"Why the implied APR of Boros and the futures basis should be close: a simple yet rigorous explanation" ---TL;DR--- Let’s state the conclusion upfront: On the same expiration date, the "annualized basis of the settlement contract" and the "implied APR obtained after Boros fixes the funding rate" are actually pricing the same thing— the "cost and return" from holding until expiration. It's just different ways of consuming the same piece of meat.

2/4 Intuitive Explanation: Two different ways to eat, but it's the same piece of meat. Imagine you want to lock in the net cost (or net profit) of "holding BTC until the end of September" in advance: 🔷 Route A: Spot + Futures Short Method: Long spot + Short futures Intuition: Futures are usually slightly more expensive than spot, and this "premium" will converge to zero at expiration; you have locked in this "premium" in advance. Significance: This route directly expresses the "net value of holding costs and profits at expiration" as a fixed annualized return, which we call basis. 🔷 Route B: Long spot + Short perp (perpetual contract) + Short YU on Boros Method: Long spot + Short perp, capturing funding rates; funding rates will fluctuate and are unstable. Solution: Short YU on Boros to fix the funding rate for the upcoming period, resulting in a fixed annualized line called Implied APR. Significance: Similarly, it fixes the "net value of holding costs and profits at expiration" into an annualized return, but the path is "perp + fixation." Same piece of meat, two ways to eat (futures vs perp + YU). Theoretically, the fixed annualized returns on both sides should be similar; if they differ significantly, there will be arbitrage to pull them back.

3/4 Small Example Time to expiration: 60 days You see that the futures contract is 1.2% more expensive than the spot; annualized, that's about over 7%, which is the basis. At the same time, the Implied APR obtained from fixing the funding rate in Boros is also around 7%. If one day the Implied APR jumps to 9%, while the basis is only 7%: Large funds would prefer to take the route of "perp + short YU" for higher returns; Conversely, they would prefer to go with "long spot + short futures." This "optimal switching" is the force that drives the convergence of the two.

4/4 Why there is a "slight bias" in reality (but not enough to go off the rails lol) It's actually quite understandable; just because the two are close doesn't mean they are exactly the same. The deviation comes from "how to pay and where to pay." 🔷 Different capital occupation and margin structure The margin requirements (IM/maintenance margin) for the two paths are different, leading to different capital occupation → the opportunity cost of capital is different, resulting in a slight deviation in the reported annualized return. To be honest, although the leverage ratio is currently very low, the capital occupation for Boros shorting YU is also usually low (because you are trading the "discounted value of future earnings," not the entire spot), but note that this value is not zero. 🔷 Transaction fees and impact costs Market depth, slippage, etc., can make one side slightly more expensive or cheaper. The current Boros market still has room for further deepening. The implied APR's no-arbitrage band is likely quite wide, but I haven't estimated it in detail. If everyone is interested, I will further model and analyze it later.

Forget to @boros_fi