Measuring leverage, including the hidden kind
How repeated depositing and borrowing turns into a multiple of the starting position — and how to spot it in a book.
This lesson has had no expert review. It was written for this platform and against the evidence it cites; nobody has gone through it independently.
Learning objectives
- You can compute the effective leverage of a recursive position.
- You can explain why a portfolio with no borrowing can still be leveraged.
Check your prior knowledge
Answer these for yourself before reading on. Wherever you hesitate is where this lesson pays off.
- What happens when you post what you borrowed as collateral again?
- What determines how often that can be repeated?
- How does leverage affect the distance to the liquidation threshold?
Core concept
Recursion creates leverage without new credit
Depositing, borrowing against it, depositing what was borrowed and so on multiplies the starting position. Each round is smaller than the last, bounded by the permitted loan-to-value, and the sum converges. Formally there is no single large loan — there are many small ones, and their result is leverage visible in no individual position.
Leverage shortens the price buffer
Higher leverage means not only more return per euro deployed but, above all, a shorter path to the liquidation threshold. The return grows linearly with leverage while the distance to the threshold shrinks — and liquidations are procyclical, so they bite exactly when the market is already thin.
Even with no borrowing of your own
A portfolio can be leveraged without borrowing itself: if it sits in a market whose users mostly run recursive positions. If the main collateral's price drops there, liquidations happen simultaneously, utilization jumps, and your own withdrawal gets tight — although your position is unleveraged. So the question is not only “am I leveraged” but “how leveraged is the market I am in”.
Definitions
- Effective leverage
- The ratio of the total position to the equity actually deployed.
- Recursive position
- A position in which borrowed funds are posted as collateral again.
Model
Your own borrowing — directly readable
Recursive positions — recognizable only from the sequence
Products that lever internally — from the product description
The market's overall leverage — from utilization and collateral structure
Formulas
Effective leverage under repeated borrowing
Leverage = 1 / (1 − LTV)- LTV
- loan-to-value used per round, as a decimal
Limit: The limit for infinitely many rounds. In practice, transaction costs and minimum sizes bound the number of rounds, and actual leverage sits below this — close enough to serve as an upper bound.
Worked example
One million becomes four
- Equity
- USD 1.0m
- LTV used per round
- 75 %
- Liquidation threshold
- 80 %
Leverage = 1 / (1 − 0.75) = 4. Total position about USD 4m, USD 3m of it borrowed. The buffer to the threshold is, on paper, only a few percent of collateral price decline.
Four times the position, four times the return effect — and a buffer that barely survives an ordinary trading day.
Reading: The return figure on such a position is not comparable with that of an unleveraged position in the same market. Putting them side by side compares two different risks through the same percentage.
Interactive model
The worked example, with movable figures. Estimate first what happens — then check.
Leverage from repeated borrowing
Each round borrows against the previous one — leverage approaches 1 / (1 − LTV) and the buffer shrinks.
Estimate first, then check
Estimate first: how many rounds does it take at 75 % LTV to reach 3.9× leverage? And what collateral price decline is enough for liquidation at 4× leverage and an 80 % threshold?
The starting values are the worked example's own figures — change one input at a time.
Leverage after these rounds: 3.9×. Limit 1 / (1 − LTV): 4×. Buffer to liquidation: 7.0%.
What the model does not show: Every round borrows against the same collateral in the same market. Interest on the loan, gas per round and a second oracle for the borrowed asset are missing; the buffer is therefore more likely too large than too small.
Retrieval
Exercise on real data
Open a lending market, read its maximum loan-to-value and compute the leverage it theoretically permits. Record what that says about the market overall.
Look at loan-to-value and utilization →Application
How do you report the effective leverage of a book that also contains products levering internally?
Related case studies
Institutional reading
- Bank
- Is looked-through leverage of products held captured in the risk report?
- Asset management
- Does the mandate permit leverage — and does the limit apply on a look-through basis?
Metrics in this lesson
Key takeaways
- Repeated borrowing creates leverage with no single large loan.
- The return grows linearly with leverage while the price buffer shrinks.
- The market's leverage reaches an unleveraged position too — through utilization.