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Consider the following five monthly returns: 8% -4% 9% 12% - 1% a
Consider the following five monthly returns: 8% -4% 9% 12% - 1% a. Calculate the arithmetic average monthly return over this period and express your answer as a percentage per month b. Calculate the geometric average monthly return over this period. c. Calculate the monthly variance over this period. d. Calculate the monthly standard deviation over this period. a. The arithmetic average is 1%. (Round to two decimal places.)
Expert Solution
a. Arithmetic Return =(Return Month 1+Return Month 2+Return Month 3+Return Month 4+Return Month 5)/5
=(8%-4%+9%+12%-1%)/5 =4.80%
b. Geometric Return =((1+8%)*(1-4%)*(1+9%)*(1+12%)*(1-1%))^(1/5)-1 =4.62%
c. Monthly Variance =((8%-4.80%)^2+(-4%-4.80%)^2+(9%-4.80%)^2+(12%-4.80%)^2+(-1%-4.80%)^2)/(5-1)=0.00477
d. Standard Deviation =Monthly Variance^0.5 =0.00477^0.5 =6.91%
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