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Estimation Error in Mean Returns and the Mean-Variance Efficient Frontier

Estimation Error in Mean Returns and the Mean-Variance Efficient Frontier
Author: Majeed Simaan
Publisher:
Total Pages: 31
Release: 2017
Genre:
ISBN:

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In this paper, we build estimation error in mean returns into the mean-variance (MV) portfolio theory under the assumption that returns on individual assets follow a joint normal distribution. We derive the conditional sampling distribution of the MV portfolio along with its mean and risk return when the sample covariance matrix is equal to a constant matrix. We use the mean squared error (MSE) to characterize the effects of estimation error in mean returns on the joint sampling distributions and examine how such error affects the risk-return tradeoff of the MV portfolios. We show that the negative effects of error in mean returns on the joint sampling distributions increase with the decision maker's risk tolerance and the number of assets in a portfolio, but decrease with the sample size.


On the Estimation Error in Mean-Variance Efficient Portfolio Weights

On the Estimation Error in Mean-Variance Efficient Portfolio Weights
Author: Frans de Roon
Publisher:
Total Pages: 19
Release: 2004
Genre:
ISBN:

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This paper derives the asymptotic covariance matrix of estimated mean-variance efficient portfolio weights, both for gross returns (without a riskfree asset available) and for excess returns (in excess of the riskfree rate). When returns are assumed to be normally distributed, we obtain simple formulas for the covariance matrices. The results show that the estimation error increases as the risk aversion underlying the portfolio decreases and as the (asymptotic) slope or Sharpe ratio of the mean-variance frontier increases. For the tangency portfolio, there is an additional estimation risk because the location of the tangency portfolio is not known beforehand. The empirical analysis of efficient portfolios based on the G7 countries indicates that the estimation error can be big in practice. It also shows that the standard errors that assume normality are usually very close to the standard errors that do not assume normality in returns, except for portfolios close to the Global Minimum Variance portfolio.


Efficient Asset Management

Efficient Asset Management
Author: Richard O. Michaud
Publisher: Oxford University Press
Total Pages: 145
Release: 2008-03-03
Genre: Business & Economics
ISBN: 0199715793

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In spite of theoretical benefits, Markowitz mean-variance (MV) optimized portfolios often fail to meet practical investment goals of marketability, usability, and performance, prompting many investors to seek simpler alternatives. Financial experts Richard and Robert Michaud demonstrate that the limitations of MV optimization are not the result of conceptual flaws in Markowitz theory but unrealistic representation of investment information. What is missing is a realistic treatment of estimation error in the optimization and rebalancing process. The text provides a non-technical review of classical Markowitz optimization and traditional objections. The authors demonstrate that in practice the single most important limitation of MV optimization is oversensitivity to estimation error. Portfolio optimization requires a modern statistical perspective. Efficient Asset Management, Second Edition uses Monte Carlo resampling to address information uncertainty and define Resampled Efficiency (RE) technology. RE optimized portfolios represent a new definition of portfolio optimality that is more investment intuitive, robust, and provably investment effective. RE rebalancing provides the first rigorous portfolio trading, monitoring, and asset importance rules, avoiding widespread ad hoc methods in current practice. The Second Edition resolves several open issues and misunderstandings that have emerged since the original edition. The new edition includes new proofs of effectiveness, substantial revisions of statistical estimation, extensive discussion of long-short optimization, and new tools for dealing with estimation error in applications and enhancing computational efficiency. RE optimization is shown to be a Bayesian-based generalization and enhancement of Markowitz's solution. RE technology corrects many current practices that may adversely impact the investment value of trillions of dollars under current asset management. RE optimization technology may also be useful in other financial optimizations and more generally in multivariate estimation contexts of information uncertainty with Bayesian linear constraints. Michaud and Michaud's new book includes numerous additional proposals to enhance investment value including Stein and Bayesian methods for improved input estimation, the use of portfolio priors, and an economic perspective for asset-liability optimization. Applications include investment policy, asset allocation, and equity portfolio optimization. A simple global asset allocation problem illustrates portfolio optimization techniques. A final chapter includes practical advice for avoiding simple portfolio design errors. With its important implications for investment practice, Efficient Asset Management 's highly intuitive yet rigorous approach to defining optimal portfolios will appeal to investment management executives, consultants, brokers, and anyone seeking to stay abreast of current investment technology. Through practical examples and illustrations, Michaud and Michaud update the practice of optimization for modern investment management.


Computational Finance and Financial Econometrics

Computational Finance and Financial Econometrics
Author: Eric Zivot
Publisher: CRC Press
Total Pages: 500
Release: 2017-01-15
Genre:
ISBN: 9781498775779

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This book presents mathematical, programming and statistical tools used in the real world analysis and modeling of financial data. The tools are used to model asset returns, measure risk, and construct optimized portfolios using the open source R programming language and Microsoft Excel. The author explains how to build probability models for asset returns, to apply statistical techniques to evaluate if asset returns are normally distributed, to use Monte Carlo simulation and bootstrapping techniques to evaluate statistical models, and to use optimization methods to construct efficient portfolios.


