What is the standard deviation of the returns on a stock given the following information? $$\begin{array} { l c c }
{ \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
\text { Boom } & .28 & .175 \
\text { Normal } & .67 & .128 \
\text { Recession } & .05 & .026
\end{array}$$
A) 3.57 percent
B) 3.28 percent
C) 3.89 percent
D) 3.42 percent
E) 4.01 percent

Question

What is the standard deviation of the returns on a stock given the following information? $$\begin{array} { l c c } 
 { \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
\text { Boom } & .28 & .175 \
\text { Normal } & .67 & .128 \
\text { Recession } & .05 & .026
\end{array}$$
A) 3.57 percent
B) 3.28 percent
C) 3.89 percent
D) 3.42 percent
E) 4.01 percent

Quizplus · Accepted Answer

To find the standard deviation, we need to calculate the variance first. The formula for variance is:

$Var(X) = \sum_{i=1}^n p_i(x_i - \mu)^2$

where $n$ is the number of possible states of the economy, $p_i$ is the probability of state $i$, $x_i$ is the rate of return in state $i$, and $\mu$ is the expected rate of return.

The expected rate of return can be calculated as:

$\mu = \sum_{i=1}^n p_ix_i$

Using the given information, we can calculate the expected rate of return as:

$\mu = 0.28(0.175) + 0.67(0.128) + 0.05(0.026) = 0.12998$

Now, we can calculate the variance:

$Var(X) = 0.28(0.175 - 0.12998)^2 + 0.67(0.128 - 0.12998)^2 + 0.05(0.026 - 0.12998)^2 = 0.001076$

Finally, the standard deviation is the square root of the variance:

$\sqrt{Var(X)} = \sqrt{0.001076} = 0.0328$

So the answer is B).

What Is the Standard Deviation of the Returns on a Stock