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( 2)



>>

Chapter
Across the Disciplines


5
Why This Chapter Matters To You
Accounting: You need to understand the
relationship between risk and return
because of the effect that riskier projects
will have on the firm™s annual net income
and on your efforts to stabilize net income.

Risk
Information systems: You need to under-
stand how to do sensitivity and correlation
analyses in order to build decision pack-
and Return
ages that help management analyze the
risk and return of various business oppor-
tunities.
Management: You need to understand
the relationship between risk and return,
and how to measure that relationship in
order to evaluate data that come from
finance personnel and translate those
data into decisions that increase the value
of the firm.
Marketing: You need to understand that
LEARNING GOALS
although higher-risk projects may produce
higher returns, they may not be the best
Understand the meaning and
LG1
choice for the firm if they produce an fundamentals of risk, return, and risk
erratic earnings pattern and do not opti- aversion.
mize the value of the firm.
Describe procedures for assessing
LG2
Operations: You need to understand how and measuring the risk of a single
investments in plant assets and purchases asset.
of supplies will be measured by the firm
Discuss risk measurement for a single
LG3
and to recognize that decisions about
asset using the standard deviation
such investments will be made by evaluat-
and coefficient of variation.
ing the effects of both risk and return on
Understand the risk and return
the value of the firm. LG4
characteristics of a portfolio in terms
of correlation and diversification, and
the impact of international assets on a
portfolio.
Review the two types of risk and
LG5
the derivation and role of beta in
measuring the relevant risk of both an
individual security and a portfolio.
Explain the capital asset pricing
LG6
model (CAPM) and its relationship to
the security market line (SML).

189
190 PART 2 Important Financial Concepts



T he concept that return should increase if risk increases is fundamental to
modern management and finance. This relationship is regularly observed in
the financial markets, and important clarification of it has led to Nobel prizes. In
this chapter we discuss these two key factors in finance”risk and return”and
introduce some quantitative tools and techniques used to measure risk and return
for individual assets and for groups of assets.




Risk and Return Fundamentals
LG1


To maximize share price, the financial manager must learn to assess two key
determinants: risk and return. Each financial decision presents certain risk and
return characteristics, and the unique combination of these characteristics has an
impact on share price. Risk can be viewed as it is related either to a single asset or
to a portfolio”a collection, or group, of assets. We will look at both, beginning
portfolio
A collection, or group, of assets. with the risk of a single asset. First, though, it is important to introduce some fun-
damental ideas about risk, return, and risk aversion.



Risk Defined
In the most basic sense, risk is the chance of financial loss. Assets having
risk
The chance of financial loss or, greater chances of loss are viewed as more risky than those with lesser chances
more formally, the variability of of loss. More formally, the term risk is used interchangeably with uncertainty
returns associated with a given
to refer to the variability of returns associated with a given asset. A $1,000 gov-
asset.
ernment bond that guarantees its holder $100 interest after 30 days has no risk,
because there is no variability associated with the return. A $1,000 investment
in a firm™s common stock, which over the same period may earn anywhere
from $0 to $200, is very risky because of the high variability of its return. The
more nearly certain the return from an asset, the less variability and therefore
the less risk.
Some risks directly affect both financial managers and shareholders. Table 5.1
briefly describes the common sources of risk that affect both firms and their share-
holders. As you can see, business risk and financial risk are more firm-specific and
therefore are of greatest interest to financial managers. Interest rate, liquidity, and
market risks are more shareholder-specific and therefore are of greatest interest to
stockholders. Event, exchange rate, purchasing-power, and tax risk directly affect
both firms and shareholders. The box on page 193 focuses on another risk that
affects both firms and shareholders”moral risk.

return
The total gain or loss experi-
Return Defined
enced on an investment over a
given period of time; calculated Obviously, if we are going to assess risk on the basis of variability of return, we
by dividing the asset™s cash
need to be certain we know what return is and how to measure it. The return is
distributions during the period,
the total gain or loss experienced on an investment over a given period of time. It
plus change in value, by its
is commonly measured as cash distributions during the period plus the change in
beginning-of-period investment
value, expressed as a percentage of the beginning-of-period investment value. The
value.
191
CHAPTER 5 Risk and Return


TABLE 5.1 Popular Sources of Risk Affecting Financial Managers
and Shareholders

Source of risk Description

Firm-Specific Risks

Business risk The chance that the firm will be unable to cover its operating costs. Level is driven by the firm™s
revenue stability and the structure of its operating costs (fixed vs. variable).
Financial risk The chance that the firm will be unable to cover its financial obligations. Level is driven by the
predictability of the firm™s operating cash flows and its fixed-cost financial obligations.

Shareholder-Specific Risks

Interest rate risk The chance that changes in interest rates will adversely affect the value of an investment. Most
investments lose value when the interest rate rises and increase in value when it falls.
Liquidity risk The chance that an investment cannot be easily liquidated at a reasonable price. Liquidity is signif-
icantly affected by the size and depth of the market in which an investment is customarily traded.
Market risk The chance that the value of an investment will decline because of market factors that are inde-
pendent of the investment (such as economic, political, and social events). In general, the more a
given investment™s value responds to the market, the greater its risk; and the less it responds, the
smaller its risk.

