Web Appendix 08A: Calculating Beta Coefficients
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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.
e. The Security Market Line (SML) shows the relationship between risk as measured by beta and the required rate of
return for all securities.
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 –7.69% –8.60%
2 11.75% 13.00%
3 17.15% 19.00%
a. 0.71
b. 0.73
c. 0.90
d. 0.91
e. 1.00
Web Appendix 08A: Calculating Beta Coefficients
Web Appendix 08A: Calculating Beta Coefficients
Copyright Cengage Learning. Powered by Cognero.
Page 6
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 5.00%, and the required
return on an average stock (or the “market”) is 9.00%. Your security analyst tells you that Stock S’s expected rate of return
is equal to 12.00%, while Stock R’s expected rate of return is equal to 14.00%. 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 –16.09% –10.39% –8.00%
2 18.08% 11.71% 9.00%
3 48.23% 31.21% 24.00%
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. 0.80
b. 0.53
c. 0.71
d. 0.56
e. 0.73
