Financial Market as Driver for Disparity in Wealth Accumulation—A Receding Horizon Approach

In this paper we study the extent to which the financial market has contributed to wealth disparities. To that end we introduce a stochastic dynamic model of wealth accumulation with preferences, consumption and portfolio choice, which roughly replicates the long-term evolution of assets under management. Using a receding horizon approach for solving nonlinear model predictive control (NMPC) in finite time, we run simulations with three types of investors (conservative, moderate and aggressive) corresponding, roughly, to the social population segments identified in Piketty (Le capital au XXIe siècle, Seuil, Paris, 2013) for thinking about distributional matters, namely the lower segment (bottom 50%), the middle segment (middle 40%), and the upper segment (upper 10%) respectively. We estimate the impact on the end wealth distribution of first, investor-level characteristics (calibrated for each investor class), which directly impact the saving rate; and second, higher expected returns for wealthier (aggressive) investors in the top decile through the availability of leverage. We find that differences in investor-level characteristics (and significantly the length of the receding horizon) combined with access to leverage are sufficient to generate fat tails. Though results are obtained in a stochastic approach, the outcomes are less related to stochastic shocks than to some feedback and scale effects operating in favor of some investors in the financial market.