Before revision: 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.
After revision: The purpose of this short note is to state the Capital Asset Pricing Model : The market exposure depends on the rank, and the benchmark moves as a general L\'evy process.