Disentangling the Role of Variance and Covariance Information in Portfolio Selection Problems

Disentangling the Role of Variance and Covariance Information in Portfolio Selection Problems
Author: Andre A. P. Santos
Publisher:
Total Pages: 34
Release: 2018
Genre:
ISBN:

The covariation among financial asset returns is often a key ingredient used in the construction of optimal portfolios. Estimating covariances from data, however, is challenging due to the potential influence of estimation error involved specially in high dimensional problems, which can impact negatively the performance of the resulting portfolios. We address this question by putting forward a simple approach to disentangle the role of variance and covariance information in the case of mean-variance efficient portfolios. Specifically, mean-variance portfolios can be represented as a two-fund rule: one fund is a fully invested portfolio that depends on diagonal covariance elements whereas the other is a long-short, self financed portfolio depending on off-diagonal elements. We characterize the contribution of each of these two components to the overall performance in terms of out-of-sample returns, risk, risk-adjusted returns, and turnover. Finally, we provide an empirical illustration of the proposed portfolio decomposition using both simulated and real market data.

A Sparsity-Driven Solution Method for the Cardinality Constrained Mean-Variance Portfolio Selection Problem

A Sparsity-Driven Solution Method for the Cardinality Constrained Mean-Variance Portfolio Selection Problem
Author: Shan Jiang
Publisher:
Total Pages: 0
Release: 2023
Genre:
ISBN:

Cardinality constrained mean-variance (CCMV) portfolio selection problem is commonly formulated as a mixed integer quadratic program (MIQP) that can be solved by a branch-and-bound scheme or metaheuristics. Yet, computational efficiency remains to be a major issue. In this study, we propose a novel metaheuristic method based on the concepts of sparse recovery for solving large-size problems. Using the relationship between investment risk and portfolio sparsity, we develop a "sparsity-driven" binary search framework for solving the CCMV portfolio selection problem through a sequence of quadratically constrained sparse recovery problems. For computational efficiency, a sub-one quasi-norm minimization model is adopted to find high-quality approximate solutions of each sparse recovery problem using a specially designed gradient-descent based algorithm. Then, a final solution to the original CCMV portfolio selection problem is obtained by incorporating the approximate solution information to the binary search framework to solve one MIQP problem in a much more reduced size. Computational experiments using the historical stock data from the S&P's Compustat North America Database provided by Wharton Research Database Service clearly indicate the superior performance of the proposed approach in terms of quality of solutions and speed of computation. It runs orders faster than the commonly used CPLEX solver for solving large-size problems. Comparison with the state-of-the-art perspective reformulation approach in the literature shows that the proposed approach is more efficient for solving large-size CCMV portfolio selection problems, especially for those without a diagonally dominant covariance matrix. Another experiment with a genetic-algorithm-based heuristic method shows that the quality of solutions found by the proposed approach significantly outperforms that of the heuristic method.

Handbook of Portfolio Construction

Handbook of Portfolio Construction
Author: John B. Guerard, Jr.
Publisher: Springer Science & Business Media
Total Pages: 796
Release: 2009-12-12
Genre: Business & Economics
ISBN: 0387774394

Portfolio construction is fundamental to the investment management process. In the 1950s, Harry Markowitz demonstrated the benefits of efficient diversification by formulating a mathematical program for generating the "efficient frontier" to summarize optimal trade-offs between expected return and risk. The Markowitz framework continues to be used as a basis for both practical portfolio construction and emerging research in financial economics. Such concepts as the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT), for example, provide the foundation for setting benchmarks, for predicting returns and risk, and for performance measurement. This volume showcases original essays by some of today’s most prominent academics and practitioners in the field on the contemporary application of Markowitz techniques. Covering a wide spectrum of topics, including portfolio selection, data mining tests, and multi-factor risk models, the book presents a comprehensive approach to portfolio construction tools, models, frameworks, and analyses, with both practical and theoretical implications.

