Usually they behave complementary to each other. You can see from the chart that except towards 2nd week of may 2021, we started seeing the anomally of this pattern. Meaning both Dollar index and Bitcoin both following same downward momentum. This anomally shall result in great opportunity in reversal for either of the two. Considering recent developments in monitory stance by FED and macros, i think BTC has better probability of winning. But this should not be considered an investment advice and any mistakes in observation to be forgiven.
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