Please focus on Question C Please show all work Consider a 1

Please focus on Question C. Please show all work.

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

First we would calculate the forward price as per provided in Part 1 F0 = (S0 + U)e^rt F0 = (400+2)e^0.10 F0 = 402*1.105171      444.28 The forward rate is $444.28 and one year forward purchase is $445 The forward price is lower than the one year forward purchase (445-444.28) 0.72 So we can buy the stock and sell the future so earn arbitrage profit of $ 0.72 If the asset provides a lump sum income distribution mid year that is of $ 50 The present value of this income 50/(1.10^0.50) $47.67 F0 = (400+2-47.67)e^0.10 F0 = 354.33*1.105171 $391.60 Here the theoretical forward price is less than the future rate of stock So we can buy the stock now and sell the future so we would earn arbitrage profit of (445-391.60) of $ 53.40