Do non-resident aliens pay taxes on foreign investments?

Since these are not effectively connected to a US trade or business you operate (which would be taxed at 'resident' rates regardless of your residence), and you are physically present at least half the year, YES these are taxed at 30% or the treaty rate applicable to your nationality. See Pub 519 'Sales or Exchanges of Capital Assets' and particularly the subsection '183-day rule'. To be clear, like for citizens and residents, only realized gains are reported and taxed; 'paper' gains are ignored -- except if you become a lawful permanent resident (aka green card holder) and then abandon or lose that status (or are a citizen and relinquish your citizenship, but that doesn't apply to you) and have really large paper gains (like millions of dollars).

You might want to familiarize yourself with the rest of Pub 519 as well, since US tax for non-resident aliens is even more complicated and often bizarre than that for citizens and residents, which is quite bad enough. It can also be downloaded in PDF by going up to the parent page using the link at the top of the page. Enjoy your stay :-)