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	economics investment Style Investing (Stocks) todo: delete Part 8 of the the investment sequence Fama-French Three-Factor Model Any discussion of style investing should probably start with Eugene Fama - the "father of modern finance" Eugene Fama and winner of the Nobel prize for his "empirical analysis of asset prices" The Prize in Economic Sciences 2013. His most famous contribution is proposing the three levels of market efficiency, but this is closely followed by his extension of the single factor model based on the capital asset pricing model to include two additional observations: small firms and firms with high book-to-market ratios tend to outperform the market even after controlling for market risk ($\beta$) Fama–French three-factor model. . He actually found results much more impressive than just this, namely The Cross-Section of Expected Stock Returns: Though, to give credit where its do, its worth pointing out he acknowledged these individual insights were found by other people The Cross-Section of Expected Stock Returns. After controlling for the book-to-market ratio, leverage no longer correlates with higher return After controlling for market capitalization and the book-to-market ratio, the E/P ratio no longer correlates with higher returns. After controlling for market capitalization, $\beta$ no longer correlates with higher returns. In other words, they find the CAPM model to be completely wrong! This also explains why I found virtually no correlation between $\beta$ and returns when I looked at 100 stocks between 1984 and 2017 Marjanovic. You may think this disproves the CAPM, and I think Fama would agree with you. You may think this disproves the efficient market hypothesis - and there Fama does not: he's pretty adamant that all a paper can do is prove that either the market is not efficient or that the pricing model is wrong, but that it's impossible to prove which is the case. For the skeptical, Fama cites an alternative reason small firms might yield better returns in an efficient market Chan Is there any criticism of the study itself? I haven't seen any besides the obvious: just because the strategy worked in the past (1963 - 1990 in this case) doesn't mean it works now. If this is true, there are two possible reasons: (a) the market itself changed, presumably getting more efficient over time. and (b) the relationship is statistical luck. The original study offers some indication of (a): $\beta$ did predict returns between 1941 and 1965 - but even this goes away after controlling for firm size, suggesting what changed was the relationship between $\beta$ and firm size, not either of them and returns. The authors reported no evidence that their favored model has weakened over time. In my opinion (b) is only plausible for the market capitalization parameter since its p-values ranged from 0.05 to 0.00065. Once you consider all the plausible other parameters that might predict stock trends, this seems plausibly due to chance. The book-to-market ratio's p-values, however, ranged from roughly 1-in-100,000 to roughly 1-in-a-billion, which seems really implausible to be by chance alone. Let's consider these two factors in more detail. Firm Size Since its discovery in 1981, the association between firm size on returns has shrunken and/or disappeared except maybe in January. A meta-analysis found significant publication bias in the literature. After accounting for this bias, they estimate a premium for small firms of about 1.72pp per year Firm size and stock returns: A quantitative survey A literature review of the size effect. I suspect after accounting for the decrease in the effect over time would reduce this estimate further to ~1.5pp . I decided to do some more recent validation using Vanguard ETFs from the early 200s until today. I found the VSMAX and VXF (indices that tracked small firms) outperformed the wider market by about 0.8% annually, though the t-score was only 0.5. I arrived at this result via two separate methods: first by modeling stocks using a single-index model, second looking at the differences in each index's returns each month and using the average of those differences. The "January" effect is fascinating in its own right: not only is the size much effect larger in January, stock returns in general are typically much larger. Within January, the effect is concentrated particularly in the beginning. The one explanation I've come across is essentially that (a) investors sell in December to harvest losses for tax purposes, (b) then re-buy in January, and (c) small firms are illiquid enough that this can significant affect prices in the short-term. This explanation is quite different from the original explanation for firm size bias: smaller firms have greater risk. For arguments against this view see pg 54 - 56 Falkenstein. Book-to-Market Ratio todo Other Factors Momentum todo: Carhart four-factor model Carhart four-factor model Fama-French Five Factor Model todo: the Fama-French Three-Factor Model with two additional factors (robustness of operating profit and investment aggressiveness) Fama–French three-factor model Arbitrage Pricing Theory todo Arbitrage pricing theory (pg 33 - 36) Wikipedia contributors. (2021, July 14). Carhart four-factor model. In Wikipedia, The Free Encyclopedia. Retrieved 21:10, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Carhart_four-factor_model&oldid=1033568498 Wikipedia contributors. (2021, October 16). Fama–French three-factor model. In Wikipedia, The Free Encyclopedia. Retrieved 10:08, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Fama%E2%80%93French_three-factor_model&oldid=1050249685 Chan, K. C., & Chen, N. F. (1991). Structural and return characteristics of small and large firms. The journal of finance, 46(4), 1467-1484. https://doi.org/10.1111/j.1540-6261.1991.tb04626.x Wikipedia contributors. (2021, September 14). Eugene Fama. In Wikipedia, The Free Encyclopedia. Retrieved 09:53, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Eugene_Fama&oldid=1044262637 The Prize in Economic Sciences 2013. (2013). Royal Swedish Academy of Sciences. https://www.nobelprize.org/prizes/economic-sciences/2013/press-release/ Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. The Journal of Finance, 47(2), 427–465. https://doi.org/10.1111/j.1540-6261.1992.tb04398.x Fama, E. F., & French, K. R. (2008). Dissecting anomalies. The Journal of Finance, 63(4), 1653-1678. https://doi.org/10.1111/j.1540-6261.2008.01371.x Crain, M. A. (2011). A literature review of the size effect. Available at SSRN 1710076. https://dx.doi.org/10.2139/ssrn.1710076 Galariotis, E. C. (2014). Contrarian and momentum trading: a review of the literature. Review of Behavioral Finance. https://doi.org/10.1108/RBF-12-2013-0043 Zaremba, A. (2019). The cross section of country equity returns: A review of empirical literature. Journal of Risk and Financial Management, 12(4), 165. https://doi.org/10.3390/jrfm12040165 Woo, K. Y., Mai, C., McAleer, M., & Wong, W. K. (2020). Review on efficiency and anomalies in stock markets. Economies, 8(1), 20. https://doi.org/10.3390/economies8010020 Alhenawi, Y. (2015). On the interaction between momentum effect and size effect. Review of Financial Economics, 26(1), 36-46. https://doi.org/10.1016/j.rfe.2015.03.005 Astakhov, A., Havranek, T., & Novak, J. (2019). Firm size and stock returns: A quantitative survey. Journal of Economic Surveys, 33(5), 1463-1492. https://doi.org/10.1111/joes.12335 Marjanovic. B. (2017). Huge Stock Market Dataset. https://www.kaggle.com/borismarjanovic/price-volume-data-for-all-us-stocks-etfs Falkenstein, E. G. (2009). Risk and return in general: Theory and evidence. Available at SSRN 1420356. http://doi.org/10.2139/ssrn.1420356 Wikipedia contributors. (2021, September 19). Arbitrage pricing theory. In Wikipedia, The Free Encyclopedia. Retrieved 02:05, February 1, 2022, from https://en.wikipedia.org/w/index.php?title=Arbitrage_pricing_theory&oldid=1045254819

