Your firm's analyst believes that economic conditions during the next year will be either strong,normal,or weak,and she thinks that Crary Inc.'s returns will have the probability distribution shown below.What's the standard deviation of Crary's returns as estimated by your analyst? (Hint: Use the formula for the standard deviation of a population,not a sample.) $\begin{array}{l}
\text { Economic }\
\begin{array}{lrr}
{\text { Conditions }} & \text { Prob. } &{\text { Return }} \
\hline \text { Strong } & 30 \% & 32.50 \% \
\text { Normal } & 40 \% & 10.25 \% \
\text { Weak } & 30 \% & -15.75 \%
\end{array}
\end{array}$

Question

Quizplus · Accepted Answer

To calculate the standard deviation of Crary's returns, we first need to find the expected return (mean) and then use it to calculate the variance before taking the square root to get the standard deviation.1. Calculate the expected return (mean):$$E(R) = (0.30 \times 32.50\%) + (0.40 \times 10.25\%) + (0.30 \times -15.75\%) = 9.75\% + 4.10\% - 4.725\% = 9.125\%$$2. Calculate the variance:$$Var(R) = (0.30 \times (32.50\% - 9.125\%)^2) + (0.40 \times (10.25\% - 9.125\%)^2) + (0.30 \times (-15.75\% - 9.125\%)^2)$$$$Var(R) = (0.30 \times (23.375\%)^2) + (0.40 \times (1.125\%)^2) + (0.30 \times (-24.875\%)^2)$$$$Var(R) = (0.30 \times 0.0547) + (0.40 \times 0.0013) + (0.30 \times 0.0619)$$$$Var(R) = 0.01641 + 0.00052 + 0.01857 = 0.0355$$3. Calculate the standard deviation:$$SD(R) = \sqrt{Var(R)} = \sqrt{0.0355} = 0.1884 \text{ or } 18.84\%$$The closest answer provided is 18.71%, which is option B.

Your Firm's Analyst Believes That Economic Conditions During the Next