The S&P 500 has fallen around 5.75% since the post-FOMC high. The dollar has risen against most currencies in the same period. It begs the question what is the current statistical relationship between stocks and the dollar.

To set the table, consider the year-to-date performance. The S&P 500 has fallen almost 7%.The dollar has risen against nearly every other currency. The notable exceptions are the Swiss franc, which strengthened dramatically after the SNB lifted its cap on the currency. The yen has also risen against the dollar this year, though its 0.13% rise can be accounted for by today’s price action alone. Excluding countries that peg their currencies against the dollar, the greenback has risen against all the emerging market currencies as well. Still, some observers have argued that the dollar has become correlated with stocks.

Yet their arguments are not particularly robust. First, for the dollar they use the Dollar Index. The problem with this is that the Dollar Index is a weirdly-weighted index that gives much weight to the euro and currencies that gravitate in the euro’s orbit, like the Swiss franc and Swedish krona. It is not a trade-weighted index as two of the US biggest trading partners, Mexico and China, are not included.

Second, they talk about correlation but do not actually get their hands dirty with the data. Instead, they show two time series with two different scales and through what amounts to a curve fitting exercise show how the two lines move in tandem. Correlation is a statistical relationship and cannot simply be eyeballed.

Third, as investors we are interested in the correlation of returns not the correlation of the level of two time series. To offer a more robust analysis, we looked at the correlation of the euro-dollar and the dollar-yen and the US S&P 500 on the basis of percentage change. Using Bloomberg analytics, here is what we found:

This Great Graphic shows the rolling 60-day correlation between the percentage change in the S&P 500 and the percentage change in the euro. There are three things to note. First there is a negative correlation. And not only is it negative (-0.52), but it is negative by the most since 2003.

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