A rank-based model of competing Brownian particles, introduced in (Banner, Fernholz, Karatzas, 2005), captures the dependence of stock dynamics on size: Small stocks have higher growth rate but higher volatility than large stocks, on average. However, in this model, geometric returns of stocks have Gaussian tails. We modify this model using Capital Asset Pricing Model : The market exposure depends on the rank, and the benchmark moves as a general L\'evy process. We show that this model fits real market data. We discuss stability and long-term convergence .
The purpose of this short note is to state the Capital Asset Pricing Model for size deciles from Center for Research in Securities Prices database, and construct a related continuous-time model for Stochastic Portfolio Theory with rank-based Levy particles. We regress equity premia for size deciles over the equity premium for the top decile, and modify the model for continuous time. We simulate the resulting capital distribution curve .
R
A rank-based model of competing Brownian particles, introduced in (Banner, Fernholz, Karatzas, 2005), captures the dependence of stock dynamics on size: Small stocks have higher growth rate but higher volatility than large stocks, on average. However, in this model, geometric returns of stocks have Gaussian tails. We modify this model using
The purpose of this short note is to state the
R
: The market exposure depends on the rank, and the benchmark moves as a general L\'evy process. We show that this model fits real market data. We discuss stability and long-term convergence
for size deciles from Center for Research in Securities Prices database, and construct a related continuous-time model for Stochastic Portfolio Theory with rank-based Levy particles. We regress equity premia for size deciles over the equity premium for the top decile, and modify the model for continuous time. We simulate the resulting capital distribution curve