Chapter
5
Analysis of Risk and Return
Copyright ©2003 South-Western/Thomson Learning
Introduction
• This chapter develops the risk-return
relationship for individual projects
(investments) and a portfolio of
projects.
Risk and Return
•
•
•
Risk refers to the potential variability of
returns from a project or portfolio of projects.
Returns are generated from cash flows.
Risk-free returns are known with certainty.
–
•
U.S. Treasury Securities
Check out interest rates on the following
URLs
–
–
http://www.stls.frb.org/fred/data/irates.html
http://www.bloomberg.com/
Expected Return
• Expected return is a weighted average of
the individual possible returns.
^
• The symbol for expected return, r, is
called “r hat.”
• r = Sum (all possible returns  their
probability)
^
n
 rˆ   rj p j
j 1
Let’s Analyze Risk
• Standard Deviation is an absolute
measure of risk. See Tables 5.2, 5.3, and
5.4 and Figure 5.1.
n
2
ˆ
σ   ( rj  r ) p j
j 1
Let’s Analyze Risk
TABLE 5.2 Probability Distribution of Returns from Duke and TI
Rate of Return Anticipated under Each State of the Economy
State of the Economy
Probability
Duke
TI
Recession
0.2
10%
-4%
Normal
0.6
18%
18%
Boom
0.2
26%
40%
1.0
Let’s Analyze Risk
TABLE 5.3 Expected Return Calculation for Investment in Duke and TI
Duke
TI
rj
pj
rj * pj
rj
pj
rj * pj
10%
0.2
2.0%
-4.0%
0.2
-0.8%
18%
0.6
10.8%
18%
0.6
10.8%
26%
0.2
5.2%
40%
0.2
8.0%
18.0%
Expected return (^r)
Expected return (^r)
18.0%
Let’s Analyze Risk
TABLE 5.4 Computation of Standard Deviations of Return for Duke
j
rj
^r
pj
rj  ^r (rj  ^r)2
(rj  ^r)2pj
Recession 10%
18%
-8%
64
0.2
12.8
Normal
18%
18%
0
0
0.6
0
Boom
26%
18%
8%
64
0.2
12.8
25.6
Summation of (rj  ^r)2pj for j = 1,…, n (where n = 3)
5.06%
Standard Deviation of Summation of (rj  ^r)2pj for j = 1,…, n
(where n = 3)
Let’s Analyze Risk
TABLE 5.4 Computation of Standard Deviations of Return for TI
j
rj
^r
pj
rj  ^r (rj  ^r)2
Recession
-4%
18%
-22%
484
0.2
Normal
18%
18%
0
0
0.6
Boom
40%
18%
22%
484
0.2
Summation of (rj  ^r)2pj for j = 1,…, n (where n = 3)
Standard Deviation of Summation of (rj  ^r)2pj for j = 1,…, n
(where n = 3)
(rj  ^r)2pj
96.8
0
96.8
193.6
13.91%
Let’s Analyze Risk
• Coefficient of variation v is a relative
measure of risk.
σ
v
rˆ
• Risk is an increasing function of time.
See Figure 5.3.
Calculating the Z Score
• Z score measures the number of
standard deviations a particular rate of
^
return r is from the expected value of r.
See Figure 5.2.
• Z score = Target score – Expected value
Standard deviation
Calculating the Z Score
• What’s the probability of a loss (i.e., a
negative return) on an investment with
an expected return of 20 percent and a
standard deviation of 17 percent?
• (0% – 20%)/17% = –1.18 rounded
• From table V = 0.1190 or 11.9 percent
probability of a loss
Coefficient of Variation
• The coefficient of variation is an
appropriate measure of total risk when
comparing two investment projects of
different size.
Coefficient of Variation
• Consider two assets, T and S. Asset T
has expected annual returns of 25% and
a standard deviation of 20%, whereas
Asset S has expected annual returns of
10% and a standard deviation of 18%.
Although Asset T has a higher standard
deviation than Asset S, intuition tells us
that Asset T is less risky, because its
relative variation is smaller.
Coefficient of Variation
• Coefficient of variation of Asset T is 0.8
(= 20%/25%)
• Coefficient of variation of Asset S is 1.8
(= 18%/10%)
Risk-Return Relationship
Required return = Risk-free return
+ Risk premium
Real rate of return
Risk-free rate
Expected inflation
premium
Check out the risk-free rate at this Web site:
http://www.cnnfn.com/markets/rates.html
Risk-Free Rate of Return
• The real rate of return is the return that
investors would required from a security
having no risk of default in a period of no
expected inflation. It is the return
necessary to convince investors to
postpone current, real consumption
opportunities.
