Investments: Analysis and Behavior of Asset Pricing

Investments: Analysis
and Behavior
Chapter 5- Asset Pricing
Theory and Performance
Evaluation
©2008 McGraw-Hill/Irwin

5-2
Learning Objectives
 Know the theory and application of the CAPM.
 Learn multifactor pricing models.
 Realize the limitations of asset pricing models.
 Assess the performance of a portfolio.
 Compute alpha, Sharpe, and Treynor measures

5-3
Capital Asset Pricing Model (CAPM)
 Elegant theory of the relationship between risk
and return
 Used for asset pricing
 Risk evaluation
 Assessing portfolio performance
 William Sharpe won the Nobel Prize in Economics in
1990
 Empirical record is poor

5-4
CAPM Basic Assumptions
 Investors hold efficient portfolios—higher expected
returns involve higher risk.
 Unlimited borrowing and lending is possible at the
risk-free rate.
 Investors have homogenous expectations.
 There is a one-period time horizon.
 Investments are infinitely divisible.
 No taxes or transaction costs exist.
 Inflation is fully anticipated.
 Capital markets are in equilibrium.
Examine CAPM as an extension to portfolio theory:

5-8
The Equation of the CML is:
 Y = b + mX
This leads to the Security Market Line (SML)
 
 
F
M
M
P
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5-9
SML:
risk-return trade-off for individual securities
 Individual securities have
 Unsystematic risk
 Volatility due to firm-specific events
 Can be eliminated through diversification
 Also called firm-specific risk and diversifiable risk
 Systematic risk
 Volatility due to the overall stock market
 Since this risk cannot be eliminated through
diversification, this is often called nondiversifiable risk.

5-11
The equation for the SML leads to the CAPM
   
   
 
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β is a measure of relative risk
 β = 1 for the overall market.
 β = 2 for a security with twice the systematic risk of
the overall market,
 β = 0.5 for a security with one-half the systematic
risk of the market.

5-13
Using CAPM
 Expected Return
If the market is expected to increase 10% and
the risk free rate is 5%, what is the expected
return of assets with beta=1.5, 0.75, and -0.5?
 Beta = 1.5; E(R) = 5% + 1.5  (10% - 5%) = 12.5%
 Beta = 0.75; E(R) = 5% + 0.75  (10% - 5%) = 8.75%
 Beta = -0.5; E(R) = 5% + -0.5  (10% - 5%) = 2.5%
 Finding Undervalued Stocks…(the SML)

5-15
CAPM and Portfolios
 How does adding a stock to an existing portfolio
change the risk of the portfolio?
 Standard Deviation as risk
 Correlation of new stock to every other stock
 Beta
 Simple weighted average:
 Existing portfolio has a beta of 1.1
 New stock has a beta of 1.5.
 The new portfolio would consist of 90% of the old portfolio
and 10% of the new stock
 New portfolio’s beta would be 1.14 (=0.9×1.1 + 0.1×1.5)


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5-16
Estimating Beta
 Need
 Risk free rate data
 Market portfolio data
 S&P 500, DJIA, NASDAQ, etc.
 Stock return data
 Interval
 Daily, monthly, annual, etc.
 Length
 One year, five years, ten years, etc.

5-17
Market Index variations
Constant 0.001
Std Err of Y Est 0.005
R Squared 18.67%
No. of Observations 52
Degrees of Freedom 50
Beta estimate 1.19
Std Err of Coef. 0.351
t-statistic 3.39
Constant 0.001
R Squared 9.94%
Beta estimate 0.549
t-statistic 2.356

5-18
Interval variations
Constant 0.0001
R Squared 33.09%
Beta estimate 1.039
t-statistic 67.07
Constant 0.017
R Squared 31.79%
Beta estimate 1.258
t-statistic 3.98

5-19
Problems using Beta
 Which market index?
 Which time intervals?
 Time length of data?
 Non-stationary
 Beta estimates of a company change over time.
 How useful is the beta you estimate now for thinking about
the future?
 Other factors seem to have a stronger empirical
relationship between risk and return than beta
 Not allowed in CAPM theory
 Size and B/M

5-20
Multifactor models
 Arbitrage Pricing Theory (APT)
 Multiple risk factors, one of which may be beta
 What are these factors, F1, F2, etc.?
 Unexpected inflation, risk yield spread, oil prices,…
 Example
 Specify an APT model with three factors; the CAPM beta (F1),
unexpected inflation (F2), and the risk yield spread (F3).
 A company being analyzed has risk factor sensitivities of b1 =
1.2, b2 = -2.2, and b3 = 0.1. The intercept, α, was 3.5%. The risk
premium on the market was 5%, unexpected inflation turned out
to be +2%, and the yield spread is 4%, what risk premium should
the company have earned?

