If you’re an investor, financial analyst or a financial manager, by now, you’ve definitely heard of the Fama-French three-factor model.

But just because you heard about it, doesn’t mean that you understand it, what it’s used for and how to use it yourself.

And that is why we’re here!

In short, this model describes stock returns, which is one of the most important factors investors take into consideration when choosing which project, product or company is worth their time and money.

But, I’m not going to lie; the Fama-French model is a tricky business.

So, today, we will cover everything you need to know, including:

  1. What is the Fama-French three-factor model?
  2. Why is it so important?
  3. How was it created?
  4. How is it calculated?
  5. What is it used for?
  6. What other types of models exist?

We will cover all the details and yet explain everything as simple as possible.

Turn off the WIFI on your phone, grab a cup of coffee, grab a pen and paper and prepare to learn!

Buckle up!


Since the Fama-French three-factor model is one of the most known tools to describe stock returns, first, we will shortly cover why this subject is important.

You probably know from the movies that many investors out there focus on prices of stocks that are changing over time. They compare the movement of the prices from time to time.

However, this is a common mistake, and here’s why.

Stocks usually pay out in dividends – distribution of reward that is a part of the companies’ earnings to their respective shareholders.

They are managed by the companies’ board of directors and can be issued as stock, shares, cash or in other ways, while cash dividends are the most common option.

Funds, as well as companies, are often known for paying out dividends to their trusted shareholders.

To get a clear picture of how stocks perform over a period of time, we should take into consideration capital gains as well as dividends.

This is very useful when it comes to evaluating stocks and comparing investment results when stocks are held for different periods of time.


This model is actually an extension to a model which existed before – the CAPM (Capital Asset Pricing Model).

CAPM is a one-factor model, and it explains the portfolio’s returns with the amount of risk it contains, according to the market.

Basically, CAPM explains portfolio performance primarily using the performance of the market as a whole.

The Capital Asset Pricing Model

CAPM describes the relationship between expected return in stocks and systematic risk.

This is the first model of this kind. It is widely known and used for pricing risky securities and generating expected returns for assets, based on the risk and cost of capital.

The following formula is used to calculate it:

ERi = Rf + βi*(ERm – Rf)


  1. ERi= Expected return of investment
  2. Rf= Risk-free rate (time value of money)
  3. βi= Beta of the investment (a measure of risk)
  4. ERm= Expected return of the market
  5. (ERm– Rf) = Market risk premium

Logically, investors want to have compensation for the risk and the time value of money, which is represented by the risk-free rate.

The other parts of the equation are there to address all additional risks the investor is facing.

The beta of the investment measures the amount of risk the investment adds to the portfolio which resembles the market.

  1. If the Beta is greater than one, the stock is riskier than the market itself.
  2. If the Beta is equal to less than one, the formula will assume that the risk of a portfolio will be reduced.

The Market risk premium is the return expected from the market. The stock’s Beta is multiplied by the Market risk premium, and the result gives the manager or investor a required return which can be later used to figure out the value of the asset.

So, what’s the main point?

The main goal of the CAPM formula is to determine if the stock is valued as it should be.

The question CAPM answers is: is the value of the stock good when its expected return is compared to the risk and time value of money?

Disadvantages of CAPM

CAPM has been proven not to be so reliable in practice.

None the less, it is still widely used because of its simplicity. It is still one of the easiest tools to compare alternatives when investing.

But, one of the problems that this model has is that, when we include the Beta in the formula, we are assuming that the risk can be completely measured by a stock’s price volatility. But, moving the price in two different directions is not equally risky.

CAPM also assumes that the Risk-free rate stays the same during the period of discounting.

In real life, holding periods last for more than 10 years, so it’s highly unlikely that this rate stays the same for that entire period.

When the Risk-free rate is increased, the stock can end up being overvalued because the cost of capital has increased as well.

Finally, the biggest concern regarding CAPM is that future cash flows can be estimated for the process of discounting.

If this was the case, an investor or a manager could estimate the stock return value precisely, and then there would be no need for CAPM at all.

