Asset prices, funds' size and portfolio weights in equilibrium with heterogeneous and long-lived funds

We perform a detailed asymptotic analysis of the equilibrium behavior of the asset prices, wealth size and portfolio weights in complete markets equilibria, with long-lived funds. In equilibrium, the fund with the (closest to) log preference will dominate the other funds in size, in the long-run, with probability one. On the other hand, two funds on the opposite sides of the log preference will never dominate each other in expected size. In the very long run, the price behavior of the risky asset will be determined solely by the fund closest to the log preference. However, the price drift and volatility still are affected by higher risk aversions, and the optimal portfolio weights contain a hedging component, positive (negative) for the risk aversions higher (lower) than log. The hedging component is monotone increasing in risk aversion for the times further away from the terminal horizon, but it may become monotone decreasing closer to the terminal horizon. For earlier, but still asymptotically infinite times, the price behavior is impacted also by the funds with risk aversions greater than one. Selling short is never optimal. There are distinct increasing time periods such that the price has the same asymptotic behavior in each period. The long-run per-period return gets lower with time