DeFi Protocols for Loanable Funds: Interest Rates, Liquidity and Market Efficiency

1 INTRODUCTION

• Loanable-funds markets let borrowers and savers shift consumption across time, borrowing against future income or earning interest on deposited funds.The paper describes these markets as matching savers with would-be borrowers; savers’ deposits earn interest.Source: §1 · p. 1
• PLFs currently require borrowers to provide collateral, limiting their ability to borrow beyond assets they already hold.The paper notes that this constrains “true” borrowing in which an agent takes on net debt.Source: §1 · p. 1
• In PLFs, protocol-level interest-rate mechanisms respond to the supply and demand for funds and are commonly decided through governance.The rate-setting mechanism provides the preconditions for reaching market equilibrium.Source: §1 · p. 1
• The paper investigates how deployed PLFs set rates, experience illiquidity, and satisfy Uncovered Interest Parity within Compound.It also examines interest-rate interdependence across Compound, dYdX, and Aave for DAI and USDC using a Vector Error Correction Model.Source: §1 · p. 1

Contributions

• Periods of illiquidity are common and often shared across PLFs, with liquidity sometimes concentrated among as few as three accounts controlling about 50% of funds.The study analyzes rates, utilization, and borrowed and supplied funds across three large PLFs, and makes its dataset publicly available.Source: Contributions · p. 2
• The paper finds that Uncovered Interest Parity typically does not hold within Compound, suggesting its markets may be relatively inefficient and agents may not fully respond to rate incentives.It reports weak evidence that UIP holds as the time horizon increases.Source: Contributions · p. 2
• DAI, ETH, and USDC rates often cluster around the kink in a kinked interest-rate model.The paper presents a taxonomy of interest-rate models with three categories: linear, non-linear, and kinked rates.Source: Contributions · pp. 1–2
• Cointegrating relationships between DAI and USDC markets indicate some rate interdependence across protocols, with evidence of Compound market power.The paper reports that Compound appears to influence borrowing rates on smaller PLFs.Source: Contributions · p. 2

2.1 Ethereum

• Ethereum smart contracts are deterministic programs that interact through on-chain transactions and execute atomically, reverting state changes if execution fails.They can interact with other smart contracts when those interactions occur directly on-chain.Source: §2.1 · p. 2

2.2 DeFi

• DeFi relies on distributed-ledger technology for security and integrity, with pseudonymous participants and incentives used to encourage rule-following.Unlike regular finance as described here, DeFi participants’ identities are not all known and behavior cannot be enforced through regulation.Source: §2.2 · p. 2

2.3 DeFi lending markets

• PLFs protect longer-term loans with overcollateralization, while flash loans can be uncollateralized because a transaction reverses if repayment fails.Collateral is liquidated when its value falls below a protocol’s threshold.Source: §2.3 · p. 2

2.4 Stablecoins

• Stablecoins use price-stabilization mechanisms: fiat-collateralized examples include USDT and USDC, while DAI is cryptoasset-collateralized.DAI borrowers pledge overcollateralized cryptocurrency, and arbitrageurs are incentivized to trade when its price deviates from the peg.Source: §2.4 · p. 2
• These secured loans require borrowers to pledge collateral they already own, so they cannot enter net debt.The passage identifies this as a constraint on loans of this type in DeFi lending protocols.Source: §2.4 · p. 2

3.1 Comparison to traditional lending

• PLFs pool funds and match borrowers with lenders through smart contracts, rather than operating as functional equivalents of banks.Banks primarily provide financing through money creation rather than lending out savers’ pre-existing funds.Source: §3.1 · p. 3

3.2 Use cases

• PLFs support margin trading, including short sells and leveraged longs, while allowing suppliers of loanable funds to earn interest.Margin is collateral given to a counterparty to cover the credit risk posed by the agent.Source: §3.2 · p. 3

3.3 Design space dimensions

• Variable interest rates adjust with the ratio of borrowed to supplied funds, which can incentivize repayment during low liquidity.Loans have unlimited maturities, so variable rates may fluctuate after a borrow position opens.Source: §3.3.1 · p. 3

3.3.2 Reserve factor.

• A reserve factor sets aside part of borrowers’ accrued interest for periods of illiquidity, reducing the interest received by lenders.Lender interest is the interest paid by borrowers less the reserve factor.Source: §3.3.2 · p. 3

3.3.4 Governance mechanism.

• PLF governance commonly uses protocol-specific ERC-20 tokens whose holders’ voting weight is proportional to their stake.Token holders can propose new features and changes to the existing protocol.Source: §3.3.4 · p. 3

4 INTEREST RATE MODELS

• Utilization is defined using total loans and gross deposits; the Interest Rate Index updates when users mint, redeem, borrow, repay, or liquidate, and a reserve factor directs some interest to reserves.The index is calculated each time an interest rate changes.Source: §4 · p. 3
• PLFs use three main variable-rate models: linear, non-linear, and kinked.The model can differ across protocols and across markets within a protocol.Source: §4 · p. 3

