Naive Diversification: Risk vs Number of Holdings (2D)

Portfolio Composition

Number of holdings N 12

Average pairwise correlation ρ̄ 0.30

Average stock volatility σ̄ 30%

Live Readouts

Portfolio risk σₚ

17.3%

Systematic floor

16.4%

Risk reduced

42.3%

Diversifiable left

5.5%

How it works

For an equally-weighted portfolio of N stocks with average individual variance σ̄² and average pairwise correlation ρ̄, portfolio variance is:

σₚ² = σ̄²/N + ρ̄·σ̄²·(N-1)/N

As N → ∞:  σₚ² → ρ̄·σ̄²   (systematic risk floor)

The first term is unsystematic (diversifiable) risk — it shrinks as 1/N because independent, idiosyncratic swings cancel out across holdings. The second term is systematic (market) risk — it survives no matter how many stocks you hold, because it comes from the average correlation between them, not their number.

N slider — sets how many equally-weighted holdings are in the portfolio; the wheel of holding dots and the marker on the risk curve update instantly.
ρ̄ slider — average correlation between any two holdings. Higher correlation thickens the correlation web between the dots and raises the systematic floor the curve flattens toward; a negative value fades the web and can push the floor toward zero.
σ̄ slider — average volatility of a single holding, which sets the curve's starting height at N = 1 and the size of the central risk disc.
Animate — grows the portfolio one holding at a time from N = 1 to N = 60 so you can watch the curve fall and flatten in real time.
Drag / scroll on the diagram — pan and zoom the view; nothing about the math changes, it just lets you inspect the wheel or the curve more closely.

This is why textbook advice caps out around 20–30 stocks for "enough" diversification: past that point you are mostly just holding market (systematic) risk, which no amount of naive diversification removes — only hedging or holding uncorrelated asset classes does.

Individual holdings Portfolio risk disc (σₚ) Risk-vs-N curve · current N marker

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