This paper examines the estimating and forecasting performance of the different and various Generalized Autoregressive Conditional Heteroscedasticity-GARCH’s models in relation to Capital Asste Pricing Model (CAPM) model. We apply the CAPM model with ordinary least squares (OLS) method to investigate if an ARCH (Autoregressive Conditional Heteroscedasticity) is presented and we are trying to decide and to analyze which GARCH model is the most appropriate and the best fitted for the financial time series that we have chosen. We apply CAPM model in the financial time series of the share prices of Technology-Software Sector in Athens Exchange stock market for the period January 1st of 2002 to October 30th of 2007 for the enterprises “Unibrain” “MLS Informatics” and “Dionic” respectively , from April 2nd of 2002 to 30th October of 2007 for the enterprise “Compucon”, from August 2nd of 2002 to 30th October of 2007 for the enterprise “Centric”, and finally from February 2nd of 2004 to 30th October of 2007 for the enterprise “Ilyda”. Additionally, we apply roiling regressions, where the full programming routines in EVIEWS and MATLAB are described detailed. We conclude that the slope β coefficient of CAPM model is not constant through the time period of rolling regressions we apply. In the final part we examine a simple Arbitrage Pricing Theory (APT) model.
Inhaltsverzeichnis (Table of Contents)
- Abstract
- Introduction
- Section 1
- Section 2
- Section 3
- Section 4
- Section 5
- Conclusions
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper aims to evaluate the performance of the Capital Asset Pricing Model (CAPM) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting and estimating the Athens Exchange Stock Market. It investigates the appropriateness of different GARCH models for financial time series data and analyzes whether the CAPM's beta coefficient remains constant over time using rolling regressions.
- Application of CAPM and GARCH models to the Athens Exchange.
- Analysis of ARCH effects and heteroskedasticity in CAPM estimations.
- Evaluation of the consistency of the CAPM beta coefficient over time.
- Comparison of CAPM and Arbitrage Pricing Theory (APT) model estimations.
- Exploration of different GARCH model specifications (EGARCH, GJR, GARCH-M).
Zusammenfassung der Kapitel (Chapter Summaries)
Introduction: This chapter introduces the paper's objective: to estimate the CAPM model introduced by Sharpe (1964) and Lintner (1965). It highlights the model's difficulty due to its nonlinear estimation of financial time series and outlines the structure of the paper, with Section 1 detailing the theoretical form of the CAPM and GARCH models, Section 2 presenting a statistical summary of the time series data, Section 3 outlining the ARCH methodology applied to the CAPM model, Section 4 covering the estimation of the GARCH models, and Section 5 discussing a simple APT model.
Section 1: This section lays the theoretical foundation by presenting the basic form of the CAPM model and its limitations, noting its reliance on unrealistic assumptions. It then introduces three major GARCH models (EGARCH, GJR, and GARCH-M) and the ARCH component model, emphasizing the importance of the disturbance term in econometric estimation and the significance of the beta coefficient in assessing risk and expected return. The section concludes with a discussion of OLS estimation and the potential non-constancy of the beta coefficient, leading into the use of ARCH methodology to explore potential ARCH effects.
Section 2: This chapter focuses on the preliminary statistical analysis of the chosen time series data from the Athens Exchange's Technology-Software sector. The goal is to assess characteristics such as leptokurtosis and stationarity, and importantly, to detect the presence of ARCH effects – a crucial step before applying more sophisticated models like GARCH. This section lays the groundwork for the subsequent model estimations, ensuring the data's suitability for the analysis.
Section 3: This section details the application of the ARCH methodology to the CAPM model. It explains how the presence of ARCH effects (heteroscedasticity) is investigated for each price index individually. The methodology involves testing for autocorrelation in the disturbance term. A key aspect discussed is the use of rolling regressions to determine if the beta coefficient (β) remains constant over time. The findings from this section directly inform the choice and application of GARCH models in the following section.
