Consider the following scenario:
The Hong Kong Dollar has been pegged to the US Dollar since 1983. If, for example, the US tightens monetary policy by raising interest rates, this will cause capital to flow out of Hong Kong where interest rates are relatively lower and the Hong Kong Dollar would appreciate. The Hong Kong Monetary Authority would then be obliged to buy the HKD with its official foreign reserves of USD.
I understand how this all works but I am unsure of why subsequently, there would also be an "automatic decrease" in the money supply in Hong Kong, causing Hong Kong interest rates to rise. How does a decrease in a central bank's foreign reserves lead to a decrease in the country's money supply?