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Empirical Testing of the asset pricing models Multifactor Models and


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

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

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

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.

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?

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
  • Record the estimates of the variance of the
    residuals for individual stocks.

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
  • 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.

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.

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).

  • R-Squared is the coefficient of
  • The higher the R2, the better the line fits the
  • For the multiple regressions, we need to use the
    adjusted R-Squared.
  • In the index model, R2 systematic risk/total
  • 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.

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

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

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
  • Another problem The CAPM is concerned with
    expected returns, whereas we can only observe
    actual returns.

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

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,

Testing the CAPM with Portfolios Fama-MacBeth
  • 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.

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.

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.

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.

Human Capital and the CAPM JW study (1996)
  • Two more factors should be considered
  • the most important non-traded asset is human
  • 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.

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.

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
  • Variations in expected returns with business
    conditions is due to variation in the risks of
    bonds and stocks.

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.

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
  • Economic forecast data for the U.S. can be
    obtained from the Website of Feds Philadelphias
  • Beating the stock market by analysing real
    economic activity ahead of any other agents
    requires the skill that forecasters do not yet

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)

CRR (1986) 3 Factor Results
  • They use the traditional 2-pass method to
    estimate factor risk premiums (ls)
  • Note items with () are not statistically

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

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.
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