Unfortunately, CAPM wasn’t flexible enough – it used only one variable to describe stock returns. It also didn’t take into consideration situations with outperformance.


So, professors Fama and French created a new one, with two extra risk factors.

Therefore, making it a better tool for performance evaluation.

To the original factor, which is the market risk factor, two more were added.

These two (SMB and HML) were added because of their consistent contribution to portfolio performance.

Nowadays, it is very popular as a measurement for portfolio performance and for predicting future stock returns.

Even today, there is a lot of debate about the outperformance tendency:

  1. Does it happen because of market efficiency?
  2. Or does it happen because of market inefficiency?

To support the first theory, it is stated that outperformance happens because of the excess risk which value stocks and small-cap stocks.

This excess risk is the result of a higher cost of capital and greater business risk.

Supporters of the second statement explain the outperformance with incorrect pricing of the value of companies by market participants. Long-term, with value adjusts, this leads to the excess return.


This is the way of thinking on which the Fama-French model is based on:

  1. Small-cap high-value companies usually do better than the overall market
  2. Higher investments usually lead to bigger and better returns
  3. Value companies outperform growth companies

Professors Eugene Fama and Kenneth French, who were professors at the University of Chicago Booth School of Business, designed this model back in the 1990s to describe stock returns in portfolio management and asset pricing.

The Fama-French three-factor model (in future uses – the Fama-French model) pays attention to three major factors:

  1. Market risk
  2. Company size – Outperformance of small vs big companies
  3. Value factors – Outperformance of high book/market vs small book/market companies

One of the scientists, Eugene Fama, shared the Nobel Memorial Prize in Economic Sciences. This shows just how appreciated this professor is in the field of economics and how valued his work is.

His contribution to the Fama-French model led to it being widely used by investors and financial managers today to help with making important decisions.

This model is basically the result of an econometric regression of historical stock prices.

It’s based on the assumption that the riskier environment, the higher the compensation should be, which should lead to bigger earnings potential.

An interesting fact is that the model was originally designed for just 4 countries:

  1. Canada
  2. United States of America
  3. United Kingdom
  4. Japan

Of course, local factors lead to better results and conclusion than global factors, because they better explain the variation of time series in stock returns.

So, with a few adjustments and with updated risk factors, the model also became useful for Asia, Europe and other regions.


All of this seems rational, but how do I put it to use?

Well, when we talk about the Fama-French model, in order to describe stock returns, our final goal is to calculate the portfolio’s expected rate of return.

This is done with the following formula:

Portfolio’s Expected Rate of Return =

Risk-free Rate + Market Risk Premium + SMB + HML


= rf + ß1*(r– rf) + ß2*(SMB) + ß3*(HML) +  


  1. = Portfolio’s Expected Rate of Return
  2. r= Riskfree Return Rate
  3. ß1,2,3 = Factor’s Coefficient – originally there was just 1, now there are 3 of them. This is the main innovation in the Fama-French model.
  4. (r– rf= Market Risk Premium
  5. SMB(Small Minus Big) = Historic excess returns of small-cap companies over large-cap companies
  6. HML(High Minus Low) = Historic excess returns of value stocks* over growth stocks**
  7. = Risk

*Value stocks are stocks which have a high book to price ratio

**Growth stock are stocks which have a low book to price ratio

The historic excess values can be found for free on Kenneth French’s website.

Last 3
Last 12
Fama/French 3 Research Factors
Fama/French 5 Research Factors (2×3)
Fama/French Research Portfolios
Size and Book-to-Market Portfolios
Small Value
Small Neutral
Small GrowthBig Value
Big Neutral
Big Growth
Size and Operating Profitability Portfolios
Small Robust
Small Neutral
Small WeakBig Robust
Big Neutral
Big Weak
Size and Investment Portfolios
Small Conservative
Small Neutral
Small AggressiveBig Conservative
Big Neutral
Big Aggressive

Calculation of the Fama-French three-factor model is commonly done in software programs capable of handling big data. Excel is one of the most popular ones out there.

