Description

No arbitrage assumption is equivalent to the existence of a positive random variable, called a stochastic discount factor (SDF. In general, the SDF depends on many variables. Many studies focus on aggregate consumption and customarily assume a representative agent whose preferences have an expected utility representation over consumption sets. We refer to the projection of the stochastic discount factor on the set of returns as the pricing kernel (PK). The pricing kernel is the derivative of the risk-neutral measure with respect to the physical measure. The pricing kernel provides another way to characterize investors' preference or aversion over gains and losses. This is typically done by investigating the shape or monotonicity patterns of the pricing kernel. A decreasing PK is consistent with a risk-averse representative agent, while an increasing PK with a risk-loving agent.