Andre is considering an investment in Bristol Inc. and has gathered the following information. What is the expected standard deviation for a share of the firm's stock?

State of the Economy Probability of theState Conditional Expected ReturnBristol Inc.

Recession. 40 - 10%

Steady. 20 10%

Boom. 40 45%

a. 5.14%

b. 20.13%

c. 24.78%

d. 614.00%

c. 24.78%

Explanation:

For computing the expected standard deviation first we have to find out the expected rate of return which is shown below:

Expected rate of return = Respective return * Respective probability

= (0.4 * - 10) + (0.2 * 10) + (0.4 * 45)

= 16%

Now we have to find out the total probability which is shown below:

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

0.4 - 10 0.4 * (-10-16) ^2 = 270.4

0.2 10 0.2 * (10 - 16) ^2 = 7.2

0.4 45 0.4 * (45 - 16) ^2 = 336.4

Total = 614%

As we know that

So

Standard deviation = [Total probability * (Return - Expected Return) ^2 : Total probability]^ (1 : 2)

= (614) ^ (1 : 2)

= 24.78%