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.
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.
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