Question

You decide to invest in a portfolio consisting of 23 percent Stock X, 44 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio?

State of Economy Probability of State of Economy Return if State Occurs

Stock X Stock Y Stock Z
Normal 0.82 11.30% 4.70% 13.70%
Boom 0.18 18.60% 26.60% 18.10%


a. 1.80%
b. 4.90%
c. 6.13%
d. 2.41%
e. 7.15%

Answer 1

b. 4.90%

Step-by-step explanation:

the portfolio's return in a normal economy:

= (0.23 x 11.3%) + (0.44 x 4.7%) + (0.33 x 13.7%) = 9.119%

the portfolio's return in a booming economy:

= (0.23 x 18.6%) + (0.44 x 26.6%) + (0.33 x 18.1%) = 21.955%

weighted average return:

(0.82 x 9.119%) + (0.18 x 21.955%) = 11.42948%

standard deviation:

= {[0.82 x (9.119% - 11.42948%)²] + [0.18 x (21.955% - 11.42948%)²]}⁰°⁵

= (0.000437742 + 0.001994158)⁰°⁵ = 0.0024319⁰°⁵ = 0.049 = 4.9%

The standard deviation of a stock or a portfolio measures the risk of the stock or the portfolio. The lower the standard deviation, the less risky the stock or portfolio.