You find a certain stock that had returns of 14.2 percent, –22.1 percent, 28.1 p

Question

You find a certain stock that had returns of 14.2 percent, –22.1 percent, 28.1 percent, and 19.1 percent for four of the last five years. Assume the average return of the stock over this period was 12.2 percent.

What was the stock’s return for the missing year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Stock's return %

What is the standard deviation of the stock’s returns? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation %

Explanation / Answer

Average return=Total returns/Total time period

12.2=(14.2-22.1+28.1+19.1+x)/5[where x=return for missing year]

(12.2*5)=39.3+x

x=(61-39.3)

=21.7%=return for missing year

Standard deviation=[Total (Return-mean)^2/(Time Period-1)]^(1/2)

[1571.16/(5-1)]^(1/2)

=(1571.16/4)^(1/2)

=19.82%(Approx).

Return (Return-mean)^2 14.2 (14.2-12.2)^2=4 -22.1 (-22.1-12.2)^2=1176.49 28.1 (28.1-12.2)^2=252.81 19.1 (19.1-12.2)^2=47.61 21.7 (21.7-12.2)^2=90.25 Total=1571.16%

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