Simple Linear Regression 31
exposure to the S&P 500, she could sell all the stocks and, with the funds
received, invest in a Treasury bill. By using a stock index futures contract,
the manager can eliminate exposure to the S&P 500 by hedging, and the
hedged position will earn the same return as that on a Treasury bill. The
manager thereby saves on the transaction costs associated with selling a
stock portfolio. Moreover, when the manager wants to get back into the
stock market, rather than having to incur the transaction costs associated
with buying stocks, she simply removes the hedge by buying an identical
number of stock index futures contracts.
In practice, hedging is not a simple exercise. When hedging with stock
index futures, a perfect hedge can be obtained only if the return on the port-
folio being hedged is identical to the return on the futures contract.
The effectiveness of a hedged stock portfolio is determined by:
■ (^) The relationship between the cash portfolio and the index underlying
the futures contract.
■ (^) The relationship between the cash price and futures price when a hedge
is placed and when it is lifted (liquidated).
The difference between the cash price and the futures price is called the
basis. It is only at the settlement date that the basis is known with certainty.
At the settlement date, the basis is zero. If a hedge is lifted at the settlement
date, the basis is therefore known. However, if the hedge is lifted at any other
time, the basis is not known in advance. The uncertainty about the basis
at the time a hedge is to be lifted is called basis risk. Consequently, hedging
involves the substitution of basis risk for price risk.
A stock index futures contract has a stock index as its underlying. Since
the portfolio that an asset manager seeks to hedge will typically have differ-
ent characteristics from the underlying stock index, there will be a difference
in return pattern of the portfolio being hedged and the futures contract. This
practice—hedging with a futures contract that is different from the underly-
ing being hedged—is called cross hedging. In the commodity futures mar-
kets, this occurs, for example, when a farmer who grows okra hedges that
crop by using corn futures contracts, because there are no exchange-traded
futures contracts in which okra is the underlying. In the stock market, an
asset manager who wishes to hedge a stock portfolio must choose the stock
index, or combination of stock indexes, that best (but imperfectly) tracks
the portfolio.
Consequently, cross hedging adds another dimension to basis risk,
because the portfolio does not track the return on the stock index perfectly.
Mispricing of a stock index futures contract is a major portion of basis risk
and is largely random.