Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns:
$$\begin{array}{l}
\begin{array} { c c r }
\text { Eccrorric State }&\text { Probability } & \text { Return } \
\text { fast growth }&0.20 & 60\% \
\text {slow growth }&0.50 & 13\% \
\text { recession }&0.15 & - 45\%\
\text { depression }&0.15 & - 45\%\
\end{array}
\end{array}$$
A) 9.5 percent; 32.43 percent
B) 9.5 percent; 21.96 percent
C) 9.5 percent; 18.97 percent
D) 9.5 percent; 29.18 percent

Question

Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns:
$$\begin{array}{l}
\begin{array} { c c r } 
\text { Eccrorric State }&\text { Probability } & \text { Return } \
\text { fast growth }&0.20 & 60\% \
\text {slow growth }&0.50 & 13\% \
\text { recession }&0.15 & - 45\%\
\text { depression }&0.15 & - 45\%\
\end{array}
\end{array}$$
A) 9.5 percent; 32.43 percent
B) 9.5 percent; 21.96 percent
C) 9.5 percent; 18.97 percent
D) 9.5 percent; 29.18 percent

Quizplus · Accepted Answer

The expected return is calculated by multiplying each return by its probability and summing these products: $0.20 \times 60\% + 0.50 \times 13\% + 0.15 \times (-45\%) + 0.15 \times (-45\%) = 9.5\%$. The standard deviation requires calculating the variance first, which involves squaring the difference between each return and the expected return, multiplying by the probability, and then summing these. The square root of the variance gives the standard deviation, which is approximately 32.43 percent in this case.

Compute the Expected Return and Standard Deviation Given These Four