From Uncertainty To Stability: Ultimate Guide To DeFi Fixed Interest Rate Protocols (Ⅰ)
Why DeFi needs fixed rate products, and how they are made.
Author：
Ethan C., Researcher of EM3DAO, EVG, Hakka Finance
Lucien Lee, CEO of Hakka Finance
Ping Chen, Founder of Hakka Finance
>>>Portal to Part II<<<
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The DeFi space has been growing at a breakneck pace over the past few years, with both trading and lending emerging as its two most crucial pillars.
Regarding trading, the AMM model, unprecedented in financial history, has surpassed the capabilities of the order book model and serves now as a standard of on-chain liquidity. On the lending side, markets have also shifted from peer-to-peer lending to a peer-to-pool model. Ethlend, the predecessor of Aave, is an illustration of the peer-to-peer lending model in the order book method. Although it enjoys the benefits of a precise maturity date and a fixed interest rate, the matching efficiency is extremely low before sufficient liquidity, so the DeFi market eliminated it. It is proven that the perpetual lending pool model that regulates interest rates through supply and demand is the most suitable for blockchain, such as Compound and Aave.
However, if a lending system lacks a maturity mechanism, it must rely on other forces to balance supply and demand. The lending pool applies the utilization rate — interest rate feedback control mechanism — i.e. raise interest rates when supply falls short of demand and encourage deposit/repayment; cut interest rates when supply exceeds demand and promote borrowing/withdrawing. Although Aave claims to have a fixed-rate borrowing function, it still maintains a mechanism to increase interest rates for fixed-rate borrowing. It can be said that interest rate fluctuations are arguably an inevitable phenomenon in the perpetual lending pools.
However, floating interest rates are not conducive to long-term financial planning and leveraged investment. In particular, the high volatility of interest rates in the DeFi field makes floating-rate loans extremely risky. Take Aave USDT Borrowing Rate in the second half of 2021 as an example; the interest rate fluctuates drastically and can instantly rise from 3.73% to 61% in one day (2021/10/29~30). Such a high degree of uncertainty hinders the development of DeFi to a larger market scale. In contrast, most debt markets in traditional finance are driven by fixed-rate loans. Stable and predictable interest rates allow lenders/borrowers to have more control over their investment portfolios and be willing to adopt more diverse and more complex financial products.
And yet, borrowing and lending as fundamental components of investment portfolio construction are usually expected to have predictable interest rates. For instance, capital guarantee funds are based on fixed-income products, e.g., real estate mortgage bonds, government bonds. In addition, the demand for certainty cost of leveraged positions in Bitcoin needs borrowing at fixed interest rates, too. Predictable interest rates are regarded as necessary to develop complex financial products.
At the time of writing, the total outstanding loan of the whole DeFi lending protocol is approximately 23.6 billion USD. In contrast, the global debt market is estimated to be 128 trillion US dollars.
As more users and institutions enter the DeFi market, the demand for fixed interest rates will continue to increase. Therefore, we predict that the provision of a fixed interest rate protocol will become the new holy grail of DeFi. It will also be an indispensable primitive for the next wave of DeFi’s exponential growth.
Fixed Interest Rate in DeFi
Yield assets, such as lending, LPing, liquidity mining, and yield aggregation, are everywhere in DeFi. Almost all of them are floating interest rates determined by the dynamics of market forces. However, everyone has a different risk tolerance.
Rather than bearing the floating interest rate of the market, some people will prefer a stable rate hoping to control future returns while determining the borrowing cost in advance to avoid market fluctuations and associated variable costs. Because of the demand for fixed-rate interest, various fixed-rate products have emerged in the DeFi space. This article will cover a few of them, such as Yield Protocol, Pendle Finance, HiFi, Element Finance, Notional Finance, Swivel, Sense Protocol, BarnBridge, and Tranche. Each protocol has its own way of forming a fixed interest rate, which we will classify according to the mechanism used below.
Mechanism Overview
First, of principal importance is the “fixed interest rate source.” Unlike the variable interest rate deposits provided by Compound/Aave, when someone wants to obtain fixed income that is not affected by market fluctuations, another person must be the counterparty and guarantee to pay a certain interest instead of interacting with a lending pool. There are two sources of such guaranteed interest: one is the fixed interest paid by the borrower, and the other is achieved through the redistribution of interest among the lenders.
1. Fixed-rate Loan
The method of paying fixed interest by the borrower in DeFi is not far from Bitfinex’s lending model. Both borrow through the agreed date, agreed amount, and predetermined interest rate, but the former uses some more suitable methods for the blockchain, such as changing peer-to-peer lending to peer-to-pool, trading/borrowing through AMM for price (interest rate) discovery.
One mechanism to achieve this goal is “trading zero-coupon bonds.” The lender buys zero-coupon bonds at a discount, equivalent to a fixed-rate deposit, and can receive the funds on the denomination at the maturity date. The borrowers can use collateral assets to issue zero-coupon bonds and sell them into cash at a discount; they must repay the assets after maturity to get back the collateral. The difference between the denomination of the zero-coupon bond loaned from the system and the cash obtained after the sale is the loan interest. Since the cost of borrowing is the income of deposits, it is possible to achieve equilibrium through market supply and demand to determine a fixed interest rate acceptable to both borrowers and lenders.
