Blueberry Risk Methodology

This blog post provides a summary of Gauntlet’s risk methodology for leveraged borrowing on Blueberry. We note that this is a pre-launch methodology that will be refined over time. Future analysis of post-launch data will give us more information as to how to optimally model protocol risk-reward and user behavior.

Definitions

To start, we review a few definitions that are used in the methodology. We use the variable D to represent the initial debt value of a position and C to represent the initial isolated collateral value. The leverage ratio L is then given by L = D / C. We use the variable P to represent the collateral of a position, excluding the isolated collateral portion. The position risk is then represented by R = (D - P) / C. Liquidation is triggered if R is greater or equal to the liquidation threshold and insolvency occurs when R > 1.

Liquidation Threshold

In this part, we only consider empirical user positions. Based on a snapshot of current user positions, we find the liquidation thresholds that maximize borrowing power conditional on a fixed tolerance for insolvency. This adjustment requires a 5 step process, as shown below. 

1. Iterate over possible liquidation thresholds (eg. 50%, 55%, 60%, etc.)
2. Simulate a large number of asset price trajectories for each liquidation threshold setting, as shown in the chart below

3. Compute the percentage of trials that went insolvent, given existing user positions
4. For each position, select the highest liquidation threshold such that the rate of insolvent trials is less than or equal to the specified tolerance. This maximizes user borrowing power and protocol revenue conditional on a fixed tolerance for risk.
5. Finally, since liquidation thresholds are set based on the isolated collateral asset, we aggregate the results to obtain the maximum liquidation threshold for each isolated collateral type. This balances the risk-reward tradeoff proportional to the value of existing user positions.

Given the new liquidation thresholds, we then proceed to update leverage ratios, max position sizes, and max aggregate position sizes. 

Leverage Ratio

In this step, we consider all hypothetical future position configurations. For a given strategy, taking all the possible combinations of borrowed and isolated collateral assets gives us a single position configuration. We repeat this process for all strategies.

1. For each hypothetical future position, iterate over potential leverage ratios (eg. 2, 3, 4, etc.)
2. Simulate a large number of asset price trajectories for each liquidation threshold setting
3. Using the liquidation thresholds derived in the previous step, compute the percentage of trials that went insolvent.
4. For each position, select the highest leverage ratio such that the rate of insolvent trials is less than or equal to the specified tolerance. This maximizes user capital efficiency conditional on a fixed tolerance for risk.

The relationship between strategy type, insolvency tolerance, and leverage ratio is shown in the chart below.

Max Position Size

If slippage increases with size, the max position size can be calculated directly from the slippage function, liquidation threshold, and leverage ratio. In this framework, the max position size is equal to the size at which slippage fully offsets the profitability of a liquidation. After choosing the leverage ratio for each strategy and collateral asset, we directly compute the max position size, as shown in the chart below.

Max Aggregate Position Size

Our standard supply cap methodology for lending protocols places an upper bound on the amount of an asset that can be designated as collateral and therefore sold upon liquidation. We derive the maximum aggregate position size for a given strategy by applying the supply cap methodology to the underlying assets and isolated collateral, excluding any components that are not relevant to Blueberry.

Collateral Weights

Seized collateral is comprised of collateral and isolated collateral assets. To compute the relative amount of each, we require a ratio of their values. For instance, if this ratio is 2:1, then the collateral comprises 2/3 of the value of the assets sold, and the isolated collateral comprises 1/3 of this value. Using the variables as defined in the intro, we can calculate the ratio as:

Blueberry Money Market

The Blueberry Money Market is a conventional money market that facilitates leveraged borrowing via the Blueberry protocol. Since users do not interact with the Blueberry Money Market directly, most parameters used in typical money market protocols are not relevant here. We use our standard methodology for setting supply caps, similar to the Max Aggregate Position Size discussed above. At present, we do not extend our methodology to any other parameters, as they do not affect the functioning of the market as designed.

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