Maximizing Your Interest: The Key to Optimal Rates is Total Borrowing Size
Tldr: In a new research paper, we show that current interest rate curves are not suitable for optimising lending market KPIs such as revenue and TVL, and suggest new forms of curves that are likely to do a better job.
Since on-chain order books are infeasible, DeFi lending markets decide on the borrower interest rate according to the utilization ratio between total supply (deposits) and total borrowing (debt). By doing so they hope to reflect the market demand curve (similar to how DEX AMMs work) and to mitigate high utilization ratio.
Having optimal utilization ratio in mind, they set an interest rate curve hoping that with this curve the market will converge to the optimal utilization. In practice, as there are many unknowns, this approach does not result in optimal utilization ratio. In a new research paper, we show that even in theory this approach is not optimal, and suggest that the interest rate should be either a constant number or a function that depends on the total borrowing size, and should depend on utilization only once it exceeds the optimal utilization ratio.
Lending market KPIs
Lending markets aim to maximize their revenues and minimize their risk. Another key metric that is important for visibility and growth is to increase the market TVL (and here we define the TVL as the total amount of deposits).
In the context of interest rate curves, risk may arise when the market utilization is very high, and this can be mitigated by setting up a very high interest rate when the utilization is too high. Hence, for the rest of the blog post we focus only on revenues and TVL.
It is an easy observation that the amount of deposits is expected to increase as the suppliers interest rate goes up. Furthermore, the protocol revenues are taken as a fee on the supplier interest rate. Hence, maximizing the supplier interest rate will optimize both the protocol revenues and TVL, and therefore it should be the main objective when setting up an interest rate curve.
In the paper we prove that this goal is equivalent to maximizing the multiplication of total borrowing size with the borrowing interest rate.
We say that an interest rate is optimal, if it maximizes the above.
Theoretical model
We assume that the demand for supply and borrow depends on the supplier and borrower interest rate. And show that if these demands can be approximated by two linear functions (one for supply and one for borrow) then the optimal interest rate is obtained when the demand for borrow is half the demand that exists when interest rate is 0.
We show that setting up a constant interest rate function that is optimal requires less information about the supply and borrow demand functions, in comparison to a linear interest rate curve that depends on the utilization. We further show that if the interest rate function depends on the total borrowing size, then even less information is needed.
We show that some of the conclusions hold even if the supply and borrow demand functions are non linear.
Practical implications
Platforms rarely have full information about their users’ demand function. Hence, we cannot prove that our model strictly outperforms current practices.
However, we believe that current practices that aim to optimize utilization, rather than key metrics such as revenue and growth (TVL) are arbitrary at best.
In addition, our approach requires platforms to reason only about how borrowers would behave, while the current practice requires them to have information on both suppliers and borrowers behaviour.
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