Jaksa Cvitanic
Asset Prices, Funds' Size and Portfolio Weights in Equilibrium
with Heterogeneous and Long-Lived Funds
We perform a detailed asymptotic analysis of equilibrium
behavior of asset prices, wealth size and portfolio weights in complete
markets equilibria, with long-lived funds. In equilibrium, the fund
with the (closest to) log preferences will dominate 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, surprisingly, the price drift and volatility
still are affected by higher risk aversions, and optimal portfolio
weights contain a hedging component, positive (negative) for risk
aversion higher (lower) than log. For earlier, but still asymptotically
infinite times, the price behavior is also impacted by the funds whose
risk aversions are 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.