  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.
