Fama-French three factor model

Developed by Eugene Fama and Kenneth French , the Fama-French three-factor model is a modern business finance model that explains stock returns. It can be seen as an extension of the capital asset pricing model . The three factors are (1) market risk, (2) the excess return of small versus large firms, and (3) the excess return of companies with low P / B versus companies with high P / B.

Overview

The traditional Capital Asset Pricing Model (CAPM) uses only one stock-specific variable, beta, to explain the return on a portfolio or stock in terms of market return. In contrast, the Fama-French three-factor model uses three variables. Fama and French first found that stocks with two distinct characteristics outperformed the market as a whole : (i) stocks with a small market capitalization and (ii) stocks with a high ratio of book value to market value of equity , also called value stocks. Therefore, they expanded the CAPM to include two factors that reflect the risk of the stocks with regard to the named properties:

${\ displaystyle r = R_ {f} + \ beta _ {3} (R_ {m} -R_ {f}) + b_ {s} \ cdot {\ mathit {SMB}} + b_ {v} \ cdot {\ mathit {HML}} + \ alpha}$

Here is the portfolio or stock return, the risk-free interest rate and the return of the overall market. The "three-factor " is similar to the classic but not identical, since the two additional factors also provide an explanation. stands for "small ( market capitalization ) minus big" and for "high (book-market value ratio) minus low"; they measure the difference in returns between small and large stocks and between value and growth stocks. These factors are calculated using portfolios to which stocks have been assigned based on their market capitalization and their book-to-market ratio. Historical time series for the US stock market are available on Kenneth French's website. ${\ displaystyle r}$ ${\ displaystyle R_ {f}}$ ${\ displaystyle R_ {m}}$ ${\ displaystyle \ beta}$ ${\ displaystyle \ beta}$ ${\ displaystyle {\ mathit {SMB}}}$ ${\ displaystyle {\ mathit {HML}}}$

${\ displaystyle \ alpha}$ denotes the unexplained difference and can be described as active return (or management influence). The active return is the difference between the portfolio return and a benchmark return. The benchmark return can be, for example, the risk-free interest rate. If this means that a fund manager has generated value beyond the risk factors described. One states that the influence of the risk factors was recorded exactly and that the trading behavior of the manager had no influence on the return (assumption: efficient market, see market efficiency hypothesis ). The three factor model can therefore also be used to describe the effectiveness of a fund manager. ${\ displaystyle \ alpha> 0}$ ${\ displaystyle \ alpha = 0}$

After and are available, the associated coefficients and are estimated by means of a linear regression and can assume both positive and negative values. For the American stock market, the Fama-French three-factor model explains more than 90% of the variance in portfolio returns, whereas the CAPM can only explain 70% on average. ${\ displaystyle {\ mathit {SMB}}}$ ${\ displaystyle {\ mathit {HML}}}$ ${\ displaystyle b_ {s}}$ ${\ displaystyle b_ {v}}$

Griffin shows that the Fama-French factors are country-specific and shows that local factors are better at explaining the time variance in stock returns than global factors. Eugene Fama and Kenneth French compared multifactor models with global and local risk factors for four regions (North America, Europe, Japan, and Asia / Pacific) and concluded that local risk factors were better at pricing regional portfolios than global risk factors. Time series for the USA, global and regional (North America, Europe, Japan, Asia excluding Japan) Stock markets are available For individual countries researchers offer factor time series for Great Britain and Switzerland, among others. For Germany several institutions currently offer current Fama-French factors free of charge:

Artmann / Finter / Kempf / Koch / Theissen (2012), CFR Cologne
Brückner / Lehmann / Schmidt / Stehle (2014), HU Berlin
Hanauer / Kaserer / Rapp (2013), TU Munich
Schmidt / Schrimpf / von Arx / Wagner / Ziegler (2011), University of Zurich
Marmi / Poma, Scuola Normale Superiore di Pisa
Frazzini, AQR Capital Management

The latter three providers offer data sets for several countries. The time series mentioned are compared by Brückner / Lehmann / Schmidt / Stehle (2014) for the German market. They show that caution is required when using the factors and that different results may be achieved depending on the data set used.

