Asset Pricing Under Keeping Up With the Joneses and Heterogeneous Beliefs

When agents agree to disagree about the expected growth rate of the aggregate endowment process, we study the asset price dynamics under "Keeping up with the Joneses" (KUJ) meaning that each agent maximizes the expected life-time CRRA utility of his relative consumption to the other agent in the economy. By solving the optimal consumption policies analytically, we obtain the market equilibrium under heterogeneous beliefs. We provide conditions for agents' long-run survival and show that the market price of risk, risk-free rate, price-dividend ratio in market equilibrium are the consumption share weighted averages of these variables under each agent's belief. We also show the cyclical behaviour of Sharpe ratio, risk-free rate, price and dividend ratio and stock volatility. Through Monte Carlo simulations, we find that, when the less risk averse agent is relatively optimistic, allowing a small amount of disagreement between agents can explain many market characterizes including excess volatility, a high equity premium and a low risk-free rate identified in financial markets.