## Statistical arbitrage with vine copulas.(English)Zbl 1407.62178

Summary: We develop a multivariate statistical arbitrage strategy based on vine copulas – a highly flexible instrument for linear and nonlinear multivariate dependence modeling. In an empirical application on the S&P 500, we find statistically and economically significant returns of 9.25% p.a. and a Sharpe ratio of 1.12 after transaction costs for the period from 1992 until 2015. Tail risk is limited, with maximum drawdown at 6.57%. The high returns can only partially be explained by common sources of systematic risk. We benchmark the vine copula strategy against other variants relying on the multivariate Gaussian and $$t$$-distribution and we find its results to be superior in terms of risk and return characteristics. The multivariate dependence structure of the vine copulas is time-varying, and we see that the share of copulas capable of modelling upper and lower tail dependences increases well over 90% at times of high market turmoil.

### MSC:

 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62P05 Applications of statistics to actuarial sciences and financial mathematics
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