Question

There is a probability of 25 percent that the economy will boom; otherwise, it will be normal. Stock Q is expected to return 18 percent in a boom and 9 percent otherwise. Stock R is expected to return 9 percent in a boom and 5 percent otherwise. What is the standard deviation of a portfolio that is invested 40 percent in Stock Q and 60 percent in Stock R?

a. 0.7%
b. 1.4%
c. 2.6%
d. 6.8%
e. 8.1%

Answer 1

c. 2.6%

Step-by-step explanation:

Calculation to determine the standard deviation

First step is to calculate E(r)Boom

E(r)Boom = (0.40 ×0.18) + (.0.60 ×0.09)

E(r)Boom= 0.126

Second step is to calculate E(r)Normal

E(r)Normal = (0.40×0.09) + (0.60×0.05)

E(r)Normal = 0.066

Third step is to calculate E(r)Portfolio

E(r)Portfolio = (0.25×0.126) + (0.75×0.066)

E(r)Portfolio = 0.081

Fourth Step is to calculate VarPortfolio

VarPortfolio = [0.25(0.126 - 0.081)^2] + [0.75(0.066- 0.081)^2]

VarPortfolio= 0.000675

Last step is to calculate Standard Deviation

Standard deviation= 0.000675^.5

Standard deviation= 2.6%

Therefore the the standard deviation is 2.6%