Carhart four-factor model: Explained | TIOmarkets
BY TIO Staff
|มิถุนายน 27, 2567The Carhart four-factor model is a financial model used to evaluate the performance of mutual funds and portfolios. It expands upon the three-factor model developed by Fama and French, adding a fourth factor - momentum - to the equation. This model is widely used in the world of finance and trading, providing a comprehensive tool for assessing the risk and return of investments.
Understanding the Carhart four-factor model is essential for anyone involved in trading, as it provides a robust framework for evaluating the performance of assets. In this glossary entry, we will delve into the details of this model, explaining its components, its uses, and its implications for trading.
Origins of the Carhart Four-Factor Model
The Carhart four-factor model was developed by Mark Carhart in 1997 as an extension of the Fama and French three-factor model. Carhart, a portfolio manager and financial researcher, introduced the momentum factor to account for the persistence of outperforming and underperforming stocks. His research showed that stocks with high returns over the past year tend to continue performing well, and vice versa.
The model was groundbreaking at the time, as it provided a more comprehensive framework for evaluating the performance of mutual funds. It has since been widely adopted in the finance industry, and is still used today as a key tool for portfolio evaluation and asset pricing.
Carhart's Contribution to Financial Modeling
Mark Carhart's introduction of the momentum factor was a significant contribution to financial modeling. Prior to his work, the Fama and French model was the dominant tool for evaluating portfolios, but it did not account for the momentum effect. Carhart's research filled this gap, providing a more complete picture of portfolio performance.
The momentum factor is now widely recognized as a key determinant of stock returns. It has been incorporated into many other financial models and strategies, demonstrating the lasting impact of Carhart's work.
Components of the Carhart Four-Factor Model
The Carhart four-factor model consists of four factors: market risk, size, book-to-market value, and momentum. Each of these factors is used to explain the excess returns of a portfolio or mutual fund.
The market risk factor is the excess return of the market portfolio, which includes all risky assets. The size factor is the difference in returns between small and large companies. The book-to-market factor is the difference in returns between high and low book-to-market companies. The momentum factor is the difference in returns between stocks that have performed well in the past and those that have performed poorly.
Understanding Market Risk
Market risk, also known as systematic risk or beta, is the risk associated with the overall market. It cannot be eliminated through diversification. In the Carhart model, the market risk factor is used to account for the excess return of the market portfolio over the risk-free rate.
This factor is based on the Capital Asset Pricing Model (CAPM), which states that the expected return of an asset is equal to the risk-free rate plus the asset's beta times the market premium. The market risk factor in the Carhart model is essentially the market premium, or the excess return of the market portfolio.
Understanding Size and Book-to-Market Factors
The size and book-to-market factors in the Carhart model are based on the Fama and French three-factor model. The size factor, also known as the small-minus-big (SMB) factor, is the difference in returns between small and large companies. The book-to-market factor, also known as the high-minus-low (HML) factor, is the difference in returns between high and low book-to-market companies.
These factors are used to account for the excess returns of small companies over large companies and high book-to-market companies over low book-to-market companies. Research has shown that small companies and high book-to-market companies tend to have higher returns than large companies and low book-to-market companies, respectively.
Understanding the Momentum Factor
The momentum factor, also known as the up-minus-down (UMD) factor, is the difference in returns between stocks that have performed well in the past and those that have performed poorly. This factor is based on the momentum effect, which states that stocks with high returns over the past year tend to continue performing well, and vice versa.
The momentum factor is the key addition of the Carhart model to the Fama and French model. It provides a way to account for the persistence of stock returns, which is not explained by the market risk, size, and book-to-market factors.
Applications of the Carhart Four-Factor Model
The Carhart four-factor model is used in a variety of applications in finance and trading. Its primary use is in evaluating the performance of mutual funds and portfolios. By accounting for the four factors, the model can provide a comprehensive assessment of a fund's or portfolio's risk and return.
In addition to portfolio evaluation, the Carhart model is also used in asset pricing. By incorporating the momentum factor, the model can provide more accurate pricing of assets, taking into account the persistence of stock returns.
Portfolio Evaluation
The Carhart model is a powerful tool for evaluating the performance of mutual funds and portfolios. By accounting for the four factors, it can provide a comprehensive assessment of a fund's or portfolio's risk and return. This can help investors and portfolio managers make more informed decisions about their investments.
For example, the model can be used to evaluate the performance of a mutual fund by comparing its returns to those of a benchmark portfolio that has the same exposure to the four factors. If the fund's returns are higher than the benchmark's, this suggests that the fund manager has skill. If the fund's returns are lower, this suggests that the fund manager lacks skill.
