Through The Looking Glass: A Survey Of Decentralized Finance

We are witnessing a renaissance at the intersection of mathematics, computer science, and finance, and the intellectual capital that is coming into the space continues to accelerate. — Read more from Identity Element  here or follow on Twitter

In just two months since my last piece, “The Case For Ethereum,” the cryptocurrency landscape reached its next milestone with the launch of EIP-1559 on August 4th. As alluded to in the previous piece, EIP-1559 meant quite a bit for the Ethereum ecosystem, the greatest change being a modification to the amount of ETH minted at block settlement. As of writing, EIP-1559 is responsible for burning ~53k ETH, which, at ETH’s current price of ~$3,200, equates to ~$170 million. If Bitcoin’s halvening’s was the impetus for its rally over past last year, one could assert that – if the market incorrectly anticipated the burn rate of ETH as a result of EIP-1559 – this event should lead to a significant revaluation of ETH over the coming months. Time will tell if these hyper-bullish calls materialize.

Perhaps more important to Ethereum’s longevity than EIP-1559 has been the pace of innovation within decentralized finance, or DeFi. We have seen the release of new stablecoins, automated market makers (AMMs) released on decentralized exchanged (DEXs), and unique financial products created due to the manner these platforms are designed. We are witnessing a renaissance at the intersection of mathematics, computer science, and finance, and the intellectual capital that is coming into the space continues to accelerate.

This renaissance is not occurring in a vacuum – the individuals underwriting this progress are extremely motivated to alter the economic landscape. I believe we are still in very early innings of these developments, and the DeFi community has made its intentions clear. Broadly speaking, DeFi platforms purport to:

• Develop mathematics to displace traditional finance operations (lending, market making, securitizing)
• Eliminate redundant overhead associated with traditional operations (office space, salaried employees, raising of capital) through the application of software
• Liberalize the profitability of financial operations to the anonymous collective supplying the capital

This piece is a survey of the large players in the landscape. It will broadly discuss the advancements made by each of these players, and wrap up with additional philosophical musings about the space, sharing thoughts about our path forward.

Uniswap and Curve: decentralized exchanges (DEX) and automated market making (AMM)

The landscape of DeFi changed completely with the launch of the DEX Uniswap and its AMM platform. Uniswap revolutionized crypto markets by introducing an algorithm that quotes potential buyers a price based on the assets sitting within a liquidity pool. The formulation of the algorithm ensures there is no notion of a limit order – there is only the price of the pool at some snapshot in time. Indeed, Uniswap’s constant product algorithm – x*y=k – completely transformed the viability of DeFi upon its launch back in 2018.

To borrow an example from this terrific blog post, suppose we are interested in a liquidity pool comprised of apples and pears. A liquidity pool is simply a pool of x apples and y pears, where the apples and pears committed to the pool are sourced from Ethereum participants. Any Ethereum user can add apples and pears to this pool, and in doing so, they receive the fees generated from the market making process in addition to incentives offered by the platform. Fees normally equate to 0.25% of the value of the transaction, adjusted for one’s share of the liquidity pool.

Consequently, Uniswap and other DEXs eviscerate the overhead associated with launching large scale trading operations we see in traditional finance – there is no need to hire traders, develop internal infrastructure, maintain office space, and raise capital. The smart contract containing x*y=k is the market maker, the capital is raised from an anonymous collective, and the infrastructure sits within the Ethereum virtual machine. We touched upon the destruction of human capital in “On Bits and Blockchains,” and while we are still a time away from DeFi seriously threatening traditional finance, the seeds may be planted for the future discussed at the end of that piece.

Back to our apples and pears. Suppose a buyer wants to purchase some quantity x’ apples from the pool. Since there must remain a fixed product k at the end of the transaction, the buyer must forfeit y’ pears to complete this transaction. y’ can always be obtained for any value of x’ prior to a transaction occurring, and it follows that the transition state of the curve below can always be known assuming the initial quantities of x and y that sit in the pool at some point in time (an example is provided in the footnotes below). [1] This relationship is represented graphically below:

The next large advancement in the AMM space came when Curve made the realization that the impermanent loss suffered by liquidity providers can be mitigated by developing a new AMM invariant, or a fixed constant model, i.e. f(x1,x2,…,xn)=c for some constant c. Impermanent loss occurs when the prices of assets in a pool change over time. The larger the change in price, the greater the impermanent loss suffered by a liquidity provider. [2] Consequently, Curve managed to improve upon Uniswap’s constant product model by introducing a stableswap invariant.

