This paper is focused on comparing the Capital Asset Pricing Model, the Fama-French Three Factor model and two modified versions of the Fama-French Model in their ability to explain excess returns. The first modified model contains the same explanatory variables as the Fama-French Model but with an additional AR(1) process. The second modification contains instead of an additional AR(1) an AR(2) process.
Evaluated by the adjusted R² and the Akaike information criterion, the Fama-French model yields a higher model-fit than the CAPM. The modified Fama-French Model with an AR(2) process leads to significant results for the twice lagged return in the model in four out of six tested portfolios. Therefore, the in-sample regression reveals a higher model-fit of the modified Fama-French model with AR(2) in comparison to the other three models.
Since the results differ from a regression in the subsequent period, the results are most likely spurious. Nevertheless, the authors show the high-er model-fit of the Fama-French Three Factor Model in relation to the CAPM.
Inhaltsverzeichnis (Table of Contents)
- Introduction to Risk and Return
- Modeling Risk
- Capital Asset Pricing Model
- Fama-French Three-Factor-Model
- Modified Fama-French Models
- Methodology, Portfolios and Data
- Time-Series Data
- Procedure of the Regression
- Conducting the Regression
- Evaluation of the Regression Results
- Conclusion
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper aims to compare the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and two modified versions of the Fama-French model in their ability to explain excess returns. The modifications involve incorporating AR(1) and AR(2) processes. The objective is to determine which model provides the best fit for the data.
- Comparison of CAPM and Fama-French Models
- Assessment of model fit using adjusted R² and Akaike information criterion
- Analysis of the impact of AR(1) and AR(2) processes on model performance
- Evaluation of the statistical significance of regression results
- Exploration of potential spurious correlations
Zusammenfassung der Kapitel (Chapter Summaries)
Introduction to Risk and Return: This chapter introduces the fundamental concept of the relationship between risk and return in finance. It discusses the trade-off investors face between risk and expected return, highlighting the importance of defining the type of risk that warrants a risk premium. The chapter explains the significance of systematic risk (market risk) versus idiosyncratic risk (specific risk) and the diversification effect in reducing idiosyncratic risk. The limitations of the Markowitz portfolio selection model are also briefly mentioned, setting the stage for the subsequent introduction of more sophisticated models to explain asset returns.
Modeling Risk: This chapter presents three models for explaining asset returns: the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and modifications of the Fama-French model. It introduces the CAPM as a single-factor model, contrasting it with the Fama-French model's multi-factor approach rooted in arbitrage pricing theory. The chapter details the modifications to the Fama-French model, incorporating AR(1) and AR(2) processes to potentially improve its explanatory power. These modifications are central to the empirical analysis conducted later in the paper.
Methodology, Portfolios and Data: This chapter outlines the methodology used in the empirical analysis, including a description of the time-series data used, the procedure for conducting the regressions, and the specific details of the regression analysis itself. The choice of data and the detailed explanation of the regression procedure are crucial for understanding the validity and replicability of the study's results. This chapter lays the groundwork for interpreting the results presented in the subsequent chapter.
Schlüsselwörter (Keywords)
Capital Asset Pricing Model (CAPM), Fama-French Three-Factor Model, excess returns, risk, return, systematic risk, idiosyncratic risk, AR(1) process, AR(2) process, adjusted R², Akaike information criterion, portfolio returns, model fit, spurious regression.
Frequently Asked Questions: A Comprehensive Language Preview
What is the main topic of this paper?
This paper compares the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and two modified versions of the Fama-French model in their ability to explain asset excess returns. The modifications involve incorporating AR(1) and AR(2) processes. The core objective is to determine which model best fits the data.
What models are compared in this study?
The study compares the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and two modified Fama-French models that incorporate AR(1) and AR(2) processes.
What are the key themes explored in the paper?
Key themes include comparing the CAPM and Fama-French models, assessing model fit using adjusted R² and the Akaike information criterion, analyzing the impact of AR(1) and AR(2) processes on model performance, evaluating the statistical significance of regression results, and exploring potential spurious correlations.
What is the methodology used in the paper?
The methodology involves time-series data and regression analysis. The paper details the procedure for conducting the regressions, including the specific steps and considerations involved. The choice of data and regression procedure are explained to ensure the validity and replicability of the study's results.
What data is used in the empirical analysis?
The paper utilizes time-series data, the specific details of which are provided in the "Methodology, Portfolios and Data" chapter. The chapter also outlines the procedure for conducting the regressions.
How are the regression results evaluated?
The regression results are evaluated using measures such as adjusted R² and the Akaike information criterion to assess model fit. The statistical significance of the results is also evaluated.
What are the key findings of the study (in general terms)?
The study aims to determine which of the compared models (CAPM, Fama-French, and modified Fama-French models) provides the best fit for explaining asset excess returns. The specific findings are presented in the "Evaluation of the Regression Results" chapter.
What are the limitations of the Markowitz portfolio selection model, as discussed in the paper?
The paper briefly mentions the limitations of the Markowitz portfolio selection model, which serves as a basis for introducing more sophisticated models to explain asset returns, like the CAPM and Fama-French models.
What are the key concepts explained in the "Introduction to Risk and Return" chapter?
This chapter introduces the fundamental relationship between risk and return, the trade-off between risk and expected return, systematic vs. idiosyncratic risk, and the diversification effect in reducing idiosyncratic risk.
What is the role of AR(1) and AR(2) processes in the study?
AR(1) and AR(2) processes are incorporated as modifications to the Fama-French model to potentially improve its explanatory power. Their impact on model performance is a central focus of the analysis.
What are the keywords associated with this paper?
Capital Asset Pricing Model (CAPM), Fama-French Three-Factor Model, excess returns, risk, return, systematic risk, idiosyncratic risk, AR(1) process, AR(2) process, adjusted R², Akaike information criterion, portfolio returns, model fit, spurious regression.
- Quote paper
- Christoph Lohrmann (Author), 2014, Comparison of the CAPM, the Fama-French Three Factor Model and Modifications, Munich, GRIN Verlag, https://www.grin.com/document/304738
