Question

Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 20% chance of happening, while Normal economy has 80% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in part (1), can you decide which stock to invest? 3) Calculate Beta for stock ABC and XYZ 4) If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks? How does this result influence your investment decision?

Answer 1

1. Expected Return, Variance and Standard Deviation of Stock ABC and XYZ

Workings:

2. Based on the result above, since the expected return is higher in stock ABC, investment is preferred in Stock ABC

3. Beta for Stock ABC and XYZ

4. Fair expected rate of return using CAPM

CAPM (Capital Asset Pricing Model) = Risk free rate + (Beta * (Market return-risk free rate).

Risk free rate = 3%

Fair expected rate of return using CAPM for Stock ABC = 3% + (3*(6.4%-3%)) = 13.2%

Fair expected rate of return using CAPM for Stock XYZ = 3% + (0.50*(6.4%-3%)) = 4.7%

Stock ABC has a very high beta of 3 and thus this is more riskier but has higher return potential. Stock XYZ has low-beta of 0.5 implying this stocks has less risk but at the same time with lower returns. If the investor is a risk taker, stock ABC can be invested and if the investor is risk averse, stock XYZ to be invested.