Curve’s algorithm flattens the belly of the constant product curve, thereby decreasing the slippage involved in a transaction, reducing impermanent loss of liquidity providers, and supporting larger transactions. This is for the following reason — at every point on the dark blue line below, (1) the derivative of the line is less than that of the dotted purple line (lower transaction cost) and (2) the number of points in which the second order derivative changes is similarly much smaller (hence larger transactions are supported). The dotted purple line below is the familiar constant product curve in our apples/pears example, and the blue curve is Curve’s innovative invariant. Since the blue curve is below the purple curve at all points of x and y, the stableswap invariant is a superior AMM model relative to x*y=k due to the reasons listed in the previous sentence.

Curve recently expanded its suite of invariant algorithms by developing a new invariant that creates a similar curve for non-stablecoin cryptocurrencies which display positive correlations in price. Since positively correlated price tend to move in tandem, this once again serves to reduce impermanent loss and enables larger transactions for Curve users.[3]

Borrowing and Lending on AAVE

In addition to transacting on DEXs, Etheruem users can borrow and lend assets on platforms like AAVE by using logic encoded in smart contracts (where a smart contract is just a fancy term for code that exists in the Ethereum Virtual Machine, or a software vending machine sitting in Ethereum’s blockchain, as we discussed in “The Case For Ethereum,” linked above).[4] To ensure that borrowing and lending is trustless, and that “delinquent” creditors make good on their payments, most loans in DeFi are collateralized; once the face value of your outstanding loan reaches some fraction of the capital it is secured against, the position is liquidated. For AAVE, this liquidation threshold is defined below:

DeFi lending platforms are unique in that they are not entities enforcing the liquidation of capital if a threshold has been breached. Indeed, other participants in the Ethereum ecosystem are incentivized to liquidate an under-collateralized position because they have the right to receive the collateralized assets at a discount.

For instance, suppose the balance of a loan of 0.50 ETH, collateralized by 1 ETH, grew to become 0.85 ETH since the borrower did not pay down the loan over time (a 0.50 ETH would take years to become 0.85 ETH at current variable APYs, but this is a simple example to drive liquidations home). A liquidator need only pay 0.95 ETH to receive 1 ETH. Mechanically, 0.85 ETH would be allocated toward repaying the debt, and the remaining 0.1 ETH would be swapped for the 1 ETH that was posted as collateral. Liquidations are consequently a highly competitive and profitable form of arbitrage – or MEV (Miner Extractable Value – this is discussed further in the footnote) – that exist on the Ethereum blockchain.[5][6] Additionally, the incentive for liquidators to close under-collateralized positions contributes to the overall health of the AAVE platform

More central to AAVE’s core value proposition are its borrowing rates, which are computed through a proprietary interest rate model. This model is designed to increase interest rates when capital on AAVE is scarce and lowers interest rates when capital is plentiful. This makes sense intuitively – high interest rates discourage borrowing and encourage lending, and low interest rates encourage borrowing while discouraging (to some extent) lending. [7] Below are the snapshots of the interest rates offered on AAVE, where the interest rate is denominated in the respective asset. Additionally, I have provided the model used to obtain these rates.

You can see how some of the APY’s have an additional APR, and this APR is an additional reward offered by AAVE via the issuance of its own token. So, AAVE matches depositors with borrowers, and generates profits through the spread that exists between rates of borrowing and lending.

This spread – the difference between the APYs for borrowing and lending – is used to secure the AAVE protocol. Indeed, AAVE has a “Safety Module,” which is a treasury of sorts that can be accessed in the event of a “Shortfall Event,” or an event in which liquidity providers cannot meet their obligations. A Shortfall Event can be triggered by holders of AAVE’s governance tokens, upon which 30% of tokens staked in the Safety Module will be used to close liquidity provider’s deficits. Any existing deficit will be eliminated via dilution of AAVE equity, i.e., by issuing new AAVE tokens.

Once again, the incentive for staking tokens into AAVE’s Safety Module are rewards. Users gain an increased share of the fees generated by AAVE’s ecosystem and receive additional rewards via the issuance of new AAVE tokens – staking provides users with an additional 6.59% APR on the dollar value of the tokens staked.

