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Tag: Quantitative

  • Part 1: Quantitative Crypto Insight: Stablecoins and Risk-Free Rate | by Coinbase | Apr, 2022

    Part 1: Quantitative Crypto Insight: Stablecoins and Risk-Free Rate | by Coinbase | Apr, 2022

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    By George Liu and Matthew Turk

    Coinbase Logo

    In part one of this quant research piece, we introduce the decentralized finance (DeFi) collateralized lending platform known as Compound Finance and discuss its use case for stablecoins, in comparison to the notion of a “risk-free” interest rate from traditional finance (TradFi). Our goal is to tie these concepts together to educate on how different types of low-risk investment work within the TradFi and crypto markets.

    This introduction examines stablecoin lending yield and shares insights on yield performance, volatility, and the factors driving lending yield. Part two of this piece will examine the factors that drive lending yield in more detail.

    Stablecoins are a niche part of the ever-growing crypto ecosystem, primarily used by crypto investors as a practical and cost-efficient way to transact in cryptocurrency. The invention of stablecoins in the crypto ecosystem is brilliant because of the following properties:

    • Similar to the fiat currencies used in model economies, stablecoins provide stability in price for people transacting across digital currencies or between fiat and digital currencies.
    • Stablecoins are native crypto tokens that can be transacted on-chain in a decentralized manner without involvement of any central agency.

    With the growing adoption of cryptocurrencies by investors from the TradFi world, stablecoins have become a natural exchange medium between the traditional and crypto financial worlds.

    Two of the shared core concepts in the traditional and crypto financial worlds are the concepts of risk and return. Expectedly, investors are likely to demand higher return for higher risk. During the current Russia-Ukraine war, the Russian interest rate increased from an average of approximately 9% to 20% in 2 weeks, which is a clear indication of how the financial market reacts to risk.

    Central to the framework of risk and return is the notion of a “risk-free” rate. In TradFi, this rate serves as a baseline in judging all investment opportunities, as it gives the rate of return of a zero-risk investment over a period of time. In other words, an investor generally considers this baseline rate as a minimum rate of return he or she expects for any investment, because rational investors would not take on additional risk for a return lower than the “risk-free” rate.

    One example of a “risk-free” asset is the U.S. Treasury debt asset (treasury bonds, bills, and notes), which is a financial instrument issued by the U.S. government. When you buy one of these instruments, you are lending the U.S. government your money to fund its debt and pay the ongoing expenses. These investments are considered “risk-free” because their payments are guaranteed by the U.S. government, and the chance of default is extremely low.

    A “risk-free” rate is always associated with a corresponding period/maturity. In the example above, treasury debt assets could have different maturities, and the corresponding risk-free rate (also called treasury yield) are different as well.

    The duration could be as short as one day, in which case we call it overnight risk-free rate or general collateral rate. This rate is associated with the overnight loan in the money market and its value is decided by the supply and demand in this market. The loans are typically collateralized by highly rated assets like treasury debt, and are thus deemed risk-free as well.

    Source: WallStreetMojo

    With the growth in acceptance of crypto assets and the corresponding market globally, crypto based investing has become a popular topic for people who have been previously exposed only to the traditional financial market. When entering into a new financial market like this, the first thing these investors generally observe is the risk-free rate, as it will be used as the anchor point for evaluating all other investment opportunities.

    There is no concept of treasury debt in the crypto world, and as such, the “low-risk” (rather than risk-free) interest rate is achieved in DeFi collateralized lending platforms such as Compound Finance. We use the term “low-risk” here, because Compound Finance, along with many other DeFi collateralized lending platforms, are not risk-free, but rather subject to certain risks such as smart contract risk and liquidation risk. In the case of liquidity risk, a user who has negative account liquidity is subject to liquidation by other users of the protocol to return his/her account liquidity back to positive (i.e. above the collateral requirement). When a liquidation occurs, a liquidator may repay some or all of an outstanding loan on behalf of a borrower and in return receive a discounted amount of collateral held by the borrower; this discount is defined as the liquidation incentive. To summarize risk in DeFi, the closest we can get to risk-free is low-risk.

    To clarify, for the sake of this post (and part two), we are looking into Compound V2. On Compound, users interact with smart contracts to borrow and lend assets on the platform. As shown in the example diagram above:

    • Lenders first supply stablecoins (or other supported assets) such as DAI to liquidity pools on Compound. Contributions of the same coin form a large pool of liquidity (a “market”) that is available for other users to borrow.
    • The borrower can borrow stablecoins (take a loan) from the pool by providing other valuable coins like ETH as collateral in the above diagram. The loans are over-collateralized to protect the lenders such that for each $1 of the ETH used as the collateral, only a portion of it (say 75 cents) can be borrowed in stablecoins.
    • Lenders are issued cTokens to represent their corresponding contributions in the liquidity pool.
    • Borrowers are also issued cTokens for their collateral deposits, because these deposits will form their own liquidity pools for other users to borrow as well.