Firm and Shareholder Risks

Event risk The chance that a totally unexpected event will have a significant effect on the value of the firm
or a specific investment. These infrequent events, such as government-mandated withdrawal of a
popular prescription drug, typically affect only a small group of firms or investments.
Exchange rate risk The exposure of future expected cash flows to fluctuations in the currency exchange rate. The
greater the chance of undesirable exchange rate fluctuations, the greater the risk of the cash flows
and therefore the lower the value of the firm or investment.
Purchasing-power risk The chance that changing price levels caused by inflation or deflation in the economy will
adversely affect the firm™s or investment™s cash flows and value. Typically, firms or investments
with cash flows that move with general price levels have a low purchasing-power risk, and those
with cash flows that do not move with general price levels have high purchasing-power risk.
Tax risk The chance that unfavorable changes in tax laws will occur. Firms and investments with values
that are sensitive to tax law changes are more risky.




expression for calculating the rate of return earned on any asset over period t, kt,
is commonly defined as
Ct Pt Pt 1
kt (5.1)
Pt 1

where
kt actual,expected, or required rate of return during period t
Ct cash (flow) received from the asset investment in the time period
t 1 to t
Pt price (value) of asset at time t
Pt price (value) of asset at time t 1
1
192 PART 2 Important Financial Concepts


The return, kt, reflects the combined effect of cash flow, Ct, and changes in value,
Pt Pt 1, over period t.
Equation 5.1 is used to determine the rate of return over a time period as
short as 1 day or as long as 10 years or more. However, in most cases, t is 1 year,
and k therefore represents an annual rate of return.

Robin™s Gameroom, a high-traffic video arcade, wishes to determine the return on
EXAMPLE
two of its video machines, Conqueror and Demolition. Conqueror was purchased
1 year ago for $20,000 and currently has a market value of $21,500. During the
year, it generated $800 of after-tax cash receipts. Demolition was purchased
4 years ago; its value in the year just completed declined from $12,000 to $11,800.
During the year, it generated $1,700 of after-tax cash receipts. Substituting into
Equation 5.1, we can calculate the annual rate of return, k, for each video machine.

$800 $21,500 $20,000 $2,300
Conqueror (C): kC 11.5%
$20,000 $20,000

$1,700 $11,800 $12,000 $1,500
Demolition (D): kD 12.5%
$12,000 $12,000

Although the market value of Demolition declined during the year, its cash flow
caused it to earn a higher rate of return than Conqueror earned during the same
period. Clearly, the combined impact of cash flow and changes in value, mea-
sured by the rate of return, is important.


Historical Returns
Investment returns vary both over time and between different types of invest-
ments. By averaging historical returns over a long period of time, it is possible to
eliminate the impact of market and other types of risk. This enables the financial
decision maker to focus on the differences in return that are attributable primar-
ily to the types of investment. Table 5.2 shows the average annual rates of return



TABLE 5.2 Historical Returns for
Selected Security
Investments (1926“2000)

Investment Average annual return

Large-company stocks 13.0%
Small-company stocks 17.3
Long-term corporate bonds 6.0
Long-term government bonds 5.7
U.S. Treasury bills 3.9

Inflation 3.2%
Source: Stocks, Bonds, Bills, and Inflation, 2001 Yearbook
(Chicago: Ibbotson Associates, Inc., 2001).
193
CHAPTER 5 Risk and Return



In Practice
FOCUS ON ETHICS What About Moral Risk?
The poster boy for “moral risk,” holder wealth maximization has to for employees with concerns;
the devastating effects of unethi- be ethically constrained. weeding out employees who do
cal behavior for a company™s What can companies do to not share the company™s ethics
investors, has to be Nick Leeson. instill and maintain ethical corpo- values before those employees
This 28-year-old trader violated rate practices? They can start by can harm the company™s reputa-
his bank™s investing rules while building awareness through a tion or culture; assigning an indi-
secretly placing huge bets on code of ethics. Nearly all Fortune vidual the role of ethics director;
the direction of the Japanese 500 companies and about half of and evaluating leaders™ ethics
stock market. When those all companies have an ethics code in performance reviews (as at
bets proved to be wrong, the spelling out general principles of Merck & Co.).
$1.24-billion losses resulted in right and wrong conduct. Compa- The Leeson saga under-
the demise of the centuries-old nies such as Halliburton and scores the difficulty of dealing
Barings Bank. Texas Instruments have gone into with the “moral hazard” problem,
More than any other single specifics, because ethical codes when the consequences of an
episode in world financial history, are often faulted for being too individual™s actions are largely
Leeson™s misdeeds underscored vague and abstract. borne by others. John Boatright
the importance of character in Ethical organizations also argues in his book Ethics in
the financial industry. Forty-one reveal their commitments through Finance that the best antidote is to
percent of surveyed CFOs admit the following activities: talking attract loyal, hardworking employ-
ethical problems in their organiza- about ethical values periodically; ees. Ethicists Rae and Wong tell
tions (self-reported percents are including ethics in required train- us that debating issues is fruitless
probably low), and 48 percent of ing for mid-level managers (as at if we continue to ignore the char-
surveyed employees admit to Procter & Gamble); modeling acter traits that empower people
engaging in unethical practices ethics throughout top management for moral behavior.
such as cheating on expense and the board (termed “tone at the
accounts and forging signatures. top,” especially notable at Johnson
We are reminded again that share- & Johnson); promoting openness




for a number of popular security investments (and inflation) over the 75-year
period January 1, 1926, through December 31, 2000. Each rate represents the
average annual rate of return an investor would have realized had he or she pur-
chased the investment on January 1, 1926, and sold it on December 31, 2000.
You can see that significant differences exist between the average annual rates of
return realized on the various types of stocks, bonds, and bills shown. Later in
this chapter, we will see how these differences in return can be linked to differ-
ences in the risk of each of these investments.



Risk Aversion
Financial managers generally seek to avoid risk. Most managers are risk-averse”
risk-averse
The attitude toward risk in which for a given increase in risk they require an increase in return. This attitude is
an increased return is required
believed consistent with that of the owners for whom the firm is being managed.
for an increase in risk.
Managers generally tend to be conservative rather than aggressive when accepting
risk. Accordingly, a risk-averse financial manager requiring higher return for
greater risk is assumed throughout this text.
194 PART 2 Important Financial Concepts


Review Questions

5“1 What is risk in the context of financial decision making?
5“2 Define return, and describe how to find the rate of return on an investment.
5“3 Describe the attitude toward risk of a risk-averse financial manager.



Risk of a Single Asset
LG2 LG3

The concept of risk can be developed by first considering a single asset held in
isolation. We can look at expected-return behaviors to assess risk, and statistics
can be used to measure it.