Risk-Free Rate of Return
• The second component of the risk-free
rate of return is an inflation premium or
purchasing power loss premium.
Investors required compensation for
expected losses in purchasing power
when they postpone current
consumption and lend funds.
Consequently, a premium for expected
inflation is included in the required return
on any security.
Risk-Free Rate of Return
• The inflation premium is normally equal
to investors’ expectations about future
purchasing power changes. If, for
example, inflation is expected to average
4 percent over some future period, the
risk-free rate of return on U.S. Treasury
bills (assuming a real rate of return of 3
percent) should be approximately equal
to 7 percent.
Risk-Free Rate of Return
• At any point in time, the required riskfree rate of return on any security can be
estimated from the yields on short-term
U.S. government securities, such as 90day Treasury bills.
Risk-Free Rate of Return
• When considering return requirements
on all types of securities, it is important
to remember that increases in expected
inflation rates normally lead to increases
in the required rates of return on all
securities.
Risk Premium
• A risk premium is a potential “reward”
that an investor expects to receive when
making a risky investment.
• Investors are generally considered to be
risk averse; that is, they expect, on
average, to be compensated for the risk
they assume when making an
investment.
Risk Premium
• The rate of return required by investors
in financial assets is determined in the
financial marketplace and depends on
the supply of funds available as well as
the demand for these funds.
Risk Premium
• Investors who buy bonds receive interest
payments and a return of principal as
compensation for postponing
consumption and accepting risk.
• Similarly, common stock investors
expect to receive dividends and price
appreciation from their stocks.
Risk Premium
• The rate of return required by investors
represents a cost of capital to the firm.
This required rate of return is used by a
firm’s managers when computing the net
present value of the cash flows expected
to be generated from the company’s
investment.
Risk Premium
• The required rate of return on a security
is also an important determinant of the
market value of financial securities,
including common stock, preferred stock,
and bonds.
Risk Premium
• The risk premium assigned by an
investor to a given security in
determining the required rate of return is
a function of several different risk
elements as you can see in the next
several slides.
Risk Premium
• Maturity risk premium
• Default risk premium
• Seniority risk premium
• Marketability risk premium
• Business risk
• Financial risk
Maturity risk premium
• The return required on a security is
influenced by the maturity of that
security. The term structure of interest
rates is the pattern of interest rate yields
(required returns) for securities that differ
only in the length of time to maturity.
• The longer the time to maturity, the
higher the required return on the
security.
• See Figure 5.4.
Term Structure of Interest Rates
• Expectations theory
• Liquidity premium theory
• Market segmentation theory
Expectations Theory
• According to the expectations theory,
long-term interest rates are a function of
expected future (that is, forward) shortterm interest rates.
• If future short-term interest rates are
expected to rise, the yield curve will tend
to be upward sloping. In contrast, a
down-sloping yield curve reflects an
expectation of declining future short-term
interest rates.
Expectations Theory
• According to the expectations theory,
current and expected future interest
rates are dependent on expectations
about future rates of inflation.
• Many economic and political conditions
can cause expected future inflation and
interest rates to rise or fall.
– These conditions include expected future
government deficits (or surplus), changes in
Federal Reserve monetary policy and
cyclical business conditions.
Liquidity Premium Theory
• The liquidity (or maturity) premium
theory of the yield curve holds that
required returns on long-term securities
tend to be greater the longer the time to
maturity.
• The maturity premium reflects a
preference by many lenders for shorter
maturities because the interest rate risk
associated with these securities is less
than longer-term securities.
Liquidity Premium Theory
• As we shall see in Chapter 6, the value
of a bond tends to vary more as interest
rates change, the longer the term to
maturity. Thus, if interest rates rise, the
holder of a long-term bond will find that
the value of the investment has declined
substantially more than that of the holder
of a short-term bond.
Liquidity Premium Theory
• In addition, the short-term bondholders
has the option of holding the bond for the
short time remaining to maturity and then
reinvesting the proceeds from that bond
at the new higher interest rate. The longterm bondholder must wait much longer
before this opportunity is available.
Liquidity Premium Theory
• Accordingly, it is argued that whatever
the shape of the yield curve, a liquidity
(or maturity) premium is reflected in it.
