# Introducing Rates Arbitrage to DeFi

#### TL;DR

*Arbitrage is possible in spot/futures markets, but Rates Arbitrage is not possible with today’s lend/borrow protocols.**Infinity’s enterprise-grade risk management system enables tokens and credit risk to be composable, leading to a revolution in the DeFi ecosystem.**Infinity enables Rates Arbitrage and Arbitrageurs can single-handedly multiply their prevailing TVL and lead to a rapid expansion of TVL in DeFi.*

We are going to introduce Rates Arbitrage, while something not really possible in Crypto today given the prevailing issues on the composability of risk (discussed below), this ties into what Infinity Exchange is building as a protocol and why. But first, let’s cover a few of the basic concepts which collectively make up Rates Arbitrage.

## What is Arbitrage?

Arbitrage is a concept centered around the idea of earning risk-free profit.

First step is to find two different prices of the same asset in the financial markets that presents a trader with the opportunity to (near) simultaneously buy one for lower and sell the other for higher and thereby pocketing the difference (or spread) for a risk-free profit.

Let’s start with an example in the spot or futures market.

In the above (theoretical) example, we have the price of Bitcoin trading at $24,000 on Exchange 1 (left) and $25,000 on Exchange 2 (right). **We’ve identified arbitrage, which, in this case, is where the price of an asset which is different in two different places**.

Now we need to capture it.

### Step 1: Buy BTC at the Lower Price

In the above diagram, we have a trader (let’s call them an ‘Arbitrageur’) on Exchange 1:

- Pay $24,000; and
- Receive 1 BTC.

From this trade, we say the Arbitrageur is “short ($24,000) cash” and “long (1) BTC”.

### Step 2: Sell BTC at the Higher Price

In the above diagram, the Arbitrageur now goes to Exchange 2 and:

- Sells 1 BTC; and
- Receives $25,000.

From this trade, we say the Arbitrageur is “short (1) BTC” and “long ($25,000) cash”.

### Full Cycle: Earning the Spread

Putting it all together. The spot/futures arbitrage includes 2 legs, where the Arbitrageur buys an asset (BTC) for a lower price from one exchange (Exchange 1) and sells the same asset (BTC) for a higher price on another exchange (Exchange 2), thereby earning a risk-free profit, in our example $1,000.

So long as the arbitrage opportunity exists, the Arbitrageur could rinse and repeat the above process, over and over again, going back and forth, driving the price of BTC on exchange 1 slowly upwards and BTC on exchange 2 downwards until the ‘dislocation’ no longer exists. This example, however, only applies to the spot/futures market. The world of interest rates is a bit different. Let’s dive in.

## Rates Arbitrage, in theory

In the interest rates world, arbitrage works slightly differently.

In the above diagram, we have a *theoretical* example with the two big borrow/lend protocols, Aave and Compound, where Aave’s borrow rate is 2% and Compound’s lend rate is 7%.

Important to note that Rates Arbitrage typically deals with the same ‘underlying’, in the above example being USDC, in order to limit the number of variables.

### Rates differential, not price differential

The price of USDC is the same on Aave and Compound, that is 1 USDC on Aave is equivalent to 1 USDC on Compound. In the earlier spot/futures arbitrage example, an Arbitrageur achieves a risk-free profit from buying and selling the ** price differential**, where BTC trades at $24,000 on Exchange 1 and $25,000 on Exchange 2, then (near) simultaneously buys 1 BTC from Exchange 1 and sells 1 BTC to Exchange 2.

In the case of Aave and Compound, an Arbitrageur is seeking a risk-free profit from buying and selling the ** rates differential **where (say) USDC can be borrowed at a lower interest rate on one protocol and lent at a higher interest rate on another protocol. In the above example, an Arbitrageur could borrow (say) 10 million USDC at 2% from Aave and deposit 10 million USDC at 7% with Compound, and effectively generate a risk-free profit of 5% (or 500,000 USDC, annualized, in the below diagram if the rates were to stay the same).

### Rates Arbitrage on Aave/Compound

In its native form, USDC (ERC20) does not pay any interest; that is, if you hold USDC in your wallet, it would not inherently generate any yield, until you lend it out. Aave and Compound are two big borrow/lend protocols which pay an interest rate on USDC.

In our example, we assume that an Arbitrageur could borrow USDC from Aave at 2% and lend to Compound at 7%, thereby earning a risk-free yield of 5%. How does this work in practice?

