From a price to a rate
A PT pays, at maturity, the underlying worth one unit of the accounting asset. If it costs P units today and matures in d days, holding it to maturity multiplies the money by 1/P over d days. Pendle states that as a yearly rate: implied APY = (1 / P)^(365 / d) − 1.
A worked case: a PT at 0.97 with 120 days left. 1 / 0.97 is 1.0309; raised to the power 365 / 120 it is 1.097. The implied APY is 9.7%.
Pendle writes the same formula through the YT, as (1 + YT price / PT price)^(365 / d) − 1. It is the same number: the two prices add up to one unit, so 1 + YT / PT equals 1 / PT.
Fixed yield
A buyer who holds a PT to maturity earns the implied APY at the price paid, in the accounting asset, provided the PT redeems in full. This is what Pendle calls fixed yield. Three things stand outside it: the price paid includes the price impact of the trade and the swap fee; the rate is fixed in the accounting asset, not in dollars; and it holds only while the underlying keeps its value.
The underlying APY
The underlying APY is what the underlying asset has been earning lately, at its variable rate: on Pendle's pages, its average over the last seven days, rewards included. A YT holder receives the yield actually earned until maturity, less Pendle's fee. When the implied APY is above the underlying APY, the market prices the yield to come above what has been earned lately; when it is below, the reverse. Neither number says what the yield will be.
Why the implied rate moves
The implied APY moves whenever PT or YT is traded. Buying PT raises its price and lowers the rate; buying YT does the opposite. A large trade in a small pool moves it far, and the move lasts until other trades bring it back. Expected changes in the underlying's yield, incentives and points attached to the YT, and the cost of borrowing against PT all show up in it.
What the number does not say
- It is not a measure of the underlying's risk. A high implied APY can come from a high expected yield, from incentives or points, or from a market that sees a risk in the token, and the number does not say which.
- It does not include the cost of entering or leaving: the price impact of the trade, the swap fee, and the time a way out takes before maturity.
- It holds for the whole period to maturity. A PT sold before maturity is sold at that day's rate, which may be higher or lower.