Enabling Short Selling in Bonding Curves — Part 2
This is Part 2 of a series. Other Parts can be found in the list:
Part 1: Overview of Short Selling Design in Bonding Curves
Part 2: Simple Scenario with Single Short Position
Part 3: Complex Scenario with Multiple Short Positions
Part 4: Performance & Privacy Improvement
Part 2: Simple Scenario with Single Short Position
In this part, we start with a simple scenario: one short seller has one single short position. We will explore the challenges and develop some solutions.
1. What is the Challenge?
The most critical challenge is “Short Squeeze”[1][2], where the token price moves up and short sellers are forced to close their short positions. In particular, the broker contract should guarantee that short sellers can pay back the borrowed bonded tokens and interests to the lenders in any situation.
As shown in the diagram, the short sellers sold borrowed tokens at price A and pushed the token price to B. The shaded area represents the number of reserved tokens from this sale. If there are new buy transactions and the token price moves up to C, the short seller cannot buy back the same amount of bonded tokens using the received reserved tokens. As such, the short seller cannot cover his short position and the lender loses money.
2. Deposit of Collaterals
The risk of a short squeeze increases as the token price fluctuates. If there is no buffer layer available, short sellers cannot tolerate any price increase.
To this end, short sellers are required to deposit a certain amount of reserved tokens as collaterals, which will be used to purchase bonded tokens in case of a price increase. It has been illustrated in the below diagram:
The red shaded area represents the collateral deposit that is used to cover the short position at a higher price, where the sale of short selling is not enough. Clearly, more collateral deposit indicates short sellers can tolerate more fluctuation in token price; otherwise, they will be forced to cover short positions with a very small price increase.
3. Threshold Price
The short seller desires to delay the time point when the short position must be covered in case of the increasing token price. They will have more time to wait and cover the short position when the token price moves below his short selling price to make a profit.
I , the lender will take more risk of losing his bonded tokens at the same time, because the short position may never be able to be covered due to the high token price.
To resolve this conflict of interest, we introduce “threshold price” to figure out the latest moment that the short position must be covered:
Let us define some variables for illustration purpose:
- S: the number of reserved tokens from the sale of short selling;
- C: the number of reserved tokens as a collateral deposit;
- k: the number of bonded tokens that had been sold in short selling;
- f(x): the analytic formula that defines the Bonding Curve, where x is the number of bonded token supply;
- Pt: the threshold price implies that the short position must be covered when the token price reaches this price;
- N: the token supply corresponding to the threshold price Pt;
- I: the maximum value of the accumulated interest that the short seller needs to pay the lender.
We can define the equation to describe the constraint as:
This formula implies that the cost of reserved tokens used to cover the short position at the threshold price Pt should not exceed the total available fund for purchase, which is the sum of sale proceeds S and collateral deposit C excluding the maximum value of the accumulated interest I.
With this formula, we can solve for the variable N and further calculate the threshold price Pt = f(N). Therefore, when the token price increases and reaches the threshold price Pt, the short seller must cover the short position to return the borrowed bonded token and pay the interests to the lender.
The threshold price represents the highest token price that the short seller can tolerate before he is forced to cover the short position.
Note that the threshold price will be updated when the loan-shifting happens. This is because the short seller needs to pay extra interest to the new lender and the variable I changes accordingly.
4. Single Short Position Scenario
Let us consider the scenario:
- one short seller has sold the borrowed bonded tokens and made the collateral deposit to the broker contract.
- there is a new “buy” transaction from the users, which will move the token price upward.
This is the exact moment the broker contract needs to determine whether the short position should be covered. Specifically, the broker contract will first calculate the token price after the new “buy” transaction is executed, and then compare this calculated price with the threshold price of the short position.
There are two different scenarios as shown in the figure below. The yellow shaded area shows the new “buy” transaction that pushes up the token price to be higher, while the blue shaded area indicates the covering of short position at the threshold price.
If these two shaded areas have overlap, the short position must be covered. Otherwise, the short position can remain to be open.
- Left Scenario: the short position does not need to be covered because the price after the new “buy” transaction is lower than the threshold price. The short seller can tolerate more price increase and securely cover the short position in the future.
- Right Scenario: the short position must be covered first because the price after the new “buy” transaction is higher than the threshold price. The short seller has no way to securely cover the short position if the “buy” transaction is executed and moves the token price up.
In the Right Scenario, the buyer of the new “buy” transaction may get a higher token price because the covering of short position moves up the token price. Therefore, the broker contract may need to confirm the new purchase token price with the buyer before executing the “buy” order. If the buyer disagrees with the new price, both transactions can be canceled.
5. Reference
[1] “Short Squeeze”, Wikipedia, https://en.wikipedia.org/wiki/Short_squeeze
[2] James Chen, “Short Squeeze”, Investopedia, Dec 8, 2017. https://www.investopedia.com/terms/s/shortsqueeze.asp
