What is the variance of the returns on a security given the following information?
$\begin{array}{lrr}
\text { state of the Economy}&\text { Probabllity}&\text { Rate of}\
&\text {of State of Economy}&\text {Return if}\
&&\text {State Occurs}\
\text { Boom } & .20 & 16 \% \
\text { Normal } & .50 & 8 \% \
\text { Recession } & .30 & -8 \%
\end{array}$
A)79.36%
B)83.35%
C)87.73%
D)89.23%
E)90.98%

Question

Quizplus · Accepted Answer

The variance of the returns on a security is calculated as the weighted average of the squared deviations of the returns from the expected return. The expected return is the sum of the products of the probabilities of each state of the economy and the rate of return if that state occurs. In this case, the expected return is:(0.20 * 0.16) + (0.50 * 0.08) + (0.30 * -0.08) = 0.08The variance is then calculated as:(0.20 * (0.16 - 0.08)^2) + (0.50 * (0.08 - 0.08)^2) + (0.30 * (-0.08 - 0.08)^2) = 0.07936Therefore, the variance of the returns on the security is 79.36%.

What Is the Variance of the Returns on a Security