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What is the relationship between the dollar index and the trend of gold, and under what circumstances will it rise or fall together?
Because gold is denominated in dollars, the dollar index is negatively correlated with gold.

Under normal circumstances, the dollar index rises and gold falls; The dollar index fell, while gold rose.

It is rare to see the same ups and downs, but it does exist. Just like last night, the dollar index and gold and silver rose and fell together. The recent occurrence of this situation is directly related to the QE4 quantitative easing of the Federal Reserve.