Professor Megginson FIN 5043BAD5283

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Chapter 6
Risk And Return CAPM And Beyond
Professor MegginsonFIN 5043/BAD5283
Spring Semester 2007
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Efficient Risky Portfolios

• Variance of return - a poor measure of risk

Investors can only expect compensationfor
systematic risk Asset pricing models aim to
define andquantify systematic risk
Begin developing pricing model by askingAre
some portfolios better than others?
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Are Some Portfolios Better Than Others?
Efficient portfolios achieve the highest possible
return for any level of volatility
Two Asset Portfolios
E(RP)
?P
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Expanding The Feasible Set On The Efficient
Frontier
EF including domestic foreign assets
E(RP)
EF including domestic stocks, bonds, and real
estate
EF for portfolios of domestic stocks
?P
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Are Some Portfolios Better Than Others?
Efficient portfolios achieve the highest possible
return for any level of volatility
Two Asset Portfolios
E(RP)
?P
What happens when we add a risk-free asset to the
picture?
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Illustrating The Efficient Frontier Using P/Fs Of
Four Stocks

• Why do assets that are not themselves on the
  efficient frontier (Point D in Figure The
  Efficient Frontier With Many Assets) survive?
• Answer their value in a p/f with other assets
• If negatively correlated, stock D may reduce p/f
  variance
• Demonstrate p/f construction using four stocks
  Berkshire Hathaway, Microsoft, 3M Praxair
• Table next slide shows 16 p/fs four with 100 in
  each stock
• Portfolios 5, 7, 10, 12, 16, plot the efficient
  frontier
• All but 16 (100 Praxair) are p/fs of at least
  two stocks
• Microsoft (1) plots very low by itself, but is
  part of five of the six efficient p/fs.
• Reason negatively correlated with other three
  stocks.

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Expected Return And Standard Deviation For
Various Portfolios
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16 100 Praxair
Efficient Frontier
8100 3M
1 100 Microsoft
4 100 Berkshire
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Riskless Borrowing And Lending
How would a portfolio with 100 (50) in asset X
and 100 (50) in asset Y perform?
Portfolio has lower return but also less
volatility than 100 in X Portfolio has higher
return and higher volatility than 100 in
risk-free
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Riskless Borrowing And Lending (Continued)
What if we sell short asset Y instead of buying
it?Borrow 100 at 6Must repay 106
Invest 300 in X Original 200 investment plus
100 in borrowed funds
Expected return on the portfolio is 12. Higher
expected return comes at the expense of greater
volatility
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Riskless Borrowing And Lending (Continued)
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Portfolios Of Risky Risk-Free Assets
E(RP)
CML

12
borrowing

10

8
lending

RF6
?P
0
16.33
24.49
8.16
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New Efficient Frontier
E(RP)
old efficient frontier

MVP

RF
?P
0
All efficient portfolios consist of some
combination of the risk-free asset and risky
portfolio M. Called the two-fund separation
principle
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Equilibrium And CAPM
Only one risky portfolio is efficient
The line connecting Rf to the market portfolio -
called the Capital Market Line
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Focus On Individual Assets Rather Than Portfolios
An assets expected return depends only on its
systematic risk
An assets systematic risk depends on how it
covaries with other assets
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Beta

• The numerator is the covariance of the stock with
  the market
• The denominator is the markets variance

In the CAPM, a stocks systematic risk is
captured by beta
The higher the beta, the higher the expected
return on the stock
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Beta And Expected Return
Beta measures a stocks exposure to market risk

• The market risk premium is the reward for bearing
  market risk
• Rm - Rf

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The Security Market Line

• Plots the relationship between expected return
  and betas
• In equilibrium, all assets lie on this line
• If stock lies above the line
• Expected return is too high
• Investors bid up price until expected return
  falls
• If stock lies below the line
• Expected return is too low
• Investors sell stock, driving down price until
  expected return rises

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The Security Market Line
E(RP)
SML
Slope E(Rm) - RF Market Risk Premium (MRP)


RM
RF

? 1.0
?i
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Calculating Expected Returns
E(Ri) Rf ß E(Rm) Rf

• Assume
• Riskfree rate 2
• Expected return on the market 8

When Beta 0, The Return Equals The Risk-Free
Return When Beta 1, The Return Equals The
Expected Market Return
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Calculating Required Return Using The Security
Market Line
slope E(Rm) RF Market Risk Premium (MRP)
MRP 8 - 2 6 ?Y ?X
E(RP)
SML
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RM8
5
RF2
1.5
?i
?i 1.0
0.5
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Estimating Betas

• Collect data on a stocks returns and returns on
  a market index
• Plot these points on a graph
• Yaxis measures stocks return
• X-axis measures markets return
• Plot a line (using regression) through the points
• Slope of line equals beta
• R-square value measures the percentage of risk
  that is systematic

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Interpreting Beta Coefficients
Selected Beta Coefficients and Their
Interpretation
Beta Comment
Interpretation
2.0 1.0 0.5
Twice as responsive, or risky, as the market
Move in same direction as market
Same response or risk as the market (I.e.,
average risk)
Only half as responsive, or risky, as the market
Unaffected by market movement
0
Only half as responsive, or risky, as the market
-0.5 -1.0 -2.0
Move in opposite direction as market
Same response or risk as the market (I.e.,
average risk)
Twice as responsive, or risky, as the market
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Betas Of Individual Stocks
Beta Coefficients for Selected Stocks
Stock Beta
Stock
Beta
Source Value Line investment Survey (New York
Value Line Publishing, January 3, 10, 17 24,
2003)
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Calculating Required Return, Given Beta And
Expected Market Return

• Calculate Required Return, R
• R Rf ß(Rm - Rf)
• Must assume either that return on the market, Rm
  , known or that market risk premium, MRP (Rm -
  Rf), is known
• Example If the rate of return on U.S T-Bills
  (Rf) is 2.0 and equity risk premium (Rm - Rf) is
  8.0, what would be the required return for
• General Electric, ß1.30
• Procter Gamble ß0.60

Can now plot SML using Rf 2.0, ßGE1.30 ,
ßPG0.60 and Equity risk premium (Rm - Rf )8.0
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Using The Security Market Line
The SML and where PG and GE place on it
r
SML
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12.4
slope E(Rm) RF MRP 10 - 2 8 ?Y
?X

10
6.8
5
Rf 2
?
1
2
GE
PG
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Shifts In The SML Due To A Shift In Required
Market Return
r
SML1
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SML2
11.1
Shift due to change in market risk premium from
8 to 7

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6.2
5
Rf 2
?
1
2
GE
PG
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Shifts In The SML Due To A Shift In The Risk-Free
Rate
SML2
r
SML1
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14.4
Shift due to change in risk-free rate from 2 to
4, with market risk premium remaining at 8.
Note all returns increase by 2

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8.8
5
Rf 4
?
1
2
GE
PG
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Alternatives To CAPM

• The CAPM is a single-factor model
• Market Risk Is The Only Source Of Systematic Risk
• Multi-factor models allow for several independent
  sources of systematic risk
• Arbitrage Pricing Theory
• Fama-French Model

Betas represent sensitivities to each source of
risk Terms in parenthesis are the rewards for
bearing each type of risk.
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CAPM And Beyond
Market should reward only systematic
risk Risk-averse investors should hold only
efficient portfolios Under CAPM, optimal
portfolio is market portfolio Beta measures
systematic risk in CAPM Alternative models - APT
and Fama-French model