Title: Chapter 5 Analysis of Risk and Return
1Chapter 5Analysis of Risk and Return
2Introduction
 This chapter develops the riskreturn
relationship for individual projects
(investments) and a portfolio of projects.
3RETURN  TERMINOLOGY
 ExAnte Returns
 ExPost Returns
 HPRs  covered previously
 Please annualize your returns
 You should consider compounding
 If a stock grew from 10 to 20 over 5 years, we
do not say it grew by 100
4Expected Return Given Probability
Distribution
5 Required return Riskfree rate of return
Risk premium  Riskfree rate (rf) 1. Real rate of
return 
 2. Expected
inflation premium  Decreases in inflation rates normally leads to
decreases in the required rate of return for all
securities. The reverse is also true.
6Expected 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)
7Risk Premium
 Maturity risk premium
 Consider the Yield Curve (Slide 13) and
theories of the Term Structure of Interest Rates  Default risk premium
 Seniority risk premium
 Marketability and liquidity risk premium
8Risk Premium  Continued
 Business risk
 Variability of the firms operating earnings over
time  Financial risk
 Additional variability in a companys earnings
per share caused by the use of fixedcost sources
of funds, such as debt and preferred stock
(OPM)
9Risk 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 For
instance, US Treasury Securities
10RiskReturn Relationship
 Required return Riskfree return Risk
premium  Real rate of
return  Riskfree rate
 Expected
inflation premium
11U.S. Treasury I Bonds
 The I Bond earnings rate is a combination of two
separate rates  Fixed Rate of return
 A semiannual inflation rate based on the CPIU
 For May 1, 2005 October 30, 2005
 Fixed Rate 1.20
 Inflation Rate 1.79
 Composite Rate 4.80
 http//publicdebt.treas.gov/sav/sbirate2.htm
12Expected Inflation Premium
 Compensates investors for the loss of purchasing
power due to inflation
13Yield Curve June 4, 2005, Source Bloomberg
Source Bloomberg Web Site http//www.Bloomberg.
com/markets/C13.html
14Explaining the Term Structure of Interest Rates
 Expectations theory
 Geometric Average of current and expected future
shortterm rates  Liquidity Premium theory
 Liquidity Preference
 Market Segmentation theory
 Preferred Habitat Theory
15MEASURING RISK
 Risk refers to the potential variability of
returns from a project or portfolio of projects  The possibility that actual cash flows (returns)
will be different from forecasted cash flows  Risk free returns are known with certainty
 US Treasury Securities
16MEASURING RISK  Continued
 We can look at risk in two different ways
 In terms of an individual security
 In terms of a portfolio of securities
 One common way to measure total risk is to look
at the variability of return by computing the
standard deviation of the returns. Then calculate
the Coefficient of Variation.  Risk is typically an increasing function of time.
17Standard Deviation
 ExAnte Data(probability distribution)
 Risk may be defined using some probability
concepts.
18Standard Deviation
 EXPost Data or Equal Probability
19More on the Standard Deviation
 The larger the standard deviation the larger the
risk  Standard Deviation is an absolute measure of risk
 Z score measures the of standard deviations a
particular return r is from the expected value r
if the outcomes are normally distributed.
20Coefficient of Variation
 Coefficient of variation v is a relative measure
of risk  Calculated by dividing the standard deviation by
the mean or expected return  It is better to use coefficient of variation to
measure total risk when comparing investments of
different sizes
21Calculating the Z Score

