This paper provides a simple way to alleviate the problem of reduced beta spread in cross-sectional tests of the CAPM by repackaging the data with zero-weight portfolios. When the CAPM is true and the data are repackaged, simulation shows that the average values of the intercept and slope converge to their true values more rapidly and there are striking increases in R2 and the power of the tests. When the CAPM is false the slope and intercept of the regression change.
.FF(1993) show that the model is a good description of returns on portfolios formed on size and BE/ME. FF(199$) use the model to explain industry returns. Here we show that the three-factor model captures the returns to portfolios formed on E/P, C/P, and sales growth.
FF(1993) show that the model is a good description of returns on portfolios formed on size and BE/ME. FF(199$) use the model to explain industry returns. Here we show that the three-factor model captures the returns to portfolios formed on E/P, C/P, and sales growth
For example, if a stock was trading at $35 per share six months ago and is currently trading at $40 per share, then its six-month price momentum would be 40 - 35 or 5.Unfortunately, this formula is not normalized, and therefore makes it is difficult to compare stocks selling at different price points. A stock experiencing a 1% price movement from $300 to $303 would have a momentum value of three. A second stock experiencing a 100% increase in price from $3 to $6 also has a momentum value of three.
In the empirical research, Buying past winners, and selling past losers, allowed investors to achieve above average returns over the period 1956 to 1989. In particular, stocks that were classified based on their prior 6-month performance, and held for 6 months realized an excess return of over 12% per year on average.
4-quartile model:1m lookback/1m holding period (25%-1-1) and the 12m lookback/6m holding period (25%-12-6) portfolios showed the strongest evidence of momentum20 fractile model:Two portfolios, being 5%-1m-1m and 5%-12m-6m were identified as having superior in-sample performance.
We used additional selection criterias of sharpe ratio, maximum loss in a period and the percentage number of positive returns divided by the number of negative returns to build reliability into the model. This led to the selection of a quintile (5 fractiles) sorting. We filtered out selections that suggested shorter lookback period for longer holding periods. As an example, while the table above suggests that we should adopt a portfolio which looks back 3 months and has a holding period of 12 months (20%-3m-12m), we find this to be a random outcome that is not sustainable. Once again, the 20%-1m-1m and 20%-12m-6m portfolios prevailed as the preferred portfolios.
Rate of change: For example, if a stock was trading at $35 per share six months ago and is currently trading at $40 per share. The stock selling at $303 per share that was trading at $300 six months ago would have a Rate of Change of 3 / 300 or 1%, while the second stock would have a Rate of Change of 3 / 3 or 100%.Moving average: For example, the plot might contain 28-day moving averages of price momentum along with daily price momentum figures. Buy signals can be triggered when price momentum travels above its moving averages and stays there for several trading days, while sell signals can be triggered when price momentum travels below its moving average.
Fundamental analysts believe that a stock is bought and sold based on its intrinsic value but not historical price momentum.However, fundamental analysts can also use price momentum to their advantage by adopting what is termed a contrarian investing strategyOne could argue the further a stock moves from its true market value, the greater the opportunity for profits. By tracking price momentum, and using this as a screening tool, fundamental analysts can then assess if a stock is undervalued or overvalued by evaluating the company's long-term financial health and earnings power.
Sort each year when collect data:+ mitigate backfilling bias: require that a firm be listed on Compustat for two years before it is included in the data set +
The asset growth rate varies from an average median value of -22% for the low growth group to 83% for the high growth group. Firms in both the high and low growth groups are relatively small with a median assets and market capitalization of $26 million and $25 million, respectively, for the low growth group and $81 million and $121 million, respectively for the high growth group. Equal- and value-weighted portfolios are formed based on the asset growth deciles. what is the difference between equal and value weighed portfolio?
Over the 39 years in our sample On an equal weighting, the low growth monthly portfolio return is 1.94%, whereas the return of the high growth portfolio is only 0.35%. On a value weighting, the spread between low growth and high growth returns is 1.05% per month. Both values are highly statistically significant. Why strong?Regress asset growth rate and stock return – statistically significant (** 1%, other is 5%)The returns continue to be monotonically related to asset growth rates and the difference in returns maintains its economic and statistical significance.
