If you’re interested in finance, you’ve probably heard of the Carhart Four Factor Model. Created by Mark Carhart in 1997, it’s a widely accepted method for analyzing the risk and return of investment portfolios. But what exactly is this model, and how does it work?
At its core, the Carhart Four Factor Model seeks to explain the excess returns of mutual funds. It breaks down these returns into four distinct factors: market risk, size risk, value risk, and momentum risk. By using these factors, investors can gain a more nuanced understanding of an investment’s performance and make more informed decisions.
But where did the Carhart Model come from, and how does it differ from other models in finance? And perhaps more importantly, how can you use it to improve your own investment strategy? In this blog post, we’ll explore the history and mechanics of the Carhart Four Factor Model, compare it to other popular models like the FamaFrench 5Factor Model and the UMD Factor, and provide a stepbystep guide to calculating the model’s four factors. By the end, you’ll have a comprehensive understanding of the Carhart Four Factor Model and how it can benefit your investment portfolio.
Carhart Four Factor Model
If youâ€™re an investor, youâ€™re likely looking for ways to maximize your returns and minimize your risks. One model that can help with this is the Carhart Four Factor Model. This model was developed in 1997 and uses four factors to explain the variation in portfolio returns.
The Four Factors
The four factors in the Carhart Four Factor Model are:
 Market risk
 Size risk
 Value risk
 Momentum risk
Market risk is the risk associated with investing in the overall stock market. Size risk is the risk associated with investing in small companies. Value risk is the risk associated with investing in companies that are considered undervalued. Momentum risk is the risk associated with investing in companies that have had good recent returns.
How it Works
The Carhart Four Factor Model works by analyzing the returns of a portfolio based on these four factors. By understanding how much of a portfolioâ€™s returns are driven by these factors, investors can adjust their investments to take advantage of the most profitable factors while minimizing risks.
For example, if the market is performing well, an investor can choose to invest in large companies to take advantage of size risk. If the market is performing poorly, an investor can choose to invest in undervalued companies to take advantage of value risk.
The Carhart Four Factor Model is a great tool for investors who want to maximize their returns and minimize their risks. By analyzing the four factors of market risk, size risk, value risk, and momentum risk, investors can make more informed decisions about their investments. If youâ€™re an investor looking for a way to optimize your portfolio, the Carhart Four Factor Model is definitely worth checking out.
Understanding the UMD Factor in the Carhart Four Factor Model
One of the most exciting applications of the Carhart Four Factor Model in finance research is the identification of the UMD factor. The UMD factor or UpminusDown factor is an indicator of the momentum in the financial market. It accounts for the difference in returns between winning stocks and losing stocks, which is sometimes referred to as the “winnerminusloser” effect. In this section, we delve deeper into the UMD factor, its calculation, interpretation, and significance in the Carhart Four Factor Model.
Calculation of the UMD Factor
The UMD factor in the Carhart Four Factor Model is calculated by subtracting the average monthly returns of the bottom decile of stocks based on their past performance from the average monthly returns of the top decile of stocks based on their past performance. The resulting difference is the value of the UMD factor for that month.
Interpretation of the UMD Factor
The UMD factor tells us whether the investors’ sentiment towards winning stocks or losing stocks is stronger. A positive value of the UMD factor indicates that the winning stocks outperform the losing stocks, suggesting there is momentum in the financial market. Alternatively, a negative value of the UMD factor indicates that the losing stocks outperform the winning stocks, suggesting the presence of mean reversion in the market.
Significance of the UMD Factor
The UMD factor is a vital component of the Carhart Four Factor Model as it enhances the model’s ability to explain asset pricing anomalies above and beyond the standard threefactor model. It accounts for the tendency of investors to perpetuate their investment decisions based on past performance, leading to a more profound effect of momentum in the market than predicted by the threefactor model. Incorporating the UMD factor in asset pricing models can improve their explanatory power and provide a better understanding of the financial market’s dynamics.
In conclusion, the UMD factor is a crucial element in the Carhart Four Factor Model as it captures the momentum effect in the financial market. It provides investors with insights into the trend of winners vs losers in the market, enhancing their ability to make informed investment decisions. By accounting for the momentum effect in asset pricing, researchers and investors can better understand the dynamics of the financial market.
