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.

The purpose of this research is to investigate devising the optimal position liquidation strategies in financial markets. During the transaction of large block orders, investors need to maximize their profits against the losses caused by price slippage. We employed a sample-path based stochastic programming approach to obtain a dynamic lower-bound optimal trading strategy with Conditional Value-at-Risk constraint. We analyzed the optimization problems with different types of objective functions determined by distinct market impact functions. Nonanticipativity and risk constraints are discussed and properly imposed to avoid anticipating solutions and to control risk. A new formulation is proposed to obtain a lower-bound of the optimal position liquidation problem. A case study is implemented in the run-file environment of Portfolio Safeguard. Lower-bound optimal strategies are obtained from problems with and without risk constraints. The result also verifies the supposed improvement of computational efficiency in the new formulation.

We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.

We consider the problem of portfolio liquidation with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We consider the risk-reward tradeoff both from the point of view of classic mean-variance optimization, and from the standpoint of Value at Risk. This analysis leads to general insights into optimal portfolio trading, and to several applications including a definition of liquidity-adjusted value at risk.

Top economist Gary Shilling shows you how to prosper in the slow-growing and deflationary times that lie ahead While many investors fear a rapid rise in inflation, author Gary Shilling, an award-winning economic forecaster, argues that the global economy is going through a long period of de-leveraging and weak growth, which makes deflation far more likely and a far greater threat to investors than inflation. Shilling explains in clear language and compelling logic why the world economy will struggle for several more years and what investors can do to protect and grow their wealth in the difficult times ahead. The investment strategies that worked for last 25 years will not work in the next 10 years. Shilling advises readers to avoid broad exposure to stocks, real estate, and commodities and to focus on high-quality bonds, high-dividend stocks, and consumer staple and food stocks. Written by one of today's best forecasters of economic trends-twice voted by Institutional Investor as Wall Street's top economist Clearly explains what to invest in, what to avoid, and how to cope with a deflationary, slow-growth economy Demonstrates how Shilling has been consistently right about major economic trends since he began forecasting in the early 1980s Filled with in-depth insights and practical advice, this timely guide lays out a convincing case for why investors need to be prepared for a long period of weak growth and deflation-not inflation-and what you can do to prosper in the difficult times ahead.

Praise for Robust Portfolio Optimization and Management "In the half century since Harry Markowitz introduced his elegant theory for selecting portfolios, investors and scholars have extended and refined its application to a wide range of real-world problems, culminating in the contents of this masterful book. Fabozzi, Kolm, Pachamanova, and Focardi deserve high praise for producing a technically rigorous yet remarkably accessible guide to the latest advances in portfolio construction." --Mark Kritzman, President and CEO, Windham Capital Management, LLC "The topic of robust optimization (RO) has become 'hot' over the past several years, especially in real-world financial applications. This interest has been sparked, in part, by practitioners who implemented classical portfolio models for asset allocation without considering estimation and model robustness a part of their overall allocation methodology, and experienced poor performance. Anyone interested in these developments ought to own a copy of this book. The authors cover the recent developments of the RO area in an intuitive, easy-to-read manner, provide numerous examples, and discuss practical considerations. I highly recommend this book to finance professionals and students alike." --John M. Mulvey, Professor of Operations Research and Financial Engineering, Princeton University

This paper reviews the literature on financial crises focusing on three specific aspects. First, what are the main factors explaining financial crises? Since many theories on the sources of financial crises highlight the importance of sharp fluctuations in asset and credit markets, the paper briefly reviews theoretical and empirical studies on developments in these markets around financial crises. Second, what are the major types of financial crises? The paper focuses on the main theoretical and empirical explanations of four types of financial crises—currency crises, sudden stops, debt crises, and banking crises—and presents a survey of the literature that attempts to identify these episodes. Third, what are the real and financial sector implications of crises? The paper briefly reviews the short- and medium-run implications of crises for the real economy and financial sector. It concludes with a summary of the main lessons from the literature and future research directions.

High public debt often produces the drama of default and restructuring. But debt is also reduced through financial repression, a tax on bondholders and savers via negative or belowmarket real interest rates. After WWII, capital controls and regulatory restrictions created a captive audience for government debt, limiting tax-base erosion. Financial repression is most successful in liquidating debt when accompanied by inflation. For the advanced economies, real interest rates were negative 1⁄2 of the time during 1945–1980. Average annual interest expense savings for a 12—country sample range from about 1 to 5 percent of GDP for the full 1945–1980 period. We suggest that, once again, financial repression may be part of the toolkit deployed to cope with the most recent surge in public debt in advanced economies.

Efficiently Inefficient describes the key trading strategies used by hedge funds and demystifies the secret world of active investing. Leading financial economist Lasse Heje Pedersen combines the latest research with real-world examples and interviews with top hedge fund managers to show how certain trading strategies make money - and why they sometimes don't. -- from back cover.