Diversification benefits in the cryptocurrency market under mild explosivity

We investigate whether cryptocurrencies provide diversification benefits to risk averters via a stochastic spanning methodology. We avoid the conceptual and statistical problems of non-stationary returns by providing a modification of the second order stochastic dominance relation and of the related notion of stochastic spanning. These are compatible with a mildly explosive framework for the logarithm prices, along with conditions for asymptotic negligibility of bubbles. In the empirical application, we construct optimal portfolios, both with and without cryptocurrencies, and evaluate their comparative performance both in- and out-of-sample. A conservative modification of a t-test is presented to test the null hypothesis of non-dominance of an optimal portfolio that includes cryptocurrencies over the traditional portfolio of only stocks, bonds and cash. The augmented portfolio is found to be a good diversification option for some risk averse investors in the full sample period and in a sub-period of high cryptocurrency returns.