For example, the borrower pledges assets and issues a one-year $1,100 zero-coupon bond, then sold to the lender at a discount price of $1,000 in the market. The lender receives the equivalent of a $1,000 bond with a fixed interest rate of 10% for one year. At maturity, the borrower must pay $1,100 face value to redeem the zero-coupon bond, giving the borrower a $1,000 loan with a fixed interest rate of 10% for one year. The advantage of using zero-coupon bonds with a fixed interest rate is that they are not subject to reinvestment risk, unlike interest-bearing bonds. When investors receive interest and reinvest the interest earned, their total return is unpredictable. Investors have to bear the risk of changes in market interest rates because market interest rates can change at any time. A zero-coupon bond is a financial instrument that provides complete certainty of return at the time of purchase.
Related protocols: Yield Protocol, Notional Finance, HiFi
2. Yield Redistribution
The former is essentially an independent lending market. The latter method is based on existing yield sources, which can be deposited with floating interest rates, or Yield Farming, which derives a secondary market for trading interest rates; different trading modes can be divided into two types: “split principal & interest” and “structured product.”
2–1. Split Principal & Interest
Given a source of income, we can split the return on investment into two parts: principal and interest, pricing them separately. For example, you can sell “the interest you will earn of $10,000 USDC deposited in Aave after one year” as a product; if someone is willing to buy it for $400 USDC, you get a 4% fixed-income investment. You can also understand that parties A and B invest $9,600 and $400 respectively in Aave and agree that A will get $10,000 and B will get the rest a year later to achieve the effect of pre-arranged profit distribution.
The way to achieve the above is to split the principal and interest in the lending protocol and tokenize them. Before settlement, the pricing of interest tokens depends on the market’s expectations of future interest rates; principal tokens are equivalent to zero-coupon bonds, which can redeem assets at face value after the maturity date. Zero-coupon bonds will be at discount based on the time value of the asset in the market before the expiry date.
From the above example, it is easy to understand how the separation of principal and interest can achieve fixed-rate lending. On the other hand, to achieve a fixed-rate borrowing, one can buy interest tokens at the time of borrowing, and theoretically, as long as the fluctuation between the APR of lending and borrowing is very closely correlated, the floating interest rate of the loan will be offset by the floating value of the interest tokens, thus achieving a fixed-rate borrowing. In practice, the trend of interest rates between borrowing and lending may not be exactly the same depending on the utilization rate of the lending pools, so only a partial hedging effect is achieved.
Related protocols: Element Finance, Pendle Finance, Swivel, Sense Protocol
2–2. Structured Product
The interest rate on deposits is floating on the lending protocol. However, since the future interest is uncertain, and everyone has different risk tolerance and the opportunity cost of capital, the risk can be re-allocated according to individual needs.
Structured funds can split the interest income into different grades according to investors’ risk preferences and regroup them into various financial derivatives.
It is essentially leveraged financing, but because the income from selling fixed-rate bonds is usually used to increase holdings of the same variable interest rate assets, the effect is similar to the principal-interest split and the redistribution of interest rates.
For example, we can design a two-tier(tranche) fund with a 5% cut-off, where Class A is a lower-risk product with priority return distribution (fixed rate) and Class B is a higher-risk product with higher return (floating rate), and all the money in the fund is deposited into Aave. If the accumulated interest rate exceeds 5%, Class A investor will receive only 5% of the agreed return and Class B investor gets the rest of the excess return. Otherwise, if the accumulated interest rate is less than 5%, Class B investors’ principal will be used to make up for the part of less than 5% of Class A investors’ interest until Class B investors’ investment is completely lost.
Related protocols: BarnBridge, Tranche
Protocols Overview
Fixed-rate Loan
The easiest way to achieve a fixed-rate loan in DeFi is to mint/purchase zero-coupon bonds.
The zero-coupon bond is a type of IOU. The issuer promises that the holder can exchange the face value of funds 1:1 on the maturity date. Because the funds have time value, the zero-coupon bond will be traded in the market at a discount before maturity. The size of the discount varies by market interest rates and the maturity date. The more significant the discount, the higher the return at maturity, and vice versa.
The lender purchases zero-coupon bonds at a discount and redeems the assets at the denomination on the maturity date, equivalent to borrowing at a fixed interest rate. The borrower provides assets as collateral in order to mint zero-coupon bond, then sells it into cash to achieve the effect of a fixed interest rate loan.
The difference between the various protocols lies in how the zero-coupon bond is priced in a way suitable for blockchain, which we will discuss in-depth in the later AMM chapter.
Yield Protocol
Yield Protocol uses zero-coupon bonds (fyDai) as a protocol to achieve fixed-rate lending. After the maturity date, fyDai can redeem Dai at a 1:1 rate.
The mechanism for fixed-rate lending and borrowing is as follows:
- Fixed-rate lending: purchase a zero-coupon bond (fyDai) at a discount and redeem it after the maturity date, earning a fixed interest.
For example, Alice buys 1050 fyDai for 1000 Dai. If it expires in one year, it can be exchanged for 1050 Dai at that time, which is equivalent to a fixed annualized lending interest of 5%.
- Fixed-rate borrowing: deposit ETH as collateral, mint fyDai and then sell fyDai for Dai. Since fyDai will be traded at a discount, the amount of Dai received will decrease. The difference between the two is the pre-determined borrowing cost.
