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

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