# Space Pool LP Returns
# The Big Picture
Before going into detail, here is a high level summary of how being a Space Pool LP (e.g. providing sP-wstETH/wstETH liquidity (opens new window)) compares to some relevant benchmarks in multiple market action scenarios. It’s important to note here that the below statements are assuming that yield for the target asset (meaning the yield-bearing token on which the pool is based, e.g. wstETH) is positive and that the Space Pool liquidity is provided until maturity.
A Space Pool LP:
- Outperforms the underlying asset (e.g. ETH) in every case
- Outperforms traditional Yieldspace AMM (opens new window) LPs (currently used by other yield stripping protocols) in every case
- Outperforms the target asset (e.g. wstETH) in most cases (expanded on below)
Below we will give much greater detail on what drives this performance, and how market action can impact it.
Caveat emptor, caveat lector: This document is an analysis of hypothetical cases used to illustrate some of the important dynamics that impact Space Pool LP returns. This is not a comprehensive description of the risks and rewards associated with Space Pool LP shares.
# What is a Space Pool Share
A Space Pool Share is a claim to liquidity provided in the Space AMM. The Space AMM (opens new window) is an automated market maker used by the Sense protocol to allow trading between 3 assets:
A “Target Asset,” which can be any yield-bearing token (e.g. wstETH).
A “Principal Token” (PT (opens new window)) which is a redeemable claim to a fixed amount of target asset principal after maturity, fixed in value terms of the underlying (e.g. sP-wstETH (opens new window)).
The Space AMM allows anyone to be a liquidity provider (LP) for trading between these three assets, and to collect fees from that trading. The Space Pool design is an upgrade to the Yieldspace Invariant (opens new window) design, with the biggest difference being what assets are used to provide liquidity.
In a traditional Yieldspace Invariant pool, liquidity is provided in terms of (1) a PT (a fixed yield version of a yield-bearing token like sP-wstETH for wstETH) and (2) that PT’s “underlying” ****(the non yield-bearing token that underlies a yield-bearing token, like ETH for wstETH).
In a Space Pool, the LP instead provides liquidity in terms of the PT (e.g. sP-wstETH) and the yield-bearing target asset itself (e.g. wstETH). This means that the Space Pool LP is collecting yield every block on both of the provided assets while a traditional Yieldspace Invariant LP is not (note  at end: we do not have footnotes, so this is how I will approximate them). Because of this, Space pools LPs outperform traditional Yieldspace Invariant LPs in any market conditions that don’t include negative yields on the target.
The purpose of having a trading venue for PTs is to have a market determine an “implied rate” (IR (opens new window)). This is the annualized rate of return a buyer of PTs would earn by buying and holding the PTs until their maturity date, when the PTs become redeemable for a fixed amount of the target asset. This yield is expressed in the market as a discount in the price of those PTs vs the value of the principal (target) to which they are a claim. That discount approaches zero as the maturity date comes closer, and becomes zero when the PTs are directly redeemable for the principal.
The difference in the value of a PT and its target asset defines a fixed implied rate (the IR) that can be:
(1) Collected by buying and holding PTs (opens new window) until maturity.(2) Traded against (if you think the actual collected rate of target will outperform the IR) by buying and holding YTs. (opens new window)
A Space Pool share is a token with a proportional claim to the assets used to provide a Space Pool’s liquidity for a specific series (opens new window).
# What Drives Space Pool Share Performance?
The drivers of Space Pool LP performance are different from traditional (Uniswap V2 style) constant-product AMMs.
Liquidity is provided in terms of two yield-bearing assets that are heavily correlated with each-other (having the same underlying exposure). What is being “priced in” by those assets’ proportional weight in the pool is an implied rate: the spot price of PTs has to change as maturity is approached in order to reflect the same spot rate (implied by that PT price at a different time to maturity). The same implied rate corresponds to a different PT price 12 months from maturity than it does 1 month from maturity. To accommodate this change, the curve that determines the rate at which one asset can be converted into the other against the pool’s liquidity changes shape depending on how much time remains until maturity.
All in all, adding in the element of time to maturity as well as the additional yield being earned on the provided assets makes the return profile for Space Pool LPs more complicated.
Nonetheless, let’s break this down and get a glimpse behind the curtain of Space Pool performance.
Each of these items deserves a brief description:
- Trading fees are the fees earned by the LPs as traders come and trade YTs, PTs and target against each other. In our analysis below, we will assume these are zero, since they only provide additional upside and are defined by pool liquidity vs trading volume (rather than market action). We will link a simulator at the end that can give some return analytics that include trading fees in semi-random trading scenarios (within custom parameters).
