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
  add-in and add the Analysis toolpak on your
  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
How to Read the Results

• 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
  adjusted R-Squared.
• 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.
• Beta is dead!
• 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),
  default spread (a proxy for business conditions),
  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, term spread, and dividend yields
  are measures of business conditions.
• Default spread the difference between the yield
  for corporate bonds and the long term Treasury
  bonds. The larger spread indicates a worsening
  business condition.
• 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
Predict the Business Cycle?

• 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
  estimate factor risk premiums (ls)
• 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.