For example, Bob pledges 1 ETH in the protocol and lends 1000 Dai at a 5% annualized rate. If the maturity date is one year later, it means that Bob owes the system 1050 fyDai, and he can only redeem his collateral after returning the debt.
It is worth mentioning that in Yield Protocol V1, the entire service is built on top of MakerDAO. Therefore, the whole loan position can be transferred to MakerDAO after maturity, and the fixed interest rate can also be converted to a floating rate. At this time, depositors can receive DAI Saving Rate, and borrowers have to pay the stability fee.
In the new V2 version, Yield has abandoned the integration with MakerDAO. But it also breaks the limitations of MakerDAO and can support more collateral, including yvUSDC, ENS, etc., and can support borrowing in other tokens/assets, such as USDC.
In addition, since the value of zero-coupon bonds will change over time, Yield Protocol has created a new AMM curve, “YieldSpace.” The unique nature of this curve is suitable as a liquidity pool for zero-coupon bonds and can also improve capital efficiency. As a result, this AMM has become the standard of zero-coupon bond and has been adopted by relevant protocols.
Liquidity Position Management
Since each issue of the zero-coupon bond has a different maturity date and price, a separate liquidity pool is required for each issue to be traded. Currently, bonds of Yield Protocol are six months in length. In order to eliminate the need for liquidity providers to make frequent position adjustments, the liquidity in Yield Protocol is automatically rolled over to the latest issue upon maturity so that liquidity providers can continue to earn fees passively.
Notional
Notional also employs trading and lending to mint zero-coupon bonds (fCash) to achieve fixed-rate borrowing. Market supply and demand determine the borrowing rate in this case.
The most significant difference from Yield Protocol is that the underlying asset in Notional Finance’s system is cToken, which is the wrapped token of Compound. Therefore, the liquidity pool for trading zero-coupon tokens is fCash/cToken. This design enables the funds stored in the liquidity pool to generate interest over time, increasing capital efficiency by liquidity providers.
The mechanism for fixed-rate lending and borrowing is as follows:
- Fixed-rate lending: the lender pays DAI; the system will first deposit it in Compound in exchange for cDAI, and then buy zero-coupon bond fDAI in the liquidity pool. The purchase price determines the size of the fixed lending interest rate.
- Fixed-rate borrowing: after depositing ETH as collateral, fDAI can be minted and sold into cDAI, and finally, DAI is retrieved from Compound to achieve fixed-rate borrowing. The difference between fDAI and DAI is the borrowing cost.
Since the underlying asset in the pool is cToken, the fixed interest rate after maturity will automatically convert to Compound’s floating rate.
Unified Liquidity Management
The underlying asset in Notional is cToken. Although there are many pools in the protocol at the same time, if you want to be a liquidity provider, you only need to deposit the cToken at the unified portal, and the system will automatically allocate the liquidity to each liquidity pool via governance.
Depositing a cToken gives you an “nToken” as a liquidity certificate that has no expiration date, and is always redeemable. The part of deposited cTokens would be used to buy fCash and pairs it together as the liquidity. Thus, the blended interest rate of nToken will be between the yield of zero-coupon bonds and the net deposit rate in Compound.
Although the yield of providing liquidity is lower than buying zero-coupon bonds (fCash) directly, it also has the advantage of earning transaction fees. Besides, Notional supports nToken as Collateral. Therefore, liquidity providers could leverage (like Alpha) nTokens to amplify their profits by minting some nTokens, borrowing against their nTokens, and then minting more nTokens.
HiFi Finance
HiFi Finance, formerly known as Mainframe, also adopts the zero-coupon bonds fixed-rate lending paradigm, the same mechanism as Yield Protocol. In both cases, the borrower provides collaterals to issue zero-coupon bonds and then sells them to the lender to achieve the effect of a fixed-rate borrowing. It is worth mentioning that in their v0 version whitepaper, there’s a liquidity pool for directly liquidating undercollateralized debts (similar to Liquity’s stability pool.) In addition, the liquidation guarantee pool and collateral can also be used for flash loans to make more use of idle funds and earn extra income.
However, there is almost no difference between the current HiFi V1 design and Yield Protocol. Not only the AMM model is based on YieldSpace, but also the design of the stability pool disappears. Instead, it provides a script for liquidators to liquidate debts with Uniswap v2 flash swaps, which are also truly similar to other products.
Yield Redistribution
As mentioned in the previous chapter, fixed-rate borrowing can be achieved by selling zero-coupon bonds to lenders at a discount. In this case, the interest rate is determined by the lender—borrower market mechanism.
Another way to achieve the fixed interest rate is to deposit all funds into a lending protocol or a yield aggregator to receive a floating interest rate and then redistribute the interest according to each person’s risk preference.
There are two types of “Yield Redistribution”, one is “Split Principle & Interest” and another one is “Structure product.”
Split Principle & Interest
After deploying capital into lending protocols or yield aggregators, we can split the principal and interest and tokenize them.
Principal tokens can be redeemed for the underlying assets at a 1:1 ratio after the expiry date. Although there is no borrowing behavior in this model, its nature can still be equivalent to a zero-coupon bond. Yield tokens represent the interest that will be produced in the future, and the mechanism of how to redeem future interest varies depending on the protocol.
