Question

Suppose the current price on a stock is $25, the stock has an annual dividend yield of 2.5%. The risk-free rate is 5%. If a futures contract on this stock is available with a 3-month maturity, what should its price be? If the future price in the market is $25.50, how can you structure an arbitrage position.

Answer 1

Future price = Spot price of the stock + Dividend yield + yield on holding the same amount of money if invested at risk free rate

= 25 - 25 *2.5% * 3 /12 +25*5% * 3/12

= 25 - 0.15625 + 0.3125

= $25.16

Future price in the market is $25.50

Arbitrage can be done using following steps.

Step 1 : Borrow $25 today @ risk free rate for 3 months ie $25 @ 5%

So amount to paid after 3 months = 25 + 25*5%*3/12

= 25 +0.3125 = 25.3125

Step 2 : Buy stock with the borrowed money.

Step 3: Enter into a futures contract to sell the stock after 3 months @ 25.50

Step 4 : After 3 months sell the stock @ 25.50. We receive $25.50

Step 5 : Dividend received on the stock = 25 * 2.5%*3/12

= 0.15625

Step 6 : Amount return to the lender = @$25.3125

Step 7 : Profit = 25.50 +0.15625 - 25.3125

= 0.34375