Question

A hedge fund can enter a 6-month forward contract on a stock for a forward price of $41. The current stock price is $40. The 6-month risk-free rate is 3% (per year) and the stock pays no dividends. Describe an arbitrage opportunity.

Please, help me with this .

Answer 1

In an effficient market,

Should be Forward Price of a stock is = Current stock Price + Interest Rate for the forward period.

In the gaive case,

Should be Forward price = 40 X (1.03)^1/2.....................[fwd period is 6 months]

= $40.60

As you can see, Should be Forward price is not equal to the actual Forward Price, therefor there exists an Arbitrage opportunity which is shown in the below steps.

Step 1: (T = 0) Sell stock 6 month Forward at $41

Inflow = outflow = 0

Step 2: (T=0) Buy Stock Spot @ $40 by borrowing the money from somewhere at 3% (Rf) for 6 months.

Step 3: (T = 6 month) Inflow = $41 ........................( from Forward sell contract)

Step 4: (t= 6 months) Outflow = $40 X (1.03)^1/2..........................(repayment of loan with interest)

= $ 40.60

Therefore arbitrage profit = Inflow - Outflow

= 41 - 40.60

= $ 0.40