Download Introduction to Financial Management

11-1
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
• Know how to calculate expected
returns
• Understand:
– The impact of diversification
– The systematic risk principle
– The security market line and the riskreturn trade-off
11-2
Chapter Outline
11.1 Expected Returns and Variances
11.2 Portfolios
11.3 Announcements, Surprises, and Expected
Returns
11.4 Risk: Systematic and Unsystematic
11.5 Diversification and Portfolio Risk
11.6 Systematic Risk and Beta
11.7 The Security Market Line
11.8 The SML and the Cost of Capital: A Preview
11-3
Expected Returns
• Expected returns are based on the
probabilities of possible outcomes
E( R ) 
n
p R
i 1
i
i
Where:
pi = the probability of state “i” occurring
Ri = the expected return on an asset in state i
Return to
Quick Quiz
11-4
Example: Expected Returns
State (i)
Recession
Neutral
Boom
E(R)
p(i)
0.25
0.50
0.25
1.00
E(R)
Stock A Stock B
E(Ra)
E(Rb)
-20%
30%
15%
15%
35%
-10%
11%
13%
n
E ( R )   pi R i
i 1
11-5
Variance and Standard Deviation
• Variance and standard deviation measure
the volatility of returns
• Variance = Weighted average of squared
deviations
• Standard Deviation = Square root of variance
n
σ   p i ( R i  E ( R ))
2
2
i 1
Return to
Quick Quiz
11-6
Portfolios
• Portfolio = collection of assets
• An asset’s risk and return impact how the
stock affects the risk and return of the
portfolio
• The risk-return trade-off for a portfolio is
measured by the portfolio expected
return and standard deviation, just as
with individual assets
11-7
Portfolio Expected Returns
• The expected return of a portfolio is the
weighted average of the expected
returns for each asset in the portfolio
• Weights (wj) = % of portfolio invested in
each asset
m
E ( RP )   w j E ( R j )
j 1
Return to
Quick Quiz
11-8
Portfolio Risk
Variance & Standard Deviation
• Portfolio standard deviation is NOT
a weighted average of the standard
deviation of the component
securities’ risk
– If it were, there would be no benefit to
diversification.
11-9
Portfolio Variance
• Compute portfolio return for each state:
RP,i = w1R1,i + w2R2,i + … + wmRm,i
• Compute the overall expected portfolio
return using the same formula as for
an individual asset
• Compute the portfolio variance and
standard deviation using the same
formulas as for an individual asset
Return to
Quick Quiz
11-10
Announcements, News and
Efficient markets
• Announcements and news contain both
expected and surprise components
• The surprise component affects stock prices
• Efficient markets result from investors trading
on unexpected news
– The easier it is to trade on surprises, the more
efficient markets should be
• Efficient markets involve random price
changes because we cannot predict surprises
11-11
Returns
• Total Return = Expected return +
unexpected return
R = E(R) + U
• Unexpected return (U) = Systematic
portion (m) + Unsystematic portion (ε)
• Total Return = Expected return
E(R)
+ Systematic portion
m
+ Unsystematic portion ε
= E(R) + m + ε
11-12
Systematic Risk
• Factors that affect a large number of
assets
• “Non-diversifiable risk”
• “Market risk”
• Examples: changes in GDP, inflation,
interest rates, etc.
Return to
Quick Quiz
11-13
Unsystematic Risk
• = Diversifiable risk
• Risk factors that affect a limited number of
assets
• Risk that can be eliminated by combining
assets into portfolios
• “Unique risk”
• “Asset-specific risk”
• Examples: labor strikes, part shortages,
etc.
Return to
Quick Quiz
11-14
The Principle of Diversification
• Diversification can substantially reduce
risk without an equivalent reduction in
expected returns
– Reduces the variability of returns
– Caused by the offset of worse-thanexpected returns from one asset by betterthan-expected returns from another
• Minimum level of risk that cannot be
diversified away = systematic portion
11-15
Standard Deviations of Annual Portfolio Returns
Table 11.7
11-16
Portfolio Conclusions
• As more stocks are added, each new
stock has a smaller risk-reducing impact
on the portfolio
 sp falls very slowly after about 40
stocks are included
– The lower limit for sp ≈ 20% = sM.
Forming well-diversified portfolios can
eliminate about half the risk of owning a
single stock.
11-17
Portfolio Diversification
Figure 11.1
11-18
Total Risk = Stand-alone Risk
Total risk = Systematic risk + Unsystematic risk
– The standard deviation of returns is a measure
of total risk
• For well-diversified portfolios, unsystematic
risk is very small
Total risk for a diversified portfolio is
essentially equivalent to the systematic risk
11-19
Systematic Risk Principle
• There is a reward for bearing risk
• There is no reward for bearing risk
unnecessarily
• The expected return (market required
return) on an asset depends only on that
asset’s systematic or market risk.
Return to
Quick Quiz
11-20
Market Risk for Individual Securities
• The contribution of a security to the
overall riskiness of a portfolio
• Relevant for stocks held in well-diversified
portfolios
• Measured by a stock’s beta coefficient
• For stock i, beta is:
i = (ri,M si) / sM = siM / sM2
• Measures the stock’s volatility relative to
the market
11-21
The Beta Coefficient
i = (ri,M si) / sM = siM / sM2
Where:
ρi,M = Correlation coefficient of this asset’s returns with
the market
σi = Standard deviation of the asset’s returns
σM = Standard deviation of the market’s returns
σM2 = Variance of the market’s returns
σiM = Covariance of the asset’s returns and the market
Slides describing covariance and correlation
11-22
Interpretation of beta
If  = 1.0, stock has average risk
If  > 1.0, stock is riskier than average
If  < 1.0, stock is less risky than average
Most stocks have betas in the range of 0.5
to 1.5
• Beta of the market = 1.0
• Beta of a T-Bill = 0
•
•
•
•
11-23
Beta Coefficients for Selected Companies
Table 11.8
11-24
Beta and the Risk Premium
• Risk premium = E(R ) – Rf
• The higher the beta, the greater the risk
premium should be
• Can we define the relationship between
the risk premium and beta so that we can
estimate the expected return?
– YES!
11-25
SML and Equilibrium
Figure 11.4
11-26
Reward-to-Risk Ratio
• Reward-to-Risk Ratio:
E ( Ri )  R f
i
• = Slope of line on graph
• In equilibrium, ratio should be the same for all
assets
• When E(R) is plotted against β for all assets, the
result should be a straight line
11-27
Market Equilibrium
• In equilibrium, all assets and portfolios
must have the same reward-to-risk ratio
• Each ratio must equal the reward-to-risk
ratio for the market
E ( R A )  Rf E ( R M  Rf )

