Are there investable securities that grow nonlinearly/exponentially with the underlying asset?

External question — Personal Finance Stack Exchange Author: Tal Original post: https://money.stackexchange.com/questions/114641 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Let's say I'm a commodities trader, and Jesus Christ himself has just told me that gold is about to become much, much more valuable. We'll leave the debate on whether that's insider trading to another day :) I have any number of ways to invest in gold. I could trade gold directly on COMEX, buy futures and other options on their respective exchanges, or perhaps diversify off the commodities market entirely by investing in stocks of the largest producers of gold — Newmont Goldcorp comes to mind. But considering Jesus himself gave me this advice, I want to maximize my return. Depending on which margin accounts I hold at my respective brokerages, I could increase my returns a few times using leverage. I could also borrow privately and use the borrowed money as collateral to increase my leverage. Not a very good move under normal circumstances, but considering the big man himself said so, let's do it. But each of these approaches only linearly multiplies my returns, and I want to go exponential if possible. If the value of gold doubles, I want my principal to quadruple. If the value of gold triples, I want my principal to increase nine-fold. Given my confidence in the investment, I'm more than willing to accept equally exponential losses should gold decrease in value. What options are there for such a hypothetical investment?