The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes.

This paper introduces the moment interaction between different assets in the semi-nonparametric modeling of a multivariate distribution. We analyze bivariate portfolios where skewness and kurtosis may interact between different assets, showing that these new parameters may be significant pieces of information, particularly for measuring risk. Model performance for risk assessment is tested with backtesting techniques considering equally weighted portfolios of the S&P 500 and Nasdaq 100 indices and major cryptocurrencies (Bitcoin and Ethereum), the latter with high-frequency data. The results show adequate performance in terms of Value-at-Risk, Median Shortfall, and Expected Shortfall, especially for high confidence levels.