Quantile Consumption-Capital Asset Pricing

The Consumption-Capital Asset Pricing Model is a statement about the mean of asset returns anddoes not provide any information on the returns' quantiles. Using quantile maximization decisiontheory, this paper considers a quantile-based Euler equation that states that the asset price is afunction of the quantiles of the payoff, consumption growth, stochastic discount factor and riskaversion. Assuming that the consumption growth rate is log-elliptically distributed, we show thatreturns' quantiles are non-monotone functions of the consumption growth volatility. Using data fromthe United States and United Kingdom, empirical evidence validates our theoretical results and showsthat this volatility is a driving factor of the returns' distribution.