Question

Suppose that the risk-free interest rate is 8% per annum with continuous compounding and that the dividend yield on a stock index is 3% per annum with continuous compounding. The index is standing at 350 and the futures price for a contract deliverable in 6months is 360.

#1) What should be the theoretical futures price for the stock index?

#2) What arbitrage opportunities does this create?

		#1) theoretical futures price = $366.38
		#1) theoretical futures price = $358.86
		#1) theoretical futures price = $355.87
		#1) theoretical futures price = $368.35
		#2) long futures contracts, and short the shares underlying the index
		#2) long futures contracts, and buy the shares underlying the index
		#2) short futures contracts, and short the shares underlying the index
		#2) short futures contracts, and buy the shares underlying the index

Answer 1

Theoretical Futures Price

= Index x (risk free interest rate - dividend yield) x 6/12

= 350 x (8%-3%) x 6/12 = 358.75

Since the price is 360 after 6 months, the arbitrage should be short futures contracts and by the shares underlying the index