macrocephalopod

I thought about power perpetuals a bit more and I really like the design. If price of the underlying goes S to S’ and back to S, price of the power perp also round-trips (unlike a leveraged token, which has a lower price in this scenario because it rebalances to higher leverage)

Obviously that advantage needs to be paid for, and it’s paid for in the premium/funding rate that longs pay to shorts. Some simple math shows how to interpret the funding rate.

If the underlying returns R, then the squared power perp returns 2R + R^2 (in price terms, ignoring funding). We can compare that to a 2x leveraged position in perpetuals. We want to equate the _expected_ returns of the power perp and 2x levered perp to avoid risk-neutral arb,

So get 2R + R^2 - F’ = 2R - 2F where F’ is the funding on the power perp and F is the funding on the perp. Taking expectations gives σ^2 - F’ = -2F which can be rearranged in two interesting ways,

1. F’ = 2F + σ^2 so the funding on the power perp is at least 2x the funding on the perp, and typically much more. Plugging in some realistic numbers I would expect a funding rate of 0.2-0.4% per day for the power perp — that’s huge!

2. σ^2 = F’ - 2F, this is more interesting since both F and F’ are observable and you can use them to derive an at-the-money implied vol for the underlying. Could use this in a yield strategy (sell power perps and hedge) or to do vol arb of power perps vs options.

I think you could go further — the higher order power perps depend on R^3, R^4 etc and I haven’t bothered to do the math but I’m pretty sure you could get an implied skewness/kurtosis from their traded prices which gives you most of a vol surface.