- The following are the historic returns for the Chelle Computer Company:

Based on this information, compute the following:

- The correlation coefficient between Chelle Computer and the General Index.
- The standard deviation for the company and the index.
- The beta for the Chelle Computer Company.

- As an equity analyst, you have developed the following return forecasts and risk estimates for two different stock mutual funds (Fund T and Fund U):
- If the risk-free rate is 3.9 percent and the expected market risk premium (i.e.,
*E*(*R*_{M}) −*RFR*) is 6.1 percent, calculate the expected return for each mutual fund according to the CAPM. - Using the estimated expected returns from Part a along with your own return forecasts, demonstrate whether Fund T and Fund U are currently priced to fall directly on the security market line (SML), above the SML, or below the SML.
- According to your analysis, are Funds T and U overvalued, undervalued, or properly valued?

- Draw the security market line for each of the following conditions:
- (1)
*RFR =*0.08;*R*_{M}(proxy) = 0.12

(2) *R _{z} =* 0.06;

*R*

_{M}(true) = 0.15

- Rader Tire has the following results for the last six periods. Calculate and compare the betas using each index.
- If the current period return for the market is 12 percent and for Rader Tire it is 11 percent, are superior results being obtained for either index beta?

**Chapter 9**

**3**. You have been assigned the task of estimating the expected returns for three different stocks: QRS, TUV, and WXY. Your preliminary analysis has established the historical risk premiums associated with three risk factors that could potentially be included in your calculations: the excess return on a proxy for the market portfolio (MKT), and two variables capturing general macroeconomic exposures (MACRO1 and MACRO2). These values are: λMKT = 7.5%, λMACRO1 = −0.3%, and λMACRO2 = 0.6%. You have also estimated the following factor betas (i.e., loadings) for all three stocks with respect to each of these potential risk factors:- Calculate expected returns for the three stocks using just the MKT risk factor. Assume a risk-free rate of 4.5%.
- Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate.
- Discuss the differences between the expected return estimates from the single-factor model and those from the multifactor model. Which estimates are most likely to be more useful in practice?
- What sort of exposure might MACRO2 represent? Given the estimated factor betas, is it really reasonable to consider it a common (i.e., systematic) risk factor?
**5**. Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship:- If λ1 = 4% and λ2 = 2%, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year.
- Suppose that you know that next year the prices for Stocks A, B, and C will actually be $31.50, $35.00, and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these mispriced securities. What is the profit from your investment? You may assume that you can use the proceeds from any necessary short sale.
- a. Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant?
- How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature?
- Suppose you are now told that the three factors in Exhibit 9.12represent the risk exposures in the Fama-French characteristic-based model (i.e., excess market,
*SMB,*and*HML*). Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why. - Suppose it is further revealed that Factor 3 is the
*HML*factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why.