An Empirical Test of Pricing Kernel Monotonicity

A recent literature in finance concerns a curious recurring feature of estimated pricing kernels. Classical theory dictates that the pricing kernel { defined loosely as the ratio of Arrow security prices to an objective probability measure { should be a decreasing function of aggregate resources. Yet a large number of recent empirical studies appear to contradict this prediction. The nonmonotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. The test involves assessing the concavity of the ordinal dominance curve associated with the risk neutral and physical return distributions. We apply the test using thirteen years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months.