Section 4: Building on the results from Section 3, this chapter presents the estimations of the various GARCH models (EGARCH, GJR, and GARCH-M) previously introduced. The focus is on applying these models where ARCH effects are detected in the CAPM estimations. Similar to Section 3, rolling regressions are employed to analyze the stability of model parameters over time. This comparative approach allows for a thorough investigation of the most appropriate GARCH model for the data under consideration.
Section 5: This section introduces a simple APT model, contrasting its estimation (via cross-sectional regression) with a similarly estimated CAPM model. This comparative analysis allows for the assessment of the relative strengths and weaknesses of these two fundamental asset pricing models in the context of the Athens Exchange's Technology-Software sector. The section provides a concluding comparison and insights derived from contrasting the results of both models.
Schlüsselwörter (Keywords)
Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), GARCH models (EGARCH, GJR, GARCH-M), ARCH effects, heteroskedasticity, rolling regressions, beta coefficient, Athens Exchange Stock Market, financial time series, econometrics, portfolio return, risk-free rate, market portfolio return.
Frequently Asked Questions: A Comprehensive Language Preview of CAPM and GARCH Models in Forecasting the Athens Exchange Stock Market
What is the main focus of this paper?
This paper evaluates the performance of the Capital Asset Pricing Model (CAPM) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting and estimating the Athens Exchange Stock Market. It investigates the appropriateness of different GARCH models for financial time series data and analyzes whether the CAPM's beta coefficient remains constant over time using rolling regressions.
What models are used in the analysis?
The study utilizes the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), and various GARCH models, including EGARCH, GJR, and GARCH-M. These models are applied to analyze financial time series data from the Athens Exchange's Technology-Software sector.
What are the key objectives of the research?
The key objectives include applying CAPM and GARCH models to the Athens Exchange data, analyzing ARCH effects and heteroskedasticity in CAPM estimations, evaluating the consistency of the CAPM beta coefficient over time, comparing CAPM and APT model estimations, and exploring different GARCH model specifications.
What data is used in this study?
The research utilizes time series data from the Athens Exchange's Technology-Software sector. The data is statistically analyzed to assess characteristics like leptokurtosis and stationarity, and to detect ARCH effects before applying more complex models.
How is the CAPM model applied and analyzed?
The paper examines the CAPM model, highlighting its limitations and the challenges posed by the nonlinear estimation of financial time series. It investigates the presence of ARCH effects (heteroskedasticity) using autocorrelation tests on the disturbance term and employs rolling regressions to assess the constancy of the beta coefficient over time.
What role do GARCH models play in the analysis?
GARCH models (EGARCH, GJR, and GARCH-M) are used to address ARCH effects (heteroskedasticity) detected in the CAPM estimations. Rolling regressions are also applied to these GARCH models to analyze the stability of model parameters over time, allowing for a comparison of model appropriateness.
How are the CAPM and APT models compared?
A simple APT model is introduced and its estimation (via cross-sectional regression) is compared with a similarly estimated CAPM model. This comparison allows for an assessment of the relative strengths and weaknesses of these two asset pricing models in the context of the Athens Exchange's Technology-Software sector.
What are the key findings (in summary)?
The study provides a detailed analysis of CAPM and GARCH model performance in the context of the Athens Exchange. It explores the presence and implications of ARCH effects, examines the stability of the beta coefficient over time, and compares the performance of CAPM and APT models. The specific findings regarding the best-performing model and the stability of parameters are detailed within the individual sections of the paper.
What are the key terms and concepts used throughout the paper?
Key terms include Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), GARCH models (EGARCH, GJR, GARCH-M), ARCH effects, heteroskedasticity, rolling regressions, beta coefficient, Athens Exchange Stock Market, financial time series, econometrics, portfolio return, risk-free rate, and market portfolio return.
- Quote paper
- Eleftherios Giovanis (Author), 2007, Application of Capital Asset Pricing (CAPM) and Arbitrage Pricing Theory (APT) Models in Athens Exchange Stock Market, Munich, GRIN Verlag, https://www.grin.com/document/146639
