I think I will tithe on any increase, but not on the principle (assuming that I already tithed on the principle before investing it). It is best with a couple of examples:
Example 1: Investing in Stocks
Earn $100,000 in salary. Pay tithing of $10,000 on this money in the year I earn it (leftover is $90,000 that I transfer to a specific investment stock account as cash). I can withdraw up to $90,000 tithing free. After the original $90,000 is returned, I tithe on the rest as it is withdrawn from the specific investment account. Funds can essentially compound in the investment account "tithing free" until I take them out as return of capital (not tithed a second time) or return on capital (tithed). When I close out the account, I first make sure that I have taken out the original $90,000 of investment and then pay tithing on the rest.
Example 2: Investing in Businesses
I would treat stocks (a part of a business) and private businesses the same. The only difference is liquidity. Earn $100,000 in salary. Pay tithing of $10,000 on this money in the year I earn it (leftover is $90,000 that I buy a mechanics shop with). I can withdraw up to $90,000 tithing free in salary, dividends and less tangible benefits from the business. After the equivalent value of $90,000 is returned, I tithe on the rest as it is withdrawn from the specific business. The value of the business could go up or down, the business could re-invest back into itself some of its profits without paying tithing. If the business is sold, I first make sure that I take out the original $90,000 tithing free and then tithe on the rest at that time. I would not have someone quote me on the value of my private business in the middle of operations and pay tithing (unless I felt a specific prompting to do so).
Example 3: Investing in Currencies
For investing in other currencies or gold, I would treat them like another investment account. However, if I am spending that money directly without physically switching over to my home currency, I would first pay tithing on that amount as if I had changed it to my home currency before making the purchase. I would not (again, unless prompted to), pay tithing on the current market price.