Alan Aa E. 1. Portfolio expected return and standard deviation Wilson holds a tw

Question

Alan Aa E. 1. Portfolio expected return and standard deviation Wilson holds a two-stock portfolio that invests equally in Kelevra Industries and Old Glory Insurance Company (50% of his portfolio is in each stock), Each stock's expected return for the next year will depend on market conditions. The stocks' expected returns if there are poor, average, or great market conditions are shown below: Kelevra Old Glory Market Condition Probability Industries Insurance Co. 0.25 12% 2% OO 14% Average 0.50 6% 14% 0.25 46% Great What is the portfolio's expected return over the next year? O 10.75% 11.00% 10.50% 9.25% 9.00% O What is the expected standard deviation of portfolio return? O 10.65% O 13.47% O 10.99% O 13.10% O 12.02% What is the coefficient of variation (CV) for the portfolio's expected return? O 1.409 Q 1.139 O 1.165 O 1.219 O 1.195

Explanation / Answer

Market Condition Portfolio return:

Poor =50.% x -12.% + 50.% x -2.%

Poor = -7.00%

Average =50.% x 14.% + 50.% x 6.%

Average = 10.00%

Great = 50.% x 46.% + 50.% x 14.%

Great = 30.00%

What is the portfolio's expected return over the next year?

Solution-

Poor = -7.00%*0.2500

Poor = -1.75%

Average = 10.00%*0.5000

Average = 5.00%

Great = 30.00%*0.2500

Great = 7.5%

Expected Return = -1.75% + 5.00% + 7.5%

Expected Return =10.75%

What is the expected standard deviation of portfolio return?

Solution-

Poor=(-7.%)-10.75% =-0.1752= -0.030625

Poor =0.25 x -0.030625 = 0.007656

Average =(10%)-10.75%= (-0.0075)2 = -0.000056

Average = 0.5 x 0.000056 = 0.000028

Great =(30.%)-10.75% =(0.1925)2 =0.037056

Great = 0.25 x 0.037056= 0.009264

Variance = 0.007656+ 0.000028+ 0.009264

Variance = 0.016948

So,

Standard Deviation = (0.016948)1/2

Standard Deviation = 13.10%

What is the expected standard deviation of portfolio return?

Solution-

Coefficient of variation= Standard deviation / Mean

Coefficient of variation= 13.10% / 10.75%

Coefficient of variation=1.219

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