A
M
11-28
Security Market Line
• The security market line (SML) is the
representation of market equilibrium
• The slope of the SML = reward-to-risk
ratio:
(E(RM) – Rf) / M
• Slope = E(RM) – Rf = market risk premium
– Since  of the market is always 1.0
11-29
The SML and Required Return
• The Security Market Line (SML) is part of
the Capital Asset Pricing Model (CAPM)
E ( Ri )  Rf  E ( RM )  Rf  i
E ( Ri )  Rf  RPM  i
Rf = Risk-free rate (T-Bill or T-Bond)
RM = Market return ≈ S&P 500
RPM = Market risk premium = E(RM) – Rf
E(Ri) = “Required Return”
11-30
Capital Asset Pricing Model
• The capital asset pricing model (CAPM)
defines the relationship between risk and
return
E(RA) = Rf + (E(RM) – Rf)βA
• If an asset’s systematic risk () is known,
CAPM can be used to determine its
expected return
11-31
SML example
Expected vs Required Return
Stock
A
B
E(R)
14%
10%
Beta
1.3
0.8
Assume: Market Return =
Risk-free Rate =

Req R
13.4%
11.1%
Undervalued
Overvalued
12.0%
7.5%

E ( Ri )  R f  E ( RM )  R f  i
11-32
Factors Affecting Required Return
E( Ri )  Rf  E( RM )  Rf  i
• Rf measures the pure time value of
money
• RPM = (E(RM)-Rf) measures the
reward for bearing systematic risk
• i measures the amount of systematic
risk
11-33
Portfolio Beta
βp = Weighted average of the Betas of the
assets in the portfolio
Weights (wi) = % of portfolio invested in
asset i
n
 p  wi i
i 1
11-34
Covariance of Returns
• Measures how much the returns on two
risky assets move together.
Cov(a , b)  s ab
s ab   Ra  E ( Ra )Rb  E ( Rb ) pi
i
i
i
11-35
Correlation Coefficient
• Correlation Coefficient = ρ (rho)
• Scales covariance to [-1,+1]
– -1 = Perfectly negatively correlated
– 0 = Uncorrelated; not related
– +1 = Perfectly positively correlated
s ab
r ab 
s as b
11-36
Two-Stock Portfolios
• If r = -1.0
– Two stocks can be combined to form a
riskless portfolio
• If r = +1.0
– No risk reduction at all
• In general, stocks have r ≈ 0.65
– Risk is lowered but not eliminated
• Investors typically hold many stocks
11-37
Chapter 11
END