Question

The sp500 today is at 2677.55 and the sp500 futures settlement price for December 2018 is at 2649.2. An investor decides to put $662,300 in a mutual fund which trakcs the sp500 and, at the same time, enter in an unspecified number of sp500 futures. The standard deviation of the sp500 returns is 10.2% and the average returns 10.9%. Decide if the investor should enter the short or long, and how many futures contracts he should take. Calculate the gains/losses for the mutual fund alone and the fund plus however many futures you decide the investor should take. Calculate all for December, supposing a year, and suppose the sp500 can vary by one std.

Answer 1

Assuming the investment is made on January 1, 2018 and the futures expiry date is December 31, 2018.

SP500 on Jan. 1 is 2677.55 with avg. return of 10.9% having standard deviation of 10.2%.

Given, in a year the SP500 can vary by 1 standard deviation.

Thus the lowest possible value of SP500 = Today’s Value + [(Avg. Return – 1 * Standard deviation) * Today’s value]

                                                                = 2677.55 + [(10.9 – 1* 10.2) % * 2677.55] = 2679.42

Highest possible value of SP500 = Today’s Value + [(Avg. Return + 1 * Standard deviation) * Today’s value]

                                                                = 2677.55 + [(10.9 + 1* 10.2) % * 2677.55] = 3237.16

Since the value of SP500 is does not go below 2679.42 in worst case scenario, which is higher than the futures settlement price. Hence the investor should enter into short contact in futures market.

No. of contracts taken = 662300 / 2649.20 = 250

The mutual fund investment tracks the SP500, hence there will be gains from the investment.

When SP500 performs badly:

Gain from Mutual fund = 662300 * (10.9 – 10.2) % = $463.31

When SP500 performs at its best:

Gain from Mutual fund = 662300 * (10.9 + 10.2) % = $138420.70

Thus the gain from mutual would be anything between $463.31 and $138420.70 depending upon the performance of SP500.

Gains from futures investment when SP500 performs badly = (2679.42 – 2649.20) * 250 = $7555

Gains from futures investment when SP500 performs at its best = (3237.16 – 2649.20) * 250 = $146990

Therefore, gain from mutual fund and futures would be between $8018.31 and $285410.7.