Fundamental Factor Models: What To Move To The LHS

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Introduction

Fundamental factor models are a crucial tool in factor investing, allowing investors to identify and capture the underlying drivers of stock returns. These models are based on the idea that stock returns can be explained by a set of common factors, such as value, size, and momentum. However, when building and interpreting these models, a key decision arises: what variables to move to the left-hand side (LHS) of the regression equation. In this article, we will explore the best practices for moving known variables to the LHS of fundamental factor model regressions.

Understanding the LHS of a Regression Equation

Before we dive into the specifics of fundamental factor models, it's essential to understand the concept of the LHS of a regression equation. In a standard linear regression, the LHS represents the dependent variable, which is the variable being predicted or explained. In contrast, the right-hand side (RHS) represents the independent variables, which are the factors that are used to explain the dependent variable.

The Role of the LHS in Fundamental Factor Models

In fundamental factor models, the LHS typically represents the stock return, which is the variable being explained. The RHS, on the other hand, represents the factors that are used to explain the stock return. However, when building these models, it's common to include additional variables on the LHS, such as known factors or control variables. These variables are often referred to as "moving to the LHS" or "including on the LHS."

Why Move Variables to the LHS?

There are several reasons why investors might choose to move variables to the LHS of a fundamental factor model regression:

  • Control for known factors: By including known factors on the LHS, investors can control for their impact on the stock return and isolate the effect of the fundamental factors.
  • Improve model fit: Including additional variables on the LHS can improve the model's fit and reduce the residual variance.
  • Enhance interpretability: By including known factors on the LHS, investors can gain a better understanding of the relationships between the variables and the stock return.

Best Practices for Moving Variables to the LHS

While there is no one-size-fits-all approach to moving variables to the LHS of fundamental factor model regressions, there are some best practices to keep in mind:

  • Start with a simple model: Begin with a basic model that includes only the fundamental factors and then add additional variables on the LHS as needed.
  • Choose variables carefully: Select variables that are relevant to the stock return and the fundamental factors being examined.
  • Avoid multicollinearity: Be mindful of multicollinearity between the variables on the LHS and the fundamental factors on the RHS.
  • Monitor model fit: Regularly check the model's fit and adjust the LHS variables as needed to maintain a good fit.

Common Approaches to Moving Variables to the LHS

There are several common approaches to moving variables to the LHS of fundamental factor model regressions:

  • Including known factors: This involves including known factors, such as value or size, on the L to control for their impact on the stock return.
  • Including control variables: This involves including control variables, such as industry or sector, on the LHS to control for their impact on the stock return.
  • Including interaction terms: This involves including interaction terms between the fundamental factors and the LHS variables to capture non-linear relationships.

Example: Including Known Factors on the LHS

Suppose we are building a fundamental factor model that includes the value factor (BV/TA) and the size factor (MKT CAP). We might include the value factor on the LHS to control for its impact on the stock return:

R_{it} = \alpha_i + \beta_{i,1} (BV/TA)_{t} + \beta_{i,2} (MKT CAP)_{t} + \epsilon_{it}

In this example, the value factor (BV/TA) is included on the LHS to control for its impact on the stock return.

Conclusion

Moving variables to the LHS of fundamental factor model regressions is a crucial step in building and interpreting these models. By following best practices and choosing variables carefully, investors can create models that are more accurate and informative. Whether including known factors, control variables, or interaction terms, the key is to select variables that are relevant to the stock return and the fundamental factors being examined. By doing so, investors can gain a deeper understanding of the relationships between the variables and the stock return, ultimately leading to better investment decisions.

References

  • Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465.
  • Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-82.
  • Fama, E. F., & French, K. R. (2006). Profitability, cash flows, and the cross-section of stock returns. Financial Analysts Journal, 62(4), 48-54.
    Fundamental Factor Models: Q&A =====================================

Introduction

In our previous article, we explored the best practices for moving variables to the LHS of fundamental factor model regressions. However, we understand that there are still many questions and uncertainties surrounding this topic. In this article, we will address some of the most frequently asked questions (FAQs) related to fundamental factor models and moving variables to the LHS.

Q: What is the difference between a fundamental factor model and a traditional regression model?

A: A fundamental factor model is a type of regression model that is specifically designed to capture the underlying drivers of stock returns. Unlike traditional regression models, which focus on explaining the dependent variable, fundamental factor models focus on explaining the stock return using a set of common factors, such as value, size, and momentum.

Q: Why do I need to move variables to the LHS of a fundamental factor model regression?

A: Moving variables to the LHS of a fundamental factor model regression allows you to control for their impact on the stock return and isolate the effect of the fundamental factors. This can help you to better understand the relationships between the variables and the stock return, ultimately leading to better investment decisions.

Q: How do I choose which variables to move to the LHS of a fundamental factor model regression?

A: When choosing which variables to move to the LHS of a fundamental factor model regression, consider the following factors:

  • Relevance: Choose variables that are relevant to the stock return and the fundamental factors being examined.
  • Correlation: Avoid including variables that are highly correlated with the fundamental factors on the RHS.
  • Multicollinearity: Be mindful of multicollinearity between the variables on the LHS and the fundamental factors on the RHS.

Q: What are some common mistakes to avoid when moving variables to the LHS of a fundamental factor model regression?

A: Some common mistakes to avoid when moving variables to the LHS of a fundamental factor model regression include:

  • Including too many variables: Avoid including too many variables on the LHS, as this can lead to multicollinearity and reduce the model's fit.
  • Including variables that are highly correlated with the fundamental factors: Avoid including variables that are highly correlated with the fundamental factors on the RHS, as this can lead to multicollinearity and reduce the model's fit.
  • Failing to monitor model fit: Regularly check the model's fit and adjust the LHS variables as needed to maintain a good fit.

Q: How do I know if I have moved the right variables to the LHS of a fundamental factor model regression?

A: To determine if you have moved the right variables to the LHS of a fundamental factor model regression, consider the following factors:

  • Model fit: Check the model's fit and adjust the LHS variables as needed to maintain a good fit.
  • Interpretability: Consider whether the variables on the LHS are easy to interpret and understand.
  • Relevance: Consider whether the variables on the LHS are relevant to the stock return and the fundamental factors being examined.

Q: Can use machine learning algorithms to improve the performance of a fundamental factor model regression?

A: Yes, you can use machine learning algorithms to improve the performance of a fundamental factor model regression. Some popular machine learning algorithms for this purpose include:

  • Random forests: Random forests are an ensemble learning method that can be used to improve the performance of a fundamental factor model regression.
  • Gradient boosting: Gradient boosting is a machine learning algorithm that can be used to improve the performance of a fundamental factor model regression.
  • Neural networks: Neural networks are a type of machine learning algorithm that can be used to improve the performance of a fundamental factor model regression.

Conclusion

In conclusion, moving variables to the LHS of a fundamental factor model regression is a crucial step in building and interpreting these models. By following best practices and choosing variables carefully, investors can create models that are more accurate and informative. Whether using traditional regression models or machine learning algorithms, the key is to select variables that are relevant to the stock return and the fundamental factors being examined. By doing so, investors can gain a deeper understanding of the relationships between the variables and the stock return, ultimately leading to better investment decisions.

References

  • Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465.
  • Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-82.
  • Fama, E. F., & French, K. R. (2006). Profitability, cash flows, and the cross-section of stock returns. Financial Analysts Journal, 62(4), 48-54.