The liquidity premium is larger for longterm bonds than for short-term bonds.
Market Segmentation Theory
• According to market segmentation
theory, the securities markets are
segmented by maturity. Furthermore,
interest rates within each maturity
segment are determined to a certain
extent by the supply and demand
interactions of the segment’s borrowers
and lenders.
Market Segmentation Theory
• If strong borrower demand exists for
long-term funds and these funds are in
short supply, the yield curve will upward
sloping. Conversely, if strong borrower
demand exists for short-term funds and
these funds are in short supply, the yield
curve will be downward sloping.
Limitation of the choice of
Maturities
• Several factors limit the choice of
maturities by lender. One such factor is
the legal regulations that limit the types
of investments commercial banks,
savings and loan associations,
insurance companies, and other financial
institutions are permitted to make.
Limitation of the choice of
Maturities
• Another limitation faced by lenders is the
desire (or need) to match the maturity
structure of their liabilities with assets of
equivalent maturity.
Limitation of the choice of
Maturities
• For example, insurance companies and
pension funds, because of the long-term
nature of their contractual obligations to
clients, are interested primarily in making
long-term investments. Commercial
banks and money market funds, in
contrast, are primarily short-term lenders
because a large proportion of their
liabilities is in the form of deposits that
can be withdraw on demand.
Default risk premium
• U.S. government securities are generally
considered to be free of default risk. That
is, the risk that interest and principal will
not be paid as promised in the bond
indenture.
• In contrast, corporate bonds are subject
to varying degrees of default risk.
Investors require higher rates of return
on securities subject to default risk.
Default risk premium
• Bond rating agencies, such as Moody’s
and Standard & Poor’s, provide
evaluations of the default risk of many
corporate bonds in the form of bond
ratings.
• The yields on bonds increases as the
risk of default increases, reflecting the
positive relationship between risk and
required return.
Default risk premium
• Over time, the spread between the
required returns on bonds having various
levels of default risk varies, reflecting the
economic prospects and the resulting
probability of default.
Seniority risk premium
• Corporations issue different types of
securities. These securities differ with
respect to their claim on the cash flows
generated by company and the claim on
company’s assets in the case of default.
Seniority risk premium
• A partial listing of these securities, from
the least senior (that is, from the security
having the lowest priority claim on cash
flows and assets) to the most senior,
includes common stock, preferred
stocks, income bonds, subordinated
debentures, debentures, second
mortgage bonds, and first mortgage
bonds.
Seniority risk premium
• Generally, the less senior the claims of
security holder, the greater the required
rate of return demanded by investors in
that security.
Seniority risk premium
• For example, the holders of bonds
issued by ExxonMobil are assured that
they will receive interest and principal
payments on these bonds except in the
highly unlikely event that the company
faces bankruptcy. In contrast,
ExxonMobil common stockholders have
no such assurance regarding dividend
payments.
Seniority risk premium
• In the case of bankruptcy, all senior
claim holders must be paid before
common stockholders receive any
proceeds from the liquidation of the firm.
Accordingly, common stockholders
require a higher rate of return on their
investment in ExxonMobil stock than do
the company’s bondholders.
Marketability risk premium
• Marketability risk refers to the ability of
an investor to buy and sell a company’s
securities quickly and without a
significant loss of value.
Marketability risk premium
• For example, there is very little
marketability risk for the shares of stock
of most companies that are traded on
the New York or American Stock
Exchange or listed on the NASDAQ
system for over-the-counter stocks. For
these securities, there is an active
market. Trades can be executed almost
instantaneously with low transaction
costs at the current market price.
Marketability risk premium
• The marketability risk premium can be
significant for securities that are not
regularly traded, such as the shares of
many small- and medium-size firms.
Business risk
• The business risk of a firm refers to the
variability in the firm’s operating earnings
over time.
• Business risk is influenced by many
factors, including the variability in sales
and operating costs over a business
cycle, the diversity of a firm’s product
line, the market power of the firm, and
the choice of production technology.
Financial risk
• Financial risk refers to the additional
variability in a company’s earnings per
share that results from the use of fixedcost sources of funds, such as debt and
preferred stock.
• In addition, as debt financing increases,
the risk of bankruptcy increases.
