Designing Yield Tokens

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

Introduction

DeFi is home to a universe of yield-bearing activities, such as lending, staking, and protocol dividends. Due to Ethereum’s composability, moving from one to another is often as easy as swapping between tokens. These yield-bearing assets represent a share of a yield-generating activity, and each carries a unique, floating cash flow realized in real-time, commonly measured as an annual percentage yield (APY). Examples include Compound’s cTokens and Uniswap LP shares.

Earning a variable rate is simple but limited. Users looking to manage risk by hedging interest rate volatility or profit from interest rate movements are left underserved.

Numerous projects are actively working to fill this gap. These Fixed Income protocols, or those enabling fixed rates and future yield trading, fall into three main camps:

• Tranches/structured products (BarnBridge, Saffron, 88mph)
• Zero-coupon loan facilities (Notional, Yield, Hifi, UMA)
• Stripping protocols (Pendle, Element, Swivel)

Of these, we’ll be focusing on stripping protocols, which decompose yield-bearing assets into their principal and yield components, packaging them behind two fixed-term, maturing assets. Like tokenized rights, these assets redeem for the principal and yield components in the future. Teams have experimented with different naming schemes, but for this post, we’ll use the following terms to describe them:

• Target: Yield Bearing Asset
• Principal Tokens (PTs): Tokenized right to the Target’s principal component
• Yield Tokens (YTs): Tokenized right to the Target’s yield component

Because the PT and YT prices are a function of the Target’s APY, they enable future yield trading. PT holders will benefit from a fall in the Target’s APY, whereas YT holders will benefit from its rise.

PTs are like zero-coupon bonds, delivering a single cash flow at maturity. They are simple and easy to value. On the other hand, YTs are like floating rate bonds, delivering unknown cash flows at future date(s). They are more complex and harder to value, but they present fertile ground for financial innovation. This is why we see different YT designs in the market.

In this post, we’ll discuss different methods for creating a claim on future yields. We’ve explored their trade-offs and wish to share our research as they become more widespread. Below is a quick taxonomy of the YT design space where we analyze existing solutions and present a simple framework for thinking about YT design.

A Primer on YTs

YTs are a tokenized claim to future on-chain cash flows for a particular asset. Let’s get straight to an example to make this concrete.

Concrete Example

Consider Compound Dai (cDAI):

An issuer places a quantity of cDAI tokens valued at 100 DAI into a stripping protocol, committing to a 2-month lockup.

The stripping protocol produces:

• 100 PTs, which will redeem for 100 DAI worth of cDAI in 2 months
• 100 YTs, which will pay the floating-rate cash flows on that cDAI for 2 months
• PTs will price at a discount to 100 DAI (say $99.58), whereas YTs will price as the discounted expected future interest payments (say $0.42).

The cash flow may not be known when the YT is minted, similar to a variable rate fixed income instrument, but the underlying cash flow source is always known, which is enough to unlock valuable use cases. For example, if the source is money market lending, YTs enable hedging of borrow rates and trading of supply rates. In later sections, we’ll introduce different YT designs, analyze their attributes and discuss their differing use cases.

Design Space

Let’s zoom in and further break down a YT into two parts:

1. PY (Past Yield): Realized cash flows
2. FY (Future Yield): Projected future cash flows

Note that PY cannot decrease once accrued but FY will fall over time, given static market expectations.

Here’s an interactive tool showing PY and FY as a function of the Target’s APY and time.

YT construction centers around the management of PY. We introduce three designs:

• Drag — PY delivered at maturity
• Collect — PY delivered before maturity
• Recycle — PY reinvestment before maturity

Drag

tl;dr — These YTs Drag along PY until maturity.

A Drag YT keeps PY until maturity, and YT holders redeem all of it on or after maturity. Both the PY and FY are discounted back to the present day from maturity. They are similar to a PT with a floating redemption value.

Projects using Drag YTs:

• Element: https://paper.element.fi/#3-yield-tokens
• APWine: https://docs.apwine.fi/
• Tempus: https://bit.ly/2VOV3Ri

Collect

tl;dr — A holder can Collect PY before maturity.

A Collect YT distributes PY as it accrues, allowing YT holders to receive PY before maturity. PY is valued in today’s terms, whereas FY is discounted back to the present day using a discount factor associated with its time of delivery. They are similar to a coupon bond, but one that lacks a principal cash flow and has a near-continuous coupon stream.

There are two types of Collect YT positions:

• Passive positions — PY left untouched will exhibit behavior similar to Drag YTs. However, Collect YTs may differ from time to time, given they get cash sooner.
• Active positions — holders actively reinvest their PY into more YTs will emulate Recycle YTs.