Remaining years have consistent resultsresults are similar if one omits those firms that have experienced an equity offering or acquisition around the portfolio formation year. Over 39 years in the sample period, there are only 4 years returns of low growth stocks < returns of high growth stocks (exceptions are only a small margin)Asset growth effect is not simply due to poor returns for firms following such events as equity offerings or corporate takeovers
*: 5%**: 1%
The t-statistic for asset growth is -6.07. In comparison, the t-statistics for the book-to-market ratio, capitalization, and past 6- and 36-months returns is 3.38, -1.41, 0.95, and 0.44. Even the twice lagged asset growth measure maintains important explanatory power in the regression with a t-statistic of -2.83. The asset growth rate maintains important explanatory power across all three capitalization levels. The coefficients (t-statistics) for the small cap, medium cap, and large cap sub-samples are respectively, -0.07 (-5.19), -0.07 (-4.30), and -0.05 (-3.59). As none of the other variables maintains statistical significance across all sub-samples, the asset growth rate appears to be at least as important as any of the other prevailing firm characteristics in explaining returns.
More investments more costs less returnsBig companies (undervalued by the market) invest on low risk project lower return?The book-to-market ratio attempts to identify undervalued or overvalued securities by taking the book value and dividing it by market value. In basic terms, if the ratio is above 1 then the stock is undervalued; if it is less than 1, the stock is overvalued. Limitation: - In explanation: reasons could be from variation of risks or mispricing and authors are not certain which one!empirical facts are difficult to reconcile with traditional risk-based explanations, and rather that the effect is at least partially due to the systematic market mispricing of growing businesses.
Strong negative relationship between the growth of total firm assets and firm stock returns Ex: Over the past 40 years, low asset growth stocks have maintained a return premium of 20% per year over high asset growth stocks. Asset growth rate maintains an economically and statistically important ability to forecast returns in both large and small capitalization stocks Ex:asset growth rate maintains large explanatory power with respect to other previously documented determinants of the cross-section of returns (i.e., size, prior returns, book-to-market ratios)
Stock Return Forecast - Theory and Empirical Evidence
The estimation for the dynamics of betas (Ghysels & Jacquier)<br />Empirical limitation of beta<br />Conditional betas depend on firm characteristics & state variables driving the opportunity set<br />Levered equity betas rise with financial leverage<br />
The estimation for the dynamics of betas (Ghysels & Jacquier)<br />
The estimation for the dynamics of betas (Ghysels & Jacquier)<br />Estimate dynamics<br />Design an instrumental variables estimator of α, γ, and the dynamics of the true unobserved <br />
Quarterly betas have strong autocorrelation on the order of 0.95; standard method much lower ~ 0.6<br />Variables don’t explain much of time series variation of portfolio quarterly betas.<br />Cannot use overlapping long-window filters to estimate the dynamics of β, but could predict future s effectively<br />Daily returns produce uniformly better beta filters than monthly<br />The estimation for the dynamics of betas (Ghysels & Jacquier) - Finding<br />
Estimation of expected return (Jan Bartholdy, Paula Peare)<br />Instruments for estimating beta: the return on a market index and the return on the stock, over the estimation period<br />Simple OLS regression<br />Finding: <br />5 years of monthly data and an equal-weighted index provide the best estimate. <br />Performance of the model is very poor<br />Explains on average 3% of difference in returns<br />
Cross-sectional tests of the CAPM (Grauer, Janmaat)<br />Alleviate problem of reduced beta spread in cross-sectional tests of CAPM<br />Repackage the data with zero-weight portfolios<br />When CAPM is true<br />Simulation shows average values of the intercept and slope converge to their true values more rapidly<br />R2 and power of the tests increase<br />When the CAPM is false<br />Slope and intercept of the regression change<br />
Conclusion<br />Used widely by academics and practitioners<br />Simple model<br />May forecast effectively for the expected return<br />Limitation of beta<br />Just measure systematic risk<br />Require a large sample of stock ->significant expense<br />
Fama French three-factor framework 1/6<br />Chan and Chen (1991)<br />Huberman and Kandel (1987)<br />cov(returns,distress)<br />Covariation in returns on small stock<br />The need for multi-factor model to improve the CAPM model<br />
Fama French three-factor framework 2/6<br />Solution: three-factor model<br />Fama and French (1996)<br />Anomalies largely disappear in the three-factor model<br />Capture much of the cross-sectional variation in average stock returns<br />
Fama French three-factor framework 3/6<br />Market premium: excess return on a broad market portfolio<br />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<br />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<br />
Fama French three-factor framework 4/6<br />The Fama French model is the time series multivariate regression<br />E(RM) - Rf, E(SMB), and E(HML) are expected premiums, and the factor sensitivities or loadings<br />i, si, hi areslopes in the time-series regression<br />i is the error term of the formula<br />
