# Calculation of Standard Deviation and Variance

Question

The following table gives data on daily changes in the spot price and futures price for a certain commodity:

ΔS    +5    +8    -2    +3    -5    +0    -2    +7    +3    +7
ΔF    +2    +4    -1    +0    +1    -1    -7    +2    +5    +8

(a)  Use the data to calculate a minimum variance hedge ratio for an investor who holds the commodity and plans to sell it soon. Ignore tailing adjustments to account for daily settlement.
(b)  Evaluate how well a hedging strategy based on the minimum variance hedge ratio would have worked for each day of the 10-day period covered by the data, i.e. compute the value of your hedge for each of the ten days by adding losses/gains from both the spot and futures positions.
(c)  What is the cumulative gain/loss over the 10 days?
(d)  What is the daily standard deviation in your gain/losses? (e)  What is the daily standard deviation without your hedge?
(f )  What is the daily standard deviation if you use a (not optimal) hedge of 1 short position in the futures?

Summary

The question belongs to Statistics and it is about calculating variance in hedge ratio for an investor. The profit or loss has been calculated along with the standard deviation of profit and loss has also been calculated.

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