what is the fama and french three factor model 
the fama and french three factor model or the fama french model for short is an asset pricing model developed in 1992 that expands on the capital asset pricing model capm by adding size risk and value risk factors to the market risk factor in capm this model considers the fact that value and small cap stocks outperform markets on a regular basis by including these two additional factors the model adjusts for this outperforming tendency which is thought to make it a better tool for evaluating manager performance investopedia joules garciaunderstanding the fama and french three factor modelnobel laureate eugene fama and researcher kenneth french former professors at the university of chicago booth school of business attempted to better measure market returns and through research found that value stocks outperform growth stocks 1 similarly small cap stocks tend to outperform large cap stocks as an evaluation tool the performance of portfolios with a large number of small cap or value stocks would be lower than the capm result as the three factor model adjusts downward for observed small cap and value stock outperformance the fama and french model has three factors the size of firms book to market values and excess return on the market in other words the three factors used are small minus big smb high minus low hml and the portfolio s return less the risk free rate of return smb accounts for publicly traded companies with small market caps that generate higher returns while hml accounts for value stocks with high book to market ratios that generate higher returns in comparison to the market 2there is a lot of debate about whether the outperformance tendency is due to market efficiency or market inefficiency in support of market efficiency the outperformance is generally explained by the excess risk that value and small cap stocks face as a result of their higher cost of capital and greater business risk in support of market inefficiency the outperformance is explained by market participants incorrectly pricing the value of these companies which provides the excess return in the long run as the value adjusts investors who subscribe to the body of evidence provided by the efficient markets hypothesis emh are more likely to agree with the efficiency side the formula is rit rft it 1 rmt rft 2smbt 3hmlt itwhere rit total return of a stock or portfolio i at time trft risk free rate of return at time trmt total market portfolio return at time trit rft expected excess returnrmt rft excess return on the market portfolio index smbt size premium small minus big hmlt value premium high minus low 1 2 3 factor coefficients begin aligned r it r ft alpha it beta 1 r mt r ft beta 2smb t beta 3hml t epsilon it textbf where r it text total return of a stock or portfolio i text at time t r ft text risk free rate of return at time t r mt text total market portfolio return at time t r it r ft text expected excess return r mt r ft text excess return on the market portfolio index smb t text size premium small minus big hml t text value premium high minus low beta 1 2 3 text factor coefficients end aligned rit rft it 1 rmt rft 2 smbt 3 hmlt it where rit total return of a stock or portfolio i at time trft risk free rate of return at time trmt total market portfolio return at time trit rft expected excess returnrmt rft excess return on the market portfolio index smbt size premium small minus big hmlt value premium high minus low 1 2 3 factor coefficients fama and french highlighted that investors must be able to ride out the extra volatility and periodic underperformance that could occur in a short time investors with a long term time horizon of 15 years or more will be rewarded for losses suffered in the short term using thousands of random stock portfolios fama and french conducted studies to test their model and found that when size and value factors are combined with the beta factor they could then explain as much as 95 of the return in a diversified stock portfolio given the ability to explain 95 of a portfolio s return versus the market as a whole investors can construct a portfolio in which they receive an average expected return according to the relative risks they assume in their portfolios the main factors driving expected returns are sensitivity to the market sensitivity to size and sensitivity to value stocks as measured by the book to market ratio any additional average expected return may be attributed to unpriced or unsystematic risk fama and french s five factor modelresearchers have expanded the three factor model in recent years to include other factors these include momentum quality and low volatility among others in 2014 fama and french adapted their model to include five factors along with the original three factors the new model adds the concept that companies reporting higher future earnings have higher returns in the stock market a factor referred to as profitability the fifth factor referred to as investment relates the concept of internal investment and returns suggesting that companies directing profit towards major growth projects are likely to experience losses in the stock market 3