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Factor-based Asset Pricing Models










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Fama-French 3-factor asset pricing model

The asset pricing model, developed by Eugene Fama and Kenneth French, is widely accepted as one of the most successful Factor-based Asset-Pricing Models ever created. Derived with empirical arguments in mind,
Fama-French model provides much better fit to real data then popular
CAPM.

Fama-French 3-factor asset-pricing model corresponds to the following 3-factor regression (for further notations look in
Factor-based Asset-Pricing Models):

Three factor portfolios that enter the above equation have the following financial meaning:
  1. M represents market portfolio — the same factor that appears in CAPM.
  2. SMB (Small Minus Big) portfolio represents zero-investment portfolio that is long in small-cap stocks and short in big-cap stocks.
  3. HML (High Minus Low) portfolio represents zero-investment portfolio that is long in high book-to-market stocks (so-called “Value” stocks) and short in low book-to-market stocks (so-called “Growth” stocks).
Fama-French model is based on the observation that small cap stocks and “Value” stocks historically tend to do better than market as a whole. A very natural way to formalize this empirical fact is to write down the above regression equation. While -statistics for CAPM usually takes values of around . 0 85, Fama-French model is capable of accounting for almost all variation in individual assets.

Note. The reason why Fama-French model is so successful in fitting stock data is far form being obvious. One of intuitively appealing explanations is that SMB and HML portfolios serve as “correction factors” for a
broad-based index, commonly used as market portfolio. Since broad index puts more weight in big-cap and “growth” stocks rather than in small-caps and “value” stocks respectively, it may lead to some bias between broad-based index and practically unobservable market portfolio. It is quite possible that SMB and HML portfolios simply “correct” the broad index for the mentioned effect.

The historical data for SMB and HML portfolios can be downloaded from
Kenneth French’s website.












 
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