Chapter 13
RETURN, RISK AND THE SECURITY MARKET LINE
SLIDES
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
13.16
13.17
13.18
13.19
13.20
13.21
13.22
13.23
13.24
13.25
13.26
13.27
13.28
13.29
13.30
13.31
13.32
13.33
13.34
13.35
13.36
13.37
13.38
Key Concepts and Skills
Chapter Outline
Expected Returns
Example: Expected Returns
Variance and Standard Deviation
Example: Variance and Standard Deviation
Another Example
Portfolios
Example: Portfolio Weights
Portfolio Expected Returns
Example: Expected Portfolio Returns
Portfolio Variance
Example: Portfolio Variance
Another Example
Expected versus Unexpected Returns
Announcements and News
Efficient Markets
Systematic Risk
Unsystematic Risk
Returns
Diversification
Table 13.7
The Principle of Diversification
Figure 13.1
Diversifiable Risk
Total Risk
Systematic Risk Principle
Measuring Systematic Risk
Table 13.8
Total versus Systematic Risk
Work the Web Example
Example: Portfolio Betas
Beta and the Risk Premium
Example: Portfolio Expected Returns and Betas
Reward-to-Risk Ratio: Definition and Example
Market Equilibrium
Security Market Line
The Capital Asset Pricing Model (CAPM)
A-162 CHAPTER 13
SLIDES – CONTINUED
13.39
13.40
13.41
13.42
Factors Affecting Expected Return
Example – CAPM
Figure 13.41
Quick Quiz
CHAPTER WEB SITES
Section
13.2
13.3
13.5
13.6
End-of-chapter material
Web Address
www.bloomberguniversity.com
www.quicken.com
www.investopedia.com/university
www.wallstreetcity.com
moneycentral.msn.com
quote.yahoo.com
finance.yahoo.com
money.cnn.com
www.stockscreener.com
www.amex.com
CHAPTER ORGANIZATION
13.1
Expected Returns and Variances
Expected Return
Calculating the Variance
13.2
Portfolios
Portfolio Weights
Portfolio Expected Returns
Portfolio Variance
13.3
Announcements, Surprises, and Expected Returns
Expected and Unexpected Returns
Announcements and News
13.4
Risk: Systematic and Unsystematic
Systematic and Unsystematic Risk
Systematic and Unsystematic Components of Return
13.5
Diversification and Portfolio Risk
The Effect of Diversification: Another Lesson from Market History
The Principle of Diversification
Diversification and Unsystematic Risk
Diversification and Systematic Risk
CHAPTER 13 A-163
13.6
Systematic Risk and Beta
The Systematic Risk Principle
Measuring Systematic Risk
Portfolio Betas
13.7
The Security Market Line
Beta and the Risk Premium
The Security Market Line
13.8
The SML and the Cost of Capital: A Preview
The Basic Idea
The Cost of Capital
13.9
Summary and Conclusions
ANNOTATED CHAPTER OUTLINE
Slide 13.1
Slide 13.2
Key Concepts and Skills
Chapter Outline
Lecture Tip, page 415: You may find it useful to emphasize the
economic foundations of the material in this chapter. Specifically,
we assume that:
-Investor rationality: Investors are assumed to prefer more money
to less and less risk to more, all else equal. The result of this
assumption is that the ex ante risk-return trade-off will be upward
sloping.
-As risk-averse return-seekers, investors will take actions
consistent with the rationality assumptions. They will require
higher returns to invest in riskier assets and are willing to accept
lower returns on less risky assets.
-Similarly, they will seek to reduce risk while attaining the desired
level of return, or increase return without exceeding the maximum
acceptable level of risk.
13.1.
Expected Returns and Variances
A.
Expected Return
A-164 CHAPTER 13
Let n denote the total number of states of the economy, Ri the
return in state i, and pi the probability of state i. Then the expected
return, E(R), is given by:
n
E(R)   p i R i
i 1
Example:
State of economy
Probability Return Product
+1% change in GDP
.25
-.05
-.0125
+2% change in GDP
.50
.15
.0750
+3% change in GDP
.25
.35
.0875
Sums
1.00
E(R) = .15
Projected risk premium = expected return minus risk-free rate =
E(R) – Rf
Slide 13.3
Slide 13.4
Expected Returns
Example: Expected Returns
B.
