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WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
1. Which of the following statements is CORRECT?
a.
The CAPM is an ex ante model, which means that all of the variables should be historical values that can
reasonably be projected into the future.
b.
The beta coefficient used in the SML equation should reflect the expected volatility of a given stock's return
versus the return on the market during some future period.
c.
The general equation: Y = a + bX + e, is the standard form of a simple linear regression where b = beta, and X
equals the independent return on an individual security being compared to Y, the return on the market, which
is the dependent variable.
d.
The rise-over-run method is not a legitimate method of estimating beta because it measures changes in an
individual security's return regressed against time.
2. Given the following returns on Stock J and the "market" during the last three years, what is the beta coefficient of Stock
J? (Hint: Think rise over run.)
Year
Stock J
Market
1
−13.85%
−8.63%
2
22.90%
12.37%
3
35.15%
19.37%
a.
1.58
b.
1.66
c.
1.75
d.
1.84
e.
1.93
WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
3. Stock X and the "market" have had the following rates of returns over the past four years.
Year
Stock X
Market
1
12.00%
14.00%
2
5.00%
2.00%
3
11.00%
14.00%
4
−7.00%
−3.00%
60% of your portfolio is invested in Stock X and the remaining 40% is invested in Stock Y. The risk-free rate is 6% and
the market risk premium is also 6%. You estimate that 14% is the required rate of return on your portfolio. What is the
beta of Stock Y?
a.
1.72
b.
1.91
c.
2.10
d.
2.31
e.
2.54
WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
4. Hanratty Inc.'s stock and the stock market have generated the following returns over the past five years:
Year
Hanratty
Market (r M)
1
13.00%
9.00%
2
18.00%
15.00%
3
−5.00%
−2.00%
4
23.00%
19.00%
5
6.00%
12.00%
What is the estimated beta of Hanratty Inc.'s stock?
a.
1.0333
b.
1.1481
c.
1.2757
d.
1.4032
e.
1.5436
5. Below are the returns for the past five years for Stock S and for the overall market:
Year
Stock S
Market (r M)
1
12.00%
8.00%
2
34.00%
28.00%
3
−29.00%
−20.00%
4
−11.00%
−4.00%
5
45.00%
30.00%
What is the estimated beta of Stock S?
a.
1.4320
b.
1.5036
c.
1.5788
d.
1.6577
e.
1.7406
WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
6. Given the following returns on Stock Q and "the market" during the last three years, what is the difference in the
calculated beta coefficient of Stock Q when Year 1 and Year 2 data are used as compared to Year 2 and Year 3 data?
(Hint: Think rise over run.)
Year
Stock Q
Market
1
6.30%
6.10%
2
−3.70%
12.90%
3
21.71%
16.20%
a.
9.17
b.
9.63
c.
10.11
d.
10.62
e.
11.15
WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
Exhibit 8A.1
You have been asked to use a CAPM analysis to choose between Stocks R and S, with your choice being the one whose
expected rate of return exceeds its required return by the widest margin. The risk-free rate is 6%, and the required return
on an average stock (or the "market") is 10%. Your security analyst tells you that Stock S's expected rate of return is equal
to 11%, while Stock R's expected rate of return is equal to 12%. The CAPM is assumed to be a valid method for selecting
stocks, but the expected return for any given investor (such as you) can differ from the required rate of return for a given
stock. The following past rates of return are to be used to calculate the two stocks' beta coefficients, which are then to be
used to determine the stocks' required rates of return:
Year
Stock R
Stock S
Market
1
−15.00%
0.00%
−5.00%
2
5.00%
5.00%
5.00%
3
25.00%
10.00%
15.00%
Note: The averages of the historical returns are not needed, and they are generally not equal to the expected future returns.
7. Refer to Exhibit 8A.1. Calculate both stocks' betas. What is the difference between the betas? That is, what is the value
of betaR − betaS? (Hint: The graphical method of calculating the rise over run, or (Y2 − Y1) divided by (X2 − X1) may aid
you.)
a.
1.3538
b.
1.4250
c.
1.5000
d.
1.5750
e.
1.6538
WEB APPENDIX 08A—CALCULATING BETA COEFFICIENTS
8. Refer to Exhibit 8A.1. Set up the SML equation and use it to calculate both stocks' required rates of return, and
compare those required returns with the expected returns given above. You should invest in the stock whose expected
return exceeds its required return by the widest margin. What is the widest positive margin, or greatest excess return
(expected return − required return)?
a.
1.97%
b.
2.19%
c.
2.43%
d.
2.70%
e.
3.00%