The main difference between the various protocols lies in how principal tokens and yield tokens are priced in a way suitable for the blockchain, which we will discuss in-depth in the later AMM chapter.
Yield tokens can be divided into two different models:
- Drag — Past yield delivered upon maturity
- Collect — Past yield delivered before maturity
Element Finance
All funds in Element Finance will be deposited into Yearn Finance, and the deposited funds will be split into principal tokens (PT) and yield tokens (YT).
PT is equivalent to a zero-coupon bond, redeemable after maturity. In contrast, YT represents future interest, which can be exchanged for the actual interest incurred during this period after maturity.
Under this system, we are able to create two markets: “fixed-rate” and “long future interest.”
- Fixed-rate Deposit
Purchasing PT is equivalent to depositing at a fixed interest rate. The price of PT determines the APR of the deposit: the lower the price, the more profits at maturity and the higher the APR, and vice versa.
Another approach is directly selling the newly minted YT after depositing funds into Element Finance, realizing future interest in advance to achieve fixed income.
- Long Future Interest rate
The price of YT represents the market’s expectations of future interest rate, and the higher the accumulated interest during the period, the higher the settled price of YT.
We can long interest rates by buying YT. As long as the assets redeemed after maturity exceed the purchase cost, a profit can be earned.
In addition to buying YT directly, another way is to deposit funds in Element first, sell PT, repeatedly deposit cash obtained into Element, and execute it over and over again to maximize the amount of YT in hand.
Pendle Finance
Pendle Finance, similar to Element Finance, also splits the deposited funds into principal tokens (OT, Ownership Token) and yield tokens (YT, Yield Token). The main difference lies in the operating mechanism behind its yield token.
In Element Finance, YT will accumulate the interest incurred: the more the accumulated interest, the higher the redemption price after settlement; while in Pendle Finance the interest generated by the principal will be directly sent to YT’s holders. Holding YT in Pendle Finance represents the right to obtain interest income before maturity continuously. As maturity approaches, the net value of this right will diminish and eventually go to zero.
- Fixed-rate Deposit
If you want to have a fixed-rate deposit on Pendle Finance, you must first deploy capital into the protocol, mint OT and YT, sell YT, cash-out future interest in advance. - Long Future Interest
Similarly, investors who are bullish on the interest rate can purchase YT to gain exposure to the interest rate. They can profit from this strategy if the purchase cost is lower than their accumulated interest. Same as Element, they can also deposit funds, sell OT, and then deposit cash repeatedly to maximize the amount of YT (leveraged interest rate). - Fixed-rate for LP Tokens
Besides lending and vault functions, Pendle Finance also supports Sushi’s LP tokens as underlying assets to tokenize future income generated by transaction fees. It can also use fixed-rate deposits or leverage to increase yield.
Swivel
Swivel was formerly known as DefiHedge. Again, there is no big difference between Swivel and Element. Deposit funds and split funds into two tokens: principal (zcTokens) and yield (nTokens). Investors can earn a fixed interest rate by selling nTokens at the beginning and keeping zcTokens. In contrast, the counterparty’s nTokens holders receive a floating interest rate.
The most different feature of Swivel from other principle — interest split protocols is that while the others have tried to use AMM to provide liquidity in both principal and interest tokens, it insists to use off-chain order book as its trading model. The reasons behind that we will discuss in-depth in the AMM section.
Sense Protocol
Sense Protocol adopts the same model, splitting funds into principal tokens (Zeros) and yield tokens (Claims). The yield token of Sense Protocol is similar to Pendle Finance; both constantly deliver interest to holders of yield tokens, but Sense Protocol’s trading mechanism is slightly different. We will compare more in the AMM chapter.
Structured Product
Structured funds divide and redistribute fund returns or net assets to create investment targets with different levels of risk and return. Usually, a structured fund is divided into two classes: one receives fixed remuneration, and the other receives residual revenue.
Suppose we call “the parts with lower expected returns but with higher priority in the distribution of income” as “A-class shares,” and “parts with higher expected returns but with subsequent distribution of income” as “B-class shares.” The nature of B-class shares is to “borrow” money from A-class shares to amplify the income and has a certain leverage characteristic. Because B-class shares “borrowed” the assets from A-class shares, B-class shares are responsible for paying the fixed interest of the A-class shares.
BarnBridge
BarnBridge is a structured product with the interest rate as the target, consisting of “Junior Pool” and “Senior Bond.” Funds from both sides will invest in the underlying protocol (Compound or Aave) to generate yield, but the income distribution rules are different.
The liquidity providers of Junior Pool will receive ERC20 tokens, representing their investment shares. Junior has no maturity and receives floating income. Senior Bond buyers can choose the investment time (up to one year), and the position will be held in the form of ERC721. Senior gets a fixed income, it can’t be redeemed before maturity but the NFT can be transferred.
Since the interest rate of the underlying protocol is floating, it may suddenly become super low, part of Junior Pool’s liquidity will be locked to ensure that Senior holders can redeem the promised principal plus yield at maturity. Therefore, the redemption of Junior Pool has to go through a specific process, and there are two options:
- Immediate redemption: The part promised to be allocated to the Senior is deducted in advance, and the rest can be reclaimed.
- Delayed redemption after swapping into bonds: mint NFT according to the weighted maturity date of Senior, and redemption will be made after the maturity date without additional deduction of fees.