The valuation of AAVE consequently becomes relatively straightforward – does the rate of retained earnings offset the dilution of AAVE tokens via reward issuance? If so, then AAVE seems a reasonable allocation. However, AAVE’s “earnings” are highly dependent upon the amount of capital locked into, and that spreads that exist within, the platform, so its valuation is subject to significant fluctuations from even a fundamental perspective.

yearn: Yield Farming and the Alchemy of DeFi

Perhaps even more interesting than the opportunities that sit in lending platforms and DEXs, however, are the yields offered by yield aggregators. These platforms enable individuals seeking high APRs and APYs to participate in yield farming, which is the practice of capturing the value being created within the DeFi yield landscape through optimized position structuring.

The business model of yield aggregators is simple – they charge users a fee for depositing assets within their farms, and in return, construct optimal routes to maximize returns for the assets deposited based on yield opportunities that sit within, or across, other platforms.

For instance, yearn boosts the returns offered on platforms like Curve by implementing strategies which increase the base yields of Curve’s standard rewards by leveraging the tokenomics of Curve and other related opportunities. Lending platforms and DEXs have a strong incentive to protect the valuation of their reward tokens within the marketplace because the APYs on rewards offered would plummet if these reward tokens were sold by users simultaneously. [9]

To prevent this, lending platforms and AMMs incentivize users to lock their tokens into vaults by issuing additional rewards for users who elect to forgo their initial spot tokens in favor of governance tokens, or tokens that provide users the ability to vote on key strategic decisions. Thus, yield aggregators enable users to capitalize upon this incentive structure by offering access to the same pools that would exist within a lending platform or DEX, but often at a much larger yield due to these structuring quirks.

A very clear example of such a yield boost can be seen across yearn and Curve’s reward pools:

Curve offers users a maximum of a 30% APY in its tri-crypto pool, whereas yearn manages to offer a base APY of 42% for the same pool. This discrepancy exists because yearn is performing additional operations with the Curve platform, and across other platforms, to generate additional yield relative to staking in Curve’s tri-crypto pool in isolation.

These additional rewards do come at a cost; yearn charges users a 2% fee for assets deposited into its vaults as well as a 20% performance fee. [10] The revenue generated by these fees are then used to buy YFI (yearn’s token) which is then used to finance governance, security, or perform other enhancements that secure the protocol. [11]

Derivatives, Insurance, and Fractionalization

There have been new additions to the suite of DeFi platforms beyond those previously mentioned, indicating the breadth of development that is pushing the space forward. dYdX is a decentralized exchange (DEX) offering crypto derivatives such as options and perpetual futures; Nexus Mutual is providing insurance on other DeFi tokens in the event protocols get exploited or other adverse events occur; and fractionalization is currently occurring in the non-fungible token (NFT) space, which is an effort to raise funds to purchase an illiquid NFT asset, where each user is distributed their share of the underlying asset (where these shares can be trades freely in the secondary market).

I highly recommend the reader take a look at the developments above if this piques their curiosity. These platforms (much like the other platforms covered in this piece) are very much in their nascent stages and significant edge can be accumulated by simply having a deep understanding of the underlying software, mathematics, incentives, and use cases for new project launches.

Philosophical Musings: Through the Looking Glass

Rarely can I write a piece without feeling the urge to take a bit of an artistic license to share more abstract frameworks of thought. This piece has been different in tone relative to pieces I’ve written historically since I wanted to provide readers with a survey of the current state of DeFi. But now that this survey has been (largely) accomplished, I will be exercising my artistic license. Specifically, I will offer my thoughts on how these DeFi platforms have fit into the broader philosophical framework I’ve been cultivating throughout this crypto series in months prior.

The arrival of the coronavirus accelerated our shift toward a digital world. This acceleration uniquely benefited several industries, and due to the price appreciation of large cryptocurrencies such as Bitcoin, it forced a significant amount of talent to re-evaluate the efficacy of the crypto industry. We have seen previously believed to be esoteric-and-redundant cryptographic methods leveraged to enhance transaction speed, new mathematics developed to generalize financial operations (as covered broadly in paragraphs prior), and new software languages to enable humans to provide unique instructions for blockchain based operations.

This is a space for the intellectually curious. Significant edge can be obtained by thoroughly understanding the mechanics of a platform, scrutinizing the code underlying crypto applications, and understanding the motivations of other players within these nascent markets. The main reason for my lack of output on the blog of late is due to my interest in this space – the amount of opportunity is mind numbing, the problem set is intoxicating, and the skill set that is rewarded rests at the intersection of computer science, mathematics, and finance.

