Destabilizing Optimal Trading Strategies in the Stock Market

A simple dynamic general equilibrium model of trading strategies is presented, where investors apply optimal investment strategies with stock and bond based on Merton (1971). Our investors
employ two dynamic asset allocation strategies: Constant Proportion Portfolio Insurance (CPPI), and
Constant Mix (CM) strategy, being demand and supply strategies of portfolio insurance in the underlying assets markets. We show that it is optimal for the portfolio insurer to buy shares, and for the
CM investor to sell shares as their portfolios increase in value due to liquidity shocks, (and vice
versa) enabling us to define a Walrassian clearing mechanism for shares periodically. The resulting
equilibrium price dynamics is a generalized diffusion that may oscillate at high volatilities if portfolio
insurance dominates the market, but the price path can obtain low variability if the contrarian investors dominate. The aggregate effect of the low risk-averse, portfolio insurers increase toward their
planning horizon, resulting in an increasing price path, trade volume, and return volatility as the horizon gets closer. In spite of their destabilizing effect on equilibrium prices, regulatory agencies cannot
prohibit such strategies since they stem from optimal asset allocation rules between stocks and bonds
that each individual investor can apply, while the aggregate, unobservable values matters.