Risk and Required Returns for Various
Types of Securities
• Figure 5.5 illustrates the relationship
between required rates of return and
risk, as represented by the various risk
premiums. As shown in Figure 5.5, the
lower risk security is represented by
short-term U.S. Treasury bills. All other
securities have one or more elements of
additional risk, resulting in increasing
required returns by investors.
Risk and Required Returns for Various
Types of Securities
• The order illustrated in this figure is
indicative of the general relationship
between risk and required returns of
various security types.
Risk and Required Returns for Various
Types of Securities
• There will be situations that result in
differences in the ordering of risk and
required returns.
– For example, it is possible that the risk of
some junk (high-risk) bonds may be so
great that investors required a higher rate of
return on these bonds than they required on
high-grade common stocks.
Investment Diversification and
Portfolio Risk Analysis
• Most individuals and institutions invest in
a portfolio of assets, that is, a collection
of two or more assets.
• Portfolio risk, the risk associated with
collections of financial and physical
assets. The questions of importance are
as follows:
– What return can be expected to be earned
from the portfolio?
– What is the risk of the portfolio?
Investment Diversification and
Portfolio Risk Analysis
• Consider the following example.
Suppose that Alcoa (the aluminum
industry’s largest producer) is
considering diversifying into gold mining
and refining. During economic boom
periods, aluminum sales tend to be brisk;
gold, on the other hand, tends to be
most in demand during periods of
economic uncertainty.
Investment Diversification and
Portfolio Risk Analysis
• Therefore, let us assume that the returns
from the aluminum business and the
gold mining business inversely, or
negatively, related. If Alcoa expands into
gold mining and refining, its overall
return will tend to be less variable than
individual returns from these business.
This effect is illustrated in Figure 5.6.
Investment Diversification and
Portfolio Risk Analysis
• Panel (a) shows the variation of rates of
return in the aluminum industry; panel
(b) shows the corresponding variation of
returns from gold mining over the same
time frame; and panel (c) shows the
combined rate of return for both lines of
business.
Investment Diversification and
Portfolio Risk Analysis
• As can be seen from Figure 5.6, when
the return from aluminum operation is
high, the return from gold mining tends
to be low, and vice versa. The combined
returns are more stable and therefore
less risky.
Investment Diversification and
Portfolio Risk Analysis
• This portfolio effect of reduced variability
results because a negative correlation
exists between the returns from
aluminum operations and the returns
from gold mining.
Investment Diversification and
Portfolio Risk Analysis
• The correlation between any two
variables is a relative statistical measure
of the degree to which these variables
tend to move together.
• The correlation coefficient measures
the extent to which high (or low) values
of one variable are associated with high
(or low) values of another.
Investment Diversification and
Portfolio Risk Analysis
• Values of the correlation coefficient can
range from +1.0 for perfectly positively
correlated variables to -1.0 for perfectly
negatively correlated variables. If two
variables are unrelated (that is,
uncorrelated), the correlation coefficient
between these two variables will be 0.
See Figure 5.7.
Investment Diversification and
Portfolio Risk Analysis
• Figure 5.7 illustrates perfect positive
correlation, perfect negative correlation,
and zero correlation for different pairs of
common stock investments.
• For perfect positive correlation, panel
(a), high (low) rates of return from Stock
L are always associated with high (low)
rates of return from Stock M.
Investment Diversification and
Portfolio Risk Analysis
• For perfect negative correlation, panel
(b), however the opposite is true; high
rates of return from Stock P are
associated with low rates of return from
Stock Q and vice versa.
• For zero correlation, panel (c), no
perceptible pattern or relationship exists
between the rates of return on Stocks V
and W.
Characteristics of the Securities
Comprising the Portfolio
• Expected return
• Standard deviation, 
• Correlation coefficient
• Efficient portfolio
Investment Diversification and
Portfolio Risk Analysis
• If a portion, wA, of the available funds
(wealth) is invested in Security A, and
the remaining portion, wB, is invested in
Security B, the expected return of the
portfolio is as follows (See Figure 5.8):
Investment Diversification and
Portfolio Risk Analysis
rp  wA rA  wB rB
$ invested in A
wA 
$ invested in A+$ invested in B
$ invested in B
wB 
$ invested in A+$ invested in B
If borrowing and short-sales are prohibited,
0  wA  1; 0  wB  1; wA  wB  1
Investment Diversification and
Portfolio Risk Analysis
• The expected return from any portfolio of
n securities or assets is equal to the sum
of the expected returns from each
security times the proportion of the total
portfolio invested in that security:
n
rp   wi ri
i 1
where
 wi  1 and 0  w  1,
i
if borrowing and short-sales are prohibited.
