# Producing the tangency portfolio as a corner portfolio

Reza Keykhaei; Mohamad-Taghi Jahandideh

RAIRO - Operations Research - Recherche Opérationnelle (2013)

- Volume: 47, Issue: 3, page 311-320
- ISSN: 0399-0559

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topKeykhaei, Reza, and Jahandideh, Mohamad-Taghi. "Producing the tangency portfolio as a corner portfolio." RAIRO - Operations Research - Recherche Opérationnelle 47.3 (2013): 311-320. <http://eudml.org/doc/275019>.

@article{Keykhaei2013,

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.},

author = {Keykhaei, Reza, Jahandideh, Mohamad-Taghi},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {M-V optimization; parametric quadratic programming; critical line algorithm; capital allocation line; tangency portfolio; mean-variance optimization},

language = {eng},

number = {3},

pages = {311-320},

publisher = {EDP-Sciences},

title = {Producing the tangency portfolio as a corner portfolio},

url = {http://eudml.org/doc/275019},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Keykhaei, Reza

AU - Jahandideh, Mohamad-Taghi

TI - Producing the tangency portfolio as a corner portfolio

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 3

SP - 311

EP - 320

AB - 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.

LA - eng

KW - M-V optimization; parametric quadratic programming; critical line algorithm; capital allocation line; tangency portfolio; mean-variance optimization

UR - http://eudml.org/doc/275019

ER -

## References

top- [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. Zbl0906.65064MR1469261
- [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. Finance39 (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. Zbl1181.90211MR2587884
- [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. Zbl1165.91404MR2157865
- [7] H.M. Markowitz, Portfolio selection. J. Finance7 (1952) 77–91.
- [8] H.M. Markowitz, The optimization of a quadratic function subject to linear constraints. Naval Res. Logist. Quarterly3 (1956) 111–33. MR80577
- [9] H.M. Markowitz, Portfolio selection: Efficient diversification of investments. John Wiley, New York (1959). MR103768
- [10] H.M. Markowitz, Mean-variance analysis in portfolio choice and capital markets. Basil Blackwell, Oxford, UK (1987). Zbl0757.90003MR1094565
- [11] H.M. Markowitz and P. Todd, Mean-variance analysis in portfolio choice and capital markets. Frank J. Fabozzi Associates, New Hope, Pennsylvania (2000). Zbl0757.90003
- [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. MR2885126
- [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. Zbl1278.90295
- [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. Zbl0978.91034MR1850790
- [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. Zbl0959.91023

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