Compute the standard deviation given these four economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | }
\hline \begin{array} { l }
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.40 & 50 \% \
\hline \text { Slow Growth } & 0.40 & 10 \% \
\hline \text { Recession } & 0.10 & - 10 \% \
\hline \text { Depression } & 0.10 & - 5 \% \
\hline
\end{array}$$
A)6.71 percent
B)22.5 percent
C)23.37 percent
D)52.20 percent

Question

Compute the standard deviation given these four economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | } 
\hline \begin{array} { l } 
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.40 & 50 \% \
\hline \text { Slow Growth } & 0.40 & 10 \% \
\hline \text { Recession } & 0.10 & - 10 \% \
\hline \text { Depression } & 0.10 & - 5 \% \
\hline
\end{array}$$
A)6.71 percent
B)22.5 percent
C)23.37 percent
D)52.20 percent

Quizplus · Accepted Answer

To find the standard deviation, we need to find the expected return and variance.

The expected return is:

$$0.4(50\%) + 0.4(10\%) + 0.1(-10\%) + 0.1(-5\%) = 16\%$$

The variance is:

$$(0.5-0.16)^2(0.4) + (0.1-0.16)^2(0.4) + (-0.1-0.16)^2(0.1) + (-0.05-0.16)^2(0.1) = 0.0544$$

The standard deviation is the square root of the variance:

$$\sqrt{0.0544} = 0.2337 \approx 23.37\%$$

Therefore, the best choice is C.

Compute the Standard Deviation Given These Four Economic States, Their