Risk Assessment
Sensitivity analysis and probability distributions can be used to assess the general
level of risk embodied in a given asset.

sensitivity analysis
Sensitivity Analysis
An approach for assessing risk
that uses several possible-return Sensitivity analysis uses several possible-return estimates to obtain a sense of the
estimates to obtain a sense of the
variability among outcomes. One common method involves making pessimistic
variability among outcomes.
(worst), most likely (expected), and optimistic (best) estimates of the returns asso-
range ciated with a given asset. In this case, the asset™s risk can be measured by the range
A measure of an asset™s risk,
of returns. The range is found by subtracting the pessimistic outcome from the
which is found by subtracting the
optimistic outcome. The greater the range, the more variability, or risk, the asset
pessimistic (worst) outcome from
is said to have.
the optimistic (best) outcome.

Norman Company, a custom golf equipment manufacturer, wants to choose the
EXAMPLE
better of two investments, A and B. Each requires an initial outlay of $10,000,
and each has a most likely annual rate of return of 15%. Management has made
pessimistic and optimistic estimates of the returns associated with each. The three
estimates for each asset, along with its range, are given in Table 5.3. Asset A
appears to be less risky than asset B; its range of 4% (17% 13%) is less than
the range of 16% (23% 7%) for asset B. The risk-averse decision maker would
prefer asset A over asset B, because A offers the same most likely return as B
(15%) with lower risk (smaller range).

Although the use of sensitivity analysis and the range is rather crude, it does
give the decision maker a feel for the behavior of returns, which can be used to
estimate the risk involved.


Probability Distributions
Probability distributions provide a more quantitative insight into an asset™s risk.
probability
The probability of a given outcome is its chance of occurring. An outcome with
The chance that a given outcome
an 80 percent probability of occurrence would be expected to occur 8 out of 10
will occur.
195
CHAPTER 5 Risk and Return


TABLE 5.3 Assets A and B

Asset A Asset B

Initial investment $10,000 $10,000
Annual rate of return
Pessimistic 13% 7%
Most likely 15% 15%
Optimistic 17% 23%
Range 4% 16%




times. An outcome with a probability of 100 percent is certain to occur. Out-
comes with a probability of zero will never occur.

Norman Company™s past estimates indicate that the probabilities of the pes-
EXAMPLE
simistic, most likely, and optimistic outcomes are 25%, 50%, and 25%, respec-
tively. Note that the sum of these probabilities must equal 100%; that is, they
probability distribution
must be based on all the alternatives considered.
A model that relates prob-
abilities to the associated
A probability distribution is a model that relates probabilities to the associ-
outcomes.
ated outcomes. The simplest type of probability distribution is the bar chart,
bar chart
which shows only a limited number of outcome“probability coordinates. The
The simplest type of probability
bar charts for Norman Company™s assets A and B are shown in Figure 5.1.
distribution; shows only a limited
number of outcomes and associ- Although both assets have the same most likely return, the range of return is
ated probabilities for a given
much greater, or more dispersed, for asset B than for asset A”16 percent versus
event.
4 percent.
continuous probability If we knew all the possible outcomes and associated probabilities, we could
distribution develop a continuous probability distribution. This type of distribution can be
A probability distribution show-
thought of as a bar chart for a very large number of outcomes. Figure 5.2 presents
ing all the possible outcomes and
continuous probability distributions for assets A and B. Note that although assets
associated probabilities for a
A and B have the same most likely return (15 percent), the distribution of returns
given event.




FIGURE 5.1
Probability of Occurrence




Probability of Occurrence




Asset A Asset B
Bar Charts
.60 .60
Bar charts for asset A™s and
.50 .50
asset B™s returns
.40 .40
.30 .30
.20 .20
.10 .10

05 9 13 17 21 25 05 9 13 17 21 25
Return (%) Return (%)
196 PART 2 Important Financial Concepts


FIGURE 5.2




Probability Density
Continuous Probability
Distributions
Asset A
Continuous probability
distributions for asset A™s
and asset B™s returns
Asset B


0 5 7 9 11 13 15 17 19 21 23 25
Return (%)




for asset B has much greater dispersion than the distribution for asset A. Clearly,
asset B is more risky than asset A.




Risk Measurement
In addition to considering its range, the risk of an asset can be measured quanti-
tatively by using statistics. Here we consider two statistics”the standard devia-
tion and the coefficient of variation”that can be used to measure the variability
of asset returns.


Standard Deviation
The most common statistical indicator of an asset™s risk is the standard deviation,
standard deviation ( k)
The most common statistical
k, which measures the dispersion around the expected value. The expected value
indicator of an asset™s risk; it
of a return, k, is the most likely return on an asset. It is calculated as follows:1
measures the dispersion around
the expected value. n
k kj Prj (5.2)
expected value of a return (k ) j1
The most likely return on a given
where
asset.

kj return for the jth outcome
Prj probability of occurrence of the jth outcome
n number of outcomes considered




1. The formula for finding the expected value of return, k, when all of the outcomes, kj, are known and their related
probabilities are assumed to be equal, is a simple arithmetic average:
n
kj (5.2a)
j1
k n

where n is the number of observations. Equation 5.2 is emphasized in this chapter because returns and related prob-
abilities are often available.
197
CHAPTER 5 Risk and Return


TABLE 5.4 Expected Values of Returns for
Assets A and B
Weighted value
Possible Probability Returns [(1) (2)]
outcomes (1) (2) (3)

Asset A
Pessimistic .25 13% 3.25%
Most likely .50 15 7.50
Optimistic .25 17 4.25
Total 1.00 Expected return 15.00%

Asset B

Pessimistic .25 7% 1.75%
Most likely .50 15 7.50
Optimistic .25 23 5.75
Total 1.00 Expected return 15.00%




The expected values of returns for Norman Company™s assets A and B are pre-
EXAMPLE
sented in Table 5.4. Column 1 gives the Prj™s and column 2 gives the kj™s. In each
case n equals 3. The expected value for each asset™s return is 15%.

