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.
Table of Contents
Introduction
Section 1
Section 2.
Section 3.
Section 4
Section 5
Objectives & Topics
This paper investigates the performance of various Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in the context of the Capital Asset Pricing Model (CAPM) using data from the Athens Exchange stock market. It aims to determine the most appropriate model for financial time series and explores whether the Beta coefficient remains constant over time using rolling regressions.
- Application and estimation of CAPM using ordinary least squares (OLS)
- Evaluation of ARCH and GARCH model variants including EGARCH, GJR-GARCH, and GARCH-M
- Statistical analysis of financial time series characteristics (leptokurtosis, stationarity)
- Implementation of rolling regressions to test the stability of Beta coefficients
- Comparative analysis between CAPM and Arbitrage Pricing Theory (APT) models
Excerpt from the Book
Section 1
As it was mentioned above the CAPM model was introduced in 1964 and four decades later is still widely used in applications, as the evaluation of managed portfolios performance (Fama and French, 2004). Sharpe pointed out that the only covariance that matters is that between the security’s return and that on the market portfolio. So the risk is known as the Beta coefficient which can be easily estimated with the simple linear regression (OLS) of the security’s return against that on the market portfolio (Booth, 1999).
The equation of the straight line has the theoretical form
Ri = a + bβi (1)
, where β is the Beta coefficient. If α is the free-risk interest rate and b is been substituted with the relation RM − RF then the CAPM model has the theoretical form
Ri = RF + βi (RM − RF) (2)
Summary of Chapters
Introduction: Provides an overview of the CAPM, its limitations regarding nonlinear financial time series, and sets the agenda for the subsequent sections.
Section 1: Discusses the theoretical framework of the CAPM and introduces various GARCH models, including EGARCH, GJR-GARCH, and GARCH-in-Mean, to account for heteroscedasticity.
Section 2: Presents a statistical and graphical summary of the selected stock time series, testing for leptokurtosis, stationarity, and ARCH effects.
Section 3: Estimates the linear CAPM model for specific stocks and the sector index, while testing for ARCH effects, autocorrelation, and the stability of the Beta coefficient.
Section 4: Applies various GARCH models to the stocks identified with ARCH effects to evaluate volatility clustering.
Section 5: Discusses and estimates an APT model using cross-sectional regression, comparing its explanatory power and reliability against the CAPM model.
Keywords
CAPM, APT, GARCH, EGARCH, GJR-GARCH, Athens Exchange, Beta coefficient, volatility, rolling regressions, heteroskedasticity, leptokurtosis, financial time series, stock returns, market portfolio, factor analysis.
Frequently Asked Questions
What is the primary focus of this research paper?
The paper examines the estimating and forecasting performance of different GARCH models in relation to the CAPM using stocks from the Technology-Software sector of the Athens Exchange.
What are the central thematic fields addressed?
The research focuses on financial econometrics, specifically volatility modeling, stock market return analysis, and model comparison between CAPM and APT.
What is the primary objective of this study?
The main goal is to evaluate if CAPM models suffer from heteroscedasticity, to identify the best-fitting GARCH model for specific time series, and to test the temporal stability of the Beta coefficient.
Which statistical methodologies are employed?
The study utilizes OLS regression, ARCH/GARCH modeling (including EGARCH, GJR-GARCH, and GARCH-M), ADF unit root tests, rolling regressions, and factor analysis.
What does the main body of the work cover?
The work provides theoretical foundations, statistical summaries of datasets, estimations of linear CAPM, subsequent GARCH modeling for volatile series, and a comparative analysis using the Arbitrage Pricing Theory (APT).
Which specific stocks are analyzed in the study?
The research analyzes stocks from the Technology-Software sector in the Athens Exchange, specifically "Unibrain", "MLS Informatics", "Dionic", "Compucon", "Centric", and "Ilyda".
Why are rolling regressions used?
Rolling regressions are used to investigate whether the slope Beta coefficient of the CAPM remains constant over time, as the results suggest that it fluctuates.
How does the performance of CAPM compare to the APT model?
While the APT model showed high explanatory power, the study concludes that for the specific five-year period and sector analyzed, the CAPM is often considered more appropriate.
What are the findings regarding the "Calendar anomalies"?
The project concludes that the General Index of the Athens Stock Market exhibited a January effect, but not a Monday effect, during the period of 2002 to 2007.
- 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