- Yield on PTs will vary based on the implied rate. The PTs are a claim to a fixed amount of principal at the maturity date. In the meantime, they are constantly collecting yield (losing their discount) at a rate equal to the implied rate. Changes in the implied rate affect this in three ways:
- The level of the implied rate defines what rate you are earning on the PT portion of your portfolio at any given time
- Rising implied rates cause negative price impact to PTs, whereas falling rates cause positive price impact.
- PT price changes alter the proportion of PTs vs target you hold, therefore altering what percent of your pooled capital is collecting the implied rate vs the target rate as yield
- Yield on Target is only affected by the implied rate insofar as the level of the implied rate (combined with time until maturity) defines the price of PTs. In an AMM the price corresponds to what portion of the pool’s capital is held in one asset vs the other. This means that price of PTs also dictates your nominal exposure to target (and therefore your nominal exposure to target yield). It is also, of course, impacted by what the variable yield on target turns out to be (although we will hold that constant in our analysis below to simplify matters).
- Impermanent Loss exists, but is a small amount (because pooled assets are highly correlated). IL is a less useful metric in isolation here than it is for constant product AMMs, because, in the case of a Space Pool, it would be defined against a meaningless benchmark: some arbitrary portfolio of combined PTs and Target (see note  at end). The Space pool also (like the traditional Yieldspace Invariant pool) gets rid of the time based IL from the PT price drift as maturity approaches and discount fades (so the IL that does exist comes only from implied rate changes).
There are simply more components at play in a Space Pool. Implied rate changes can have different impacts depending on the time to maturity, and even depending on implied rate level.
We can still get a grip on the overall shape of returns in different market action scenarios, though. To do so, we are going to put yield on PTs, yield on Target, and impermanent loss into one bucket (getting rid of trading fees, which would only provide further upside) and get a sense of the overall impact that changes in the implied rate have on Space Pool share performance.
# Impact of Implied Rate Changes on Space Pool LPs
In the below examples we try to hold most other variables constant and look at the isolated impact of implied rate changes on pool performance. For every example, we assume the realized target yield (e.g. wstETH) is flat at 10%, we start by adding liquidity to a space pool 12 months before its maturity at an implied rate of 10% (see note  at end), and then see how the value of the Space Pool Share will change as the implied rate changes linearly to a new value over the course of those twelve months.
For the median case used “I.R. to 10%”, the Space Pool IR stays flat at ten percent. Since the realized target rate is held constant at ten percent as well, and we are assuming no trading fees, the performance in that example will be identical to simply holding target.
In the 10% case the Space LP holder is exposed to some composite of a PT earning a flat 10% yield, and target also earning a flat 10% yield, and so it is equivalent to just holding target and getting that 10% yield. In the following charts, we will simply mark the “I.R. to 10%” case as “Target.”
# All Cases Have Positive Return Over Underlying
In the below chart we see the return over underlying for the Space Pool LP (e.g. return over ETH for a sP-wstETH/wstETH pool). Even without trading trading fees, the Space Pool LP significantly outperforms the underlying regardless of implied rate market action.
# Some Cases Can Overperform Target, Some Can Underperform Target
Since a more comparable alternative would be performance relative to target (e.g. wstETH for sP-wstETH/wstETH pool), the below chart shows return vs target. As you can see, the Space Pool LP outperforms target significantly in the cases where yield compresses to lower levels from the 10% starting point. For cases where the yield rises moderately, the Space Pool can underperform the target’s 10% realized yield while still providing a positive return vs underlying. In the extreme case of rates rising all the way to 50%, though, the Space Pool share once again starts to outperform target. The reasons for this will be explained in a later section.
# Outperforms in Falling IR Environments
So why does the Space Pool share outperform in the falling I.R. environments?
The short answer is that the Space Pool LP gets price appreciation in their PTs as yields compress, even as there is a countervailing pressure of the pool composition shifting to hold a smaller proportion of PTs. As an example, a 12 mo PT claim to 1 ETH worth of wstETH pricing in a 10% yield would be worth about 0.90 ETH. If it moves to price in a 5% yield instead, its price moves up to 0.95 ETH. This yield compression “pulls forward” some of the 10% yield a holder of the PT would have gotten simply by holding until maturity and redeeming. That return boost is somewhat offset because your % PT composition is falling as the PTs’ nominal value rises. But, for every bit of PT that drops out of your composition, the space pool is replacing it with a bit of target (e.g. wstETH), which in the example we are using is yielding 10%.
# Moderate Rising Implied Rates Can Cause Underperformance Vs Target
In two of our cases, where the priced in implied rate rises moderately, the Space Pool share (sP-wstETH/wstETH) underperforms the target asset (wstETH). Even more interestingly, they underperform more dramatically at the start, and then begin to narrow the gap as maturity approaches.
