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

Financial Innovation

Table 7 CoVaR and ΔCoVaR computed from GMV for Portfolio 1

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	0.9	0.13	0.14	0.01	0.13	0.01
ETH	0.03	0.14	0.18	0.07	0.11	0.1
XRP	0.06	0.18	0.18	0.11	0.07	0.06
ADA	0	0.14	0.18	0.1	0.08	0.08
LINK	0	0.14	0.18	0.11	0.06	0.06
LTC	0	0.14	0.18	0.08	0.1	0.1
BCH	0	0.14	0.18	0.09	0.1	0.1
XLM	0	0.13	0.18	0.1	0.09	0.09
BNB	0.01	0.15	0.18	0.09	0.09	0.09
DOGE	0	0.18	0.17	0.12	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; \({\Delta CoVaR}_{q}^{p|i}={CoVaR}_{q}^{p|i}-{CoVaR}_{0.5}^{p|i}\). It measures the vulnerability of the portfolio to the contagion from tail-risk events of the asset i