According to the Capital Asset Pricing Model (CAPM), the risk associated with a capital asset is proportional to the slope ß1 (or simply ß) obtained by regressing the asset's past returns with the corresponding returns of the average portfolio called the market portfolio. (The return of the market portfolio represents the return earned by the average investor. It is a weighted average of the returns from all the assets in the market.) The larger the slope ß of an asset, the larger is the risk associated with that asset. A ß of 1.00 represents average risk. The returns from an electronics firm's stock and the corresponding returns for the market portfolio for the past 15 years are given below.
| Market Return (%) |
Stock's Return (%) |
| 16.02 |
21.05 |
| 12.17 |
17.25 |
| 11.48 |
13.1 |
| 17.62 |
18.23 |
| 20.01 |
21.52 |
| 14 |
13.26 |
| 13.22 |
15.84 |
| 17.79 |
22.18 |
| 15.46 |
16.26 |
| 8.09 |
5.64 |
| 11 |
10.55 |
| 18.52 |
17.86 |
| 14.05 |
12.75 |
| 8.79 |
9.13 |
| 11.6 |
13.87 |
Question
1. Carry out the regression and find the ß for the stock. What is the regression equation?
2. Does the value of the slope indicate that the stock has above-average risk? (For the purposes of this case assume that the risk is average if the slope is in the range 1 ± 0.1, below average if it is less than 0.9, and above average if it is more than 1.1.)
3. Give a 95% confidence interval for this ß. Can we say the risk is above average with 95% confidence?
4. If the market portfolio return for the current year is 10%, what is the stock's return predicted by the regression equation? Give a 95% confidence interval for this prediction.
5. Construct a residual plot. Do the residuals appear random?
6. Construct a normal probability plot. Do the residuals appear to be normally distributed?
7. (Optional) The risk-free rate of return is the rate associated with an investment that has no risk at all, such as lending money to the government. Assume that for the current year the risk-free rate is 6%. According to the CAPM, when the return from the market portfolio is equal to the risk-free rate, the return from every asset must also be equal to the risk-free rate. In other words, if the market portfolio return is 6%, then the stock's return should also be 6%. It implies that the regression line must pass through the point (6, 6). Repeat the regression forcing this constraint. Comment on the risk based on the new regression equation.