The basic reason for the initial underperformance is the inverse of what boosts initial returns in the falling yields case we described before this one. Rising yields depress the nominal price of PTs, and increase the proportion of PTs you hold in the pool. But, PTs also are always collecting a yield equal to the implied rate. So, while the implied rate depresses their price, they will also start collecting a higher and higher yield. Because they are a large portion of your pool, and now collecting a rate higher than the rate that target is collecting, the pool’s overall performance starts to catch up to target. At the end of the day, after all, they have to become redeemable for a fixed amount of principal. At some point, price appreciation as the maturity approaches becomes more impactful than price depreciation from the IR increasing (even though the IR is continuing to rise). We will discuss the dynamics behind this further in the section below.
# Pool Outperforms Target In Extreme Rising Implied Rate Environments
In the below example we see the extreme case of the two competing forces on Space Pool performance in rising rate environments that we have already discussed. As the IR in this case shoots linearly up to 50% at maturity, the initial price depreciation of PTs causes underperformance of the Space Pool. As maturity approaches, however, the PTs that have become such a large portion of the pool due to their depressed price are also collecting such a strong yield that the pool overcomes the initial dip and eventually achieves a better return than holding target. This case also demonstrates the dangers of not holding space pool shares until the series maturity (if you leave early you can even underperform underlying).
Below we show the composition of the pooled assets and the spot rate being collected by the PTs at any given time. As you can see, in this extreme case, the pooled assets quickly become predominantly PTs, and the IR (which is also the yield those PTs are collecting) becomes extremely high. By the end you have your last month, where your pool is almost entirely PTs and those PTs are earning nearly 50% yield, which is helping the pool catch up in its overall performance.
Additionally, all things being equal, the closer you are to maturity the less of an impact a 1% change in implied rate would have on the nominal value of your PT.
A PT ten years from maturity going from a 0% annualized IR to a 1% annualized IR has to go from being worth 1 underlying to being worth 0.9 underlying (+1% in IR terms means -10% in price). But, a PT one year from maturity going from a 0% annualied IR to a 1% annualized I.R. only goes from 1 to 0.99 underlying (+1% in IR terms means -1% in price).
On top of that, the % change required in PT nominal price for a 1% change in IR is diminished as the level of I.R. goes up. Below we show the negative impact on PT price of a 5% change in IR at different maturities for three different cases of IR level.
All in, PT price can rise or fall in a period of IR increase when netted with the collected yield. Let’s talk through the combined impact on an example of change in IR netting out against collected IR (the “collected I.R” being the price appreciation from the decreasing discount as time until maturity approaches zero).
A PT with a twelve month maturity that goes linearly from a priced in 0% rate to a priced in 1% rate over the first month of its existence will “accrue interest” in the form of a price increase at an average annualized rate of around 0.5% over that period. That positive value accrual is negligible (~0.04%)(see note ). At the same time it will lose something close to 1% (see note ) of its value from an increase in the discount rate. This nets to a negative return that is still around 1%(see note ).
Another twelve month PT moving from 21% to 20% will accrue (from the fading discount) at an average annualized rate of around 20.5% over that month for a much more meaningful ~1.57% (see note ) boost in value, while also losing around 1% (see note ) of its value from an increase in the discount. This nets to a positive return of around 0.57% (see note ).
At higher yields the same change in implied rate might not be enough to create an overall negative return in that time period. In one case the nominal price of the PT moves down against the underlying asset, while in the other case it moves up.
It’s also important to note that this extreme rate level case is not dependent on a linear rise as we use in the examples above. Sitting at an implied rate level higher than the target yield helps performance vs target (collecting a higher yield on the PTs), and compressing from that high level can also help performance (by re-boosting PT price and “pulling forward” that yield).
Here’s an example where yields simply go up halfway to the extreme case (up to 30%) at the six month mark, and then sit there. The Space Pool still ends up outperforming target. For the second half of this period, most of your portfolio is PTs, and those PTs are earning a 3x higher yield than target (30% vs 10%).
And here’s an example where yields go up halfway through the extreme case, and then compress back down to the initial 10%. The Space Pool still ends up outperforming target.
Ultimately, When IR sits at higher levels than the target yield, the LP is collecting a better yield than target. When the IR sits at lower levels than target yield, the LP is collecting worse yields than target.
But, IRs changing affects returns differently. Rising IRs exert a negative pressure on returns versus target (due to falling PT price) and falling IRs exert a positive pressure on returns versus target (due to rising PT price).
