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A Note on Universal Bilinear Portfolios

Department of Economics, School of Public and Global Affairs, College of Liberal Arts and Sciences, Northern Illinois University, 514 Zulauf Hall, DeKalb, IL 60115, USA
Int. J. Financial Stud. 2021, 9(1), 11; https://0-doi-org.brum.beds.ac.uk/10.3390/ijfs9010011
Received: 8 January 2021 / Revised: 5 February 2021 / Accepted: 10 February 2021 / Published: 24 February 2021
This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of “universal portfolios”. I generalize Cover’s benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hindsight for the realized sequence of asset prices. A bilinear trading strategy is a mini two-period active strategy whose final capital growth factor is linear separately in each period’s gross return vector for the asset market. I apply Thomas Cover’s ingenious performance-weighted averaging technique to construct a universal bilinear portfolio that is guaranteed (uniformly for all possible market behavior) to compound its money at the same asymptotic rate as the best bilinear trading strategy in hindsight. Thus, the universal bilinear portfolio asymptotically dominates the original (1-linear) universal portfolio in the same technical sense that Cover’s universal portfolios asymptotically dominate all constant-rebalanced portfolios and all buy-and-hold strategies. In fact, like so many Russian dolls, one can get carried away and use these ideas to construct an endless hierarchy of ever more dominant H-linear universal portfolios. View Full-Text
Keywords: on-line portfolio selection; universal portfolios; robust procedures; model uncertainty; constant-rebalanced portfolios; asymptotic capital growth; kelly criterion on-line portfolio selection; universal portfolios; robust procedures; model uncertainty; constant-rebalanced portfolios; asymptotic capital growth; kelly criterion
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MDPI and ACS Style

Garivaltis, A. A Note on Universal Bilinear Portfolios. Int. J. Financial Stud. 2021, 9, 11. https://0-doi-org.brum.beds.ac.uk/10.3390/ijfs9010011

AMA Style

Garivaltis A. A Note on Universal Bilinear Portfolios. International Journal of Financial Studies. 2021; 9(1):11. https://0-doi-org.brum.beds.ac.uk/10.3390/ijfs9010011

Chicago/Turabian Style

Garivaltis, Alex. 2021. "A Note on Universal Bilinear Portfolios" International Journal of Financial Studies 9, no. 1: 11. https://0-doi-org.brum.beds.ac.uk/10.3390/ijfs9010011

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