Question

Based on the following data;

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

Recession                                      0.2                                4%                                  -20%

Normal Growth                            0.65                               8%                                   20%

Boom                                             0.15                             16%                                   60%   

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

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

the portfolio is formed by investing 50% of the funds in Stock A and the rest in Stock B.

Answer 1

Answer a.

Stock A:

Expected Return = 0.20 * 0.04 + 0.65 * 0.08 + 0.15 * 0.16
Expected Return = 0.0840 or 8.40%

Variance = 0.20 * (0.04 - 0.084)^2 + 0.65 * (0.08 - 0.084)^2 + 0.15 * (0.16 - 0.084)^2
Variance = 0.001264

Standard Deviation = (0.001264)^(1/2)
Standard Deviation = 0.0356 or 3.56%

Stock B:

Expected Return = 0.20 * (-0.20) + 0.65 * 0.20 + 0.15 * 0.60
Expected Return = 0.1800 or 18.00%

Variance = 0.20 * (-0.20 - 0.18)^2 + 0.65 * (0.20 - 0.18)^2 + 0.15 * (0.60 - 0.18)^2
Variance = 0.055600

Standard Deviation = (0.055600)^(1/2)
Standard Deviation = 0.2358 or 23.58%

Answer b.

Weight of Stock A = 0.50
Weight of Stock B = 0.50

Recession:

Expected Return = 0.50 * 0.04 + 0.50 * (-0.20)
Expected Return = -0.08

Normal:

Expected Return = 0.50 * 0.08 + 0.50 * 0.20
Expected Return = 0.14

Boom:

Expected Return = 0.50 * 0.16 + 0.50 * 0.60
Expected Return = 0.38

Portfolio:

Expected Return = 0.20 * (-0.08) + 0.65 * 0.14 + 0.15 * 0.38
Expected Return = 0.1320 or 13.20%

Variance = 0.20 * (-0.08 - 0.1320)^2 + 0.65 * (0.14 - 0.1320)^2 + 0.15 * (0.38 - 0.1320)^2
Variance = 0.018256

Standard Deviation = (0.018256)^(1/2)
Standard Deviation = 0.1351 or 13.51%