Question

What is the standard deviation of a stock that has a 10% chance of earning 18%, a 10% chance of making 11%, a 40% chance of making 5%, and a 40% chance of making 22%?
A. 7.95%.
B. 13.70%.
C. 7.78%.
D. 13.05%.

Answer 1

Answer:

A. 7.95%.

Explanation:

Calculate the expected rate of return for the investment as follows:

$\begin{aligned}\text { Expected rate of return } &=(\text { Probability } \times \text { Rate of return })+(\text { Probability } \times \text { Rate of return })+\\&(\text { Probability } \times \text { Rate of retum }) \\=&(0.40 \times 15 \%)+(0.50 \times 10 \%)+(0.10 \times-3 \%) \\=& 0.06+0.05-0.003 \\=& 0.107$

Calculate the standard deviation of the investment as follows:

$\begin{aligned}\text { Standard deviation }=&\left\{\begin{array}{l} \text { Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)+ \\\text { (Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)+ \\\text { (Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)\end{array}\right.$

=$\sqrt{\left(0.40 \times(0.15-0.107)^{2}\right)+\left(0.50 \times(0.10-0.107)^{2}\right)+} \\=\sqrt{0.0007396+0.0000245+0.0018769} \\=\sqrt{0.002641} \\=0.05139066063011$