In June and July 2021, Aave and Compound's aggregate borrower was already at its liquidation price. A crash was unnecessary. Bertomeu, Martin and Sall reach that conclusion without inspecting a single wallet: R_I rose above one at the peak.
The depositor owns a crypto-backed claim
DeFi lending brings together two trades. A depositor supplies stablecoins to a pool and receives a token such as aUSDC or cUSDC, redeemable for the underlying. A borrower pledges unpegged collateral, usually ETH, then draws stablecoins against it. The paper uses $0.80 of loan per $1 of collateral to illustrate the loan-to-value. Borrowers commonly sell those stablecoins for additional unpegged coin.
The borrower must maintain a health factor above one. Once it falls below that level, decentralized liquidation opens the position to a third party, who repays the loan and receives the collateral plus a bonus.
The depositor's token deserves the attention. Its claim rests on a basket of cryptocurrency, backed by collateral committed to the protocol. In the paper's words, "Unlike a traditional money fund, lending pools do not report a net asset value." The depositor therefore owns an instrument resembling a new stablecoin with crypto reserves. The Terra-UST collapse, involving 12 billion USD of circulating supply, made the category everyone's problem. Total DeFi lending deposits climbed from roughly 500 million USD in January 2020 to nearly 40 billion in May 2022.
The authors start with a two-date model containing one yield-seeking stablecoin depositor and one borrower who pledges ETH for stablecoins. They map that model onto observable totals at the coin level. Daily calculations cover Aave and Compound from April 1 2021 to May 18 2022. The sample contains 27,804 daily token-level observations, collected from Ethereum through public Dune queries for the a- and c-tokens.
Maker is left out because its borrowers mint DAI instead of borrowing a depositor's coin. DAI and TerraUSD are also excluded from the stable coins, following a definition that the paper links to proposed U.S. legislation S.3970.
Why was the series missing?
Investor-level leverage cannot be measured at all. The paper's footnote explains why: wallets are anonymous, some belong to exchanges, and large investors use several, "making it infeasible to consolidate net positions at the investor level." A separate gap runs through the literature. The authors put it plainly: "there is no systematic assessment of the positions taken by lenders and borrowers."
Their answer is a synthetic aggregate. They sum deposits and borrowings for each coin across all traders, treating negative positions as borrowings. This two-sided total separates into a depositor side made up of pegged coins and a borrower side made up of unpegged coins.
The useful choice comes next. Total borrowing divided by total lending stays below one by construction. The authors regard that cap as a problem because lenders and borrowers are separate traders carrying different exposures. Such a ratio cannot describe June and July 2021, when R_I exceeded one. The measure crosses that boundary only after stablecoin borrowings are matched against borrowers' excess unpegged collateral.
Two ratios and the space between them
R_I measures liquidation. It divides stablecoin borrowings by net unpegged deposits, weighting each coin by its liquidation threshold. R_II measures impairment. It increases those borrowings by the liquidation bonus, then divides by unweighted net unpegged deposits.
Both ratios are interpreted as price levels. A reading of one says current coin prices already trigger the event. The proportional decline still required equals 1 minus the value.
Thresholds and bonuses create the full gap between the measures. There is no volatility model or correlation matrix. System-level distance to default emerges from aggregate coin totals and two protocol parameters. This is the part of the paper I would reuse.
At the peak
R_I stood above one at the peak. R_II still indicated roughly 35% of further downside before deposited collateral became impaired.
The liquidation threshold tau_j, which sits below one, supplies the depositor's buffer between those readings. Liquidator bonuses push in the opposite direction. R_II grosses stablecoin borrowings up by (1+pi_j), so a larger bonus raises the ratio and moves impairment nearer. In the paper's scenario 2b, the amount left unpaid to the pool increases with pi.
After about six months of consolidation, 1 minus R_I was roughly 30% at the end of the sample. A crash of at least that magnitude would carry the synthetic borrower into liquidation territory.
The checks carry less weight than the abstract
The measures decline when crypto prices rise, the expected sign. A 1,000 index-point increase in NCI is associated with a reduction of 0.119 to 0.152 in R_I, with standard errors from 0.011 to 0.019. For R_II, the corresponding decline is 0.056 to 0.094, with standard errors of 0.009 to 0.015. Every estimate is significant at the 1% level across 852 observations, or 790 when lagged controls are included.
Explanatory power remains thin. R² ranges from 0.117 to 0.176 for R_I and from 0.043 to 0.155 for R_II. NCI carries weights of 61.7% Bitcoin and 35.09% Ethereum. Together, crypto prices and macro controls account for 4 to 18 percent of variation in the measures, and no more.
Validation against liquidations consists of a quintile plot. Liquidations are scaled by lagged borrowings and winsorized at 1% and 99%. They increase across quintiles for both measures. We did not find a coefficient or t-statistic for that relationship.
The authors themselves explain the weakness of liquidations as a stand-in. They "may not necessarily occur during normal market conditions, because a borrower is often better-off closing the position" before owing the bonus. They continue: "Nevertheless, liquidations are a proxy for elevated risks." The table uses plain OLS standard errors on daily levels. We found no Newey-West or clustered variant, so we would expect reported significance to fall after correcting the errors for autocorrelation.
The horizon creates another limit. Interest is omitted because the paper considers it negligible over one to two days. The resulting object is an instantaneous solvency measure. The abstract promises early warning signals, while the body makes a narrower claim: "Our objective, by contrast, is to develop a measure that can be easily tracked in a time-series with aggregate data and may point to a need to conduct detailed stress tests if positions become sufficiently risky." The conclusion describes the work as "a first step".
We did not find a test showing whether a high reading comes before losses. Table 1 regresses the risk measures on same-day and 1-day-lagged crypto prices and macro controls. Prices therefore explain risk in that exercise, rather than risk anticipating losses. Figure 3 sorts liquidations, scaled by lagged borrowings, into quintiles of the measures without a stated lead. Figure 2 simply plots the two measures through time.
Netting remains unresolved. When one account deposits and borrows the same coin, both D and B are inflated. The wallet problem prevents that overlap from being cleaned.
We could not run this. Computing the measures requires daily token-level deposits and borrowings for each protocol, together with every collateral asset's liquidation threshold and bonus as they stood on each day. Our available data consist of spot crypto OHLCV and news. Reconstructing R_I from prices alone would discard the mechanism: changes in the pool's composition.
One test from useful
Put this on a monitoring screen.
Thirteen and a half months of daily observations from two protocols, Aave and Compound, justify no stronger use.
A lead-lag regression would change my view: realized depositor impairment or liquidation volume on lagged R_II, with the horizon specified. I would also want a sensitivity run that restores DAI to the stablecoin bucket. The classification changes both the numerator and denominator for both measures, and the paper does not test it.
A governance coin supplies the capital behind the depositor tail. The paper says this in its conclusion, naming the Compound coin among the protections against under-collateralized lending and comparing it with the Luna mechanism during the Terra USD collapse. We encountered the same structure while reviewing a loss-distribution fit for DeFi operational risk (/articles/defi-buffers-fund-the-average-year-and-5-of-the-tail). Two ratios that public queries can calculate every morning at least show where that structure has become thinnest.