Abstract
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.
Highlights
The analysis of portfolio risk requires statistical models and techniques that accurately capture the dependence between prices or returns of individual assets and account for salient characteristics of the individual distributions
Stage 2: Using the standardized variables filtered through the estimates obtained in stage 1, conditional correlations for each pairwise variables are estimated under a bivariate Gram–Charlier density for dynamic conditional correlation (DCC) and with joint estimation for dynamic equicorrelation (DECO)
In this paper we have shown that the estimation of conditional correlation is dependent on the model specification, the SNP being a flexible and accurate approach that can be estimated with ease by means of either “recursive” DCC or “restrictive” DECO estimation
Summary
The analysis of portfolio risk requires statistical models and techniques that accurately capture the (time-varying) dependence between prices or returns of individual assets and account for salient characteristics of the individual (marginal) distributions. Alternative versions have been proposed to tackle different problems: positivity [19], two-step estimation [20], approximation properties [21], generalizations to other distributions [22], method of moments estimation [23], time-varying conditional moments [24], specifications in vector notation [25], or risk forecasting [26] These models preserve the asymptotic approximation property, and are very tractable from both the theoretical and empirical viewpoint. This research is focused on assessing the performance of the multivariate positive GC distribution [27], that implies a symmetric distribution being positive in the whole domain for capturing the risk of highly volatile assets To this end, we analyze portfolios of cryptocurrencies, which are modeled as AR-GJR-GARCH [28] (i.e., considering asymmetric conditional variances) and a covariance structure consistent to either DCC or DECO.
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