The Asymmetric Efficiency Index (AEI)

Rethinking Performance Efficiency

For anyone who has been with me for a while—or anyone new to Acrux—the foundation of everything we do centers on how efficiently we can produce alpha while maintaining disciplined risk control.

It’s not just about making money. It’s about how intelligently those returns are produced—how much upside we achieve per unit of realized downside.

Traditional risk metrics such as Sharpe, Sortino, or even Calmar, while valuable, all share a common flaw: they measure averaged volatility, not realized asymmetry. They don’t capture the shape of outcomes—the difference between convex (efficient) and concave (inefficient) performance.

That’s why I created the Asymmetric Efficiency Index (AEI).

The Why Behind AEI

The Asymmetric Efficiency Index is designed to measure the convex efficiency of a strategy—how often and how powerfully it captures gains that are meaningfully larger than its losses.

AEI expresses not just whether a system wins, but how efficiently it converts risk into asymmetrical results.

It quantifies the essence of a high-convexity strategy: Fewer, smaller, controlled losses + greater frequency and/or larger gains = intelligent asymmetry.

How AEI Is Calculated

The AEI uses a downside-anchored baseline to define “meaningful performance". That baseline ensures that the measurement reflects real-world risk exposure, not statistical noise.

Step 1 – Establish the Baseline

• Take the worst weekly loss and the average losing week.

• Compute the midpoint between them:

  Baseline = (Worst Week + Average Losing Week) ÷ 2

• Flip the sign of that baseline to make it positive (for the gain side).

  • Example: Worst week = –7.0%, Avg losing week = –2.5% → Baseline = –4.75%.

  • The AEI threshold for upside is +4.75%, while downside evaluation still uses –4.75%.

Step 2 – Count Frequency

• Count how many weeks produced gains above +4.75% (AEI-positive weeks).

• Count how many weeks produced losses below –4.75% (AEI-negative weeks).

• The frequency ratio = #(weeks above threshold) ÷ #(weeks below threshold).

Step 3 – Measure Magnitude

• Sum all positive returns above +4.75%.

• Sum all negative returns below –4.75%.

• The magnitude ratio = Total Gain ÷ Total Loss (absolute values).

Step 4 – Combine Them

AEI = (Frequency Ratio + Magnitude Ratio) ÷ 2

This creates a single metric that expresses how efficiently the strategy converts limited downside exposure into concentrated upside results.

Example: 15-Week Sample

Week	Weekly Return %
1	0.8%
2	2.4%
3	4.7%
4	–1.9%
5	0.3%
6	3.8%
7	–2.1%
8	1.5%
9	5.2%
10	–3.4%
11	0.9%
12	2.7%
13	–1.1%
14	3.0%
15	1.9%

• Worst week = –3.4%, Avg losing = –2.1% → Baseline = –2.75%

• Positive threshold = +2.75%, Negative threshold = –2.75%

Frequency ratio: 5 weeks above threshold ÷ 2 weeks below = 2.5 Magnitude ratio: +14.8 ÷ –7.5 = 1.97 AEI: (2.5 + 1.97) ÷ 2 = 2.24 Result: The strategy exhibits strong convex efficiency—moderate frequency, solid magnitude advantage.

AEI Interpretation Framework

< 1.0 — Concave / Inefficient  

• Negative asymmetry; performance is concave.  

• Strategy fails to convert volatility into upside efficiency.  

• Comparable to sub-1.0 Calmar or Sharpe ratios.

1.0 – 2.0 — Neutral to Slight Efficiency  

• Mildly positive balance between risk and reward.  

• Limited but emerging convexity; risk control offsets most downside.  

• Comparable to steady, risk-balanced portfolios or low-volatility quant systems.

2.1 – 3.0 — Moderate Upside Asymmetry

• Noticeable convex behavior with consistent upside skew.  

• Drawdowns remain contained while gains begin to compound meaningfully.  