Remember, this is a three-factor model. To best explain it further, let’s look at each factor one by one.

1. Market Risk Premium

What does this part of the formula mean?

(r– rf)

The market risk premium basically represents the difference between the expected return of the market and the risk-free return rate. It gives the investor returns above the risk-free rate.

2. Small minus big market capitalization (SMB)

This factor is commonly known as the “small firm effect”. or the “size effect”, where size is determined by the company’s market capitalization. It represents a historic excess of small-cap companies over large-cap companies.

A side effect which is based on the market capitalization of a company is SMB. Its factor’s coefficient is calculated via linear regression, and it can have negative and positive values.

Again, the logic behind the Fama-French model is that higher returns come from small-cap companies, rather than large-cap companies.

3. High minus low book-to-market ratios (HML)

HML is used to show the spread in returns between companies which have high and companies which have a low book to market ratios (value companies and growth companies).

Its factor’s coefficient is also calculated using linear regression, and it can have a negative as well as a positive value.

This third factor shows that in the long run, growth companies have lower returns than value companies. This is why they are at the second place in the formula.

The HML factor is used to evaluate profit margins, short-term and long-term. It states the anticipated performance of security in the future. In the formula high minus low, we calculate the associated range.

Using HML we can see if a manager is relying on the value premium to earn an abnormal return, by investing in stocks with high book-to-market ratios.

If this is the case, then a positive relation to the HML factor is shown.

This explains why the portfolios returns are accredited only to the value premium. The original excess of the manager will decrease because the model is able to explain more of the portfolio’s return.

It’s not officially stated by the creators, Fama and French, why book-to-price ratios measure risk.

However, there are theories that have been mentioned. If a stock has a high book-to-price ratio, it could mean that the stock is “distressed”.

This means that it’s not likely for future earnings to happen and that is the reason why the stock is selling low.

It could also mean that the stock capital is intensive. Intensive stock capital happens when stocks are more vulnerable to low earnings during slow times in economics.

What would happen if a firm which isn’t capital intensive were to become “distressed”?

This is one of the questions these theories do not answer. They both make sense, but when you think about them, they explain completely different situations.

There is a third theory which states that the broad market index weighs stocks in accordance to the market capitalization. This makes it biased to size and blind for valuation.

This leads to thinking that the added two factors in this model are just a couple of tweaks, which address these problems.

This is the reason why momentum was added as another factor, to show where capitalization has been putting their money lately, instead of showing where it has been put for years, like the market capitalization factor shows.

Momentum was later added as a factor to a different version of the Fama-French model, but we will cover more on that later in the article.


All of this is fine to me, but how do I put in practice what I’ve learned here?

Well, we’ve established that when we look long-term, small companies have a tendency to outperform large companies. Also, value companies do better than growth ones.

Fama and French studied the model further and found that it can explain the majority of diversified portfolio returns.

It explains a whole 90% of it to be exact, where the original CAPM described just 70% of diversified portfolio returns.

I’m an investor, how do I use this model?

Fama and French insist that investors must be ready to handle extra periodic underperformance and short-term volatility that can happen in a short period of time.

To put it bluntly – if you are investing for 10 or more years, you will be rewarded in the long run for your periodic losses in the short run.

When you combine size and value factors with their beta factors, they explain about 90% of the return in your diversified stock portfolio.

This was proven when Fama and French ran their studies with thousands of random stock portfolio to test their model.

With this model, you as an investor can construct a portfolio where you can see the average expected return, all according to the relative risks you’ve assumed.

The main factors which drive the expected returns are:

  1. market sensitivity
  2. size sensitivity
  3. value stocks sensitivity, measured by the book to market ratio

If any additional average expected return occurs, it is attributed to unsystematic or unpriced risk.

Using the model, it is possible to separate the skill of the investor from the higher returns.

If the three factors can completely explain the portfolio’s performance, what is the manager doing?

The high returns didn’t happen because of his or her abilities or skills.

Well, the manager should contribute to good performance by picking good stocks. Unfortunately, there isn’t a formula yet which makes decisions for you perfectly. Making good decisions is still a skill only people possess.