Mark Carhart: The Creator of Carhart Four Factor Model
Mark Carhart is an American economist who is best known for his development of the Carhart Four Factor Model. He earned a Ph.D. in Finance from the University of Chicago in 1985 and has spent over 30 years in the financial industry.
Early Career
Carhart began his career as a professor at the University of Southern California and the University of Chicago. He later transitioned to the financial industry, where he spent several years working for the investment management firm Goldman Sachs.
The Carhart Four Factor Model
In 1997, Carhart published a paper titled “On Persistence in Mutual Fund Performance,” which introduced the Carhart Four Factor Model. The model measures fund performance based on four factors: market risk, size, value, and momentum.
Impact on the Financial Industry
The Carhart Four Factor Model has had a significant impact on the financial industry. It has been widely used by investors to analyze mutual fund performance and has helped to improve the accuracy of fund ratings.
Current Work
Carhart is currently a professor of finance at the Johnson Graduate School of Management at Cornell University. He continues to research and publish papers on various topics related to finance and economics.
In conclusion, Mark Carhart’s contribution to the financial industry cannot be overstated, and his Carhart Four Factor Model has revolutionized the way investors analyze mutual fund performance. His work continues to impact the financial world, making him a highly respected figure in the industry.
Carhart (1997)
In 1997, Mark Carhart published a study titled “On Persistence in Mutual Fund Performance.” This study was groundbreaking, as it introduced the fourfactor model for securities analysis. The “carhart four factor model,” as it’s commonly called, includes the market factor, size factor, value factor, and momentum factor.
The Market Factor
The market factor is the most straightforward of the four. It’s the return that investors can expect from investing in the broad market, typically represented by the S&P 500 index. This factor is essential because it provides a benchmark against which investors can measure the performance of their investments.
The Size Factor
The size factor refers to the returns of smallcap stocks compared to largecap stocks. Smallcap stocks have historically outperformed largecap stocks, and this factor attempts to capture the excess returns that come from investing in smallcap stocks.
The Value Factor
The value factor compares the returns of value stocks to growth stocks. Value stocks are those that have low pricetobook ratios, while growth stocks are those that have high pricetobook ratios. Historically, value stocks have outperformed growth stocks, and this factor attempts to capture that trend.
The Momentum Factor
The momentum factor measures the returns of stocks that have recently performed well. It attempts to capture the trend that “winning” stocks tend to keep winning, at least in the short term.
Carhart’s study showed that mutual funds could persistently beat the market by using these four factors to select and weight stocks. The study was a gamechanger, as it showed that there was more to securities analysis than simply looking at a company’s financials. These factors became the foundation of modern securities analysis and are widely used by investors and fund managers today.
Four Factor Capital LLC
Four Factor Capital LLC is an investment management firm that specializes in quantitative and systematic strategies. The firm’s investment approach is based on the Carhart four factor model, which is a widely used model that helps investors to make better investment decisions. In this section, we will explore Four Factor Capital LLC in more detail and explain how the firm uses the Carhart four factor model to generate alpha.
Overview of Four Factor Capital LLC
Based in New York City, Four Factor Capital LLC was founded in 2008 by a team of experienced investment professionals. The firm’s mission is to create alpha for its clients by using quantitative and systematic investment strategies. Four Factor Capital LLC currently manages approximately $611 million in assets under management (AUM).
Investment Strategy
Four Factor Capital LLC’s investment strategy is based on the Carhart four factor model, which was introduced by Mark Carhart in 1997. The model uses four factors to explain the performance of stocks: market risk, size, value, and momentum. The firm’s investment team uses this model to identify mispricings in securities and generate alpha.
Performance
Four Factor Capital LLC has a track record of producing strong riskadjusted returns over the long term. The firm’s flagship fund, the Four Factor Fund LP, has delivered an annualized return of 9.32% since its inception in 2009, with a Sharpe ratio of 1.63. The fund has outperformed its benchmark, the Russell 3000 Index, by 3.01% annually.
