Download or read book A State Variable Decomposition Approach for Solving Portfolio Choice Problems written by Lorenzo Garlappi and published by . This book was released on 2008 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a new method for the solution of dynamic portfolio choice problems. Our approach consists of decomposing each state variable into a sum of its conditional mean and the corresponding zero-mean shock. Such a state variable decomposition (SVD) allows efficient computation of the conditional expectations required for the solution of the dynamic optimization problem. Under commonly used distributional assumptions for the state variable shocks (e.g., normality or lognormality), this decomposition allows closed-form evaluation of such expectations, thus avoiding computationally intensive quadrature or simulation-based techniques. Our approach can easily handle intermediate consumption, multiple risky assets, multiple state variables, portfolio constraints, non-expected utility preferences as well as portfolio problems in which wealth is not a redundant state variable. We illustrate the accuracy of the method by comparing our solution to either the analytical solution, whenever available, or the solution obtained by quadrature methods. Finally, we employ our method to solve a large-scale strategic asset allocation problem with recursive preferences and predictable asset returns similar to the one solved by Campbell, Chan, and Viceira (2003) via log-linear approximation. Our approach allows us to impose realistic no borrowing and short-selling constraints and its precision, unlike that of the log-linear approximation, does not rely on the elasticity of intertemporal substitution being close to unity. The versatility of our approach makes it a suitable solution method for a wide range of dynamic problems in finance and economics.
Download or read book Incorporating Options in Static and Dynamic Portfolio Optimization written by Sylvain Gervais and published by . This book was released on 2009 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Portfolio Choice with State Dependent Adjustments written by Peter Farkas and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we discuss a new method for solving the portfolio choice problem which models state-dependent quantity adjustment using boundary crossing events. This new method has several advantages: first, we can solve for the optimal portfolio weights without parametric assumptions, by deriving them directly from the data. Next, we can describe the full distribution of the portfolio's value, not just its moments. Finally, we can easily deal with important practical issues, such as transaction costs, leveraged positions and no-ruin conditions, or the cost of margin financing. In particular, the method allows us to analyze leveraged positions in discrete time under zero ruin probability. Analyzing historical stock data suggests that historically, the log-optimal portfolio was a not too extensive leveraged purchase of a diversified stock portfolio, therefore leveraging does not necessarily imply risk-seeking behavior. We also show that depending on how much weight we allocate to this diversified stock portfolio, the downside risk measured as 5% VAR of the portfolio's value may be decreasing or increasing over time. Consequently, an objective functions which incorporates the VAR of the portfolio's value or operate with VAR constrains result in horizon-dependent portfolio weights. We also present some evidence suggesting that the log-optimal portfolio weights are time-dependent. Finally, irrespective of what weight we chose for the diversified stock portfolio, it is log-optimal to reduce exposure to the stock market if the predicted volatility is high, and increase it in low volatility periods.
Download or read book Topics in Dynamic Portfolio Choice Problems written by Poomyos Wimonkittiwat and published by . This book was released on 2013 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study two important generalizations of dynamic portfolio choice problems: a portfolio choice problem with market impact costs and a portfolio choice problem under the Hidden Markov Model. In the first problem, we allow the presence of market impact and illiquidity. Illiquidity and market impact refer to the situation where it may be costly or difficult to trade a desired quantity of assets over a desire period of time. In this work, we formulate a simple model of dynamic portfolio choice that incorporates liquidity effects. The resulting problem is a stochastic linear quadratic control problem where liquidity costs are modeled as a quadratic penalty on the trading rate. Though easily computable via Riccati equations, we also derive a multiple time scale asymptotic expansion of the value function and optimal trading rate in the regime of vanishing market impact costs. This expansion reveals an interesting but intuitive relationship between the optimal trading rate for the illiquid problem and the classical Merton model for dynamic portfolio selection in perfectly liquid markets. It also gives rise to the notion of a liquidity time scale. Furthermore, the solution to our illiquid portfolio problem shows promising performance and robustness properties. In the second problem, we study dynamic portfolio choice problems under regime switching market. We assume the market follows the Hidden Markov Model with unknown transition probabilities and unknown observation statistics. The main difficulty of this dynamic programming problem is its high-dimensional state variables. The joint probability density function of the hidden regimes and the unknown quantities is part of the state variables, and this makes the problem suffer from the curse of dimensionality. Though the problem cannot be solved by any standard fashions, we propose approximate methods that tractably solve the problem. The key is to approximate the value function by that of a simpler problem where the regime is not hidden and the parameters are observable (the C-problem). This approximation allows the optimal portfolio to be computed in a semi-explicit way. The approximate solution shares the same structure with the solution of C-problem, but at the same time it provides clear insight into the unobservable extension. In addition, the performance of the proposed methods is reasonably close to the upper-bound obtained from the information relaxation problem.
