Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257756 
Year of Publication: 
2021
Citation: 
[Journal:] International Journal of Financial Studies [ISSN:] 2227-7072 [Volume:] 9 [Issue:] 1 [Article No.:] 11 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-17
Publisher: 
MDPI, Basel
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.
Subjects: 
asymptotic capital growth
constant-rebalanced portfolios
kelly criterion
model uncertainty
on-line portfolio selection
robust procedures
universal portfolios
JEL: 
D81
D83
G11
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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