318  Estimating the Cost of Capital 
index of large U.S. companies. Outside the United States, financial analysts 
rely on either a regional index like the MSCI Europe Index or the MSCI World 
Index, a value-weighted index comprising large stocks from 23 developed 
countries, including the United States.
Most well-diversified indexes, such as the S&P 500 and MSCI World Index, 
are highly correlated (the two indexes had a 97 percent correlation between 
2000 and 2018). Thus, the choice of index will have only a small effect on beta. 
Do not, however, use a local market index, which some data services provide. 
Most countries are heavily weighted in only a few industries and, in some 
cases, a few companies. Consequently, when measuring beta versus a local 
index, you are not measuring market-wide systematic risk, but often a com-
pany’s sensitivity to a particular set of industries.
Beta Smoothing  Many academics and beta services also adjust a company’s 
raw beta closer to the mean of all companies, a process called smoothing. 
Smoothing moves the point estimate of beta toward the overall average. Con-
sider the simple smoothing process used by Bloomberg:
Adjusted Beta
Raw Beta
=
+
(
)
0 33
0 67
.
.
This formula smooths raw regression estimates toward 1. For instance, a raw 
beta of 0.5 leads to an adjusted beta of 0.67, while a raw beta of 1.5 leads to an 
adjusted beta of 1.34.
Bloomberg’s smoothing mechanism dates to Marshall Blume’s observation 
that betas revert to the mean.18 Today, more advanced smoothing techniques 
exist.19 Although the proof is beyond the scope of this book, the following 
adjustment will reduce beta estimation error:
β
σ
σ
σ
σ
σ
σ
β
ε
ε
ε
ε
adj
raw
=
+







+
−
+








2
2
2
2
2
2
1
1
b
b
where
 σε = standard error of the regression beta
σb = cross-sectional standard deviation of all betas
The raw regression beta receives the most weight when the standard error of 
beta from the regression (σε) is smallest. In fact, when beta is measured perfectly 
(σε = 0), the raw beta receives all the weight. Conversely, if the regression pro-
vides no meaningful results (σε is very large), you should set beta equal to 1.0.
Since we are using an industry peer beta for Costco, we did not smooth 
regression results.
18 M. Blume, “Betas and Their Regression Tendencies,” Journal of Finance 30 (1975): 1–10.
19 For instance, see P. Jorion, “Bayes-Stein Estimation for Portfolio Analysis,” Journal of Financial and 
Quantitative Analysis 21 (1986): 279–292.

Estimating the Cost of Equity  319
Creating an Industry Beta  Estimating beta is an imprecise process. We used 
historical regression to estimate Costco’s beta at 0.85. But the regression’s R-
squared was only 30 percent, and the standard error of the beta estimate was 
0.17. Using two standard errors as a guide, a statistician would feel confident 
Costco’s true beta lies between 0.5 and 1.18—hardly a tight range.
To reduce the noise around beta estimates, use industry, rather than company-
specific, betas. Companies in the same industry face similar operating risks, so they 
should have similar operating betas. If estimation errors across companies are 
uncorrelated, overestimates and underestimates of individual betas will tend to 
cancel, and an industry median (or average) beta will produce a superior estimate.
Consider two similarly skilled companies competing for a large customer 
contract. Depending on which company wins the contract, one company’s 
stock price will rise; the other company’s stock price will fall. If the market 
rises during this period, the winning company will have a higher measured 
beta, and the losing company will have a lower measured beta, even though 
the contract selection had nothing to do with market performance. Using an 
industry beta to proxy for company risk lessens the effect of random shocks.
Simply using the median of an industry’s raw regression betas overlooks 
a second important factor: leverage. A company’s beta is a function of not 
only its operating risk, but also the financial risk it takes. Shareholders of a 
company with more debt face greater risks, and this increase is reflected in 
beta. Therefore, to compare companies with similar operating risks, you must 
first strip out the effect of leverage. Only then can you compare betas across 
an industry.
To undo the effect of leverage (and its tax shield), we rely on the theories 
of Franco Modigliani and Merton Miller, introduced in Chapter 10. According 
to Modigliani and Miller, the weighted average risk of a company’s financial 
claims equals the weighted average risk of a company’s economic assets. In 
Appendix C, we present this concept algebraically and rearrange the equation 
to isolate the risk of equity, as measured by beta. The general equation for the 
beta of equity is as follows:
β
β
β
β
β
β
e
u
u
d
txa
u
txa
D
E
V
E
=
+
−
(
) −
−
(
)
where
 bu = beta of the company’s operating assets
 bd = beta of the company’s debt
 btxa = beta of the company’s interest tax shields
 D = market value of the company’s debt
 E = market value of the company’s equity
Vtxa = present value of the company’s interest tax shields
To simplify the formula further, if the company maintains a constant ratio 
of debt to equity, the value of tax shields will fluctuate with the value of