A Note on Universal Bilinear Portfolios

Alex Garivaltis
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Alex Garivaltis: 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

IJFS, 2021, vol. 9, issue 1, 1-17

Abstract: 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.

Keywords: on-line portfolio selection; universal portfolios; robust procedures; model uncertainty; constant-rebalanced portfolios; asymptotic capital growth; kelly criterion (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2021
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