Assessing portfolio vulnerability to systemic risk: a vine copula and APARCH-DCC approach

Financial Innovation

Table 5 Estimated \(\mathrm{CoVaR}\) and \(\Delta \mathrm{CoVaR}\) measures for Portfolio 1 under Market-weighted portfolio (MWP) strategy

Asset	\({\omega }_{i}\)	\({VaR}_{q}\left({L}_{i}\right)\)	\({CoVaR}_{q}^{p\|i}\)	\({CoVaR}_{0.5}^{p\|i}\)	\({\Delta CoVaR}_{q}^{p\|i}\)	\(a{L}_{i}\)
BTC	0.59	0.13	0.15	0.03	0.12	0.04
ETH	0.28	0.14	0.17	0.05	0.12	0.08
XRP	0.03	0.18	0.17	0.11	0.07	0.06
ADA	0.03	0.14	0.18	0.09	0.09	0.09
LINK	0.01	0.14	0.17	0.11	0.07	0.07
LTC	0.01	0.14	0.17	0.07	0.11	0.11
BCH	0	0.14	0.18	0.08	0.1	0.1
XLM	0	0.13	0.18	0.09	0.09	0.09
BNB	0.05	0.15	0.18	0.08	0.09	0.09
DOGE	0.01	0.18	0.17	0.11	0.06	0.06

q = 0.05; \({\omega }_{i}\) are the weights corresponding to market capitalization; \({L}_{i}\) is the vector of profit/loss; \(a{L}_{i}\) is the additional loss on the other components of the portfolio induced by the loss incurred by asset i. It is given by \(a{L}_{i}={\Delta CoVaR}_{q}^{p|i}-{\omega }_{i}{VaR}_{q}\left({L}_{i}\right)\); \({CoVaR}_{q}^{p|i}\) is the VaR of the portfolio conditional upon asset i being in a state of distress; \({\Delta CoVaR}_{q}^{p|i}={CoVaR}_{q}^{p|i}-{CoVaR}_{0.5}^{p|i}\). This measures the vulnerability of the portfolio to contagion from the tail risk events of asset i