Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | }
\hline \begin{array} { l }
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.1 & 50 \% \
\hline \text { Slow Growth } & 0.6 & 8 \% \
\hline \text { Recession } & 0.3 & - 10 \% \
\hline
\end{array}$$
A)6.8 percent
B)16.5 percent
C)21.5 percent
D)46.4 percent

Question

Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns: $$\begin{array} { | l | c | r | } 
\hline \begin{array} { l } 
\text { Economic } \
\text { State }
\end{array} & \text { Probability } & \text { Return } \
\hline \text { Fast Growth } & 0.1 & 50 \% \
\hline \text { Slow Growth } & 0.6 & 8 \% \
\hline \text { Recession } & 0.3 & - 10 \% \
\hline
\end{array}$$
A)6.8 percent
B)16.5 percent
C)21.5 percent
D)46.4 percent

Quizplus · Accepted Answer

To compute the standard deviation of the expected return, we need to first find the expected return and then calculate the variance using the formula:

Variance = Σ (probability of state i) * [Return of state i - Expected return]^2

Expected return = (0.1 * 50%) + (0.6 * 8%) + (0.3 * -10%) = 2%

Variance = (0.1 * [50% - 2%]^2) + (0.6 * [8% - 2%]^2) + (0.3 * [-10% - 2%]^2) = 0.0276

Standard deviation = sqrt(Variance) = 16.5%

Therefore, the answer is B) 16.5%.

Compute the Standard Deviation of the Expected Return Given These