A stock market model based on CAPM and market size

We introduce a new system of stochastic differential equations which models dependence market beta and unsystematic risk upon size, measured by capitalization. fit our model using size deciles data from Kenneth French’s library. This is somewhat similar to generalized volatility-stabilized models. The novelty work twofold. First, we take into account the difference between price total returns (in other words, wealth processes). Second, with actual data. study long-term properties this equations, reproduce observed linearity capital distribution curve. In “Appendix”, analyze size-based real-world index funds.