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

Financial Innovation

Table 9 CoVaR and ΔCoVaR computed from GMV for Portfolio 2

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	0.08	0.07	0.07	0	0
ETH	0	0.07	0.07	0.07	0	0
LTC	0	0.07	0.07	0.07	0	0
NYA	0	0.07	0.09	0.03	0.06	0.06
IXIC	0	0.07	0.1	0.05	0.04	0.04
GSPC	0.33	0.07	0.09	0.04	0.06	0.04
N100	0	0.07	0.09	0.02	0.06	0.06
FTSE	0.66	0.08	0.08	0.02	0.07	0.02
FCHI	0	0.08	0.09	0.04	0.06	0.06
DJI	0	0.07	0.09	0.03	0.06	0.06

NYSE COMPOSITE (NYA), NASDAQ Composite (IXIC), S&P 500 (GSPC), Euronext 100 Index (N100), FTSE 100 (FTSE), CAC 40 (FCHI) and Dow Jones Industrial Average (DJI), Bitcoin (BTC), Ethereum (ETH) and Litecoin (LTC). 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