The interest rate of Senior is determined by the following formula:
The yield rate is the three-day moving average of Compound/Aave interest rate, which is then discounted according to the liquidity utilization rate in the pool to become the Senior Yield. Because Senior Yield is always lower than or the same as the current interest rate of the underlying protocol, Junior can earn extra rewards in the long run. Still, in the situation where the interest rate suddenly plummets, it may result in less profit or even loss for Juniors.
Tranche Finance
The similarity between Tranche Finance and BarnBridge is that they are both structured products. Tranche Finance divides its products into Tranche A with a fixed interest rate and Tranche B with a floating interest rate (both are ERC20 tokens). But unlike BarnBridge, which determines interest rates based on the fixed/floating ratio in the pool, Tranche Finance doesn’t have an automated interest rate mechanism at all. Instead, DAO (token holder) decides how much interest should be issued to people with a fixed interest rate through voting. So, in essence, Tranche A is not a fixed interest rate and might be voted to change the interest rate higher or lower at any time.
As shown in the above picture, the spread between FIXED and VARIABLE is vast, and governance can unilaterally decide how much FIXED should be changed.
What Type of AMM Fits Zero-coupon Bond and Principal Tokens
Liquidity is fundamental for market-shaping, whether for zero-coupon bonds, principal tokens, or yield tokens. Centralized exchange adopts order matching for buyers and sellers, whose liquidity is provided by order placers from both sides. This mechanism can enhance the efficiency of price discovery but does not fit the system with relatively scarce resources and low efficiency, such as blockchain. Hence, AMM has been developed in the blockchain world. The liquidity of AMM is provided by a third party — Liquidity Providers (LP) while the quotation is determined by an equation designed beforehand.
Different equations correspond to different “curves.” We can design a reasonable quotation mechanism based on traded assets.
Take Uniswap v2, for example. The Constant Product Market Maker Model adopted by Uniswap is as follows:
x × y = k
The marginal quote in this curve is price = y/x, which is the ratio of two assets. The price will change along with the reserves of the two assets. This model fits price irrelevant assets with more fluctuations.
Another extreme example, mStable, uses Constant Sum Market Making mechanism.
x + y = k
The price in this curve is always price = 1. No matter how the reserves of two assets in the pool change, the exchange rate is always 1. That model can be perfectly applied to stable assets with exactly the same value.
However, zero-coupon bonds, principal or interest tokens (principal tokens are essentially zero-coupon bonds) have a common feature: their values change over time, but the previous two AMMs fail to fit this feature. In the following, we’re going to discuss how to design a suitable AMM model for zero-coupon bonds and interest tokens.
Zero-coupon bond pricing and features
The price of zero-coupon bonds is decided by the interest rate and maturity, calculated by discounting the face value, i.e., taking into account the future cash flow compounding, to the present value. Here is the formula:
PV = FV ÷ (1 + r)^n
where:
PV = current price, the present value
FV = the future value of money, the face value of the bond
r = interest rate
n = the number of years until maturity
The above pricing formula shows that the price of a zero-coupon bond will change over time even though the market interest rate remains unchanged. The closer the maturity date, the closer the bond’s price will be to the denomination, and eventually, the exchange rate between the two will converge to 1.
On the other hand, if the price of zero-coupon bonds stays constant, the interest rate r will keep going up as the expiry day approaches.
AMM Curve for zero-coupon bond
Given that x × y = kin Uniswap is taken as AMM curve. If there is no trading happening in the pool, the price of the zero-coupon bond stays constant. As it gets closer to maturity, the APY of bonds would be increased and attract more investors to arbitrage. That results in the loss for liquidity providers.
On the other hand, given that x + y = k in mStable is taken as AMM curve. The exchange rate will be always 1. Bonds cannot be traded with a discount by the expiry day to react to its internal time value change.
Therefore, we need a curve that can automatically change the quote along with time. In more detail, the price of zero-coupon bonds should be sensitive to price changes initially and can change according to the market dynamics and will converge to 1 as the expiry day is approaching.
Yield Protocol and Notional realize fixed-interest lending protocols by purchasing or minting zero-coupon bond tokens, while Element and Pendle divide tokens into principal (zero-coupon-bond like) and interest tokens. In the following, these five AMM curves will be further elaborated. Finally, we’ll discuss Swivel, the one which didn’t adopt AMM but the order book.
YieldSpace
YieldSpace is a customized curve, particularly for zero-coupon bonds. The parameters include time t. The larger t means longer time to maturity. As the expiry day is approaching, t gets closer to 0.
By utilizing calculus, the curve can be proven to be x × y = k as t = 1 and the curve will become a line x + y = k as t = 0. That mechanism allows users to trade bonds according to market interest rates before the expiry day. As the maturity date approaches, the bond price will get close to $1 and investors can redeem the face value of the bond. This is the exact feature of zero-coupon bonds.
Furthermore, YieldSpace curve has the “constant interest rate” feature.
Theoretically, if there is no change in market supply and demand for zero-coupon bonds, the interest rate of zero-coupon bonds shall be consistent. The invariant of supply and demand means that the reserves of two assets are invariable in the x × y = k AMM model. Thus, the price of zero-coupon bonds keeps the same.
