QuantAMM

Summary

The trend portion calculation in the _getWeights function deviates from the whitepaper specification for the channel-following strategy. The deviation involves an additional division by 2⋅𝑆, which reduces the magnitude of the trend contribution. This discrepancy impacts the behavior of the trend-following component, particularly for larger price gradients, leading to potential underperformance in capturing trends.

Vulnerability Details

The whitepaper defines the trend portion as:

In the _getWeights function, the following steps calculate the trend portion:

1. Absolute Gradient Calculation

This computes ∣𝑔∣, the absolute value of the price gradient, as required

1. Scaling the Absolute Gradient

Here, the absolute gradient is scaled down by 2⋅𝑆. This step is not specified in the whitepaper.

1. Exponentiation

The scaled gradient is raised to the power of the exponent

1. Reintroducing the Sign

1. Combining with the Envelope

The division by 2⋅𝑆 during the scaling step artificially reduces the magnitude of the trend portion. This scaling is not part of the whitepaper’s formula, leading to smaller contributions from the trend-following component, especially for larger price gradients.

Impact

The division by 2⋅𝑆 dampens the trend portion’s magnitude. As a result:

• For small gradients, the trend portion may become negligible, diminishing the system’s ability to respond to subtle market trends.

• For large gradients, the reduced trend magnitude may fail to capitalize on significant directional changes.

Tools Used

Manual Review

Recommendations

Remove the division by 2⋅𝑆 in the scaling of the absolute gradient

If the division by 2⋅𝑆 is intentional (e.g., for stability or design constraints), document this deviation in the code and any associated documentation to ensure transparency.