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Producing the tangency portfolio as a corner portfolio

Published online by Cambridge University Press:  26 August 2013

Reza Keykhaei  and
Mohamad-Taghi Jahandideh
Reza Keykhaei
Affiliation:
Department of Mathematics, Khansar Faculty of Computer and Mathematics, University of Isfahan, Isfahan 81746-73441, Iran.. r.keykhaei@math.iut.ac.ir
Mohamad-Taghi Jahandideh
Affiliation:
College of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran.; jahandid@cc.iut.ac.ir
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Abstract

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset. In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio. So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via computing the corner portfolios. Moreover, we show that how this method can be used for tracing out the M-V efficient frontier when problem contains a riskless asset in which the borrowing is not allowed.

Keywords

M-V OptimizationParametric Quadratic ProgrammingCritical Line AlgorithmCapital Allocation LineTangency Portfolio
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 3 , July 2013 , pp. 311 - 320
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

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References

M.J. Best, An algorithm for the solution of the parametric quadratic programming problem, in Applied mathematics and parallel computing: Festchrift for KLaus Ritter, H. Fischer, B. Riedmüller, S. Schäfller, eds. Physica-verlag (1996) 57–76.
Best, M.J. and Grauer, R.R., The efficient set mathematics when the mean variance problem is subject to general linear constraints. J. Econ. Bus. 42 (1990) 105–120. Google Scholar
Z. Bodie, A. Kane and A.J. Marcus, Investments, 8rd edn. McGraw-Hill Irwin, New York (2009).
Dybvig, P.H., Short sales restrictions and kinks on the mean variance frontier. J. Finance 39 (1984) 239–244. Google Scholar
Hirschberger, M., Qi, Y. and Steuer, R.E., Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming. Eur. J. Oper. Res. 204 (2010) 581–588. Google Scholar
Jacobs, B.I., Levy, K.N. and Markowitz, H.M., Portfolio optimization with factors, scenarios, and realistic short positions. Oper. Res. 53 (2005) 586–599. Google Scholar
Markowitz, H.M., Portfolio selection. J. Finance 7 (1952) 77–91. Google Scholar
Markowitz, H.M., The optimization of a quadratic function subject to linear constraints. Naval Res. Logist. Quarterly 3 (1956) 111–33. Google Scholar
H.M. Markowitz, Portfolio selection: Efficient diversification of investments. John Wiley, New York (1959).
H.M. Markowitz, Mean-variance analysis in portfolio choice and capital markets. Basil Blackwell, Oxford, UK (1987).
H.M. Markowitz and P. Todd, Mean-variance analysis in portfolio choice and capital markets. Frank J. Fabozzi Associates, New Hope, Pennsylvania (2000).
Merton, R.C., An analytical derivation of the efficient portfolio frontier. J. Financial Quant. Anal. 7 (1972) 1851–1872. Google Scholar
A. Niedermayer and D. Niedermayer, Applying Markowitz’s critical line algorithm, in Handbook of portfolio construction, J.B. Guerard (Ed.), Springer-Verlag, Berlin (2010) 383–400.
W.F. Sharpe, The Sharpe ratio. J. Portfolio Manage. Fall (1994) 49–58.
Stein, M., Branke, J. and Schmeck, H., Efficient implementation of an active set algorithm for large-scale portfolio selection. Comput. Oper. Res. 35 (2008) 3945–3961. Google Scholar
Tobin, J., Liquidity preference as a behavior towards risk. Rev. Econ. Stud. 25 (1958) 65–86. Google Scholar
Tütüncü, R.H., A note on calculating the optimal risky portfolio. Finance Stoch. 5 (2001) 413–417. Google Scholar
Vörös, J., Kriens, J. and Strijbosch, L.W.G., A note on the kinks at the mean variance frontier. Eur. J. Oper. Res. 112 (1999) 236–239. Google Scholar