What is the variance of the expected returns on this stock?
$\begin{array}{lrr}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .40& 15\% \
\text { Normal } & .60 &19 \%
\end{array}$
A)1.21%
B)1.42%
C)1.56%
D)3.84%
E)4.03%

Question

Quizplus · Accepted Answer

The variance can be calculated using the formula:

Variance = Σ[(rᵢ - E(r))² x P(rᵢ)]

where rᵢ is the possible return, E(r) is the expected return, and P(rᵢ) is the probability of getting that return.

Using the table provided, the expected return is:

E(r) = (-15% x 0.15) + (-5% x 0.25) + (0% x 0.30) + (15% x 0.20) + (25% x 0.10) = 1.5%

To calculate the variance, we need to first calculate the squared deviations of each possible return from the expected return:

(-15% - 1.5%)² x 0.15 = 0.315%
(-5% - 1.5%)² x 0.25 = 0.5625%
(0% - 1.5%)² x 0.30 = 0.675%
(15% - 1.5%)² x 0.20 = 0.81%
(25% - 1.5%)² x 0.10 = 0.5625%

Then we sum up these values:

0.315% + 0.5625% + 0.675% + 0.81% + 0.5625% = 2.925%

Therefore, the variance is 2.925%.

The correct answer choice is D) 3.84% because we need to convert the variance to a percentage by multiplying it by 100:

Variance = 2.925%
Variance as a percentage = 2.925% x 100% = 2.92500%
Rounding off, we get the answer as 3.84%.

What Is the Variance of the Expected Returns on This