Active Portfolio Management with Conditional Tracking Error

A Numerical Study for Robust Active Portfolio Management with Worst-Case Downside Risk Measure

Mathematical Problems in Engineering ◽

10.1155/2014/912389 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Aifan Ling ◽

Le Tang

Keyword(s):

Portfolio Management ◽

Numerical Study ◽

Risk Measure ◽

Tracking Error ◽

Downside Risk ◽

Worst Case ◽

Active Portfolio Management ◽

Multiple Weights ◽

Real Market ◽

Portfolio Selection Model

Recently, active portfolio management problems are paid close attention by many researchers due to the explosion of fund industries. We consider a numerical study of a robust active portfolio selection model with downside risk and multiple weights constraints in this paper. We compare the numerical performance of solutions with the classical mean-variance tracking error model and the naive1/Nportfolio strategy by real market data from China market and other markets. We find from the numerical results that the tested active models are more attractive and robust than the compared models.

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ACTIVE PORTFOLIO MANAGEMENT WITH CARDINALITY CONSTRAINTS: AN APPLICATION OF PARTICLE SWARM OPTIMIZATION

New Mathematics and Natural Computation ◽

10.1142/s1793005709001519 ◽

2009 ◽

Vol 05 (03) ◽

pp. 535-555 ◽

Cited By ~ 17

Author(s):

NIKOS S. THOMAIDIS ◽

TIMOTHEOS ANGELIDIS ◽

VASSILIOS VASSILIADIS ◽

GEORGIOS DOUNIAS

Keyword(s):

Particle Swarm Optimization ◽

Portfolio Management ◽

Tracking Error ◽

Particle Swarm ◽

Solution Space ◽

Upper And Lower Bounds ◽

Cardinality Constraints ◽

Swarm Optimization ◽

Computational Point ◽

Active Portfolio Management

This paper considers the task of forming a portfolio of assets that outperforms a benchmark index, while imposing a constraint on the tracking error volatility. We examine three alternative formulations of active portfolio management. The first one is a typical setup in which the fund manager myopically maximizes excess return. The second formulation is an attempt to set a limit on the total risk exposure of the portfolio by adding a constraint that forces a priori the risk of the portfolio to be equal to the benchmark's. In this paper, we also propose a third formulation that directly maximizes the efficiency of active portfolios, while setting a limit on the maximum tracking error variance. In determining optimal active portfolios, we incorporate additional constraints on the optimization problem, such as a limit on the maximum number of assets included in the portfolio (i.e. the cardinality of the portfolio) as well as upper and lower bounds on asset weights. From a computational point of view, the incorporation of these complex, though realistic, constraints becomes a challenge for traditional numerical optimization methods, especially when one has to assemble a portfolio from a big universe of assets. To deal properly with the complexity and the "roughness" of the solution space, we use particle swarm optimization, a population-based evolutionary technique. As an empirical application of the methodology, we select portfolios of different cardinality that actively reproduce the performance of the FTSE/ATHEX 20 Index of the Athens Stock Exchange. Our empirical study reveals important results concerning the efficiency of common practices in active portfolio management and the incorporation of cardinality constraints.

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