Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock? $\begin{array}{lrr}
&\text { Probability } &\text { Stock's }\
\text {State of}&\text { of State }&\text {Expected}\
\underline{\text { the Economy }} & \underline{\text { Occurring }} &\underline{ \text { Return }} \
\text { Boom }& 0.45 & 25 \% \
\text { Normal } & 0.50 & 15 \% \
\text { Recession } & 0.05 & 5 \%
\end{array}$

A) 0.2839
B) 0.3069
C) 0.3299
D) 0.3547
E) 0.3813

Question

Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock? $\begin{array}{lrr}
&\text { Probability } &\text { Stock's }\
\text {State of}&\text { of State }&\text {Expected}\ 
\underline{\text { the Economy }} & \underline{\text { Occurring }} &\underline{ \text { Return }} \
\text { Boom }& 0.45 & 25 \% \
\text { Normal } & 0.50 & 15 \% \
\text { Recession } & 0.05 & 5 \%
\end{array}$

A) 0.2839
B) 0.3069
C) 0.3299
D) 0.3547
E) 0.3813

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated as the standard deviation divided by the expected return. First, calculate the expected return: $E(R) = (0.45 \times 25\%) + (0.50 \times 15\%) + (0.05 \times 5\%) = 19.5\%$. Then, calculate the variance: $\sigma^2 = 0.45(25\% - 19.5\%)^2 + 0.50(15\% - 19.5\%)^2 + 0.05(5\% - 19.5\%)^2 = 0.0072$. The standard deviation $\sigma = \sqrt{0.0072} = 0.0849$. Finally, CV = $\sigma / E(R) = 0.0849 / 0.195 = 0.3069$.

Roenfeld Corp Believes the Following Probability Distribution Exists for Its