Remarks on a copula-based conditional value at risk for the portfolio problem

We deal with a multivariate conditional value at risk. Compared with the usual notion for the single random variable, a multivariate value at risk is concerned with several variables, and thus, the relation between each risk factor should be considered. We here introduce a new definition of copula-based conditional value at risk, which is real valued and ready to be computed. Copulas are known to provide a flexible method for handling a possible nonlinear structure; therefore, copulas may be naturally involved in the theory of value at risk. We derive a formula of our copula-based conditional value at risk in the case of Archimedean copulas, whose effectiveness is shown by examples. Numerical studies are also carried out with real data, which can be verified with analytical results.     

Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19

In this paper, we study the long memory behavior of the hourly cryptocurrency returns during the COVID-19 pandemic period. Initially, we apply different tests against the spurious long memory, with the results indicating the presence of true long memory for most cryptocurrencies. Yet, using the multivariate test, the series are found to be contaminated by level shifts or smooth trends. Then, we adopt the wavelet-based multivariate long memory approach suggested by Achard and Gannaz (2016) to model their long memory connectivity. The findings indicate a change in persistence for all series during the sample period. The fractal connectivity clustering indicates a similarity among Ethereum (ETH) and Litecoin (LTC), Monero (XMR), Bitcoin (BTC), and EOC token (EOS), while Stellar (XLM) is clustered away from the remaining series, indicating the absence of any interdependence with other crypto returns. Overall, shocks arising from COVID-19 crisis have led to changes in long-run correlation structure.     

Should investors include green bonds in their portfolios? Evidence for the USA and Europe

The green bond market has seen a rapid growth world widely in recent years. This paper explores the role of green bonds in asset allocation using the dynamic R-vine copula-based mean-CVaR approach. We compare the performance of portfolios including green bonds with that of portfolios including conventional bonds in the U.S. and European markets. Empirical results show that portfolios with green bonds outperform portfolios with conventional bonds in terms of risk-adjusted returns in the majority of cases in both markets. The benefit of green bonds comes from both the increase in the return and the decrease in the volatility for most of the cases. Overall, our findings suggest that green bonds are beneficial to investors.     

Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models

Many static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice favours simpler, static models such as historical simulation or its variants. Most academic research focuses on dynamic models in the GARCH family. While numerous studies examine the accuracy of multivariate models for forecasting risk metrics, there is little research on accurately predicting the entire multivariate distribution. However, this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using various proper multivariate scoring rules to evaluate forecasts of eight-dimensional multivariate distributions: exchange rates, interest rates and commodity futures. This way, we test the performance of static models, namely, empirical distribution functions and a new factor-quantile model with commonly used dynamic models in the asymmetric multivariate GARCH class.     

Estimating Lower Tail Dependence Between Pairs of Poverty Dimensions in Europe

This article provides an innovative method for measuring the dependence between pairs of poverty dimensions using a semiparametric copula approach that permits us to account for the importance of extreme low values. The association between pairs of poverty dimensions at the lower tail is easily measured using the parameter estimates of the specified parametric copula, and no further calculations are needed. This approach is used to measure the bivariate lower tail dependence between the dimensions of the AROPE rate in Europe at two time points (2009 and 2018). The findings reveal a statistically significant increase in the lower tail dependence between 2009 and 2018 in several European countries.