Four Factor Capital LLC is a leading investment management firm that uses the Carhart four factor model to generate alpha for its clients. The firm’s investment approach is based on a quantitative and systematic strategy that has delivered strong riskadjusted returns over the long term. Investors who are interested in a factorbased investment approach may want to consider Four Factor Capital LLC as a potential investment option.
FourFactor Model in Finance
In finance, the fourfactor model is a way of predicting the returns on investment in the stock market. The model takes into account four broad categories that are thought to be major drivers of stock returns. These include:
Market Risk Premium
This factor is the excess return an investor can expect to receive by investing in the stock market over the nominal riskfree rate. It’s a reflection of the extra risk investors are taking on by investing in the market rather than a completely safe investment.
Size Premium
This factor indicates that smaller companies tend to outperform larger companies in the stock market, all other things being equal. It’s often measured by comparing the performance of smallcap stocks to that of largecap stocks.
Value Premium
Value stocks are those that are trading at a lower price relative to their intrinsic value. This factor indicates that value stocks tend to outperform growth stocks, which are those that are trading at a higher price relative to their intrinsic value.
Momentum Premium
This factor suggests that stocks that have performed well in the past are likely to continue performing well in the future. It’s often measured by looking at the performance of stocks over a period of six to 12 months.
The fourfactor model is a popular tool used by finance professionals to help them predict stock returns. While it’s not a perfect predictor, it does take into account multiple factors that can impact returns, making it a useful tool for investors looking to make informed decisions.
In summary, understanding the fourfactor model is an important aspect of investing in the stock market. By taking into account the different factors that can impact returns, investors can make informed decisions that can lead to better overall performance.
FamaFrench 5Factor Model
The Carhart fourfactor model is an extension of the FamaFrench threefactor model and seeks to explain stock returns by including a fourth factor, momentum. However, some researchers believe that the FamaFrench model still lacks the ability to explain all the variations observed in the market. As a result, Fama and French proposed the FamaFrench 5factor model, which includes two additional factors that may better capture the sources of variation in stock returns.
Factors in the FamaFrench 5Factor Model
The FamaFrench 5factor model includes the same factors as the 3factor and 4factor models, which are Size, BooktoMarket, and Market Risk, and momentum. The two additional factors are:

Investment factor: This factor attempts to capture the effect of corporate investment on stock returns. The investment factor is defined as the difference in returns between firms with high and low levels of asset growth.

Profitability factor: This factor captures the effect of earnings quality on stock returns. The profitability factor is defined as the difference in returns between firms with high and low profitability ratios.
Criticisms of the FamaFrench 5Factor Model
While the FamaFrench 5factor model has been widely accepted, it has also received some criticism. Some argue that the addition of the investment and profitability factors is not justified. For instance, the investment factor has been criticized for its lack of robustness and the difficulty of measuring it. The profitability factor has also been criticized for the possibility of being a spurious factor that overlaps with other factors.
In conclusion, the FamaFrench 5factor model is an extension of the FamaFrench 3factor and 4factor models. It seeks to capture the sources of variation in stock returns by including two additional factors: investment and profitability. While some criticized these additional factors, the FamaFrench 5factor model remains one of the most widelyused models for explaining stock returns.
Understanding Fama Four Factor Model
When it comes to investment, everyone wants to know how to maximize their returns. Eugene Fama and Kenneth French, two finance researchers, introduced the FamaFrench ThreeFactor Model in 1993. They later added a fourth factor in 2015, making it the Fama Four Factor Model.
What is Fama Four Factor Model
The Fama Four Factor Model is a mathematical tool used to analyze and predict stock market returns. The model attempts to explain the returns earned by investors by incorporating four variables that have historically affected stock prices. These variables are:
 Market Risk Premium
 Size effect
 Value effect
 Profitability effect
The Market Risk Premium (MRP) is the extra return investors expect to receive for taking on the risk of investing in the stock market. On the other hand, the Size Effect refers to the observation that smaller companies have higher returns than larger companies. The Value Effect refers to the observation that cheaper stocks have higher returns than more expensive stocks. Lastly, the Profitability Effect refers to the observation that more profitable companies have higher returns than less profitable companies.