The cases in this analysis where LPs underperformed target were when:
(1) IRs go up, BUT
(2) Not high or for long enough that the pool’s extra yield offsets price decrease, AND
(3) Also don’t come back down such that a price increase offsets the price decrease.
An important note here: there are situations that don’t appear as a case in this analysis where you could also underperform target– they have the same fundamental causes (rising rates that are not offset by collecting a higher rate, or lower rates that are not offset by price increases from rates falling). For example, if you enter at an IR below the target’s yield, and the IR stays below the target’s yield, you could underperform target. Or, for more complex example, if rates go to zero and then come back up, it could lead to underperformance (if the re-rising of the rates offsets the price increase from rates falling, and the PTs spend a good while accruing yield at a below target rate).
Regardless, you are still getting yield over underlying (see note )in these cases when the IR market action would cause you to underperform target yields– and that is still not including any trading fees.
# Outperforms Traditional Yieldspace Invariant Equivalent in All Cases
As long as the yield on target is positive, Space Pools outperform traditional Yieldspace Invariant pools regardless of market action.
In most cases the performance of a Space Pool vs a traditional Yieldspace Invariant pool is driven by the fact that the Space pool holds a bunch of yield-bearing target (e.g. wstETH), whereas the Yieldspace Invariant pool holds a bunch of non yield-bearing underlying (e.g. ETH).
In situations where the target experiences negative yield, like a major liquidation for a target asset that gets its yield from a lending platform (like cETH), it would be possible for a Space Pool to underperform its traditional Yieldspace Invariant equivalent.
For targets that don’t have a negative yielding mode, but do carry smart contract risk (as all things do in crypto) that smart contract risk is largely shared by both traditional Yieldspace Invariant pools and Space pools (if the value of wstETH went to 0, an attacker could mint an arbitrarily large number of PTs and use them to buy all of the ETH in a Yieldspace Invariant).
In normal market conditions, though (non-negative yield environments) Space Pools always outperform.
Ultimately the Space Pools have an extremely attractive performance profile whether compared to target, underlying, or traditional Yieldspace Invariant pools as an alternative. We welcome any additional external analysis done on this, and hope to provide more formalized mathematical descriptions of the impact of IR price action on Space Pool Share performance: this document only provides an illustrative case study of various examples within constrained idealized conditions, and is not a comprehensive description of all risks involved in Space Pool LP Shares.
In real life, target yield will vary and wiggle, implied rate paths will be less smooth and move in both directions, and the pool could start out at an implied yield way above or below the target asset’s actual yield. With all of that said, we hope this was a useful glimpse into LP performance for the Space AMM, and has given you a sense of the return profile and some of the dynamics at play. In the future we’ll have to do more analysis, including the impact of keeping or selling YTs that are created when liquidity is added has on returns (YTs are issued when adding liquidity from target or underlying).
If you’re curious about seeing some more “real life” looking examples, we have built a tool that will show returns and run actual trades through a simulated Space Pool semi-randomly based on parameters you can fool around with. You can find that tool here (opens new window).
 Other aspects of Yieldspace Invariant pools are largely preserved (changing curve from constant product to constant sum to eliminate loss from PT price drift, etc.). Also, the comparison here is assuming that we are comparing a space pool to a traditional Yieldspace Invariant pool for the same PT, and that trading fees and implied rate price action are the same between the two.
 A reasonable benchmark for the performance of being a 50/50 LP to a Uniswap pool with ETH and USDC is a portfolio of 50/50 ETH and USDC. Impermanent loss is measured against this benchmark, and so makes sense to use as a metric in that case. In our case, “Impermanent Loss” would be measured against some random mix of PTs and target. That is not a useful benchmark: it is not an alternative someone would hold, and most readers don’t intuitively know how IR price action would cause that to perform. We think a much better benchmark (a more realistic alternative) is just the return of holding target, to which we will compare Space Pool returns below.
 Timeshift for this pool is assumed to be 12 years, as it is for all Space Pools created by Sense at time of writing.
 (1+0.005) ^ (1/12)-1
 In a slightly different counterfactual where it just changed the I.R. at 12 months until maturity, the price impact would be (1–0.00) ^ (12/12)-(1–0.01) ^ (12/12) = 0.01 || -1%
 (1–0.00) ^ (12/12)-(1–0.01) ^ (11/12) = -.0092 || -0.92%
 (1+0.205) ^ (1/12)-1
 In a slightly different counterfactual where it just changed the I.R. at 12 months until maturity, the price impact would be (1–0.20) ^( 12/12) -(1–0.21)^(12/12) = 0.01 || -1%
 (1–0.20) ^ 12/12)-(1–0.21) ^ (11/12) = 0.0057 || 0.57%
 Assuming liquidity is provided until maturity.