Volatility and Correlation

Volatility and Correlation
Author: Riccardo Rebonato
Publisher: John Wiley & Sons
Total Pages: 864
Release: 2005-07-08
Genre: Business & Economics
ISBN: 0470091401

In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School

Market Risk Analysis, Practical Financial Econometrics

Market Risk Analysis, Practical Financial Econometrics
Author: Carol Alexander
Publisher: John Wiley & Sons
Total Pages: 437
Release: 2008-05-27
Genre: Business & Economics
ISBN: 0470998016

Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors; Estimation of symmetric and asymmetric, normal and Student t GARCH and E-GARCH parameters; Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization; Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management; Simulation of normal mixture and Markov switching GARCH returns; Cointegration based index tracking and pairs trading, with error correction and impulse response modelling; Markov switching regression models (Eviews code); GARCH term structure forecasting with volatility targeting; Non-linear quantile regressions with applications to hedging.

GARCH Models

GARCH Models
Author: Christian Francq
Publisher: John Wiley & Sons
Total Pages: 469
Release: 2011-06-24
Genre: Mathematics
ISBN: 1119957397

This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation and tests. The book also provides coverage of several extensions such as asymmetric and multivariate models and looks at financial applications. Key features: Provides up-to-date coverage of the current research in the probability, statistics and econometric theory of GARCH models. Numerous illustrations and applications to real financial series are provided. Supporting website featuring R codes, Fortran programs and data sets. Presents a large collection of problems and exercises. This authoritative, state-of-the-art reference is ideal for graduate students, researchers and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.

Handbook of Finance, Financial Markets and Instruments

Handbook of Finance, Financial Markets and Instruments
Author: Frank J. Fabozzi
Publisher: John Wiley & Sons
Total Pages: 868
Release: 2008-11-03
Genre: Business & Economics
ISBN: 0470391073

Volume I: Financial Markets and Instruments skillfully covers the general characteristics of different asset classes, derivative instruments, the markets in which financial instruments trade, and the players in those markets. It also addresses the role of financial markets in an economy, the structure and organization of financial markets, the efficiency of markets, and the determinants of asset pricing and interest rates. Incorporating timely research and in-depth analysis, the Handbook of Finance is a comprehensive 3-Volume Set that covers both established and cutting-edge theories and developments in finance and investing. Other volumes in the set: Handbook of Finance Volume II: Investment Management and Financial Management and Handbook of Finance Volume III: Valuation, Financial Modeling, and Quantitative Tools.

High-Frequency Financial Econometrics

High-Frequency Financial Econometrics
Author: Yacine Aït-Sahalia
Publisher: Princeton University Press
Total Pages: 683
Release: 2014-07-21
Genre: Business & Economics
ISBN: 0691161437

A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Introduction to Risk Parity and Budgeting

Introduction to Risk Parity and Budgeting
Author: Thierry Roncalli
Publisher: CRC Press
Total Pages: 430
Release: 2016-04-19
Genre: Business & Economics
ISBN: 1482207168

Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of investment after the global fina

Handbook of Economic Forecasting

Handbook of Economic Forecasting
Author: Graham Elliott
Publisher: Elsevier
Total Pages: 667
Release: 2013-08-23
Genre: Business & Economics
ISBN: 0444627405

The highly prized ability to make financial plans with some certainty about the future comes from the core fields of economics. In recent years the availability of more data, analytical tools of greater precision, and ex post studies of business decisions have increased demand for information about economic forecasting. Volumes 2A and 2B, which follows Nobel laureate Clive Granger's Volume 1 (2006), concentrate on two major subjects. Volume 2A covers innovations in methodologies, specifically macroforecasting and forecasting financial variables. Volume 2B investigates commercial applications, with sections on forecasters' objectives and methodologies. Experts provide surveys of a large range of literature scattered across applied and theoretical statistics journals as well as econometrics and empirical economics journals. The Handbook of Economic Forecasting Volumes 2A and 2B provide a unique compilation of chapters giving a coherent overview of forecasting theory and applications in one place and with up-to-date accounts of all major conceptual issues. - Focuses on innovation in economic forecasting via industry applications - Presents coherent summaries of subjects in economic forecasting that stretch from methodologies to applications - Makes details about economic forecasting accessible to scholars in fields outside economics