Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | l | l | }
\hline \begin{array} { l }
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.20 & 60 \% \
\hline \text { Slow Growth } & 0.50 & 13 \% \
\hline \text { Recession } & 0.15 & - 15 \% \
\hline \text { Depression } & 0.15 & - 45 \% \
\hline
\end{array}$$
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: $$\begin{array} { | l | l | l | } 
\hline \begin{array} { l } 
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.20 & 60 \% \
\hline \text { Slow Growth } & 0.50 & 13 \% \
\hline \text { Recession } & 0.15 & - 15 \% \
\hline \text { Depression } & 0.15 & - 45 \% \
\hline
\end{array}$$
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 the sum of the products of the probabilities and the returns:(0.20 x 60%) + (0.50 x 13%) + (0.15 x -15%) + (0.15 x -45%) = 9.5%The standard deviation is the square root of the variance, which is the sum of the squared differences between the returns and the expected return, weighted by the probabilities:[(0.20 x (60% - 9.5%)^2) + (0.50 x (13% - 9.5%)^2) + (0.15 x (-15% - 9.5%)^2) + (0.15 x (-45% - 9.5%)^2)]^0.5 = 29.18%

Compute the Expected Return and Standard Deviation Given These Four