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## Empirical Testing of the asset pricing models Multifactor Models and

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### Application of Regression to the Testing of the Asset-pricing models ... First-pass regression: estimate alphas, betas on individual stocks using the ... – PowerPoint PPT presentation

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Title: Empirical Testing of the asset pricing models Multifactor Models and

1
Lecture 5
• Empirical Testing of the asset pricing models
Multi-factor Models and
• Market Anomalies

2
Outline of the Lecture
• Review Regression Analysis
• Application of Regression to the Testing of the
Asset-pricing models
• Beta, B/M ratio, and size effect Fama-French
three factor model
• Macro variables and asset pricing Chen-Roll-Ross
three factor model
• Market Anomalies

3
Regression Analysis
• Regression analysis a statistical tool for the
investigation of relationships between variables.
• In order to see the association between them and
• For the purpose of predicting the future value of
the dependent variable.
• In a single factor CAPM, we wish to test whether
the market index is a common factor which affects
assets' returns.

4
Market Model Regression
• For each asset i, one can estimate
• We often use a firms monthly stock return data
for the previous 5 years to estimate the beta.
• Why do not use daily data?
• Why uses 5 year long data?

5
First-Pass Regression
• First-pass regression estimate alphas, betas on
individual stocks using the market model
regression (1).
• Then calculate the average (excess) return of
each stock and the market index during the sample
period.
• Record the estimates of the variance of the
residuals for individual stocks.

6
Example Problem 1, Chpt. 13
• To do the first pass regression on asset A
• The excess return on the market index is the
independent variable
• The stock As excess return is the dependent
variable
• Click Tools and find Data Analysis tool pack
(if you cannot find it, you need to click
Excel), and then click Regressions.

7
Regression Procedure
• In the Input Y Range fill c3 to c14
• In the Input X Range fill b3 to b14
• In the Output options click New Worksheet Ply,
insert the name Stock A
• Then click OK.
• The regression result of equation (1) for Stock A
will appear on the separate worksheet named
Stock A.

8
• The R2 coefficient is given in Cell B5 For
multiple variables regression, you should report
the adjusted R2 in Cell B6.
• a is in B17 (with the t-stat in D17) b is in B18
(with the t-stat in D18) the estimated s2ei is
equal to D13.
• Both estimated a, b for stock A are not
statistically different from zero. Check the
t-stat. (Or check P-value. For any significance,
P-value should be lower than 0.10 or 0.05).

9
Interpretations
• R-Squared is the coefficient of
goodness-of-fit.
• The higher the R2, the better the line fits the
observations.
• For the multiple regressions, we need to use the
• In the index model, R2 systematic risk/total
risk.
• T-statistics tests whether an estimated parameter
is statistically significantly different from
zero. The significance of the test can be checked
with the p-value from the table.

10
Second-Pass Regression
• Second-pass regression
• where betas, excess returns, and residual
variances (unique risks) are obtained from the
first-pass regressions.

11
Hypothesis Testing
• According to the CAPM,
• However, Lintner, Miller and Scholes found that
Sample average, using annual data
• The empirical SML is too flat -- it rejects the
CAPM.

12
Rolls Critique
• Rolls major point is that the CAPM is not
testable unless the exact composition of the true
market portfolio is known and used in the test.
• Joint null hypothesis underlying the test
security markets are efficient and returns behave
according to a pre-specified model (such as the
CAPM).
• Another problem The CAPM is concerned with
expected returns, whereas we can only observe
actual returns.

13
Measurement Error in Beta
• Tests using individual stocks may suffer from the
error-in-variable problem.
• Beta cannot be measured in the first-pass
regression without error. When this happens, the
slope coefficient in the regression equation (2)
will be biased downward and the intercept biased
upward.

14
Testing the CAPM with PortfoliosBlack, Jensen,
Scholes (1972)
• To overcome the error-in-variable problem, Black,
Jensen and Scholes formed 10 portfolios based on
the magnitude of estimated individual betas, then
estimated, using monthly data
• They found more supportive evidence,

15
Testing the CAPM with Portfolios Fama-MacBeth
(1973)
• Fama and MacBeth (1973) formed 20 portfolios
based on the magnitude of estimated individual
betas, then estimated
• They found that g0 , g2 and g3 are not
significant. The slope, g1, is less than the
market risk premium, but not significantly so.

