Two Trees: Asset Price Dynamics Induced by Market Clearing
If stocks go up, investors may want to rebalance. But investors cannot all rebalance. Expected returns mustrise (or other moments must change) so that the average investor is happy to hold the total market portfolio despite its greater allocation to stocks. In this way, of market clearing can give rise to complex asset market dynamics. We study this phenomenon in a simple model. Our model has two ``Lucas trees.'' Each tree has i.i.d. dividend growth, and the representative investor has log utility. We find analytical solutions to the model. Asset price-dividend ratios, expected returns, and return variances vary through time. A dividend shock leads to ``underreaction'' in some states, as expected returns rise and prices slowly adjust to the dividend, and ``overreaction'' in other states. Expected returns and excess returns are predictable by price-dividend ratios in the time series and in the cross section, roughly matching value effects and return forecasting regressions. Returns generally display negative serial correlation and cross-serial correlation, leading to ``momentum,'' but the opposite sign is possible as well. A shock to one asset's dividend affects the price and expected return of the other asset, leading to substantial cross-correlation of returns even when there is no cross-correlation of cash flows, and giving the appearance of `contagion.'' Market clearing also allows the ``inverse portfolio'' problem to be solved, in which the weights of the assets in the market portfolio are ``inverted'' to solve for the parameters of the assets' return generating process.
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