Stock Beta and its
Estimation
by
Dr. Yi
1
Let’s re-define risk more
precisely.
 Stand-alone Risk (or total risk)
= Market Risk + Diversifiable Risk
2
Systematic Risk



Risk factors that affect a large
number of assets such as marketwide news
Also known as non-diversifiable risk
or market risk
Includes such things as changes in
GDP, inflation, interest rates, etc.
3
Unsystematic Risk



Risk factors that affect a limited
number of assets such as firm-specific
news
Also known as unique risk,
diversifiable risk, idiosyncratic risk, and
firm-specific risk
Includes such things as labor strikes,
part shortages, etc.
4
Pop Quiz:
Systematic Risk or Unsystematic Risk?




The government announces that inflation unexpectedly
jumped by 2 percent last month.
Systematic Risk
One of Big Widget’s major suppliers goes bankruptcy.
Unsystematic Risk
The head of accounting department of Big Widget
announces that the company’s current ratio has been
severely deteriorating.
Unsystematic Risk
Congress approves changes to the tax code that will
increase the top marginal corporate tax rate.
Systematic Risk
5
Average annual
standard deviation (%)
49.2
Diversifiable risk
23.9
19.2
Nondiversifiable
risk
1
10
20
30
40
1,000
Number of stocks
in portfolio
6
The Principle of Diversification
 Diversification
can substantially reduce the
variability of returns
 This reduction in risk arises because worse
than expected returns from one asset are
offset by better than expected returns from
another
 However, there is a minimum level of risk
that cannot be diversified away and that is
the systematic portion
7
Keown, Martin, Petty - Chapter 6
8
In summary,

Risk can be viewed in two ways:
– On a stand-alone basis.
– In a portfolio context.


In a portfolio context, only relevant
risk is systematic risk.
Systematic risk = Market risk
9
How is market risk measured for
individual securities?


The risk that remains after diversifying is market
risk, or the risk that is inherent in the market.
And it can be measured by the degree to which a
given stock tends to move up or down with the
market.

Market risk is defined as the contribution of a
security to the overall riskiness of the portfolio.
– The return of the well-diversified portfolio is a function
of market risk only.

It is measured by a stock’s beta coefficient, which
measures the stock’s volatility relative to the
market.
10
Measuring Systematic Risk

Beta (b)
– A security’s beta is related to how
sensitive its underlying revenues and
cash flows are to general economic
conditions. Stocks in cyclical industries,
are likely to be more sensitive to
systematic risk and have higher betas
than stocks in less sensitive industries.
Measuring Systematic Risk

Beta (b)
– The expected percent change in the
excess return of a security for a 1%
change in the excess return of the market
portfolio.

Beta differs from volatility. Volatility measures
total risk (systematic plus unsystematic risk),
while beta is a measure of only systematic
risk.
Measuring Systematic Risk
 We
use the beta coefficient to measure
systematic risk
 What does beta tell us?
– A beta of 1 implies the asset has the same
systematic risk as the overall market
– A beta < 1 implies the asset has less
systematic risk than the overall market
– A beta > 1 implies the asset has more
systematic risk than the overall market
13
Betas With Respect to the S&P 500 for Individual
Stocks and Average Betas for Stocks in Their
Industries (based on monthly data for 2000-2005)
Statistically (or algebraically), beta
can be expressed as follows:
 i 
bi  
 iM
M 
bi 
Cov(ri , rM )

2
M
Note: We will not derive these equations.
15
How are betas calculated?


Run a regression with returns on the
stock in question plotted on the Y axis
and returns on the market portfolio
plotted on the X axis.
The slope of the regression line,
which measures relative volatility, is
defined as the stock’s beta
coefficient, or b.
16
Use the historical stock returns
to calculate the beta for KWE.
Year
1
2
3
4
5
6
7
8
9
10
Market
25.7%
8.0%
-11.0%
15.0%
32.5%
13.7%
40.0%
10.0%
-10.8%
-13.1%
KWE
40.0%
-15.0%
-15.0%
35.0%
10.0%
30.0%
42.0%
-10.0%
-25.0%
25.0%
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Calculating Beta for KWE
40%
kKWE
20%
kM
0%
-40%
-20%
0%
20%
40%
-20%
-40%
kKWE = 0.83k M + 0.03
R2 = 0.36
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How is beta calculated?




The regression line, and hence beta, can
be found using a calculator with a
regression function or a spreadsheet
program. In this example, b = 0.83.
Analysts typically use four or five years’ of
monthly returns to establish the regression
line. Some use 52 weeks of weekly
returns.
Most stocks have betas in the range of 0.5
to 1.5.
Can a stock have a negative beta?
19
Interpreting Regression Results

The R2 measures the percent of a
stock’s variance that is explained by
the market. The typical R2 is:
– 0.3 for an individual stock
– over 0.9 for a well diversified portfolio
20