Fama-French三因子模型简介

Introduction to the Fama-French three-factor model

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The Fama-French three-factor model (referred to as the Fama-French model) is an asset pricing model developed in 1992. This model adds scale risk and value risk factors based on the capital asset pricing model (CAPM), and expands market risk factors. The model takes into account the phenomenon that value and small-cap stocks regularly outperform the market. By introducing these two additional factors, the model adjusts for this excess performance, which is thought to make it a more effective tool for assessing managers' performance.

Main points

• The Fama-French three-factor model is an asset pricing model that adds scale risk and value risk factors based on the capital asset pricing model.
• This model was developed in the 1990s by Nobel Prize winner Eugene Fama and his colleague Kenneth French.
• The model is basically the result of an econometric regression of historical stock prices.

Understand the Fama-French three-factor model

Nobel laureate Eugene Fama and researcher Kenneth French, a former professor at the University of Chicago Booth School of Business, aimed to more accurately measure market returns and found through research that value stocks outperformed growth stocks. [1] Likewise, small-cap stocks tend to outperform large-cap stocks. As a valuation tool, portfolios containing a large number of small-cap or value stocks generally underperform the CAPM results because the three-factor model adjusts downward for the observed outperformance of small-cap and value stocks.

The three factors of the Fama-French model include company size, book-to-market ratio and market excess returns. In other words, the model uses small-cap stocks minus large-cap stocks (SMB), high book-to-market minus low book-to-market (HML), and portfolio return minus risk-free rate. SMB considers publicly traded companies with smaller market capitalizations, which typically generate higher returns, while HML analyzes value stocks with high book-to-market ratios, which generate higher returns compared to the market. [2]

Controversy remains between market efficiency and market inefficiency regarding the causes of overperformance. Proponents of the market efficiency argument argue that outperformance can often be explained by the excess risk faced by value and small-cap stocks due to their higher cost of capital and greater business risk. The argument in favor of market inefficiency is that market participants make mistakes in pricing the value of these companies, thereby providing excess returns in the long run. Investors who believe in the evidence for the efficient markets hypothesis (EMH) are more likely to subscribe to the idea of ​​market efficiency.

The formula is:

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Fama and French emphasized that investors must be able to withstand additional volatility and cyclical underperformance that may occur in the short term. Investors with investment horizons of 15 years or more will be rewarded for losses in the short term. Fama and French tested their model by studying thousands of random stock portfolios and found that when combining size and value factors with beta factors, it can explain up to 95% of the returns on diversified stock portfolios.

Considering that the model is able to explain up to 95% of portfolio returns, investors can construct a portfolio that earns an average expected return based on the relative risk assumed by their portfolio. The main factors driving expected returns include market sensitivity, size sensitivity and value stock sensitivity, which are measured by book-to-market ratio. Any additional average expected returns may be attributable to unpriced or unsystematic risk.

Fama and French’s five-factor model

In recent years, researchers have expanded the three-factor model to include additional factors. These factors include "momentum," "quality," and "low volatility," among others. In 2014, Fama and French adapted their model to include five factors. On the basis of the original three factors, the new model adds a concept, that is, companies with higher profits in the future tend to have higher returns in the stock market. This factor is called profitability.

The fifth factor, called "Investment," is related to the concept of internal investment and returns, suggesting that companies that plow their profits into major growth projects may face losses in the stock market. [3]

The significance of the Fama-French three-factor model to investors

The Fama-French three-factor model emphasizes that investors must be able to tolerate additional volatility and the potential for cyclical underperformance in the short term. Investors with investment horizons of 15 years or more will profit from losses in the short term. Given that the model can explain up to 95% of the returns of a diversified stock portfolio, investors can tailor their portfolios to achieve average expected returns based on the relative risk they bear.

The main factors driving expected returns include market sensitivity, size sensitivity and value stock sensitivity, which are measured by book-to-market ratio. Any additional average expected returns may be attributable to unpriced or unsystematic risk.

What are the three factors of the model?

The Fama-French model has three factors: company size, book-to-market ratio, and market excess returns. In other words, the model uses small-cap stocks minus large-cap stocks (SMB), high book-to-market minus low book-to-market (HML), and portfolio return minus risk-free rate. SMB considers publicly traded companies with smaller market capitalizations, which typically generate higher returns, while HML analyzes value stocks with high book-to-market ratios, which generate higher returns compared to the market.

What is the Fama-French five-factor model?

In 2014, Fama and French adjusted their model to include five factors. In addition to the original three factors, the new model adds the concept that companies that report higher future profits generally have higher returns in the stock market. This factor is called profitability. The fifth factor, called "Investment," relates to internal investment and return scenarios, suggesting that companies that use their profits for major growth projects may face losses in the stock market.

References

[1] Eugene F. Fama and Kenneth R. French. "Value versus Growth: The International Evidence." The Journal of Finance, Volume 53, No. 6, 1988, Pages 1975-1999.

