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: :r=R_f+\beta(R_m-R_f)+b_s\cdot\mathit{SMB}+b_v\cdot\mathit{HML}+\alpha 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. ==Discussion==