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Forex independent investments
Unless you are buying a significant value of your goods in USD then the relative strength of USD versus your local currency will have little to no effect on what the value of your investments is worth to you. In fact only (de|in)flation will effect your purchasing power. If your investments are in your local currency and your future expenses (usage of the returns on the investments) will be in your local currency FX has no effect. To answer your question, however, since all investments involve flows of money there can be no investment (other than perhaps gold which is really a form of currency) that isn't bound to at least one currency. In general investments are expected to be valued against the investor's home currency (I tend to call it "fund currency" as I work with hedge funds) as the return on the investment will be paid out in the fund currency and returns will be compared on the same basis. If investments are to be made internationally then it is necessary to reduce, or "hedge" the exchange rate risk. This is normally done using FX swaps or futures that allow an exchange rate in the future to be locked in today. Far from being unbound from FX moves these derivatives are closely bound to any moves but crucially are bound in the opposite direction to the hoped for FX move. an example of this would be if I'm investing 100GBP (my local currency) in a US company XYZ corp which I expect to do well. Suppose I get 200USD for my 100GBP and so buy 1 * 200USD shares in XYZ. No matter what happens to XYZ stock any move in GBP/USD will affect my P&L so I buy a future that allows me to exchange 200USD for 100GBP in 6 month's time. If GBP rises I can sell the future and make money on both the higher exchange rate and the increase in XYZ corp. If GBP falls I can keep the future until maturity and exchange the 200USD from XYZ corp for 100GBP so I only take the foreign exchange hit on any profits. If I expect my profits to be 10USD I can even buy futures such that I can lock in the exchange rate for 110USD in 6 months so that I will lose even less of my profit from the exchange rate move.