Mean-absolute deviation portfolio optimization model under transaction costs

Konno, Hiroshi; Wijayanayake, A.

doi:10.1016/s0453-4514(00)87111-2

Cited by 30 publications

(9 citation statements)

References 7 publications

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“…While the original Markowitz model forms a quadratic programming problem, following the initial works on its linear programming (LP) approximation [23,27], many attempts have been made to linearize the portfolio optimization procedure (c.f., [26] and references therein). The LP solvability is very important for applications to real-life financial decisions where the constructed portfolios have to meet numerous side constraints (including the minimum transaction lots [13]) and take into account transaction costs [11]. of the our LP computable models comparing their performances on the asset allocation problem while using historical values of 81 sectorial S&P500 indices.…”

Section: Introductionmentioning

confidence: 99%

On Extending the LP Computable Risk Measures to Account Downside Risk

Krzemienowski

Ogryczak

2005

Comput Optim Applic

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Abstract.A mathematical model of portfolio optimization is usually quantified with mean-risk models offering a lucid form of two criteria with possible trade-off analysis. In the classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. Following Sharpe's work on linear approximation to the mean-variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving linear programming (LP) problems. Typical LP computable risk measures, like the mean absolute deviation (MAD) or the Gini's mean absolute difference (GMD) are symmetric with respect to the below-mean and over-mean performances. The paper shows how the measures can be further combined to extend their modeling capabilities with respect to enhancement of the below-mean downside risk aversion. The relations of the below-mean downside stochastic dominance are formally introduced and the corresponding techniques to enhance risk measures are derived. The resulting mean-risk models generate efficient solutions with respect to second degree stochastic dominance, while at the same time preserving simplicity and LP computability of the original models. The models are tested on real-life historical data.

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Section: Introductionmentioning

confidence: 99%

On Extending the LP Computable Risk Measures to Account Downside Risk

Krzemienowski

Ogryczak

2005

Comput Optim Applic

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“…We compare conditional value-at-risk and conditional drawdown-atrisk with more established mean-absolute deviation, maximum loss, and market-neutrality approaches. These risk management criteria allow for the formulation of linear portfolio rebalancing strategies and have proven their high efficiency in various portfolio management applications (Andersson et al [2001], Chekhlov et al [2000], Dembo and King [1992], Duarte [1999], Konno and Wijayanayake [1999], Konno and Yamazaki [1991], Palmquist et al [1999], Rockafellar andUryasev [2000, 2001], Ziemba and Mulvey [1998], Zenios [1999], and Young [1998]). The choice of hedge funds as a subject for the portfolio optimization strategy is stimulated by a strong interest in this class of assets, by both practitioners and scholars, due in part to their return properties.…”

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confidence: 99%

“…The classical Markowitz theory identifies risk with the volatility (standard deviation) of a portfolio. In the present study we investigate a portfolio optimization problem with five different constraints on risk, including conditional value-at-risk (Rockafellar andUryasev [2000, 2001]), conditional drawdown-at-risk (Chekhlov et al [1999]), mean-absolute deviation (Konno and Yamazaki [1991], Konno and Shirakawa [1994], Konno and Wijayanayake [1999]), maximum loss (Young [1998]), and market neutrality (beta of the portfolio equals zero). 3 The first two risk measures represent relatively new developments in the risk management field.…”

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confidence: 99%

Risk Management for Hedge Fund Portfolios

Krokhmal

Uryasev²,

Zrazhevsky

2002

JAI

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“…• When transaction costs φ j (x j ) are assumed to be concave, then (3.65) is a linearly constrained convex minimization problem, which is in [72] solved using a branchand-bound algorithm. They test the model on data of up to 200 assets.…”

Section: Mad Under Transaction Costsmentioning

confidence: 99%

Mean-Variance Portfolio Optimization : Eigendecomposition-Based Methods

Mayambala¹

2015

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Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance was used as a measure of risk, which gave rise to the wellknown mean-variance portfolio optimization model. Although other mean-risk models have been proposed in the literature, the mean-variance model continues to be the backbone of modern portfolio theory and it is still commonly applied. The scope of this thesis is a solution technique for the mean-variance model in which eigendecomposition of the covariance matrix is performed.The first part of the thesis is a review of the mean-risk models that have been suggested in the literature. For each of them, the properties of the model are discussed and the solution methods are presented, as well as some insight into possible areas of future research.The second part of the thesis is two research papers. In the first of these, a solution technique for solving the mean-variance problem is proposed. This technique involves making an eigendecomposition of the covariance matrix and solving an approximate problem that includes only relatively few eigenvalues and corresponding eigenvectors. The method gives strong bounds on the exact solution in a reasonable amount of computing time, and can thus be used to solve large-scale mean-variance problems.The second paper studies the mean-variance model with cardinality constraints, that is, with a restricted number of securities included in the portfolio, and the solution technique from the first paper is extended to solve such problems. Near-optimal solutions to large-scale cardinality constrained mean-variance portfolio optimization problems are obtained within a reasonable amount of computing time, compared to the time required by a commercial general-purpose solver.v Populärvetenskaplig sammanfattningFör den som har kapital att investera kan det vara svårt att avgöra vilka investeringar som är mest fördelaktiga. Till stöd för beslutet kan matematiska modeller användas och denna avhandling handlar om hur man kan beräkna lösningar till sådana modeller. De investeringsalternativ som betraktas är finansiella instrument som är föremål för daglig handel, som aktier och obligationer.En investerare placerar kapital i finansiella instrument eftersom de förväntas ge en god avkastning över tiden. Samtidigt är sådana placeringar alltid förknippade med risktagande. Förväntad avkastning och risk varierar kraftigt mellan olika instrument. Till exempel ger placeringar i statsobligationer typiskt mycket låg avkastning till mycket låg risk, medan placeringar i aktier i nystartade bolag som utvecklar nya läkemedel kan ge mycket hög avkastning samtidigt som risken är mycket hög.Att investera kan ses som en avvägning mellan den förväntade avkastningen och den risk som investeringen innebär, och typiskt är hög förväntad avkastning också associerade med e...

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Mean-absolute deviation portfolio optimization model under transaction costs

Cited by 30 publications

References 7 publications

On Extending the LP Computable Risk Measures to Account Downside Risk

On Extending the LP Computable Risk Measures to Account Downside Risk

Risk Management for Hedge Fund Portfolios

Mean-Variance Portfolio Optimization : Eigendecomposition-Based Methods

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