# Fama French 3 Factor Model

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between systematic risk and anticipated returns. It is a model commonly used by companies to calculate their cost of capital. They may also use some other models. However, CAPM considers the systematic risk of investments, making it a prime choice for risky investments. There are some variations of the CAPM as well, such as the Fama-French Three-Factor Model.

### What is the Fama French 3 Factor Model?

The Fama-French 3 Factor Model aims to extend the usefulness of the CAPM. This model considers two other factors apart from the systematic risk related to an investment. Most small-cap stocks outperform markets regularly. Similarly, high book-to-market value companies tend to outperform those with a low book-to-market value.

The Fama-French model considers both possibilities. It does so by considering three factors. Firstly, it includes the market risk that CAPM already encompasses. In addition to that, it also reflects size risk and value risk. Therefore, this model extends on the CAPM functionality by considering crucial factors prevalent in the market.

Since the Fama-French 3 factor model includes more risks, it also tweaks the formula used for CAPM.

### What is the formula for the Fama French 3 Factor Model?

The Fama-French 3 factor model expands the original CAPM formula, which is as below.

Expected Rate of Return = Risk-free Rate of Return + Market Risk Premium

However, the above formula only considers the market risk. As mentioned, the Fama-French 3 factor model also includes two other risks, which are size risk and value risk. Therefore, the Fama-French 3 factor model formula is as below.

Expected Rate of Return = Risk-free Rate of Return + Market Risk Premium + SMB + HML

Mathematically, the formula for the model is as below.

r = rf + β1(rm – rf) + β2(SMB) + β3(HML)

Given below is what each of the symbols in the above formula represents.

r = Expected rate of return

rf = Risk-free rate of return

β = Factor’s coefficient

(rm – rf) = Market risk premium

SMB (Small Minus Big) = Size premium

HML (High Minus Low) = Value premium

### What is the Importance of the Fama French 3 Factor Model?

The Fama-French 3 factor model explains more than 90% of the diversified portfolio’s returns. In comparison, the CAPM only explains 70% of it. It considers any outperformance tendencies of the two types of stocks mentioned above. By including the two extra risk factors, the Fama-French 3 factor model provides more flexibility to investors.

The model also explains that over a long time, investors get rewards for any losses they suffer in the short-term. Therefore, they can absorb any short-term volatility and periodic underperformances over a short period of time. Recently, there has been another variant of the Fama-French 3 factor model which considers even more factors.

The Fama-French Five-Factor Model is a recent development based on the three-factor model that considers some additional factors. These include low volatility, momentum, and quality. Overall, the Fama-French model is crucial for investors looking to move beyond the traditional CAPM.

### Conclusion

The Capital Asset Pricing Model is a financial model that explains the relationship between systematic risk and anticipated returns. The Fama-French 3 Factor Model extends on CAPM’s functionality by considering two additional factors. These include size risk and value risk. This model is crucial for various reasons mentioned above.

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