Asset Pricing
The Carhart model is also used in asset pricing. By incorporating the momentum factor, the model can provide more accurate pricing of assets, taking into account the persistence of stock returns. This can help investors and traders make more informed decisions about buying and selling assets.
For example, the model can be used to price a stock by estimating its expected return based on its exposure to the four factors. If the stock's actual return is higher than its expected return, this suggests that the stock is undervalued. If the stock's actual return is lower than its expected return, this suggests that the stock is overvalued.
Limitations of the Carhart Four-Factor Model
While the Carhart four-factor model is a powerful tool for evaluating portfolios and pricing assets, it has its limitations. One limitation is that it assumes that the four factors are the only determinants of stock returns. However, research has shown that there are other factors that can affect stock returns, such as liquidity and profitability.
Another limitation is that the model assumes that the relationships between the factors and stock returns are linear. However, research has shown that these relationships can be nonlinear. For example, the relationship between size and stock returns can be curvilinear, with both very small and very large companies having higher returns than medium-sized companies.
Assumption of Factor Exclusivity
The Carhart model assumes that the four factors - market risk, size, book-to-market value, and momentum - are the only determinants of stock returns. This assumption is a simplification of the complex reality of the stock market, where many other factors can affect stock returns.
Research has identified several other factors that can affect stock returns, such as liquidity, profitability, and investment. These factors are not included in the Carhart model, which can limit its accuracy in explaining stock returns. However, the model can still provide a useful approximation of stock returns, especially for large, liquid stocks.
Assumption of Linearity
The Carhart model assumes that the relationships between the factors and stock returns are linear. This means that the model expects a straight-line relationship between each factor and stock returns. However, research has shown that these relationships can be nonlinear.
For example, the relationship between size and stock returns can be curvilinear, with both very small and very large companies having higher returns than medium-sized companies. The relationship between book-to-market value and stock returns can also be nonlinear, with both very high and very low book-to-market companies having higher returns than medium book-to-market companies. These nonlinear relationships are not captured by the Carhart model, which can limit its accuracy in explaining stock returns.
Conclusion
The Carhart four-factor model is a powerful tool for evaluating the performance of mutual funds and portfolios, and for pricing assets. It provides a comprehensive framework for assessing the risk and return of investments, taking into account four key factors: market risk, size, book-to-market value, and momentum.
While the model has its limitations, it is still widely used in the finance industry, and provides a valuable tool for traders and investors. Understanding the Carhart four-factor model can help you make more informed decisions about your investments, and can enhance your understanding of the complex world of finance and trading.
Start Applying the Carhart Four-Factor Model with TIOmarkets
Now that you're equipped with the knowledge of the Carhart four-factor model, it's time to put theory into practice. Join TIOmarkets, a top-rated forex broker, and start trading on a platform where you can apply this model across 300+ instruments in 5 markets. With over 170,000 accounts opened in more than 170 countries, TIOmarkets is committed to providing you with low fees and a robust trading environment. Enhance your trading skills with our educational resources and step-by-step guides. Ready to take the next step in your trading journey? Create a Trading Account today and start trading with confidence.
Risk disclaimer: CFDs are complex instruments and come with a high risk of losing money rapidly due to leverage. You should consider whether you understand how CFDs work and whether you can afford to take the high risk of losing your money. Never deposit more than you are prepared to lose. Professional client’s losses can exceed their deposit. Please see our risk warning policy and seek independent professional advice if you do not fully understand. This information is not directed or intended for distribution to or use by residents of certain countries/jurisdictions including, but not limited to, USA & OFAC. The Company holds the right to alter the aforementioned list of countries at its own discretion.
Join us on social media
Behind every blog post lies the combined experience of the people working at TIOmarkets. We are a team of dedicated industry professionals and financial markets enthusiasts committed to providing you with trading education and financial markets commentary. Our goal is to help empower you with the knowledge you need to trade in the markets effectively.
ซื้อขายอย่างมีความรับผิดชอบ: CFD เป็นตราสารที่ซับซ้อนและมีความเสี่ยงสูงที่จะสูญเสียเงินลงทุนทั้งหมดเนื่องจากเลเวอเรจ
ผลิตภัณฑ์เหล่านี้อาจไม่เหมาะสำหรับนักลงทุนทุกคน และคุณควรแน่ใจว่าคุณเข้าใจความเสี่ยงที่เกี่ยวข้อง