Download or read book Dynamic Portfolio Choice written by Michael W. Brandt and published by . This book was released on 2001 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simulation-based method for solving realistic portfolio choice problems that potentially involve non-standard preferences and a large number of assets with arbitrary return distribution. Specifically, the return distribution can be time-varying as a function of many observable or unobservable state variables and can even be path-dependent. Furthermore, the method is flexible enough to accommodate intermediate consumption, parameter and model uncertainty, and portfolio constraints. We first establish the properties of the method for the choice between a stock index and cash when the stock returns are either iid or predictable by the dividend yield. We then explore the optimal asset allocation across ten industry portfolios that exhibit momentum through its empirical pattern of own- and cross-serial correlations of returns.
Download or read book A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability written by Michael W. Brandt and published by . This book was released on 2009 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simulation-based method for solving discrete-time portfolio choice problems involving non-standard preferences, a large number of assets with arbitrary return distribution, and, most importantly, a large number of state variables with potentially path-dependent or non-stationary dynamics. The method is flexible enough to accommodate intermediate consumption, portfolio constraints, parameter and model uncertainty, and learning. We first establish the properties of the method for the portfolio choice between a stock index and cash when the stock returns are either iid or predictable by the dividend yield. We then explore the problem of an investor who takes into account the predictability of returns but is uncertain about the parameters of the data generating process. The investor chooses the portfolio anticipating that future data realizations will contain useful information to learn about the true parameter values.
Download or read book Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids written by Peter Schober and published by . This book was released on 2019 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, I propose a dynamic programming approach with value function iteration to solve Bellman equations in discrete time using spatially adaptive sparse grids. In doing so, I focus on Bellman equations used in finance, specifically to model dynamic portfolio choice over the life cycle. Since the complexity of the dynamic programming approach -- and other approaches -- grows exponentially in the dimension of the (continuous) state space, it suffers from the so called curse of dimensionality. Approximation on a spatially adaptive sparse grid can break this curse to some extent. Extending recent approaches proposed in the economics and computer science literature, I employ local linear basis functions to a spatially adaptive sparse grid approximation scheme on the value function. As economists are interested in the optimal choices rather than the value function itself, I discuss how to obtain these optimal choices given a solution to the optimization problem on a sparse grid. I study the numerical properties of the proposed scheme by computing Euler equation errors to an exemplary dynamic portfolio choice model with varying state space dimensionality.
Download or read book On Optimal Portfolio Choice Under Stochastic Interest Rates written by Abraham Lioui and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In an economy where interest rates and stock price changes follow fairly general stochastic processes, we analyse the portfolio problem of an expected utility investor. When the investment opportunity set is driven by an arbitrary number of state variables, the optimal portfolio strategy is known to contain a speculative element and Merton-Breeden hedging terms against the fluctuations of each and every state variable. While the first component is well identified and easy to work out, the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics. Using a new decomposition of the optimal wealth, we show that the optimal strategy can be simplified to include, in addition to the speculative component, only two Merton-Breeden type hedging elements, however large is the number of state variables. The first one is associated with interest rate risk and the second one with the risk brought about by the co-movements of the spot interest rate and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Moreover, the investor's horizon is shown explicitly to play a crucial role in the optimal strategy design, in sharp contrast with the traditional decomposition.
