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*

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