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A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes

A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes
Author: Yannick Malevergne
Publisher:
Total Pages: 38
Release: 2007
Genre:
ISBN:
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We derive a theoretical two-factor model which has empirically a similar explanatory power as the Fama-French three-factor model. In addition to the usual market risk, our model accounts for a diversification risk, proxied by the equally-weighted portfolio, and which results from an quot;internal consistency factorquot; appearing for arbitrary large economies, as a consequence of the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavy-tailed as in real economies. Our model rationalizes the superior performance of the Fama and French three-factor model in explaining the cross section of stock returns: the size factor constitutes an alternative proxy of the diversification factor while the book-to-market effect is related to the increasing sensitivity of value stocks to this factor.

Strategic Analysis Of Financial Markets, The (In 2 Volumes)

Strategic Analysis Of Financial Markets, The (In 2 Volumes)
Author: Steven D Moffitt
Publisher: World Scientific Publishing Company
Total Pages: 1119
Release: 2017-03-24
Genre: Business & Economics
ISBN: 9813143770
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Volume 1 of 'The Strategic Analysis of Financial Markets,' — Framework, is premised on the belief that markets can be understood only by dropping the assumptions of rationality and efficient markets in their extreme forms, and showing that markets still have an inherent order and inherent logic. But that order results primarily from the 'predictable irrationality' of investors, as well as from people's uncoordinated attempts to profit. The market patterns that result do not rely on rationality or efficiency.A framework is developed for understanding financial markets using a combination of psychology, statistics, game and gambling analysis, market history and the author's experience. It expresses analytically how professional investors and traders think about markets — as games in which other participants employ inferior, partially predictable strategies. Those strategies' interactions can be toxic and lead to booms, bubbles, busts and crashes, or can be less dramatic, leading to various patterns that are mistakenly called 'market inefficiencies' and 'stylized facts.'A logical case is constructed, starting from two foundations, the psychology of human decision making and the 'Fundamental Laws of Gambling.' Applying the Fundamental Laws to trading leads to the idea of 'gambling rationality' (grationality), replacing the efficient market's concept of 'rationality.' By classifying things that are likely to have semi-predictable price impacts (price 'distorters'), one can identify, explore through data analysis, and create winning trading ideas and systems. A structured way of doing all this is proposed: the six-step 'Strategic Analysis of Market Method.' Examples are given in this and Volume 2.Volume 2 of 'The Strategic Analysis of Financial Markets' — Trading System Analytics, continues the development of Volume 1 by introducing tools and techniques for developing trading systems and by illustrating them using real markets. The difference between these two Volumes and the rest of the literature is its rigor. It describes trading as a form of gambling that when properly executed, is quite logical, and is well known to professional gamblers and analytical traders.But even those elites might be surprised at the extent to which quantitative methods have been justified and applied, including a life cycle theory of trading systems. Apart from a few sections that develop background material, Volume 2 creates from scratch a trading system for Eurodollar futures using principles of the Strategic Analysis of Markets Method (SAMM), a principled, step-by-step approach to developing profitable trading systems. It has an entire Chapter on mechanical methods for testing and improvement of trading systems, which transcends the rather unstructured and unsatisfactory 'backtesting' literature. It presents a breakout trend following system developed using factor models. It also presents a specific pairs trading system, and discusses its life cycle from an early, highly profitable period to its eventual demise. Recent developments in momentum trading and suggestions on improvements are also discussed.

Fat-Tailed and Skewed Asset Return Distributions

Fat-Tailed and Skewed Asset Return Distributions
Author: Svetlozar T. Rachev
Publisher: John Wiley & Sons
Total Pages: 385
Release: 2005-09-15
Genre: Business & Economics
ISBN: 0471758906
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While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.

Theory of Zipf's Law and Beyond

Theory of Zipf's Law and Beyond
Author: Alexander I. Saichev
Publisher: Springer Science & Business Media
Total Pages: 176
Release: 2009-11-04
Genre: Business & Economics
ISBN: 3642029469
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Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all rm levels with random processes of rm’s births and deaths yield Zipf’s law under a “balance” condition between a rm’s growth and death rate. We nd that Gibrat’s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rms’ sizes increase asy- totically proportionally to the size of the rm and that the instantaneous growth rate increases not faster than the volatility, the distribution of rm sizes follows Zipf’s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipf’s law is more a consequence of random growth than systematic returns: in particular, for large rms, volatility must dominate over the instantaneous growth rate.

Unifying Themes in Complex Systems VII

Unifying Themes in Complex Systems VII
Author: Ali A. Minai
Publisher: Springer Science & Business Media
Total Pages: 318
Release: 2012-12-22
Genre: Science
ISBN: 3642180035
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The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists of all fields, engineers, physicians, executives, and a host of other professionals to explore common themes and applications of complex system science. With this new volume, Unifying Themes in Complex Systems continues to build common ground between the wide-ranging domains of complex system science.

Essays in Asset Pricing

Essays in Asset Pricing
Author: Junxiong Gao
Publisher:
Total Pages: 0
Release: 2023
Genre:
ISBN:
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This dissertation comprises three papers examining questions in asset pricing, investigating the implications of new asset pricing theories on the cross-section and time series of asset prices. The papers are as follows: Chapter 1 studies how the fat-tailed distribution of US firm size generates extra risk premiums compared to the classical theory. The author refers to this fat tail as "granularity" and shows that it breaks the diversification of idiosyncratic risks assumed by arbitrage pricing theory (APT) to imply factor models. In the cross-section, large firms have higher idiosyncratic risk premiums than small firms despite having a lower level of risk. This finding explains the negative relation between idiosyncratic risk and risk premium, known as the "idiosyncratic risk premium puzzle." On aggregate, the level of granularity, measured by the Pareto distribution, explains market expected returns since it determines the under-diversification of idiosyncratic risk. Chapter 2 (joint work with Rossen Valkanov and Yan Xu) investigates the joint dynamics and predictability of asset returns for the equity, treasury, and foreign asset investment sectors, utilizing their respective valuation ratios constructed from their intertemporal budget constraints. We propose a new framework that enforces an aggregate accounting identity of the three sectors using a constrained estimation by the GMM method, which accounts for the cyclical movement of the whole economy. Our key finding shows that the government surplus-to-debt ratio negatively predicts the risk premium in the equity and foreign asset investment sectors. Our results suggest that incorporating data from all three sectors and imposing aggregate budget constraints can help to better identify how the fiscal policy adjustment channel propagates throughout the economy. Chapter 3 presents a model for modeling the correlation dynamics of stock returns using a conditional factor model. In this model, the employment of factors helps to reduce the estimation dimension by presenting the asset returns' covariance matrix as a quadratic function of the conditional covariance with factors. The factor structure allows for a closed-form solution for the inverse and determinant of the covariance matrix, which is convenient for computing the likelihood function and allocating a minimum variance portfolio. The model accurately fits the realized correlation among S&P 500 stocks computed from 5-minute data. It also generates out-of-sample minimum variance portfolios with a higher information ratio.

Comparison of the CAPM, the Fama-French Three Factor Model and Modifications

Comparison of the CAPM, the Fama-French Three Factor Model and Modifications
Author: Christoph Lohrmann
Publisher: GRIN Verlag
Total Pages: 42
Release: 2015-08-18
Genre: Business & Economics
ISBN: 3668032238
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Seminar paper from the year 2014 in the subject Economics - Finance, grade: 6,0 (Schweizer Notensystem), University of Liechtenstein, früher Hochschule Liechtenstein, language: English, abstract: 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.

