3. An investment management firm has a client who would like to temporarily reduce his exposure to equities by converting a $25 million equity position to cash for a period of four months. The client would like this reduction to take place without liquidating his equity position. The investment management firm plans to create a synthetic cash position using an equity futures contract. This futures contract is priced at 1170.10, has a multiplier of

$250, and expires in four months. The dividend yield on the underlying index is 1.25%, and the risk-free rate is 2.75%.

A. Calculate the number of futures contracts required to create synthetic cash.

B. Determine the effective amount of money committed to this risk-free transaction and the effective number of units of the stock index that are converted to cash.

C. Assume that the stock index is at 1031 when the futures contract expires. Show how this strategy is equivalent to investing the risk-free asset, cash.