Question

There is a stock index futures contract maturing in one year. The risk-free rate of interest for borrowing is 3.5% per annum, and the corresponding risk-free rate for lending is 0.6% per annum lower. Assume that you can reinvest all dividends received up to futures maturity and thereby receive 1.4 index points at futures maturity. The current level of the stock index is 3,674 index points. The bid-ask spread involved in trading the index basket of stocks is 2 index points, and there are additional 2 index points stock borrowing fees payable at maturity in case there is short-selling involved. Finally, round-trip commissions in the futures market are 8 index points and payable at the start. There are no other transactions costs involved in arbitrage. What is the highest futures price that will not allow arbitrage? Use one decimal place for your answer.

Answer = 3,810.5

Answer 1

The current bid ask quotes of the Index should be 3673 - 3675

Case 1

If stock index is purchased now by borrowing money

Borrow (3675+8) at 3.5% and buy the Index. and also pay the round trip commission

Amount payable at maturity = (3675+8)*1.035 -1.4 (received as dividends) = 3810.51

So, if the Futures price is below 3810.51, there will be no arbitrage

Hence, the maximum Futures price is 3810.51

Case 2

If stock index is short sold for 3673

Get (3673-8) and invest the same at 0.6% for 1 year

Amount available at maturity = (3673-8)*1.006 - 2-1.4 =3683.59

So, if the Futures price is above 3683.59, there will be no arbitrage

So, the minimum value of Futures is 3683.59 for no arbitrage

and range of Futures price values for no arbitrage (3683.59, 3810.59)

So, the highest futures price for no arbitrage is 3810.51