Question

There is a stock index futures contract maturing in one year. The risk-free rate of interest for borrowing is 5.0% per annum, and the corresponding risk-free rate for lending is 1.0% per annum lower. Assume that you can reinvest all dividends received up to futures maturity and thereby receive 0.6 index points at futures maturity. The current level of the stock index is 2,496 index points. The bid-ask spread involved in trading the index basket of stocks is 7 index points, and, in case there is short-selling involved, there are additional 3 index points stock borrowing fees payable when the stock is returned to the lender at maturity. Finally, round-trip commissions in the futures market are 3 index points and payable at the start. There are no other transaction costs involved in arbitrage. What is the lowest futures price that will not allow arbitrage? The answer is 2585.5. How do you solve this?

Answer 1

Let's execute this arbitrage:

• Short sell the index
• Buy the index future

The cash flows will be as follow:

	Cash flows at t = 0
Short sell the index	2,496.00
[-] Bid ask spread	7.00
[-] Short selling borrowing fees	3.00
Net stock price	2,486.00

So, you will lend it @ 5% - 1% = 4%

Hence, the proceeds at t = 1 = 2,486 x (1 + 4%) =  2,585.44

Hence, Future price should be at least 2,585.44 to prevent this arbitrage.

PS: I see you have mentioned the aswer as 2,585.5; I believe there must be some rounding off differences between what I have here and what you have at your end.