Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T22:25:22.994Z Has data issue: false hasContentIssue false
  • English
  • Français

Tangency portfolios in the LP solvable portfolio selectionmodels

Published online by Cambridge University Press:  25 July 2012

Reza Keykhaei  and
Mohamad Taghi Jahandideh
Reza Keykhaei
Affiliation:
College of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran. [email protected]; [email protected]
Mohamad Taghi Jahandideh
Affiliation:
College of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran. [email protected]; [email protected]
Get access

Abstract

A risk measure in a portfolio selection problem is linear programming (LP) solvable, ifit has a linear formulation when the asset returns are represented by discrete randomvariables, i.e., they are defined by their realizations under specifiedscenarios. The efficient frontier corresponding to an LP solvable model is a piecewiselinear curve. In this paper we describe a method which realizes and produces a tangencyportfolio as a by-product during the procedure of tracing out of the efficient frontier ofrisky assets in an LP solvable model, when our portfolio contains some risky assets and ariskless asset, using nonsmooth optimization methods. We show that the test of finding thetangency portfolio can be limited only for two portfolios. Also, we describe that how thismethod can be employed to trace out the efficient frontier corresponding to a portfolioselection problem in the presence of a riskless asset.

Keywords

Linear programmingLP solvable portfolio selection modelssubgradienttangency portfolioAneja-Nair method
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 2 , April 2012 , pp. 149 - 158
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aneja, Y.P. and Nair, K.P.K., Bicriteria transportation problem. Manage. Sci. 25 (1979) 73–78. Google Scholar
M.S. Bazaraa, J.J. Jarvis and H.D. Sherali, Linear programming and network flows, 3rd edition. John Wiley & Sons, New York (2005).
Cai, X.Q., Teo, K.L., Yang, X.Q., and Zhou, X.Y., Portfolio optimization under a minimax rule. Manage. Sci. 46 (2000) 957–972. Google Scholar
J.-B. Hiriart-Urruty and C. Lemaréchal. Convex analysis and minimization algorithms I. Springer, Berlin, Heidelberg, New York (1993).
Konno, H. and Yamazaki, H., Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage. Sci. 37 (1991) 519–529. Google Scholar
Lust, T. and Teghem, J., Two-phase pareto local search for the biobjective traveling salesman problem. J. Heuristics 16 (2010) 475–510. Google Scholar
Mansini, R., Ogryczak, W. and Speranza, M.G., On LP solvable models for portfolio selection. Informatica 14 (2003) 37–62. Google Scholar
Markowitz, H.M., Portfolio selection. J. Financ. 7 (1952) 77–91. Google Scholar
Rockafellar, R.T. and Uryasev, S., Optimization of conditional value-at-risk. J. Risk 2 (2000) 21–41. Google Scholar
Sharpe, W.F., The Sharpe ratio. J. Portfolio Manage. Fall (1994) 49–58. Google Scholar
Teo, K.L. and Yang, X.O., Portfolio selection problem with minimax type risk function. Ann. Oper. Res. 101 (2001) 333–349. Google Scholar
Tütüncü, R.H., A note on calculating the optimal risky portfolio. Finance Stochastics 5 (2001) 413–417. Google Scholar
Yitzhaki, S., Stochastic dominance, mean variance, and Ginis mean difference. Amer. Econ. Rev. 72 (1982) 178–185. Google Scholar
Young, M.R., A minimax portfolio selection rule with linear programming solution. Manage. Sci. 44 (1998) 673–683. Google Scholar