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Is USD/CAD not very correlated to EUR/USD? The USD might go in the same direction in each pair in general but it takes its own route. As opposed to the well correlated pairs below:
AUD/USD, GBP/USD and USD/CHF are pretty well correlated to EUR/USD.
Is USD/CAD is not that well correlated with other USD pairs then can it act as a source of diversification?
I did not include JPY because it has so much intervention I find it very hard to analyse. In fact IMHO it is more of a fixed currency than a free-floating currency.
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