Introducing Sense Space

the most capital-efficient fixed-rate AMM

2022.03.10 Edit: Zeros & Claims rebranded to Principal Tokens (PTs) & Yield Tokens (YTs) https://bit.ly/3t2EcJ2

Last month, we announced our partnership with Rari Capital to build a Sense Fuse pool and permit PT & YT borrowing/lending. Today, we’re excited to share an update on Sense Space, our new AMM.

For those short on time, here is a tl;dr:

• We’ve moved away from Uniswap V3 for now because of rebalancing costs & YT price volatility.
• Our new AMM, Space, is built atop Balancer V2, implements the yieldspace invariant, and is the central market for PT / YT trading.
• Space introduces a novel accounting mechanism that permits the use of a yield-bearing quote asset, allowing it to be the safest and highest yielding zero-coupon token AMM for Liquidity Providers (LPs).
• Public testnet launch scheduled for early Jan.
• Mainnet launch scheduled for Q1. Join our community on Discord as we prepare for launch, and follow us on Twitter for updates!

At Sense, we’re focused on empowering individuals and businesses with the tools to protect themselves from interest rate volatility and take capital-efficient bets on future yields.

Several months ago, we released the Sense Protocol Litepaper, which introduced the protocol’s architecture & proposed an initial liquidity venue for PTs & YTs: Uniswap V3 markets quoted against their respective yield-bearing assets.

Below, we introduce Sense Space, a new AMM pool built on Balancer V2. The following sections share context on the valuation peg of stripping protocols, our evaluative criteria for trading venues, and an overview of Space.

We assume our readers have a baseline understanding of Sense & Yield Token (YT) Design, so if a refresher is needed, here are some resources:

• On Sense
• On Yield Token (YT) Design

If you just want to learn about Space and its use cases, skip to the Introducing Space section. Otherwise, let’s dive in:

Our north star

Sense is a debtless, stripping protocol. It allows users to deposit yield-bearing assets and issue PTs & YTs, which represent its principal and yield components, respectively. By selling off PTs or YTs after issuance, users are directly selling off distinct portions of the yield-bearing asset.

However, when held together, the combined position of PTs & YTs is equivalent to the price of the yield-bearing asset.

We can express this relationship mathematically and apply it to all fixed-income stripping protocols (Sense, Pendle, Element, Tempus, etc). It states that the price of one Principal Token (PT) plus the price of one Drag Yield Token (YT) is equivalent to the price of one yield-bearing asset (Target).

In theory, the market prices of PTs & Drag YTs should be equivalent to the Target valuation. However, whether this valuation peg is seen in practice is dependent on numerous factors, such as participation from arbitrageurs and the protocol’s support for early redemption, which allows users to combine an equal amount of PTs & YTs and withdraw the Target before maturity.

Circling back to Sense, we can apply this valuation peg to PTs and YTs, as they represent the principal and yield components of some yield-bearing asset. Although YTs use the Collect YT design and not the Drag YT design, we assume that all past yield (PY) is still held within the YT position, allowing us to use a similar, financially equivalent formula. And because Sense permits early redemption, we can be confident that the relationship will exist in practice.

With this expression, we were intrigued by an AMM that preserves this relationship for an LP position, as it would offer a competitive yield in low-volume environments. The design goal was devilishly simple: assure LPs that their net position will always be equivalent to at least the yield-bearing asset.

A blessing and a curse

After further analysis, it became clear that this AMM design is hypothetical or too complex to develop within our schedule.

The main problem is that Sense’s markets experience inter-market price discovery, meaning that the free market actively decides the price by trading against the AMM. In contrast, most price discovery of the largest crypto markets (e.g. ETH/USD) occurs on liquid off-chain centralized exchanges.

When price discovery occurs outside AMM pools, AMMs can pull in price information to adjust pool parameters and defend against impermanent loss before trades occur; this class of AMMs is called Dynamic AMMs (DAMMs).

