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Fama–French three-factor model
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Fama–French three-factor model
In asset pricing and portfolio management, the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were colleagues at the University of Chicago Booth School of Business, where Fama still works. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences for his empirical analysis of asset prices. The three factors are:
There is academic debate about the last two factors.
Factor models are statistical models that attempt to explain complex phenomena using a small number of underlying causes or factors. The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to compare the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables.
They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:
Here r is the portfolio's expected rate of return, Rf is the risk-free return rate, and Rm is the return of the market portfolio. The "three factor" β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work. SMB stands for "Small [market capitalization] Minus Big" and HML for "High [book-to-market ratio] Minus Low"; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks, alpha is the error term.
Fama and French defined the factors SMB and HML by constructing value-weighted portfolios based on breakpoints of the market capitalization and book-to-market (BTM) ratio. First, all NYSE, Amex, and NASDAQ stocks are split into the groups small and big using the median NYSE market capitalization, with small being stocks below, and big above the median. Second, NYSE, Amex and NASDAQ stocks are categorized into low, medium, and high book-to-market equity. These groups are defined by the ranked (i.e. from highest to lowest) BTM ratio of NYSE stocks. Low stocks are the bottom 30%, medium are the middle 40%, and high are the top 30%. Firms with a negative book value of equity were excluded from calculating the original breakpoints and portfolios. The groups are then used to form six portfolios, one for each combination of market capitalization and BTM ratio.
The factors are then determined by the simple average portfolio returns. SMB is defined as the difference between the average return of all small portfolios and the average return of all big portfolios. HML describes the difference between the average high and average low portfolio returns.
Historical factor values may be accessed on Kenneth French's web page. Moreover, once SMB and HML are defined, the corresponding coefficients bs and bv are determined by linear regressions and can take negative values as well as positive values.
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Fama–French three-factor model
In asset pricing and portfolio management, the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were colleagues at the University of Chicago Booth School of Business, where Fama still works. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences for his empirical analysis of asset prices. The three factors are:
There is academic debate about the last two factors.
Factor models are statistical models that attempt to explain complex phenomena using a small number of underlying causes or factors. The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to compare the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables.
They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:
Here r is the portfolio's expected rate of return, Rf is the risk-free return rate, and Rm is the return of the market portfolio. The "three factor" β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work. SMB stands for "Small [market capitalization] Minus Big" and HML for "High [book-to-market ratio] Minus Low"; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks, alpha is the error term.
Fama and French defined the factors SMB and HML by constructing value-weighted portfolios based on breakpoints of the market capitalization and book-to-market (BTM) ratio. First, all NYSE, Amex, and NASDAQ stocks are split into the groups small and big using the median NYSE market capitalization, with small being stocks below, and big above the median. Second, NYSE, Amex and NASDAQ stocks are categorized into low, medium, and high book-to-market equity. These groups are defined by the ranked (i.e. from highest to lowest) BTM ratio of NYSE stocks. Low stocks are the bottom 30%, medium are the middle 40%, and high are the top 30%. Firms with a negative book value of equity were excluded from calculating the original breakpoints and portfolios. The groups are then used to form six portfolios, one for each combination of market capitalization and BTM ratio.
The factors are then determined by the simple average portfolio returns. SMB is defined as the difference between the average return of all small portfolios and the average return of all big portfolios. HML describes the difference between the average high and average low portfolio returns.
Historical factor values may be accessed on Kenneth French's web page. Moreover, once SMB and HML are defined, the corresponding coefficients bs and bv are determined by linear regressions and can take negative values as well as positive values.