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In "Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach" by Christoffersen et al. (2012), the authors present the concept of Conditional Diversification Benefit of a portfolio, based on the expected shortfall, defined as (confidence level $\alpha$ is omitted for legibility reasons):

$$CDB_t = \frac{\overline{ES}_t-ES_t}{\overline{ES}_t-\underline{ES}_t}$$

where $\overline{ES}_t$ is the upper bound of portfolio's ES when there is no diversification, i.e. $\overline{ES}_t = \sum_{i=1}^n w_i ES_{i,t}$ (where $i$ stands for asset $i$), $\underline{ES}_t$ is the lower bound of portfolio's expected shortfall, which by definition coincides with the respective VaR, and $ES_t$ is the actual estimate. In their paper (where each asset is an index representing the economy of a country) they find that $CDB_t$ has declined over the last 15-20 years as a result of increasing dependence between different countries' economies.

In my project I'm using sector-specific indexes rather than country-specific indexes. My findings differ from Christoffersen et al. (2012): my $CDB_t$ stays relatively constant over time, with some minor fluctuations (the biggest upward fluctuation during the financial crisis), and a plot of the average correlations (average correlation of asset $i$ with assets $(1, ..., i-1, i+1, ...n))$ confirms that these have actually declined, leading to increasing $CDB_t$ during the crisis.

Is this not plausible, or may this be given by the fact that different sectors are diversely hit by the crisis, with some sectors that lost tons of money while others maybe profited from it, or at least are not harmed by it (for example health care companies vs. financial institutions), whereas country-related indexes (which in developed countries include stocks from all industries) are constructed in a fairly similar way, and therefore tend to correlate more during volatile times? Maybe you have an intuitive answer, or a reference to industry correlations during the crisis?

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From my experience, I think your results are plausible. Due to the globalization, economies and stock markets from different countries are much more connected than in the past. Furthermore, since the financial crisis of 2008, central bank policies have also converged more and more (e.g. in the US, Euro-Zone, Japan and UK you have zero-interest-rate policy). From this you would expect an increase of correlation aka a fall of diversification benefits through country diversification.

Regarding the results of your study, one can also imagine that correlation between certain sectors has declined over time. The credo in capital markets for a couple of years now is (unfortunately) 'risk-on' or 'risk-off'. Fund managers (and traders) allocate their assets regarding the actual risk-status. Simplified, in 'risk-on' they are overweighted in growth-oriented companies whereas in 'risk-off'-mode, their prefer stable value stocks. Since most sectors can easily characterised as one or the other (on average), it makes sense that the performance difference/correlation of sectors has increased/decreased in dependence of the current risk/market mode.

Furthermore, one could argue that the segment of active funds is dominated by single-country oriented funds and not globally-investing portfolios. From this perspective, the fund managers with the larger influence are the ones which can only allocate among different sectors to manage their risk and not the managers which could also use a country shift for this purpose.

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  • $\begingroup$ Thanks for your answer. I appreciate both points made for supporting the decrease of industry correlation. I wonder whether may have some sources I could refer to in my study? $\endgroup$ – Kondo Sep 2 '16 at 19:06

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