One of your most sophisticated investors, Joseph
DeLuca, believes that the stock market
will decline and hence reduce the value of his substantial portfolio. However,
he does not want to sell the stocks, because the sales would generate a substantial
federal capital gains tax liability in the current tax year. He recently read
that futures may be used to reduce the risk of loss from price changes as well
as vehicles designed to speculate on price changes. You have been his personal
financial planner for many years, and he has asked you to develop a strategy
using futures to achieve his goal of protecting his gains without selling the
securities in the current year.

Since DeLuca has a long position in stocks, you realize that
he needs a short position in futures to reduce the risk of loss. Since his
portfolio is both substantial and well diversified, you decide to limit your
choices to index futures. The portfolio is worth several million dollars, but you
decide to use $1,000,000 as the basis for all comparisons since any other
amount could be expressed as a multiple of $1,000,000. You notice that an index
of the market is 100 and there exists a futures contract with a value that is
500 times the index. The margin requirement is $2,000 per contract. You decide
that the best means to explain the strategy using futures is to answer a series
of questions that illustrate how the futures may be used to meet DeLuca’s goal
of deferring the tax obligation until the next year while protecting his gains,
These questions are as follows:

1. What is the value of the contract in terms of the index?

2. How many contracts would DeLuca have to sell to hedge $1,000,000?
Why should DeLuca sell rather than purchase the contracts?

3. How many cash will DeLuca have to put up to meet the
margin requirement? If the annual interest rate on money market securities is 6
percent, what is the interest lost from the margin requirement if the position
must be maintained for two months?

4. If the market declined by 5 percent, what will happen to the
value of the contracts? Could DeLuca take funds out of the position to reduce
the lost?

5. If the beta of his portfolio is 1.0 and the market declines
by 5 percent, how much would he lose on a $1,000,000 portfolio?

6. If the beta of the portfolio were less than 1.0, could DeLuca
take funds out of the position to reduce the interest lost?

7. Suppose the beta of the portfolio is 0.75 and DeLuca
sells 15 contracts. The market then rises by 10 percent; what are the profits
and losses on the portfolio and on the contracts? What is the net profit or

8. When the contracts expire, will DeLuca have to deliver
the securities he owns to cover the contracts?

9. Does the strategy of using futures contracts achieve its objective?