    How much interest a borrower needs to pay on their loans, and how much interest a lender can receive in return, is determined by the protocol formulas (based on supply/demand). It is not the intention of this blog to give a comprehensive introduction to the Compound protocol and the many formulas involved (interested parties please refer to the whitepaper for an in-depth education). Rather, we would like to focus on the yield that an investor can generate by providing liquidity to the pool, which will facilitate our yield comparison between the two financial worlds.

    A Compound user receives cTokens in exchange for providing liquidity to the lending pool. While the amount of cTokens he holds stays the same through the process, the exchange rate that each unit of cToken can be redeemed with to get the fund back keeps going up. The more loans are taken out of the pool, the more interest rate will be paid by the borrowers, and the quicker the exchange rate will go up. So in this sense, the exchange rate is an indication of the value of the asset that a lender has invested over time, and the return from time T1 to T2 can be simply obtained as

    R(T1,T2)=exchangeRate(T2)/exchangeRate(T1)-1.

    Additionally, annualized yield for this investment (assuming continuous compounding) can be calculated as

    Y(T1,T2)=log(exchangeRate(T2)) — log(exchangeRate(T1))/(T2-T1)

    While the Compound pools support many stablecoin assets such USDT, USDC, DAI, FEI etc, we are only going to analyze the yields on collateralized lending for the top 2 stablecoins by market cap, i.e. USDT and USDC, with market capitalizations of $80B and $53B respectively. Together, they make up over 70% of the total market for stablecoins.

    Here below are the plots of the annualized daily, weekly, monthly, and biannual yields generated according to the formulas in the previous section. As one can see, the daily yield is pretty volatile, while the weekly, monthly, and biannual yields are respectively the smoothed version of the prior granular plot. USDT and USDC have pretty similar patterns in the plot, as lending of both of these assets experienced high yield and high volatility for the start of 2021. This indicates there are some systematic factors there that are affecting the DeFi lending market as a whole.

    Source: The Graph

    One hypothesis of the systemic factors that could affect the lending yield involves crypto market data such as BTC/ETH prices and their corresponding volatilities. To illustrate an example (higher risk in this case), when BTC and ETH are in an ascending trend, it is believed that many bull-chasing investors will borrow from the stablecoin pools to buy BTC/ETH and then use the purchased BTC/ETH as collateral to borrow more stablecoins, and then repeat this cycle until the leverage is at a satisfying high level. This leverage effect helps the investors to magnify their returns as BTC/ETH keeps going up. We will explore this analysis more in part two of this blog post.

    Future Directions

    This blog has given a broadly applicable introduction to DeFi collateralized lending through the lens of Compound Finance and how it compares to “risk-free” rates from TradFi. As mentioned above, in part two of this blog post, we will further examine collateralized lending yields and share our insights on yield performance, volatility, and driving factors.

    We, as part of the Data Science Quantitative Research team, aim to get a good holistic understanding of this space from a quantitative perspective that can be used to drive new Coinbase products. We are looking for people that are passionate in this effort, so if you are interested in Data Science and in particular Quantitative Research in crypto, come join us.

    The analysis makes use of the Compound v2 subgraph made available through the Graph Protocol. Special thanks to Institutional Research Specialist, David Duong, for his contribution and feedback.

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  • Quantitative Crypto Insight: an analysis of triangular arbitrage transactions in Uniswap v2 | by Coinbase | Feb, 2022

    Quantitative Crypto Insight: an analysis of triangular arbitrage transactions in Uniswap v2 | by Coinbase | Feb, 2022

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    Coinbase

    By Indra Rustandi, Nabil Benbada, Yao Ma

    In traditional finance, an arbitrage is an opportunity to make a positive gain with virtually no risk involved by taking advantage of pricing discrepancies that are present in the markets. These pricing discrepancies are an indication that some inefficiencies are present in the markets.

    Arbitrageurs will exploit these opportunities to make a profit and thus remove the pricing discrepancies, bringing back the markets to a more efficient state.

    In FX markets, a typical arbitrage trade is the triangular arbitrage which involves at least 3 currencies:

    This arbitrage would take advantage of any deviation in price between the above three pairs.

    Here, in an efficient market, we should always have:

    In this example:

    Here, any deviation from this equilibrium will lead to an arbitrage opportunity. For example, if Euro was cheaper relative to USD.

    Uniswap is a decentralized exchange venue that allows two kinds of activities:

    1. Provide liquidity of a given pair of ERC-20 tokens
    2. Swap one ERC-20 token for another ERC-20 token

    For the remainder of the post, we will focus on the second version of Uniswap (Uniswap v2), first deployed in May 2020. And since we are interested in triangular arbitrage, let us first explain how a swap is priced.

