Carhart 4-Factor Model

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Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

The Carhart four-factor model is an approach to portfolio management that adds an extra dimension to the widely recognized Fama–French three-factor model.

First proposed by Mark Carhart, this advanced model integrates a momentum factor into traditional asset pricing of stocks.

This approach broadens the analytical parameters, offering a more comprehensive and detailed understanding of market dynamics.


Key Takeaways – Carhart 4-Factor Model

  • The Carhart four-factor model adds a momentum factor to the Fama-French three-factor model, enhancing portfolio management by providing a more comprehensive understanding of market dynamics.
  • The Fama-French three-factor model explains stock market returns based on risk, value, and company size, while the Carhart model expands on this by including momentum as a factor.
  • The financial industry has seen further evolution beyond the Carhart model, with the introduction of additional factors in multi-factor models such as the Fama-French five-factor model, the Q-factor model, and the Stambaugh-Yuan four-factor model. These models aim to improve the accuracy of predicting stock returns and understanding market behavior.


The Fama–French Three-Factor Model

In order to fully appreciate the Carhart four-factor model, one must first understand the foundational Fama–French three-factor model.

Developed in the 1990s, the Fama–French model put forward the argument that the majority of stock market returns could be explained by three factors:

  • risk
  • value, and
  • company size

Risk, represented by the market risk premium, reflects the difference between the expected return on the market portfolio and the risk-free rate.

This parameter has been a cornerstone of asset pricing models since the advent of the Capital Asset Pricing Model (CAPM).

Value stocks, typically those with high book-to-market ratios, have historically outperformed their counterparts.

This has been substantiated by numerous studies, including one by Fama and French in 1992, where they analyzed stock returns from 1963 to 1990 and found that high book-to-market stocks earned significantly higher average returns than low book-to-market stocks.

Company size has also been shown to play a role in determining stock returns.

Small-cap stocks, or those with smaller market capitalizations, have been found to outperform large-cap stocks.

In the same study by Fama and French, small firms exhibited an average return of 17.5% compared to 12.5% for large firms from 1963 to 1990.


The Carhart Four-Factor Model

Mark Carhart introduced the fourth factor, momentum, to this pre-existing model in 1997.

The momentum factor is defined as the speed or velocity of price changes in a stock, security, or tradable instrument.

It assumes that stocks that have performed well in the past will continue to perform well, and conversely, stocks that have performed poorly will continue to perform poorly.

Carhart’s inclusion of momentum as a factor came after an extensive study on mutual fund performance from 1962 to 1993.

He found that momentum significantly impacts stock returns, concluding that the Fama–French model, without the momentum factor, could not explain the entirety of stock returns.

Carhart’s Four Factor Model, also known in the industry as the Monthly Momentum Factor (MOM), led to more accurate predictions and improved understanding of the behavior of financial markets.

For instance, the model proved better at explaining the cross-sectional variation in average stock returns than its three-factor predecessor.


Fama French Carhart Model


Evolution Beyond the Four-Factor Model

Since the development of the Carhart Four-Factor Model, the financial industry has witnessed the inclusion of additional factors in multi-factor models.

This evolution represents ongoing efforts to enhance the accuracy of predicting stock returns and understanding market dynamics.


The Fama-French Five-Factor Model

Firstly, the Fama-French model itself evolved into a five-factor model in 2014.

The additional two factors Fama and French added were profitability and investment.

Profitability, also termed as ‘Robust Minus Weak’ (RMW), is a quality factor.

It assumes that companies with higher profitability, defined as high operating profitability, tend to generate higher returns.

Investment, also known as ‘Conservative Minus Aggressive’ (CMA), is another factor.

It suggests that companies that invest conservatively tend to have higher returns than those investing aggressively.


The Q-Factor Model

In addition to the Fama-French Five-Factor model, the Q-Factor model, proposed by Hou, Xue, and Zhang in 2015, introduced another set of four factors:

  • investment
  • return on equity (ROE)
  • expected growth, and
  • financial leverage

Investment is similar to the factor proposed by Fama and French. The model assumes that firms with high total asset growth have lower expected returns.

Return on Equity (ROE) measures a corporation’s profitability by revealing how much profit a company generates with the money shareholders have invested.

Stocks with high ROE have historically delivered higher returns.

Expected growth is another factor incorporated in the Q-Factor model.

It suggests that firms with higher expected earnings growth tend to generate higher stock returns.

Financial Leverage, the ratio of total debt to total equity, is used to measure a company’s financial risk.

According to the Q-Factor model, firms with high financial leverage ratios tend to have lower expected stock returns.


The Stambaugh-Yuan Four-Factor Model

Another model developed around the same time is the Stambaugh-Yuan Four-Factor Model.

This model introduced mispricing factors based on characteristics like net stock issues (NSI), composite equity issuance (CEI), total accruals to total assets (TATA), and net operating assets (NOA).

The model assumes that these factors are indicators of mispricing and can predict future stock returns.


FAQs – Carhart Four-Factor Model

What Do Factor Models Do?

Factor models in finance are statistical tools used to explain and predict asset returns.

They analyze the relationship between a set of factors and the returns of a portfolio or security.

These factors represent specific characteristics or risk factors that influence asset returns, such as market risk, company size, value, profitability, momentum, and more.

By identifying and quantifying these factors, factor models help investors and portfolio managers understand and manage the sources of risk and return in their investments.

They provide insights into asset pricing, portfolio construction, and risk management strategies.

What Is Factor Investing?

Factor investing is an investment strategy in which securities are chosen based on attributes that are associated with higher returns.

These attributes, known as “factors,” are characteristics of a company or security that financial researchers have identified as driving market returns and risk over time.

Factor investing goes beyond the traditional approach of looking at asset class or sector alone and looks at the underlying elements that may drive the performance of an asset.

There are several well-known factors that investors may consider, including:

  1. Size: Smaller companies (as measured by market capitalization) tend to outperform larger ones over the long term, although they can be more volatile.
  2. Value: Companies with lower price-to-earnings (P/E) ratios and lower price-to-book (P/B) ratios have historically provided higher returns than more expensive companies.
  3. Momentum: Stocks that have performed well in the recent past tend to continue performing well in the near term.
  4. Quality: Companies with strong fundamentals, such as stable earnings, low debt, and strong management, tend to perform better over the long term.
  5. Volatility: Lower-volatility stocks have often outperformed higher-volatility stocks on a risk-adjusted basis.

Factor investing can be implemented through individual stock selection or through ETFs and mutual funds that are designed to target specific factors.

This strategy requires a thorough understanding of the factors and ongoing monitoring, as factor performance can vary over time. It is often used as part of a diversified portfolio strategy.

It is often systematic in nature.



The Carhart four-factor model represents an evolution in the understanding of market dynamics and asset pricing.

By incorporating the momentum factor into the Fama–French model, it delivers a more robust and comprehensive approach to predicting stock returns.

Supported by a substantial body of empirical evidence, it has emerged as a tool in modern portfolio management.

The evolution from the Fama-French Three-Factor Model to the Carhart Four-Factor Model, and subsequently to other models with even more factors, represents a continuing journey to capture the complex dynamics of stock returns.

These additions provide a more detailed view of the market, assisting investors and portfolio managers in their decision-making processes.

However, while these factors help in explaining and predicting returns, they should not be viewed as a guarantee of performance.

Their effectiveness can vary depending on market conditions, periods of examination, and the specific universe of stocks considered.