You Are Examining the Pricing of Futures on the S&P

question 11

Essay

You are examining the pricing of futures on the S&P 500.The spot level of the S&P 500 index is 250,and the riskless rate is 5%.It is January 1,2003,and the futures contract expires March 31,2003.The dividend yield by month of year is as follows:
month: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
yield: 0.1% 0.1% 0.5% 0.1% 0.1% 0.5% 0.1% 0.1% 0.5% 0.1% 0.1% 0.5%
a. What is the theoretical price of this futures contract?
b. Will this contract ever sell for less than the spot level of the index? If so, what is the earliest time at which this will happen? (Assume that the riskless rate and the dividend yield do not change between January 1, 2003, and March 31, 2003.)
c. Assume now that this contract is correctly priced (= theoretical price) and that you have a portfolio of $50 million that you would like insured against market movements until March. If the portfolio has a beta of 1.25, how would you protect yourself against market risk?
d. Assuming you protect yourself against market movements, what would your expected return be on the protected portfolio through March 1990?

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Definitions:

Effective Rate

The actual interest rate of an investment or loan, taking into account the effects of compounding.

Compounded Semi-Annually

Interest calculation method where the interest is added to the principal sum twice a year, causing the interest to earn interest.

Strip Bond

A type of bond where the principal and regular coupon payments have been separated and are sold individually as zero-coupon bonds.

Interest

The cost of borrowing money, typically expressed as a percentage of the borrowed amount, paid by the borrower to the lender.