George Samartzis | Searcharxiv

arXiv2022

Dynamic Estimates Of The Arrow-Pratt Absolute And Relative Risk Aversion Coefficients

We derive a closed-form expression capturing the degree of Relative Risk Aversion (RRA) of investors for non-"fair" lotteries. We argue that our formula is superior to earlier methods that have been proposed, as it is a function of only three variables. Namely, the Treasury yields, the returns and the market capitalization of a specific market index. Our formula, is tested on CAC 40, EURO, S&P 500 and STOXX 600, with respect to the market capitalization of each index, for different time periods. We deduce that the investors in these markets exhibit Decreasing Absolute Risk Aversion (DARA) through all the different time periods that we consider, while the degree of RRA has altered between being constant, decreasing or increasing. Furthermore, we propose a simple and intuitive way to measure the degree to which a wrong assumption with respect to the utility function of an investor will affect the structure of his portfolio. Our method is built on a two asset portfolio framework. Namely, a portfolio consisting of one risky and one risk-free asset. Applying our method, the empirical findings indicate that the weight invested in the risky asset varies substantially even among utility functions with similar characteristics.

econ.GN↗

arXiv2022

On The Equivalence Of The Mean Variance Criterion And Stochastic Dominance Criteria

We study the necessary and sufficient conditions under which the Mean-Variance Criterion (MVC) is equivalent to the Maximum Expected Utility Criterion (MEUC), for two lotteries. Based on Chamberlain (1983), we conclude that the MVC is equivalent to the Second-order Stochastic Dominance Rule (SSDR) under any symmetric Elliptical distribution. We then discuss the work of Schuhmacher et al. (2021). Although their theoretical findings deduce that the Mean-Variance Analysis remains valid under Skew-Elliptical distributions, we argue that this does not entail that the MVC coincides with the SSDR. In fact, generating multiple MV-pairs that follow a Skew-Normal distribution it becomes evident that the MVC fails to coincide with the SSDR for some types of risk-averse investors. In the second part of this work, we examine the premise of Levy and Markowitz (1979) that "the MVC deduces the maximization of the expected utility of an investor, under any approximately quadratic utility function, without making any further assumption on the distribution of the lotteries". Using Monte Carlo Simulations, we find out that the set of approximately quadratic utility functions is too narrow. Specifically, our simulations indicate that $\log{(a+Z)}$ and $(1+Z)^a$ are almost quadratic, while $-e^{-a(1+Z)}$ and $-(1+Z)^{-a}$ fail to approximate a quadratic utility function under either an Extreme Value or a Stable Pareto distribution.

q-fin.PM↗