Investment Diversification and
Portfolio Risk Analysis
• The risk for a two-security portfolio,
measured by the standard deviation of
portfolio returns, is computed as follows:
σ p  wA2 σ 2A  wB2 σ 2B  2 wA wB ρ AB σ Aσ B
Note: ρ AB
σ AB

σ Aσ B
Investment Diversification and
Portfolio Risk Analysis
• The risk of a portfolio containing n
securities, measured by the standard
deviation of portfolio returns, is
computed as follows:
σp 
n
n
 ww ρ σ σ
i 1
j 1
i
j ij
i
j
• The double summation sign indicates
that all possible combinations of i and j
should be included in calculating the
total value.
Investment Diversification and
Portfolio Risk Analysis
• When the returns from the two securities
are perfectly positively correlated, the
risk of the portfolio is equal to the
weighted average of the risk of the
individual securities. Thus, no risk
reduction is achieved when perfectly
positively correlated securities are
combined in a portfolio.
• See Table 5.6.
• See Case I of Figure 5.9. (p. 175)
Investment Diversification and
Portfolio Risk Analysis
Investment Diversification and
Portfolio Risk Analysis
Investment Diversification and
Portfolio Risk Analysis
• When the correlation coefficient between
the returns on two securities is less than
1.0, diversification can reduce the risk of
a portfolio below the weighted average
of the total risk of the individual
securities. The less positively correlated
the returns from two securities, the
greater the portfolio effects of risk
reduction.
• See Case II of Figure 5.9. (p. 175)
Investment Diversification and
Portfolio Risk Analysis
Investment Diversification and
Portfolio Risk Analysis
• When the returns from the two securities
are perfectly negatively correlated,
portfolio risk can be reduced to zero. In
other words, with a perfect negative
correlation of returns between two
securities, there will always be some
proportion of the securities that will result
in the complete elimination of portfolio
risk.
• See Case III of Figure 5.9. (p. 175)
Investment Diversification and
Portfolio Risk Analysis
Efficient Portfolio
• Has the highest
possible return
for a given 
• Has the lowest
possible  for a
given expected
return
^
r
a
c
b
Risk
a and c are preferred to b
a and c are efficient
Efficient Portfolios and the Capital
Market Line (CML)
• Consider the graph shown in Figure
5.10. Each dot within the shaded area
represents the risk (standard deviation)
and expected return for an individual
security available for possible
investment. The shaded area (or
opportunity set) represents all the
possible portfolio found by combining the
given securities in different proportions.
Efficient Portfolios and the Capital
Market Line (CML)
• The curved segment from A to B on the
boundary of the shaded area represents
the set of efficient portfolios, or the
efficient frontier.
• A portfolio is efficient if, for a given
standard deviation, there is no other
portfolio with a higher expected return, or
for a given expected return, there is no
other portfolio with a lower standard
deviation.
Efficient Portfolios and the Capital
Market Line (CML)
• Risk-averse investors, in choosing their
optimal portfolios, need only consider
those portfolios on the efficient frontier.
• The choice of an optimal portfolios,
whether portfolio A that minimizes risk or
portfolio B that maximizes expected
return or some portfolio on the efficient
frontier, depends on the investors’
attitude toward risk.
Efficient Portfolios and the Capital
Market Line (CML)
• More conservative investors will tend to
choose lower-risk portfolios (closer to A);
more aggressive investors will tend to
select higher-risk portfolios (closer to B).
Efficient Portfolios and the Capital
Market Line (CML)
• If investors are able to borrow and lend
money at the risk-free rate (rf), they can
obtain any combination of risk and
expected return on the straight line
joining rf and portfolio m as shown Figure
5.11.
Efficient Portfolios and the Capital
Market Line (CML)
• When the market is in equilibrium,
portfolio m represents the Market
Portfolio, which consists of all available
securities, weighted by their respective
market values. The line joining rf and m
is known as the capital market line.
Efficient Portfolios and the Capital
Market Line (CML)
• The capital market line has an intercept
of rf and a slope of (rm – rf)/(m – 0) = (rm –
rf)/m.
• The slope of the capital market line
measures the equilibrium market price of
risk or the additional expected return that
can be obtained by incurring one
additional unit of risk (one additional
percentage point of standard deviation).