The expression for the standard deviation of returns, k, is2
n
k)2
(kj Prj (5.3)
k
j1


In general, the higher the standard deviation, the greater the risk.

Table 5.5 presents the standard deviations for Norman Company™s assets A and
EXAMPLE
B, based on the earlier data. The standard deviation for asset A is 1.41%, and the
standard deviation for asset B is 5.66%. The higher risk of asset B is clearly
reflected in its higher standard deviation.

Historical Returns and Risk We can now use the standard deviation as a
measure of risk to assess the historical (1926“2000) investment return data in
Table 5.2. Table 5.6 repeats the historical returns and shows the standard devia-



2. The formula that is commonly used to find the standard deviation of returns, k, in a situation in which all out-
comes are known and their related probabilities are assumed equal, is
n
k)2
(kj
j1
(5.3a)
k
n 1
where n is the number of observations. Equation 5.3 is emphasized in this chapter because returns and related prob-
abilities are often available.
198 PART 2 Important Financial Concepts


TABLE 5.5 The Calculation of the Standard Deviation
of the Returns for Assets A and Ba
(kj k)2 k)2
i kj k kj k Prj (kj Prj

Asset A

1 13% 15% 2% 4% .25 1%
2 15 15 0 0 .50 0
3 17 15 2 4 .25 1
3
k)2
(kj Prj 2%
j1

3
k)2
(kj Prj 2% 1.41%
k
A j1



Asset B

1 7% 15% 8% 64% .25 16%
2 15 15 0 0 .50 0
3 23 15 8 64 .25 16
3
k)2
(kj Prj 32%
j1

3
k)2
(kj Prj 32% 5.66%
kB
j1


aCalculations in this table are made in percentage form rather than decimal form”e.g., 13%
rather than 0.13. As a result, some of the intermediate computations may appear to be incon-
sistent with those that would result from using decimal form. Regardless, the resulting stan-
dard deviations are correct and identical to those that would result from using decimal rather
than percentage form.




tions associated with each of them. A close relationship can be seen between the
investment returns and the standard deviations: Investments with higher returns
have higher standard deviations. Because higher standard deviations are associ-
ated with greater risk, the historical data confirm the existence of a positive rela-
tionship between risk and return. That relationship reflects risk aversion by mar-
ket participants, who require higher returns as compensation for greater risk. The
historical data in Table 5.6 clearly show that during the 1926“2000 period,
investors were rewarded with higher returns on higher-risk investments.

Coefficient of Variation
The coefficient of variation, CV, is a measure of relative dispersion that is useful
coefficient of variation (CV )
A measure of relative dispersion in comparing the risks of assets with differing expected returns. Equation 5.4
that is useful in comparing the gives the expression for the coefficient of variation:
risks of assets with differing
expected returns. k
CV (5.4)
k
The higher the coefficient of variation, the greater the risk.
199
CHAPTER 5 Risk and Return


TABLE 5.6 Historical Returns and Standard
Deviations for Selected Security
Investments (1926“2000)

Investment Average annual return Standard deviation

Large-company stocks 13.0% 20.2%
Small-company stocks 17.3 33.4
Long-term corporate bonds 6.0 8.7
Long-term government bonds 5.7 9.4
U.S. Treasury bills 3.9 3.2

Inflation 3.2% 4.4%
Source: Stocks, Bonds, Bills, and Inflation, 2001 Yearbook (Chicago: Ibbotson Associates,
Inc., 2001).




When the standard deviations (from Table 5.5) and the expected returns (from
EXAMPLE
Table 5.4) for assets A and B are substituted into Equation 5.4, the coefficients of
variation for A and B are 0.094 (1.41% 15%) and 0.377 (5.66% 15%),
respectively. Asset B has the higher coefficient of variation and is therefore more
risky than asset A”which we already know from the standard deviation.
(Because both assets have the same expected return, the coefficient of variation
has not provided any new information.)

The real utility of the coefficient of variation comes in comparing the risks of
assets that have different expected returns.

A firm wants to select the less risky of two alternative assets”X and Y. The
EXAMPLE
expected return, standard deviation, and coefficient of variation for each of these
assets™ returns are


Statistics Asset X Asset Y

(1) Expected return 12% 20%
9%a
(2) Standard deviation 10%
0.50a
(3) Coefficient of variation [(2) (1)] 0.75
aPreferred asset using the given risk measure.



Judging solely on the basis of their standard deviations, the firm would prefer
asset X, which has a lower standard deviation than asset Y (9% versus 10%).
However, management would be making a serious error in choosing asset X over
asset Y, because the dispersion”the risk”of the asset, as reflected in the coeffi-
cient of variation, is lower for Y (0.50) than for X (0.75). Clearly, using the coef-
ficient of variation to compare asset risk is effective because it also considers the
relative size, or expected return, of the assets.
200 PART 2 Important Financial Concepts


Review Questions

5“4 Explain how the range is used in sensitivity analysis.
5“5 What does a plot of the probability distribution of outcomes show a deci-
sion maker about an asset™s risk?
5“6 What relationship exists between the size of the standard deviation and
the degree of asset risk?
5“7 When is the coefficient of variation preferred over the standard deviation
for comparing asset risk?



