Implications of Asset Prices for the Market Pricing Kernel

Abstract

A vital interest in financial research is to derive information about the distribution of the market pricing kernel, about the state price density or, equivalently, about the risk-neutral probability distribution and the risk-free rate. As shown in the previous chapter this knowledge would enable the pricing of any asset. The traditional approach to gain insights into the properties of the market pricing kernel is to start by choosing a functional form for the pricing kernel and then test equation (2.1) empirically. Recently, more suggestive approaches attempt to reveal properties of the market pricing kernel without assuming an explicit functional form. These approaches first examine asset returns or asset prices and then analyze which properties the market pricing kernel must exhibit to be consistent with these data. One can distinguish theoretical and empirical approaches. The theoretical approaches make assumptions about the distribution or the stochastic process of asset returns or prices, whereas the empirical approaches use observed data. The first part of this chapter briefly surveys one of the theoretical approaches. Then, two empirical approaches, one employing cross-sectional data and one employing time series data, are compared. The approach that employs time series data to place restrictions on the moments of the unconditional distribution of the market pricing kernel is applied in chapter 7 and is therefore described in greater detail.