Performance of the reverse Helmbold universal portfolio

2017 ◽  
Author(s):  
Choon Peng Tan ◽  
Kee Seng Kuang ◽  
Yap Jia Lee
Keyword(s):  
Universal Portfolio

scholarly journals A Note on Universal Bilinear Portfolios

2021 ◽  
Vol 9 (1) ◽  
pp. 11
Author(s):  
Alex Garivaltis
Keyword(s):  
Growth Factor ◽  
Trading Strategy ◽  
Weighted Averaging ◽  
Asset Market ◽  
Best Constant ◽  
Capital Growth ◽  
Universal Portfolios ◽  
Universal Portfolio ◽  
Technical Sense ◽  
Constant Rebalanced Portfolios

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.

scholarly journals The Finite and Moving Order Multinomial Universal Portfolio

2013 ◽  
Vol 435 ◽  
pp. 012039 ◽  
Author(s):  
Choon Peng Tan ◽  
Sook Theng Pang
Keyword(s):  
Universal Portfolio

scholarly journals UNIVERSAL RISK BUDGETING

2021 ◽  
Author(s):  
ALEX GARIVALTIS
Keyword(s):  
Side Information ◽  
Covariance Structure ◽  
Mathematical Finance ◽  
Risk Budgeting ◽  
Capital Budget ◽  
New Family ◽  
Black Scholes ◽  
Universal Portfolios ◽  
Universal Portfolio ◽  
Dirichlet Priors

I juxtapose Cover’s vaunted universal portfolio selection algorithm ([Cover, TM (1991). Universal portfolios. Mathematical Finance, 1, 1–29]) with the modern representation of a portfolio as a certain allocation of risk among the available assets, rather than a mere allocation of capital. Thus, I define a Universal Risk Budgeting scheme that weights each risk budget, instead of each capital budget, by its historical performance record, á la Cover. I prove that my scheme is mathematically equivalent to a novel type of [Cover, TM and E Ordentlich (1996). Universal portfolios with side information. IEEE Transactions on Information Theory, 42, 348–363] universal portfolio that uses a new family of prior densities that have hitherto not appeared in the literature on universal portfolio theory. I argue that my universal risk budget, so-defined, is a potentially more perspicuous and flexible type of universal portfolio; it allows the algorithmic trader to incorporate, with advantage, his prior knowledge or beliefs about the particular covariance structure of instantaneous asset returns. Say, if there is some dispersion in the volatilities of the available assets, then the uniform or Dirichlet priors that are standard in the literature will generate a dangerously lopsided prior distribution over the possible risk budgets. In the author’s opinion, the proposed “Garivaltis prior” makes for a nice improvement on Cover’s timeless expert system, that is properly agnostic and open to different risk budgets from the very get-go. Inspired by [Jamshidian, F (1992). Asymptotically optimal portfolios. Mathematical Finance, 2, 131–150], the universal risk budget is formulated as a new kind of exotic option in the continuous time Black–Scholes market, with all the pleasure, elegance, and convenience that entails.

scholarly journals Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio

2018 ◽  
Vol 29 (3) ◽  
pp. 773-803 ◽  
Author(s):  
Christa Cuchiero ◽  
Walter Schachermayer ◽  
Ting‐Kam Leonard Wong
Keyword(s):  
Portfolio Theory ◽  
Stochastic Portfolio Theory ◽  
Numéraire Portfolio ◽  
Universal Portfolio ◽  
Numeraire Portfolio
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