no. 3
Producing the tangency portfolio as a corner portfolio
RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 3, pp. 311-320.

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.

DOI : 10.1051/ro/2013041
Classification : 91G10, 90C20, 90C29
Mots clés : M-V optimization, parametric quadratic programming, critical line algorithm, capital allocation line, tangency portfolio 
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Keykhaei, Reza; Jahandideh, Mohamad-Taghi. Producing the tangency portfolio as a corner portfolio. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 3, pp. 311-320. doi : 10.1051/ro/2013041. http://www.numdam.org/articles/10.1051/ro/2013041/

[1] 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. | MR | Zbl

[2] M.J. Best and R.R. Grauer, The efficient set mathematics when the mean variance problem is subject to general linear constraints. J. Econ. Bus. 42 (1990) 105-120.

[3] Z. Bodie, A. Kane and A.J. Marcus, Investments, 8rd edn. McGraw-Hill Irwin, New York (2009).

[4] P.H. Dybvig, Short sales restrictions and kinks on the mean variance frontier. J. Finance 39 (1984) 239-244.

[5] M. Hirschberger, Y. Qi and R.E. Steuer, Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming. Eur. J. Oper. Res. 204 (2010) 581-588. | MR | Zbl

[6] B.I. Jacobs, K.N. Levy and H.M. Markowitz, Portfolio optimization with factors, scenarios, and realistic short positions. Oper. Res. 53 (2005) 586-599. | MR | Zbl

[7] H.M. Markowitz, Portfolio selection. J. Finance 7 (1952) 77-91.

[8] H.M. Markowitz, The optimization of a quadratic function subject to linear constraints. Naval Res. Logist. Quarterly 3 (1956) 111-33. | MR

[9] H.M. Markowitz, Portfolio selection: Efficient diversification of investments. John Wiley, New York (1959). | MR

[10] H.M. Markowitz, Mean-variance analysis in portfolio choice and capital markets. Basil Blackwell, Oxford, UK (1987). | MR | Zbl

[11] H.M. Markowitz and P. Todd, Mean-variance analysis in portfolio choice and capital markets. Frank J. Fabozzi Associates, New Hope, Pennsylvania (2000). | Zbl

[12] R.C. Merton, An analytical derivation of the efficient portfolio frontier. J. Financial Quant. Anal. 7 (1972) 1851-1872.

[13] 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. | MR

[14] W.F. Sharpe, The Sharpe ratio. J. Portfolio Manage. Fall (1994) 49-58.

[15] M. Stein, J. Branke and H. Schmeck, Efficient implementation of an active set algorithm for large-scale portfolio selection. Comput. Oper. Res. 35 (2008) 3945-3961. | Zbl

[16] J. Tobin, Liquidity preference as a behavior towards risk. Rev. Econ. Stud. 25 (1958) 65-86.

[17] R.H. Tütüncü, A note on calculating the optimal risky portfolio. Finance Stoch. 5 (2001) 413-417. | MR | Zbl

[18] J. Vörös, J. Kriens and L.W.G. Strijbosch, A note on the kinks at the mean variance frontier. Eur. J. Oper. Res. 112 (1999) 236-239. | Zbl

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