However, LPs are subject to adverse selection without external price discovery and dynamic AMMs, meaning prices move against them on average, as seen in all constant product AMMs (e.g., UniswapV2). In these types of AMMs, LPs can avoid impermanent loss when the asset prices are mean-reverting. However, in the context of PTs & YTs, mean reversion is not guaranteed. PT prices eventually settle on a known amount of Underlying, and YT prices are highly volatile.

With all that said, inter-market price discovery is a blessing in disguise, and in fact, it’s a powerful feature, not a bug. When PTs & YTs are traded, their prices define the market interest rate at a specific point on a yield curve, allowing users to infer future interest rates and even protocol risk.

The result is expressive interest rate markets and a crystal ball into the future DeFi economy.

After realizing this, we adjusted our goals, expectations, and defined metrics for an ideal yet realistic liquidity venue for PTs & YTs.

Our Journey

For several months, we explored the design space and assessed liquidity strategies against the following metrics:

1. Principal Protection — An LP’s principal investment is fully protected in Underlying terms (e.g. protection to principal investment in DAI when market-making PTs/YTs for cDAI or f6-DAI).
2. Capital efficiency — Both the base & quote assets in a two-token market are earning yield while dormant (e.g. in between trades).
3. No-setup UX — Users can provide liquidity with a single blockchain transaction. They need not run any off-chain software or trading bots (as is required to market makers on 0x, for example).
4. Unopinionated — Permissive design that allows uninhibited free-market interest rate discovery. The interest rate implied by the PT/YT price is dynamic and is not suggested by the liquidity venue in any way. There are no assumptions of future interest rates.

Using these evaluative metrics, we explored numerous configurations, and have listed each one with their respective shortcomings:

• Underlying quoted markets — Not principally protected. Too much impermanent loss.
• Yieldspace invariant — Not capitally efficient. The quote asset is a non-yielding Underlying asset.
• Target quoted markets — Not principally protected. IL exists with upward or downward sloping yield curves.
• PT/YT market — Not principally protected. Future YT prices are unknown and too volatile.
• Uniswap V3 — Gas costs are prohibitive on L1.
• Off-chain order book — Too much operational overhead. Users need to run a market-making bot.
• Custom AMM invariants — High R&D costs.

After much tinkering & analysis, we’re excited to share the development of an AMM that checks off every evaluative metric. In the next couple of sections, we’ll dive into the high-level design, unpack its use cases, and share its backtest performance.

Introducing Space 🌌

Sense Space is a PT/Target AMM Pool built on Balancer V2. Each series has a unique Space, and all PT & YT trading goes through its liquidity. At its core, it implements the yieldspace invariant, which offers the following benefits:

1. An LPs principal investment is protected in Underlying terms if they hold until series’ maturity
2. No time-dependent impermanent loss (which exists in Underlying quoted markets)
3. Less slippage & price impact as maturity is approached

However, to improve capital efficiency atop a vanilla yieldspace implementation, Space allows LPs to deposit a yield-generating quote asset, i.e. the Target, instead of the PT’s Underlying, as was originally conceived.

To handle Target instead of Underlying, Space leverages its knowledge of the Target’s scale, or scaling factor. Let’s look at each section in its accounting logic:

1. Initialization:

To start, when Space is initialized, an initial scale (s_i) is recorded.

2. Add liquidity:

Next, when the first LP adds liquidity, their Target deposit (D_t) is multiplied by (s_i) to determine the initial total LP shares (BPT_{total}):

As is used in most AMMs, all subsequent liquidity additions will use the relative size of an LPs’ Target deposit (D_t) to mint new BTPs:

As yield accrues, a unit of Target represents an ever-increasing amount of Underlying, so for a fixed Underlying investment, LPs will need to deposit less Target if adding liquidity later in a series.

3. Swap:

Next, when a swap occurs, an amount of “virtual” Underlying (R_{underlying}) is deduced from Space’s Target reserves (R_t) and used in conjunction with the “virtual” PTs (R_{zeros}) the yieldspace invariant.

