Investments: Analysis and Behavior of Asset Pricing

Asset Pricing
Theory and Performance
Evaluation

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

2. 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

3. 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

4. 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. 5-5

6. 5-6

7. 5-7

8. 5-8
The Equation of the CML is:
Y = b + mX
This leads to the Security Market Line (SML)
 
FM
M
P
F
P
M
FM
FP
RRE
RSD
RSD
R
RSD
RSD
RRE
RRE



)(
)(
)(
gives grearrangin
)(
)(
)(

9. 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.

10. 5-10

11. 5-11
The equation for the SML leads to the CAPM  
 
 
 
FMiF
FM
M
Mi
F
Mi
M
FM
Fi
RRR
RR
)R(VAR
RRCOV
R
RRCOV
)R(VAR
RR
RRE





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.

12. 5-12

13. 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)

14. 5-14

15. 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) 


n
i
iiP w
1


16. 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.

17. 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
Std Err of Y Est 0.005
R Squared 9.94%
No. of Observations 52
Degrees of Freedom 50
Beta estimate 0.549
Std Err of Coef. 0.233
t-statistic 2.356

18. 5-18
Interval variations
Constant 0.0001
Std Err of Y Est 0.0002
R Squared 33.09%
No. of Observations 9090
Degrees of Freedom 9088
Beta estimate 1.039
Std Err of Coef. 0.016
t-statistic 67.07
Constant 0.017
Std Err of Y Est 0.054
R Squared 31.79%
No. of Observations 36
Degrees of Freedom 34
Beta estimate 1.258
Std Err of Coef. 0.316
t-statistic 3.98

19. 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

20. 5-20
Multifactor models
Arbitrage Pricing Theory (APT)
Multiple risk factors, one of which may be beta
What are these factors, F
1, F
2, 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 b
1=
1.2, b
2= -2.2, and b
3= 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?
iNNiiiifi
FbFbFbaRR  
2211  %5.5%41.0%22.2%52.1%5.3 
fi
RR

21. 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.htmliiifmiifi
HMLbSMBbRRbaRR  )()()(
321

22. 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.

23. 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.  
iiiifmiifi
UMDbHMLbSMBbRRbaRR 
4321
)()()(

24. 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

25. 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.

26. 5-26
Alpha
Given CAPM, a portfolio should earn the return of:
E(R
P)= R
F+ β
P(R
M-R
F)
So, if R
F= 5%, β
P = 1.2, R
M= 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. Alphais the difference between
what it did earn and what is should have earned.
α
P= R
P-R
F-β
P(R
M-R
F)
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

27. 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 Tickerestimatet-statisticestimatet-statisticR sq.
American Century Ultra TWCUX 0.010 0.12 0.977 25.69 92.8%
Fidelity Advisors Growth OpportunityFAGOX 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).

28. 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
RSD
RR
P
FP
portfoliofor Risk Total
portfolioon return Excess
)(
ratio Sharpe 



29. 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
PRR
P
FP
portfoliofor risk Systematic
portfolioon return Excess
IndexTreynor 




30. 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. 4.1
%5.0
%2.0%9.0
)(
ratio Sharpe 




P
FP
RSD
RR 41.0
7.1
%2.0%9.0
IndexTreynor 




P
FP
RR
 67.1
%3.0
%2.0%7.0
ratio Sharpe 

 50.0
0.1
%2.0%7.0
IndexTreynor 



31. 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