    Uniswap belongs to the category of “constant-product market”. In this category, the product of the liquidities of the two ERC-20 tokens in the pair of interest is constant:

    For illustration purposes, say token A is WETH while token B is USDC, and we have in the WETH-USDC pool 1,000 WETH and 3,000,000 USDC. Then,

    Assume now that we want to swap 1 WETH to USDC, how much USDC can we obtain? Our trade would increase the liquidity for WETH to 1,001 WETH. In order to maintain the constant product, we have:

    So the amount of USDC that we receive in the swap is:

    So in our swap, we receive an effective WETH/USDC rate of 2,997.

    A few things to note here:

    • This example doesn’t include fees to focus on the pricing.
    • The effective WETH/USDC rate can change when we swap a different amount of WETH. This is called slippage. In this example, the effective price “slipped” by 3 USDC or 0.1%.
    • Our WETH/USDC rate is purely determined by the liquidities available in the venue and is not dependent on how WETH/USDC is quoted on other venues. This is yet another possible source of arbitrage, albeit one that is beyond the scope of this post.

    Based on the discussion so far on both triangular arbitrage and Uniswap, a natural question is how prevalent triangular arbitrage opportunities are in Uniswap v2. We try to answer this question indirectly by analyzing Uniswap v2 swap trades that take advantage of triangular arbitrage opportunities. More specifically, we focus on the following characteristics:

    • All the trades are executed in the same transaction to reduce the risk of prices moving and affecting the arbitrage opportunities.
    • All the trades involve only Uniswap v2. With this, we miss triangular arbitrage trades that involve multiple venues (e.g. simultaneous swaps on Uniswap and Sushiswap).
    • All the tokens involved in the trades offset except for one token: the gain token, for which the sender will gain more at the end of the trade series.

    After analyzing over 68 million Uniswap v2 swaps since Uniswap v2 was deployed until the end of 2021, we found 1,371,122 swaps grouped in 429,315 transactions taking advantage of triangular arbitrage opportunities in Uniswap v2.

    On a monthly basis, we see a pronounced peak in October 2020, while the number of trades taking advantage of triangular arbitrage opportunities have been decreasing since. There are many factors that might have caused this (rise of competing DEXes, arbitrage opportunities mechanically decreasing due to the market becoming more efficient…). We are currently exploring these leads to try and explain this behavior.

    Next, we see which tokens are most often used as gain tokens. WETH is the clear front runner here with 417,229 trades. 2nd-4th place are occupied by stablecoins: USDC, USDT, DAI. In total, we identified 123 distinct tokens used as gain tokens, but the top four tokens account for more than 99% of the trades.

    How many legs were typically used to trade these opportunities? A majority of these trades were done using three legs. Quite a significant number also involved up to 6 legs.

    How profitable are these trades? For WETH, a high proportion of the 417,229 trades involving WETH are profitable (about 94% when accounting for gas). The most profitable trade gained around 280 WETH, but the average and median gas-adjusted gains are much smaller (average: 0.08 WETH, median: 0.012 WETH).

    For USDC, the trade with the most gain accumulated more than 14,000 USDC, but on average, the gain was around 97 USDC, while the median gain was almost 28 USDC.

    Let us now consider the individual addresses (without revealing any specific ones) behind these trades. We found that these trades were initiated by 4,784 unique addresses, the most active of which initiated more than 16,000 trades. In total, 94 unique addresses initiated more than 1,000 trades each. When using WETH as the gain token, the most profitable address managed to accumulate more than 1,100 WETH as a result of its trades; in the case of USDC as the gain token, the most profitable address accumulated almost 35,000 in USDC.

    Last but not least, let us now discuss at a high level how these triangular arbitrage opportunities are detected and how the corresponding trades are executed.

    We need to monitor the prices, likely using an automated process, in the Uniswap v2 pools. Given the prices for various pairs, an algorithm can run a search to see which combinations of pairs give rise to triangular arbitrage opportunities, potentially also incorporating opportunities identified from pending transactions in the mempool.

    Once opportunities are identified, then we move to the execution aspect. One key consideration is minimizing slippage, and it naturally leads toward having the swaps being executed within a single transaction. Another consideration is avoiding front-running or sandwich attacks, for which Flashbots Auction can be beneficial.

    Here, we have just scratched the surface in terms of understanding and maximizing the potential of decentralized finance. We, as part of the Data Science Quantitative Research team, aim to get a good holistic understanding of this space from a quantitative perspective that can be used to drive new Coinbase products. We are looking for people that are passionate in this effort, so if you are interested in Data Science and in particular Quantitative Research in crypto, come join us.

    The analysis makes use of the Uniswap v2 subgraph made available through the Graph Protocol. Thanks to Luke Youngblood and Xavier Lu for their contribution and feedback.

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