16
Fama-French 3 Factor Model
• Fama and French (1993) run the regression
• where a1gt0, a4gt0 and insignificant a2lt0, a3lt0
and significant.
• FF interpret size and P/B as proxies for
unobservable risk factors that have been omitted
from the beta-only asset pricing relation.

17
An Alternative View on B/M
• Lakonishok, Shleifer and Vishny (1994)
• show that the high B/M firms generally have
earnings declines over the preceding 3-5 years.
• Claim that the market over-reacts to these
firms poor performance, and the price of these
firms gets pushed too low.
• The price recovers when the firms do not do as
badly as expected, and the firms on average
experience high returns.

18
Inconsistency with the FF Interpretation
• The premia related to size and P/B are
significant primarily due to the large premia
observed in January. Outside January the premia
are insignificant, see Daniel and Titman (1997).
• If the premia represent compensation for risk, it
is reasonable to expect that compensation to be
earned uniformly throughout the year, it is an
unusual kind of risk that manifests itself only
in one month.

19
Human Capital and the CAPM JW study (1996)
• Two more factors should be considered
• the most important non-traded asset is human
capital
• Betas are cyclical with business cycles.
• Jaganathan and Wang (1996) used a proxy for
changes in the value of human capital (based on
the rate of change in aggregate labor income),
as well as size and beta, and they found that the
improvements of these tests are quite dramatic,
see Figure 13.2 and Table 13.2.

20
Stocks and Bonds in Business Cycles
• In general, expected returns on stocks and long
term bonds move together.
• Default spread the difference between the yield
for corporate bonds and the long term Treasury
bonds. The larger spread indicates a worsening
• Term Spread the difference between long term
Treasury bonds vs. short term Treasury bills. A
negative term spread indicates a higher chance of
a recession in the near future.

21
Possible Explanations
• Expected returns on stocks and bonds are lower
when economic conditions are strong and higher
when conditions are weak.
• When business conditions are poor, income is low
and expected returns on stocks and bonds must be
high to induce substitution from consumption to
investment.
• Variations in expected returns with business
conditions is due to variation in the risks of
bonds and stocks.

22
Gains through Timing the Cycle
• Since stocks fall prior to a recession, investors
want to switch out of stocks and into Treasury
bills, returning to stocks when prospects for
economic recovery look good.
• Based on research done by Jeremy Siegel, the
excess returns from timing is 1.8 (4.8) per
year if you can predict the peak and trough one
month (4 months) before it occurs.

23
• Wall Street economists desperately try to predict
the next recession or upturn. That is, they have
to watch and analyse the leading economic
indicators.
• Economic forecast data for the U.S. can be
obtained from the Website of Feds Philadelphias
office.
• Beating the stock market by analysing real
economic activity ahead of any other agents
requires the skill that forecasters do not yet
have.

24
Chen, Roll and Ross (1986)
• CRR (an example of APT multi-factor model)
examines the following macro variables
• YP Yearly growth rate in industrial production
• MP monthly growth rate in industrial production
• DEI change in expected inflation
• UI unanticipated inflation
• UPR unanticipated change in default spread (Baa
and under - Aaa)
• UTS unanticipated change in the term structure
(long term govt bond - T-bill rate)

25
CRR (1986) 3 Factor Results
• They use the traditional 2-pass method to
• Note items with () are not statistically
significant.

26
Pricing Anomaliesa Summary
• January effect. Possible explanation tax loss
selling?
• Turn-of-the-month effect.
• Size.
• M/B ratios.
• Reversal and momentum.

27
Momentum and Reversal Effects
• Many studies have documented that
• Short-term momentum there are positive short
term auto-correlation of stock returns, for
individual stocks and the market as a whole.
(short here refers to periods on the order of
three to twelve months).
• Long-term reversal stocks that have had the
lowest returns over any given five-year period
tend to have high returns over the subsequent
five years.