Question

Based on the following data;

(a) calculate the expected return and the standard deviation of returns for each stock.

State of the Economy         Probability      Stock A Rate of Return   Stock B Rate of Return

Recession                                  0.25                                 6%                                 -20%

Normal Growth 0.45                                7%                                  13%

Boom                                         0.3                                 11%                                   33%      

(b) Calculate the expected return and the standard deviation on the portfolio, where

the portfolio is formed by investing 65% of the funds in Stock A and the rest in Stock B

Answer 1

Answer a.

Stock A:

Expected Return = 0.25 * 0.06 + 0.45 * 0.07 + 0.30 * 0.11
Expected Return = 0.0795 or 7.95%

Variance = 0.25 * (0.06 - 0.0795)^2 + 0.45 * (0.07 - 0.0795)^2 + 0.30 * (0.11 - 0.0795)^2
Variance = 0.000415

Standard Deviation = (0.000415)^(1/2)
Standard Deviation = 0.0204 or 2.04%

Stock B:

Expected Return = 0.25 * (-0.20) + 0.45 * 0.13 + 0.30 * 0.33
Expected Return = 0.1075 or 10.75%

Variance = 0.25 * (-0.20 - 0.1075)^2 + 0.45 * (0.13 - 0.1075)^2 + 0.30 * (0.33 - 0.1075)^2
Variance = 0.038719

Standard Deviation = (0.038719)^(1/2)
Standard Deviation = 0.1968 or 19.68%

Answer b.

Weight of Stock A = 0.65
Weight of Stock B = 0.35

Recession:

Expected Return = 0.65 * 0.06 + 0.35 * (-0.20)
Expected Return = -0.0310

Normal:

Expected Return = 0.65 * 0.07 + 0.35 * 0.13
Expected Return = 0.0910

Boom:

Expected Return = 0.65 * 0.11 + 0.35 * 0.33
Expected Return = 0.1870

Portfolio:

Expected Return = 0.25 * (-0.0310) + 0.45 * 0.0910 + 0.30 * 0.1870
Expected Return = 0.0893 or 8.93%

Variance = 0.25 * (-0.0310 - 0.0893)^2 + 0.45 * (0.0910 - 0.0893)^2 + 0.30 * (0.1870 - 0.0893)^2
Variance = 0.006483

Standard Deviation = (0.006483)^(1/2)
Standard Deviation = 0.0805 or 8.05%