Question

Over the past six years, a stock had annual returns of 10 percent, 5 percent, 7...

Over the past six years, a stock had annual returns of 10 percent, 5 percent, 7 percent, 8 percent, 2 percent, and -11 percent, respectively. What is the standard deviation of these returns?

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Answer #1
Solution:
The standard deviation of these returns =7.61%
Working Notes:
Average return(Er)= Sum of returns/ No. of returns
=(0.10 + 0.05 +0.07+0.08+0.02+(-0.11))/6
=0.21/6
=0.035
Standard deviation = Square root of (variance)
Variance[(s.d.)^2] =[(r1 -Er)^2+(r2 -Er)^2+(r3 -Er)^2+(r4 -Er)^2+(r5 -Er)^2+(r6 -Er)^2]/(n-1)
= [(0.10 - 0.035)^2 + (0.05 - 0.035)^2 +(0.07 - 0.035)^2+(0.08 - 0.035)^2+(0.02 - 0.035)^2+(-0.11 - 0.035)^2]/(6-1)
= (0.004225 + 0.000225 +0.001225+0.002025+0.000225+0.021025)/5
=0.00579
Standard deviation = Square root of (variance)
=Square root of (variance)
= (0.00579)^(1/2)
=0.076092
=0.0761
=7.61%
Please feel free to ask if anything about above solution in comment section of the question.
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