6
Analysis of Risk and Return
©2006 Thomson/South-Western
Introduction

This chapter develops the risk-return
relationship for individual projects
(investments) and a portfolio of projects.
2
Risk and Return
Risk refers to the potential variability of
returns from a project or portfolio of
projects.
Returns are 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/
3
Expected Return

A weighted average of the individual possible
returns

The set of all possible returns is referred to^ as
the “distribution of returns”

^ r , is called “r
The symbol for expected return,
hat.”
^

r = Sum (all possible returns  their probability)
4
Standard Deviation

Standard Deviation is an absolute measure of
risk.

Z score measures the number of standard
deviations a particular rate of return r is from the
expected value of r.
See table V page T5 and slide 6

Coefficient of variation v is a relative measure of
risk.

Risk is an increasing function of time.
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6
Calculating the Z Score
Target score – Expected value
Standard deviation

Z score =

What’s the probability of a loss on an
investment with an expected return of 20
percent and a standard deviation of 7 percent?

(0% – 20%)/17% = –1.18 rounded

From table V = 0.1190 or 11.9 percent
probability of a loss
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8
Coefficient of Variation


The coefficient of variation is a
relative measure of risk.
The coefficient of variation is an
appropriate measure of total risk
when comparing two investment
projects of different size.
9
Risk-Return Relationship
Required return = Risk-free return + Risk
premium
Check out the risk-free rate at this Web site:
http://www.cnnfn.com/markets/rates.html
10
What Makes Up the Risk-Free Rate?

The risk-free rate of return is the sum of
two components:
Real rate of return
+ expected inflation premium

The inflation premium compensates investors
for the loss of purchasing power due to inflation
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Sources of the Risk Premium

Maturity risk premium

Default risk premium

Seniority risk premium

Marketability risk premium
13
Explaining the Maturity Premium
What causes interest rates to change
with the time to maturity?

Expectations theory

Liquidity premium theory

Market segmentation theory
14
Business Risk and Financial Risk

Business risk refers to the variability
of operating earnings over time.

Financial risk refers to the additional
variability in earnings per share
resulting from the use of debt
financing.
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Conceptual Risk-Return Relationship
16
17
Characteristics of the Securities
Comprising the Portfolio

Expected return

Standard deviation, 

Correlation coefficient
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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
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Diversification

The Portfolio effect is the risk reduction
accompanying diversification.
Systematic
Risk
Unsystematic
Diversifiable
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Expected Return on a Portfolio

A portfolio has common stock from
companies A and B. Stock from A makes
up 75% of the portfolio and has an
expected return of 12%. Stock from B
makes up 25% of the portfolio and has an
expected return of 16%.
^rp = 0.75(12%) + 0.25(16%)
= 13.0%
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Standard Deviation of Portfolio
Return

The standard deviations of returns for the
securities for companies A and B are
10%(σa) and 20%(σb), respectively. With a
correlation coefficient(ρab) between the
returns on the securities equal to +0.50,
the standard deviations of return for the
same portfolio is:
σp = √(.75)2(10)2 + (.25)2(20)2 + 2(.75)(.25)(+.50)(10)(20)
= 10.90%
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23
(a) Perfect Positive Correlation for
Two Investments
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(b) Perfect Negative Correlation for
Two Investments
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(c) Zero Correlation for Two
Investments
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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

Unsystematic risk
caused by factors
unique to the firm



diversifiable
strikes
government
regulations
management’s
capabilities
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Systematic Risk is Measured by
Beta, 

A measure of the volatility of a securities
return compared to the Market Portfolio
βj 
Cov ariance j,m
Variance j,m
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The Characteristic Line


A regression line of periodic rates of
return for security j and the Market
Index
Search for (stock beta) on this search
engine:

http://www.altavista.digital.com/
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32
Beta Measures Slope
Slope = β
Return
on
GM
Return on Market Index
33
SML Shows the Relationship
Between r and ß
^
r
SML
^
rf

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35
36
Required Rate of Return

The required return for any security j may
be defined in terms of systematic risk, j,
^
the expected market return, rm, and the
^
expected risk free rate, rf.
k j  rˆ β j (rˆ  rˆ )
f
m
f
37
Risk Premium

^
(rm – rf)

Slope of security market line

Will increase or decrease with

uncertainties about the future economic
outlook

the degree of risk aversion of investors
38
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 
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CAPM Assumptions

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Investors hold welldiversified portfolios
Competitive markets
Borrow and lend at
the risk-free rate
Investors are risk
averse
No taxes




Investors are
influenced by
systematic risk
Freely available
information
Investors have
homogeneous
expectations
No brokerage charges
40
Major Problems in the Practical
Application of the CAPM

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Estimating expected future market returns
Determining an appropriate rf
^
Determining the best estimate of 
Investors don’t totally ignore
unsystematic risk.
Betas are frequently unstable over time.
Required returns are determined by
macroeconomic factors.
41
International Investing

Appears to offer diversification benefits

Returns from DMCs tend to have high
positive correlations.

Returns from MNCs tend to have lower
correlations.

Obtains the benefits of international
diversification by investing in MNCs or
DMCs operating in other countries
42
Risk of Failure is Not Necessarily
Captured by Risk Measures

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.
43
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.
44
Ethical Issues

Growth in high-risk junk bonds

Savings and loan industry

Insurance industry
45