Risk of a Portfolio
LG4


In real-world situations, the risk of any single investment would not be viewed
independently of other assets. (We did so for teaching purposes.) New invest-
ments must be considered in light of their impact on the risk and return of the
portfolio of assets. The financial manager™s goal is to create an efficient portfolio,
one that maximizes return for a given level of risk or minimizes risk for a given
level of return. The statistical concept of correlation underlies the process of
efficient portfolio
diversification that is used to develop an efficient portfolio.
A portfolio that maximizes return
for a given level of risk or
minimizes risk for a given level
Correlation
of return.

correlation
Correlation is a statistical measure of the relationship between any two series of
A statistical measure of the
numbers. The numbers may represent data of any kind, from returns to test
relationship between any two
scores. If two series move in the same direction, they are positively correlated. If
series of numbers representing
the series move in opposite directions, they are negatively correlated.
data of any kind.
The degree of correlation is measured by the correlation coefficient, which
positively correlated
ranges from 1 for perfectly positively correlated series to 1 for perfectly nega-
Describes two series that move
tively correlated series. These two extremes are depicted for series M and N in
in the same direction.
Figure 5.3. The perfectly positively correlated series move exactly together; the per-
negatively correlated
fectly negatively correlated series move in exactly opposite directions.
Describes two series that move
in opposite directions.

correlation coefficient
Diversification
A measure of the degree of
correlation between two series.
The concept of correlation is essential to developing an efficient portfolio. To
reduce overall risk, it is best to combine, or add to the portfolio, assets that
perfectly positively correlated
Describes two positively have a negative (or a low positive) correlation. Combining negatively correlated
correlated series that have a
assets can reduce the overall variability of returns. Figure 5.4 shows that a port-
correlation coefficient of 1.
folio containing the negatively correlated assets F and G, both of which have
perfectly negatively correlated the same expected return, k, also has that same return k but has less risk (vari-
Describes two negatively
ability) than either of the individual assets. Even if assets are not negatively
correlated series that have a
correlated, the lower the positive correlation between them, the lower the
correlation coefficient of 1.
resulting risk.
uncorrelated Some assets are uncorrelated”that is, there is no interaction between their
Describes two series that lack
returns. Combining uncorrelated assets can reduce risk, not so effectively as com-
any interaction and therefore
bining negatively correlated assets, but more effectively than combining posi-
have a correlation coefficient
tively correlated assets. The correlation coefficient for uncorrelated assets is close
close to zero.
201
CHAPTER 5 Risk and Return


FIGURE 5.3 Perfectly Positively Correlated Perfectly Negatively Correlated
Correlations
N
The correlation between
series M and series N




Return




Return
N

M
M

Time
Time




to zero and acts as the midpoint between perfect positive and perfect negative
correlation.
The creation of a portfolio that combines two assets with perfectly positively
correlated returns results in overall portfolio risk that at minimum equals that of
the least risky asset and at maximum equals that of the most risky asset. How-
ever, a portfolio combining two assets with less than perfectly positive correla-
tion can reduce total risk to a level below that of either of the components, which
in certain situations may be zero. For example, assume that you manufacture
machine tools. The business is very cyclical, with high sales when the economy is
expanding and low sales during a recession. If you acquired another machine-
tool company, with sales positively correlated with those of your firm, the com-
bined sales would still be cyclical and risk would remain the same. Alternatively,
however, you could acquire a sewing machine manufacturer, whose sales are
countercyclical. It typically has low sales during economic expansion and high
sales during recession (when consumers are more likely to make their own
clothes). Combination with the sewing machine manufacturer, which has nega-
tively correlated sales, should reduce risk.

Table 5.7 presents the forecasted returns from three different assets”X, Y, and
EXAMPLE
Z”over the next 5 years, along with their expected values and standard devia-
tions. Each of the assets has an expected value of return of 12% and a standard
deviation of 3.16%. The assets therefore have equal return and equal risk. The
return patterns of assets X and Y are perfectly negatively correlated. They move


FIGURE 5.4 Portfolio of
Assets F and G
Asset F Asset G
Diversification
Return Return Return
Combining negatively
correlated assets to diversify
risk



k k



Time Time Time
202 PART 2 Important Financial Concepts


TABLE 5.7 Forecasted Returns, Expected Values, and Standard
Deviations for Assets X, Y, and Z and Portfolios XY
and XZ

Assets Portfolios

XYa XZb
Year X Y Z (50%X 50%Y) (50%X 50%Z)

2004 8% 16% 8% 12% 8%
2005 10 14 10 12 10
2006 12 12 12 12 12
2007 14 10 14 12 14
2008 16 8 16 12 16
Statistics:c
Expected value 12% 12% 12% 12% 12%
d
Standard deviation 3.16% 3.16% 3.16% 0% 3.16%

aPortfolioXY, which consists of 50% of asset X and 50% of asset Y, illustrates perfect negative correlation because
these two return streams behave in completely opposite fashion over the 5-year period. Its return values are calculated
as shown in the following table.


Forecasted return

Asset X Asset Y Portfolio return calculation Expected portfolio return, kp
Year (1) (2) (3) (4)

2004 8% 16% (.50 8%) (.50 16%) 12%
2005 10 14 (.50 10%) (.50 14%) 12
2006 12 12 (.50 12%) (.50 12%) 12
2007 14 10 (.50 14%) (.50 10%) 12
2008 16 8 (.50 16%) (.50 8%) 12

bPortfolioXZ, which consists of 50% of asset X and 50% of asset Z, illustrates perfect positive correlation because
these two return streams behave identically over the 5-year period. Its return values are calculated using the same
method demonstrated in note a above for portfolio XY.
cBecause the probabilities associated with the returns are not given, the general equation, Equation 5.2a in footnote 1,
is used to calculate expected values as demonstrated below for portfolio XY.


12% 12% 12% 12% 12% 60%
kxy 12%
5 5


The same formula is applied to find the expected value of return for assets X, Y, and Z, and portfolio XZ.
dBecause the probabilities associated with the returns are not given, the general equation, Equation 5.3a in footnote 2,
is used to calculate the standard deviations as demonstrated below for portfolio XY.


12%)2 12%)2 (12% 12%)2 12%)2 12%)2
(12% (12% (12% (12%
kxy 51

0% 0% 0% 0% 0% 0
% 0%
4 4

The same formula is applied to find the standard deviation of returns for assets X, Y, and Z, and portfolio XZ.
203
CHAPTER 5 Risk and Return


in exactly opposite directions over time. The returns of assets X and Z are per-
fectly positively correlated. They move in precisely the same direction. (Note: The
returns for X and Z are identical.)3

Portfolio XY Portfolio XY (shown in Table 5.7) is created by combining equal
portions of assets X and Y, the perfectly negatively correlated assets.4 The risk in
this portfolio, as reflected by its standard deviation, is reduced to 0%, and the
expected return value remains at 12%. Because both assets have the same
expected return values, are combined in equal parts, and are perfectly negatively
correlated, the combination results in the complete elimination of risk. Whenever
assets are perfectly negatively correlated, an optimal combination (similar to the
50“50 mix in the case of assets X and Y) exists for which the resulting standard
deviation will equal 0.

