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:

ProbabilityReturnProbability × (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%

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