Is there some kind of synthetic ETF that magnifies changes to exchange rates so that if, for example, the Canadian dollar increases by 5% with respect to the American dollar, the ETF will go up by 10% and vice versa? Is there another way to hedge against currency risk without tying up a lot of capital?
I'm somewhat shocked that I can't find a leveraged Canadian Dollar to American Dollar ETF. It's possible one exists but if it is not on Bloomberg (or even Wikipedia) it likely doesn't exist. Interestingly, I found a CAD/EUR 3x leveraged ETF, but not a USD one.
You could look at using the CAD/EUR and EUR/USD 3x levered ETFs, but given the awful issues with leveraged ETFs I'm not even sure I can recommend this even in the short term as a solution.
The traditional way of hedging currency without tying up lots of capital is to use currency futures or forwards. The margins on these contracts are quite reasonable if you are an institution, but may be prohibitive as an individual investor. Check where you trade. Also, there can be complications about rolling these contracts that may make them a pain for an individual. Still, if you really need to do the hedging and are willing to put in the work this is the place to start.
Of course, if you are looking for a hedged common index like the S&P 500, that type of ETF certainly exists and it is cheap and you avoid the margins.