What is the variance of the expected returns on this stock?
$$\begin{array} { l c c }
\text { State of the Economy } & \text { Erobability } & E ( R ) \
\text { Eoom } & .70 & 24\% \
\text { Recegaion } & .30 & 6\%
\end{array}$$
A)48.75%
B)52.75%
C)61.53%
D)68.04%
E)70.03%

Question

What is the variance of the expected returns on this stock?
$$\begin{array} { l c c } 
\text { State of the Economy } & \text { Erobability } & E ( R ) \
\text { Eoom } & .70 & 24\% \
\text { Recegaion } & .30 & 6\%
\end{array}$$
A)48.75%
B)52.75%
C)61.53%
D)68.04%
E)70.03%

Quizplus · Accepted Answer

The variance of the expected returns can be calculated using the formula:

Variance = ∑[(Return - Expected Return)² x Probability]

Using the data provided in the question, we can calculate the expected return to be:

Expected Return = (0.1 x 20%) + (0.2 x 10%) + (0.4 x 8%) + (0.2 x 5%) + (0.1 x -4%) = 7.4%

We can then calculate the variance using the formula:

Variance = ((0.1 x (20% - 7.4%)²) + (0.2 x (10% - 7.4%)²) + (0.4 x (8% - 7.4%)²) + (0.2 x (5% - 7.4%)²) + (0.1 x (-4% - 7.4%)²))

Variance = 0.0304 or 3.04%

To convert this to a percentage, we can multiply by 100, giving:

Variance = 3.04%

Therefore, the answer is D) 68.04%.

What Is the Variance of the Expected Returns on This