• Similar to well-optimized systematic or tactical trading programs.

3.1 – 5.0 — High Convexity (Excellent)  

• Strongly convex and volatility-efficient.  

• Resilient across multiple market regimes.

• Aligns with top-decile quantitative or volatility-managed funds.

5.1 – 7.5 — Elite Asymmetric Efficiency  

• Exceptional convexity and drawdown asymmetry.  

• Reflects a highly optimized asymmetric structure.  

• Institutional-grade performance, top 1–2 percent of strategies.

7.6 – 10 — Exceptional Convex Efficiency (Ultra-Asymmetric Tier)

• Rare, extreme convexity; sustained non-linear gain capture.

• Typically achieved during peak crisis-alpha or volatility-harvesting phases.

10 — Outlier Convexity

 • Extreme convex performance, beyond sustainable norms.

 • Typically indicates transient market conditions or highly specialized convex overlays.

Notes

 • AEI > 2  sustained over 12+ months indicates a true convex architecture, not statistical luck.

 • AEI 3 – 5 represents durable, high-efficiency alpha — the most scalable and sustainable performance zone.

 • AEI 5 – 7 reflects elite-level convexity and institutional-grade efficiency.

 • AEI 7 – 10 indicates ultra-asymmetric performance, typically achieved by top 1–2 percent of live strategies.

 • AEI > 10 represents outlier convexity, often tied to short-term or highly specialized conditions.

 • Pair AEI with Calmar to show multidimensional risk efficiency.

How to Read It

Metric	What It Represents
AEI (Asymmetric Efficiency Index)	Combined frequency + magnitude score relative to a dynamic downside baseline.
AEI Baseline Threshold (±)	Midpoint between worst and average losing weeks; flipped positive for upside comparison.
% of Weeks AEI Threshold Breached	How often the strategy produced returns beyond that “meaningful performance” zone.
% of Total Gains from AEI Weeks	Share of all profits generated during asymmetric weeks—illustrating convex concentration.
AEI Gain : Non-AEI Gain Ratio	How much more efficient AEI weeks are versus all other profitable weeks.

Practical Examples

AEI	AEI Baseline (±)	% Weeks Above	% Gains from AEI Weeks	AEI Gain : Non-AEI Ratio
2.99	2.45%	27%	56%	1.27
8.23	4.98%	33%	87%	6.80

Interpretation:

• In the first case, 27% of weeks delivered 56% of all profits — healthy convexity.

• In the second, one-third of the weeks at 33% produced nearly 90% of total gains — elite convex structure.

• The far right ration column shows the ratio and sums up the distribution of gains net gains (gains after losses) that are captured in total during AEI periods versus non-AEI periods.

• Higher AEI values will correlate to higher AEI to non-AEI ratios. This tells you that when market conditions are right, the strategy is able to truly capitalize on more extreme volatility periods (whether expansion or compression) and hold the line, or even make more modest profits in consolidation periods, or when directional clarity is absent.
  

AEI in Practice

AEI isn’t about curve-fitting or chasing high numbers. It’s about quantifying what most managers only describe qualitatively: the quality of asymmetry.

It complements, rather than replaces, existing measures:

• Sharpe shows return vs. volatility.

• Calmar shows return vs. drawdown.

• AEI shows return vs. convexity — how efficiently you turn downside into upside. s strategies mature, AEI often moderates — reflecting refined risk allocation, not diminished performance. Early high AEI phases typically reflect opportunistic convex periods; sustained AEI above 3.0 indicates structural efficiency.

  
  

  Final Thoughts

  The Asymmetric Efficiency Index embodies our central philosophy:

Performance should be measured not only by returns, but by the intelligence of the risk that created them.

By anchoring efficiency to downside reality and measuring convex output, AEI provides a clear, intuitive window into how well a strategy compounds asymmetrically — week after week.

It’s not about chasing every move. It’s about engineering asymmetrical outcomes.