6533b82cfe1ef96bd128e964

RESEARCH PRODUCT

Proportional Small Sample Bias in Pricing Kernel Estimations

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description

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 a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a 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 center even when the true pricing kernel fulfills these. This contributes to alternative, statistical explanations for the puzzling shape in pricing kernel estimations.