How closely the world's stock markets actually move together

The daily correlation between Nikkei 225 and the S&P 500 is 0.10, which reads as two markets that barely notice each other. It is an artefact. Tokyo closes before New York opens, so "the same calendar day" pairs a Japanese session with an American session that had not happened yet. Compare each Japanese session with the *previous* American one and the figure rises to 0.32. Nothing about the markets changed; only the alignment did.

That is why the headline matrix on this page is monthly. Over a calendar month the few hours of offset stop mattering, and what is left is the thing a reader wants: how much of one market's move is shared with another's. Every pair is computed over the months both indices actually existed for, and the observation count is in each cell's tooltip, because a 0.9 built from sixty months and one built from a thousand are not the same claim.

The lowest correlation in the table is Shanghai Composite at 0.12 against the S&P 500 — a genuinely separate market, driven by a domestic investor base and a different policy cycle, and one of the few remaining places where "diversification" is more than a word. The European indices sit at the other end, high enough that a portfolio split between New York and Frankfurt is closer to one position than to two.

Then the crisis columns. Every pair here is more correlated inside the 2008 and 2020 windows than over its own full history, and the increase is largest for the pairs that looked most diversifying in calm periods. This is the practical failure mode of an international allocation: the correlation you sized the position with is the average one, and the correlation you get in the month you need it is the crisis one.