4.1 Model one: linear rates

• Linear borrowing rates rise with utilization, while saving rates scale the borrowing rate by utilization, keeping the borrower-saver spread positive.The borrowing rate is a linear function of utilization; some of the spread may be kept as reserves.Source: §4.1 · p. 4

4.2 Model two: non-linear rates

• The dYdX non-linear model lets rates rise at an increasing rate as utilization grows, strengthening incentives for suppliers to supply and borrowers to repay.Source: §4.2 · p. 4

4.3 Model three: kinked rates

• Kinked models sharply change borrower and saver incentives beyond a utilization threshold; the authors suggest the kink may become a Schelling point for convergence.Compound’s saving rate also accounts for utilization and a reserve factor.Source: §4.3 · p. 4

4.4 Making rates stable

• Aave offers variable or stable borrowing rates, but its stable rate can be revised when it deviates too much from the market rate.The variable rate uses different slopes below and at or above optimal utilization; that threshold was 0.8 and was updated to 0.9 in May 2020.Source: §4.4 · pp. 4–5

4.5 Summary

• Across the reviewed models, incentives for borrowers and savers at high utilization are a key feature.Source: §4.5 · p. 5

5.1 Liquidity and illiquidity across PLFs

• ETH markets maintain high liquidity, while DAI and USDC frequently reach low liquidity; some low-liquidity periods are shared across protocols, especially dYdX and Aave in January–mid-March 2020.The analysis uses total supply minus total borrows as available liquidity.Source: §5.1.1 · p. 5, Figure 2 · p. 6, Figure 3 · p. 6

5.1.1 Liquidity.

• On Black Thursday, total funds locked across DeFi fell from 897.2m USD to 559.42m USD; Compound’s DAI market then faced prolonged low liquidity before recovering and becoming low-liquidity again after mid-April.The recovery occurred around the same time as increased liquidity on dYdX and Aave.Source: §5.1.1 · p. 5

5.1.2 Illiquidity.

• Only Aave caps utilization at 100%; Compound and dYdX have repeatedly exceeded full utilization for DAI, with dYdX rates reaching 50% and Compound rates staying below 25%.Aave’s optimal utilization target was 80% during the measurement period, and its DAI rates exceeded Compound’s at high utilization.Source: §5.1.2 · pp. 6–7, Figure 5 · p. 6

5.1.3 Fund distribution.

• For DAI, just 3 accounts control 50.3% of locked funds on Compound; the same number control 60.0% of ETH and 47.3% of USDC.The authors report similar concentration patterns on Aave and dYdX and note that concentrated suppliers could sharply reduce liquidity.Source: §5.1.3 · p. 7, Figure 6 · p. 7

5.2 Case Study: DAI on Compound

• On Compound, realized DAI interest rates cluster at the kink across the observed periods, including after the base rate fell by 49.04% and after it was set to zero.After the base-rate reduction, typical utilization appears to shift below the kink; with the base rate at zero and the multiplier increased nearly 1000%, rates still cluster at the kink.Source: §5.2 · pp. 7–8

5.3 Summary

• The section’s summary highlights shared illiquidity, concentrated locked funds, and DAI-on-Compound interest rates clustered around the kink across observation periods.The Compound case study covers DAI during differing utilization levels and interest-rate regimes.Source: §5.2 · p. 7, §5.3 · p. 8

6 MARKET EFFICIENCY

• Market efficiency means prices would be unaffected by revealing the relevant information to all market participants; it helps assess market maturity and responsiveness.The authors also connect efficiency to whether high-utilization interest rates reliably incentivize agents to save and borrow as intended.Source: §6 · p. 8

6.1 Uncovered Interest Parity

• UIP is a no-arbitrage condition under which expected exchange-rate adjustment offsets interest-rate differences, leaving a risk-neutral investor indifferent between assets.If the condition holds, investors cannot make a risk-free profit.Source: §6.1 · p. 9

6.2 UIP in a PLF

• The authors test UIP across all possible token pairs within Compound, where a risk-neutral investor should be indifferent between saving or borrowing either token.Compound is selected as the largest PLF at the time of writing.Source: §6.2 · p. 10

6.3 Empirical approach

• The empirical specification assumes rational expectations and tests UIP both with a restricted intercept and with an unrestricted intercept that may reflect a risk premium.Borrowing and saving rates are tested separately across token pairings.Source: §6.3 · p. 10

6.4 UIP regression results - borrowing rates

• At daily frequency, borrowing and saving UIP are rejected for all 20 pairs; weekly evidence is mixed, with H0 consistent for 8/20 pairs in each analysis.The authors report no daily evidence supporting UIP, but some weekly evidence that is supportive.Source: §6.4 · p. 10, §6.5 · p. 10
• WBTC is excluded from the borrowing-rate analysis because of data quality issues.The borrowing- and saving-rate regressions use heteroskedasticity- and autocorrelation-robust standard errors.Source: §6.4 · p. 10

