Expected Return, Variance, Std. Deviation and Cofficient of Variation: Magee Inc

Question

Expected Return, Variance, Std. Deviation and Cofficient of Variation: Magee Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72. State of the Economy Probability of State Occurring Stock's Expected Return Boom 20% 24.15% Normal 50% 13.50% Recession 30% –13.30%

Available answers: 15.68%, 10.69%, 16.39%, 13.54%, 14.26%

Explanation / Answer

variance= sum of probaility*(expected return- return on each state)^2

Expected return=sum of (Prob* individual return)

=(.2*24.15%)+(.5*13.5%)+(30%*-13.3%)

=7.59%

variance=.2*(7.59%-24.15%)^2+.5*(7.59%-13.5%)^2+.3*(7.59%- -13.3%)^2

=2.032%

standard deviation=variance^0.5

=14.26%

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