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ABOUT FAMA-FRENCH THREE FACTOR MODEL

In asset pricing and portfolio management the Fama-French three factor model is a model

designed by Eugene Fama and Kenneth French to describe stock returns.

The traditional asset pricing model, known formally as the Capital Asset Pricing Model, CAPM,

uses only one variable, beta, to describe the returns of a portfolio or stock with the returns of the

market as a whole. In contrast, the FamaFrench model uses three variables. Fama and French

started with the observation that two classes of stocks have tended to do better than the market as

a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (BtM, customarily

called value stocks, contrasted with growth stocks). They then added two factors to CAPM to

reflect a portfolio's exposure to these two classes:

Here r is the portfolio's rate of return, R f is the risk-free return rate, and K m is the return of the

whole stock market. The "three factor" is analogous to the classical 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.

These factors are calculated with combinations of portfolios composed by ranked stocks (BtM

ranking, Cap ranking) and available historical market data. Historical values may be accessed

on Kenneth French's web page.

Moreover, once SMB and HML are defined, the corresponding coefficients b s and bv are

determined by linear regressions and can take negative values as well as positive values. The

Fama-French Three Factor model explains over 90% of the diversified portfolios returns,

compared with the average 70% given by the CAPM (within sample). The signs of the

coefficients suggested that small cap and value portfolios have higher expected returnsand

arguably higher expected riskthan those of large cap and growth portfolios.

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TESTING OF THE MODEL IN INDIA:

The model has been tested on Ultra Tech Cement Ltd.

Data Set:

A universe of 30 companies that form a part of the SENSEX was taken to identify the big

and small companies, according to asset base, and those with highest and lowest Book to

Market ratios. The test has been done over the time period of one financial year 2009-2010, where in

monthly close values of share prices have been taken. The 91-day Treasury bill rate as on March 30, 2010 has been taken as a proxy for risk

free rate for the period concerned.

Methodology:

The thirty companies representing the market were sorted in order of their asset base and

Book to Market ratios and five companies each were selected. Their average monthly returns were computed and the values of SMB and HML were

arrived at. The other required variables were computed and a regression analysis was run using

Microsoft Excel. Such regression computed the values of beta for the different variables and all the values

were put into the equation for Expected Return. This return was compared with the actual annual return and was found to be very low.

Inference & Conclusion:

The expected return was around 49% while the actual return was as high as 103%. Such difference implies that the security was underpriced.

Limitations of the Study:

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The data set taken as a market representative was very small. The time period under analysis was short. The results of the study can be improved by working on the above limitations.