Question

An analyst has developed the following probability distribution for the rate of return for a common stock.

Answer 1

Answer:

a. E(x) = 5.2000%

b. Variance = 122.16

Standard Deviation = 11.05

Step-by-step explanation:

Given

Scenario Probability Rate of Return

1 0.20 −16 %

2 0.40 7 %

3 0.40 14 %

a.

Expected Rate of Return = E(x)

E(x) = (-16% * 0.20) + (0.40 *7%) + (0.40 * 14%)

E(x) = -3.2% + 2.8% + 5.6%

E(x) = 5.2%

E(x) = 5.2000%

b.

Variance also known as the average of the squared differences from the Mean.

To calculate variance, start by calculating the mean, or average, of your sample. Then, subtract the mean from each data point, and square the differences. Next, add up all of the squared differences

Variance =

V = σ²= (−16 − 5.2)² * 0.20 + (7 − 5.2)² * 0.40 + (14 − 5.2)² * 0.40

V = σ² =122.16

Standard Deviation = σ = √SD

σ = √122.16

σ = 11.05124427383631

σ = 11.05 --- Approximated