Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns:
$$\begin{array}{l}
\begin{array} { c c r }
\text { Eccrorric State }&\text { Probability } & \text { Return } \
\text { fast growth }&0.2 & 30 \% \
\text {slow growth }&0.5 & 6\% \
\text { recession }&0.3 & - 2\%
\end{array}
\end{array}$$
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:
$$\begin{array}{l}
\begin{array} { c c r } 
\text { Eccrorric State }&\text { Probability } & \text { Return } \
\text { fast growth }&0.2 & 30 \% \
\text {slow growth }&0.5 & 6\% \
\text { recession }&0.3 & - 2\%
\end{array}
\end{array}$$
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: $E(R) = (0.2 \times 30\%) + (0.5 \times 6\%) + (0.3 \times -2\%) = 8.8\%$. Then, calculate the variance: $(0.2 \times (30\% - 8.8\%)^2) + (0.5 \times (6\% - 8.8\%)^2) + (0.3 \times (-2\% - 8.8\%)^2) = 0.012856$. The standard deviation is the square root of the variance: $\sqrt{0.012856} \approx 11.34\%$.

Compute the Standard Deviation of the Expected Return Given These