Why does the dollar go down when the stock market goes up and vice versa?

When interest rates decline, that is good for the stock market because it lowers the cost of capital for businesses operating in the US. They can obtain funds easier to grow. At the same time, lower rates in the US make the dollar a less attractive investment for foreigners, because they get paid less interest when they buy US Treasury bonds. So they demand less of Treasury bonds, and that means they demand fewer dollars to buy these Treasuries. Less demand for dollars causes the dollar to decline. So there you have it! A declining dollar often correlates with a better US stock market.