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Tail Mean Variance Portfolio Selection With Estimation Risk
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Book Synopsis Tail Mean-Variance Portfolio Selection with Estimation Risk by : Zhenzhen Huang
Download or read book Tail Mean-Variance Portfolio Selection with Estimation Risk written by Zhenzhen Huang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean and covariance of asset returns in the optimal portfolio weight with their sample counterparts. The plug-in method inevitably introduces estimation risk and usually has poor out-of-sample performance. We propose an optimal combination of the plug-in and 1/N rules to improve out-of-sample performance. Our proposed combined portfolio consistently outperforms both the plug-in and 1/N portfolios on both simulated and real-world datasets.
Book Synopsis Portfolio Selection With Robust Estimation by : Victor DeMiguel
Download or read book Portfolio Selection With Robust Estimation written by Victor DeMiguel and published by . This book was released on 2007 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better out-of-sample. But even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional minimum-variance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.
Book Synopsis Fat-Tailed and Skewed Asset Return Distributions by : Svetlozar T. Rachev
Download or read book Fat-Tailed and Skewed Asset Return Distributions written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2005-09-15 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.
Book Synopsis Robust Mean-Variance Portfolio Selection by : Cédric Perret-Gentil
Download or read book Robust Mean-Variance Portfolio Selection written by Cédric Perret-Gentil and published by . This book was released on 2007 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates model risk issues in the context of mean-variance portfolio selection. We analytically and numerically show that, under model misspecification, the use of statistically robust estimates instead of the widely used classical sample mean and covariance is highly beneficial for the stability properties of the mean-variance optimal portfolios. Moreover, we perform simulations leading to the conclusion that, under classical estimation, model risk bias dominates estimation risk bias. Finally, we suggest a diagnostic tool to warn the analyst of the presence of extreme returns that have an abnormally large influence on the optimization results.
Book Synopsis Sparse and Stable Portfolio Selection with Parameter Uncertainty by : Jiahan Li
Download or read book Sparse and Stable Portfolio Selection with Parameter Uncertainty written by Jiahan Li and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of alternative mean-variance portfolio strategies have been recently proposed to improve the empirical performance of the classic Markowitz mean-variance framework. Designed as remedies for parameter uncertainty and estimation errors in portfolio selection problems, these alternative portfolio strategies deliver substantially better out-of-sample performance. In this paper, we first show how to solve a general portfolio selection problem in a linear regression framework. Then we propose to reduce the estimation risk of expected returns and the variance-covariance matrix of asset returns by imposing additional constraints on the portfolio weights. With results from linear regression models, we show that portfolio weights derived from new approaches enjoy two favorable properties: sparsity and stability. Moreover, we present insights into these new approaches as well as their connections to alternative strategies in literature. Four empirical studies show that the proposed strategies have better out-of-sample performance and lower turnover than many other strategies, especially when the estimation risk is large.
Book Synopsis Portfolio Selection with Mental Accounts and Estimation Risk by : Gordon J. Alexander
Download or read book Portfolio Selection with Mental Accounts and Estimation Risk written by Gordon J. Alexander and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In Das, Markowitz, Scheid, and Statman (2010), an investor divides his or her wealth among mental accounts with short selling being allowed. For each account, there is a unique goal and optimal portfolio. Our paper complements theirs by considering estimation risk. We theoretically characterize the existence and composition of optimal portfolios within accounts. Based on simulated and empirical data, there is a wide range of account goals for which such portfolios notably outperform those selected with the mean-variance model for plausible risk aversion coefficients. When short selling is disallowed, the out performance still typically holds but to a considerably lesser extent.
Book Synopsis Mean-Variance Optimal Portfolio Selection with a Value-At-Risk Constraint by : Hui Deng
Download or read book Mean-Variance Optimal Portfolio Selection with a Value-At-Risk Constraint written by Hui Deng and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mean-variance Optimal Portfolio Selection With a Value-at-risk Constraint" by Hui, Deng, 鄧惠, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. DOI: 10.5353/th_b4189721 Subjects: Risk Portfolio management - Mathematical models
Book Synopsis Time-Consistent Mean-Variance Portfolio Selection with Only Risky Assets by : Chi Seng Pun
Download or read book Time-Consistent Mean-Variance Portfolio Selection with Only Risky Assets written by Chi Seng Pun and published by . This book was released on 2018 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-consistency and optimal diversification (minimum-variance) criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytic solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytic solution of the time-consistent mean-variance strategy with risky assets via the solution of the Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.
Book Synopsis Mean-Variance Optimization Using Forward-Looking Return Estimates by : Patrick Bielstein
Download or read book Mean-Variance Optimization Using Forward-Looking Return Estimates written by Patrick Bielstein and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its theoretical appeal, Markowitz mean-variance portfolio optimization is plagued by practical issues. It is especially difficult to obtain reliable estimates of a stock's expected return. Recent research has therefore focused on minimum volatility portfolio optimization, which implicitly assumes that expected returns for all assets are equal. We argue that investors are better off using the implied cost of capital based on analysts' earnings forecasts as a forward-looking return estimate. Correcting for predictable analyst forecast errors, we demonstrate that mean-variance optimized portfolios based on these estimates outperform on both an absolute and a risk-adjusted basis the minimum volatility portfolio as well as naive benchmarks, such as the value-weighted and equally-weighted market portfolio. The results continue to hold when extending the sample to international markets, using different methods for estimating the forward-looking return, including transaction costs, and using different optimization constraints.
