Question

There is a stock index futures contract maturing in one year. The risk-free rate of interest for borrowing is 4.7% per annum with annualized compounding, and the corresponding risk-free rate for lending is 0.3% per annum lower. Assume that you can reinvest all dividends received up to futures maturity and thereby receive 1.2 index points at futures maturity. The current level of the stock index is 3,385 index points. The bid-ask spread involved in trading the index basket of stocks is 3 index points, and there are additional 10 index points stock borrowing fees payable at maturity in case there is short-selling involved. Finally, round-trip commissions in the futures market are 9 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 1

The current bid ask quotes of the Index should be 3383.5 - 3386.5

Case 1

If stock index is purchased now by borrowing money

Borrow (3386.5+9) at 4.7% and buy the Index.

Amount payable at maturity = (3386.5+9)*1.047 -1.2 = 3553.889

So, if the Futures price is below 3553.889, there will be no arbitrage

Case 2

If stock index is short sold for 3383.5

Get (3383.5-9) and invest the same at 0.3% for 1 year

Amount available at maturity = (3383.5-9)*1.003 - 10-1.2 =3373.42

So, if the Futures price is below 3553.889, there will be no arbitrage

So, range of Futures price values for no arbitrage (3373.42, 3553.889)

So, the highest futures price for no arbitrage is 3553.889