What a Single 3.07x Hides: From Mechanism to Distribution

Description and use

A single 3.07x amplification was presented as a definitive result, but it is actually the median of a distribution ranging from -15% to -32%. Adding a Monte‑Carlo shell reveals the full risk picture and shows how interventions affect tail risk.

Problem

Risk reports often present a single amplification factor (e.g., 3.07x) for a shock, ignoring the inherent uncertainty and producing misleading headlines.

Outcome

The single 3.07x amplification is the median of a distribution ranging from -15% to -32%, with a 1‑in‑100 tail near -28%. The distribution framework shows that interventions compress the tail but leave the median unchanged.

Workflow

• 1. Define priors for net gamma (mean -0.666, σ 0.15, range -1.0 to 0.0) and shock size (mean -5%, σ 2%, range -12% to -1%).
• 2. Set number of Monte Carlo paths to 2,000 with a fixed random seed for reproducibility.
• 3. For each path, sample a gamma and a shock from their priors.
• 4. Run the deterministic dealer‑gamma spiral for the sampled inputs.
• 5. Record the resulting drawdown for each path.
• 6. Aggregate results to produce a distribution of drawdowns and compute exceedance probabilities.
• 7. Report the median, p10, p1, worst‑case, and EP curve to provide a comprehensive risk picture.
• 8. Compare intervention scenarios (e.g., flow cut) within the same distribution framework to assess tail compression.
• 9. Publish the updated findings and source code on GitHub.
• 10. Solicit reader feedback to refine priors and model assumptions.

Evidence

The single 3.07x is the median of a distribution that runs to -32%.

Source

The EP curve says it in the form a risk report actually uses: P(drawdown ≤ …).

Source