Portfolio XZ Portfolio XZ (shown in Table 5.7) is created by combining equal
portions of assets X and Z, the perfectly positively correlated assets. The risk in
this portfolio, as reflected by its standard deviation, is unaffected by this combi-
nation. Risk remains at 3.16%, and the expected return value remains at 12%.
Whenever perfectly positively correlated assets such as X and Y are combined,
the standard deviation of the resulting portfolio cannot be reduced below that of
the least risky asset; the maximum portfolio standard deviation will be that of the
riskiest asset. Because assets X and Z have the same standard deviation (3.16%),
the minimum and maximum standard deviations are the same (3.16%), which is
the only value that could be taken on by a combination of these assets. This result
can be attributed to the unlikely situation that X and Z are identical assets.


Correlation, Diversification, Risk, and Return
In general, the lower the correlation between asset returns, the greater the poten-
tial diversification of risk. (This should be clear from the behaviors illustrated in
Table 5.7.) For each pair of assets, there is a combination that will result in the
lowest risk (standard deviation) possible. How much risk can be reduced by this
combination depends on the degree of correlation. Many potential combinations
(assuming divisibility) could be made, but only one combination of the infinite
number of possibilities will minimize risk.
Three possible correlations”perfect positive, uncorrelated, and perfect nega-
tive”illustrate the effect of correlation on the diversification of risk and return.
Table 5.8 summarizes the impact of correlation on the range of return and risk for
various two-asset portfolio combinations. The table shows that as we move from
perfect positive correlation to uncorrelated assets to perfect negative correlation,
the ability to reduce risk is improved. Note that in no case will a portfolio of
WW assets be riskier than the riskiest asset included in the portfolio. Further discussion
W
of these relationships is included at the text™s Web site (www.aw.com/gitman).


3. Identical return streams are used in this example to permit clear illustration of the concepts, but it is not necessary
for return streams to be identical for them to be perfectly positively correlated. Any return streams that move (i.e.,
vary) exactly together”regardless of the relative magnitude of the returns”are perfectly positively correlated.
4. For illustrative purposes it has been assumed that each of the assets”X, Y, and Z”can be divided up and com-
bined with other assets to create portfolios. This assumption is made only to permit clear illustration of the concepts.
The assets are not actually divisible.
204 PART 2 Important Financial Concepts


TABLE 5.8 Correlation, Return, and Risk for Various
Two-Asset Portfolio Combinations

Correlation
coefficient Range of return Range of risk

1 (perfect positive) Between returns of two assets Between risk of two assets held
held in isolation in isolation
0 (uncorrelated) Between returns of two assets Between risk of most risky asset
held in isolation and an amount less than risk
of least risky asset but greater
than 0
1 (perfect negative) Between returns of two assets Between risk of most risky asset
held in isolation and 0




International Diversification
The ultimate example of portfolio diversification involves including foreign assets
in a portfolio. The inclusion of assets from countries with business cycles that are
not highly correlated with the U.S. business cycle reduces the portfolio™s respon-
siveness to market movements and to foreign currency fluctuations.


Returns from International Diversification
Over long periods, returns from internationally diversified portfolios tend to be
superior to those of purely domestic ones. This is particularly so if the U.S. econ-
omy is performing relatively poorly and the dollar is depreciating in value against
most foreign currencies. At such times, the dollar returns to U.S. investors on a
portfolio of foreign assets can be very attractive. However, over any single short
or intermediate period, international diversification can yield subpar returns, par-
ticularly during periods when the dollar is appreciating in value relative to other
currencies. When the U.S. currency gains in value, the dollar value of a foreign-
currency-denominated portfolio of assets declines. Even if this portfolio yields a
satisfactory return in local currency, the return to U.S. investors will be reduced
when translated into dollars. Subpar local currency portfolio returns, coupled
with an appreciating dollar, can yield truly dismal dollar returns to U.S. investors.
Overall, though, the logic of international portfolio diversification assumes
that these fluctuations in currency values and relative performance will average
out over long periods. Compared to similar, purely domestic portfolios, an inter-
nationally diversified portfolio will tend to yield a comparable return at a lower
level of risk.

political risk
Risks of International Diversification
Risk that arises from the
possibility that a host govern-
U.S. investors should also be aware of the potential dangers of international
ment will take actions harmful to
investing. In addition to the risk induced by currency fluctuations, several other
foreign investors or that political
financial risks are unique to international investing. Most important is political
turmoil in a country will
risk, which arises from the possibility that a host government will take actions
endanger investments there.
205
CHAPTER 5 Risk and Return


harmful to foreign investors or that political turmoil in a country will endanger
investments there. Political risks are particularly acute in developing countries,
where unstable or ideologically motivated governments may attempt to block
return of profits by foreign investors or even seize (nationalize) their assets in the
host country. An example of political risk was the heightened concern after
Desert Storm in the early 1990s that Saudi Arabian fundamentalists would take
over and nationalize the U.S. oil facilities located there.
Even where governments do not impose exchange controls or seize assets,
international investors may suffer if a shortage of hard currency prevents payment
of dividends or interest to foreigners. When governments are forced to allocate
scarce foreign exchange, they rarely give top priority to the interests of foreign
investors. Instead, hard-currency reserves are typically used to pay for necessary
imports such as food, medicine, and industrial materials and to pay interest on the
government™s debt. Because most of the debt of developing countries is held by
banks rather than individuals, foreign investors are often badly harmed when a
country experiences political or economic problems.



