Calculate the return and standard deviation for the following stock, in an econo

Question

Calculate the return and standard deviation for the following stock, in an economy with five possible states. If a Boom (Probability=25%) economy occurs, then the expected return is 50%. If a Good (Probability=25%) economy occurs, then the expected return is 25%. If a Normal (Probability=20%) economy occurs, then the expected return is 15%. If a Bad (Probability=20%) economy occurs, then the expected return is 0%. If a Recession (Probability=10%) economy occurs, then the expected return is -18%. Show your work for partial credit.

Explanation / Answer

State of Economy Probability Expected Return Probable Expected Return Boom 0.25 0.5 0.125 Good 0.25 0.25 0.0625 Normal 0.2 0.15 0.03 Bad 0.2 0 0 Recession 0.1 -0.18 -0.018 Total 1 0.1995 MeanExpected Return of th stock= 19.95% Standard deviation for the stock State of Economy Expected Return Exp.Ret-Mean Return0.1995 (Exp.Ret-Mean Return0.1995 )^2 Boom 0.5 0.3005 0.0903 Good 0.25 0.0505 0.00255 Normal 0.15 -0.0495 0.00245 Bad 0 -0.1995 0.0398 Recession -0.18 -0.3795 0.14402 Total of the squared difference 0.27912 Standard deviation= Sq. Rt. Of .(27912/(6-1)) Sq. Rt. Of 0.055824 ie. 23.63%

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