Journal ArticleDOI
Computing efficient frontiers using estimated parameters
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The tradeoff between estimation error and stationarity is investigated and a method for adjusting for the bias is suggested and a statistical test is proposed to check for nonstationarity in historical data.Abstract:
The mean-variance model for portfolio selection requires estimates of many parameters. This paper investigates the effect of errors in parameter estimates on the results of mean-variance analysis. Using a small amount of historical data to estimate parameters exposes the model to estimation errors. However, using a long time horizon to estimate parametes increasers the possibility of nonstationarity in the parameters. This paper investigates the tradeoff between estimation error and stationarity. A simulation study shows that the effects of estimation error can be surprisingly large. The magnitude of the errors increase with the number of securities in the analysis. Due to the error maximization property of mean-variance analysis, estimates of portfolio performance are optimistically biased predictors of actual portfolio performance. It is important for users of mean-variance analysis to recognize and correct for this phenomenon in order to develop more realistic expectations of the future performance of a portfolio. This paper suggests a method for adjusting for the bias. A statistical test is proposed to check for nonstationarity in historical data.read more
Citations
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Journal ArticleDOI
A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms
TL;DR: In this article, a general framework for finding portfolios that perform well out-of-sample in the presence of estimation error is proposed, which relies on solving the traditional minimum-variance problem but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold.
Journal ArticleDOI
Robust portfolio selection problems
Donald Goldfarb,Garud Iyengar +1 more
TL;DR: This paper introduces "uncertainty structures" for the market parameters and shows that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs and, therefore, the computational effort required to solve them is comparable to that required for solving convex quadratic programs.
Journal ArticleDOI
Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis
TL;DR: The interplay between objective and constraints in a number of single-period variants, including semivariance models are described, revealing the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.
Book
Optimization Methods in Finance
TL;DR: In this article, the authors propose a simplex method for robust optimization in finance, using linear programming, nonlinear programming, and Quadratic programming, with the use of robust optimization tools.
Journal ArticleDOI
Portfolio Selection With Robust Estimation
TL;DR: This paper proposes a class of portfolios that have better stability properties than the traditional minimum-variance portfolios and shows analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional portfolios.
References
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Book
Modern Portfolio Theory and Investment Analysis
TL;DR: The Modern Portfolio Theory as discussed by the authors examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios, while presenting advanced concepts of investment analysis and portfolio management.
Journal ArticleDOI
The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice
TL;DR: The basic theory and extensions of mean-variance analysis are discussed in Markowitz as discussed by the authors and Ziemba & Vickson [1975] and Bawa, Brown & Klein [1979] and Michaud [1989] review some of its problems.
Book
Mean-Variance Analysis in Portfolio Choice and Capital Markets
Harry M. Markowitz,G. Peter Todd +1 more
TL;DR: In this paper, the general portfolio selection model preliminary results solution to a portfolio selection program special cases a special case portfolio selection programme is presented, and the model is used for portfolio selection.
Journal ArticleDOI
The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?
TL;DR: The Improving Portfolio Performance With Quantitative Models (IPPMQM) conference as mentioned in this paper was the first conference devoted to quantitative models for portfolio performance improvement, which was held in 1989.
Journal ArticleDOI
On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results
Michael J. Best,Robert R. Grauer +1 more
TL;DR: Brown et al. as mentioned in this paper investigated the sensitivity of mean variance-efficient portfolios to changes in the means of individual assets and found that a positively weigbted mean-variance-efficient portfolio's weights, mean, and variance can be extremely sensitive to cbanges in asset means.
Related Papers (5)
The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice
On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results
Michael J. Best,Robert R. Grauer +1 more