Product Market Competition and the Stock Market : Capitalisation, Returns and Betas

We develop a tractable RBC model of the stock market with heterogenous firms. Shares value rests on the rent extracted from proprietary technology à la Dixit-Stiglitz. We prove the existence and uniqueness of the fundamental equilibrium. Closed form solutions are provided for the market portfolio and for individual firms' valuations, and for each stock's beta, under weak assumptions on the shock processes. An increase in the degree of monopoly unambiguously increases the stock market capitalisation and reduces the stock index return. As the Lerner index tends to one, the idiosyncratic components of individual returns, generated by the productivity shocks, tend to vanish: the stock market can no longer provide instruments for trading risk beyond the stock index