Based on the above example, there are 4 legs, of which only 3 are currently possible:

- Borrow 10 million USDC from Aave, pay 2% interest rate;
- Deposit 10 million USDC with Compound, earn 7% interest rate;
- Receive 10 million cUSDC from Compound; and
- Deposit 10 million cUSDC with Aave as collateral -
**this is not currently possible**.

For completeness, to borrow 10 million USDC from Aave in the first instance, a user must have deposited some form of collateral with Aave from which a loan-to-value (LTV) could be established to borrow the USDC. The collateral on Aave might generate a yield but it would also be subject to Aave’s LTV ratio (or ‘Health Factor’).

We will discuss this in subsequent articles by introducing Infinity’s Health Score.

In theory, an Arbitrageur would iterate the above 4 steps by borrowing at the lower rate and lending at the higher rate until the arbitrage of risk-less profit no longer exists. This is a type of Rates Arbitrage.

However, in reality, Rates Arbitrage on Aave and Compound is not possible today.

Aave and Compound do not accept each other’s tokens as collateral - we refer to this as ** risk (in)composability**. In Step 4 of the above example, a user is not able to take Compound tokens ($10mm cUSDC) and deposit with Aave, and vice versa. At present, Aave is not capable of pricing or understanding the risk associated with the Compound tokens, and vice versa. The entire arbitrage process breaks down and the Arbitrageur is not able to implement Rates Arbitrage.

## Rates Arbitrage, in reality

With Infinity, risk, in particular, credit risk is composable; that is, Infinity Exchange accepts Aave aTokens, Compound cTokens, Uniswap V3 LP tokens and Curve LP tokens as collateral and users can borrow against these deposits. Revolutionary for DeFi, don’t you agree?

Today, Tokens are transferable, risk is not. With Infinity, Tokens and risk are transferable, resulting in Rates Arbitrage and a revolution to the DeFi ecosystem.

### DeFi Yields, in reality

As we illustrated in our previous articles on Utilisation (part 1, part 2), the borrow/lend protocols have wide bid-offer spreads (deadweight loss) baked into their mechanic due to uneven notional / principal matching. Therefore, **Aave and Compound’s wide bid-offer spreads makes it increasingly difficult (if not impossible) to execute Rates Arbitrage, even if their protocols were to take each other’s tokens as collateral, which they can’t.**

On the other hand, with Infinity’s Two Market Model having a zero bid-offer spread:

**State 1**: Infinity’s Rates < Aave or Compound’s: An Arbitrageur could execute arbitrage recursively by borrowing with Infinity and Lending at Aave or Compound;**State 2**: Infinity’s Rates between Aave or Compound’s: Market Forces (i.e. rational investors) would be disincentivized to use either Aave or Compound as both their lending and borrowing rates would be worse than Infinity’s**State 3**: Infinity’s Rates > Aave or Compound’s: Market Forces would attract lenders to Infinity thus driving infinity’s rate back to State 2 above. This process would be accelerated if Aave and Compound were to accept Infinity’s iTokens as collateral (currently, they do not).

As you can see in the three states, Infinity’s rate is driven by market forces and as such, is stochastic in nature. As such, with Infinity’s collateral risk management system and interest rate having a tighter spread, this will establish Infinity’s rate as the market clearing interest rate.

## Rates Arbitrage with Infinity

Infinity can take three types of collateral:

- Basic tokens: USDC, USDT, DAI, ETH, WBTC
- Deposit tokens: aETH (Aave), cETH (Compound)
- Complex tokens: Curve LP Tokens, Uniswap V3 LP Tokens

The ability for Infinity to accept these types of collateral fundamentally changes the DeFi ecosystem by enabling Rates Arbitrage.

Infinity establishes a much deeper financial market enabled by its enterprise-grade risk management system taking more complex collateral unseen in DeFi today. While this enables Rates Arbitrage, we need to consider ‘where are the rates’ and whether there is a sufficient level of arbitrage to be enabled.

Let’s evaluate the scenario where Infinity’s borrow / lend rates are lower than both of the rates at Aave and Compound. Recall: Infinity has zero bid-offer spread, while Aave and Compound have a wide bid-offer spread.

