Comparing the Riskiness of Dependent Portfolios via Nested L-Statistics

Annals of Actuarial Science, 11(2), 237-252, 2017

22 Pages Posted: 14 Sep 2016 Last revised: 17 Nov 2017

See all articles by Ranadeera Samanthi

Ranadeera Samanthi

Central Michigan University

Wei Wei

University of Wisconsin - Milwaukee

Vytaras Brazauskas

University of Wisconsin - Milwaukee

Date Written: December 18, 2015

Abstract

A nonparametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a required condition for the test to work. In this paper, we investigate how performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study where we consider three different risk measures: conditional tail expectation, proportional hazards transform, and mean. Further, three portfolios are generated from exponential, Pareto, and lognormal distributions, and their interdependence is modeled with the three-dimensional t and Gaussian copulas. It is found that the presence of strong positive dependence (comonotonicity) makes the test very liberal for all the risk measures under consideration. For types of dependence that are more common in an insurance environment, the effect of dependence is less dramatic but the results are mixed, i.e., they depend on the chosen risk measure, sample size, and even on the test's significance level. Finally, we illustrate how to incorporate such findings into sensitivity analysis of the decisions. The risks we analyze represent tornado damages in different regions of the United States from 1890 to 1999.

Keywords: Copulas, risk measures, insurance portfolios, hypothesis tests, Gini index

Suggested Citation

Samanthi, Ranadeera and Wei, Wei and Brazauskas, Vytaras, Comparing the Riskiness of Dependent Portfolios via Nested L-Statistics (December 18, 2015). Annals of Actuarial Science, 11(2), 237-252, 2017, Available at SSRN: https://ssrn.com/abstract=2837863

Ranadeera Samanthi

Central Michigan University ( email )

Department of Mathematics
Pearce Hall 206I
Mt Pleasant, MI 48859
United States

Wei Wei

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53211
United States

Vytaras Brazauskas (Contact Author)

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53201
United States

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