High order universal portfolios
ArXiv ID: 2311.13564 “View on arXiv”
Authors: Unknown
Abstract
The Cover universal portfolio (UP from now on) has many interesting theoretical and numerical properties and was investigated for a long time. Building on it, we explore what happens when we add this UP to the market as a new synthetic asset and construct by recurrence higher order UPs. We investigate some important theoretical properties of the high order UPs and show in particular that they are indeed different from the Cover UP and are capable to break the time permutation invariance. We show that under some perturbation regime the second high order UP has better Sharp ratio than the standard UP and briefly investigate arbitrage opportunities thus created. Numerical experiences on a benchmark from the literature confirm that high order UPs improve Cover’s UP performances.
Keywords: Universal Portfolios, Arbitrage, Portfolio Optimization, Time Series Analysis
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 4.0/10
- Quadrant: Lab Rats
- Why: The paper introduces high-order recursive modifications of the universal portfolio, involving significant theoretical derivations (e.g., asymptotic properties, Sharpe ratio comparisons, and breaking time permutation invariance) and heavy mathematical notation, scoring high on complexity. However, the empirical validation is limited to a brief mention of numerical experiments on a benchmark without detailed backtest methodology, code, or robust statistical reporting, placing it in the Lab Rats quadrant.
flowchart TD
A["Research Goal<br>Investigate Higher-Order Universal Portfolios"] --> B["Methodology<br>Construct UP_k Recursively"]
B --> C["Data Input<br>Benchmark Time Series Data"]
C --> D["Computational Process<br>Simulate & Compute Sharpe Ratios"]
D --> E["Outcome 1<br>Breaks Time Permutation Invariance"]
D --> F["Outcome 2<br>Higher Sharpe Ratio under Perturbation"]
D --> G["Outcome 3<br>Identifies Arbitrage Opportunities"]