Mean Reversion and Consumption Smoothing

Abstract

Most models of the evolution of wealth and consumption assume that wealth volatility and risk premium are constant. But in fact, volatility declines, and risk premium seems to decline, as wealth rises. A model that allows mean reversion in the sense that the risk premium declines as wealth rises can help explain both the “consumption smoothing puzzle” and the “equity premium puzzle.” In an example of such a model that gives us an analytic solution, direct and derived risk aversion are both constant, but differ.

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