QUESTION 6

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:

- 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.

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

- 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?

QUESTION 10

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.

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: λ_{MKT} = 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

- 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?

QUESTION 5

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

E(R_{A}) = (1.1)λ_{1 }+ (0.8)λ_{2 }

E(R_{B}) = (0.7)λ_{1 }+ (0.6)λ_{2 }

E(R_{C}) = (0.3)λ_{1 }+ (0.4)λ_{2 }

- If λ
_{1}*=*4% and λ_{2}= 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

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