Question

- Assume the company can experience the following return with the following probability
Scenario probability Expected return
A 0.2 +30%
B 0.3 +15%
C 0.1 -10%
D ? -20%


i- Compute the expected return.
ii- Compute the expected value of $2000 investment over a coming year.
iii- Compute the standard deviation of the percentage return over the coming year iv- If the risk-free return is 7 percent, what is the risk premium for a stock market investment

Answer 1

i. The expected return is 1.5%.

ii. The expected value of $2,000 is $30 ($2,000 x 1.5%).

iii. The standard deviation of the percentage return  = 0.085 ($\sqrt{0.007175}$) or 8.5%.

iv. If the risk-free return is 7 percent, the risk premium for a stock market investment is 1.5% (8.5% - 7%).

Data and Calculations:

Scenario  Probability  Expected      Expected    Variance   Squared

                                      Return            Value                         Variance

A                     0.2            +30%            0.06         0.045       0.002025

B                     0.3            +15%             0.045       0.03         0.0009

C                     0.1             -10%             -0.01        -0.005       0.000025

D                    0.4             -20%            -0.08        -0.065      0.004225

                                                            0.015                          0.007175    

D's probability = 0.4 (1 - (0.2 + 0.3 + 0.1) or 40%

Expected return = (0.2 x 0.3 + 0.3 x 0.15 + 0.1 x -0.10 + 0.4 x -0.20)

= (0.06 + 0.045 - 0.01 - 0.08)

= 0.015

= 1.5%

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