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A stock had returns of 19.02 percent, 22.72 percent, −16.16 percent, 9.44 percent, and 28.51 percent...

A stock had returns of 19.02 percent, 22.72 percent, −16.16 percent, 9.44 percent, and 28.51 percent for the past five years. What is the standard deviation of the returns?

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Expert Solution

R D=R-12.706 E=D^2
Year Return(percentage) Deviation from Mean Deviation Squared
1 19.02 6.314 39.8666
2 22.72 10.014 100.2802
3 -16.16 -28.866 833.246
4 9.44 -3.266 10.66676
5 28.51 15.804 249.7664
SUM 63.53 SUM 1233.826
Mean return 12.706 (63.53/5)
Variance of Return =(Sum of Deviation Squared)/(5-1)
Variance of return 308.45648 (1233.826/4)
Standard Deviation =Square Root of (Variance)
Standard deviation of Returns(%) 17.5629291 (SQRT(308.45648)
Standard deviation of Returns 17.56% (Rounded to two decimals)
Excel STDEV function can also be used over returns to find Standard Deviation
Standard Deviation 17.5629291 (Excel Command ;STDEV(19.02,22.72,-16.16,9.44,28.51))
Standard Deviation 17.56%

jeff jeffy answered 8 months ago
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