Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions f(xj) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved f(xj) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe f(xj). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.

This paper compares three methods for assessing the contagion of risk among ten Globally Significant International Banks, known as GSIBs, listed on the New York Stock Exchange with daily and weekly data sets from 2007 to 2020, based on Machine Learning and Network Analysis. In particular we identify the banks which are the largest net sources or transmitters of risk, and net receptors of risk. We also examine the response of regulatory actions, in the form of fines and BIS Bin Classification for capital adequacy. Under alternative risk measures, of Range Volatility (RV) of share prices, Credit Default Swap (CDS) premia, and Conditional Value at Risk (ΔCoVar), there is a stronger and significant connection between Contagion and the BIS Bin classifications relative to the connections between Contagion and banking fines, either in the amount or frequency of the fines. These results show that BIS bin classifications respond positively to underlying signals of increased contagion in the form of Range Volatility (RV) and ΔCoVar measures but not to CDS risk premia.