Portfolio theory for squared returns correlated across time

Ernst Eberlein; Dilip B. Madan

doi:10.1186/s41546-016-0001-4

Article Contents

2016, Volume 1: 1. Doi: 10.1186/s41546-016-0001-4

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Portfolio theory for squared returns correlated across time

Ernst Eberlein^1, , and
Dilip B. Madan²

1 University of Freiburg, Freiburg im Breisgau, Germany;
2 University of Maryland, College Park, USA

Ernst Eberlein, eberlein@stochastik.uni-freiburg.de

Received: January 11, 2016

Revised: June 09, 2016

Published: September 2020

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Abstract

Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic portfolio problem is formulated and implemented. This development leads to a mean ask price frontier, where the latter employs concave distortions. The modeling permits access to skewness via randomized drifts. Optimal portfolios maximize a conservative market value seen as a bid price for the portfolio. On the mean ask price frontier we observe a tradeoff between the deterministic and random drifts and the volatility costs of increasing the deterministic drift. From a historical perspective, we also implement a mean-variance analysis. The resulting mean-variance frontier is three-dimensional expressing the minimal variance as a function of the targeted levels for the deterministic and random drift.

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References

[1]	Acharya, VV, Pedersen, LH:Asset pricing with liquidity risk. J. Financ. Econ 77, 375-410 (2005)
[2]	Ait-Sahalia, Y, Brandt, MW:Variable selection for portfolio choice. J. Financ 56, 1297-1351 (2001)
[3]	Bajeux-Besnainou, I, Portait, R:Dynamic asset allocation in a mean-variance framework. Manag. Sci 44, 79-95 (1998)
[4]	Bansal, R, Dahlquist, M, Harvey, CR:Dynamic Trading Strategies and Portfolio Choice. Working Paper, Duke University (2004)
[5]	Barndorff-Nielsen, OE, Shephard, N:Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J. R. Stat. Soc. B 64, 253-280 (2002)
[6]	Basak, S, Chabakauri, G:Dynamic mean-variance asset allocation. Rev. Financ. Stud 23, 2970-3016 (2010)
[7]	Bielecki, T, Jin, H, Pliska, SR, Zhou, XY:Continuous-time mean-variance portfolio selection with bankruptcy prohibition. Math. Financ 15, 213-244 (2005)
[8]	Brandt, MW, Goyal, A, Santa-Clara, P, Stroud, JR:A simulation approach to dynamic portfolio choice with an application to learning about predictability. Rev. Financ. Stud 18, 831-873 (2005)
[9]	Brandt, MW:Portfolio Choice Problems. In:Ait-Sahalia, Y, Hansen, LP (eds.) Handbook of Financial Econometrics, Chapter 5, pp. 269-336. Elsevier, Amsterdam (2009)
[10]	Brandt, MW, Santa-Clara, P:Dynamic portfolio selection by augmenting the asset space. J. Financ 61, 2187-2218 (2006)
[11]	Campbell, JY, Viceira, LM:Strategic Asset Allocation:Portfolio Choice for Long Term Investors. Oxford University Press, Oxford (2002)
[12]	Cherny, A, Madan, D:New measures for performance evaluation. Rev. Financ. Stud 22, 2571-2606 (2009)
[13]	Cochrane, JHL:A mean-variance benchmark for intertemporal portfolio theory. J. Financ 69, 1-49 (2014)
[14]	Cvitanic, J, Lazrak, A, Wang, T:Implications of the Sharpe ratio as a performance in multi-period settings.J. Econ. Dyn. Control 32, 1622-1649 (2008)
[15]	Cvitanic, J, Zapatero, F:Introduction to the Economics and Mathematics of Financial Markets. MIT Press, Cambridge, MA (2004)
[16]	Duffie, D, Richardson, H:Mean-variance hedging in continuous time. Ann. Appl. Probab 1, 1-15 (1991)
[17]	Hong, H, Scheinkman, J, Xiong, W:Asset float and speculative bubbles. J. Financ 61, 1073-1117 (2006)
[18]	Jagannathan, R, Ma, T:Risk reduction in large portfolios:why imposing the wrong constraints helps. J.Financ 58, 1651-1683 (2003)
[19]	Kusuoka, S:On law invariant coherent risk measures. Adv. Math. Econ 3, 83-95 (2001)
[20]	Leippold, M, Trojani, F, Vanini, P:Geometric approach to multiperiod mean variance optimization of assets and liabilities. J. Econ. Dyn. Control 28, 1079-1113 (2004)
[21]	Lim, AEB, Zhou, XY:Mean-variance portfolio selection with random parameters in a complete market.Math. Oper. Res 27, 101-120 (2002)
[22]	MacLean, LC, Zhao, Y, Ziemba, WT:Mean-variance versus expected utility in dynamic investment analysis. Comput. Manag. Sci 8, 3-22 (2011)
[23]	Madan, DB:Conic portfolio theory. Int. J. Theor. Appl. Financ (2016). doi:10.1142/SO219024916500199
[24]	Madan, DB, Pistorius, M, Stadje, M:On Dynamic Spectral Risk Measures and a Limit Theorem. Working Paper, Imperial College, London (2015)
[25]	Markowitz, HM:Portfolio selection. J. Financ 7, 77-91 (1952)
[26]	Markowitz, HM:Foundations of portfolio theory. J. Financ 46, 469-477 (1991)
[27]	Skiadas, C:Asset Pricing Theory. Princeton University Press, Princeton, NJ (2009)
[28]	Strotz, RH:Myopia and inconsistency in dynamic utility maximization. Rev. Econ. Stud 23, 165-180 (1956)
[29]	Zhou, XY, Li, D:Continuous-time mean-variance portfolio selection:a stochastic LQ framework. Appl.Math. Optim 42, 19-33 (2000)