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

Financial Innovation

Table 14 Estimated CoVaR q and ΔCoVaR measures for Portfolio 2 under MV-PSO portfolio (MVPSO) 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	0.19	0.08	0.06	0.04	0.02	0.01
ETH	0.07	0.07	0.06	0.04	0.02	0.01
LTC	0.12	0.07	0.06	0.04	0.02	0.01
NYA	0.16	0.07	0.07	0.03	0.04	0.03
IXIC	0.07	0.07	0.07	0.03	0.03	0.03
GSPC	0.12	0.07	0.07	0.03	0.04	0.03
N100	0.01	0.07	0.07	0.03	0.04	0.03
FTSE	0.11	0.08	0.07	0.03	0.03	0.02
FCHI	0	0.08	0.07	0.04	0.03	0.03
DJI	0.16	0.07	0.07	0.03	0.04	0.03

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