Simple Linear Regression 33

and

rI = aI + BIF rF + eI

where rF=the return on the stock index futures contract
BIF=the beta of the stock index relative to the stock index futures
contract
aI=the intercept of the relationship
eI=the error term

Given BPI and BIF , the minimum risk hedge ratio can then be expressed as

Hedge ratio = BPI × BIF

The R^2 of the regression will indicate how good the estimated relationship
is, and thereby allow the asset manager to assess the likelihood of success of
the proposed hedge.
The number of contracts needed can be calculated using the following
three steps after BPI and BIF are estimated:

Step 1. Determine the equivalent market index units of the market by

dividing the market value of the portfolio to be hedged by the cur-

rent index price of the futures contract:

(^) Equivalentmarketindexunits=Marketvalueooftheprotfoliotobehedged
Currentindexvalue ofthefuturescontract
Step 2. Multiply the equivalent market index units by the hedge ratio to
obtain the beta-adjusted equivalent market index units:
Beta-adjusted equivalent market index units
= Hedge ratio × Equivalent market index units
or
Beta-adjusted equivalent market index units
= BPI × BIF × Equiv5alent market index units
Step 3. Divide the beta-adjusted equivalent units by the multiple speci-
fied by the stock index futures contract:
Number ofcontracts
Beta-adjustedequivale

nntmarketindexunits
Multipleofthecontraact
We will use two examples to illustrate the implementation of a hedge
and the risks associated with hedging.