Question

Suppose the market portfolio is equally likely to increase by 35% or decrease by 5%. Also suppose that the risk-free interest rate is 5%.

a. Use the beta of a firm that goes up on average by 50% when the market goes up and goes down by 10% when the market goes down to estimate the expected return of its stock. How does this compare with the stock's actual expected return?
b. Use the beta of a firm that goes up on average by 24% when the market goes down and goes down by 15% when the market goes up to estimate the expected return of its stock. How does this compare with the stock's actual expected return?

Answer 1

To estimate the expected return of a stock, we use the formula: expected return = risk-free rate + beta * (expected market return - risk-free rate). For the first stock, the expected return is 29%. For the second stock, the expected return is -73%. The first stock is expected to outperform its actual return, while the second stock is expected to underperform.

Step-by-step explanation:

a. To estimate the expected return of the stock, we can use the formula: expected return = risk-free rate + beta * (expected market return - risk-free rate). In this case, the risk-free rate is 5% and the market portfolio has an equal chance of increasing by 35% or decreasing by 5%. The beta of the stock is calculated as follows: beta = (change in stock return) / (change in market return) = (50% - (-10%)) / (35% - (-5%)) = 0.8. Therefore, the expected return of the stock is 5% + 0.8 * (35% - 5%) = 5% + 0.8 * 30% = 5% + 24% = 29%.

b. Using the same formula, we can calculate the expected return for the second stock. The beta is calculated as follows: beta = (change in stock return) / (change in market return) = (-15% - 24%) / (-5% - 15%) = -39% / -20% = 1.95. Therefore, the expected return of the stock is 5% + 1.95 * (-5% - 35%) = 5% + 1.95 * (-40%) = 5% - 78% = -73%.

In comparison to the stock's actual expected return, we can see that the expected return for the first stock (29%) is higher than its actual expected return, while the expected return for the second stock (-73%) is lower. This suggests that the first stock is expected to outperform its actual return, while the second stock is expected to underperform.