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

Financial Innovation

Table 6 Estimated \(\mathrm{CoVaR}\) and \(\Delta \mathrm{CoVaR}\) measures for Portfolio 2 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	0.01	0.08	0.06	0.06	0	0
ETH	0	0.07	0.06	0.06	0	0
LTC	0	0.07	0.07	0.06	0.01	0.01
NYA	0.28	0.07	0.07	0.01	0.06	0.04
IXIC	0.13	0.07	0.09	0.03	0.05	0.04
GSPC	0.39	0.07	0.07	0.01	0.06	0.04
N100	0.04	0.07	0.09	0.03	0.05	0.05
FTSE	0.02	0.08	0.09	0.04	0.05	0.05
FCHI	0.03	0.08	0.09	0.04	0.05	0.04
DJI	0.11	0.07	0.08	0.02	0.06	0.05

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