economics investment

Style Investing (Stocks)

todo: delete

Fama-French Three-Factor Model

Any discussion of style investing should probably start with Eugene Fama - the "father of modern finance" Eugene Fama and winner of the Nobel prize for his "empirical analysis of asset prices" The Prize in Economic Sciences 2013.

His most famous contribution is proposing the three levels of market efficiency, but this is closely followed by his extension of the single factor model based on the capital asset pricing model to include two additional observations: small firms and firms with high book-to-market ratios tend to outperform the market even after controlling for market risk ($\beta$) Fama–French three-factor model. . He actually found results much more impressive than just this, namely The Cross-Section of Expected Stock Returns:

After controlling for the book-to-market ratio, leverage no longer correlates with higher return
After controlling for market capitalization and the book-to-market ratio, the E/P ratio no longer correlates with higher returns.
After controlling for market capitalization, $\beta$ no longer correlates with higher returns. In other words, they find the CAPM model to be completely wrong!

You may think this disproves the CAPM, and I think Fama would agree with you. You may think this disproves the efficient market hypothesis - and there Fama does not: he's pretty adamant that all a paper can do is prove that either the market is not efficient or that the pricing model is wrong, but that it's impossible to prove which is the case. For the skeptical, Fama cites an alternative reason small firms might yield better returns in an efficient market Chan

Is there any criticism of the study itself? I haven't seen any besides the obvious: just because the strategy worked in the past (1963 - 1990 in this case) doesn't mean it works now. If this is true, there are two possible reasons: (a) the market itself changed, presumably getting more efficient over time. and (b) the relationship is statistical luck.

The original study offers some indication of (a): $\beta$ did predict returns between 1941 and 1965 - but even this goes away after controlling for firm size, suggesting what changed was the relationship between $\beta$ and firm size, not either of them and returns. The authors reported no evidence that their favored model has weakened over time.

In my opinion (b) is only plausible for the market capitalization parameter since its p-values ranged from 0.05 to 0.00065. Once you consider all the plausible other parameters that might predict stock trends, this seems plausibly due to chance. The book-to-market ratio's p-values, however, ranged from roughly 1-in-100,000 to roughly 1-in-a-billion, which seems really implausible to be by chance alone.