Fama French three-factor framework 5/6<br />Book-to-market equity and slopes on HML proxy for relative distress<br />
Fama French three-factor framework (Bartholdy, Peare) 6/6<br />Estimate for beta for each factor, using simple OLS regression, 5 years of monthly data<br />Findings:<br />Fama French model is at best able to explain, on average, 5% of differences in returns on individual stocks, independent of the index used<br />Small gain in explanatory power of Fama French probably does not justify extra work for including two additional factors (size premium & value premium)<br />
Trading strategy<br />Take advantage of human behavior e.g. "herding" mentality, overreaction to news<br />Employing price momentum means taking additional risk<br />Higher return should be rewarded<br />Jegadeesh N. and Titman S., 1993<br />
Fric, P., 'Use of Momentum in trading across Industry Sectors'<br />Model 1: 4-quartile model. Best performers<br />1m lookback & 1m holding period<br />12m lookback & 6m holding<br />Model 2: 20 fractile model (long 5% top & short 5% bottom)<br />Select these two portfolios for observation<br />
Model 3: Sustainable Return Model - quintile (5 fractiles)<br />Finding: momentum is not sustainable<br />The two selected portfolios still prevail<br />Fric, P., 'Use of Momentum in trading across Industry Sectors'<br />
Application of the Price momentum<br />1. Technical analyst<br />2. Fundamental analyst<br />
Technical analyst<br />Buy past winners<br />Sell past losers<br />Technical analysts prefer<br />Past price performance<br />Historical market information<br />Two main usage: rate of change & moving average<br />(Reeves 2008)<br />
Fundamental Analysis<br />Contrarian investing strategy<br />Take the opposite approach<br />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.<br />Use Relative Strength (Reeves 2008)<br />
Asset Growth<br />Cooper, M. J., Gulen, H. & Schill, M. J. 2009. The Asset Growth Effect in Stock Returns<br />Lipson, M. L., Mortal, S. & Schill, M. J. 2008. What Explains the Asset Growth Effect in Stock Returns?<br />
Data & Methodology<br />Broad sample of US stocks over past 40 years (from 1968 to 2007)<br />Stock returns: NYSE, Amex and NASDAQ<br />Total assets data: CRSP and Compusat<br />Sort stocks in year t+1 based on the asset growth rate in year t defined as: <br />
Data & Methodology<br />Asset growth deciles<br />
Finding I<br />Strong negative relationship between the asset growth rate and the portfolio returns<br />Annual mean returns over 39 years<br />
Finding II<br /><ul><li>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 </li></li></ul><li>Finding III<br />Asset growth effect is more important for small capitalization stocks<br />T-stat for relationship between small size firm and asset growth rate is higher.<br />Regression results according to firm size<br />
Finding IV<br />Larger explanatory power with respect to other previously documented factors (i.e, size, prior returns, book-to market ratios, momentum…)<br />
Explanations<br />Risk-based explanation<br />More investments more costs, exposure to more risks less returns<br />Arbitrage-based explanation<br />Study suggests that asset growth effect does not arise from changes in risk but rather from mispricing.<br />
Asset Growth - Key Findings<br /><ul><li>Strong negative relationship between the firm’s asset growth and stock returns
Larger explanatory power than other previously factors (i.e, size, prior returns, book-to market ratios, momentum…)
Asset growth effect is more important for small capitalization stocks</li></li></ul><li>Empirical Research<br />
The Research<br />Purpose: extend Fama French, Momentum and Asset Growth research<br />Methodology: daily data of Coca-Cola (KO) in 2005<br />
Statistics<br />Momentum is very significant to forecast power<br />Beta is less significant in forecast power compared to actual return<br />
Key Findings<br />CAPM alone is somewhat limited<br />Three-factor model greatly improve forecasting power<br />Four-factor model and five-factor model: trade-off between forecasting power (R2 increases by 0.57%) and efforts<br />Limitation: selection bias (KO is a mature company with less volatility and little asset growth), beta rolling period<br />
Historical, Contemporary and Future Research<br />
Application of Forecast in practice<br />Forecast<br />Multivariate model<br />Market information, market movement, algorithm trading<br />Avoid pitfall of over-reliance on forecast<br />
References<br />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.<br />Chan, K. C., and Chen, N., 1991, 'Structural and return characteristics of small and large firms', Journal of Finance 46, 1467-1484, 1991<br />Cooper, M. J., Gulen, H. & Schill, M. J. 2009, 'The Asset Growth Effect in Stock Returns' <br />Fama E. F., and French, K. R., ‘Multifactor Explanations of Asset Pricing Anomalies’, Journal of Finance, vol. LI, no.1, 1996<br />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> <br />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.<br />Huberman G., Kandel S., 1987, ‘Mean-variance spanning’, Journal of Finance 42, 873-888, 1987<br />Jegadeesh, N., and Titman, S., 1993, ‘Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency’<br />Lipson, M. L., Mortal, S. & Schill, M. J. 2008, 'What Explains the Asset Growth Effect in Stock Returns?' <br />