Download or read book Predictions Nonlinearities and Portfolio Choice written by Friedrich Christian Kruse and published by BoD – Books on Demand. This book was released on 2012 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance researchers and asset management practitioners put a lot of effort into the question of optimal asset allocation. With this respect, a lot of research has been conducted on portfolio decision making as well as quantitative modeling and prediction models. This study brings together three fields of research, which are usually analyzed in an isolated manner in the literature: - Predictability of asset returns and their covariance matrix - Optimal portfolio decision making - Nonlinear modeling, performed by artificial neural networks, and their impact on predictions as well as optimal portfolio construction Including predictability in asset allocation is the focus of this work and it pays special attention to issues related to nonlinearities. The contribution of this study to the portfolio choice literature is twofold. First, motivated by the evidence of linear predictability, the impact of nonlinear predictions on portfolio performances is analyzed. Predictions are empirically performed for an investor who invests in equities (represented by the DAX index), bonds (represented by the REXP index) and a risk-free rate. Second, a solution to the dynamic programming problem for intertemporal portfolio choice is presented. The method is based on functional approximations of the investor's value function with artificial neural networks. The method is easily capable of handling multiple state variables. Hence, the effect of adding predictive parameters to the state space is the focus of analysis as well as the impacts of estimation biases and the view of a Bayesian investor on intertemporal portfolio choice. One important empirical result shows that residual correlation among state variables have an impact on intertemporal portfolio decision making.
Download or read book Encyclopedia of Finance written by Cheng-Few Lee and published by Springer Nature. This book was released on 2022-09-12 with total page 2746 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Finance comprehensively covers the broad spectrum of terms and topics relating finance from asset pricing models to option pricing models to risk management and beyond. This third edition is comprised of over 1,300 individual definitions, chapters, appendices and is the most comprehensive and up-to-date resource in the field, integrating the most current terminology, research, theory, and practical applications. It includes 200 new terms and essays; 25 new chapters and four new appendices. Showcasing contributions from an international array of experts, the revised edition of this major reference work is unparalleled in the breadth and depth of its coverage.
Download or read book Strategic Financial Planning Over the Lifecycle written by Narat Charupat and published by Cambridge University Press. This book was released on 2012-05-28 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a final-year college level textbook on personal finance, jointly written by business school and mathematics professors. It is aimed at a wide audience of people who are interested in wealth management from a more rigorous perspective. It may be used in both personal applications and professional classrooms.
Download or read book Strategic Asset Allocation written by John Y. Campbell and published by OUP Oxford. This book was released on 2002-01-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.
Download or read book INFORMS Annual Meeting written by Institute for Operations Research and the Management Sciences. National Meeting and published by . This book was released on 2009 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Computing written by Roman Trobec and published by Springer Science & Business Media. This book was released on 2009-06-18 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of parallel programming and architectures is essential for simulating and solving problems in modern computational practice. There has been rapid progress in microprocessor architecture, interconnection technology and software devel- ment, which are in?uencing directly the rapid growth of parallel and distributed computing. However, in order to make these bene?ts usable in practice, this dev- opment must be accompanied by progress in the design, analysis and application aspects of parallel algorithms. In particular, new approaches from parallel num- ics are important for solving complex computational problems on parallel and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today’s parallel computing. These range from parallel algorithmics, progr- ming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerical integ- tion, number theory and their applications in computer simulations, which together form the kernel of the monograph. We expect that the book will be of interest to scientists working on parallel computing, doctoral students, teachers, engineers and mathematicians dealing with numerical applications and computer simulations of natural phenomena.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Management written by Srikanta Patnaik and published by Springer Nature. This book was released on 2021-05-29 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely review of cutting-edge applications of computational intelligence to business management and financial analysis. It covers a wide range of intelligent and optimization techniques, reporting in detail on their application to real-world problems relating to portfolio management and demand forecasting, decision making, knowledge acquisition, and supply chain scheduling and management.
Download or read book Multi Period Trading Via Convex Optimization written by Stephen Boyd and published by . This book was released on 2017-07-28 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.
