Rational Mispricing with Unpredictable Demand Shocks

Abstract

Movements in prices depend both on innovations to cashflows and changes in investors' demands, which can be modelled as fluctuations in the cross-sectional distribution of wealth across a fixed set of investment objectives. This paper explores the risk that arises when investors do not have perfect information about the wealth distribution to accurately forecast demand shocks, and, as a result, cannot forecast prices accurately, despite having perfect information about cashflows. To take into account this risk, investors plan their consumption for all realisations of the wealth distribution that are possible according to their subjective beliefs about the wealth distribution. This makes markets highly incomplete, and derivative assets become non-redundant. Derivatives serve a dual purpose: they allow investors to adjust consumption for different realisations of the wealth distribution, and provide information required to implement optimal allocation decisions. Asset prices depend on the sensitivity of stochastic discount factor and assets' payoffs to the wealth distribution, creating differences in expected returns between assets that are unrelated to their cashflow risk. Prices of derivatives deviate from the expected cost of creating synthetic derivatives through dynamic trading, creating apparent mispricings between derivatives and primary assets. The imprecise information about the wealth distribution can also induce a demand for dynamic trading, leaving passive investment strategies no longer optimal. Our results also have implications for arbitrage activity, informational efficiency of prices, and the role of financial innovation.