Testing Monotonicity of Pricing Kernels

Abstract

In this master thesis a mechanism to test mononicity of empirical pricing kernels (EPK) is presented. By testing monotonicity of pricing kernel we can determine whether utility function is concave or not. Strictly decreasing pricing kernel corresponds to concave utility function while non-decreasing EPK means that utility function contains some non-concave regions. Risk averse behavior is usually described by concave utility function and considered to be a cornerstone of classical behavioral finance. Agents prefer a fixed profit over insecure choice with the same expected value. Some of the EPKs, obtained from DAX German market, were found to be non-monotone decreasing. These findings show that agents have not always risk averse behavior. The first part of the thesis describes construction of the test. Pyke’s theorem of order statistics is used to reduce the problem to exponential model. On the basis of this model likelihood ratio test is constructed for a fixed interval. Furthemore it is expanded to a test independent from intervals using intersection of test for different intervals. In the second part test performance is evaluated for simulated and observed data. Different cases of data are simulated to estimate power of the test, first and second type errors. Then EPKs, obtained from DAX data in years 2000, 2002 and 2004 are tested for monotonicity.