What it shows: diversification only protects you to the extent your holdings move independently. This simulator builds twelve synthetic assets from a simple factor model (a shared market factor + per-sector factors + asset-specific noise), so in calm markets you see real block structure — assets correlate strongly within a sector and weakly across sectors. A market-stress slider then mixes every pairwise correlation toward 1. As it rises, the equal-weight book's volatility climbs and the effective number of independent bets Neff = N ⁄ (1 + (N−1)ρ̄) falls toward one — the same √-law that caps signal breadth, here capping portfolio diversification.
All series are synthetic and every figure is illustrative — nothing here is a performance claim, a real correlation, or investment advice. The single-/multi-factor model and equal-weight book are teaching simplifications; the stress mixing keeps the matrix a valid (positive-semidefinite) correlation matrix at every level. The empirical regularity it dramatises — that correlations spike in crises — is well documented (Longin & Solnik 2001; Ang & Chen 2002), as is the diversification-ratio lens (Choueifaty & Coignard 2008). Related tools: Signal Combination Simulator · Cointegration & Pairs Trading Simulator · Backtest Overfitting Simulator · Information Coefficient Calculator · Signal Decay Calculator · VPIN & the Volume Clock · Signal Skill Explorer.
Turn up the stress
Twelve assets across three sectors, equal-weighted. Slide market stress from a calm, idiosyncratic-driven market toward a full-blown crisis where everything moves together — and watch the matrix, the volatility, and the number of bets you really have all react live.
0% = a normal market (sector structure intact) · 100% = a crisis (every asset moves as one)
Calm market — the structure is intact
At 0% stress the average pairwise correlation is 0.23, so your twelve equal-weighted assets behave like only 3.4 independent bets. An equal-weight book's volatility is 0.54× a single asset — versus the 0.29× you'd get from twelve genuinely uncorrelated ones. Even now, in calm conditions, you never had twelve real bets — the shared market and sector factors mean you started with about 3.4. Drag the stress toward a crisis and watch even that shrink toward one.
The correlation matrix
Each cell is the correlation between two assets — pale teal is low, red is high. In a calm market the three sectors stand out as hot blocks on a cool background; as stress rises the whole grid reddens, because every pair starts moving together. The diagonal is always 1 (an asset with itself).
How much diversification you actually have
Effective bets
3.4
of 12 nominal holdings
Avg correlation ρ̄
0.23
mean of all off-diagonal pairs
Equal-weight vol
0.54×
vs 0.29× if uncorrelated
Undiversifiable floor
0.48×
√ρ̄ — vol can't drop below this
Within-sector ρ
0.49
same-sector pairs
Cross-sector ρ
0.13
different-sector pairs
Vol reduction
46%
vs holding just one
Bets at full crisis
1.1
at 90% stress
Reading this
The number of holdings is not the number of bets. Twelve assets that share a market and sector factors carry the risk of far fewer — and in a crisis, when correlations rush toward one, that count collapses toward a single bet. It's the same √-law that caps signal combination: only independent exposures count. Real diversification comes from holdings whose drivers genuinely differ — see portfolio construction and risk management for how to budget risk when correlations won't stay still.
Your bets vanish as the crisis builds
The effective number of independent bets, Neff = N ⁄ (1 + (N−1)ρ̄), across the full stress range. You start well below the 12-bet ideal (grey dashed) even in calm markets, and the curve falls toward a single bet as stress approaches a crisis. The teal marker is where your slider sits.
Why more names stop helping
Equal-weight portfolio volatility as you add assets, at the current average correlation. If the assets were uncorrelated (grey dashed) volatility would fall as 1/√N toward zero. At your ρ̄ (blue) it flattens into the floor √ρ̄ (red) — the systematic risk no number of correlated names can diversify away. The higher the stress, the higher that floor.
What to do with this
Whether breadth pays off at your correlation (the c/√ρ ceiling), and when diversification quietly collapses to a single bet.
Read the thinking behind it
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Frequently asked
- Why does diversification fail in a crisis?
- Because correlations rise toward one under stress. The slider mixes every pairwise correlation toward one; as it does, the effective number of independent bets collapses toward one and portfolio volatility approaches a floor set by the average correlation — diversification thins out exactly when you need it.
- What is the effective number of bets?
- A book of N assets at average correlation rho-bar behaves like only N divided by (1 plus (N minus 1) times rho-bar) independent positions. Twelve assets at a calm average correlation of about 0.23 already act like roughly 3.4 independent bets; in a crisis that falls toward one.
- How is the matrix generated?
- From a simple factor model — a shared market factor, per-sector factors, and idiosyncratic noise — producing block structure with higher within-sector and lower cross-sector correlation. The stress mix keeps it a valid (positive semi-definite) correlation matrix throughout.
- Can I map this to my own book?
- Use it qualitatively: reshuffle to see the block structure and drag the stress slider to feel how fast "diversified" positions converge. The lesson — that correlation, not position count, sets your real diversification — transfers to any book.
- Are these real asset correlations?
- No. All twelve assets and their correlations are synthetic and illustrative — not real instruments, and not investment advice.