Mean-Variance Optimization Using Forward-Looking Return Estimates

Mean-Variance Optimization Using Forward-Looking Return Estimates
Author: Patrick Bielstein
Publisher:
Total Pages: 43
Release: 2017
Genre:
ISBN:

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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.


Estimation Error and Portfolio Optimization

Estimation Error and Portfolio Optimization
Author: Richard O. Michaud
Publisher:
Total Pages: 25
Release: 2015
Genre:
ISBN:

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Markowitz (1959) mean-variance (MV) portfolio optimization has been the practical standard for asset allocation and equity portfolio management for almost fifty years. However, it is known to be overly sensitive to estimation error in risk-return estimates and have poor out-of-sample performance characteristics. The Resampled EfficiencyTM (RE) techniques presented in Michaud (1998) introduce Monte Carlo methods to properly represent investment information uncertainty in computing MV portfolio optimality and in defining trading and monitoring rules. This paper reviews and updates the literature on estimation error and RE portfolio optimization and rebalancing. We resolve several open issues and misunderstandings that have emerged since Michaud (1998). In particular, we show RE optimization to be a Bayesian-based generalization and enhancement of Markowitz's solution.


Quantitative Finance with Python

Quantitative Finance with Python
Author: Chris Kelliher
Publisher: CRC Press
Total Pages: 698
Release: 2022-05-19
Genre: Business & Economics
ISBN: 1000582302

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Quantitative Finance with Python: A Practical Guide to Investment Management, Trading and Financial Engineering bridges the gap between the theory of mathematical finance and the practical applications of these concepts for derivative pricing and portfolio management. The book provides students with a very hands-on, rigorous introduction to foundational topics in quant finance, such as options pricing, portfolio optimization and machine learning. Simultaneously, the reader benefits from a strong emphasis on the practical applications of these concepts for institutional investors. Features Useful as both a teaching resource and as a practical tool for professional investors. Ideal textbook for first year graduate students in quantitative finance programs, such as those in master’s programs in Mathematical Finance, Quant Finance or Financial Engineering. Includes a perspective on the future of quant finance techniques, and in particular covers some introductory concepts of Machine Learning. Free-to-access repository with Python codes available at www.routledge.com/ 9781032014432 and on https://github.com/lingyixu/Quant-Finance-With-Python-Code.


A Practitioner's Guide to Asset Allocation

A Practitioner's Guide to Asset Allocation
Author: William Kinlaw
Publisher: John Wiley & Sons
Total Pages: 271
Release: 2017-05-02
Genre: Business & Economics
ISBN: 111940245X

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Since the formalization of asset allocation in 1952 with the publication of Portfolio Selection by Harry Markowitz, there have been great strides made to enhance the application of this groundbreaking theory. However, progress has been uneven. It has been punctuated with instances of misleading research, which has contributed to the stubborn persistence of certain fallacies about asset allocation. A Practitioner's Guide to Asset Allocation fills a void in the literature by offering a hands-on resource that describes the many important innovations that address key challenges to asset allocation and dispels common fallacies about asset allocation. The authors cover the fundamentals of asset allocation, including a discussion of the attributes that qualify a group of securities as an asset class and a detailed description of the conventional application of mean-variance analysis to asset allocation.. The authors review a number of common fallacies about asset allocation and dispel these misconceptions with logic or hard evidence. The fallacies debunked include such notions as: asset allocation determines more than 90% of investment performance; time diversifies risk; optimization is hypersensitive to estimation error; factors provide greater diversification than assets and are more effective at reducing noise; and that equally weighted portfolios perform more reliably out of sample than optimized portfolios. A Practitioner's Guide to Asset Allocation also explores the innovations that address key challenges to asset allocation and presents an alternative optimization procedure to address the idea that some investors have complex preferences and returns may not be elliptically distributed. Among the challenges highlighted, the authors explain how to overcome inefficiencies that result from constraints by expanding the optimization objective function to incorporate absolute and relative goals simultaneously. The text also explores the challenge of currency risk, describes how to use shadow assets and liabilities to unify liquidity with expected return and risk, and shows how to evaluate alternative asset mixes by assessing exposure to loss throughout the investment horizon based on regime-dependent risk. This practical text contains an illustrative example of asset allocation which is used to demonstrate the impact of the innovations described throughout the book. In addition, the book includes supplemental material that summarizes the key takeaways and includes information on relevant statistical and theoretical concepts, as well as a comprehensive glossary of terms.