Question

Following are three economic states, their likelihoods, and the potential returns: Economic State Probability Return Fast...

Following are three economic states, their likelihoods, and the potential returns:

Economic State Probability Return
Fast growth 0.24 30 %
Slow growth 0.36 7
Recession 0.40 –19

Determine the standard deviation of the expected return. (Do not round intermediate calculations and round your answer to 2 decimal places.)

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Answer #1

Expected return=Respective return*Respective probability

=(0.24*30)+(0.36*7)+(0.4*-19)=2.12%

probability Return probability*(Return-Expected Return)^2
0.24 30 0.24*(30-2.12)^2=186.550656
0.36 7 0.36*(7-2.12)^2=8.573184
0.4 -19 0.4*(-19-2.12)^2=178.42176
Total=373.5456%

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

=(373.5456)^(1/2)

=19.33%(Approx).

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