6.4. HEDGING WITH FUTURES CONTRACTS 243
6.4.6 Adjusting for the Sizes of the Spot Exposure and the Futures Contract
Contract
Thus far, we have assumed that the exposure was one unit of a first foreign currency,
e, and that the size of one futures contract is one unit of another foreign currency, h.
If the exposure is a larger number, sayne, then the number of contracts one needs
to sell obviously goes up proportionally, while if the size of the futures contract isnh
rather than unity, the number of futures contracts goes down proportionally. Thus,
the generalized result is as follows: the number of contracts to be sold in order to
hedgeneunits of currency j using a futures contract with sizenhunits of currency
i is given by
hedge ratio =
ne
nh
β, (6.15)whereβcan be regression-based or a rule-of-thumb number.
Example 6.13
Suppose that you consider hedging asek 2.17m inflow usingeur futures with
a contract size ofeur125,000. A regression based on 52 points of weekly data
produces the following output:
∆S[usd/sek]= 0.003 + 0.105∆f[usd/eur]. (6.16)with an R^2 of 0.83 and a t-statistic of 15.62. Then:
- In light of the high t-statistic, we are sure that there actually is a correlation
between theusd/sekspot rate and theusd/eurfutures price. - Assuming all correlation between the two currencies is purely contemporane-
ous, hedging reduces the total uncertainty about the position being hedged by
an estimated 83 percent. If the horizon is more than one week and if there
are lead-lag reactions between the currencies, this estimate is probably too
pessimistic. - The regression-based estimated for the number of contracts to be sold is
hedge ratio =2 , 170 , 000
125 , 000
× 0 .105 = 1. 822 , (6.17)
or, after rounding, 2 contracts.6.4.7 More About Regression-based Hedges
When implementing a regression-based hedge you need to think about a number of
items:
- Estimation error Novices think of a regression coefficient as a sophisticated
number computed by clever people. Old hands dejectedly look at the huge error
margin, conveniently calculated for you by the computer program, and then sink