6.6. APPENDIX: EUROCURRENCY FUTURES CONTRACTS 251
corresponds to three months (1/4 year). Thus, as a first-order approximation,
1
1 +r..f≈ 1 −rf..= 1− 1 / 4 ×(4rf..) = 1− 1 / 4 ×[p.a. forward interest rate] (6.25)Thus, the change in the true forward price is about one-fourth of the change in
the futures quote. To bring marking to market more or less in line with normal
(price-based) contracts, the changes in the quote (or in thep.a. forward interest
rate) must be divided by four. If this were not done, ausd1m contract would, in
fact, hedge a deposit of roughlyusd4m, which would have been very confusing for
novice buyers and sellers.
Example 6.18
Suppose that you hold a five-month,usd1mCDand you want to hedge this position
against interest rate risk two months from now. If, two months from now, the three-
month interest rate drops from 4 percent to 3.9 percent, the market value of your
deposit increases from 1m/(1 + (1/4) 0.04) = 990,099.01 to 1m/(1 + (1/4) 0.039)
= 990,344.14, a gain ofusd245.13. The price quoted for a futures contract would
change by 0.1 percent or, on ausd1m contract, byusd1,000. Marking to market,
however, is one-fourth of that, orusd250. So the marking-to-market cash flows on
the eurodollar futures contract would reasonably match the 245.13-dollar change in
the deposit’s market value.
The pros and cons of interest futures, as compared toFRAs, are the same as
for any other futures contract. The main advantage is an active secondary market
where the contract can be liquidated at any moment, and the lowish entry barriers
because of the efficient way of handling security: ask for cash only if and when it is
needed. But that cannot be the end of the story. AlsoFRAs have some advantages
over T-bill futures and bond futures, and these advantages are similar to those of
forward exchange contracts over currency futures contracts, as discussed in Chapter
6.
- FFs orFRAs are pure forward contracts, which means that there is no marking to
market. It follows that, by usingFFs orFRAs, one avoids the additional interest
risk that arises from marking to market. - In the absence of marking to market, there is no ruin risk. The firm need not worry
about potential cash outflows that may lead to liquidity problems and insolvency. - In the absence of marking to market, there is an exact arbitrage relationship
between spot rates and forward rates; hence these contracts are easy to value. In
contrast, the pricing of a futures-style contract is more difficult because of interest
risk—covariance between market values and the interest-rate evolution, which in
the case of interest derivatives is, of course, stronger than for futures on currency
or stocks of commodities.