Problem on arbitrage opportunity

Question

John Chan considers purchasing a six-month stock futures contract on the shares of Li & Fung Limited. Shares of Li & Fung Limited are now presently trading at $50 per share and it is predicted that Li & Fung Limited will pay a dividend of $1 per share in one and four months. The risk free interest rate is around 5% per annum with continuous compounding.

a) Compute the estimated price of the six-month Li & Fung Limited stock futures contract.

b) When the actual futures price of Li & Fung Limited shares is $50, is there any arbitrage opportunity? Outline the steps needed to do the arbitrage.

Answer 1

a) Based on the theoretical pricing model we get the following:-

Futures Price = Underlying stock price X (1+ annualized interest rate – dividend)
Underlying stock price is $ 50 per share . Rate of interest = 5% and dividend is $1 per share
$50 x ( 1+ .005 - $ 1 per share
$ 50 x ( 1.05-1)= $ 2.5
Futures price will be $ 50+$2.5= $ 52.5

b) The attempt to make a profit by exploiting the differences in identical stocks or any financial instruments is defined as arbitrage. In the above case the actual future price being $ 50 is the same as the current trading price and hence there is no arbitrage opportunity.