Let's consider these two factors in more detail.

Firm Size

Since its discovery in 1981, the association between firm size on returns has shrunken and/or disappeared except maybe in January. A meta-analysis found significant publication bias in the literature. After accounting for this bias, they estimate a premium for small firms of about 1.72pp per year Firm size and stock returns: A quantitative survey A literature review of the size effect. I suspect after accounting for the decrease in the effect over time would reduce this estimate further to ~1.5pp .

The "January" effect is fascinating in its own right: not only is the size much effect larger in January, stock returns in general are typically much larger. Within January, the effect is concentrated particularly in the beginning.

The one explanation I've come across is essentially that (a) investors sell in December to harvest losses for tax purposes, (b) then re-buy in January, and (c) small firms are illiquid enough that this can significant affect prices in the short-term.

This explanation is quite different from the original explanation for firm size bias: smaller firms have greater risk.

For arguments against this view see pg 54 - 56 Falkenstein.

Book-to-Market Ratio

todo

Other Factors

Momentum

todo: Carhart four-factor model Carhart four-factor model

Fama-French Five Factor Model

todo: the Fama-French Three-Factor Model with two additional factors (robustness of operating profit and investment aggressiveness) Fama–French three-factor model

Arbitrage Pricing Theory

todo Arbitrage pricing theory (pg 33 - 36)

Wikipedia contributors. (2021, July 14). Carhart four-factor model. In Wikipedia, The Free Encyclopedia. Retrieved 21:10, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Carhart_four-factor_model&oldid=1033568498 Wikipedia contributors. (2021, October 16). Fama–French three-factor model. In Wikipedia, The Free Encyclopedia. Retrieved 10:08, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Fama%E2%80%93French_three-factor_model&oldid=1050249685 Chan, K. C., & Chen, N. F. (1991). Structural and return characteristics of small and large firms. The journal of finance, 46(4), 1467-1484. https://doi.org/10.1111/j.1540-6261.1991.tb04626.x Wikipedia contributors. (2021, September 14). Eugene Fama. In Wikipedia, The Free Encyclopedia. Retrieved 09:53, December 1, 2021, from https://en.wikipedia.org/w/index.php?title=Eugene_Fama&oldid=1044262637 The Prize in Economic Sciences 2013. (2013). Royal Swedish Academy of Sciences. https://www.nobelprize.org/prizes/economic-sciences/2013/press-release/ Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. The Journal of Finance, 47(2), 427–465. https://doi.org/10.1111/j.1540-6261.1992.tb04398.x Fama, E. F., & French, K. R. (2008). Dissecting anomalies. The Journal of Finance, 63(4), 1653-1678. https://doi.org/10.1111/j.1540-6261.2008.01371.x Crain, M. A. (2011). A literature review of the size effect. Available at SSRN 1710076. https://dx.doi.org/10.2139/ssrn.1710076 Galariotis, E. C. (2014). Contrarian and momentum trading: a review of the literature. Review of Behavioral Finance. https://doi.org/10.1108/RBF-12-2013-0043 Zaremba, A. (2019). The cross section of country equity returns: A review of empirical literature. Journal of Risk and Financial Management, 12(4), 165. https://doi.org/10.3390/jrfm12040165 Woo, K. Y., Mai, C., McAleer, M., & Wong, W. K. (2020). Review on efficiency and anomalies in stock markets. Economies, 8(1), 20. https://doi.org/10.3390/economies8010020 Alhenawi, Y. (2015). On the interaction between momentum effect and size effect. Review of Financial Economics, 26(1), 36-46. https://doi.org/10.1016/j.rfe.2015.03.005 Astakhov, A., Havranek, T., & Novak, J. (2019). Firm size and stock returns: A quantitative survey. Journal of Economic Surveys, 33(5), 1463-1492. https://doi.org/10.1111/joes.12335 Marjanovic. B. (2017). Huge Stock Market Dataset. https://www.kaggle.com/borismarjanovic/price-volume-data-for-all-us-stocks-etfs Falkenstein, E. G. (2009). Risk and return in general: Theory and evidence. Available at SSRN 1420356. http://doi.org/10.2139/ssrn.1420356 Wikipedia contributors. (2021, September 19). Arbitrage pricing theory. In Wikipedia, The Free Encyclopedia. Retrieved 02:05, February 1, 2022, from https://en.wikipedia.org/w/index.php?title=Arbitrage_pricing_theory&oldid=1045254819