The estimation for the dynamics of betas (Ghysels & Jacquier) Empirical limitation of beta Conditional betas depend on firm characteristics & state variables driving the opportunity set Levered equity betas rise with financial leverage
The estimation for the dynamics of betas (Ghysels & Jacquier)
The estimation for the dynamics of betas (Ghysels & Jacquier) Estimate dynamics Design an instrumental variables estimator of α, γ, and the dynamics of the true unobserved
Quarterly betas have strong autocorrelation on the order of 0.95; standard method much lower ~ 0.6 Variables don’t explain much of time series variation of portfolio quarterly betas. Cannot use overlapping long-window filters to estimate the dynamics of β, but could predict future s effectively Daily returns produce uniformly better beta filters than monthly The estimation for the dynamics of betas (Ghysels & Jacquier) - Finding
Estimation of expected return (Jan Bartholdy, Paula Peare) Instruments for estimating beta: the return on a market index and the return on the stock, over the estimation period Simple OLS regression Finding: 5 years of monthly data and an equal-weighted index provide the best estimate. Performance of the model is very poor Explains on average 3% of difference in returns
Cross-sectional tests of the CAPM (Grauer, Janmaat) Alleviate problem of reduced beta spread in cross-sectional tests of CAPM Repackage the data with zero-weight portfolios When CAPM is true Simulation shows average values of the intercept and slope converge to their true values more rapidly R2 and power of the tests increase When the CAPM is false Slope and intercept of the regression change
Conclusion Used widely by academics and practitioners Simple model May forecast effectively for the expected return Limitation of beta Just measure systematic risk Require a large sample of stock ->significant expense
Fama French three-factor framework 1/6 Chan and Chen (1991) Huberman and Kandel (1987) cov(returns,distress) Covariation in returns on small stock The need for multi-factor model to improve the CAPM model
Fama French three-factor framework 2/6 Solution: three-factor model Fama and French (1996) Anomalies largely disappear in the three-factor model Capture much of the cross-sectional variation in average stock returns
Fama French three-factor framework 3/6 Market premium: excess return on a broad market portfolio Size premium (SMB - small minus big): difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks Value premium (HML - high minus low): difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market stocks
Fama French three-factor framework 4/6 The Fama French model is the time series multivariate regression E(RM) - Rf, E(SMB), and E(HML) are expected premiums, and the factor sensitivities or loadings i, si, hi areslopes in the time-series regression i is the error term of the formula
Fama French three-factor framework 5/6 Book-to-market equity and slopes on HML proxy for relative distress
Fama French three-factor framework (Bartholdy, Peare) 6/6 Estimate for beta for each factor, using simple OLS regression, 5 years of monthly data Findings: Fama French model is at best able to explain, on average, 5% of differences in returns on individual stocks, independent of the index used Small gain in explanatory power of Fama French probably does not justify extra work for including two additional factors (size premium & value premium)
Trading strategy Take advantage of human behavior e.g. "herding" mentality, overreaction to news Employing price momentum means taking additional risk Higher return should be rewarded Jegadeesh N. and Titman S., 1993
Fric, P., 'Use of Momentum in trading across Industry Sectors' Model 1: 4-quartile model. Best performers 1m lookback & 1m holding period 12m lookback & 6m holding Model 2: 20 fractile model (long 5% top & short 5% bottom) Select these two portfolios for observation
Model 3: Sustainable Return Model - quintile (5 fractiles) Finding: momentum is not sustainable The two selected portfolios still prevail Fric, P., 'Use of Momentum in trading across Industry Sectors'
Application of the Price momentum 1. Technical analyst 2. Fundamental analyst
Technical analyst Buy past winners Sell past losers Technical analysts prefer Past price performance Historical market information Two main usage: rate of change & moving average (Reeves 2008)
Fundamental Analysis Contrarian investing strategy Take the opposite approach For example, a fundamental analyst might conclude: A stock that has been rising may now be overvalued, while a stock that has been falling may be undervalued. Use Relative Strength (Reeves 2008)
Asset Growth Cooper, M. J., Gulen, H. & Schill, M. J. 2009. The Asset Growth Effect in Stock Returns Lipson, M. L., Mortal, S. & Schill, M. J. 2008. What Explains the Asset Growth Effect in Stock Returns?
Data & Methodology Broad sample of US stocks over past 40 years (from 1968 to 2007) Stock returns: NYSE, Amex and NASDAQ Total assets data: CRSP and Compusat Sort stocks in year t+1 based on the asset growth rate in year t defined as:
Return premium of low growth stocks over high growth stocks is remarkably persistent over time.
Firm asset growth rates are a strong predictor of future returns
Finding III Asset growth effect is more important for small capitalization stocks T-stat for relationship between small size firm and asset growth rate is higher. Regression results according to firm size
Finding IV Larger explanatory power with respect to other previously documented factors (i.e, size, prior returns, book-to market ratios, momentum…)
Explanations Risk-based explanation More investments more costs, exposure to more risks less returns Arbitrage-based explanation Study suggests that asset growth effect does not arise from changes in risk but rather from mispricing.
Statistics Momentum is very significant to forecast power Beta is less significant in forecast power compared to actual return
Key Findings CAPM alone is somewhat limited Three-factor model greatly improve forecasting power Four-factor model and five-factor model: trade-off between forecasting power (R2 increases by 0.57%) and efforts Limitation: selection bias (KO is a mature company with less volatility and little asset growth), beta rolling period
References Bartholdy J & Peare P 2004, ‘Estimation of expected return: CAPM vs. Fama and French’, International Review of Financial Analysis, vol. 14, pp. 407-427, accessed 11 May 2010 from ScienceDirect. Chan, K. C., and Chen, N., 1991, 'Structural and return characteristics of small and large firms', Journal of Finance 46, 1467-1484, 1991 Cooper, M. J., Gulen, H. & Schill, M. J. 2009, 'The Asset Growth Effect in Stock Returns' Fama E. F., and French, K. R., ‘Multifactor Explanations of Asset Pricing Anomalies’, Journal of Finance, vol. LI, no.1, 1996 Fric, P., 'Use of Momentum in trading across Industry Sectors', accessed 15 May 2010, from <http://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2001/PDF/A1PDF.htm> Grauer R R & Janmaat J A 2010, ‘Cross-sectional tests of the CAPM and Fama-French three-factor model’, Journal of banking & finance, vol.34, pp. 457-470, accessed 15 May 2010 from ScienceDirect. Huberman G., Kandel S., 1987, ‘Mean-variance spanning’, Journal of Finance 42, 873-888, 1987 Jegadeesh, N., and Titman, S., 1993, ‘Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency’ Lipson, M. L., Mortal, S. & Schill, M. J. 2008, 'What Explains the Asset Growth Effect in Stock Returns?'