Capital Asset Pricing Model (Part 4)

Question 19: For Problems 17 to 19 assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16% A stock has an expected rate of return of 4%. What is its beta? Calculation of β of the Stock: Beta (β) would be calculated using the below formula: Here, . Substituting 4% as E(r), 6% as rf and 16% as E(rM) Question 20: Two investment advisers are comparing performance. One averaged a 19% rate of return and the other a 16% rate of return. However, the beta of the first investor was 1.5, whereas that of the second was 1. A. Can you tell which investor was a better selector of individual stocks (aside from the issue of general movements in the market)? B. If the T-bill rate were 6% and the market return during the period were 14%, which investor would be the superior stock selector? C. What if the T-bill rate were 3% and the market return were 15%? CAPM (capital asset pricing model) shows a relationship that exists between expected return and risk. This model states that the expected rate of return is equivalent to risk premium plus risk free-rate. The expected return of any financial asset can be calculated with the help of CAPM equation. Here, There are two investment advisers. First adviser goes with the return 19% and the second one goes with 16%. The betas of the first adviser and second adviser are 1.5 and 1 respectively. Part A It is impossible to decide which adviser is a better selector as the additional information is not provided. To decide the best one, risk-free rate, market return, and the abnormal return/alpha is required. Part B The risk-free rate and market return are 6% and 14% respectively. To decide which adviser is a better selector, it is required to find the alpha of both investments suggested by the advisers First Adviser: Determine the alpha of the investment suggested by first adviser by following below steps: Second Adviser: Determine the alpha of the investment suggested by second adviser by following below steps: The alpha of investment suggested by second adviser is 2% which is higher than that of investment suggested by adviser, which is 1%. This states that the second adviser has higher abnormal return and is superior stock selector Part C The risk-free and market return are 3% and 15% respectively. To decide which adviser is a better selector, it is required to find the alpha of both investments suggested by the advisers First Adviser: Determine the alpha of the investment suggested by first adviser by following below steps: Second Adviser: Determine the alpha of the investment suggested by second adviser by following below steps: The alpha of investment suggested by second adviser is 1% which is higher than that of investment suggested by first adviser which is -2%. This states that the second adviser has higher abnormal return and is a superior stock selector. Apart from that, the predictions made by first adviser are worthless as it has negative abnormal returns. Question 21: Suppose the rate of return on short-term government securities (perceived to be risk-free) is about 5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: A. What is the expected rate of return on the market portfolio? B. What would be the expected rate of return on a stock with beta (b) = 0? C. Suppose you consider buying a share of stock at $40. The stock is expected to pay $3 dividends next year and you expect it to sell then for $41. The stock risk has been evaluated at beta (b) = -.5. Is the stock overpriced or under-priced? Part A Calculation of Expected Rate of Return of the Portfolio:The formula to calculate the Expected Rate of Return for the portfolio: Substituting 5% for rf, 12% for E(rM) and 1 for β. Part B Calculation of Expected Rate of Return of the Portfolio with β as 0:The formula to calculate the Expected Rate of Return for the portfolio: Substituting 5% as rf,12% as E(rM) and 0 as β, Part C Calculation if the stock is overpriced or under-priced:The formula to calculate the Fair Expected Rate of Return for the stock: Substituting 5% for rf,12% for E(rM) and -0.5 for β, The formula to calculate the Actual Expected Rate of Return for the stock is as follows: Substituting, $41 as P1, $3 as D1 and $40 as P0, Question 22: Suppose that borrowing is restricted so that the zero-beta version of the CAPM holds. The expected return on the market portfolio is 17%, and on the zero-beta portfolio it is 8%. What is the expected return on a portfolio with a beta of .6? Calculation of Expected Rate of Return of the Portfolio:The Zero β version of CAPM states that the Expected Rate of Return for a Zero β portfolio is same as the Risk free Rate of Return as the portfolio assumes no Risk. The formula to calculate the Expected Rate of Return for the portfolio is as follows: Substituting 8% for rf, 17% for E(rM) and 0.6 for β.