We outlined above the process of Rates Arbitrage, that is borrowing the same asset at a lower rate and lending the same asset at a higher rate. With DeFi today, this is not possible as an iterative process as borrow / lend protocols are not capable of taking each other’s tokens, absent the issue with their wide bid-offer spreads.

With Infinity, an Arbitrageur could undertake Rates Arbitrage between that of Infinity and the Deposit / Complex tokens (highlighted above) issued by Aave, Compound, Uniswap and Curve. In the above example, an Arbitrageur would do the following:

** 1. Step 1**

- Borrow USDC from Infinity at (say) 2%;
- Deposit USDC with Aave at (say) 6% or Compound at (say) 7%;
- Establish an annualized risk-free profit position of 4% and 5%, respectively;

** 2. Step 2**

- Take the Deposit aUSDC tokens (from Aave) and cUSDC tokens (from Compound);
- Deposit with Infinity and borrow (more) USDC at (say) 2.25%; and

** 3. Reiterate steps 1 and 2.**

Note that, in practice, the LTV Infinity applies to aTokens or cTokens is less than 100%, and so 100 aUSDC collateral will not enable the user to borrow 100 USDC on each iteration. If we assume an LTV of 90%, this means the trader can borrow 90 USDC or 90% of their collateral on each iteration. Recursively, this enables the trader to leverage 100 USDC ten (10) times for the creation of 900 additional USDC or 1000 USDC total (i.e. 100 USDC x (1/(1-USDC LTV)).

The above Rates Arbitrage process will drive:

- An upward pressure on Infinity’s borrow/lend rate, due to increased borrowing; and
- A downward pressure on Aave and Compound’s lend rate, due to increased lending.

Rates Arbitrage will drive Infinity’s borrow/lend rate to a stochastic, market clearing rate.

As mentioned above, the Rates Arbitrage process applies whether Infinity’s borrow/lend rate:

- Sits below that of Aave and Compound;
- In between that of Aave and Compound; and
- Above that of Aave and Compound.

Thanks to Rates Arbitrage, Infinity’s rate market clearing rate would sit in between that of Aave and Compound, and given their wide bid-offer spreads, any rational investor would find no reason to lend or borrow from either Aave or Compound. In the above example, Infinity’s borrow/lend rate would sit:

- Below Aave’s new borrow rate and above Aave’s new lend rate; and
- Below Compound’s new borrow rate and above Compound’s new lend rate.

**Will Aave and Compound survive? That is the question**.

Given everything we’ve highlighted in today’s article, one must wonder whether the existing borrow/lend protocols in DeFi will survive with Infinity’s TMM in existence. Short answer, we believe is ‘no’, but investors are indeed irrational at times which opens up the possibility for some conditions and to be prudent we’ll go with ‘possibly, for now’. It is impossible to say whether their TVL will drop, through the recursive arbitrage argument. TVLs should explode across lending protocols and it’s only a matter of time that equilibrium will find its footing. How *does* a protocol with a wide bid-offer spread compete with a protocol with zero or low-spread?

In our white paper (soon to be released), we discuss the notion of making Infinity’s Risk Protocol available externally to the broader community through smart contracts, should any other protocol want or need to manage complex collateral (Basic, Complex tokens) or otherwise complex assets. If you are a protocol, builder or any other relevant party please don’t hesitate to get in touch with us on the below channels.

The multiplicative process of Rates Arbitrage leads to rapid TVL expansion in DeFi.

Crucially for the DeFi ecosystem, the mechanical possibility for Rates Arbitrage means Infinity has the potential to single-handedly multiply existing TVL, in multiples from the levels we currently see today. Given Infinity’s enterprise-grade risk management system is capable of taking Basic and Complex tokens, the iterative process of Rates Arbitrage means Arbitrageurs are basically multiplying TVL.

While we don’t go into the details here, the above Rates Arbitrage process could similarly be applied to Uniswap and Curve, thereby driving Uniswap and Curve’s rates down and Infinity’s up, leaving the *rates differential *as representative of the extra risk premium an Arbitrageur might be taking with Uniswap and/or Curve.

How the above will fundamentally change the DeFi ecosystem is T-B-D; but we’re excited to share what Infinity will be coming to market with, namely its Two Market Model enabling Rates Arbitrage. We’re excited to see the potential for significant TVL growth amongst traders and Arbitrageurs who could recursively trade between Infinity and Aave, Compound, Uniswap and Curve.

Spoiler Alert… (deja-vu)... This is REALLY huge.

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