158 research outputs found
Diversity and Arbitrage in a Regulatory Breakup Model
In 1999 Robert Fernholz observed an inconsistency between the normative
assumption of existence of an equivalent martingale measure (EMM) and the
empirical reality of diversity in equity markets. We explore a method of
imposing diversity on market models by a type of antitrust regulation that is
compatible with EMMs. The regulatory procedure breaks up companies that become
too large, while holding the total number of companies constant by imposing a
simultaneous merge of other companies. The regulatory events are assumed to
have no impact on portfolio values. As an example, regulation is imposed on a
market model in which diversity is maintained via a log-pole in the drift of
the largest company. The result is the removal of arbitrage opportunities from
this market while maintaining the market's diversity.Comment: 21 page
Trading Strategies Generated Pathwise by Functions of Market Weights
Almost twenty years ago, E.R. Fernholz introduced portfolio generating
functions which can be used to construct a variety of portfolios, solely in the
terms of the individual companies' market weights. I. Karatzas and J. Ruf
recently developed another methodology for the functional construction of
portfolios, which leads to very simple conditions for strong relative arbitrage
with respect to the market. In this paper, both of these notions of functional
portfolio generation are generalized in a pathwise, probability-free setting;
portfolio generating functions are substituted by path-dependent functionals,
which involve the current market weights, as well as additional
bounded-variation functions of past and present market weights. This
generalization leads to a wider class of functionally-generated portfolios than
was heretofore possible, and yields improved conditions for outperforming the
market portfolio over suitable time-horizons.Comment: 45 pages, 3 figure
Generalised Lyapunov functions and functionally generated trading strategies
This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies to be strong arbitrage relative to the market over sufficiently large time horizons. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. These theoretical results are complemented by several empirical examples using data from the S&P 500 stocks
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