30 The Basics of financial economeTrics
and futures markets move together, any loss realized by the hedger on one
position (whether cash or futures) will be offset by a profit on the other posi-
tion. When the profit and loss are equal, the hedge is called a perfect hedge.
A short hedge is used to protect against a decline in the future cash price
of the underlying. To execute a short hedge, the hedger sells a futures contract.
Consequently, a short hedge is also referred to as a sell hedge. By establishing
a short hedge, the hedger has fixed the future cash price and transferred the
price risk of ownership to the buyer of the contract.
As an example of an asset manager who would use a short hedge, con-
sider a pension fund manager who knows that the beneficiaries of the fund
must be paid a total of $30 million four months from now. This will necessi-
tate liquidating a portion of the fund’s common stock portfolio. If the value of
the shares that she intends to liquidate in order to satisfy the payments to be
made decline in value four months from now, a larger portion of the portfolio
will have to be liquidated. The easiest way to handle this situation is for the
asset manager to sell the needed amount of stocks and invest the proceeds in
a Treasury bill that matures in four months. However, suppose that for some
reason, the asset manager is constrained from making the sale today. She can
use a short hedge to lock in the value of the stocks that will be liquidated.
A long hedge is undertaken to protect against rising prices of future
intended purchases. In a long hedge, the hedger buys a futures contract, so
this hedge is also referred to as a buy hedge. As an example, consider once
again a pension fund manager. This time, suppose that the manager expects
a substantial contribution from the plan sponsor four months from now,
and that the contributions will be invested in the common stock of vari-
ous companies. The pension fund manager expects the market price of the
stocks in which she will invest the contributions to be higher in four months
and, therefore, takes the risk that she will have to pay a higher price for the
stocks. The manager can use a long hedge to effectively lock in a futwure
price for these stocks now.
Hedging is a special case of controlling a stock portfolio’s exposure to
adverse price changes. In a hedge, the objective is to alter a current or antici-
pated stock portfolio position so that its beta is zero. A portfolio with a beta
of zero should generate a risk-free interest rate. Thus, in a perfect hedge, the
return will be equal to the risk-free interest rate. More specifically, it will be
the risk-free interest rate corresponding to a maturity equal to the number
of days until settlement of the futures contract.
Therefore, a portfolio that is identical to the S&P 500 (i.e., an S&P
500 index fund) is fully hedged by selling an S&P 500 futures contract with
60 days to settlement that is priced at its theoretical futures price. The return
on this hedged position will be the 60-day, risk-free return. Notice what
has been done. If a portfolio manager wanted to temporarily eliminate all