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.
Table of Contents
1 Introduction to Risk and Return
2 Modeling Risk
2.1 Capital Asset Pricing Model
2.2 Fama-French Three-Factor-Model
2.3 Modified Fama-French Models
3 Methodology, Portfolios and Data
3.1 Time-Series Data
3.2 Procedure of the Regression
3.3 Conducting the Regression
4 Evaluation of the Regression Results
5 Conclusion
Research Objectives and Topics
This academic paper investigates and compares the explanatory power of the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and two modified versions of the Fama-French model regarding excess returns. The study aims to determine whether augmenting the standard models with autoregressive processes of the first or second order improves the model fit when evaluated against empirical financial data.
- Comparative analysis of asset pricing models (CAPM vs. Fama-French).
- Evaluation of model fit using adjusted R² and Akaike Information Criterion (AIC).
- Implementation of modified models incorporating autoregressive (AR) processes.
- Analysis of systematic risk factors and idiosyncratic risk.
- Empirical assessment of portfolio returns and statistical significance of model coefficients.
Excerpt from the Book
2.3 Modified Fama-French Models
The modified Fama-French Model (MFFM) is constructed by the author to test whether returns can be more precisely explained and predicted by enhancing the Fama-French Three-Factor-Model with autocorrelation of the returns. The author decided to test this hypothesis because some studies suggest that returns follow a short-term trend before returning to their long-term trend (mean reversion)63. The theoretical background for this deviation may be explained by time-varying risk premia or irrational behavior of market participants (behavioral finance) 64. Based on these explanations, returns might be autocorrelated in a certain order.
Autocorrelation is illustrated by an autoregressive process, which emphasizes that the current value of a variable depends on values that the variable took in previous periods65. The author assumes that the effect of autocorrelation of the returns solely exists in the first or up to the second order. This is premised on the expectation that the influence of more recent past values on the future return appears to be more plausible than of less current past values of the return. Therefore, a model with an autoregressive process of order one [AR(1)] and one with an autoregressive process of order two [AR(2)] have been created.
Summary of Chapters
1 Introduction to Risk and Return: Provides an overview of risk-return relationships and discusses the fundamental role of diversification and idiosyncratic vs. systematic risk.
2 Modeling Risk: Introduces the theoretical foundations of the Capital Asset Pricing Model (CAPM), the Fama-French Three-Factor Model, and the construction of the author's modified models.
3 Methodology, Portfolios and Data: Details the empirical approach, including data sources, time-series characteristics, and the regression procedures applied to the six test portfolios.
4 Evaluation of the Regression Results: Presents the statistical findings and evaluates the performance of the models using adjusted R² and AIC metrics.
5 Conclusion: Summarizes the findings, noting that while modified models show higher in-sample fit, their out-of-sample performance remains limited, confirming the limitations of asset pricing models.
Keywords
Capital Asset Pricing Model, CAPM, Fama-French Three-Factor Model, TFM, Arbitrage Pricing Theory, APT, Systematic Risk, Excess Returns, Autoregression, AR(1), AR(2), Portfolio Management, Econometric Modeling, Model Fit, Adjusted R-Squared
Frequently Asked Questions
What is the primary focus of this research paper?
The paper evaluates and compares the ability of different asset pricing models—specifically the CAPM and the Fama-French Three-Factor Model—to explain excess returns on financial portfolios.
Which specific models are being compared?
The study compares the classic Capital Asset Pricing Model (CAPM), the standard Fama-French Three-Factor Model, and two self-developed modified Fama-French models that incorporate AR(1) and AR(2) processes.
What is the main objective or research question?
The objective is to test if adding autoregressive components to the Fama-French model enhances its predictive and explanatory power regarding portfolio returns.
What scientific methods are utilized?
The author performs linear in-sample regressions on six distinct portfolios using monthly data, evaluating the results through adjusted R² values and the Akaike Information Criterion (AIC).
What topics are covered in the main body?
The main body covers the theoretical framework of risk, detailed mathematical representations of the pricing models, the data and methodology used for regression, and a comprehensive evaluation of the regression results.
Which keywords characterize this work?
Key terms include CAPM, Fama-French Three-Factor Model, Systematic Risk, Excess Returns, Autoregression, and Econometric Modeling.
Did the modified models provide significantly better results?
While the modified models showed higher in-sample fit in some cases, the author concludes that this does not necessarily prove superior explanatory power and suggests that findings might be spurious, as out-of-sample tests proved unsatisfactory.
Why did the author include an AR(2) process in the model?
The author hypothesized that including autoregressive processes of the first and second order could account for observed mean-reversion tendencies or irrational market behavior, potentially capturing trends not explained by the standard factors.
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- Christoph Lohrmann (Autor:in), 2014, Comparison of the CAPM, the Fama-French Three Factor Model and Modifications, München, GRIN Verlag, https://www.grin.com/document/304738