Calculating the Variance
n
Var(R)   2   p i (R i  E(R)) 2
i 1
Variance measures the dispersion of points around the mean of a
distribution. In this context, we are attempting to characterize the
variability of possible future security returns around the expected
return. In other words, we are trying to quantify risk and return.
Variance measures the total risk of the possible returns.
State of Economy
+1% change in GDP
+2% change in GDP
+3% change in GDP
Total
Probability
.25
.50
.25
1.00
Return
-.05
.15
.35
E(R) = .15
Squared Deviation
0.04
0.00
0.04
Product
.01
.00
.01
2 = .02
Standard deviation = square root of variance = .1414
Slide 13.5
Variance and Standard Deviation
Lecture Tip, page 418: Some students experience confusion in
understanding the mathematics of the variance calculation. They
may have the feeling they should divide the variance of an
CHAPTER 13 A-165
expected return by (n-1). Point out that the probabilities account
for this division. We divide by n-1 in the historical variance
because we are looking at a sample. If we looked at the entire
population (which is what we are doing with expected values), then
we would divide by 1/n to get our historical variance. This is the
same as saying that the “probability” of occurrence is the same
for all observations and is equal to 1/n.
Lecture Tip, page 419: Each individual has their own level of risk
tolerance. Some people are just naturally more inclined to take
risk and they will not require the same level of compensation as
others for doing so. Our risk preferences also change through
time. We may be willing to take more risk when we are young and
without a spouse or kids. But, once we start a family, our risk
tolerance may drop.
Slide 13.6
Slide 13.7
13.2.
Example: Variance and Standard Deviation
Another Example
Portfolios
A.
Portfolio Weights
A portfolio is a collection of assets, such as stocks and bonds, held
by an investor.
Portfolios can be described by the percentage investment in each
asset and these percentages are called portfolio weights.
Example: If two securities in a portfolio have a combined value of
$10,000 with $6000 invested in IBM and $4000 invested in GM,
then weight in IBM = 6/10 = .6 and the weight in GM = 4/10 = .4.
Slide 13.8 Portfolios
B.
Portfolio Expected Returns
The expected return on a portfolio is the sum of the product of the
expected returns on the individual securities and their portfolio
weights. Let wj be the portfolio weight for asset j and m be the
total number of assets in the portfolio; then
m
E(R)   w j E(R j )
j 1
A-166 CHAPTER 13
This formula also works if you drop the expectations and just
compute the portfolio return in each state of the economy. This is
what is necessary for the calculation of the portfolio variance in the
next section.
Slide 13.9 Example Portfolio Weights
Slide 13.10 Portfolio Expected Returns
Slide 13.11 Example: Expected Portfolio Returns
C.
Portfolio Variance
Unlike expected return, the variance of a portfolio is NOT the
weighted sum of the individual security variances. Combining
securities into portfolios can reduce the total variability of returns.
Example: Consider a portfolio with equal amounts invested in
three stocks:
State of Economy Probability Return on
A
+1% change in
.25
-.05
GDP
+2% change in
.50
.15
GDP
+3% change in
.25
.35
GDP
Expected Return
.15
Return on
B
.00
Return on
C
.20
Return on
Portfolio
.050
.10
.10
.117
.20
.00
.183
.10
.10
.117
Variances and standard deviations:
Var(A) = .25(-.05-.15)2 + .5(.15-.15)2 + .25(.35-.15)2 = .02
Std. Dev.(A) = .1414
Var(B) = .25(0 - .1)2 + .5(.1 - .1)2 + .25(.2 - .1)2 = .005
Std. Dev.(B) = .0707
Var(C) = .25(.2 - .1)2 + .5(.1-.1)2 + .25(0-.1)2 = .005
Std. Dev.(C) = .0707
Var(portfolio) = .25(.05-.117)2 + .5(.117-.117)2 + .25(.183-.117)2 =
.002
Std. Dev.(portfolio) = .047
Notice that the portfolio variance is less than any of the individual
variances.
CHAPTER 13 A-167
Slide 13.12 Portfolio Variance
Lecture Tip, page 422: In must business programs, a course in
elementary statistics is a prerequisite for the introductory finance
course. And, while students are sometimes fuzzy on the details,
they usually remember the general concept of the correlation
coefficient (and hopefully the covariance). They almost always
remember that the correlation coefficient is bounded by –1 and 1.
