Question

A. A stock's returns have the following distribution:

Answer 1

Answer:

Following are the response to the given question:

Explanation:

For question 1:

The weighted average of each return is the expected return.

$Expected\ return = 0.1 \times -0.22 + 0.2 \times -0.12 + 0.3 \times 0.17 + 0.2 \times 0.33 + 0.2 \times 0.56$

                           $= 0.1830 \\\\= 18.30\%$

For question 2:

Standard deviation is a measured source of the square deviations from the mean via probability.

$Std \ dev = [0.1 \times (0.183-(-0.22))^2 + 0.2 \times (0.183-(-0.12))^2 + 0.3\times(0.183-0.17)^2 + 0.2\times (0.183-0.33)^2 + 0.2\times (0.183-0.56)^2]^{(\frac{1}{2})}$

             $= 0.2596 \\\\= 25.96\%$

For question 3:

For point a:

$\text{Coefficient of variation} = \frac{std \ dev}{expected\ return}$

                                    $=\frac{0.2596}{0.183} \\\\= 1.42$

For point b:

As per the CAPM:  $\text{Required return = risk free rate + beta}\times \text{market risk premium}$

$\to 16\% = 4.5\% + beta\times 5\%\\\\\to beta = 2.3$

 In Option I:

When the beta of the stock exceeds 1.0, the change in the required rate of return must be higher than the increase in the premium of market risk. Beta is the degree to which stock return changes as market returns change.

 $\text{Required return = risk free rate + beta}\times \text{market risk premium}$

$Required \ return = 4.5\% + 2.3\times 7\%\\\\Required \ return = 20.6\%$