However, from the price formula of the zero-coupon bond, if we want to stick the interest rate to the same as time goes by, the price of the zero-coupon bond should be raised. While x × y = k AMM model cannot react to the price changes along with time spontaneously, the curve of YieldSpace can increase the price of the zero-coupon bond automatically. Hence, it could bring the critical effect, constant interest rate, for zero-coupon bonds AMM.
Therefore, if the market interest rate stays constant, there will be no arbitrage opportunity even if the time changes; LPs won’t bear the time-dependent impermanent loss.
For example, given that a zero coupon bond with 10% interest rate and going to expire in one year.
the initial price is $0.909 1 ÷ (1.1)^1 = 0.909
the price after half-year is $0.953 1 ÷ (1.1)^0.5 = 0.953
the price after a year is $1 1 ÷ (1.1)^0 = 1
If no one trades, the reserves of two tokens stay the same, and the market interest rate remains 10%. Six months later, the slope of the curve changes along with t is getting small causes the price of the zero-coupon bond to go up to $0.953 and will rise to $0.976 nine months later and eventually $1.
Dynamic Trading Fees
Mainstream AMM models charge a fixed percentage from trading volume. For example, Uniswap V2 charges 0.3% as fees. However, the mechanism does not fit zero-coupon bond pools because, by the maturity day, the 0.3% fees will impact annual rates grandly.
Given that a zero coupon bond has fixed APY of 10%. The annual rate changes along time with a 0.3% trading fee (as follows).
As the maturity date is approaching, trading fees’ impacts on annual rates become more fierce and the scale of change is exponentially increasing.
Therefore, in YieldSpace, the fee calculation is taking a fixed percentage from interests. As maturity is approaching, the interests that can be produced becomes lower so the trading fees tend to be lower.
Virtual Liquidity: Enhanced capital efficiency
Generally, the price of zero-coupon bonds is not supposed to be higher than its face value, which means the exchange rate of the token should always be less than $1. If the value is over $1, then there’s an opportunity for arbitrage.
In the above AMM, the distribution of liquidity will be symmetric to x = y, which is both sides of the line that the exchange rate is 1, but the price of zero-coupon bonds will never be over $1, which indicates that half of the fund in the pool is idle. As a result, YieldSpace introduces virtual liquidity. Half of the zero-coupon bonds in the pool are provided by the virtual reserve, and the capital efficiency can be thereby greatly enhanced.
Notional
From YieldSpace case study, we can summarize that an AMM curve suitable for zero-coupon bonds has three conditions:
- The system automatically adjusts the price as the maturity date approaches to keep the interest rate constant even though there is no transaction incoming.
- As the maturity day approaches, the price curve becomes flattened, making the price less sensitive to reverse changes.
- Trading fees should not be charged with a fixed percentage. The fees should become lower as the expiry day approaches.
Notional introduces three parameters to satisfy these three needs.
Anchor
This parameter controls the center of the price curve. The exchange rate (fCash per Currency) will become smaller along with time and finally converge to 1.
If not considering price impacts caused by trading, the interest rate can stay constant with the adjustment of Anchor and avoid the impact on interest rates by time.
Scalar
This parameter indicates the price’s sensitivity. The smaller the “Scalar”, the steeper the curve, and the more volatility the price. As the expiry day approaches, the curve tends to become flattened, making the liquidity concentrated to the price center defined by the anchor.
Trading Fee
To reduce the trading fee’s impact on annual rates, trading fees have a feature of linear decrement to 0 along with time.
Notional AMM Curve
In combination with these three parameters, we can deduce the pricing equation of Notional AMM:
Element Finance
In Element Finance, the deposits will be divided into principal and interest tokens. Due to different characteristics, Element Finance designs two liquidity pools.
Principal token pool:
Principal tokens, equal to zero-coupon bonds, are debt securities for investors to redeem their principal as the term is expired. Hence, the principal token pool in Element chooses YieldSpace AMM Curve.
Yield token pool:
Yield tokens allow investors to redeem their accumulated interests after expiry. But the future yield is uncertain, and the price may fluctuate fiercely due to market demand and supply. Thus, the interest token pool selects x × y = k curve for better price discovery.
Pendle Finance
Pendle Finance also splits principal and yield into separate tokens, but what differentiates it from Element is the mechanism of yield tokens. Holding Pendle’s YT means holding the right to claim interests in the period. As investors hold the tokens for a longer period, they can get more profits, and the value of tokens will decrease to 0 over time.
Principal token pool:
In Pendle, the principal tokens can refer to a type of zero-coupon bonds, but it chooses SushiSwap as the liquidity pool instead of YieldSpace or Notional AMM mechanisms.
SushiSwap uses the x × y = k model. The curve will not change along with time, which means the liquidity providers inevitably need to bear the impermanent loss along with time change; applying SushiSwap also means that Pendle gives up the feature of using OT as zero-coupon bonds. That decision not only makes fixed-rate depositing more complicated but also worsens the user experience.
Yield token pool:
In Pendle, the value of YT will definitely become 0 in the end. If taken x ∗ y = k as AMM curve, the time value of interest tokens will become lower as time passes. That would attract arbitrages, resulting in the loss of liquidity providers. Eventually, the value of the liquidity pool becomes 0.
To solve this problem, Pendle references Balancer curve and introduces more time-dependent parameters, enabling the weights of two tokens to change along with time.