Why is Fama Four Factor Model Important
The Fama Four Factor Model is incredibly important because it allows investors to make more informed decisions about their investments. By incorporating these four variables into their analysis, investors can gain a better understanding of why certain stocks perform better than others. They can also use the model to help them identify which stocks are likely to perform well in the future.
Overall, the Fama Four Factor Model has become an essential tool for investors looking to maximize their returns. By incorporating this model into their analysis, investors gain a competitive edge in the stock market.
The 4 Factors of the Carhart Model Explained
The Carhart model is a financial model that helps investors to estimate the risk and return of investment in stocks. It is named after its creator, Mark Carhart, who came up with the model in 1997. The Carhart model has four factors that investors must consider when analyzing the performance of a stock. These factors are:
Market Risk
Market risk refers to the risk of investing in the stock market in general. The stock market can be volatile, and the prices of stocks can fluctuate wildly. Market risk is one of the most significant risks in the Carhart model, and investors should always consider it when analyzing the risk and return of investment.
Size Risk
Size risk refers to the size of the company that the investor is investing in. Smaller companies tend to be riskier than larger companies. Therefore, investing in a small company can yield high returns, but it can also lead to significant losses.
Value Risk
Value risk refers to the price of the stock relative to the company’s fundamentals. Value stocks are stocks that are undervalued by the market, while growth stocks are stocks that are overvalued by the market. Value risk is an essential factor in the Carhart model since investing in undervalued stocks can lead to high returns.
Momentum Risk
Momentum risk refers to the tendency of stocks to continue performing well or poorly over a short period of time. Momentum stocks are those that have been performing well in the market and can continue to do so in the future. Momentum risk is another crucial factor in the Carhart model as it is a significant driver of stock returns over a short period.
In summary, the Carhart model has four factors that investors must consider when analyzing the performance of a stock. These factors are market risk, size risk, value risk, and momentum risk. By considering these factors, investors can make informed decisions about which stocks to invest in and which stocks to avoid.
How Do You Calculate the Carhart Four Factor Model
The Carhart four factor model is a widelyused and wellregarded method for determining the return on investment in the context of the stock market. Understanding how to calculate the Carhart four factor model is essential for investors who are looking to make informed financial decisions. In this subtopic, weâ€™ll provide a brief overview of the four factors that make up the Carhart four factor model and delve into the steps involved in calculating it.
The Four Factors of the Carhart Four Factor Model
The Carhart four factor model measures the return on an investment based on four primary factors – market risk, size, value, and momentum.

Market risk: This factor is also known as beta, which is a measurement of an asset’s volatility compared to the overall market. A beta of 1 indicates that a stock’s price will fluctuate in the same way as the market as a whole, whereas a beta greater than 1 implies that it is more volatile than the market.

Size: This factor is based on the idea that smaller companies tend to outperform larger companies. This notion is known as the “size effect,” and it has been observed across various markets, including the stock market.

Value: The value factor is based on the belief that undervalued stocks tend to outperform overvalued stocks. This factor looks at the pricetobook ratio, which measures a company’s equity value relative to its book value.

Momentum: This factor takes into account the momentum of a stock’s price, which is based on the assumption that stocks with strong past performance tend to continue performing well for some time.
Calculating the Carhart Four Factor Model
To calculate the Carhart four factor model, you need to follow these steps:
 Collect the necessary data for your investment.
 Calculate the monthly returns for your investment.
 Calculate the excess returns for each factor by subtracting the riskfree rate from the factor returns.
 Regress the excess returns of your investment on the four factors: market risk, size, value, and momentum.
 Use the regression coefficients to determine the proportion of your investment’s return that can be attributed to each factor.
While this may seem complex, many websites provide calculators that make it easy to calculate the Carhart four factor model. It may also be helpful to consult with a financial advisor who can provide additional guidance on this method.
In conclusion, the Carhart four factor model is an essential tool for investors who are looking to make informed financial decisions. While it may seem complex at first, understanding the four factors that make up this model and the steps involved in calculating it is necessary for anyone looking to invest in the stock market.