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In a typical leverage futures contract the value of a position can be negative. That is to say, if you go long \$100 with 10x leverage at a price of \$50 and you then sell at \$40, the value of the position at the time of execution is negative:

(1000 / 50 * 50) - (1000 / 50 * 40) = -$200.

Is there a type of contract where the worst case loss is zero but there is still leverage - so the payoff is logarithmic instead of linear - and what is the name of this type of contract?

For example, if we take a long contract, as the price approaches zero, the value of the position approaches zero and as the price approaches infinity the value of the position approaches some limited amount. The value of the position sits on a logarithmic curve between zero and this limit (e.g. A maximum of $50000). The steepness of the curve is dependent on the leverage; A lower leverage will approach the limit more slowly and a higher leverage will approach the limit more quickly.

What is the name for this kind of payoff structure/contract and are there any existing instruments/derivatives that implement this?

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    $\begingroup$ Answering you're question in the headline, there exist a product called daily leverage certificates, where you can maximum lose your initial investment. However, it does not conform to your example, since the leverage creates a linear payoff (to infinity, theoretically). Maybe this will be of help? $\endgroup$ – Pleb Jan 14 at 9:40

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