Portfolio Theory for Squared Returns Correlated Across Time

43 Pages Posted: 26 Jul 2015 Last revised: 2 Mar 2016

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: January 20, 2016

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.

Keywords: Correlated Gamma Processes, Distorted Expectations, Conic Portfolio Theory

JEL Classification: G10, G11, G13

Suggested Citation

Eberlein, Ernst and Madan, Dilip B., Portfolio Theory for Squared Returns Correlated Across Time (January 20, 2016). Robert H. Smith School Research Paper No. RHS 2635632, Available at SSRN: https://ssrn.com/abstract=2635632 or http://dx.doi.org/10.2139/ssrn.2635632

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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