This supplementary Technical Appendix contains formal proofs of the propositions which are stated in Anyfantaki, S., S. Arvanitis, S., Th. Post, Th. and N. Topaloglou, 2019, 'Stochastic Bounds for Portfolio Analysis', available at SSRN:"https://ssrn.com/abstract=3181869 "...

We investigate whether alternative asset classes should be included in optimal portfolios of the most prominent investor personae in the Behavioral Finance literature, namely, the Cumulative Prospect Theory, the Markowitz and the Loss Averse types of investors. We develop a stochastic spanning...

We investigate the degree to which cryptocurrencies provide diversification benefits to an investor. We use a stochastic spanning methodology to construct optimal portfolios with and without cryptocurrencies, evaluating their comparative performance both in- and out-of-sample. Empirical analysis...

This paper investigates the diversification contribution of four main precious metals (i.e., gold, silver, platinum, and palladium) to a traditional portfolio of stocks, bonds, cash, and currencies, as well as the impact of the global financial crisis of 2008 on that contribution. We use a...