Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | }
\hline \begin{array} { l }
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.2 & 30 \% \
\hline \text { Slow Growth } & 0.5 & 6 \% \
\hline \text { Recession } & 0.3 & - 2 \% \
\hline
\end{array}$$
A)8.4 percent
B)10.87 percent
C)11.34 percent
D)24.09 percent

Question

Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | } 
\hline \begin{array} { l } 
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.2 & 30 \% \
\hline \text { Slow Growth } & 0.5 & 6 \% \
\hline \text { Recession } & 0.3 & - 2 \% \
\hline
\end{array}$$
A)8.4 percent
B)10.87 percent
C)11.34 percent
D)24.09 percent

Quizplus · Accepted Answer

To compute the standard deviation, first calculate the expected return: (0.2 * 30%) + (0.5 * 6%) + (0.3 * -2%) = 8.8%. Then, calculate the variance: 0.2*(30%-8.8%)^2 + 0.5*(6%-8.8%)^2 + 0.3*(-2%-8.8%)^2 = 0.012857. Finally, take the square root of the variance to get the standard deviation: √0.012857 = 11.34%.

Compute the Standard Deviation of the Expected Return Given These