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Hi, I'm reading a paper [1] and don't quite understand how the weighted average of log returns is computed. Is it just a linear combination of said log returns? But if so, how does this help to reduce correlation due to disparity in composition? Thanks.
"For each bank, an equally- weighted average of the returns of the remaining banks in the sample is used as a proxy for financial system. In this way, the resulting system return portfolios can be considered as representative of European financial system allowing the study of possible spillover effects between a stressed institution and financial system. Moreover, this approach rules out any spurious correlation that may be induced due to sizeable disparity in the composition of financial system proxy.
For example, HSBC has a total contribution of 20.5% in the composition of STOXX Europe 600 Banks Index. As a result, if the corresponding index is used as a proxy for the financial system, systemic risk estimates generated conditional on HSBC will be severely affected by the simultaneous presence and large scale factor of HSBC in financial system’s portfolio proxy. "
[1] Karimalis, E.N., Nomikos, N.: Measuring systemic risk in the European banking sector: A Copula CoVaR approach (2014)
"For each bank, an equally- weighted average of the returns of the remaining banks in the sample is used as a proxy for financial system. In this way, the resulting system return portfolios can be considered as representative of European financial system allowing the study of possible spillover effects between a stressed institution and financial system. Moreover, this approach rules out any spurious correlation that may be induced due to sizeable disparity in the composition of financial system proxy.
For example, HSBC has a total contribution of 20.5% in the composition of STOXX Europe 600 Banks Index. As a result, if the corresponding index is used as a proxy for the financial system, systemic risk estimates generated conditional on HSBC will be severely affected by the simultaneous presence and large scale factor of HSBC in financial system’s portfolio proxy. "
[1] Karimalis, E.N., Nomikos, N.: Measuring systemic risk in the European banking sector: A Copula CoVaR approach (2014)