Fama and French Three Factor Model

The Fama and French Three Factor Model is a corollary of the Capital Asset Pricing Model (CAPM). It determines the required rate of return on an asset. This model, espoused by Eugene Fama and Kenneth French, explains the returns that one can earn from the stocks. It uses primarily three factors to assess the return, they are:

  1. Market Risk
  2. The outperformance of Small Cap Companies
  3. The outperformance of high book to market companies

Unlike CAPM, this Model is based on the size of the firms, book-to-market values, and excess market return. The three-factor model uses the following variables:

  • Small minus big (SMB) is a ‘size effect’ based on a market economy that considers publicly traded companies through with a small market cap but generates high returns.
  • High minus low (HML) is a value premium and accounts for value stocks. They generally have a high book-to-market ratio generating high returns when compared to the market.

However, the irony is the stocks have high value, and the small-cap stocks tend to regularly outdo the general market.

Essence of Using the Fama French Model

Once you grasp the usage of this model, you can design a portfolio of small-cap and value stocks with low pricing. Many investors interested in penny stock trading should make use of this to create a diversified and risk-adjusted portfolio. CAPM explains only 70% of the risk, while the rest is dependent on CAPM’s analysis of Alpha (returns). This model is far superior to CAPM as it can explain 96% of the returns in a quantifiable measure. So instead of just looking at the market performance (index such as S&P500) for the value of risk (B), this model looks at the size and value of the stock, which makes it much more intricate.

Many 401(k) portfolios in the U.S utilize this model to create a risk diversified portfolio.

Fama and French Three Factor Model

The Formula for the Fama French Model:

Rit – Rft = ait + B1 (Rmt – Rft) + B2SMBt + B3HMLt + Eit


  • Rit : the total return of the stock, I at time t
  • Rft : the risk-free rate of return at time t
  • Rmt : the total market portfolio return at the time t
  • Rit-Rft : expected an excess return
  • Rmt-Rft : the excess return on the market portfolio
  • SMBt : the size premium (also known as small minus big)
  • HMLt : the value premium (also known as high minus low)
  • B123 is factor coefficients

How does the Model work?

This model explains the positive return with over 90% of the diversified portfolio’s returns, unlike CAPM with a 70% return. Further, the returns are derived from small size and value factors, high book-to-market ratio, and related ratios. On examining the B and size, the conclusion derives that higher returns, higher B, and small size are all correlated. Later, B is returned, controlling for size, and then no relationship is found. Assuming the stocks are partitioned by size, the forecast power of B disappears.

For so many years, there has been a lot of debate whether the market’s outperformance tendency is due to its efficiency or inefficiency. In the case of market efficiency, outperformance occurs when it faces excess risk value and small-cap stocks of a high cost of capital and high business risk. While in market inefficiency, the outperformance tends to elaborate a wrongly priced company that provides the excess return value adjustment in the long run.

Importance of the Fama French Model

The Fama French Model measures the outperformance tendency. In accordance with it, over a long span of time, small-cap stocks tend to outperform the large-cap companies, and value stocks beat the growth stocks. Like the CAPM model, this model is based on the assumption of former, high-risk investments require high returns.

Further, the model extends to the five-factor in the year 2014. The fourth variable added to the model is that the companies reporting high future earnings have high returns in the stock market (profitability). At the same time, the fifth variable is an investment which relates to the concept of internal investment and returns and suggests that companies, while directing profit towards growth projects, are likely to experience losses in the market.

Where Does the Model Stand in Relation to Investors?

The model explains a short-time horizon investor enables offsetting the extra short-term volatility and underperformance occurring periodically. While long-term horizon investors (15 years or more) reward for the loss they suffered in a short span of the term after conducting research studies of about a thousand random stock portfolios. When size and value factors combine with the beta, about 95% return emerged in the diversified portfolio.

Assuming the ability of 95% portfolio return versus the whole market, the investor constructs where he can receive the average return in accordance with the relative risks assumed. Further, the main driving force behind expected returns is sensitivity to the market, sensitivity to size, and value stocks, as measured by the book-to-market ratio. Additional returns may be termed as unpriced or unsystematic risk.

Sanjay Borad

Sanjay Bulaki Borad

MBA-Finance, CMA, CS, Insolvency Professional, B'Com

Sanjay Borad, Founder of eFinanceManagement, is a Management Consultant with 7 years of MNC experience and 11 years in Consultancy. He caters to clients with turnovers from 200 Million to 12,000 Million, including listed entities, and has vast industry experience in over 20 sectors. Additionally, he serves as a visiting faculty for Finance and Costing in MBA Colleges and CA, CMA Coaching Classes.

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