Question

Michelle is considering investing in a company's stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment Probability Return Boom 0.4 25.00% Good 0.3 15.00% Level 0.1 10.00% Slump 0.2 -5.00% Use the table of returns and probabilities above to determine the expected return on Michelle's investment? (Round answer to 3 decimal places, e.g. 0.076.) Expected return _______ Use the table of returns and probabilities above to determine the standard deviation of the return on Michelle's investment? (Round answer to 5 decimal places, e.g. 0.07680.) Standard deviation _________ Open Show Work Click if you would like to Show Work for this question:

Answer 1

Expected return= 0.165

Standard deviation = 0.07762

Step-by-step explanation:

Given the following :

State - - - - - - - probability - - return

Boom - - - - - - - 0.4 - - - - - - - - 25%

Good - - - - - - - - 0.3 - - - - - - - 15%

Level - - - - - - - - 0.1 - - - - - - - - 10%

Slump - - - - - - - -0.2 - - - - - - - -5%

Expected return on investment :

Probability × rate of return

(0.4 × 25%) + (0.3 × 15%) + (0.1 × 10%) + (0.2 × 5%)

(0.4 × 0.25) + (0.3 × 0.15) + (0.1 × 0.1) + (0.2 × 0.05) = 0.165

= 16.5%

Standard deviation = √variance

Variance = probability × (return - expected return)^2

Variance = 0.4(25-16.5)^2 + 0.3(15-16.5)^2 + 0.1(10-16.5)^2 + 0.2(5-16.5)^2

Variance = 0.4(8.5)^2 + 0.3(-1.5)^2 + 0.1(-6.5)^2 + 0.2(11.5)^2

Variance = 0.4(72.25) + 0.3(2.25) + 0.1(42.25) + 0.2(132.25)

Variance = 60.25%

Standard deviation = √60.25

Standard deviation = 7.7620873%

= 0.0776208

= 0.07762 ( 5 decimal places )