A test of asymmetric comovement for state-dependent stock returns

I propose a test of asymmetric stock return comovement across states. The test can be viewed as a variation of Kendall's τ conditional on the state and has an asymptotic χ2-distribution. A refined version of the test is derived based on the Markov chain theory of regenerative cycles which substantially improves finite sample size and power properties. I show that the test has power against local alternatives, which is nonetheless compromised due to a finite sample convergence bound put on the implied local alternative data generating process. I evaluate the new test against traditional correlation-based measures and demonstrate power attrition of a state-free tail dependence test as parameter values are varied. Broad market-based ETFs and international indices are studied and in most cases there is no compelling evidence for asymmetric comovement across states. A list of related tests is given as an extension at the end.