According to fundamental beliefs, oil prices and Japan's economy should have an inverse relationship. Higher oil prices means lower GDP and the Nikkei should trend lower overtime. However, when I look at graphs between EWJ ( A Japanese ETF ) and our all-so-popular XLE, there is no real relationship. Is the Japan/Oil trade just a myth? I know Japan probably already hedges their oil reserves, if that is the case, there is no trade.
Why guess at it? Run daily returns of EWJ versus USO (or XLE, as you suggest). Takes just a few minutes.
http://www.mrci.com/special/corr180.php Looks like over the past 180 days, Nikkei futures and CL have a 0.85 positive correlation. 0.89 for Brent.
Of course those numbers are wrong. 90'ish corrs are what stock indices have with each other, not with oil. Possibly MRCI uses price levels rather than returns.
MRCI defines correlation as both instruments closing higher or lower on the same day, so you're correct that it's not based on returns.
Cursory look on BBG gives me positive return correlation, but I would still question 90% digital correlation.