# Chapter 5 ```Chapter
5
Analysis of Risk and Return
Copyright &copy;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 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
• 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)
^
Let’s Analyze Risk
• 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.
Calculating the Z Score
Target score – Expected value
• Z score =
Standard deviation
• 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
Coefficient of Variation
• The coefficient of variation is an
appropriate measure of total risk when
comparing two investment projects of
different size.
Risk-Return Relationship
Required return = Risk-free return + Risk premium
Real rate of return
Risk-free rate
Expected inflation
Check out the risk-free rate at this Web site:
http://www.cnnfn.com/markets/rates.html
• Compensates investors for the loss of
purchasing power due to inflation
• Maturity risk premium
• Default risk premium
• Seniority risk premium
• Marketability risk premium
• Financial risk
Term Structure of Interest Rates
• Expectations theory
• Liquidity premium theory
• Market segmentation theory
Characteristics of the Securities
Comprising the Portfolio
• Expected return
• Standard deviation, 
• Correlation coefficient
• Efficient portfolio
Efficient Portfolio
• Has the highest
possible return for a ^r
given 
• Has the lowest
possible  for a
given expected
return
a
c
b
Risk
a and c are preferred to b
a and c are efficient
Diversification
• The Portfolio effect is the risk
reduction accompanying diversification.
Systematic
Risk
Unsystematic
Diversifiable
CAPM: Only Systematic Risk is
Relevant
• Systematic risk caused • Unsystematic risk
by factors affecting the
caused by factors
market as a whole
unique to the firm
–
–
–
undiversifiable
interest rate changes
power
outlook
–
–
–
diversifiable
strikes
government
regulations
management’s
capabilities
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
• A regression line of periodic rates of return
for security j and the Market Portfolio
• Search for (stock beta) on this search
engine:
http://www.altavista.digital.com/
SML Shows the Relationship
Between r^ and &szlig;
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  rˆ β j (rˆ  rˆ )
f
m
f
• (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 
CAPM Assumptions
• 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
Major Problems in the Practical
Application of the CAPM
• Estimating expected future market
returns
• Determining an appropriate r^f
• 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.
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
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