1. Moving from the CAPM to Fama-French 3-factor Model

1. The CAPM drawbacks

The linear relationship between the return required on an investment and its systematic risk is represented by the CAPM formula.

 However the CAPM model is based is the following assumptions:

1.      Investors hold diversified portfolios. This assume that investors only require a return for the systematic risk of their portfolio, since the unsystematic risk has been removed  and can be ignored.

2.      Single-period transaction horizon. A standardize holding period is assumed  by the CAPM in order to make comparable the returns on different securities, so this makes useless compare a return over six months to an investment over 12 months.

3.      Perfect capital market. The assumption means that all securities are valued correctly and their returns will plot on the SML. A perfect capital market requires:

·         There are no taxes or transaction costs.

·         Perfect information is freely available to all investors having the same expectations

·         All investors are risk averse

·         All investors are rational and desire to maximize their own utility

·         There are a large number of buyers and sellers.

2. Moving to the Fama-French 3-factor Model

The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to describe the returns of a portfolio or stock with the returns of the market as a whole, describing only 70% of the diversified portfolios. However we are going to use improved version of the CAPM called the Fama-French Three-Factor Model which explain over 90%.

Fama and French started observing that there 2 classes of stocks which have tended to do better than the market as a whole. Small caps and stocks with a low price/ book value. They then added two factors to CAPM.

In contrast with the CAMP, there are 2 betas more in this model.

SMBstands for "Small (market capitalization) minus Big "this is the additional return for investors who have historically received by investing in stocks of companies with relatively small market capitalization. This additional return is often referred to as the “size premium".

HML stands for "High (book-to-market ratio) Minus low", measuring value stocks over growth stocks. The higher is the P/B or P/E the more growth is expected for the company. For example if there is apple stock which has a P/E of 18 and the Google stock has a P/E of 27, means that people are willing to pay more because they expect higher returns in the future than Apple returns. Therefore the expected growth of Google is higher.

Alphaindicates how well the fund manager is capturing the expected returns, given the portfolio's exposure 

So this formula can also be represented as:

A number of studies have reported that when the Fama–French model is applied to emerging markets the book-to-market factor retains its explanatory ability but the market value of equity factor performs poorly. In a recent paper, Foye, Mramor and Pahor (2013) propose an alternative three factor model that replaces the market value of equity component with a term that acts as a proxy for accounting manipulation

Examining β and size, they find that higher returns, small size, and higher β are all correlated.

According to the Fama-French model we can determine the following matrix.

The horizontal axis is the " Value factor" represented by SMB

The vertical axis is the "Size factor" represented by HML.