Extensions of the three factor model

The Fama-French three-factor model has been expanded several times over the years. The four -factor model by Mark Carhart ( 1997) extends the original model by an additional momentum factor , in short , which invests in last year's winners and sells last year's losers short. ${\ displaystyle {\ mathit {MOM}}}$

The five-factor model published in 2003 by Lubos Pastor and Robert F. Stambaugh also adds a liquidity factor , in short (see also liquidity ) as an additional risk factor. This states that illiquid stocks must offer the investor an additional risk premium. Both extensions helped to minimize the unexplained difference (alpha). ${\ displaystyle {\ mathit {LIQ}}}$

Fama and French also presented a five-factor model in 2015. The 5 factors are: (1) market risk, (2) company size, (3) value , (4) profitability and (5) investment patterns. This model can explain between 71% and 94% of the variance in returns between two diversified portfolios. The five-factor model therefore has a higher explanatory power than the three-factor model with regard to the mentioned factor portfolios.

criticism

The theory of the existence of factors has not been proven. Even if the theory is wrong, it is difficult to refute because such theories cannot be tested in controlled random experiments.

Web links

An overview and comparison of the factors for Germany can be found here: http://ssrn.com/abstract=2390063 .
Kenneth French

Individual evidence

^ ^A ^b ^c Eugene F. Fama, Kenneth R. French: The Cross-Section of Expected Stock Returns . In: Journal of Finance . 47, No. 2, 1992, pp. 427-465. doi : 10.2307 / 2329112 .
^ Eugene F. Fama, Kenneth R. French: Common Risk Factors in the Returns on Stocks and Bonds . In: Journal of Financial Economics . 33, No. 1, 1993, pp. 3-56. doi : 10.1016 / 0304-405X (93) 90023-5 .
^ Fama-French Three Factor Model Part I | Investor Solutions. In: investorsolutions.com. Retrieved February 29, 2016 .
^ Fama-French Three Factor Model. In: Forbes. Retrieved February 29, 2016 .
↑ Fama and French three-factor model - Bogleheads. In: www.bogleheads.org. Retrieved February 29, 2016 .
^ John M. Griffin: Are the Fama and French Factors Global or Country Specific? . In: The Review of Financial Studies . 15, No. 3, 2002, pp. 783-803. doi : 10.1093 / rfs / 15.3.783 .
^ Eugene F. Fama, Kenneth R. French: Size, value, and momentum in international stock returns . In: Journal of Financial Economics . 105, No. 3, 2012, ISSN 0304-405X , pp. 457-472. doi : 10.1016 / 0304-405X (93) 90023-5 .
↑ Kenneth French's website
^ University of Exeter Business School
↑ http://www.manuel-ammann.com/publicationsjournals.html
↑ ^a ^b ^c R. Brückner, P. Lehmann, MH Schmidt, R. Stehle: Fama / French Factors for Germany: Which Set Is Best? . In: SSRN . 2014.
^ S. Artmann, P. Finter, A. Kempf, S. Koch, E. Theissen: The Cross-Section of German Stock Returns: New Data and New Evidence . In: Schmalenbach Business Review . 64, 2012, pp. 20-43.
^ Matthias X. Hanauer, C. Kaserer, Marc S. Rapp: Risk factors and multifactor models for the German stock market . In: Business Research & Practice . 65, No. 5, 2013, pp. 469-492.
^ P. Schmidt, A. Schrimpf, U. von Arx, AF Wagner, A. Ziegler: On the Construction of Common Size, Value and Momentum Factors in International Stock Markets: A Guide with Applications . In: Swiss Finance Institute Research Paper . 10-58, 2011.
^ ^A ^b Mark M. Carhart: On Persistence in Mutual Fund Performance . In: Journal of Finance . 52, No. 1, 1997, pp. 57-82. doi : 10.2307 / 2329556 .
↑ Ulas Unlu: Evidence to Support Multifactor Asset Pricing Models: The Case of The Istanbul Stock Exchange . In: Asian Journal of Finance & Accounting . tape 5 , no. 1 , April 13, 2013, ISSN 1946-052X , p. 200 , doi : 10.5296 / ajfa.v5i1.3216 ( macrothink.org [accessed March 4, 2016]).
^ Eugene F. Fama, Kenneth R. French: A five-factor asset pricing model . In: Journal of Financial Economics . tape 116 , no. 1 , April 1, 2015, ISSN 0304-405X , p. 1–22 , doi : 10.1016 / j.jfineco.2014.10.010 ( sciencedirect.com [accessed July 4, 2020]).
↑ Marcos López de Prado: Tactical Investment Algorithms . In: SSRN Electronic Journal . 2019, ISSN 1556-5068 , doi : 10.2139 / ssrn.3459866 ( ssrn.com [accessed November 19, 2019]).