Efficient Portfolios and the Capital
Market Line (CML)
• Therefore, the equation of the capital
market line is (Figure 5.11):
rp  rf  (
rm  rf
σm
)σ p
• The above equation indicates that the
expected return for an efficient portfolio
is equal to the risk-free rate plus the
market price of risk [(rm – rf)/m] times the
amount of risk (p) of the portfolio under
consideration.
Diversification
• The Portfolio effect is the risk
reduction accompanying diversification.
Systematic
(Nondiversifiable)
Risk
Unsystematic
(Diversifiable)
Diversification
• Total Risk
= Systematic risk (nondiversifiable risk)
+ Unsystematic risk (diversifiable risk)
• See Figure 5.12.
Diversification
• Since unsystematic risk is unique to
each firm, an efficiently diversified
portfolio of securities can successfully
eliminate most of the unsystematic risk
inherent in individual securities, as is
shown in Figure 5.12.
– Randomly constructed portfolios of as few
as 10 to 15 securities on average can
successfully diversify away a large portion
of the unsystematic risk of the individual
securities.
Diversification
• The risk remaining after diversification is
market-related risk, or systematic risk,
and it cannot be eliminated through
diversification.
• Because unsystematic risk commonly
accounts for 50 percent or more of the
total risk of most individual securities, it
should be obvious that the risk-reducing
benefits of efficient diversification are
well worth the effort.
Diversification
• Given the small number of securities
required for efficient diversification by an
individual investor, as well as the
dominance of the securities markets by
many large institutional investors who
hold widely diversified portfolios, it is
safe to conclude that the most relevant
risk that must be considered for any
widely traded individual security is its
systematic risk. The unsystematic
portion of total risk is relatively easy to
diversify away.
Capital Asset Pricing Model (CAPM):
Only Systematic Risk is Relevant
• Systematic risk caused by factors
affecting the market as a whole
undiversifiable
–
–
–
interest rate changes
changes in purchasing power
change in business outlook
Capital Asset Pricing Model (CAPM):
Only Systematic Risk is Relevant
• Unsystematic risk caused by factors
unique to the firm
diversifiable
–
–
–
–
–
strikes
government regulations
management’s capabilities
availability of raw materials
effects of foreign competition
Systematic Risk is Measured by
Beta, 
• A measure of the volatility of a securities
return compared to the Market Portfolio:
j 
Covariance j,m
Variancem

ρ jm σ j σ m
σ
2
m
Systematic Risk is Measured by
Beta, 
• Search for (stock beta) on this search
engine:
http://www.altavista.digital.com/
Systematic Risk is Measured by
Beta, 
• In practice, beta may be computed as
the slope of a regression line between
periodic (usually yearly, quarterly, or
monthly) rates of return on the Market
Portfolio (as measured by a market
index, such as the Standard & Poor’s
500 Market Index) and the periodic rates
of return for Security j, as follows:
k j = a j + β j rm + e j
Systematic Risk is Measured by
Beta, 
• The regression model in the previous
slide describes a line called Security j’s
characteristic line.
• A beta of 1.0 for any security indicates
that the security is of average systematic
risk; that is, a security with a beta of 1.0
has the same risk characteristics as the
market as a whole when only systematic
risk is considered.
Systematic Risk is Measured by
Beta, 
• When beta equals 1.0, a 1 percent
increase (decline) in market returns
indicates that the systematic returns for
the individual security should increase
(decline) by 1 percent.
• Question:
What is the beta of the Market Portfolio?
Systematic Risk is Measured by
Beta, 
• A beta greater than 1.0—for example,
2.0—indicates that the security has
greater-than-average systematic risk. In
this case, when market returns increase
(decline) by 1 percent, the security’s
systematic returns can be expected to
increase (decline) by 2 percent.
Systematic Risk is Measured by
Beta, 
• A beta of less than 1.0—for example,
0.5—is indicative of a security of lessthan-average systematic risk. In this
case, a 1 percent increase (decline) in
market returns implies a 0.5 percent
increase (decline) in the security’s
systematic returns.
• Table 5.7 summarizes the interpretation
of selected betas.
Beta of Portfolio
• The beta of any portfolio of n securities
or assets is simply the weighted average
of the individual security betas:
n
 p   wj  j
j 1
Security Market Line (SML) Shows
the Relationship Between r and ß
• As discussed earlier in the chapter, the
required rate of return of any risky asset
is determined by the prevailing level of
risk-free interest rates plus a risk
premium.
