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 maturities. b) If currently the bid and ask on this 1-year futures contract are $444.5 and $445 respectively, what will you do? Please be specific and describe what this would mpy jris 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 (C is the important question, so please elaborate on this question)

Solution

Futures price = (Spot + Storage cost) * (1+risk free rate)^Time period

Futures Price = (400 + 2 ) * (1.1)^1

= 402 * 1.1

Futures Price = 442.2.

b) . Current futures price is 442.2 but in bid ask is more than this price. Hence it involves arbitrage oppurtunity. Buy the future on asset for 442.2 and sell the futures in market for bid price of 444.5 and arbitrage profit of 444.5 - 442.2 = 2.3.

C). If assets provide a lumpsum income the Futures price formula is:

Futures price = (Spot + Storage cost - Lumpsum income) * (1+risk free rate)^Time period

Hence the futures price arrived at will be less than 442.2 and the arbitrage profit can be generated as per in the previous step.