Question

The following table presents forecasted returns for three companies under various potential states of the economy:

State	Probability	Stock X	Stock Y	Stock Z
Above Average	10%	38.3%	27.1%	43.2%
Average	45%	16.7%	5.5%	12.0%
Below Average	30%	-2.5%	-4.0%	-7.0%
Recession	15%	-10.9%	-6.0%	-15.6%
Weight		55%	30%	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

Weight of Stock X = 0.55
Weight of Stock Y = 0.30
Weight of Stock Z = 0.15

Above Average:

Expected Return = 0.55 * 0.3830 + 0.30 * 0.2710 + 0.15 * 0.4320
Expected Return = 0.35675

Average:

Expected Return = 0.55 * 0.1670 + 0.30 * 0.0550 + 0.15 * 0.1200
Expected Return = 0.12635

Below Average:

Expected Return = 0.55 * (-0.0250) + 0.30 * (-0.0400) + 0.15 * (-0.0700)
Expected Return = -0.03625

Recession:

Expected Return = 0.55 * (-0.1090) + 0.30 * (-0.0600) + 0.15 * (-0.1560)
Expected Return = -0.10135

Expected Return of Portfolio = 0.10 * 0.35675 + 0.45 * 0.12635 + 0.30 * (-0.03625) + 0.15 * (-0.10135)
Expected Return of Portfolio = 0.066455

Variance of Portfolio = 0.10 * (0.35675 - 0.066455)^2 + 0.45 * (0.12635 - 0.066455)^2 + 0.30 * (-0.03625 - 0.066455)^2 + 0.15 * (-0.10135 - 0.066455)^2
Variance of Portfolio = 0.017430

Standard Deviation of Portfolio = (0.017430)^(1/2)
Standard Deviation of Portfolio = 0.1320 or 13.20%