Security Market Line (SML) Shows
the Relationship Between r and ß
• The greater the level of risk an investor
perceives about a security’s return, the
greater the required risk premium will be.
In other words, investors require returns
that are commensurate with the risk level
they perceive.
Security Market Line (SML) Shows
the Relationship Between r and ß
• The security market line (SML)
indicates the “going” required rate of
return on a security in the market for a
given amount of systematic risk and is
illustrated in Figure 5.13.
• The SML intersects the vertical axis at
the risk-free rate, indicating that any
security with an expected risk premium
equal to zero should be required to earn
a return equal to the risk-free rate.
Security Market Line (SML) Shows
the Relationship Between r and ß
• As systematic risk increases, so do the
risk premium and the required rate of
return. According to Figure 5.13, for
example, a security having a risk level of
a’ should be required to earn a 10
percent rate of return.
Security Market Line (SML) Shows
^
the Relationship
Between r and ß
r^
SML
r^f

Required Rate of Return
• The required return for any security j
may be defined in terms of systematic
risk, j, the expected market return, r^m,
and the expected risk free rate, ^rf.
k j  rˆf   j (rˆm  rˆf )
Risk Premium
• (r^m – ^
rf)
• Slope of security market line
• Will increase or decrease with
– uncertainties about the future economic
outlook
– the degree of risk aversion of investors
SML
r^
10.5% r^a
9% r^
SML
a
m
6% r^f
1.0
Risk Premium = (9% – 6%) = 3%
ka = 6% + 1.5(9% – 6%) = 10.5%
1.5 
Security Market Line and Beta
• The SML may also be defined in terms
of beta. The risk premium for any
Security j is equal to the difference
between the investors’ required return,
kj, and the risk-free rate, rf : Θj = kj – rf.
• Let rm be the expected rate of return on
the overall Market Portfolio and rf be
expected risk-free rate (i.e., the rate of
return on Treasury bills), then the market
premium is equal to Θm = rm – rf.
Security Market Line and Beta
• The beta of Security j can be
represented as follows:
j = (kj – rf )  (rm – rf)
 kj – rf = j(rm – rf)
Θj = j(rm – rf)
or
 kj = rf + j(rm – rf): CAPM
• See Figure 5.15.
SML versus CML
• Note that while the security market line
and the capital market line discussed
earlier have identical shapes (i.e.,
straight lines) with the same intercept
(i.e., risk-free rate) on the vertical axis,
they illustrate different relationships.
SML versus CML
• The security market line defines the
required (or expected) rate of return for
an individual security as a function of the
systematic risk (measured by beta) of
the security, whereas the capital market
line measures the required (or expected)
rate of return on a portfolio in terms of
the total risk (measured by the standard
deviation) of the portfolio.
CAPM Assumptions
• Investors hold well-diversified portfolios
• Competitive markets
• Borrow and lend at the risk-free rate
• Investors are risk averse
• No taxes
CAPM Assumptions
• Investors are influenced by systematic
risk
• Freely available information
• Investors have homogeneous
expectations
• No brokerage charges
Major Problems in the Practical
Application of the CAPM
• Estimating expected future market
returns
• Determining an appropriate ^
rf
• Determining the best estimate of 
• Betas are frequently unstable over time.
• Investors don’t totally ignore
unsystematic risk.
• Required returns are determined by
macroeconomic factors.
International Investing
• Appears to offer diversification benefits
• Returns from DMCs (domestic
companies) tend to have high positive
correlations.
• Returns from MNCs (multinational
companies) tend to have lower
correlations.
International Investing
• Obtains the benefits of international
diversification by investing in MNCs or
DMCs operating in other countries
Risk of Failure is Not Necessarily
Captured by Risk Measurers
• Risk of failure especially relevant
– For undiversified investor
• Costs of bankruptcy
– Loss of funds when assets are sold at
distressed prices
– Legal fees and selling costs incurred
– Opportunity costs of funds unavailable to
investors during bankruptcy proceedings.
High-Yield Securities
• Sometimes called “Junk Bonds”
• Bonds with credit ratings below
investment-grade securities
• Have high returns relative to the returns
available from investment-grade
securities
• Higher returns achieved only by
assuming greater risk.
• Ethical Issues next slide
Ethical Issues
• Growth in high-risk junk bonds
• Savings and loan industry
• Insurance industry