Question

Consider a 6-month forward contract on a stock whose current price is $40. The stock will not pay any dividend, and the risk-free interest rate is 4% per annum. The forward price of the stock is $43. Is there an arbitrage? If so, show the arbitrage strategy and resulting cash flows.

Answer 1

The forward price is given as =spot price *(1+interest rate)

Given,

Spot price =40

Interest rate =4% per annum or 4%*6/12=2% per 6 months

Hence forward price after 6 months = 40*(1+2%)=40.8

Hence the implied forward price should be =40.8

Hence implied forward price is lower than the stated forward price

Hence arbitrage opportunity exists

To obtain arbitrage benefit

Borrow $40 from market at risk free rate

Hence payment after 6 months =40*(1+2%)=40.8

Buy shares at spot =$40

Net cash flow today= borrowing - purchase of stocks

=40-40=0

Sell forward at 43

At expiry you will receive 43 and you will deliver stock to the market

Hence at expiry cash inflow =43(by sale of shares at forward price)

Cash outflow =payment of borrowing =40.8

Arbitrage profit =43-40.8=2.2