## Multi-Factor Models

### The Three-Factor Model

1

The three-factor model was developed by Fama and French in 1992. It is a multi-factor model that includes the variables for firm size, book-to-market values and excessive returns on the market.

2

The three-factor model tries to estimate the returns of a stock based on the size of the firm, its book-to-market value and its return on the market (the return of the stock minus the risk-free rates).

3

They developed the model on the idea that smaller companies tend to deliver larger returns on the market than larger companies, with smaller companies also having a lower book-to-market value.

4

The formula is: Rit Rft= αit + β1(RMtRft) + β2SMBt+ β3HMLt+ ϵit.

Where.. Rit = total return of a stock or portfolio i at time t

Rft = risk free rate of return at time t

RMt = total market portfolio return at time t

RitRft = expected excess return

RMtRft = excess return on the market portfolio (index)

SMBt = size premium (small minus big)

HMLt = value premium (high minus low)

β1,2,3 = factor coefficients​​