# Limitations on Leverage

PTN currently sets limits on leverage utilization that are similar to those offered by various exchanges. This allows our miners to start with very low leverage and expand their positions significantly. We mitigate the risks associated with high leverage by normalizing their returns relative to the highest drawdown witnessed over the previous 30 days. This helps us translate their trades into pure signals, allowing us to evaluate the long-term risk-to-reward ratio of our miners.

## Problem Statement

We have shown through simulation that our drawdown system of returns normalization will prune out a miner as they approach and exceed a drawdown limit in real-time. However, there is a nonzero chance that a Martingale strategy will not implode in the current 30 day window used for miner evaluation. While this doesn’t pose an existential threat to the system as the drawdown protects the network model from runaway inflation, it represents a sub-optimality. Given that strategies like naive Martingale are guaranteed to implode at some point, their net contribution to the system is closer to zero, as the system will absorb some level of loss less than 5% as they are pruned away. As such, we want to statistically reduce their probability of acheiving incentive along with other risky strategies whose leverage usage resembles a risk skewed distribution.

There are a few ways to accomplish this:

- Reduce the leverage boundaries
- Increase the time horizon of measurement
- Restrict the drawdown window used for risk normalization
- Restrict the rate of change on leverage utilization for a position

Increasing the time horizon of measurement from 30 days to 60 days is already on our our roadmap. Coupled with a greater emphasis on long-term returns relative to short-term returns, this increase will give us more time to evaluate the quality of each strategy and ensure that those capable of capturing long-term returns will succeed.

Restriction on the drawdown window is an implicit and imperfect way to restrict runaway leverage usage. While it may help reduce the probability of high leverage events by reducing incentives earlier, it doesn’t eliminate the possibility of extreme leverage events.

Likewise, restricting the rate of change of leverage utilization may limit our miners’ ability to embed expression into their strategies, which is particularly challenging for high-frequency traders who might place multiple orders in a short timeframe to respond dynamically to rapid price fluctuations.

Reducing the leverage boundaries seems to be the most appropriate and straightforward solution. The following logic is used to determine the most useful leverage range: Martingale, for example, relies on averaging into a position. In its most naive form, it will double the leverage usage with each new order to move the average purchasing price closer to the current value. Our current drawdown limitations of 0.25% and 5% implicitly set a boundary on leverage usage between 0.03x and 10-20x with BTC. This means that there are around 7 or 8 doubling intervals effectively permitted by the system.

The duration a Martingale might succeed before collapsing is a function of the asset’s volatility, the number of doubling intervals, and the chosen magnitudes of drop on the Martingale before doubling into the position. Our current estimation is that the uppermost duration of success before larger volatilities in the market is around 12 weeks with our current doubling interval. To eliminate its capacity to enter our scoring system, this uppermost duration of success should be closer to half of our 30-day evaluation interval. The risk may therefore be approximated by the number of doubling intervals:

Where Lmax is the maximum leverage available and Lmin is the minimum leverage available for a trade pair. We can approximate the number of doubling intervals, which is a proxy for the level of exposure:

## Proposed Changes

We propose reducing the range of available leverages to a doubling interval capacity of 5. To accomplish this, we will keep the same N doubling interval capacity between all trade pairs. Given crypto’s higher level of volatility, it will have a lower range than what is provided by forex.

### Prior Leverage Limits

Market | Lower Limit | Upper Limit | Explicit Doubling Interval Capacity | Effective Doubling Interval Capacity |
---|---|---|---|---|

Forex | 0.001 | 500 | 18 | 8 |

Crypto | 0.001 | 20 | 14 | 8 |

Indices | 0.001 | 500 | 18 | 8 |

### Proposed Leverage Limits

Market | Lower Limit | Upper Limit | Explicit Doubling Interval Capacity | Effective Doubling Interval Capacity |
---|---|---|---|---|

Forex | 0.1 | 5 | 5 | 5 |

Crypto | 0.01 | 0.5 | 5 | 5 |

Indices | 0.1 | 5 | 5 | 5 |

A drop in the effective doubling capacity from 8 to 5 should drop the upper time boundary by:

This should reduce the uppermost duration of success for Martingale from 12 weeks to less than 2 weeks, which typically isn’t enough time to be competitive with long term returns or receive rewards from the system.

## Additional Information

When the new leverage limits are introduced, existing positions with leverage either above or below the new thresholds will be subject to transition rules:

**Excess Leverage:**If your position’s leverage exceeds the new maximum limit, you will only be allowed to reduce the leverage until it complies with the new maximum threshold.**Deficit Leverage:**If your position’s leverage is below the new minimum limit, you will only be allowed to increase the leverage until it meets the new minimum criteria.

Under both of these circumstances, you will be permitted to gracefully transition to the new threshold by incrementally moving towards the new leverage limits. Positions with leverage already within the new acceptable range will remain unaffected, and closed positions will not be modified. We will continue to monitor leverage usage to identify high-risk strategies and may further reduce leverage limits if necessary.

## Timeline

Proposal Delivery: `July 9, 2024`