Question

A stock index currently has a spot price of $1,100. The risk-free rate is 9%, and the index does not pay dividends. You observe that the 3-month forward price is $990. What arbitrage strategy would you undertake?

a. Sell a forward contract, borrow $1,100, and buy the stock index

b. Sell a forward contract, lend $1,100, and short-sell the stock index

c.Sell a forward contract, borrow $1,100, and short-sell the stock index

d. Buy a forward contract, borrow $1,100, and buy the stock index

e. Buy a forward contract, lend $1,100, and short-sell the stock index

Answer 1

Answer will be E. Buy forward contract, lend $1100 and short sell the index.

By doing so, we short sell the index at $1100, and from that money we lend and earned interest @9%. So we have inflow after 3months is 1100 + (1100×9%×3/12) i.e. $1124.75

Outflow after 3 months will be of buying a forward contract of $990.

Hence net inflow will be = $(1124.75 - 990) i.e. $134.75.

Explanation on other option.....

Option A will be invalid because if we sell future we get 990 whereas buy stock at 1100 we will have loss in this transaction.

Option b and option C and option D will be invalid because in arbitrage we sell and buy simultaneously to earn a risk free profit but in option b,c there is only sell option and in option D there is only buy option.