Detractors of the crypto space will say that these applications lack viability in the domain of the tangible. There are two counterarguments to this stance – one being an argument that I have already provided (and that readers may be familiar with), and another taking the form of an adoption curve. The adoption of new technology is rarely ubiquitous. There are the innovators and early adopters in the early innings of an adoption cycle, and we seem to be resting squarely within this early adopter phase, especially with respect to the DeFi platforms covered within this piece. The early adoption phase cannot – by definition – cover all general use cases for the technology in its broadest sense – if it did, this would contradict the characterization of early adoption.

Crypto applications currently exist in a self-contained environment. They are accruing value for one another within this digital ecosystem, and only offer tangible benefits in the event an individual elects to transform their fiat currency into its digital counterpart. The yields offered by DeFi platforms appear akin to alchemy – how can a stablecoin yield 20% on an annualized basis? Hopefully this answer is clear, but to reiterate – it’s simply due to the revenue accrued by the platforms underwriting the token being issued. DeFi consequently represents a more attractive opportunity relative to the yield environment of fiat – it is already serving tangible benefits for those who map their capital into the world of crypto. The yield on money must be near 4% at a minimum, ~400bp greater than the yield a user would receive if they left their capital in a traditional savings account. [12]

This yield is obviously not without risk. Staking is by definition a risky endeavor since applications have the right to access assets in the event of shortfall events. Liquidity pools are similarly not riskless due to the possibility of impermanent loss. Yet, on a risk-adjusted basis, DeFi yields offer superior returns relative to the fiat world (I can justify this statistically, but it is a case of absence of evidence does not equate to evidence of absence), and traditional finance has taken notice.

Banks have launched coverage on the largest cryptocurrencies, hedge funds are rushing to setup crypto trading arms, and the race to find talent has begun in earnest. Capital chases the most attractive opportunities, and the biggest players in traditional finance recognize the tectonic shift that’s occurring. What’s particularly incredible is that there is room for smaller players within the space and that the playing field is currently level (but this may change later – more in the footnote). [13] Financial institutions hope to make clients dependent upon them to access the services that will exist within this space moving forward. Paying for these services may make sense for some, but it is imperative to recognize that these services come at a cost and that one can access the same suite of services independently. This is the birth of the autonomous financier – we all have a front row seat for this revolution.

Some firms are taking a stance that counters financial institutions – consider Jack Dorsey’s decision to make Square a hub for DeFi development on the Bitcoin blockchain. This announcement, in my mind, was another momentous step forward within the space. Square can offer businesses it services the ability to route fiat proceeds directly into this digital space and deploy the capital in crypto denominated checking accounts (which are nothing more than aggregated exposure to different DeFi applications like yield farms, liquidity pools, and lending platforms) that offer higher yields relative to the world of fiat.

The fractionalization of NFTs also provides a clear road map for creating a map between the digital and the tangible. Fractionalization is closely related to securitization but is distinct since it can be feasibly performed to distribute ownership of a singular asset, incurs minimal friction to implement, and enables anyone to own the potential asset of interest (as opposed to large institutions in the case of mortgage-backed securities and the like).

NFTs are the perfect guinea pig for this foray – custody is irrelevant for there are no maintenance costs, employees to hire, etc. There are bound to be growing pains with the fractionalization space, and it’s best to let these kinks be sorted in the self-contained crypto environment before we apply these solutions to tangible assets. Eventually, I can see fractionalization of home and small business ownership take place, where governance tokens are essential to this process for they enable token owners to determine who will maintain a property or run the business and how profits should be deployed, among other issues. The entity that is capable of fractionalizing tangible assets is certain to be a billion-dollar entity. The writing is on the wall.

Shifting scope strictly to the space of NFTs – it is interesting to see how this new asset class is handling the treatment of intellectual property, as well as the cult like communities being created. I’m not here to narrate on the price action we’ve been seeing – that is a separate issue – but it is undeniable that ownership of these images and other tokens has been handled in an innovative way. For instance, owners of a Bored Apes (Bored Ape Yacht Club’s NFT) maintain ownership over the intellectual property and likeness of their ape. Consequently, any proceeds generated via the likeness of their ape is distributed to them directly.