[2] Eugene F. Fama and Kenneth R. French. "Multifactor Explanations of Asset Pricing Anomalies." The Journal of Finance, Volume 51, No. 1, 1996, Pages 55-84.

[3] Journal of Financial Economics. "A Five-Factor Asset Pricing Model." Accessed Aug. 30, 2021.

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TheQuantHackers is a cutting-edge community composed of a group of people from the world's top universities and quantitative finance practitioners, dedicated to exploring the infinite possibilities in the fields of artificial intelligence (AI) and quantification (Quant). Our team members come from world-renowned universities such as the University of Cambridge, Oxford University, Harvard University, ETH Zurich, Peking University, and the University of Science and Technology of China. Our external consultants come from first-class companies such as Microsoft, HSBC, Citadel, Man Group, Citi, Jump Trading, and top domestic private equity companies.$\begin{aligned} &R_{it} - R_{ft} = \alpha_{it} + \beta_1 ( R_{Mt} - R_{ft} ) + \beta_2SMB_t + \beta_3HML_t + \epsilon_{it} \\ &\textbf{其中：} \\ &R_{it} = \text{某股票或投资组合 } i \text{ 在时间 } t \text{ 的总回报} \\ &R_{ft} = \text{时间 } t \text{ 的无风险回报率} \\ &R_{Mt} = \text{时间 } t \text{ 的市场组合总回报} \\ &R_{it} - R_{ft} = \text{预期超额回报} \\ &R_{Mt} - R_{ft} = \text{市场组合（指数）的超额回报} \\ &SMB_t = \text{规模溢价（小盘减大盘）} \\ &HML_t = \text{价值溢价（高账面市值比减低账面市值比）} \\ &\beta_{1,2,3} = \text{因子系数} \\ \end{aligned}$

Fama和French强调，投资者必须能够承受可能在短期内发生的额外波动和周期性低表现。拥有15年或更长时期投资的投资者将因短期内的损失而获得回报。Fama和French通过对数千个随机股票投资组合进行研究，测试了他们的模型，发现当将规模和价值因子与贝塔因子结合时，可以解释多达95%的多元化股票投资组合的回报。

考虑到该模型能够解释多达95%的投资组合回报，投资者可以构建一个按照其投资组合所承担的相对风险获得平均预期回报的投资组合。推动预期回报的主要因子包括市场敏感性、规模敏感性和价值股敏感性，这些因素通过账面市值比来衡量。任何额外的平均预期回报可能归因于未定价或非系统性风险。

Fama和French的五因子模型

近年来，研究人员将三因子模型扩展到包括其他因素。这些因素包括“动量”、“质量”和“低波动性”等等。2014年，Fama和French将其模型调整为包含五个因子。在原有的三个因子基础上，新模型增加了一个概念，即未来盈利较高的公司在股市中往往具备较高的回报，这个因子被称为盈利能力。

第五个因子被称为“投资”，与内部投资和回报概念相关，表明那些将利润投入重大增长项目的公司可能在股市中面临损失。[3]

Fama-French三因子模型对投资者的意义

Fama-French三因子模型强调，投资者必须能够忍受额外波动和短期内可能出现的周期性低表现。拥有15年或更长投资期限的投资者将因短期内的损失而获利。鉴于该模型可以解释多达95%的多元化股票投资组合的回报，投资者可以根据其承担的相对风险量身定制其投资组合，以获得平均预期回报。

推动预期回报的主要因子包括市场敏感性、规模敏感性和价值股敏感性，这些因子通过账面市值比来衡量。任何额外的平均预期回报可能归因于未定价或非系统性风险。

模型的三个因子是什么？

Fama-French模型有三个因子：公司的规模、账面市值比和市场的超额回报。换句话说，模型使用的小盘股减去大盘股（SMB）、高账面市值比减去低账面市值比（HML），以及投资组合收益减去无风险回报率。SMB考虑的是市值较小的上市公司，这类公司通常能带来更高的回报，而HML则分析账面市值比高的价值股，这类股票相比市场获得更高的回报。

Fama-French五因子模型是什么？

2014年，Fama和French调整了他们的模型，扩展到五个因子。除了原有的三个因子，新模型加入了一个概念，即报告未来盈利较高的公司在股市中通常拥有更高的回报，这个因子被称为盈利能力。第五个因子被称为“投资”，与内部投资和回报方案相关，表明那些将利润用于重大增长项目的公司可能在股市中面临损失。

参考文献

[1] Eugene F. Fama and Kenneth R. French. "Value versus Growth: The International Evidence." The Journal of Finance, Volume 53, No. 6, 1988, Pages 1975-1999.

[2] Eugene F. Fama and Kenneth R. French. "Multifactor Explanations of Asset Pricing Anomalies." The Journal of Finance, Volume 51, No. 1, 1996, Pages 55-84.

[3] Journal of Financial Economics. "A Five-Factor Asset Pricing Model." Accessed Aug. 30, 2021.

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