αi+1: the weight of x at time t = i + 1βi+1: the weight of y at time t = i + 1xi and yi: the reserve of x and y at time t = i
α and β are both a function of time, which will change along with time.
At t = 0, α and β are initiated at 0.5
as time approaches maturity, eventually:
α will gradually decrease to 0
β will gradually increase to 1
Take yield token YT/USDC, for example. The ratio of weights of two tokens is 50/50. At that time, the price of YT is $1. But as expiry approaches, the weight of YT will become lower. As the ratio of weights reaches 20/80, the YT price will become $1 × (20/80) = $0.25 if no one trades in the pool. Eventually, the price of YT will become $0 while the ratio of weights is 0/100.
From the above description, the AMM curve can dynamically adjust the pricing mechanism, which meets the characteristic of token value decreasing along with time. In this way, liquidity providers do not need to afford the time-dependent impermanent loss.
Sense Protocol
Sense Protocol is another split principle & interest fixed interest rate protocol. Its principal token (zcToken) is also equivalent to the zero-coupon bond, and it uses Sense Space AMM for its liquidity pool, a modified version of the aforementioned YieldSpace AMM.
Sense Space
Principle Token Pool:
Sense Space implements the invariant of YieldSpace, but it replaces the underlying assets with yield-bearing assets, allowing all assets in the liquidity pool to generate value over time and maximize capital efficiency.
However, since YieldSpace’s AMM curve concentrates liquidity around 1:1, taking zcDAI/DAI pool as an example, it would not work as expected if we only replace DAI as cDAI for zero-coupon token pair. To solve this problem, Sense Space has introduced the scaling factor, the ratio of cDAI to DAI in Compound. By mapping the value of cDAI to the amount of DAI with this parameter, the YieldSpace formula can be used to calculate the zero-coupon token’s exchange rate smoothly again.
In practice, the contract records the exchange rate between cDAI and DAI at initialization and updates the rate at each transaction, which ensures that the accumulation of cDAI interest does not affect the exchange rate between the zero-coupon bond (zcDAI) and Dai.
Yield Token Exchange:
Sense’s yield token design uses the Pendle model (Collect YT), but it doesn’t provide YT liquidity pools directly. On the contrary, it only provides PT/Target pairs (Target means yield-bearing assets in Sense).
For instance, in Sense, if you want to purchase the yield token (YT) of Compound Dai, you have to
- Deposit cDai into Sense and issue
principal tokens, zcDai+yield tokens, ccDAI - Trade zcDai to get cDai
- Now, users have both zcDai and the remaining cDai. They can repeat steps 1 & 2, and try to swap cDai for zcDai as much as possible.
Conversely, if users want to sell yield tokens:
- Flash borrow cDai from Sense Pool
- Swap cDai for principal token, zcDai
- Combine
yield token, ccDAIand borrowedprincipal token, zcDaito early redeem cDai - Payback flash loan
- Users will still have some remaining cDai
The approach to becoming LP is quite similar. The advantage is that only one principal token/yield-bearing asset AMM pool is needed and no trading model of the yield tokens is required. Hence, LP’s incomes from trading volume can be increased because the original liquidity of two pools can be gathered into one. But obviously, the cost is that the calculation process in trading becomes complicated. Users may have difficulties trading all yield-bearing tokens they have into Claim Token(YT), and at the same time, they need to spend more gas fees due to inflated contract logic.
Another approach: Swivel
Lastly, we’re going to discuss Swivel, the only protocol that does not take AMM as the pricing model. Conversely, Swivel selects the off-chain order book mechanism to solve the pricing dilemma on principal and interest tokens on AMM.
Swivel believes that interest tokens, as the derivative of interest rate, will change along with interest rates and their volatility. But the price of interest tokens in AMM can hardly respond to changes. The same situation takes place in spot markets and their derivatives. The option price needs to respond to spot price and its fluctuations in the options market. If AMM is adopted for DeFi option markets, the AMM model also needs some approaches to adjust along with those factors. Despite the rapid development of the option AMM, this type of mechanism can barely consider the volatility, which results in extremely low returns for LPs. In the analysis of DeFi option protocol, Hegic’s LP, they found that the LPs bear a huge loss.
Therefore, Swivel argues that compared to AMM, order books are more suitable for DeFi derivative trading models. In this way, market makers can not only avoid loss brought by pricing distortion but also can provide the most affordable price and trading costs to users. Besides, Swivel can provide the order book trading pairs of principal-interest tokens to allow users to exchange them directly. Unlike Element requiring to trade with two AMMs (YT-Underlying & PT-Underlying), Swivel can enhance trading efficiency.
In-depth Discussion on Efficiency Issues
Each protocol has slightly different ways to achieve fixed interest rates, and therefore has its own advantages and disadvantages in terms of “capital efficiency” and “market efficiency”.
Fixed-rate Loan vs. Yield Redistribution
The zero-coupon bonds provided by Yield/Notional are fundamentally similar to the principal tokens issued by Element/Pendle, but their mechanisms are quite different.
The most significant disadvantage of Element is the inefficiency in price discovery. Element requires respective liquidity pools for principal tokens and yield tokens, which demand more capital. Furthermore, there are two approaches to getting principal tokens. One is to mint PT + YT with underlying assets and sell YT. The other is to buy PT directly with underlying assets. Theoretically, in an efficient market, the output of those two pathways should be the same. But the limitation of blockchain and the characteristic of AMM makes it easy to have a difference between the two, which is apparently problematic.
