Question

If the economy is normal, Charleston Freight stock is expected to return 14.3 percent. If the economy falls into a recession, the stock's return is projected at a negative 8.7 percent. The probability of a normal economy is 80 percent. What is the variance of the returns on this stock

Answer 1

Answer:

0.008464

Explanation:

The computation of variance of the returns on this stock is shown below:-

Probability of recession = 100 - 80

=20%

So, expected return = Respective return × Respective probability

= (0.8 × 14.3) + (0.2 × -8.7)

= 9.7%

Probability Return Probability × (Return - Expected Return)^2

0.8                    14.3        0.8 × (14.3 - 9.7)^2 = 16.928

0.2                    -8.7        0.2 × (-8.7 - 9.7)^2 = 67.712

                                       Total = 84.64%

Standard deviation = (Total probability × (Return - Expected Return)^2 ÷ Total probability]^(1 ÷ 2)

=9.2%

Now, Variance of the returns = Standard deviation^2

= 0.092^2

=0.008464