Three and a half days to reach 10,000%? How are Fraxlend's interest rates calculated?

Author: Azuma, Planet Daily Odaily

As the personal debt risk situation of Curve founder Michael Egorov continues to escalate, discussions surrounding the Fraxlend interest rate issue are also increasing.

The reason for this is that Fraxlend employs a relatively unique interest rate adjustment mechanism, causing the loan interest rates in the CRV/FRAX market within Fraxlend to rise rapidly for most of the time from yesterday to today, "forcing" Egorov to repay $7.13 million of debt on the platform this afternoon.

So, how exactly is the interest rate of Fraxlend calculated? Why can this number rise so quickly? Combining the official documentation of Frax Finance and explanations from its developer Drake Evans, we have briefly outlined this algorithm.

According to the documentation from Frax Finance, Fraxlend uses three different interest rate change algorithms for different markets:

• Linear Interest Rate: Simply put, this is a basic algorithm where the interest rate increases linearly with market utilization.
• Time-Weighted Variable Interest Rate: An algorithm that adjusts the interest rate based on market utilization and modifies it at fixed time intervals.
• Variable Interest Rate V2: A composite algorithm that combines the first two, using a function of the linear interest rate to determine the current rate, while also applying the time-weighted variable interest rate formula to adjust the maximum rate.

Okay, you might think this explanation is even more confusing. Don't worry, let's continue.

According to Drake's explanation, the CRV/FRAX market of Fraxlend uses the second algorithm (i.e., time-weighted variable interest rate), and its operational mechanism is as follows:

• First, Fraxlend sets a target utilization range for a specific market. When the market utilization is within this range, the interest rate does not need to change.
• When the market utilization is below the target range, the interest rate will gradually decrease by a certain multiplier at specific time intervals until it reaches the minimum rate.
• When the market utilization is above the target range, the interest rate will gradually increase by a certain multiplier at specific time intervals until it reaches the maximum rate.

This specific time interval is referred to as the half-life in the design of Fraxlend, indicating the time required for the interest rate to halve when the market utilization is 0, as well as the time required for the interest rate to double when the market utilization is 0.

According to the contract for the CRV/FRAX market, its target utilization range is 75%-85%, the minimum interest rate is 0.5%, and the maximum interest rate is 10,000%, with a half-life of 12 hours.

This means that for the CRV/FRAX market:

• When the market utilization is within the 75%-85% range, the interest rate does not need to change.
• When the market utilization is below 75%, the interest rate will gradually decrease by a certain "multiplier" every 12 hours until it reaches 0.5%.
• When the market utilization is above 85%, the interest rate will gradually increase by a certain "multiplier" every 12 hours until it reaches 10,000%.

Therefore, for a considerable amount of time from yesterday to today, the overall utilization of the CRV/FRAX market in Fraxlend has remained above 85%, even approaching 100%, which has caused the loan interest rates in this pool to continue to rise.

However, this does not mean that the market's interest rates will double every 12 hours as some rumors suggest, reaching 10,000% in three and a half days (this claim originated from Delphi Digital, but in fact, Delphi Digital only cited the situation of 100% utilization and did not state that it was a general situation after exceeding 85%), because in reality, the market's utilization has not continuously remained at 100% (which is also impossible), so the aforementioned "multiplier" is not always 2 times.

According to Drake's additional introduction, when the utilization of the CRV/FRAX market exceeds 85%, the multiplier for interest rate growth varies at different levels of utilization.

As shown in the above image, when the market utilization is at 85%, the "multiplier" is 1 times, meaning the interest rate will remain unchanged; but as the utilization increases, the "multiplier" will gradually rise; until the utilization reaches 100%, the "multiplier" will become 2 times, thus beginning the doubling growth as mentioned by Delphi Digital.

Currently, with Egorov's repayment, the utilization of the CRV/FRAX market has dropped to 53.68%, which means that if this situation is maintained, the interest rate will further decrease after 12 hours. This will significantly relieve Egorov's pressure.

So it is not difficult to understand why Egorov chose to repay part of his debt to Fraxlend in advance; at least he needed to suppress the utilization rate first, otherwise, it would be unbearable for the interest rate to keep rising.