A lot of studies in emerging markets were conducted to see how the model would handle in that territory.

The High Minus Low book-to-market ratio still explains everything it should very well.

Unfortunately, the same can’t be said for the market value of equity factor. This is why a fresh three-factor model was introduced by Foye, Mramor and Pahor in 2013.

They replaced the market value of equity factor with a more useable one.


The Fama-French model has gone through changes over time. Now, there are also the four-factor and the five-factor versions of the model, which require more information to calculate but give more detailed results.

1. The Four-Factor model

This is an extension to the regular three-factor model, created by Mark Carhart. It adds the momentum factor for asset pricing of stock, commonly also known as the MOM factor (monthly momentum).

What does momentum mean?

Momentum in a stock is when the stock price is rising, and it has a tendency to keep rising. Same goes for the other way around – if the stock price is declining, momentum means it will keep going down.

Monthly momentum is the difference between the equal weighted average of the lowest performing companies and the equal-weighted average of the highest performing ones, lagging one month.

If a stock’s average of returns for the past 12 months is positive, we say that the stock is showing momentum.

The four-factor model is actively used as a model for management and mutual fund evaluation.

Momentum strategies are still very much used in financial markets where financial analysts give buy or sell recommendations based on the yearly price high/low.

2. The Five-Factor model

Back in 2014, two more factors were added to the original Fama-French model – profitability and investment.

The first being a simple difference between the returns of companies with high and low operating profitability, while the investment factor is the difference between the returns of companies which invest conservatively and those which invest aggressively.

The fourth factor, profitability, suggests that firms which report higher earnings in the future have higher returns in the stock market.

Investment is the fifth factor, and it is closely related to the concept of internal investments and returns. It suggests that companies which direct their profit to big growth projects are more likely to experience losses in the stock market.

It is found that the CAPM and the three-factor models, in some cases, don’t explain properly cross-sectional variations in portfolio returns.

In cases like these, the five-factor model is a much better choice for a tool for evaluation.


  1. The three factors are market risk, company size (SMB) and value factors (HML).
  2. The Fama-French model is an extension to the one-factor Capital Asset Pricing Model (CAPM). A new model was created because CAPM isn’t flexible and doesn’t take into consideration overperformance.
  3. Value companies do better on the market than the growing companies.
  4. The bigger and riskier the investment, the higher the payoff should be.
  5. Local factors explain better than global factors the variations in time series in stock returns.
  6. We use the Fama-French model to calculate the Portfolio’s Expected Rate of Return.
  7. No matter how precisely this model describes the stock returns, it is up to the managers or investors to choose where it would be good to invest.
  8. The four-factor model adds the momentum factor, which describes where the value of the stock will be based on the value trends.
  9. The five-factor model takes into consideration two extra factors – profitability and investment.


Analyzing the past is useful to learn from those experiences and drive conclusions from them.

However, investing in the future is even more important.

By investing we are giving up short-term gains in the hopes of gaining long-term gains.

That hope can be slim, and it can also be very big and reliable.

By calculating our risks and making our decisions based on the calculations, we improve our chances of gaining.

Every day, decisions for the company’s future are made by the investors and the company’s management.

  1. Should we do this new project?
  2. Should we invest in this other company?
  3. Should we invest in this?

All of these questions are hard to answer. The right investment will lead to a positive outcome for the company, while the wrong decision will lead to failure.

The pressure to make this kind of decision is huge.

Luckily, there are some tools that help us make the right decision.

The Fama-French three-factor model is one of the well-known tools, managers and financial experts or analysts use to calculate whether an investment is worth the time and the money or not. It takes into consideration three factors which best describe the stock return value.

Before you go on to decide your next big investment move, be sure to use this tool to up your chances of success.

Hopefully, with this article, you’ve understood all the ins and outs of the Fama-French model, and you are now ready to use it!

We hope that by next time we see each other, you’ll have already seen the payoff of your smart investments! Remember – good luck favors well-calculated risks!

The Definitive Guide to Fama-French Three-Factor Model

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