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a stock had returns of 18.34 percent, 21.53 percent, -14.63 percent, 8.93 percent, and 28 percent...

a stock had returns of 18.34 percent, 21.53 percent, -14.63 percent, 8.93 percent, and 28 percent for the past five years. what is the standard deviation of the returns
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Answer #1

Solution :- Average of last five year returns = Sum total of returns for five years / Number of years.

= (18.34 % + 21.53 % - 14.63 % + 8.93 % + 28.0 %) / 5

= 62.17 % / 5

= 12.434 %

Calculation of standard deviation of returns in the given question :-

Year Return (Return - Average return) (Return - Average return)2
1 18.34 % 5.906 % (18.34 % - 12.434 %) (5.906 %)2 = 34.8808 %
2 21.53 % 9.096 % (21.53 % - 12.434 %) (9.096 %)2 = 82.7372 %
3 (-) 14.63 % (-) 27.064 % ( - 14.63 % - 12.434 %) (- 27.064 %)2 = 732.4601 %
4 8.93 % (-) 3.504 % (8.93 % - 12.434 %) (- 3.504 %)2 = 12.2780 %
5 28.0 % 15.566 % (28.0 % - 12.434 %) (15.566 %)2 = 242.3003 %
Total 1104.6565 (approx).

Standard deviation of returns = Square root of (Return - Average return)2

= (1104.6565)1/2

= 33.2363 % (Rounded off to 33.24 %).

Conclusion :- Standard deviation = 33.24 % (approx).

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