Book Synopsis Dynamic Mean-Risk Portfolio Selection with Multiple Risk Measures in Continuous-Time by : Jianjun Gao
Download or read book Dynamic Mean-Risk Portfolio Selection with Multiple Risk Measures in Continuous-Time written by Jianjun Gao and published by . This book was released on 2014 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different risk measures emphasize different aspects of a random loss. If we examine the investment performance according to different spectra of the risk measures, any policy generated from a mean-risk portfolio model with a sole risk measure may not be a good choice. We study in this paper the dynamic portfolio selection problem with multiple risk measures in a continuous-time setting. More specifically, we investigate the dynamic mean-variance-CVaR (Conditional value at Risk) formulation and the dynamic mean-variance-SFP (Safety-First-Principle) formulation, and derive analytical solutions for both problems, when all the market parameters are deterministic. Combining a downside risk measure with the variance (the second order central moment) in a dynamic mean-risk portfolio selection model helps investors control both the symmetric central risk measure and the asymmetric downside risk at the tail part of the loss. We find that the optimal portfolio policy derived from our mean-multiple risk portfolio optimization model exhibits a feature of two-side threshold type, i.e., when the current wealth level is either below or above certain threshold, the optimal policy would dictate an increase in the allocation of the risky assets. Our numerical experiments using real market data further demonstrate that our dynamic mean-multiple risk portfolio models reduce significantly both the variance and the downside risk, when compared with the static buy-and-hold portfolio policy.
Book Synopsis Mean Variance Portfolio Management by : Kwok-Chuen Wong
Download or read book Mean Variance Portfolio Management written by Kwok-Chuen Wong and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mean Variance Portfolio Management: Time Consistent Approach" by Kwok-chuen, Wong, 黃國全, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Bjork and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Bjork et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding "optimal" wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such "bankruptcy" solution can converge to the solution in continuous counterpart as Bjork et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Bjork et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting. DOI: 10.5353/th_b5153743 S
Book Synopsis Mean-variance Optimal Portfolio Selection with a Value-at-risk Constraint by : Hui Deng (M. Phil.)
Download or read book Mean-variance Optimal Portfolio Selection with a Value-at-risk Constraint written by Hui Deng (M. Phil.) and published by . This book was released on 2009 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Characteristic-based Mean-variance Portfolio Choice by : Erik Hjalmarsson
Download or read book Characteristic-based Mean-variance Portfolio Choice written by Erik Hjalmarsson and published by . This book was released on 2009 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for "stock-picking" in international indexes, using characteristics such as value and momentum, with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.
Book Synopsis Optimal Mean-variance Portfolio Selection Using Historic and Fama-French Three-Factor Model Mean Estimation by : Corey P. O'Keefe
Download or read book Optimal Mean-variance Portfolio Selection Using Historic and Fama-French Three-Factor Model Mean Estimation written by Corey P. O'Keefe and published by . This book was released on 2001 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mean-Variance Analysis in Portfolio Choice and Capital Markets by : Harry M. Markowitz
Download or read book Mean-Variance Analysis in Portfolio Choice and Capital Markets written by Harry M. Markowitz and published by John Wiley & Sons. This book was released on 2000-02-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1952, Harry Markowitz published "Portfolio Selection," a paper which revolutionized modern investment theory and practice. The paper proposed that, in selecting investments, the investor should consider both expected return and variability of return on the portfolio as a whole. Portfolios that minimized variance for a given expected return were demonstrated to be the most efficient. Markowitz formulated the full solution of the general mean-variance efficient set problem in 1956 and presented it in the appendix to his 1959 book, Portfolio Selection. Though certain special cases of the general model have become widely known, both in academia and among managers of large institutional portfolios, the characteristics of the general solution were not presented in finance books for students at any level. And although the results of the general solution are used in a few advanced portfolio optimization programs, the solution to the general problem should not be seen merely as a computing procedure. It is a body of propositions and formulas concerning the shapes and properties of mean-variance efficient sets with implications for financial theory and practice beyond those of widely known cases. The purpose of the present book, originally published in 1987, is to present a comprehensive and accessible account of the general mean-variance portfolio analysis, and to illustrate its usefulness in the practice of portfolio management and the theory of capital markets. The portfolio selection program in Part IV of the 1987 edition has been updated and contains exercises and solutions.
Book Synopsis Mean-Variance Portfolio Selection With 'At-Risk' Constraints and Discrete Distributions by : Gordon J. Alexander
Download or read book Mean-Variance Portfolio Selection With 'At-Risk' Constraints and Discrete Distributions written by Gordon J. Alexander and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the impact of adding either a VaR or a CVaR constraint to the mean-variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean-variance model.
Book Synopsis Mean-Variance Portfolio Selection with Tracking Error Penalization by : William Lefebvre
Download or read book Mean-Variance Portfolio Selection with Tracking Error Penalization written by William Lefebvre and published by . This book was released on 2020 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by “fitting” it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.
