Book- Options, Futures and other Derivatives by John C Hull. Chapter 5- determination of Forward and Future prices.

Q. The following is a set of prices for stock index futures on the S&P 500.

Maturity Futures price

March 246.25

June 247.75

The current level of the index is 245.82 and the current annualized T-Bill rate is 6%. The annualized dividend yield is 3%. (Today is January 14. The March futures expire on March 18 and the June futures on June 17.)

(a) Estimate the theoretical basis and actual basis in each of these contracts.

(b) Using one of the two contracts, set up an arbitrage. Also show how the arbitrage will be resolved at expiration. [You can assume that you can lend or borrow at the risk-free rate and that you have no transaction costs or margins.]

(c) Assume that a good economic report comes out on the wire. The stock index goes up to 47.82 and the T-Bill rate drops to 5%. Assuming arbitrage relationships hold and that the dollar dividends paid do not change, how much will the March future go up by?