6 Analysis of Risk and Return ©2006 Thomson/South-Western.
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Transcript of 6 Analysis of Risk and Return ©2006 Thomson/South-Western.
6
Analysis of Risk and Return
©2006 Thomson/South-Western
2
Introduction
This chapter develops the risk-return relationship for individual projects (investments) and a portfolio of projects.
3
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/
4
Expected Return
A weighted average of the individual possible returns
The set of all possible returns is referred to as the “distribution of returns”
The symbol for expected return, r , is called “r hat.”
r = Sum (all possible returns their probability)
^
^
^
5
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.
6
7
Calculating the Z Score
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
Target score – Expected value Standard deviation
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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.
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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
11
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
12
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Sources of the Risk Premium Maturity risk premium
Default risk premium
Seniority risk premium
Marketability risk premium
14
Explaining the Maturity PremiumWhat causes interest rates to change
with the time to maturity?
Expectations theory
Liquidity premium theory
Market segmentation theory
15
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
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Characteristics of the Securities Comprising the Portfolio
Expected return
Standard deviation,
Correlation coefficient
19
Efficient Portfolio
Has the highest possible return for a given
Has the lowest possible for a given expected return
^ rr
aa
c bc b RiskRiska and c are preferred to ba and c are efficient
20
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%
^
22
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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(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
j,m
j,m
j Variance
Covarianceβ
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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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Beta Measures Slope
Return on Market Index
Return on GM
Slope = β
34
SML Shows the Relationship Between r and ß
r SML
rf
^
^
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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.
)ˆˆ(βˆfmjfj rrrk
^
^
38
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
^
39
SML ^
^
^
1.0
Risk Premium = (9% – 6%) = 3%ka = 6% + 1.5(9% – 6%) = 10.5%
a10.5% ra
1.5
^
6% rf
r SML
9% rm
40
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
Investors have homogeneous expectations
No brokerage charges
41
Major Problems in the Practical Application of the CAPM 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.
^
42
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
43
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.
44
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.
45
Ethical Issues
Growth in high-risk junk bonds
Savings and loan industry
Insurance industry