How do Foreign Investments by Central Banks increase the Money Supply of an Economy?

Question

Trying to understand if "money supply" and "currency in circulation" apply only to the money within the borders of the country or does it also include its money in foreign nations as well?

For Example:

Scenario 1) Swiss Central Bank has 200 billion francs circulating within Swiss borders

Scenario 2) Swiss Central Bank has 100 billion francs of money circulating in Swiss borders and the rest 100 billion invested in foreign American stocks (Hence money circulating in USA)

I ask because when the Swiss Central Bank invests in foreign stocks that money isn't being supplied to its own economy/people thus it isn't increasing its own economies money supply in a way. If inflation hits and the Swiss Central Bank decides to sell off the USA stocks and get its money back, it wouldn't have changed the amount of money supply within its actual economy/borders(hence to its people) in which case how would that curb inflation locally? I can understand the effects on Foreign Exchange but how does that impact local money supply?

I'm just trying to make sense of what this guy is saying starting at 5:45 https://youtu.be/ikBZWrz65Ic?t=344

He's saying "... a 3rd way of introducing money into the economy... buying stocks, gold or even currency of other countries."

Which brings me back to my original question of when you buy foreign investments(in their case U.S Stocks) you aren't introducing money supply into Swiss Economy but rather into U.S Economy

"... when an unexpected period of inflation hits, they can sell of these foreign assets and get their currency back thus reducing the money in circulation."

Reducing money in circulation world-wide? Yes. Reducing money in circulation in Swiss-Economy? No. Because if you had 100 billion in Swiss Economy and 100 Billion in U.S stocks and then you sold off U.S stocks you still have 100 billion in Swiss Economy. So how does it reduce INFLATION in Switzerland?

Thanks.

Answer 1

In your question you assumed that if you spend SFr 100bn on US stocks, the sellers of those stocks are getting the SFr. But that’s not true. Those sticks trade in USD, so what actually happens is that you first have to buy USD with your SFr in the FX market. Thus, the SFr end up in the hands of an FX market participant. But it’s quite likely that that person is buying the SFr in order to buy something denominated in SFr (for example an American company that wants to import Swiss goods). So actually, the SFr probably end up back in circulation in Switzerland.