Question

12.David Johnson is a portfolio manager at CFAL and has to estimate the values of two securities. The available information is shown in the table below.

Stock A Stock B

Return Probability of the return    Return    Probability of the return

19%    15%    23%    10%

15%    60%    13%    60%

11%    25%    12%    30%

a. Which of the two stocks has the higher expected return?

b. Which stock is riskier

Answer 1

Answer a.

Stock A:

Expected Return = 0.15 * 0.19 + 0.60 * 0.15 + 0.25 * 0.11
Expected Return = 0.1460 or 14.60%

Stock B:

Expected Return = 0.10 * 0.23 + 0.60 * 0.13 + 0.30 * 0.12
Expected Return = 0.1370 or 13.70%

Stock A has the higher expected return.

Answer b.

Stock A:

Variance = 0.15 * (0.19 - 0.146)^2 + 0.60 * (0.15 - 0.146)^2 + 0.25 * (0.11 - 0.146)^2
Variance = 0.00062

Standard Deviation = (0.00062)^(1/2)
Standard Deviation = 0.0250 or 2.50%

Stock B:

Variance = 0.10 * (0.23 - 0.137)^2 + 0.60 * (0.13 - 0.137)^2 + 0.30 * (0.12 - 0.137)^2
Variance = 0.00098

Standard Deviation = (0.00098)^(1/2)
Standard Deviation = 0.0313 or 3.13%

Stock B is riskier.