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Tail-Risk Laws: Skewness & Kurtosis in Your Stop-Loss Rules

Tail-Risk Laws: Skewness & Kurtosis in Your Stop-Loss Rules

  • May 25, 2025
  • Posted by: Drglenbrown1
  • Category: Trading Methodology
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Tail-Risk Laws: Skewness & Kurtosis in Your Stop-Loss Rules

Volatility isn’t just about magnitude—it’s also about shape. Introducing Tail-Risk Laws (an extension of Laws 1–7): we integrate skewness and kurtosis of ATR(200) into your stop-loss rules to adapt for asymmetry and fat tails.

Summary

  • How to measure the distribution shape of ATR(200)
  • Applying skew-tilt & kurtosis-scaling across Laws 1–7
  • Setting up alerts and dynamic rule shifts based on regime

Key Sections

  1. Formulas & Rolling-Window Setup
  2. Regime Classification Examples
  3. Live Chart with Shape-Based Buffers

1. Formulas & Rolling-Window Setup

Compute rolling skewness (γ₃) and excess kurtosis (γ₄) over your ATR(200) series using an n-bar window (e.g., n=50):

γ₃ = (1/n) Σ ((x–μ)/σ)³
γ₄ = (1/n) Σ ((x–μ)/σ)⁴ – 3

Where μ and σ are the mean and standard deviation of ATR(200) over the last n bars.

2. Regime Classification Examples

Use skewness and kurtosis to define three regimes:

  • Positive Skew, Low Kurtosis: Smaller downside tails—tighten L & reduce buffer
  • Negative Skew, High Kurtosis: Fat left tail—widen L & buffer
  • Neutral Skew/Kurtosis: Default buffer and exposure settings

3. Live Chart with Shape-Based Buffers

Overlay dynamic bands on price:

buffer = base_exposures × ATR(200)
if skew < –0.5: buffer += buffer×0.10
if kurtosis > +1: buffer += buffer×0.10
plot(EMA(200) ± buffer)

Figure 1 below shows how a high-kurtosis regime expands the buffer (red dashed), while positive skew compresses it (green dashed).

Tail-Risk Laws dynamic buffer overlay
Figure 1: Live chart overlay with shape-based buffer adjustments.

About the Author

Dr. Glen Brown, Ph.D. in Investments & Finance, is President & CEO of Global Accountancy Institute and Global Financial Engineering. With over 25 years in quant research and proprietary trading, he crafted the GATS framework and these Tail-Risk Laws to make stop-loss rules truly adaptive.

Business Model Clarification

GAI & GFE operate solely as internal proprietary trading firms. We do not offer public courses or advisory services; all methodologies serve in-house research.

Risk Disclaimer

Trading derivatives and CFDs carries substantial risk. This article is educational only and is not financial advice. Always conduct your own due diligence and consult a licensed professional. Past performance does not guarantee future results; trade at your own risk.

Hashtags: #Skewness #Kurtosis #TailRisk #ATR #StopLoss #Volatility #GATS #RiskManagement #DrGlenBrown

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