Is the Pricing Kernel U-Shaped?

There is strong empirical evidence that the pricing kernel is Ushaped,which provides a way to explain the substantial coskewnesspremium. Existing studies typically use a polynomial approximationof the pricing kernel. Problematically, these polynomials have, inmost cases, increasing parts by construction. Therefore, it is not clearwhether the increasing parts are an artifact of the chosen functionalform. Taking this concept into consideration, this paper shows thatpricing kernels, as estimated by the generalized method of momentson equity data, are still U-shaped and that the increasing part is nota statistical artifact. This conclusion derives from the fact that thefunctional form of kernels, which allows for strictly decreasing kernelsas well as for kernels with increasing parts, is still U-shaped. Theseresults arise from checking for higher order polynomials, various timehorizons, and dierent functional forms of the kernel.[....]