You may find it useful to reintroduce them to the correlation
concept here to deepen their understanding of portfolio variance.
Specifically, for a two-asset portfolio, the portfolio variance is
equal to:
w 12 σ12  w 22 σ 22  2w 1 w 2 σ1σ 2 ρ1,2
or w 12 σ12  w 22 σ 22  2w 1 w 2 σ1,2
where 1,2 is the correlation coefficient and 1,2 is the covariance.
When you expand the equation to more assets you will have a
variance term for each asset and a covariance term for each pair
of assets. As you increase the number of assets, it is easy to see
that the correlation (covariance) between assets is much more
important to determining the portfolio variance than the individual
variances.
Reconsider the previous example.
The following covariances can be computed:
cov(A,B) = .01
cov(A,C) = -.01
cov(B,C) = -.005
Using the covariances and extending the formula above to three
assets, you can compute a portfolio variance and standard
deviation:
var = (1/3)2(.02) + (1/3)2(.005) + (1/3)2(.005) + 2(1/3)(1/3)(.01) +
2(1/3)(1/3)(-.01) + 2(1/3)(1/3)(-.005) = .002
standard deviation = .047
This is just as we computed earlier.
Slide 13.13 Example: Portfolio Variance
Slide 13.14 Another Example
A-168 CHAPTER 13
Lecture Tip, page 423: Here are a few tips to pass along to
students suffering from “statistics overload”:
-The distribution is just the picture of all possible outcomes
-The mean return is the central point of the distribution
-The standard deviation is the average deviation from the mean
-Assuming investor rationality (two-parameter utility functions),
the mean is a proxy for expected return and the standard deviation
is a proxy for total risk.
13.3.
Announcements, Surprises, and Expected Returns
A.
Expected and Unexpected Returns
Total return = expected return + unexpected return
Thus, total return differs from expected return because of surprises,
or “news.” This is one of the reasons that realized returns differ
from expected returns.
Slide 13.15 Expected versus Unexpected Returns
B.
Announcements and News
Announcement – the release of information not previously
available. Announcements have two parts: the expected part and
the surprise part.
The expected part is “discounted” information used by the market
to estimate the expected return, while the surprise is news that
influences the unexpected return.
Discounted information is information that is already included in
the expected return (and the price). The tie-in to efficient markets
is obvious. The assumption here is that markets are semistrong
efficient.
Lecture Tip, page 424: It is easy to see the effect of unexpected
news on stock prices and returns. Consider the following two
cases: (1) On August 9, 2000 it was announced that Eli-Lilly’s
prozac patent would not be extended, overturning a lower court
decision. This was unexpected and the price dropped from
$108.531 to $76.875 (a 29% drop) in one day. (2) On September
22, 2000, Intel issued an earnings warning, and its stock price
CHAPTER 13 A-169
dropped from $61.468 to $47.937 (a 22% drop) in one day. There
are plenty of other examples where unexpected news causes a
change in price and expected returns.
Slide 13.16 Announcements and News
Slide 13.17 Efficient Markets
13.4.
Risk: Systematic and Unsystematic
A.
Systematic and Unsystematic Risk
Risk consists of surprises. There are two kinds of surprises:
Systematic risk is a surprise that affects a large number of assets,
although at varying degrees. It is sometimes called market risk.
Unsystematic risk is a surprise that affects a small number of assets
(or one). It is sometimes called unique or asset-specific risk.
Example: Changes in GDP, interest rates and inflation are
examples of systematic risk. Strikes, accidents and takeovers are
examples of unsystematic risk.
Lecture Tip, page 426: You can expand the discussion of the
difference between systematic and unsystematic risk by using the
example of a strike by employees. Students will generally agree
that this is unique or unsystematic risk for one company. However,
what if the UAW stages the strike against the entire auto industry.
Will this action impact other industries or the entire economy? If
the answer to this question is yes, then this becomes a systematic
risk factor. The important point is that it is not the event that
determines whether it is systematic or unsystematic risk; it is the
impact of the event.
Slide 13.18 Systematic Risk
Slide 13.19 Unsystematic Risk
B.
Systematic and Unsystematic Components of Return
Total return = expected return + unexpected return
Total return = expected return + systematic portion + unsystematic
portion
Slide 13.20 Returns
A-170 CHAPTER 13
13.5.
Diversification and Portfolio Risk
A.
