Universal portfolio algorithms in realistic-outcome markets

Abstract

Universal portfolio algorithms find investment strategies competitive against any CRP (constant rebalanced portfolio) for each and every market sequence. This work studies the problem of competitiveness over a subset of realistic, non-pathological, market sequences observed in many settings, e.g., high-frequency trading. Competitive investment in this setting will be shown to be more an extension of the easier universal 0–1 loss problem than of universal gambling (or coding). Analysis of realism-agnostic investment algorithms will show that they perform much better on in-hindsight realistic sequences than previously demonstrated. We suggest that this implies that the study of realistic universal portfolio algorithms must involve a comparison to a stronger adversary than the CRP adversary: an adversary that rebalances a portfolio often enough to avoid pathological sequences, but not so frequently that transaction costs dominate.