If a pricing kernel assigns a premium to a risk variable that differs from the one assigned by the minimum-variance admissible kernel, then the pricing kernel must exhibit more variability than the minimum-variance kernel. Based on this intuition, the authors derive a variance bound that is more stringent than that of Lars Peter Hansen and Ravi Jagannathan (1991). When the authors apply their bound to the kernel of a representative consumer with power utility, they find that the consumption risk premium increases the severity of the 'equity-premium puzzle' of Rajnish Mehra and Edward C. Prescott (1985).

ABSTRACT If a pricing kernel assigns a premium to a risk variable that differs from the one assigned by the minimum‐variance admissible kernel, then the pricing kernel must exhibit more variability than the minimum‐variance kernel. Based on this intuition, we derive a variance bound that is more stringent than that of Hansen and Jagannathan (1991) . When we apply our bound to the kernel of a representative consumer with power utility, we find that the consumption risk premium increases the severity of the “equity‐premium puzzle” of Mehra and Prescott (1985) .

If a pricing kernel assigns a premium to a risk variable that differs from the one assigned by the minimum-variance admissible kernel, then the pricing kernel must exhibit more variability than the minimum-variance kernel. Based on this intuition, we derive a variance bound that is more stringent than that of Hansen and Jagannathan (1991). When we apply our bound to the kernel of a representative consumer with power utility, we find that the consumption risk premium increases the severity of the “equity-premium puzzle” of Mehra and Prescott (1985).

Pierluigi Balduzzi, Silverio Foresi, David J. Hait, Price Barriers and the Dynamics of Asset Prices in Equilibrium, The Journal of Financial and Quantitative Analysis, Vol. 32, No. 2 (Jun., 1997), pp. 137-159