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,

How do we derive σ^2 - F’ = -2F from 2R + R^2 - F’ = 2R - 2F? I see how to get to R^2 - F’ = -2F. Thanks for the help!

So 2R on both sides can be cancelled out. Then we can take E[] (expectation) for both side. I guess E[F] = F whereas E[R^2] = E[(R-0)^2] = E[(R-meanR)^2] = sigma^2 (assume meanR=0)

Though now I read it again, I don't know how the power perp return is 2R + R^2. Can anyone help me with that? Thanks