Review Questions

5“8 Why must assets be evaluated in a portfolio context? What is an efficient
portfolio?
5“9 Why is the correlation between asset returns important? How does diver-
sification allow risky assets to be combined so that the risk of the portfolio
is less than the risk of the individual assets in it?
5“10 How does international diversification enhance risk reduction? When
might international diversification result in subpar returns? What are
political risks, and how do they affect international diversification?




Risk and Return: The Capital Asset
LG5 LG6

Pricing Model (CAPM)
The most important aspect of risk is the overall risk of the firm as viewed by
investors in the marketplace. Overall risk significantly affects investment oppor-
tunities and”even more important”the owners™ wealth. The basic theory that
capital asset pricing model
links risk and return for all assets is the capital asset pricing model (CAPM).5 We
(CAPM)
will use CAPM to understand the basic risk“return tradeoffs involved in all types
The basic theory that links risk
of financial decisions.
and return for all assets.




5. The initial development of this theory is generally attributed to William F. Sharpe, “Capital Asset Prices: A The-
ory of Market Equilibrium Under Conditions of Risk,” Journal of Finance 19 (September 1964), pp. 425“442, and
John Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital
Budgets,” Review of Economics and Statistics 47 (February 1965), pp 13“37. A number of authors subsequently
advanced, refined, and tested this now widely accepted theory.
206 PART 2 Important Financial Concepts


FIGURE 5.5
Risk Reduction
Portfolio risk and




Portfolio Risk, σkP
Diversifiable Risk
diversification




Total Risk
Nondiversifiable Risk


1 5 10 15 20 25
Number of Securities (Assets) in Portfolio




Types of Risk
To understand the basic types of risk, consider what happens to the risk of a port-
folio consisting of a single security (asset), to which we add securities randomly
selected from, say, the population of all actively traded securities. Using the stan-
dard deviation of return, kp, to measure the total portfolio risk, Figure 5.5
depicts the behavior of the total portfolio risk (y axis) as more securities are added
(x axis). With the addition of securities, the total portfolio risk declines, as a result
of the effects of diversification, and tends to approach a lower limit. Research has
shown that, on average, most of the risk-reduction benefits of diversification can
be gained by forming portfolios containing 15 to 20 randomly selected securities.
The total risk of a security can be viewed as consisting of two parts:
total risk
Total security risk Nondiversifiable risk Diversifiable risk (5.5)
The combination of a security™s
nondiversifiable risk and
Diversifiable risk (sometimes called unsystematic risk) represents the portion of
diversifiable risk.
an asset™s risk that is associated with random causes that can be eliminated
diversifiable risk
through diversification. It is attributable to firm-specific events, such as strikes,
The portion of an asset™s risk that
lawsuits, regulatory actions, and loss of a key account. Nondiversifiable risk (also
is attributable to firm-specific,
called systematic risk) is attributable to market factors that affect all firms; it can-
random causes; can be elimi-
nated through diversification. not be eliminated through diversification. (It is the shareholder-specific market
Also called unsystematic risk.
risk described in Table 5.1.) Factors such as war, inflation, international inci-
dents, and political events account for nondiversifiable risk.
nondiversifiable risk
Because any investor can create a portfolio of assets that will eliminate virtu-
The relevant portion of an asset™s
risk attributable to market ally all diversifiable risk, the only relevant risk is nondiversifiable risk. Any
factors that affect all firms;
investor or firm therefore must be concerned solely with nondiversifiable risk.
cannot be eliminated through
The measurement of nondiversifiable risk is thus of primary importance in select-
diversification. Also called
ing assets with the most desired risk“return characteristics.
systematic risk.




The Model: CAPM
The capital asset pricing model (CAPM) links nondiversifiable risk and return
for all assets. We will discuss the model in four sections. The first deals with
the beta coefficient, which is a measure of nondiversifiable risk. The second
section presents an equation of the model itself, and the third graphically
207
CHAPTER 5 Risk and Return


describes the relationship between risk and return. The final section offers
some comments on the CAPM.

Beta Coefficient
The beta coefficient, b, is a relative measure of nondiversifiable risk. It is an
beta coefficient (b)
index of the degree of movement of an asset™s return in response to a change in
A relative measure of nondiversi-
fiable risk. An index of the the market return. An asset™s historical returns are used in finding the asset™s beta
degree of movement of an asset™s
coefficient. The market return is the return on the market portfolio of all traded
return in response to a change in
securities. The Standard & Poor™s 500 Stock Composite Index or some similar
the market return.
stock index is commonly used as the market return. Betas for actively traded
market return
stocks can be obtained from a variety of sources, but you should understand how
The return on the market portfo-
they are derived and interpreted and how they are applied to portfolios.
lio of all traded securities.

Deriving Beta from Return Data An asset™s historical returns are used in
finding the asset™s beta coefficient. Figure 5.6 plots the relationship between the
returns of two assets”R and S”and the market return. Note that the horizontal
(x) axis measures the historical market returns and that the vertical (y) axis mea-
sures the individual asset™s historical returns. The first step in deriving beta
involves plotting the coordinates for the market return and asset returns from
various points in time. Such annual “market return“asset return” coordinates are
shown for asset S only for the years 1996 through 2003. For example, in 2003,
asset S™s return was 20 percent when the market return was 10 percent. By use of



FIGURE 5.6
Asset S
Asset Return (%)
(1997)
Beta Derivationa
Graphical derivation of beta 35
for assets R and S
30 (2002) (2001)
25
bS = slope = 1.30
(2003)
20
Asset R
(2000)
15
(1998) 10
(1996)
5 bR = slope = .80
Market
Return (%)
0 10 15 20 25 30 35
“20 “10
“5
(1999) “10