Projects using Collect YTs:

• Pendle: https://docs.pendle.finance/resources/lite-paper
• Swivel: https://swivel.substack.com/p/cash-flow-instruments-pt-3-interest
• Sense: https://docs.sense.finance/litepaper/#abstract

Recycle

tl;dr — This YT Recycles its PY for more YTs.

A Recycle YT extracts PY and uses it to purchase YTs at market price (YT / Target’s Underlying). Then, the newly acquired YTs are distributed to existing holders — this adds more principal to existing YT positions, thereby amplifying their FY component. The recycling mechanism is similar to an active trader that reinvests coupon payments back into their position.

Behavior

To explore the behavior of these designs, we establish two sensitivity measures:

1. Time sensitivity — % change in a YT’s price from the passing of a single day
2. Interest rate (IR) sensitivity — % change in a YT’s price from a 1% change in the expected Target interest rate

Like theta and delta in option pricing, these measures help us understand the factors that influence a YT’s price.

The results from our analysis are below. While the market price of these tokenized claims can be very different from our modeled values, the relative valuations, ie the values returned for one set of inputs compared to another, are in correct proportion. So, it’s sufficient for our purposes here of comparing % changes. Let’s look at the results of our analysis, and afterward discuss a few key takeaways.

Results

• We define price as the value of an entire YT position. For example, a Collect position consists of two balances in the holder’s wallet, a growing PY balance in Target and a static YT balance.
• Collect YTs are held by passive users who leave their PY untouched.
• We present a rudimentary valuation framework. It assumes the current Target interest rate is nominal, compounds continuously, and is stable through maturity. These assumptions create PV equations unique to each YT design.

Modeled Prices

Below are the results from our Valuation analysis, which live in this notebook.

Sensitivities

The results from our sensitivity analysis (from this notebook, which we highly recommend experimenting with).

Time Sensitivity

Although the notebook has a graph of time sensitivity vs time, we present a more intuitive graph showcasing cumulative price change over time.

Interest Rate Sensitivity

Key Takeaways

When a YT series initializes, PY does not exist for any YT, so all YT designs have equivalent IR sensitivities. As time passes, however, PY accrues and sensitivities diverge.

Drag YTs — Do not see their value fall as a function of time, but because their price is less a component of FY as maturity approaches, they suffer from IR sensitivity decay.

Collect YTs — The user’s handling of PY defines the type of Collect YT position. Passive Collect YT holders let their PY accumulate and hold a position that is similar to Drag YTs. On the other hand, Active YT holders manually recycle their PY and hold a position emulating Recycle YTs.

Recycle YTs — Reset their IR sensitivity after each recycling event and preserve their value in the best case; however, recycling inefficiencies can lead to price decay. This construction is great for passive Traders, who want constantly-preserved IR sensitivity on their balances, and do not want to be tasked with continually finding reinvestment opportunities for their capital.

As highlighted above, there are differences in behavior across the design space. We expect to see the following user types:

Traders. They purchase YTs, looking to profit from the rise in the Target’s APY (All). Two types of preferences could exist:

1. Optimizing for diminishing risk & reward (Drag, Passive Collect).
2. Optimizing for preserved risk & reward (Active Collect, Recycle).

Hedgers. They purchase YTs, looking to partially hedge the interest rate on a loan denominated in the Target’s underlying asset (Drag, Collect)

tl;dr — Recycle YTs achieve the same benefits as Active Collect YT management, but in a passive way.

Conclusion

To summarize, we discussed three different methods for tokenizing future yield: Drag, Collect, and Recycle. Each design differs in how it handles PY, or past yield, which affects its behavior in the market. Specifically, it impacts the YT’s sensitivity to time and interest rate.

To dig deeper into these assets, though, we must also recognize that they’re embedded in a much broader investment class called Fixed Income, and that these discussions only scratch the surface. Further down this road, we find yield curves, measures of investor sentiment, and a new market that informs us about discount rates.

This was a short, introductory post, and we’d love it if people chimed in with their own thoughts. The design space for fixed income in DeFi is vast, and we’re excited to keep exploring it. In the meantime, we plan to release more findings in the coming months. If you’re interested in staying looped in or getting in touch, please join our discord or reach out to us.

Thank you to the following people (and others) who read drafts of this post, including: Tom Walton-Pocock, Kurt Barry, Tom Schmidt, Jai Bhavnani, Jon Itzler, Stephen McKeon, Steven Becker, Caleb Tebbe, Kevin Zhang, Freddie Farmer, Dillon Chen, Samneet Chepal, and Dan Elitzer.

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.