6.6 Summary

• The authors find weak evidence that UIP holds as the time horizon increases, suggesting Compound may not be fully capital efficient and that currency carry trades may be profitable.They further suggest that agents may not be fully responding to PLF interest-rate incentives.Source: §6.6 · p. 10

7.1 Vector Error Correction Models

• The authors model short- and long-run borrowing-rate dynamics for DAI and USDC with a VECM, finding at most two cointegrating relationships for each token and optimum lag lengths of 5 and 3, respectively.Source: §7.1 · p. 10, §7.2 · p. 11

7.2 Results

• For DAI, Aave and dYdX adjust to Compound’s rate with short-run coefficients of 0.38 and 0.28, respectively, while Compound does not show adjustment to their rates.The authors suggest this pattern may indicate Compound has market power.Source: §7.2 · p. 11
• A positive shock to Compound’s DAI borrowing rate permanently increases borrowing rates on Aave and dYdX.Figure 13 presents the impulse response to the Compound DAI rate shock.Source: Figure 13 · p. 11, §7.2 · p. 11
• For USDC, Aave adjusts faster than dYdX, with speeds of 0.607 and 0.115, respectively; the authors also find long-run relationships linking Compound and dYdX, and Aave and dYdX.They interpret the adjustment pattern as further evidence that Compound may have market power.Source: §7.2 · pp. 11–12
• A shock to Compound’s USDC borrowing rate has a permanent effect on borrowing rates in Aave and dYdX.Figure 14 presents this impulse response.Source: Figure 14 · p. 12, §7.2 · p. 12

7.3 Robustness checks

• Robustness checks find broadly stationary cointegrating equations, no eigenvalues near the unit circle, and little residual serial correlation, though model errors are non-normally distributed.The authors conclude that the VECM models are reasonably well specified; non-normal errors may affect standard errors but should not cause parameter bias.Source: §7.3 · p. 12

7.4 Summary

• Across DAI and USDC, cointegrating relationships indicate that interest-rate changes across protocols are associated, and the authors find some evidence of Compound having market power.They suggest these patterns may reflect agents being incentivized to change protocols in response to observed rates.Source: §7.4 · p. 12

Related work

• Prior work studies Compound’s market risks and liquidation mechanism through agent-based simulations, while describes utilization and interest-rate models used by major PLFs.The simulation study reports scalability with a low probability of failure even when markets are volatile.Source: §8 · p. 12
• Research on Compound documents near- and actual-illiquidity, including episodes where a single transaction withdrew over a quarter of available liquidity and, at worst, over 95%.Aave work examines Black Thursday, including sharply elevated flash-loan use and liquidations.Source: §8 · p. 12
• In, authors distinguish traditional banks’ intermediation and financing roles, finding identical shocks have much greater real-economy effects under financing models; Brody et al. examine continuously accruing interest for cryptocurrency holders.Source: §8 · p. 12

• The paper coins Protocols for Loanable Funds (PLFs) for DeFi protocols that intermediate funds between users.Source: §9 · pp. 12–13
• High utilization often occurs within and across PLFs, while liquidity holdings can be concentrated among a small number of suppliers.A coordinated withdrawal by a few suppliers could significantly reduce available liquidity and perhaps make markets illiquid.Source: §9 · p. 13
• Uncovered Interest Parity does not hold overall, suggesting that token markets are relatively inefficient and agents may not fully respond to interest-rate incentives.Source: §9 · p. 13
• Borrowing rates across protocols influence one another, and Compound appears to have some market power to set Aave and dYdX borrowing rates.Source: §9 · p. 13

• Table A1 tracks cDAI interest-rate-model and parameter changes from 17 December 2019, omitting the earlier Jump Rate Model period for expositional clarity.Source: Table A1 · p. 14
• Tables A2 and A3 report daily-frequency UIP results for borrowing and saving rates, respectively, using Newey-West robust standard errors.The reported standard errors are robust to heteroscedasticity and autocorrelation.Source: Table A2 · p. 15, Table A3 · p. 16
• Tables A4 and A5 report weekly-frequency UIP results for borrowing and saving rates, respectively, using Newey-West robust standard errors.The reported standard errors are robust to heteroscedasticity and autocorrelation.Source: Table A4 · p. 17, Table A5 · p. 18

A.1 Vector Error Correction Models

• A VECM models stationary relationships among cointegrated non-stationary time series and estimates both long-run and short-run adjustment dynamics.When the cointegrating matrix has reduced rank, Π = αβ′, with α giving adjustment coefficients and β the long-run cointegrating equations.Source: §A.1 · p. 19
• Appendix Tables A6 and A7 report VECM results for DAI and USDC, respectively.Source: Table A6 · p. 20, Table A7 · p. 21
• Appendix Figures A1–A6 cover DAI and USDC cointegrating equations and their misspecification tests.Source: Figure A1 · p. 20, Figure A2 · p. 20, Figure A3 · p. 20