Compared to the interest rate differential issues resulting from two approaches to trading principal tokens in Element, Yield Protocol only adopts one trading pool for zero-coupon bonds, and the price is determined by the consensus on discounts (interests) reached by lenders and borrowers. But this choice is a double-edged sword. Yield Protocol and Notional are essentially independent “primary markets” for lending and borrowing. In contrast, Element and Pendle, the principal-yield separation protocols, are the “secondary markets” for interest rates built on top of the existing lending protocols.
In fixed-rate Loan type protocols, the market equilibrium of interest rates relies on the supply-demand ratio of its own liquidity pools instead of the underlying lending protocols with sufficient liquidity. Meanwhile, as an emerging lending market, it needs to attract capital to create liquidity. Therefore, the elasticity in supply and demand is quite low. For example, if Yield Protocol receives a huge deposit, the interest of fyDAI is much lower than the interests of the external market (Compound/AAVE), as the supply and demand are imbalanced, it may take longer to strike a new balance.
Enhanced market efficiency
It is notable that Notional and Swivel attempt to enhance efficiency.
Notional’s liquidity providers do not need to “allocate” capital to pools with different maturities, but into a large pool for unified dispatching by the governance instead. Notional governors could direct liquidity to the maturities where there is the greatest end-user demand for borrowing and lending, to increase market efficiency and liquidity provider’s profits.
It sounds a bit risky, but thanks to the nature of zero-coupon bond, investors are unlikely to lose money. In the worst-case scenario, investors may earn interest rates lower than the market and merely have a time-value loss.
On the other hand, Swivel abandoned AMM and adopted order book. Their statements seem reasonable: the interest rate market is similar to the options market, both are too complicated to deal with in the form of AMM. But there is a crucial point: the PnL in the interest rate market is not high and susceptible to transaction costs. Therefore, if the cost to cancel or update the order in Swivel is high, which is caused by the limitation of the off-chain order book mechanism, it might offset the advantage of high market efficiency.
Enhanced capital efficiency
On the other hand, there may be some essential paradox in LP holding zero-coupon bonds. Because investors with this type of assets theoretically long for interest incomes, but part of assets in the pool must not earn interest. To improve the efficiency, YieldSpace even discards half of the useless liquidity, which is exactly the zero-coupon bond part and makes the average interest rate even lower. Hence, for LPs, unless the trading fee is higher than the interest rate bear from the zero-coupon bond, LPs have no reason to allocate capital to AMM instead of buying bonds.
Therefore, Sense proposed to pair yield-bearing assets with zero-coupon bond tokens as LP and store assets in the form of yield-bearing assets, which will earn more interest. However, the cost is that users need to pay more gas for converting assets while depositing or withdrawing.
The structured product, BarnBridge, does not rely on AMM while issuing fixed interest NFTs but directly completes price discovery in the internal system. The most significant advantage is that all capital held by every participant in the system is yield-bearing, and there are no idle funds. Nevertheless, it also comes with a drawback.
From the perspective of market composition, “Fixed-rate Loan” and “Split principal & interest” protocols are the long — short market of interest rate, while “structured product” protocols are the hedge — speculate market of interest rate. The former is comparably natural supply-demand relations, and the latter, the speculative side, is trying to satisfy the demand of the hedge side, which is not born naturally. As risk-takers, as service providers, the counterparties of hedgers hope to earn excess returns. Thus, for the long term, the interest rate of BarnBridge Senior Bond may be lower than the interest rate of the zero-coupon bonds provided by Yield/Element.
Next step: Interest Rate Derivatives
The previous analysis repeatedly emphasized the importance of efficiency due to interest rate markets are susceptible to transaction costs. For a Bitcoin investment with a potential 100% upside, a 0.6% trading friction seems to not be a big deal, but for zero-coupon bonds only with a 4% APR, the same cost is already as much as 15% of the profits!
In fact, the real purpose for the transition from floating to fixed interest is to hedge against (or speculate on) interest rate fluctuations. Furthermore, we care about whether the real interest rate of lending/borrowing in a period can meet our initial expectations. What really should be traded is neither principals nor interests, but the “Interest Rate Differentials.”
Despite the diverse mechanisms in different interest rate protocols, they can be considered the spot markets for interest rates, which are intuitive but less efficient. In the interest rate derivative market, we merely need a small margin to trade the interest of the same notional amount of assets. Without principal, there is a higher tolerance for transaction friction and no need to lock up large amounts of capital to provide liquidity, which is super more efficient.
In the next chapter, we will elaborate on the advantages of interest rate derivatives and introduce Hakka Finance’s solution, iGain — Interest Rate Synth, a derivative based on the concept of interest rate swap.
References：
- Aave GitBook: Interest Rate Model
- Yield Protocol Docs
- YieldSpace AMM Whitepaper
- Notional Docs
- Hifi Docs
- Element Finance Docs
- Element Finance Whitepaper
- Pendle Finance Litepaper
- Pendle AMM Design Paper
- Swivel Docs
- Swivel Blog
- Sense Medium: Introducing Sense Space
- Sense Medium: Designing Yield Tokens
- Sense Docs: User Journeys
- BarnBridge Docs
- Tranche Docs
- Aavescan
