The shape of small sample biases in pricing kernel estimations
研究了定价核估计中常见的小样本偏差如何导致估计结果违反单调性，即使真实定价核满足该性质，为实证中定价核形状之谜提供了统计解释。
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kernels typically violate the commonly believed monotonicity at the centre even when the true pricing kernel fulfils these. This contributes to an alternative, statistical explanation for the puzzling shape in pricing kernel estimations.