Question

The following table presents forecasted returns for three companies under various potential states of the economy: State Probability Stock X Stock Z Stock Y 27.3% Above Average 10% 37.2% 41.0% Average 45% 17.8% 6.0% 13.6% Below Average 30% -1.2% -4.0% -7.0% Recession 15% -10.6% -16.9% -6.0% 30% Weight 55% 15% What is the standard deviation on a portfolio of these three companies constructed according to the weights given in the table? (Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).

Answer 1

Expected Return in case of Above Average =55%*37.20%+30%*27.30%+15%*41% =34.80%
Expected Return in case of Average =55%*17.80%+30%*6%+15%*13.6% =13.63%
Expected Return in case of Below Average =55%*-1.20%+30%*-4%+15%*-7% =-2.91%
Expected Return in case of Recession =55%*-10.60%+30%*-6%+15%*-16.90% =-10.17%

Expected Return of Portfolio =10%*34.80%+45%*13.63%+30%*-2.91%+15%*-10.17% =7.215%
Standard Deviation on portfolio =(10%*(34.80%-7.215%)^2+45%*(13.63%-7.215%)^2+30%*(-2.91%-7.215%)^2+15%*(-10.17%-7.215%)^2)^0.5 =13.07%
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