Calibrated rank volatility stabilized models for large equity markets

ArXiv ID: 2403.04674 “View on arXiv”

Authors: Unknown

Abstract

In the framework of stochastic portfolio theory we introduce rank volatility stabilized models for large equity markets over long time horizons. These models are rank-based extensions of the volatility stabilized models introduced by Fernholz & Karatzas in 2005. On the theoretical side we establish global existence of the model and ergodicity of the induced ranked market weights. We also derive explicit expressions for growth-optimal portfolios and show the existence of relative arbitrage with respect to the market portfolio. On the empirical side we calibrate the model to sixteen years of CRSP US equity data matching (i) rank-based volatilities, (ii) stock turnover as measured by market weight collisions, (iii) the average market rate of return and (iv) the capital distribution curve. Assessment of model fit and error analysis is conducted both in and out of sample. To the best of our knowledge this is the first model exhibiting relative arbitrage that has statistically been shown to have a good quantitative fit with the empirical features (i)-(iv). We additionally simulate trajectories of the calibrated model and compare them to historical trajectories, both in and out of sample.

Keywords: Stochastic Portfolio Theory, Rank Volatility, Relative Arbitrage, Growth-Optimal Portfolios, Ergodicity, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper is dense with stochastic calculus, SDEs, and theoretical proofs (existence, ergodicity, arbitrage), placing it in the high math category. It also demonstrates high empirical rigor by calibrating to 16 years of CRSP data, performing in/out-of-sample error analysis, and simulating trajectories.

  flowchart TD
    A["Research Goal"] --> B["Data Source"]
    B --> C["Model Calibration"]
    C --> D["Computational Analysis"]
    D --> E["Key Findings/Outcomes"]