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Chapter 5 Analysis of Risk and Return

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Yield Curve June 4, 2005, Source: Bloomberg. Source: Bloomberg Web Site: http://www.Bloomberg.com/markets/C13.html. Finance 311. 14 ... – PowerPoint PPT presentation

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Title: Chapter 5 Analysis of Risk and Return


1
Chapter 5Analysis of Risk and Return
2
Introduction
  • This chapter develops the risk-return
    relationship for individual projects
    (investments) and a portfolio of projects.

3
RETURN - TERMINOLOGY
  • Ex-Ante Returns
  • Ex-Post 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

4
Expected Return Given Probability
Distribution
5
  • Required return Risk-free rate of return
    Risk premium
  • Risk-free 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.

6
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)



7
Risk 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

8
Risk 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 fixed-cost sources
    of funds, such as debt and preferred stock
    (OPM)

9
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 For
    instance, US Treasury Securities

10
Risk-Return Relationship
  • Required return Risk-free return Risk
    premium
  • Real rate of
    return
  • Risk-free rate
  • Expected
    inflation premium

11
U.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 CPI-U
  • 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

12
Expected Inflation Premium
  • Compensates investors for the loss of purchasing
    power due to inflation

13
Yield Curve June 4, 2005, Source Bloomberg
Source Bloomberg Web Site http//www.Bloomberg.
com/markets/C13.html
14
Explaining the Term Structure of Interest Rates
  • Expectations theory
  • Geometric Average of current and expected future
    short-term rates
  • Liquidity Premium theory
  • Liquidity Preference
  • Market Segmentation theory
  • Preferred Habitat Theory

15
MEASURING 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

16
MEASURING 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.

17
Standard Deviation
  • Ex-Ante Data(probability distribution)
  • Risk may be defined using some probability
    concepts.

18
Standard Deviation
  • EX-Post Data or Equal Probability

19
More 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.


20
Coefficient 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

21
Calculating 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
22
Diversification
  • It has been shown that by constructing a
    portfolio of approximately 15-20 common stocks,
    unsystematic (diversifiable) risk can be
    virtually eliminated. (Some studies have shown
    as few as 10 randomly selected stocks will do
    it.)

23
Diversification
  • Portfolio effect is the risk reduction
    accompanying diversification

24
Mathematics 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.
25
Mathematics 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.

26
Mathematics of Portfolios -- continued.
  • For a two stock portfolio

Correlation Coefficient
Diversification can be achieved by investing in
securities that have different risk-return
characteristics. For calculations, I recommend
that you keep returns and standard deviations in
percentages and proportions in decimals.
27
Correlation 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.

28
Characteristics of Securities Comprising a
Portfolio
  • Expected Return (r)
  • Standard Deviation (sp)
  • Correlation Coefficient (?)
  • Learning Object
  • Efficient Portfolio
  • Efficient Frontier

29
Efficient Portfolio
  • Has the highest possible return for a given ?
  • Has the lowest possible ? for a given expected
    return

30
Capital Market Line (CML)
  • The capital market line is a straight line
    starting at the risk-free rate and tangent to the
    efficient frontier.
  • The efficient frontier is the set of risk-return
    choices associated with efficient portfolios.

31
Capital 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.

32
Total 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
    company-specific risk)

33
CAPMOnly 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

34
Since 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)
35
Systematic 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.
36
Beta 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.
37
More 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

38
Important 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 15-20 randomly selected
    stocks.
  • A diversified portfolio is one where the
    diversifiable or unsystematic risk has been
    virtually eliminated.

More
39
Important 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?

40
SML shows the relationship between r and ß
  • r
  • rf



SML
41
  • Beta
  • ß Systematic risk
  • Required rate of return
  • k j rf ß j ( rm - rf )




42
Beta
?j Covariance j, m Variance m
?j ? jm ? j ? m ? m2
43
Required 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






44
Risk 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

45
SML is used to find a required rate of return.
In equilibrium (an efficient market), the
required rate of return the expected rate of
return.
46
CAPM Assumptions
  • Investors hold well diversified 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
  • No brokerage charges
  • Investors have homogeneous expectations

47
Major 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

48
International 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

49
Risk 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

50
High-Yield or High-Risk 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

51
Ethical Issues
  • High Risk Securities
  • Savings and loan industry
  • Insurance industry
  • Executive Life
  • Company Practices
  • ENRON
  • Health South
  • World Com MCI
  • Adelphia Communications
  • TYCO

52
Conclusion
  • Risk vs. Return
  • Yield Curve
  • Systematic Risk
  • Unsystematic Risk
  • Efficient Portfolio
  • Beta (ß)
  • Capital Asset Pricing Model
  • Security Market Line
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