Question

Q1:                                                                                                                                         

The following table shows expected data for Alfa Stock Company, use these data to calculate the expected rate of return, and the expected risk for this stock

                                                                                                                                 

Scenario	Probability	Rate of Return
Best case	0.2	25%
Most likely	0.3	20%
Worst case	0.5	-10%

Answer:

                                                                                                                           

(1): Scenario	(2): Probability	(3): Rate of Return
Best case
Most likely
Worst case

- The expected rate of return: E(R) =                                                   

- The expected risk =   

Answer 1

Scenario	Probability	Rate of return
Best case	0.2	25%
Most likely	0.3	20%
Worst case	0.5	-10%

We have the following data:

p1 = 0.2, p2 = 0.3, p3 = 0.5

R1 = 25%, R2 = 20%, R3 = -10%

Expected Rate of return

Expected rate of return = E[R] = p1*R1 + p2*R2 + p3*R3 = 0.2*25% + 0.3*20% + 0.5*(-10%) = 6%

Expected risk

Expected risk is the standard deviation of rate of return

Variance is calculated using the formula:

Variance = σ2 = p1*(R1-E[R])2 + p2*(R2-E[R])2 + p3*(R3-E[R])2 = 0.2*(25%-6%)2 + 0.3*(20%-6%)2 + 0.5*(-10%-6%)2 = 0.00722+0.00588+0.0128 = 0.0259

Standard devaition is square-root of variance

Standard deviation or Expected risk = σ = (0.0259)1/2 = 16.0934769394311% ~ 16.09% (Rounded to two decimals)

Answers

Expected rate of return = 6%

Standard deviation = 16.09%