The Effect of Diversification: Another Lesson from Market
History
Portfolio variability can be quite different from the variability of
individual securities.
A typical single stock on the NYSE has a standard deviation of
annual returns around 50%, while the typical large portfolio of
NYSE stocks has a standard deviation of around 20%.
Video Note: “Portfolio Management” looks at the value of diversification using Tower
Records as an example.
Slide 13.21 Diversification
Slide 13.22 Table 13.7
B.
The Principle of Diversification
Principle of Diversification – principle stating that combining
imperfectly correlated assets can produce a portfolio with less
variability than the typical individual asset.
The portion of variability present in a single security is not present
in a portfolio of securities is called diversifiable risk. The level of
variance that is present in collections of assets is nondiversifiable
risk.
Slide 13.23 The Principle of Diversification
Slide 13.24 Figure 13.1
Slide 13.25 Diversifiable Risk
International Note, page 429: Common sense suggests that, to the
extent that national economies are less than perfectly positively
correlated, there may be diversification benefits to be had by
investing in foreign securities. Empirical research bears this
notion out. For example, Solnik (Financial Analysts Journal, 1974)
and Harvey (Journal of Finance, 1991) find that the returns on
U.S. stocks are significantly less than perfectly positively
correlated with returns on stocks in other industrialized countries.
As a result, the potential for risk reduction is greater when you
include international stocks in your portfolio.
CHAPTER 13 A-171
C.
Diversification and Unsystematic Risk
When securities are combined into portfolios, their unique or
unsystematic risks tend to cancel out, leaving only the variability
that affects all securities to some degree. Thus, diversifiable risk is
synonymous with unsystematic risk. Large portfolios have little or
no unsystematic risk.
D.
Diversification and Systematic Risk
Systematic risk cannot be eliminated by diversification since it
represents the variability due to influences that affect all securities
to some degree. Therefore, systematic risk and nondiversifiable
risk are the same.
Total risk = nondiversifiable risk + diversifiable risk = systematic
risk + unsystematic risk
Slide 13.26 Total Risk
13.6.
Systematic Risk and Beta
A.
The Systematic Risk Principle
The principle – The reward for bearing risk depends only on the
systematic risk of the investment.
The implication – The expected return on an asset depends only on
that asset’s systematic risk.
A corollary – No matter how much total risk an asset has, its
expected return depends only on its systematic risk.
Slide 13.27 Systematic Risk Principle
Lecture Tip, page 430: The text states that “The underlying
rationale for this principle is straightforward: Since unsystematic
risk can be eliminated at virtually no cost (by diversifying), there is
no reward for bearing it.” This is a crucial point and it is
consistent with observed behavior. The rapid growth in mutual
funds suggests that investors aggressively seek to diversify their
holdings. Further, barriers to diversification are minimal: many
A-172 CHAPTER 13
funds will open accounts with initial deposits as small as $500.
Many company-sponsored retirement plans will open accounts
with much less.
B.
Measuring Systematic Risk
Beta coefficient – measures how much systematic risk an asset has
relative to an asset of average risk.
Slide 13.28 Measuring Systematic Risk
Slide 13.29 Table 13.8 Click on the web surfer to go to
www.stockscreener.com. You can use this web site to do the exercise
discussed in the following lecture tip.
Lecture Tip, page 431: The point that “the market does not reward
risks that are borne unnecessarily,” should be strongly
emphasized, possibly with a reference back to Figure 13.1 (Slide
13.24). Many investment companies offer investors a choice
between income-oriented mutual funds, containing both bonds and
stocks in established companies with higher dividend payouts, and
growth-oriented funds that are typically composed of stocks of
smaller companies that retain most of their earnings for
reinvestment in the firm. Investors that desire growth-oriented
funds typically assume a much greater degree of systematic risk
and expect higher returns. However, both types of funds eliminate
the unsystematic portion of risk through diversification.
Lecture Tip, page 431: Students sometimes wonder just how high
a stock’s beta can get. In earlier years, one would say that, while
the average beta for all stocks must be 1.0, the range of possible
values for any given beta is from - to +.
Today, the Internet provides another way of addressing the
question. Go to www.stockscreener.com. This site allows you to
search many financial markets by fundamental criteria. For
example, as of June 21, 2000, a search of “All Exchanges” for
stocks with betas of at least 2.00 turns up 256 stocks. Restricting
the search to the NYSE still turns up 46 stocks. Encourage students
to experiment with this.
