CLT Trade Aggregator

Simulate trades from non-normal distributions and watch batch averages converge to Normal — the Central Limit Theorem made visceral.

Feb 23, 2026, Eric

The Core Idea

Individual trades can follow almost any distribution — skewed, fat-tailed, bimodal. The Central Limit Theorem says that if you average together enough independent trades, the distribution of those averages approaches Normal regardless of the underlying shape. This is why portfolio-level statistics are more reliable than single-trade statistics — and why sample size still matters before you can trust the convergence.

Controls

Underlying trade distribution:

Log-normal-like — long right tail (many small losses, rare big wins)

Trades per batch (N): 30

Larger N → stronger convergence to Normal.

5100200

Number of batches: 200

More batches → smoother histogram of averages.

505001000

Individual Trade Distribution (6,000 trades)

Red dashed = Normal fit overlaid for comparison.

μ = -0.008σ = 1.503skew = 2.545ex.kurt = 9.184

Distribution of 200-Batch Averages (N=30 per batch)

White dashed = Normal fit. The CLT predicts μ_batch = μ, σ_batch = σ/√N.

μ = -0.0077σ = 0.2643 (predicted σ/√N = 0.2744)skew = 0.353ex.kurt = 0.377

Trade skewness

2.545

Batch mean skewness

0.353

Skewness reduction

86%

Convergence Assessment

Near-normal — converging well.

CLT prediction: batch std dev ≈ σ/√N = 0.2744. Observed: 0.2643.