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Risk and Return: Empirical Arc

This article explores the empirical analysis and testing of objective CRSP data to uncover new, true, and important insights into risk and return. It examines various tests, empirical evidence, and anomalies in asset pricing theory, including the CAPM, APT, and calendar effects. The article also discusses the use of latent factors and econometric techniques in analyzing risk and return.

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Risk and Return: Empirical Arc

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  1. Risk and Return: Empirical Arc Eric Falkenstein

  2. The testing objective

  3. CRSP data • James H. Lorie and Lawrence Fisher created dataset of stocks from 1926-1964 in US • Theory and data would now show us something new, true, and important • “If I had to rank events, I would say this one (the original CRSP Master File) is probably slightly more significant than the creation of the universe“ Rex Sinquefeld

  4. First Tests: Mutual Funds • Sharpe (1965) • Sharpe (1966) • Treynor and Mazuy (1966) • Jensen (1968)

  5. George Douglas (1969) • Find variance more important than beta • Miller and Scholes (1972) • Check for • Beta measurement errors • Market proxy • Nonnormality • Skewness, • Heteroskedasticity • Changing interest rates • No size, delisting issues

  6. Asset Pricing Theory Was Always Treated Well • 1971 Institutional Investor :“The Beta Cult: The New Way to Measure Risk.” • Contrast with Efficient Markets Hypothesis

  7. Errors in Variables • High beta stocks will have positive beta bias • Sort by beta from 1929-1933 • Form 20 portfolios • Estimate beta of portfolio from 1933-39 using monthly data • Use beta to examine month-ahead returns

  8. CAPM tests • First pass • Second pass

  9. Empirical Evidence of the CAPM • Black, Jensen and Scholes (1972), Blume and Friend (1973), Fama and MacBeth (1973),

  10. Roll Critique • Real testable hypothesis of the CAPM that the market is mean-variance efficient • Given investor preferences, CAPM must hold if true • Market includes real estate, human capital, so S&P500 not ‘the market’ • Untestable

  11. Value Anomalie • Basu (1977), Statman (1980)

  12. Size Effect: Reinganum (1982) • Note relation to Beta

  13. Calendar Effects • the January effect • September effect • Monday effect • Friday effect • days before holidays • Returns only positive if use first half of each month

  14. Other Anomalies • Low-price effect • 3 year over-reaction (DeBondt and Thaler) • Accruals (noncash earnings) • Capital issuance • R&D expenditures • Momentum • Earnings announcement drift • Index additions • Dividend effects • Momentum (past 12 month’s return)

  15. APT tests • Chen, Roll, and Ross (1986) • Industrial Production change • BBB and AAA yield spread • Long term-short term yield spread • Unanticipated inflation • Anticipated inflation, • The market

  16. Latent Factor APT tests • Connor and Korajczyk • Find factors using factor analysis • First Factor looks like the Equal Weighted Equity Index • Second factor ??? • Third factor ???

  17. Empirical • Zero-beta, not risk free, asset • Jointly estimating parameters • Exact finite sample distributions • Gibbons (1982) ,Shanken (1985), Gibbons, Ross, and Shanken (1989) • reject CAPM at p-value 0.001

  18. What to make of a statistical rejection? Big deal No big deal

  19. Pedantry Alert! • Maximum Likelihood, Lagrange Multiplier, Wald Tests • Has it ever mattered? • Discriminate Analysis, Logit, Probit • continuous time vs discrete time finance • ‘ordinary’ Least Squares, 2-stage LS, 3-stage SLS

  20. Great Econometrics Very Alluring • 1950 Cowles Group: Simultaneity, FIML • 1950 Durbin & Watson serial correlation • 1953 Theil: 2 Stage Least Squares • 1960 Chow Test for Structural Change • 1974 Heckman: self-selection • 1974 McFadden et al: discreet choice • 1978 Hausman: exogeneity test • 1979 Godfrey-Breusch-Pagan-Bera: LM test • 1981: non-stationarity and cointegration • 1982 Engle: ARCH • 1982 Hansen: GMM

  21. Statistics Like Wine • Bad wine < good wine > fancy wine • $7 bottle < $30 bottle > $200 bottle • Secrets to good wine: sanitation, harvest time • Irrelevancies: fine terroir distinctions, charred French oak barrels • Bad statistics < good statistics > fancy statistics • Univariate correlations < OLS > 2SLS • Good Stats: control for omitted variables, clean data of mistakes • Irrelevancies: asymptotics, GMM, joint estimations • Abominations: back-fitting VARs, interaction terms,

  22. Fama-French (1992) • Synthesize anomalies and failure of CAPM • Show beta is just a size effect • Founding father (Fama) admits CAPM wrong

  23. Good Tests Easy to See

  24. Main Risk Factors Used From Ken French’s website SMB: Small minus Big Size HML: High minus Low Book/Market UMD: Up minus Down Stocks (Past 12 Month Return)

  25. Errors • Arithmetic Averaging of daily returns: • 1, 1.5, 1  +50%, -33% • Arithmetic avg=8%, Geometric avg=0% • Delistings • Shumway finds delisted firm monthly returns -55% on Nasdaq • Size Index: 1% increase from 1993 through 2009 • Value Index: 4% premium from 1975 through 2009

  26. New Factors for CAPM 'Part Deux' • Jagannathan and Wang (1993): per capita labor income (year-over-year) • Lettau-Ludvigson (2000): consumption, assets, and income, Vector Auto Regression • Campbell and Vuolteenaho (2002): Beta from CF and discount factor, VAR from size, yield curve, P/E ratio • ‘good beta/bad beta’

  27. Empirical Summary • Size, Value, Momentum related to returns • Not clear why, or if real • Beta not related to returns • Delistings, daily returns, bias annual returns • Most Anomalies—e.g., calendar effects---ephemeral or spurious • Sophisticated tests have been distractions (e.g., GMM)

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