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5-21
Multifactor models
 Fama-French Three Factor Model
 Beta, size, and B/M
 SMB, difference in returns of portfolio of small stocks and portfolio
of large stocks
 HML, difference in return between low B/M portfolio and high B/M
portfolio
 Kenneth French keeps a web site where you can obtain
historical values of the Fama-French factors,
mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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5-22
New Behavioral Approaches
 The design of asset pricing models began using
theories of rational investor behavior.
 Rational investors are generally thought to be risk
averse, can fully exploit all available information, and
do not suffer from psychological biases.
 The expected rate of return on investment for a given
portfolio is solely a function of the economic risks
faced.
 Investors do not always act “rational
 Behavioral risk factors like the reluctance to realize
losses, overconfidence, and momentum might be
applied to asset pricing.

5-23
Add a momentum factor…
 Those that follow behavioral finance might
argue that the SMB factor is actually a
Overreaction risk factor.
 Also add a momentum factor:
The UMD (up minus down) momentum factor is the
return on a portfolio of the best performing stocks minus
the portfolio return for the worst stocks during the
preceding twelve month period.
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5-24
Evaluating Portfolio Performance
 How well did a portfolio manager do?
 Different portfolios take different levels of risk.
 There they should earn different returns.
 Some managers have constraints
 Must invest in small cap stocks or a particular industry.
 Evaluation of a portfolio’s performance should
therefore include:
 Risk-adjusted performance
 Comparisons with similarly constrained portfolios

5-25
Benchmarks
 Comparing the portfolio to similar portfolios
 Market benchmarks
 S&P 500 Index: General market
 S&P 100 Index: Large cap
 S&P 400 Index: Mid cap
 S&P 600 Index: Small cap
 Russell 2000
 Industry benchmarks
 Dow Jones US Technology Index, DJ US Financial, DJ US
Health Care, …
 Managed Portfolio benchmarks
 Average return of all mutual funds with the same constraints
 Small cap, value strategy, international, etc.

5-26
Alpha
 Given CAPM, a portfolio should earn the return of:
E(RP) = RF + βP(RM - RF)
 So, if RF = 5%, βP = 1.2, RM = 11%
 The return should be 12.2% = 5%+ 1.2×(11%-5%)
 If the portfolio earned 13%, then it did well. If it earned
11.5%, it did poorly. Alpha is the difference between
what it did earn and what is should have earned.
αP = RP - RF - βP(RM - RF)
 Positive alphas are good!
 Alpha is an absolute measure of performance.
 What is the source of the non-zero alpha?
 Selectivity: stock picking
 Market timing

5-27
Table 5.2 Beta Estimation for Ten Large Mutual Funds Using the S&P 500 as a Market Index
Alpha Beta
Mutual Fund Ticker estimate t-statistic estimate t-statistic R sq.
American Century Ultra TWCUX 0.010 0.12 0.977 25.69 92.8%
Fidelity Advisors Growth Opportunity FAGOX 0.023 0.48 1.048 45.86 97.6%
Fidelity Contrafund FCNTX 0.153 1.75 0.717 17.18 85.3%
Fidelity Magellan Fund FMAGX -0.033 -1.05 0.995 66.95 98.9%
Fidelity Puritan FPURX 0.027 0.45 0.614 21.15 89.8%
Investment Co. of America AIVSX 0.050 0.98 0.759 30.82 94.9%
Janus Fund JANSX 0.038 0.37 1.084 22.23 90.7%
Vanguard 500 Index VFINX -0.003 -0.19 1.013 141.42 99.7%
Vanguard Wellington VWELX 0.039 0.61 0.601 19.55 88.2%
Washington Mutual AWSHX -0.025 -0.45 0.907 34.09 95.8%
Averages 0.028 0.307 0.872 42.494 93.4%
Data source: http://finance.yahoo.com (2003 data).

5-28
Sharpe Ratio
 Reward-to-variability measure
Risk premium earned per unit of total risk:
Higher Sharpe ratio is better.
Use as a relative measure.
 Portfolios are ranked by the Sharpe measure.
P
P
R
SD
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P
F
P
portfolio
for
Risk
Total
portfolio
on
return
Excess
)
(
ratio
Sharpe 



5-29
Treynor Index
 Reward-to-volatility measure
Risk premium earned per unit of systematic
risk:
Higher Treynor Index is better.
Use as a relative measure.
P
P
R
R
P
F
P
portfolio
for
risk
Systematic
portfolio
on
return
Excess
Index
Treynor 




5-30
Example
 A pension fund’s average monthly return for the year was 0.9% and the
standard deviation was 0.5%. The fund uses an aggressive strategy as
indicated by its beta of 1.7.
 If the market averaged 0.7%, with a standard deviation of 0.3%, how did
the pension fund perform relative to the market?
 The monthly risk free rate was 0.2%.
Solution:
 Compute and compare the Sharpe and Treynor measures of the fund
and market.
 For the pension fund:
 For the market:
 Both the Sharpe ratio and the Treynor Index are greater for the market
than for the mutual fund. Therefore, the mutual fund under-performed
the market.
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ratio
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Index
Treynor 
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5-31
Summary
 CAPM is an elegant model
 Used extensively in the industry
 You can find a Beta estimate on any financial information website
 Morningstar shows mutual fund risk-adjusted measures
 Used in portfolio evaluation
 However, there are estimation problems
 Doesn’t work very well
 Multifactor models work better
 Portfolios should be evaluated using risk-adjusted
measures and compared with benchmarks of similar
characteristics

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