“15
Characteristic Line S
“20
Characteristic Line R
“25

“30


a All data points shown are associated with asset S. No data points are shown for asset R.
208 PART 2 Important Financial Concepts


statistical techniques, the “characteristic line” that best explains the relationship
between the asset return and the market return coordinates is fit to the data
points. The slope of this line is beta. The beta for asset R is about .80 and that for
asset S is about 1.30. Asset S™s higher beta (steeper characteristic line slope) indi-
cates that its return is more responsive to changing market returns. Therefore
asset S is more risky than asset R.
Interpreting Betas The beta coefficient for the market is considered to be
equal to 1.0. All other betas are viewed in relation to this value. Asset betas may
be positive or negative, but positive betas are the norm. The majority of beta
coefficients fall between .5 and 2.0. The return of a stock that is half as respon-
sive as the market (b .5) is expected to change by 1/2 percent for each 1 percent
change in the return of the market portfolio. A stock that is twice as responsive as
the market (b 2.0) is expected to experience a 2 percent change in its return for
each 1 percent change in the return of the market portfolio. Table 5.9 provides
various beta values and their interpretations. Beta coefficients for actively traded
stocks can be obtained from published sources such as Value Line Investment
Survey, via the Internet, or through brokerage firms. Betas for some selected
stocks are given in Table 5.10.
Portfolio Betas The beta of a portfolio can be easily estimated by using the
betas of the individual assets it includes. Letting wj represent the proportion of
the portfolio™s total dollar value represented by asset j, and letting bj equal the
beta of asset j, we can use Equation 5.6 to find the portfolio beta, bp:
n
...
bp (w1 b1) (w2 b2) (wn bn) wj bj (5.6)
j1
n
Of course, j=1 wj 1, which means that 100 percent of the portfolio™s assets
must be included in this computation.
Portfolio betas are interpreted in the same way as the betas of individual
assets. They indicate the degree of responsiveness of the portfolio™s return to
changes in the market return. For example, when the market return increases by
10 percent, a portfolio with a beta of .75 will experience a 7.5 percent increase in
its return (.75 10%); a portfolio with a beta of 1.25 will experience a 12.5 per-
cent increase in its return (1.25 10%). Clearly, a portfolio containing mostly
low-beta assets will have a low beta, and one containing mostly high-beta assets
will have a high beta.


TABLE 5.9 Selected Beta Coefficients and
Their Interpretations

Beta Comment Interpretation

2.0 Twice as responsive as the market
Move in same
1.0 direction as Same response as the market
market
.5 Only half as responsive as the market
0 Unaffected by market movement
.5 Only half as responsive as the market
Move in opposite
1.0 direction to Same response as the market
market
2.0 Twice as responsive as the market
209
CHAPTER 5 Risk and Return


TABLE 5.10 Beta Coefficients for Selected Stocks
(March 8, 2002)

Stock Beta Stock Beta

Amazon.com 1.95 Int™l Business Machines 1.05
Anheuser-Busch .60 Merrill Lynch & Co. 1.85
Bank One Corp. 1.25 Microsoft 1.20
Daimler Chrysler AG 1.25 NIKE, Inc. .90
Disney 1.05 PepsiCo, Inc. .70
eBay 2.20 Qualcomm 1.30
Exxon Mobil Corp. .80 Sempra Energy .60
Gap (The), Inc. 1.60 Wal-Mart Stores 1.15
General Electric 1.30 Xerox 1.25
Intel 1.30 Yahoo! Inc. 2.00
Source: Value Line Investment Survey (New York: Value Line Publishing, March 8, 2002).




The Austin Fund, a large investment company, wishes to assess the risk of two
EXAMPLE
portfolios it is considering assembling”V and W. Both portfolios contain five
assets, with the proportions and betas shown in Table 5.11. The betas for the two
portfolios, bv and bw, can be calculated by substituting data from the table into
Equation 5.6:

bv (.10 1.65) (.30 1.00) (.20 1.30) (.20 1.10) (.20 1.25)
.165 .300 .260 .220 .250 1.195 1.20
bw (.10 .80) (.10 1.00) (.20 .65) (.10 .75) (.50 1.05)
.080 .100 .130 .075 .525 .91

Portfolio V™s beta is 1.20, and portfolio W™s is .91. These values make sense,
because portfolio V contains relatively high-beta assets, and portfolio W contains
relatively low-beta assets. Clearly, portfolio V™s returns are more responsive to
changes in market returns and are therefore more risky than portfolio W™s.



TABLE 5.11 Austin Fund™s Portfolios
V and W

Portfolio V Portfolio W

Asset Proportion Beta Proportion Beta

1 .10 1.65 .10 .80
2 .30 1.00 .10 1.00
3 .20 1.30 .20 .65
4 .20 1.10 .10 .75
5 .20 1.25 .50 1.05
Totals 1.00 1.00
210 PART 2 Important Financial Concepts


The Equation
Using the beta coefficient to measure nondiversifiable risk, the capital asset pric-
ing model (CAPM) is given in Equation 5.7:
kj RF [bj (km RF)] (5.7)
where
kj required return on asset j
RF risk-free rate of return, commonly measured by the
return on a U.S. Treasury bill
bj beta coefficient or index of nondiversifiable risk for asset j
km market return; return on the market portfolio of assets
The CAPM can be divided into two parts: (1) risk-free of interest, RF, which
risk-free rate of interest, RF
The required return on a risk-free is the required return on a risk-free asset, typically a 3-month U.S. Treasury bill
asset, typically a 3-month U.S.
(T-bill), a short-term IOU issued by the U.S. Treasury, and (2) the risk premium.
Treasury bill.
These are, respectively, the two elements on either side of the plus sign in Equa-
tion 5.7. The (km RF) portion of the risk premium is called the market risk pre-
U.S. Treasury bills (T-bills)
Short-term IOUs issued by the mium, because it represents the premium the investor must receive for taking the
U.S. Treasury; considered the
average amount of risk associated with holding the market portfolio of assets.6
risk-free asset.

Historical Risk Premiums Using the historical return data for selected secu-
rity investments for the 1926“2000 period shown in Table 5.2, we can calculate
the risk premiums for each investment category. The calculation (consistent with
Equation 5.7) involves merely subtracting the historical U.S. Treasury bill™s aver-
age return from the historical average return for a given investment:


Risk premiuma
Investment

. 1
( 2)



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