Question

Problem 1

On February 6, 2012, Wal

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Mart (WMT) stock was trading at $61.88. The stock was

expected to rise to $70 by the end of March 2013. On February 6, 2012, a forward

dealer offers to sell at $65 and buy at $64 a forward contract on WMT for delivery in one

month. On 2/6/2012, you can borrow or lend at a 1 month risk free interest rate of 1.2%

(annual percent rate, APR).

1.

The forward price is not an equilibrium price. Explain/Prove why the market is not in

equilibrium.

2.

How can you exploit the situation to make an arbitrage profit? Keep in mind that an

arbitrage requires no net investment but a sure profit.

Answer 1

1. The Equilibrium Price of Mart (WMT) one month forward is $61.88 * (1+(0.012 * 1/12)) = $61.94.

The dealer offers to sell at $65 and buy at $64 for delivery in one month whereas considering the risk free interest rate of 1.2% (annual percent rate, APR), the market price should have been $61.94 and hence the market is not in equilibrium.

2. Here the forward price offered by the dealer is more than the equilibrium price, hence there exist an arbitrage opportunity. The forward price is more than the equilibrium price so we can buy in the spot and sell in the forward contract. The step by step method to exploit this opportunity is as follows :

a. Borrow $61.88 at the rate of 1.2% pa

b. Invest in the share of Mart

c. Sell to the forward dealer the share of Mart at $64

d. After one month, the dealer will give $64 and we will give him the delivery of the share of Mart.

e. Repay the loan with interest to the bank i.e. $61.88 principal + $0.06 interest; Total $61.94.

f. Here we have made the sure profit of $2.06 per share.