Calculation of Standard Deviation and Variance


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?


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.

Total Word Count NA


Download Full Solution


  • HWA

    this is a very good website

  • HWA

    I have 50 questions for the same test your page is showing only 28

  • HWA

    hi can you please help or guide me to answer my assignments. thanks

  • HWA

    hi can anyone help or guide me to my assignments. thanks

  • HWA

  • HWA

    This solution is perfect ...thanks

  • HWA

    Hello Allison,I love the 2nd image that you did! I also, had never heard of SumoPaint, is something that I will have to exolpre a bit! I understand completely the 52 (or so) youtube videos that you probably watched. Sometimes they have what you want, sometimes they don't! However, it is always satisfying when you are able to produce something that you have taught yourself. Great job!Debra 0 likes

  • HWA

    Perfect bank of solution. 

  • HWA

    great !

  • HWA
    Paul Brandon-Fritzius

    thanks for the quick response. the solution looks good. :)

  • HWA
    tina Johnson

    thnx for the answer. it was perfect. just the way i wanted it. 

  • HWA

    works fine.