For my own curiosity I decided to have a quick look at the price correlations of a handful of world indices. Those correlations that are below 0.5 I have coloured red.
As expected most share a positive correlation with the only true diversification coming from the Shanghai Composite. This does pose a conundrum for index traders since it causes difficulties with diversification in the traditional sense. However,these are price correlations not return correlations. If I get some time I will redo this as returns table and see what the difference is.