 Z score

 Whats the probability of a loss 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 (page 762 of your text) 0.1190 or
11.90 percent probability of a loss
Target score Expected value Standard deviation
22Diversification
 It has been shown that by constructing a
portfolio of approximately 1520 common stocks,
unsystematic (diversifiable) risk can be
virtually eliminated. (Some studies have shown
as few as 10 randomly selected stocks will do
it.)
23Diversification
 Portfolio effect is the risk reduction
accompanying diversification
24Mathematics of Portfolios
 Portfolio Returns weighted average of the
returns of the individual stocks in the
portfolio. For a two stock portfolio
A portfolio is simply a collection of assets.
25Mathematics of Portfolios  continued.
 The risk or standard deviation of a portfolio is
more complicated. It depends on the standard
deviation of the individual stocks, the amount
invested in the stocks or weights, and the
correlation between returns of the individual
stocks.  The portfolio effect is the risk reduction
accompanying diversification.
26Mathematics of Portfolios  continued.
 For a two stock portfolio
Correlation Coefficient
Diversification can be achieved by investing in
securities that have different riskreturn
characteristics. For calculations, I recommend
that you keep returns and standard deviations in
percentages and proportions in decimals.
27Correlation and Risk Reduction
 If the securities are perfectly positively
correlated, there is no reduction in risk from
forming a portfolio.  When the correlation between returns is less than
1.0, there are risk reduction benefits.
Diversification can reduce the risk of the
portfolio below the weighted average of the total
risk of the individual securities.  The maximum risk reduction is achieved when the
returns on two securities move exactly opposite
each other so their correlation is 1.0.
28Characteristics of Securities Comprising a
Portfolio
 Expected Return (r)
 Standard Deviation (sp)
 Correlation Coefficient (?)
 Learning Object
 Efficient Portfolio
 Efficient Frontier
29Efficient Portfolio
 Has the highest possible return for a given ?
 Has the lowest possible ? for a given expected
return
30Capital Market Line (CML)
 The capital market line is a straight line
starting at the riskfree rate and tangent to the
efficient frontier.  The efficient frontier is the set of riskreturn
choices associated with efficient portfolios.
31Capital Asset Pricing Model (CAPM)
 An important theory about how assets are priced
developed in the late 1960s and early 1970s  Based upon portfolio mathematics and the
relationship between diversification and risk  From the CAPM came the security market line (SML)
which gives us a theoretical relationship between
risk and return.
32Total Risk (Which we measure with the standard
deviation (s)) can be divided into two components
 1. Systematic Risk (also called undiversifiable
or market risk)  2.Unsystematic Risk (also called diversifiable or
companyspecific risk)
33CAPMOnly Systematic Risk is Relevant
 Systematic risk
 caused by factors affecting the market as a
whole  interest rate changes
 changes in purchasing power
 change in business outlook
 terrorist attacks
 Unsystematic risk
 caused by factors unique to a firm or
industry  foreign competition
 government regulations
 managements capabilities
 strikes
34Since by diversifying an investor can eliminate
unsystematic risk, we need to be able to measure
the amount of systematic risk in a
portfolioSystematic Risk is Measured by Beta (ß)
35Systematic Risk is Measured by Beta ?
 A measure of the volatility of a securitys
return compared to the Market Portfolio
Covariance j , m
ß
Variance m
Computed as the slope of a regression line
between periodic rates of return on the Market
Portfolio and periodic rates of return for
security j.
36Beta as a Measure of Risk
 Standardized measure of how the returns on an
individual stock move with the market  Calculating a stocks beta
 Regress time series of stock returns versus time
series of market proxy returns  Characteristic line is
 kj a rm
Return on Market Index
Beta here is historical.
37More on Betas
 Beta 1 has average risk. Risk equal to that of
the market.  B1 more than average risk.
 B
 Betas for many stocks are available from the
Bridge System in the Trading Room, publications
(e.g. Value Line) or on web sites  Beta of a portfolio is a weighted average of the
betas of the stocks in the portfolio
38Important Points to Remember About Risk
Measurement
 The standard deviation(s) and coefficient of
variation are measures of total risk.  Beta is a measure of systematic risk.
 An investor can construct a diversified portfolio
by holding approximately 1520 randomly selected
stocks.  A diversified portfolio is one where the
diversifiable or unsystematic risk has been
virtually eliminated.
More
39Important Points to Remember About Risk
Measurement continued
 For an investor that holds a diversified
portfolio thinking about adding a stock to their
portfolio, which measure of risk should they
consider?  For an investor that holds only two stocks
thinking about adding a stock to their portfolio,
which measure of risk should they consider?
40SML shows the relationship between r and ß
SML
41 Beta
 ß Systematic risk
 Required rate of return

 k j rf ß j ( rm  rf )
42Beta
?j Covariance j, m Variance m
?j ? jm ? j ? m ? m2
43Required rate of return
 The required return for any security j may be
defined in terms of systematic risk, ßj , the
expected market return, rm, and the expected risk
free rate, rf
44Risk Premium
 ( rm  rf ) Market Risk Premium
 Slope of Security Market Line
 Will increase or decrease
 with uncertainties about the future economic and
political outlook  with the degree of risk aversion of investors
45SML is used to find a required rate of return.
In equilibrium (an efficient market), the
required rate of return the expected rate of
return.
46CAPM Assumptions
 Investors hold well diversified portfolios
 Competitive markets
 Borrow and lend at the riskfree rate
 Investors are risk averse
 No taxes
 Investors are influenced by systematic risk
 Freely available information
 No brokerage charges
 Investors have homogeneous expectations
47Major Problems in the Practical Application of
the CAPM
 Estimating expected future market returns
 Determining an appropriate rf
 Determining the best estimate of future ß
 Investors dont totally ignore unsystematic risk
 Betas are frequently unstable over time
 Required returns are determined by macroeconomic
factors such as inflation and interest rates
48International Investing
 Appears to offer diversification benefits
 Returns from DMCs tend to have high positive
correlations  Returns from MNCs tend to have lower
correlations  Obtain the benefits of international
diversification by investing in MNCs or DMCs
operating in other countries
49Risk of Failure is Not Necessarily Captured by
Risk Measures
 Risk of failure especially relevant for
undiversified investors  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
50HighYield or HighRisk Securities
 Oftentimes called Junk Bonds
 Bonds with credit ratings below investment grade
(BA or below) securities  May be a Fallen Angel
 Have high returns relative to the returns
available from investment grade securities  Higher returns achieved only by assuming greater
risk  Ethical Issues Next Slide
51Ethical Issues
 High Risk Securities
 Savings and loan industry
 Insurance industry
 Executive Life
 Company Practices
 ENRON
 Health South
 World Com MCI
 Adelphia Communications
 TYCO
52Conclusion
 Risk vs. Return
 Yield Curve
 Systematic Risk
 Unsystematic Risk
 Efficient Portfolio
 Beta (ß)
 Capital Asset Pricing Model
 Security Market Line