A stock index currently has a value of 1,900 and an anticipated dividend of $20

Question

A stock index currently has a value of 1,900 and an anticipated dividend of $20 over the next 6 months. The borrowing rate over the next 6 months is 2% APR, or 1% for the next 6 months. If a futures contract with a settlement date in 6 months currently offers a price of 1,910: Is the futures contract fairly priced? If not, design an arbitrage to take advantage of the mispricing, and calculate the profit. Explain why the arbitrage transaction you designed in is not really an arbitrage (why is it not risk free?).

Explanation / Answer

Present Value of Dividend =$20 /1.01 =$19.80

Adjusted Spot Price of Index = Current Price - PV of Dividend

=1900-19.80= $1880.20

Fair Future Price =Adjusted spot price*(1+periodic interest rate)

= $1880.20 * 1.01=$1899

Future Offer price =1910

Future contract is not fairly priced because Fair price is less than actual Future price

Arbitrage is possible through Sell of Future and Buy spot.

Buy spot future at 1900 from market by taking a loan for 6 month at 1%

Loan amount at 6 month = 1900*1.01 =1919

Sell value of future =1910

Dividend Received =20

Arbitrage Profit = (1910+20) - 1919 =$11

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