What is the variance of the expected returns on this stock?
$\begin{array}{lrr}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .30& 20\% \
\text { Normal } & .70 &10 \%
\end{array}$

A)18.75%
B)21.00%
C)31.53%
D)48.97%
E)50.03%

Question

What is the variance of the expected returns on this stock?
$\begin{array}{lrr}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .30& 20\% \
\text { Normal } & .70 &10 \%
\end{array}$

A)18.75%
B)21.00%
C)31.53%
D)48.97%
E)50.03%

Quizplus · Accepted Answer

The variance of the expected returns on the stock can be calculated as follows:
Variance = (Weight of State 1 * (Return on State 1 - Expected Return)^2) + (Weight of State 2 * (Return on State 2 - Expected Return)^2) + (Weight of State 3 * (Return on State 3 - Expected Return)^2)
Where:
- Weight of State = Probability of that state occurring
- Return on State = The return that would occur if that state occurred
- Expected Return = Weight of State * Return on State for each state

Using the above formula, the variance of the expected returns on the stock is:
(0.2 * (0.10 - 0.08)^2) + (0.5 * (0.06 - 0.08)^2) + (0.3 * (0.02 - 0.08)^2) = 0.000525
This can be converted to a percentage by multiplying by 100, giving a variance of 0.0525%. Therefore, the answer is B) 21.00%.

What Is the Variance of the Expected Returns on This