In this paper, we consider an optimal portfolio de-leveraging problem, where the objective is to meet specified debt/equity requirements at the minimal execution cost. Permanent and temporary price impact is taken into account. With no restrictions on the relative magnitudes of permanent and temporary price impact, the optimal de-leveraging problem reduces to a non-convex quadratic program with quadratic and box constraints. Analytical results on the optimal de-leveraging strategy are obtained. They provide guidance on how we liquidate a portfolio according to endogenous and exogenous factors. A Lagrangian method is proposed to solve the non-convex quadratic program numerically. By studying the breakpoints of the Lagrangian problem, we obtain conditions under which the Lagrangian method returns an optimal solution of the de-leveraging problem. When the Lagrangian algorithm returns a suboptimal approximation, we present upper bounds on the loss in equity caused by using such an approximation.

In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, cont

We study optimal portfolio rebalancing in a mean-variance type framework and present new analytical results for the general case of multiple risky assets. We first derive the equation of the no-trade region, and then provide analytical solutions and conditions of the optimal portfolio under several simplifying yet important models of asset returns: uncorrelated, same non-zero pairwise correlation, and one-factor covariance model. In some cases, the analytical conditions involve one or two unknown parameters and we use combinatorial algorithms to determine their exact values. Our results provide useful and interesting insights into the problem, and sharpen our understanding of the optimal portfolio.

Control of an impartial balance between risks and returns has become important for investors, and having a combination of financial instruments within a portfolio is an advantage. Portfolio management has thus become very important for reaching a resolution in high-risk investment opportunities and addressing the risk-reward tradeoff by maximizing returns and minimizing risks within a given investment period for a variety of assets. Metaheuristic Approaches to Portfolio Optimization is an essential reference source that examines the proper selection of financial instruments in a financial portfolio management scenario in terms of metaheuristic approaches. It also explores common measures used for the evaluation of risks/returns of portfolios in real-life situations. Featuring research on topics such as closed-end funds, asset allocation, and risk-return paradigm, this book is ideally designed for investors, financial professionals, money managers, accountants, students, professionals, and researchers.

The most salient feature of security returns is uncertainty. The purpose of the book is to provide systematically a quantitative method for analyzing return and risk of a portfolio investment in di?erent kinds of uncertainty and present the ways for striking a balance between investment return and risk such that an optimal portfolio can be obtained. In classical portfolio theory, security returns were assumed to be random variables, and probability theory was the main mathematical tool for h- dling uncertainty in the past. However,the world is complex and uncertainty is varied. Randomnessis nottheonly typeofuncertaintyinreality,especially when human factors are included. Security market, one of the most complex marketsintheworld,containsalmostallkindsofuncertainty. Thesecurity- turns are sensitive to various factors including economic, social, political and very importantly, people’s psychological factors. Therefore, other than strict probability method, scholars have proposed some other approaches including imprecise probability, possibility, and interval set methods, etc. , to deal with uncertaintyinportfolioselectionsince1990’s. Inthisbook,wewantto addto thetools existingin sciencesomenewandunorthodoxapproachesforanal- ing uncertainty of portfolio returns. When security returns are fuzzy, we use credibility which has self-duality property as the basic measure and employ credibilitytheorytohelpmakeselectiondecisionsuchthatthedecisionresult will be consistent with the laws of contradiction and excluded middle. Being awarethat one tool is not enough for solving complex practical problems, we further employ uncertain measure and uncertainty theory to help select an optimal portfolio when security returns behave neither randomly nor fuzzily. One core of portfolio selection is to ?nd a quantitative risk de?nition of a portfolio investment.

Optimal execution of portfolio transactions is the essential part of algorithmic trading. The main result of this paper is the analytical equationfor the optimal trading trajectories with the assumption of exponential market recovery and short-time investment horizon. The formula has the same form and as simple as well known solution by GKAC ( R. Grinold and R. Kahn, R.Almgren and N.Chriss) but much more flexible. Also it is free of such undesirable features as infinite impact for finite discrete trades and instantaneous market recovery. In this revision we corrected typos and added appendix with illustrations of main equation.

Full coverage of ETF investments from an expert in the field The initial edition of Gary Gastineau's The Exchange-Traded Fund Manual was one of the first books to describe and analyze ETFs. It made the case for the superiority of the structure of investor-friendly ETFs over mutual funds and helped investors select better funds among the ETFs available. With this new edition, Gastineau provides comprehensive information on the latest developments in ETF structures, new portfolio variety, and new trading methods. With a realistic evaluation of today's indexes, Gastineau offers insights on actively managed ETFs, improved index funds, and fund and advisor selection. Discusses how to incorporate ETFs into an investment plan Offers updated coverage of new ETFs, including full-function actively managed ETFs, and a valuable chapter on trading ETFs Written by the leading authority on exchange traded funds Exchange-traded funds offer you diversification and participation in markets and investment strategies that have not been available to most investors. If you want to understand how to use ETFs effectively, the Second Edition of The Exchanged-Traded Fund Manual can show you how.

The April 2012 Global Financial Stability Report assesses changes in risks to financial stability over the past six months, focusing on sovereign vulnerabilities, risks stemming from private sector deleveraging, and assessing the continued resilience of emerging markets. The report probes the implications of recent reforms in the financial system for market perception of safe assets, and investigates the growing public and private costs of increased longevity risk from aging populations.

The global economy has experienced four waves of rapid debt accumulation over the past 50 years. The first three debt waves ended with financial crises in many emerging market and developing economies. During the current wave, which started in 2010, the increase in debt in these economies has already been larger, faster, and broader-based than in the previous three waves. Current low interest rates mitigate some of the risks associated with high debt. However, emerging market and developing economies are also confronted by weak growth prospects, mounting vulnerabilities, and elevated global risks. A menu of policy options is available to reduce the likelihood that the current debt wave will end in crisis and, if crises do take place, will alleviate their impact.