# Discuss the differences between the expected return estimates from the single-factor model and those from the multifactor model.

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

YEAR                           CHELLE COMPUTER                GENERAL INDEX

1                                                  37                                            15

2                                                    9                                             13

3                                                  -11                                            14

4                                                     8                                             -9

5                                                    11                                            12

6                                                     4                                               9

Based on this information, compute the following:

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

QUESTION 8

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):

FORCASTED RETURN                  CAPM BETA

Fund T                                                                      9.0%                                       1.20

Fund U                                                                     10                                            0.80

1. If the risk-free rate is 3.9 percent and the expected market risk premium (i.e.,E(RM) − RFR) is 6.1 percent, calculate the expected return for each mutual fund according to the CAPM.
2. 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.
3. According to your analysis, are Funds T and U overvalued, undervalued, or properly valued?

QUESTION 10

Draw the security market line for each of the following conditions:

1. (1)RFR =0.08; RM(proxy) = 0.12

(2) Rz = 0.06; RM(true) = 0.15

1. Rader Tire has the following results for the last six periods. Calculate and compare the betas using each index.

RATES OF RETURN

Period           Rader Tire (%)               Proxy Specific Index (%)              True General Index (%)

1                           29                                             12                                               15

2                           12                                             10                                               13

3                          -12                                            -9                                                 -8

4                           17                                            14                                                18

5                           20                                            25                                                28

6                            -5                                           -10                                                0

c.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

QUESTION 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:

FACTOR LOADING

Stock                 MKT                MACRO1                        MACRO2

QRS                   1.24                     -0.42                                 0.00

TUV                  0.91                      0.52                                  0.23

WXY                 1.03                     -0.09                                 0.00

1. Calculate expected returns for the three stocks using just the MKT risk factor. Assume a risk-free rate of 4.5%.
2. Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate.
3. 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?
4. 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?

QUESTION 5

Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship:

E(RA) = (1.1)λ1 + (0.8)λ2

E(RB) = (0.7)λ1 + (0.6)λ2

E(RC) = (0.3)λ1 + (0.4)λ2

1. 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.
2. 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.

QUESTION 7

1. 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?
2. How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature?
3. Suppose you are now told that the three factors inExhibit 9.12 represent 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.
4. Suppose it is further revealed that Factor 3 is theHML factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why.

Exhibit 9.12 Monthly Excess Return Data for Two Portfolios and Three Risk Factors

Period   Portfolio A       Portfolio B         Factor 1           Factor 2          Factor 3

1         1.08%                    0.00%                 0.01%              -0.01%         -1.67%

2          7.58                      6.62                     6.89                    0.29            -1.23

3           5.03                      6.01                     4.75                 -1.45              1.92

4           1.16                     0.36                     0.66                   0.41               0.22

5         -1.98                    -1.58                    -2.95                  -3.62                4.29

6          4.26                      2.39                     2.86                  -3.40              -1.54

7         -0.75                     -2.47                   -2.72                  -4.51               -1.79

8         -15.49                   -15.46                -16.11                 -5.92                 5.69

9          6.05                      4.06                   5.95                      0.02                -3.76

10        7.70                     6.75                   7.11                      -3.36                -2.85

11         7.76                      5.52                   5.86                     1.36                -3.68

12          9.62                       4.89                  5.94                   -0.31                -4.95

13          5.25                      2.73                   3.47                    1.15               -6.16

14          -3.19                    -0.55                  -4.15                  -5.59                   1.66

15         5.40                     2.59                    3.32                     -3.82                  -3.04

16          2.39                     7.26                   4.47                       2.89                   2.80

17         -2.87                     0.10                 -2.39                       3.46                   3.08

18            6.52                     3.66                  4.72                        3.42                  -4.33

19           -3.37                   -0.60                  -3.45                       2.01                   0.70

20           -1.24                   -4.06                  -1.35                      -1.16                 -1.26

21           -1.48                     0.15                 -2.68                       3.23                  -3.18

22            6.01                     5.29                   5.80                      -6.53                 -3.19

23            2.05                     2.28                   3.20                        7.71                  -8.09

24            7.20                   7.09                    7.83                         6.98                 -9.05

25          -4.81                   -2.79                    -4.43                       4.08                  -0.16

26          1.00                     -2.04                     2.55                      21.49                -12.03

27          9.05                      5.25                     5.13                     -16.69                  7.81

28         -4.31                     -2.96                   -6.24                      -7.53                   8.59

29         -3.36                     -0.63                    -4.27                     -5.86                  5.38

30          3.86                      1.80                    4.67                        13.31                 -8.78

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