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A mutual fund has five equally likely outcomes: 15%, -7%, 5%, 2%, and -1%. Calculate the...

A mutual fund has five equally likely outcomes: 15%, -7%, 5%, 2%, and -1%. Calculate the standard deviation of the rate of return.

3.8%

9.2%

5.8%

7.3%     

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Answer #1

Probability of each=(1/5)=0.2

Expected return=Respective return*Respective Probability

=(0.2*15)+(0.2*-7)+(0.2*5)+(0.2*2)+(0.2*-1)=2.8%

Probability Return Probability*(Return-Expected Return)^2
0.2 15 0.2*(15-2.8)^2=29.768
0.2 -7 0.2*(-7-2.8)^2=19.208
0.2 5 0.2*(5-2.8)^2=0.968
0.2 2 0.2*(2-2.8)^2=0.128
0.2 -1 0.2*(-1-2.8)^2=2.888
Total=52.96%

Standard deviation=[Total Probability*(Return-Expected Return)^2/Total probability]^(1/2)

=(52.96)^(1/2)

=7.3%(Approx).

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