If a trader is swapping PTs for Target, Space converts the Underlying out (A_{out,underlying}) back into Target at the current scale (s_c) before transferring Target out (A_{out,target}) to the user.

4. Remove liquidity:

Finally, when an LP removes liquidity, they’re passing in their LP shares which represents a proportion of liquidity in both reserves, so there’s no conversion required.

With these simple accounting tricks, Space excludes accrued yield from the yieldspace invariant and reserves it for Liquidity Providers. These small changes make great improvements to the capital efficiency for trading zero-coupon tokens in DeFi.

Let’s judge Space against our four criteria:

1. Principal Protection — LP positions held until maturity are protected from losses to their principal investment in Underlying terms (e.g. DAI if the Target is f6-DAI).
2. Capital efficiency — Both pool assets are earning yield.
3. No-setup UX — Users can provide liquidity with a single blockchain transaction and need not run any software to constantly manage their position.
4. Unopinionated — The PT’s discount rate is market-driven. Space only ensures that it’s in parity with 1 Underlying worth of Target at maturity.

Everyone wins

Sense’s core users, PT holders, YT holders, and Liquidity Providers, all benefit from Space.

PT holders are predominantly interested in fixed rates. They’re more conservative, gas-sensitive, casual crypto users who aren’t participating in complex trading strategies. Space offers a low-cost means of swapping into and out of PT positions.

YT holders want exposure to rising future yields. They’re more sophisticated, less gas-sensitive, DeFi power users who perform due diligence and on-chain analysis to gain an edge in trading. Space consolidates liquidity into a single market, allowing for better price execution for their YTs.

Liquidity Providers (LPs) are long the floating rate, want to earn superior sustainable yields, and enable new use-cases in DeFi. Liquidity Providers stand to benefit most from Space for three reasons:

1. More volume — Similar to the benefit to YT holders, all PT & YT trading goes through a single market, leading to more volume and, therefore, more swap fees.
2. Principal protection — An LPs initial investment (in Underlying terms, w.r.t. the Target) is protected if they hold their position until maturity.
3. Superior yield — LPs earn yield through three sources: PTs, Target, and swap fees

Once Space is live, users can conveniently enter / exit from their PT, YT, or LP position within a single transaction. For details on the actions within each atomic transaction, head over to our documentation.

Backtest results

To demonstrate the better returns from Space, we backtested a hypothetical Space LP share using historical data from yieldspace-v1, the first yieldspace implementation. It uses the January 1st, 2022 series for the yieldspace LP share, and uses cDAI as the Target in Space.

In Oct 2020, both LP shares are worth 1 DAI at pool initialization. On Dec 12, 2021, they are worth:

• Yieldspace: 1.0031 DAI (~ 0.3% ROI)
• Space: 1.0538 (~ 5.38% ROI)

Conclusion

In this post, we introduced the fundamental valuation peg within stripping protocols, underscored the importance of interest rate discovery, and share the criteria used to evaluate trading venues for PTs & YTs. Moreover, we introduce Space and outline its benefits to PT holders, YT holders, and Liquidity Providers.

Over the coming weeks, we’ll incorporate user feedback from our private beta and prepare for an upcoming public testnet launch, scheduled for early Jan. To allow our audits to conclude and give users a proper testing window, our mainnet launch roadmap is adjusted to early Q1.

Join our community on Discord as we prepare for our public testnet launch, and follow us on Twitter for updates!

Thank you to those who read drafts of this post, including Tom Schmidt, Kurt Barry, Freddie Farmer, the Balancer Labs Team, and the Sense core team.

Disclaimer: This post is for general information purposes only. It does not constitute investment advice or a recommendation or solicitation to buy or sell any investment and should not be used in the evaluation of the merits of making any investment decision. It should not be relied upon for accounting, legal or tax advice or investment recommendations. This post reflects the current opinions of the authors and is not made on behalf of Sense Finance or its affiliates and does not necessarily reflect the opinions of Sense Finance, its affiliates or individuals associated with Sense Finance. The opinions reflected herein are subject to change without being updated.