Question

The S&P portfolio pays a dividend yield of 1% annually. Its current value is 1,300. The T-bill rate is 4%. Suppose the S&P futures price for delivery in 1 year is 1,330. Construct an arbitrage strategy to exploit the mispricing and show that your profits 1 year hence will equal the mispricing in the futures market.

Answer 1

Current value of S&P (S0) = 1,300

Risk free rate (r) = 4%

Dividend yield (y) = 1%

Maturity in year = 1

Fair Future Price (F) would be:

But, S&P Future Price is $1,330

There is mis-price thus we can arbitrage profit here.

Arbitrage Strategy:

Future Price is overvalued in the market thus,

Long 1 Future contract.

Short S&P at current price i.e $1,300

Lend $1,300 at 4% for one year

After one year

Receive from lent money = 1300*(1+0.04) = 1,352

Lost dividends = 1,300*(1.01)-1300 = $13

Total Cash inflows = 1353.05-13.07 = 1,339

Buy the S&P with Future price = $1,330

Risk free arbitrage profit = 1339-1330 = $9

Which equals to the mis-price of future price.