Slide 13.30 Total versus Systematic Risk
Slide 13.31 Work the Web Example
CHAPTER 13 A-173
C.
Portfolio Betas
While portfolio variance is not a weighted average of the
individual asset betas, portfolio betas are a weighted average of the
individual asset betas.
Example:
Stock
Amount Invested Portfolio Weight Beta Product
IBM
6000
50.00% 1.11
.555
GM
4000
33.33% 1.05
.350
Wal-Mart
2000
16.67% 1.09
.182
Portfolio
10,000
100.00%
1.087
Slide 13.32 Example: Portfolio Betas
Lecture Tip, page 433: All else equal, borrowing money will
increase a firm’s equity beta because it increases the volatility of
earnings. Robert Hamada derived the following equation to reflect
the relationship between levered and unlevered betas.
L = U(1 + D/E)
where: L = equity beta of a levered firm;
U = equity beta of an unlevered firm;
D/E = debt-to-equity ratio
13.7.
The Security Market Line
A.
Beta and the Risk Premium
A riskless asset has a beta of 0.When a risky asset with >0, is
combined with a riskless asset, the resulting expected return is the
weighted sum of the expected returns and the portfolio beta is the
weighted sum of the betas. By varying the amount invested in each
asset, we can get an idea of the relation between portfolio expected
returns and betas. This relationship is illustrated in Figure 11.2A.
As can be seen, all of the risk-return combinations lie on a straight
line. Remind the students that the equation for a line is:
y = mx + b
A-174 CHAPTER 13
where: y = expected return
x = beta
m = slope
b = y-intercept = risk-free rate
Introducing this equation now prepares the students for the SML
and the CAPM.
Slide 13.33 Beta and the Risk Premium
Lecture Tip, page 434: The example in the book illustrates a
greater than 100% investment in asset A. This means that the
investor has borrowed money on margin (technically at the riskfree rate) and used that money to purchase additional shares of
asset A. This can increase the potential returns, but it also
increases the risk.
Slide 13.34 Example: Portfolio Expected Returns and Betas
Slide 13.35 Reward-to-Risk Ratio: Definition and Example
The Reward-to-Risk Ratio is the expected return per unit of
systematic risk. In other words, it is the ratio of risk premium to
systematic risk.
The basic argument is that since systematic risk is all that matters
in determining expected return, the reward-to-risk ratio must be the
same for all assets. If it were not, people would buy the asset with
the higher reward-to-risk ratio (driving up the price and down the
return).
The fundamental result is that in a competitive market where only
systematic risk affects E(R), the reward-to-risk ratio must be the
same for all assets in the market. Consequently, the expected
returns and betas of all assets much plot on the same straight line.
Slide 13.36 Market Equilibrium
B.
The Security Market Line
The line that gives the expected return/systematic risk
combinations of assets in a well functioning, active financial
market is called the security market line.
Slide 13.37 Security Market Line
CHAPTER 13 A-175
Lecture Tip, page 439: Although the realized market risk premium
has on average been approximately 8%, the historical average
should not be confused with the anticipated risk premium for any
particular future period. There is abundant evidence that the
realized market return has varied greatly over time. The historical
average value should be treated accordingly. On the other hand,
there is currently no universally accepted means of coming up with
a good ex ante estimate of the market risk premium, so the
historical average might be as good a guess as any. In the late
1990’s, there was evidence that the risk premium had been
shrinking. In fact, Alan Greenspan was concerned with the
reduction in the risk premium because he was afraid that investors
had lost sight of how risky stocks actually are. Investors have had
a wake-up call in late 2000 and 2001.
Market Portfolios: Consider a portfolio of all the assets in the
market and call it the market portfolio. This portfolio, by
definition, has “average” systematic risk with a beta of 1. Since all
assets must lie on the SML when appropriately priced, the market
portfolio must also lie on the SML. Let the expected return on the
market portfolio = E(RM). Then, the slope of the SML = reward-torisk ratio = [E(RM) – Rf] / M = [E(RM) – Rf] / 1 = E(RM) – Rf
The Capital Asset Pricing Model: Go back to the discussion of the
equation of a line:
E(Rj) = Rf + slope(j)
E(Rj) = Rf + (E(RM) – Rf)(j)
The CAPM states that the expected return for an asset depends on:
-The time value of money, as measured by Rf
-The reward per unit risk, as measured by E(RM) - Rf
-The asset’s systematic risk, as measured by 
Slide 13.38
Slide 13.39
Slide 13.40
Slide 13.41
13.8.
