Question

a) The current price of Google is $1,300. The yield curve is flat at 5% annual interest rate, compounded every 6 months. Google will pay a dividend of $13, six months later. Consider a 6-month futures contract on Google stock, which expires right after the dividend is paid. What is the fair price of this contract?”

b) You observe that the current price of the market futures that expires in 6 months is $1,350. How would you take advantage of this mispricing?

Answer 1

a)

As per Cost of carry model ,

Fair price of the futures contract = Stock price + interest cost - dividend

= 1300 * 1.025 - 13 = 1332.50 - 13 =$1319.50

( here the interst rate is 5% compounded semiannually hence 2.5% per 6 months. )

b)

The fair price of the contract is $1319.50 but the actual price is $ 1350.00

The theoritical price is less than the actual price hence investor should S + and F - ie buy the stock @1300 and sell futures @ 1350.

No matter whatever is the actual price is in future this will fetch a profit = ( 1350-1319.50 ) = 30.50