Macintosh Lumber believes the following probability distribution exists for its stock.What is the coefficient of variation on the company's stock? $$\begin{array} { l c c }
& \text { Probability } & \text { Stock's } \
\text { State of } & \text { of State } & \text { Expected } \
\text { the Economy }& \text { Occurring } & \text { Return } \
\text { Boom } & 0.45 & 25 \% \
\text { Normal } & 0.50 & 15 \% \
\text { Recession }&0.05&5\%
\end{array}$$
A)0.2839
B)0.3069
C)0.3299
D)0.3547
E)0.3813

Question

Macintosh Lumber believes the following probability distribution exists for its stock.What is the coefficient of variation on the company's stock? $$\begin{array} { l c c } 
 & \text { Probability } & \text { Stock's } \
\text { State of } & \text { of State } & \text { Expected } \
\text { the Economy }& \text { Occurring } & \text { Return } \
\text { Boom } & 0.45 & 25 \% \
\text { Normal } & 0.50 & 15 \% \
\text { Recession }&0.05&5\%
\end{array}$$ 
A)0.2839
B)0.3069
C)0.3299
D)0.3547
E)0.3813

Quizplus · Accepted Answer

To find the coefficient of variation, we first calculate the expected return and the standard deviation of the returns, then divide the standard deviation by the expected return.Expected return ($E(R)$):$$E(R) = (0.45 \times 25\%) + (0.50 \times 15\%) + (0.05 \times 5\%) = 11.25\% + 7.5\% + 0.25\% = 19\%$$Variance ($\sigma^2$):$$\sigma^2 = 0.45(25\% - 19\%)^2 + 0.50(15\% - 19\%)^2 + 0.05(5\% - 19\%)^2$$$$= 0.45(0.06)^2 + 0.50(-0.04)^2 + 0.05(-0.14)^2$$$$= 0.45(0.0036) + 0.50(0.0016) + 0.05(0.0196)$$$$= 0.00162 + 0.0008 + 0.00098 = 0.0034$$Standard deviation ($\sigma$):$$\sigma = \sqrt{0.0034} = 0.0583$$ or 5.83%Coefficient of variation ($CV$):$$CV = \frac{\sigma}{E(R)} = \frac{5.83\%}{19\%} = 0.3069$$Therefore, the correct answer is B) 0.3069.

Macintosh Lumber Believes the Following Probability Distribution Exists for Its