Tests for detecting risk equivalent portfolios
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The aim of this paper is the development of consistent tests for the comparison of the distributions of two possibly dependent portfolios. The tests can be used to check whether the two portfolios are risk equivalent. The related testing problem can be endowed into a more general paired data framework by testing marginal homogeneity of bivariate functional data, or even paired random variables taking values in a general Hilbert space. To address this problem, we apply a Cramér-von-Mises type test statistic and suggest a bootstrap as well as permutation procedure to obtain critical values. The usually desired properties of a bootstrap and permutation test can be derived, that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations demonstrate the quality of the tests in the finite sample case and confirm the theoretical findings. Finally, we illustrate the application of the approach by comparing real financial time series.
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