, a fairly active over-the-counter market forFRAs is emerging.
4.7.3 The Valuation ofFFs (orFRAs)
We now discuss the pricing of FFs (orFRAs—both have the same value): How
should one value an outstanding contract, and how should the market set the normal
forward interest rate at a given point in time? In this section, we adopt the following
notation:
t 0 : the date on which the contract was initiated
t(≥t 0 ) : the moment the contract is valued
T 1 : the expiration date of the forward contract (that is, the date that the gains
or losses on theFRAare settled, and the date at which the notional deposit starts)
T 2 (> T 1 ) : the expiration date of the notional deposit
rtf 0 ,T 1 ,T 2 : the effective return betweenT 1 andT 2 , without annualization, promised
on the notional deposit at the date theFRAwas signed, t 0.
First consider a numerical example: