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2002 | Buch

Stochastic Portfolio Theory Kapitel lesen Erstes Kapitel lesen

Stochastic Portfolio Theory

verfasst von: E. Robert Fernholz

Verlag: Springer New York

Buchreihe : Stochastic Modelling and Applied Probability

Enthalten in: Professional Book Archive

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Über dieses Buch

Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market.
Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. On a practical level, stochastic portfolio theory has been the basis for strategies used for over a decade by the institutional equity manager INTECH, where the author has served as chief investment officer.
This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.

Inhaltsverzeichnis

Frontmatter
1. Stochastic Portfolio Theory
Abstract
In this chapter we introduce the basic definitions for stocks and portfolios, and prove preliminary results that are used throughout the later chapters. The mathematical definitions and notation that we use can be found in Karatzas and Shreve (1991), and the model for continuous stock prices can be found in, e.g., Karatzas (1997), Karatzas and Shreve (1998), and Duffle (1992). The definitions, notation, and stock price model are all fairly standard in current mathematical finance, and we make a number of fairly standard assumptions to simplify the presentation.
E. Robert Fernholz
2. Stock Market Behavior and Diversity
Abstract
In this chapter we study the diversity of the distribution of capital in an equity market. Heuristically speaking, a market is “diverse” if the capital is spread among a reasonably large number of stocks. We show that the excess growth rate of the market is related to the diversity of the capital distribution, and we use this relationship to study the long-term behavior of market diversity under the hypothesis that all the stocks have the same growth rate. It might seem that in such a market, diversity would naturally be maintained, but we shall see that this is not so, and in fact, such markets have a tendency to concentrate capital into single stocks. Dividend payments are a natural means to maintain market diversity, and we investigate the structure of this mechanism. Finally, we propose market entropy as a measure of market diversity, and study a derived portfolio called the entropy-weighted portfolio.
E. Robert Fernholz
3. Functionally Generated Portfolios
Abstract
Functionally generated portfolios are a generalization of the entropy-weighted portfolio defined in Section 2.3. In this chapter we show that a broad range of functions can be used to generate portfolios, and for functionally generated portfolios, a decomposition of the relative return analogous to that of the entropy-weighted portfolio in Theorem 2.3.4 remains valid. Theorem 2.3.4 is a prototype for the general results we present here.
E. Robert Fernholz
4. Portfolios of Stocks Selected by Rank
Abstract
The distribution of capital is of fundamental importance in stochastic portfolio theory, as are functionally generated portfolios. In this chapter we shall combine these two concepts.
E. Robert Fernholz
5. Stable Models for the Distribution of Capital
Abstract
In Chapter 2 we examined certain characteristics of the distribution of capital, but since the analytical tools at our disposal were limited, the results were incomplete. In this chapter we shall apply the methods introduced in Chapters 3 and 4 to achieve a deeper understanding of the structure of the capital distribution. In particular, local times related to the market weight processes permit us to develop a detailed model for a stable capital distribution.
E. Robert Fernholz
6. Performance of Functionally Generated Portfolios
Abstract
In this chapter we analyze the simulated behavior of several functionally generated portfolios in the U.S. stock market. The portfolios we consider are the entropy-weighted portfolio of Definition 2.3.3, the D p -weighted portfolio of Examples 3.4.4 and 4.3.5, and the large-stock and small-stock portfolios from Example 4.3.2. We also look at the relative performance of the biggest stock in the market, discussed in Example 4.3.1.
E. Robert Fernholz
7. Applications of Stochastic Portfolio Theory
Abstract
In the previous chapters we have seen a number of theoretical applications of stochastic portfolio theory; in this chapter we shall consider some practical applications. As a first application, we show how the first-order model can be used in portfolio optimization. Next, we discuss a passive strategy based on a D p -weighted version of the S&P 500 Index that has been used for institutional accounts since 1996. Manager performance is related to the change in market diversity, and we analyze this relationship and consider its implications. We propose a direct method to measure the effect that changes in the distribution of capital have on portfolio return, and use this method to analyze the poor performance of value stocks during the 1990s. Our analysis indicates that the principal cause of this disappointing performance was a shift in the capital distribution that favored the larger stocks over the period considered.
E. Robert Fernholz
Backmatter
Metadaten
Titel
Stochastic Portfolio Theory
verfasst von
E. Robert Fernholz
Copyright-Jahr
2002
Verlag
Springer New York
Electronic ISBN
978-1-4757-3699-1
Print ISBN
978-1-4419-2987-7
DOI
https://doi.org/10.1007/978-1-4757-3699-1