Convexity — Understanding Return Shape
The Convexity Score measures whether a position's losses accelerate faster than its gains — the shape of your risk, not just the size.
TL;DR
The Convexity Score measures whether a position's losses accelerate faster than its gains — the shape of your risk, not just the size.
Why This Exists
Two investments can have identical expected returns and identical standard deviations but completely different risk profiles. A covered call has concave returns (losses accelerate in a crash) while a long put has convex returns (gains accelerate). Convexity scoring captures this distinction.
How It Works
Convexity Score = 50 + (25 x skewness) - (10 x excess_kurtosis_penalty)
Clamped to 0-100. Positive skewness = convex (good). Negative skewness = concave (losses accelerate).
Example: skewness = +0.8, no excess kurtosis: 50 + (25 x 0.8) = 70 — convex strategy.
Example: skewness = -1.2, kurtosis penalty = 5: 50 - 30 - 50 = 0 (clamped) — deeply concave with fat tails.
What You See in the Platform
Each volatility strategy card shows a convexity badge: "Convex" (65+), "Linear" (35-64), or "Concave" (0-34). The portfolio view aggregates convexity and flags concave portfolios.
Where to Go Next
Read IV Regime for the volatility environment modifier, or Constraint-Based Allocation for convexity constraints.
Next up
IV Regime — How Implied Volatility Adjusts Projections
Track your learning progress in Aethon Terminal
Sign Up Free