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 $2 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 maturitiesb) If currently the bid and ask on this 1-year futures contract are $444.5 and S445 respectively, what will you do? Please be specific and describe what this would imply? c) If this asset provides a lump sunm income distribution mid year that was S50, what would happen. (This is the important queston, please focus on this question. S 1S

Solution

Greetings,

The area tested in this question is the cost of carry model of pricing futures contract and carry out arbitrage if market price is different from value calculated as per cost of carry model.

As per COC model, price of futures contract is given by -

Futures Price = Spot Price * (1+RF)^t + FV of storage costs - convenience yield - monetary benefit (if any)

So Futures price as per COC = (400+2)*(1.1) = 442.2

Actual price of futures is 444.5/445 which is more than the model value. Hence futures are overpriced in the market. One can make arbitrage by selling the futures and buying the asset spot.

Sale Price of futures is 444.5 (bid price). We will pay 400 and 2 today i.e 402 which will be borrowed at 10%. After one year, borrowing will be repaid along with interest = 442.2. We will sell the futures at 444.5 by delivering the shares already bought. Arbitrage profit will be 444.5-442.2=2.3.

This type of arbitrage where futures are overpriced, hence we sell them and buy asset spot is known as cash and carry arbitrage.

Now if the asset provides as monetary benefit then it will reduce the model value further as under -

Since benefit is provided in the mid year, hence we need to find out FV = 50*(1.1)^0.5= 52.44. So the model value = 442.2 - 52.44 = 389.76.

Futures became more overpriced. So we need to carry out cash and carry arbitrage and profit will be =444.5 - 389.76 = 54.74