NFTs have bolstered discussions on the metaverse, providing a road map for a future where gaming is a viable economic livelihood – imagine a high stakes game of – insert favorite game here – where the winner takes the proceeds from the loser in a matchup. While that may seem zero-sum at the surface, it isn’t on aggregate because these metaverse games will mint new tokens and items to be leveraged in game. Consequently, one can make some money simply by participating in the game without having to risk their assets in competition with other players (assuming these high-stakes matchups find footing).

It’s easy to let your mind run through these potential realities though; I think it’s unlikely any of us will foresee what the future of this space looks like. The pace of development is so quick in crypto time that one week away from the space is akin to a year in calendar time. The network effects that were discussed in “On Bits and Blockchains” and “The Case For Ethereum” have taken full effect. And we are all here to bear witness.

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[1] Suppose our pool initially has 100 apples (x) and 100 pears (y). It follows that 100 * 100 = 10,000. Thus, if someone came to this pool and was looking to purchase 10 apples, then we would have 90* y’ = 10,000 where y’ = balance of pears before the transaction plus the number of pears paid to the pool. Thus, the user would need to pay ~11.111111 pears into the pool in order to obtain 10 apples, since y’ must be equal to 111.111111 when the transaction is completed.

[2] For a nice discussion on impermanent loss and some examples, take a look at https://academy.binance.com/en/articles/impermanent-loss-explained

[3] The whitepapers documenting the mathematics underlying these algorithms can be found here. These papers are extremely technical and are not for the faint of heart. But they are glorious and highlight the intellectual Renaissance that is occurring in this space today. https://curve.fi/whitepaper

[4] The material used in the section can all be sourced from AAVE’s documentation found here: https://docs.aave.com/portal/

[5] For those interested in what liquidating a position might look like, checkout this link from AAVE. This provides examples for liquidating a position in Solidity, Java, and Python: https://docs.aave.com/developers/guides/liquidations

[6] MEV is perhaps Ethereum’s largest problem, but it is also the most fascinating set of opportunities I have encountered in the Ethereum blockchain. There are four main types of MEV: (1) DEX, or decentralized exchange arbitrage, (2) liquidations, (3) sandwich attacks, or the inception of a buy order, follow by a sell order located immediately before and after a buy order that is observed in the Ethereum mempool, and (4) long-tail MEV, or MEV that cannot be categorized. MEV is a high-stakes winner-take-all game. No participant is spared, and any incompetence is exploited. For the highly curious, you can read of MEV in the Twitter thread linked here, or look at Paradigm’s coverage of the subject by searching “Paradigm MEV” on Google. I promise, this does not disappoint.

[7] Documentation of AAVE’s interest rate model can be found here: https://docs.aave.com/risk/liquidity-risk/borrow-interest-rate

[9] Look no further than the tragic story of Iron Finance to see the results of one of these “bank runs.” I have a Twitter thread that covered this fiasco, so for those interested, you can read about the arbitrage that existed the day this “bank run” occurred on Iron Finance. Click here to read the thread.

[10] The 2% management fee does not occur upon deposit to the vault, however. It is incurred incrementally over the course of the year as yearn mints new vault tokens, which serves to dilute existing participants out of the pool. Again, while the 2/20 fee structure is similar to that of the traditional finance space, the mechanism underwriting the fee structure is quite novel. More documentation can be found here: https://docs.yearn.finance/yearn-finance/yvaults/overview

[11] Credit to https://defieducation.substack.com/p/yearn-finance-part-1-of-2-yes-there and for the plot below.

[12] The reason for this deals with mechanics of staking Ethereum and other assets in Proof of Stake blockchains. Since ETH can be staked at a 6% annualized clip currently, it follows that, due to the existence of lending platforms like AAVE, one can collateralize an ETH loan using USDC or another stablecoin, and stake the ETH to secure the blockchain. Since collateral ratios cannot exceed 85%, and since there are borrowing costs, the true yield of money is not 6%, but somewhere close: 6%*.85 – 1% (financing cost) = 4.1%; I think this is a reasonable estimate.

[13] The question of governance is a big one here. If a large institution obtains majority ownership of an applications tokens, they can hijack the governance structure of the chain and make decisions that are in best interest for the firm’s profitability at the expense of the platform’s health in the long run. This battle between short-term and long-term profitability is waged everyday in traditional capital markets and will make its way into crypto soon, if it has not surfaced already.