Asset Pricing Factor Models in the German Stock Market

Asset Pricing Factor Models in the German Stock Market
Author: Julian Fischer
Publisher: GRIN Verlag
Total Pages: 109
Release: 2021-06-14
Genre: Business & Economics
ISBN: 3346420094
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Master's Thesis from the year 2021 in the subject Business economics - Investment and Finance, grade: 1,7, University of Hannover (Institut für Finanzwirtschaft und Rohstoffmärkte), language: English, abstract: In this paper, we examine how various modern multifactor models, such as the Carhart factor model, five-factor model and its complement six-factor model by Fama and French, the q-factor model by Hou, Wue and Zhang, and the mispricing factor model by Stambaugh and Yuan perform in the German stock market. It is discernible that, depending on the application model, like factor spanning tests, different sortings, return anomalies, sector- and equity fund investigation, they often provide quite similar explanatory power, while in individual cases sometimes one and sometimes the other model performs better. The underlying factors contribute differently to the explanatory power depending on the time period. Thus, in case of doubt, the six-factor model is preferable, as it is the most versatile model. Since the establishment of the capital asset pricing model as a cornerstone of modern capital market theory in the 1960s, new investigations and studies have been built on this model on an ongoing basis. This continuously leads to extensions and modifications of the asset pricing models since then. These models can be used in various ways, for example to explain the pricing of risky financial assets under restrictive assumptions or to gain important insights into the relationship between expected return and risk of securities. These can be used in various ways, for example to explain the pricing of risky financial assets under restrictive assumptions or to gain important insights into the relationship between expected return and risk of securities. In this paper, we aim to answer the overarching research question of how modern asset pricing models perform for the German stock market. For this purpose, we first discuss the characteristics of the German stock market, followed by the milestones of the development of factor models, their empirical evidence and their factors, as well as internationally known return anomalies. In the subsequent part, five modern asset pricing models are tested in different scenarios of the German stock market, including factor spanning tests, different sortings, anomalies, sectors and in equity funds. For this purpose, various analytical methods are used and performed with the software “Stata”. Finally, the comprehensive results are summarized and concluded.

The Arbitrage Pricing Theory as an Approach to Capital Asset Valuation

The Arbitrage Pricing Theory as an Approach to Capital Asset Valuation
Author: Christian Koch
Publisher: GRIN Verlag
Total Pages: 76
Release: 2009-02-27
Genre: Business & Economics
ISBN: 364027718X
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Diploma Thesis from the year 1996 in the subject Business economics - Banking, Stock Exchanges, Insurance, Accounting, grade: 1,3, European Business School - International University Schloß Reichartshausen Oestrich-Winkel, language: English, abstract: A “few surprises” could be the trivial answer of the Arbitrage Pricing Theory if asked for the major determinants of stock returns. The APT was developed as a traceable framework of the main principles of capital asset pricing in financial markets. It investigates the causes underlying one of the most important fields in financial economics, namely the relationship between risk and return. The APT provides a thorough understanding of the nature and origins of risk inherent in financial assets and how capital markets reward an investor for bearing risk. Its fundamental intuition is the absence of arbitrage which is, indeed, central to finance and which has been used in virtually all areas of financial study. Since its introduction two decades ago, the APT has been subject to extensive theoretical as well as empirical research. By now, the arbitrage theory is well established in both respects and has enlightened our perception of capital markets. This paper aims to present the APT as an appropriate instrument of capital asset pricing and to link its principles to the valuation of risky income streams. The objective is also to provide an overview of the state of art of APT in the context of alternative capital market theories. For this purpose, Section 2 describes the basic concepts of the traditional asset pricing model, the CAPM, and indicates differences to arbitrage theory. Section 3 constitutes the main part of this paper introducing a derivation of the APT. Emphasis is laid on principles rather than on rigorous proof. The intuition of the pricing formula and its consistency with the state space preference theory are discussed. Important contributions to the APT are classified and briefly reviewed, the question of APT’s empirical evidence and of its risk factors is attempted to be answered. In Section 4, arbitrage theory is linked to traditional as well as to innovative valuation methods. It includes a discussion of the DCF method, arbitrage valuation and previews an option pricing approach to security valuation. Finally, Section 5 concludes the paper with some practical considerations from the investment community.