APY Calculation
Introduction
This document describes how BitFi computes and reports APY for bfBTC. We publish two complementary metrics:
- 7‑Epoch Rolling APY (“7D APY”)
- Cumulative Project APY (since genesis)
Both are derived from the on-chain exchange rate between bfBTC and BTC.
Terminology
- Epoch N: The N‑th rebasing or accounting interval at which the bfBTC/BTC exchange rate is finalized.
- T_N: Unix timestamp (in seconds) when epoch N is finalized.
- R_N: Exchange rate at epoch N, expressed as BTC per 1 bfBTC. In words, “1 bfBTC = R_N BTC.”
- S_year: Number of seconds in one year. Unless otherwise noted, S_year = 31,536,000.
- Percent vs fraction: All APY formulas below return percentage values (i.e., multiplied by 100).
Notes:
- The exchange rate R_N is expected to be non‑decreasing over time if bfBTC accrues yield in BTC.
- Timestamps must be strictly increasing: T_N > T_{N-1}.
7‑Epoch Rolling APY (“7D APY”)
Definitio
A linearized, annualized rate based on the change in the bfBTC/BTC exchange rate over the last seven epochs. Because epochs are not guaranteed to be exactly 24 hours, this “7D APY” can differ from a strict 7‑calendar‑day APY.
Formula
Where:
- R_N / R_{N-7} − 1 is the relative change over the last seven epochs.
- The fraction is scaled to an annual rate by S_year, then converted to percent by 100.
Notes:
- Require N ≥ 7.
- If T_N − T_{N-7} is very small or zero, skip the update or fallback to a safe default.
Cumulative Project APY (since genesis)
Definition
A linearized, annualized rate computed from genesis (epoch 0) to epoch N.
Formula
Where:
- R_N / R_0 − 1 is the total relative appreciation of bfBTC versus BTC since genesis.
- Linearization makes the rate easy to interpret and stable across reporting intervals.