Consider a 1year futures contract on an investment asset tha

Consider a 1-year futures contract on an investment asset that provides no income. It costs S2 per unit to store the asset, with the payment being made at the beginning of the year. Assume that the spot price is $400 per unit and the risk free rate is 10% per annum for all maturities. b) If currently the bid and ask on this 1-year futures contract are S444.5 and S445 respectively, what will you do? Please be specific and describe what this would imply? c) If this asset provides a lump sum income distribution mid year that you forgot to estimate in a above would you still be confident about your suggestion in b? Please explain

Solution

At initiation the present value of the spot and futures price (cost) should be same otherwise we will have possible arbitrage. This means that the futures price should equal the spot price plus storage cost plus the carrying cost in term if interest and minus any income yield expected from the asset during the futures tenure. In this case we have:

Spot Price (S₀) = $ 400 per unit and storage cost (c) = $ 2 per unit and risk free rate (r) = 10%.

The the futures price should be = (S₀+c) * (1+r) = 402 * 1.10 = $442.2

Since the futures price quote is $444.5 and 445 which is we can buy at 445 or sell at 444.5 but the futures price should be 442.2 we have an arbitrage which we can benefit as below:

c. If this asset pays a lumpsum income mid year then the future price should be :

Future price = (S₀ + c) * (1+r) - (Income mid year)/(1+r/2). Since the effect of mid year income distribution will be to reduce the carrying cost of the asset (by the present value of the income distribution), the arbitrage will still stay and may become even more profitable since the expected future price will become even lower than $442.2.