I have invested in Mongolia and the UK and am looking at Portugal currently. My view is pretty simple, you just really need to know the market.
I am lucky in that I can spend the required time in the country to learn the market. If you can't then I believe you are not meeting the generally accepted rule of know the market before you invest! Obviously you can use local advisers, but that is a whole other discussion.
We brought in Mongolia and while the local market has been pretty reasonable to us the FX rate went from 1 USD : 1350 MNT (Local currency) to 1 USD : 2635 MNT today. A pretty painful lose in USD terms!
Obviously Mongolia is not an established market, but I think it worth having a view on likely FX movements and a plan of what to do if they move against you.
If you look at the EU and the UK for example which have significant foreign investor interest, both potentially have material FX losses coming up due to Brexit and a few other issues. This also provides potential buying opportunities if the fundmentals of the market haven't changed.
The way we now deal with the FX risk this is diversification, I can be pretty relaxed about our Mongolian loses as it is a fraction of our investment pot.
More positively when we buy now we also now have in effect a stop lose built into the property. Depends on the specifics of the situation but for example if the FX rate reduces by over 20% or the market drops by over 20% we would seriously look at exiting the investment.
Exiting with a lose hurts, but less than being 50% down like we have experienced with Mongolia for example!
Having said all of that by investing internationally you do more than earn $, you widen your world view and get to live in amazing parts of the world where the $/quality of live metric is way better than a lot of the more expensive areas of the world.