Question

You have the following market data.

• The S&P 500 market index currently is 94.87.
• The annualized, continuously compounded dividend yield on this index is 3.71%.
• The futures contract on this index has an index multiplier of 100.
• The annualized, continuously compounded risk-free rate is 3.41%.
• The index futures contract that expires in 5 months has a futures price of 80.32.

What is the total net profit if you execute the arbitrage strategy with one futures contract?

Do not round values at intermediate steps in your calculations. Enter your answer in dollars and cents to two decimal places, but omit the $ symbol and commas. For example, enter $1,234.56 as 1234.56 as your answer.

Answer 1

The price of Futures contract with know dividend yield is given by:

F = S*exp^{^(r-q)*t}

where,

F - Futures Price of the asset

S - Spot Price of the asset

r - Risk free rate (continuously compounded) on annualized basis

q - Dividend yield (continuously compounded) on annualized basis

t - time until expiry

Putting values in the above formula, we get

F = 94.87* exp^^{(0.0341-0.0371)*(5/12)} = 94.7515

* Please note Futures price is less than the Spot price as dividend yield is more than the risk free rate.

Since, market future price of 80.3200 is less than calculated future price of 94.7515, arbitrageurs can make arbitrage profit by shorting the stocks underlying index and taking a long position (purchase) in the futures contract.

Net profit on 1 contract = 100*(94.7515-80.3200) = 1443.15

where 100 is the index multiplier