Protocols for Loanable Funds: A First Dive into DeFi Lending and Borrowing

Sam Werner
Photo credit: Jon Cellier (@frenchieeye, Unsplash)

In DeFi, a total of more than 1.6 billion USD are locked as of 26 June, 2020.
Most of these funds are locked in lending protocols, whereby DeFi participants can earn (pay) interest for supplying (borrowing) funds in a trustless and non-custodial manner. The largest DeFi protocol in terms of funds locked is Compound, with ca. 618 million USD at the time of writing (source: DeFiPulse).

In this post I want to highlight some findings from a recent piece of joined academic work with Lewis Gudgeon, Daniel Perez and William Knottenbelt on what we term Protocols for Loanable Funds (PLFs). We compared the different interest rate models which exist across PLFs and investigated market liquidity, efficiency and interdependence across three of the largest PLFs, namely Compound, Aave and dYdX. The pre-print of our paper can be found here.

Borrowing and Lending: DeFi vs the Real World

Perhaps one of the most common misconceptions in traditional finance is that a bank acts as an intermediary of savings, or loanable funds. In the traditional Intermediation of Loanable Funds (ILF) model of banking, banks serve as intermediaries of loanable funds through underwriting loans between savers and borrowers. However, this is very different from what actually happens in the real world. For instance, let’s assume Alice takes out a 100 USD loan from her bank. On her bank’s balance sheet, a loan entry for 100 USD in Alice’s name will be made on the asset side. Similarly, a deposit entry for the same amount of 100 USD will be made on the liability side. Essentially, a loan is made, yet no loanable funds have been loaned out! Hence, rather than serving as intermediaries of real-world savings, banks act as money creators, constrained by their profitability and solvency requirements. A detailed analysis of the ILF vs real-world banking models can be found here.

The main difference between real world banking and PLFs: in the latter funds are lent out which have actually been supplied by savers.

Why do we care about this? Well, DeFi has given rise to what we term Protocols for Loanable Funds (PLFs), which establish distributed ledger-based markets for loanable funds. On PLFs, borrowers have access to funds which are actually provided by suppliers, where the cost of borrowing depends on some underlying interest rate model. This is quite fascinating, as DeFi now offers a service in the form of PLFs for which traditional banks are often mistaken as providing. Hence, we want to understand more about how these protocols function and what implications PLF design choices may have on market participants.

How do PLFs work?

PLFs generally employ liquidity pools for a given market, through which market participants can supply and borrow funds. The cost of borrowing is generally a function of the available liquidity in a market and determined by the particular interest rate model employed by the PLF. Note that these interest rate models generally use floating rates, where interest is commonly accrued via interest-bearing derivative tokens, which are ERC-20 tokens that appreciate over some other token over time. For instance, suppliers of Dai on Compound receive cDai tokens in return, where the cDai tokens continuously appreciate over Dai. Hence, from simply holding on to such tokens, the token holders earn interest.

Interest Rate Models

When we classify interest rate models across PLFs, we find that there are three general model types: linear, non-linear and kinked rates. Note that Aave offers an interesting mechanism for offering a semi-stable interest rate, which takes into account the borrowing rates across other PLFs. However, we are particularly interested in the kinked interest rates, which can be found on Compound and Aave. Kinked interest rates exhibit some form of
kink, i.e. they sharply change at some defined utilization threshold.

Diving into PLFs

For our analysis, we examined three of the largest PLFs: Compound, Aave and dYdX, which at the time of writing this post contained c. 763 million USD in locked capital. We focused on three particular aspects of these protocols, namely: market liquidity, market efficiency and market dependence.

Market Liquidity — power in the hands of the few

When we examined the liquidity of shared markets across the three PLFs, we focused on the markets for DAI, ETH and USDC. We found that particularly in the markets for DAI and USDC across PLFs, periods of high and low liquidity are frequently shared. Particularly, the notion of illiquidity is interesting on PLFs, as for instance, on Compound and dYdX there were multiple occasions in the past when utilization exceeded 100%, i.e. more funds were borrowed than supplied by making use of reserves.

The utilization and borrow interest rates for the market for DAI on Aave (top), dYdX (middle) and Compound (bottom). The areas shaded in red represent periods during which utilization of funds was greater or equal to 100% (i.e. markets were illiquid).

High utilization in a market bears the risk of suppliers being unable to withdraw their loaned funds. This phenomenon has also been examined in more depth in this post. On the other hand, kinked interest rate models are designed to ensure that during such periods, the high cost of borrowing incentivizes borrowers to repay their debt, while also attracting new suppliers.

Apart from examining the frequent periods of very low liquidity across PLFs, we were also interested in the cumulative percentage of locked funds across the three PLFs. For instance, we found that on 06–04–2020 on Compound, 50.3% of locked Dai was controlled by only 3 accounts. A similar distribution of funds exists for the Compound markets USDC and ETH. Hence, a small set of accounts has the power to give rise to periods of illiquidity.

Market Efficiency

We investigated market efficiency within a PLF by testing for Uncovered Interest Parity (UIP). In traditional foreign currency markets, an investor has the choice of holding domestic or foreign currency. Under the theoretical condition of UIP, the exchange rate between two currencies should adjust such that returns are equal. For example, if we assume that the USD is worth less than the EUR and an investor is able to receive a higher interest rate in USD than in EUR, assuming UIP holds, the future exchange rate would adjust such that no risk-free profit can be made and any potential gains are offset.

In the context of PLFs under the assumption that UIP holds, a risk-neutral investor would be indifferent to holding either of the tokens for a given pair within a PLF, as the exchange rate would be expected to adjust such that no risk-free profit can be made. On the other hand, if UIP does not hold, this suggests that risk free profit can be made by market participants through currency arbitrage.

From analyzing empirical daily frequency data for borrowing and saving rates we found that within Compound, the largest PLF, UIP does not hold in most cases, suggesting i) markets are not very capital efficient at this time and ii) agents are not fully responding to monetary incentives.

Market Dependence

Lastly, we examine the inter-connectedness between PLFs, i.e. how changes in the interest rate in the market for token A on PLF 1 affect the interest rate for token A on PLF 2, and vice versa. By using a Vector Error Correction Model to model the short and long run dynamics between borrowing rates, we find evidence that suggests that to some degree interest rate changes in one protocol are associated with interest rate changes in others.

Impulse Response Function: Impact from a shock from Compound’s DAI borrow rate on Aave’s DAI borrow rate, where a positive shock to the borrowing rate results in a permanent increase in the borrowing rate on Aave.

Perhaps this implies that agents are being incentivized to change between PLFs based on the rates they observe. Furthermore, we find some evidence of Compound having more market power than others, influencing borrowing rates on smaller PLFs. For instance, we find that for borrowing rates for DAI, on Aave the rate is quickly adjusted to match changes in Compounds rate. However, this does not hold for the other way around.

For a detailed report of our findings, please check out our paper.

Looking Ahead

PLFs are attracting a lot of attention in the DeFi space. Therefore, it will be interesting to see how these protocols evolve over time (especially as new features such as semi-stable interest rates and flash loans are being adapted) and what roles market liquidity, efficiency and inter-connectedness will play in the future. Please feel free to leave any feedback in the comments below.


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