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34
Optimal versus Naive Diversification: How . . .
, 2007
"... We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Shar ..."
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Cited by 22 (1 self)
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We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certaintyequivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the samplebased meanvariance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many “miles to go” before the gains promised by optimal portfolio choice can actually be realized out of sample.
Markowitz revisited: meanvariance models in financial portfolio analysis
 SIAM Rev
, 2001
"... Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avo ..."
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Cited by 21 (1 self)
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Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.
A Brief History of Downside Risk Measures
 Journal of Investing
, 1999
"... Introduction There has been a controversy in this journal about using downside risk measures in portfolio analysis. The downside risk measures supposedly are a major improvement over traditional portfolio theory. That is where the battle lines clashed when Rom and Ferguson (1993, 1994b) and Kaplan ..."
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Cited by 15 (1 self)
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Introduction There has been a controversy in this journal about using downside risk measures in portfolio analysis. The downside risk measures supposedly are a major improvement over traditional portfolio theory. That is where the battle lines clashed when Rom and Ferguson (1993, 1994b) and Kaplan and Siegel (1994a, 1994b) engaged in a "tempest in a teapot". I should confess that I am strong supporter of downside risk measures and have used them in my teaching, research and software for the past two decades. Therefore, you should keep that bias in mind as you read this article. One of the best means to understand a concept is to study the history of its development. Understanding the issues facing researchers during the development of a concept results in better knowledge of the concept. The purpose of this paper is to provide an understanding of the measurement of downside risk. First, it helps to define terms. Portfolio theory is the application of decisionmaking tools unde
Sensitivity Analysis in (Degenerate) Quadratic Programming
 DELFT UNIVERSITY OF TECHNOLOGY
, 1996
"... In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a righthand side element ..."
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Cited by 7 (2 self)
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In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a righthand side element (or an element of the linear part of the objective) is piecewise quadratic, where the pieces can be characterized by maximal complementary solutions and tripartitions. Further, we investigate differentiability of this function. A new algorithm to compute the optimal value function is proposed. Finally, we discuss the advantages of this approach when applied to meanvariance portfolio models.
The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming
 in Advances in Sensitivity Analysis and Parametric Programming
, 1996
"... In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transitionpoints of the optimal value function. The advantage of using this approach instead of the classical approach (usin ..."
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Cited by 6 (3 self)
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In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transitionpoints of the optimal value function. The advantage of using this approach instead of the classical approach (using optimal bases) is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss differences and resemblances with the linear programming case.
SENSITIVITY ANALYSIS IN CONVEX QUADRATIC OPTIMIZATION: INVARIANT SUPPORT SET INTERVAL
, 2004
"... In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the r ..."
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Cited by 4 (2 self)
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In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so called Support Set Invariancy) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between characteristics of support set invariancy sensitivity analysis for LO and CQO.
Structured Sparsity through Convex Optimization
"... Abstract. Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the ℓ1norm. In this paper, we cons ..."
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Cited by 3 (0 self)
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Abstract. Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the ℓ1norm. In this paper, we consider situations where we are not only interested in sparsity, but where some structural prior knowledge is available as well. We show that the ℓ1norm can then be extended to structured norms built on either disjoint or overlapping groups of variables, leading to a flexible framework that can deal with various structures. We present applications to unsupervised learning, for structured sparse principal component analysis and hierarchical dictionary learning, and to supervised learning in the context of nonlinear variable selection. Key words and phrases: Sparsity, convex optimization. 1.
The Solution of a Class of Limited Diversification Portfolio Selection Problems
, 1997
"... The Solution of a Class of Limited Diversification Portfolio Selection Problems by Gwyneth Owens Butera A branchandbound algorithm for the solution of a class of mixedinteger nonlinear programming problems arising from the field of investment portfolio selection is presented. The problems in this ..."
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Cited by 2 (0 self)
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The Solution of a Class of Limited Diversification Portfolio Selection Problems by Gwyneth Owens Butera A branchandbound algorithm for the solution of a class of mixedinteger nonlinear programming problems arising from the field of investment portfolio selection is presented. The problems in this class are characterized by the inclusion of the fixed transaction costs associated with each asset, a constraint that explicitly limits the number of distinct assets in the selected portfolio, or both. Modeling either of these forms of limiting the cost of owning an investment portfolio involves the introduction of binary variables, resulting in a mathematical programming problem that has a nonconvex feasible set. Two objective functions are examined in this thesis; the first is a positive definite quadratic function which is commonly used in the selection of investment portfolios. The second is a convex function that is not continuously differentiable; this objective function, although not...
Combining Decision Analysis and Portfolio Management to Improve Project Selection
 in the Exploration and Production Firm, Journal of Petroleum Science and Engineering
, 2004
"... selection in the exploration and production firm ..."