The Capital Asset Pricing Model (CAPM)
Factors Affecting Expected Return
Example – CAPM
Figure 13.4
The SML and the Cost of Capital: A Preview
A.
The Basic Idea
A-176 CHAPTER 13
We must determine an investment’s risk and then use the CAPM to
determine the expected return on assets of similar risk.
Lecture Tip, page 442: Students should remember that in an
efficient market, security investments have a NPV = 0, on average.
However, the NPV does not imply that a company’s investments in
new projects must have an NPV of zero. Firms attempt to invest in
projects with a positive NPV, and those that are consistently
successful will trade at higher prices, all else equal. The ability to
generate positive NPV projects reflects the fundamental
differences in physical asset markets and financial asset markets.
Physical asset markets are generally less efficient than financial
asset markets, and cash flows to physical assets are often owner
dependent.
B.
The Cost of Capital
Cost of capital – the minimum expected return an investment must
offer to be attractive. Sometimes referred to as the required return.
13.9.
Summary and Conclusions
Slide 13.42 Quick Quiz
CHAPTER 13 A-177
APPENDIX A: CALCULATING BETA COEFFICIENTS
In the chapter we noted that a beta coefficient measures the amount of systematic
risk present in a particular risky asset relative to the average risky asset. (Later it was
suggested that the market portfolio would serve as an appropriate proxy for the average
risky asset.) Since risk is a function of the changes in, or “movement of” an asset’s price,
systematic risk must be attributable to the movement in a risky asset’s price relative to
the movement in the price of the average risky asset (or the market portfolio).
Given the above, we should not be surprised to find that the beta coefficient is
nothing more than a statistical measure of the relationship between the returns on asset j
and the market portfolio. This relationship is most often quantified via the use of simple
linear regression. Specifically, we estimate the following model:
Rjt = j + jRMt + j
Where: Rjt = the return on stock j in period t,
RMt = the return on the market portfolio in period t,
j, j = the intercept and the slope coefficients, respectively, and
j = the random error term.
The model above is called the “market model” and is usually estimated using
daily or monthly historical returns. (Although there are no universally accepted
guidelines, most people use approximately 250 daily returns, or 60 monthly returns to
estimate the model.) The estimated  coefficient in the model above is the beta referred to
in the chapter.
Although, it is beyond the scope of this book, it is possible to show that, given
certain assumptions about the distribution of returns, the beta coefficient is equal to the
correlation between returns on stock j and the market portfolio, times the product of the
standard deviations of the returns on stock j and the market portfolio, all divided by the
variance of the market returns. In equation form,
j = j,MjM / 2M
Consider the following monthly stock return data.
Month
Rj
RM
1
.003
.013
2
.024
.017
3
.021
.012
4
-.015
.004
5
.005
.011
6
.022
.015
7
-.021
.011
8
.017
-.010
9
.018
.011
10
.028
.013
11
.032
.021
12
-.017
-.013
Expected Return
.00975 .00875
Standard Deviation .0185
.0103
Correlation
.50276
A-178 CHAPTER 13
According to the above equation, j = .50276(.0185)(.0103)/(.0103)2 = .903.
Since, in a strict mathematical sense, the beta coefficient is simply an index measuring
the statistical relationship between the returns on stock j and the market portfolio, we
interpret the results to mean that the systematic risk of stock j is about 90 percent of that
of the average stock. (Digression: This is the source of the terms “aggressive” and
“defensive” as applied to stocks. Aggressive stocks are stocks with betas greater than 1.0;
they are more volatile than the average stock and are, therefore, more suited to investors
willing to take risks, i.e., to be aggressive. Of course, the opposite holds true for
defensive stocks.)
Notice that the beta equation also suggests that beta has the following properties.
1.
2.
The beta of the market portfolio, M, must equal one.
The beta of the risk-free asset must equal zero.
Finally, it should be noted that most people need not bother to calculate betas for
stocks they are interested in. Beta coefficients are computed by several firms (for
example, Merrill Lynch, Standard and Poor’s Corporation, Value Line, and Moody’s)
and appear in various publications, as well as at various sites on the Internet.