Impact Measurement Part Three: Generalizing Impact Measurement

In a previous article on Impact Measurement, we introduced the case of recursive accounts as a simplification of the general problem of quantifying the impact of our recommendations. Since we observe empirically that recursive accounts tend to maintain their borrowing at a constant level relative to the amount available, it is possible to extend changes in available borrow capacity to an estimate for impact using relatively simple math. In the broader case of non-recursive accounts, we must add some more steps to account for the fact that utilization may change along with parameter updates. In this article, we will look more closely at the behavior of lending protocol users in response to changes, and show some results from the overall impact analysis for our Compound recommendations.

Borrower Behavior

When borrowing limits are increased, the usage of all borrowers across the protocol relative to the limit immediately drops due to the now-larger denominator. We would then expect users to borrow more over time as they adjust for the effects of the change. In the case of recursive borrowers, this happens very quickly and we can simplify by modeling these users as effectively having constant utilization percentage.

In the general case, utilization is affected by market prices and users’ day-to-day transactions, so it may be difficult to pinpoint a clear reaction function like the one shown in the stylized example above. While users on average may adjust to a higher limit, the effect on any specific account is difficult to isolate. For this reason, our methodology for non-recursive impact focuses on determining whether utilization is broadly stable in response to parameter changes. If we can confirm the market is adapting to higher borrowing limits without persistently lower utilization, we know that changes are having the desired effect and can estimate the impact.

Looking at data from one of the larger accounts on Compound, we note that utilization has fluctuated between 35% and 70% during the course of several borrow limit increases marked by the vertical lines. Over the period observed, this account has also varied considerably in total size, as shown by the weight of the blue dots on the chart. Though the fraction of available borrow used has been volatile, the range it varies in has stayed consistent throughout all of this. As we will show in the next article, many users fit this pattern of significant short-term variability in utilization within a steady range.

In a market that generally follows this behavior, we can validate that non-recursive users are indeed adapting to higher borrowing limits efficiently. For example, if this user borrows 55% of their limit on average, an increase in the limit would grow the user’s borrow position proportionally as they adjust to the change. Though we cannot confirm this broadly holds true by looking at just a single account, the data observed supports this type of reasoning. Our methodology uses these observations conservatively when assessing impact, as we seek to verify users fit our expectations before including their contributions in the total. Now that we have set the stage by looking at the theory behind impact measurement and the details of borrower behavior, we can begin to assemble the complete impact calculation for lending risk management.

Non-Recursive Impact

In our impact analysis of Compound, we have identified several non-recursive accounts that follow the patterns described above. By estimating their equilibrium usage levels, we have been able to attribute material increases to interest earned from these accounts to our parameter recommendations. As shown in the diagram, these users have contributed an additional $3.85M of interest to Compound suppliers and reserves since November 2021 due to higher borrowing limits:

The next article on impact measurement will combine all the ideas discussed so far to provide a full view of our Compound analysis. By sharing a case study, we look to show that the theory introduced in this series is robust and applicable to complex real-world markets. Finally, with the results, we seek to demonstrate that our model’s optimizations drive quantifiable impact.

Continued in Part Four: Compound Case Study