Online Universal Dirichlet Factor Portfolios

ArXiv ID: 2308.07763 “View on arXiv”

Authors: Unknown

Abstract

We revisit the online portfolio allocation problem and propose universal portfolios that use factor weighing to produce portfolios that out-perform uniform dirichlet allocation schemes. We show a few analytical results on the lower bounds of portfolio growth when the returns are known to follow a factor model. We also show analytically that factor weighted dirichlet sampled portfolios dominate the wealth generated by uniformly sampled dirichlet portfolios. We corroborate our analytical results with empirical studies on equity markets that are known to be driven by factors.

Keywords: Online Portfolio Allocation, Factor Models, Universal Portfolios, Dirichlet Allocation, Growth Optimization, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with mathematical derivations, including factor models, growth rate bounds, and inequalities like AM-GM, which yields a high math complexity score. However, the empirical evidence is described generically (’empirical studies on equity markets’) without providing specific backtest results, datasets, or implementation details, leading to a lower empirical rigor score.

  flowchart TD
    A["Research Goal: Revisit Online Portfolio Allocation<br>Does Factor-Weighted Dirichlet Dominate Uniform Dirichlet?"]
    B["Methodology: Analytical Derivation<br>Factor Weighting & Growth Bounds"]
    C["Data: Historical Equity Market Returns<br>Known to be Factor Driven"]
    D["Computational Process: Backtesting<br>Simulate Universal Portfolios via Dirichlet Sampling"]
    E["Outcome 1: Analytical Proof<br>Factor-Weighted Strictly Dominates Uniform"]
    F["Outcome 2: Empirical Validation<br>Higher Portfolio Growth & Outperformance"]

    A --> B
    A --> C
    B --> D
    C --> D
    D --> E
    D --> F