Portfolio Diversification Check

Enter allocations and get a plain-language read on concentration, correlation, and estimated volatility.

Worked example — Portfolio Diversification Check

Average relationship	0.27
Estimated annual swing	7.85%
Typical daily move	0.49%
Bets, counting money	1.92
Bets, counting risk	1.21
Bets, counting sources	1.14
Diversification ratio	1.132

These are the values the calculator shows when the page opens. Change any input above to recompute them.

Loading interactive simulation...

Most of your risk sits in the cross terms 🖖

Open the expanded working and the tool ranks the terms of wᵀΣw by size, prints the largest fourteen, and then prints the sum of those fourteen next to the full variance — because the list had to be cut short. The reason it has to be cut short is the arithmetic that makes diversification work at all. With n holdings there are n² terms, and only n of them sit on the diagonal as the assets' own variances; the other n² − n are covariances. The tech-growth preset's four tickers give 4 variance terms against 12 covariances; europe-balanced's six give 6 against 30. Adding one holding adds a single diagonal term and 2n cross terms, so what you mainly buy is exposure to how the newcomer moves with what you already hold.

The weight that splits the risk evenly is 29%, not 50% 🖖

Switch the data to asset classes over all years and the risk table prints the two splits side by side: a 60/40 holds 60% of the money in equities and 92.7% of the variance. Enter 29 and 71 instead — both rows, since the weights are normalised by their sum — and the shares read 50.1% and 49.9%, with portfolio volatility down from 12.12% to 8.02%. That is the first move of risk parity, and it is not free: 29/71 compounds at 6.56% a year against the 60/40’s 8.34%, so a third off the volatility costs about a fifth of the return. Borrowing to lever the bond sleeve back up is the second move, and the reason the strategy needs leverage at all.

A risk share above 100% is what a hedge looks like 🖖

Same two assets, same 60/40, two eras, opposite answers. Set the period to 2000–2012 and equities and 10-year Treasuries come out correlated −0.80: equities carry 124.3% of the variance and bonds −24.3%, and the portfolio’s annual swing is 8.84%. Move to 2013–2025 and the correlation is +0.39, the shares are 80.2% and 19.8%, and the swing is 10.70%. Over all 98 years the correlation reads 0.02 and the swing 12.12% — the average of two regimes that behaved nothing like it, and a hedge you cannot count on having in the decade you need it.

Problem solved in full

Annual swing of 60% SPY and 40% AGG over a 1-year window 6 steps
60% SPY and 40% AGG, over the snapshot's 1-year window. SPY moves 0.7597% on a typical day, AGG moves 0.2591%, and their correlation is 0.2725. Find the portfolio's annual swing — then find out how much of it the correlation actually removed.
1. Weight each daily volatility before anything else, because every term below is built from these 2 products and not from the raw volatilities. The equity leg comes out 4.4 times the bond leg.
  
  $w_{1} σ_{1} = 0.60 \times 0.7597% = 0.45582%, w_{2} σ_{2} = 0.40 \times 0.2591% = 0.10364%$
2. Portfolio variance is not a weighted average of variances. With 2 assets it has 3 terms — one for each asset on its own, plus one carrying the correlation — and that cross term is the only place diversification can act.
  
  $σ_{p}^{2} = (w_{1} σ_{1})^{2} + (w_{2} σ_{2})^{2} + 2 ρ (w_{1} σ_{1}) (w_{2} σ_{2})$
3. Substitute, and look at the sizes before you add them. The SPY term is an order of magnitude larger than either of the other 2.
  
  $= 2.0777 \times 1 0^{- 5} + 1.0741 \times 1 0^{- 6} + 2.5746 \times 1 0^{- 6} = 2.4426 \times 1 0^{- 5}$
4. Take the square root and you are back to a daily percentage, which is what the panel above calls the typical daily move.
  
  $σ_{p} = 2.4426 \times 1 0^{- 5} = 4.942 \times 1 0^{- 3} = 0.49%$
5. Daily variance accumulates in proportion to the number of trading days, so daily volatility scales with the square root of it. The window is 252 trading days.
  
  $σ_{ann} = σ_{p} 252 = 0.4942% \times 15.8745 = 7.85%$
6. Now price the correlation by removing it. Set ρ = 1 and the variance becomes a perfect square, so the 2 weighted volatilities simply add — the same portfolio, with nothing offsetting anything.
  
  $ρ = 1 : σ_{p} = w_{1} σ_{1} + w_{2} σ_{2} = 0.5595% ⟹ 8.88%$
Answer

7.85% a year, from a typical daily move of 0.49%. Lockstep would have given 8.88%, so a correlation of 0.2725 was worth 1.04 percentage points — about 12% of the risk, which is thin for the effect diversification is named after. The decomposition says why: the SPY term alone is 2.0777×10⁻⁵ of the 2.4426×10⁻⁵ total, 85% of the variance, leaving 11% in the cross term and 4% in AGG. Correlation only ever touches that 11%. Drive it to 0 and the swing falls only to 7.42%; move 10 points of weight from SPY to AGG instead and it falls to 6.88%. Against a holding that already is the portfolio, what you own beats what it is correlated with.

$\frac{( w _{1} σ _{1} ) ^{2}}{σ _{p}^{2}} = \frac{2.0777 \times 1 0 ^{- 5}}{2.4426 \times 1 0 ^{- 5}} = 0.851$

Learning path

Risk, measured

Leads to Drawdown and drag the covariance matrix, and the fact that a blend does not inherit the average of its parts’ risks.

References (10)

Portfolio variance as wᵀΣw, which the tool computes term by term: H. Markowitz, "Portfolio Selection." The Journal of Finance 7(1), 77, 1952.
Splitting that variance among the holdings — the decomposition behind the risk-share column, and why the shares sum to the whole: S. Maillard, T. Roncalli and J. Teïletche, "The Properties of Equally Weighted Risk Contribution Portfolios." The Journal of Portfolio Management 36(4), 60–70, 2010.
The diversification ratio the panel reports, and the allocation that maximises it: Y. Choueifaty and Y. Coignard, "Toward Maximum Diversification." The Journal of Portfolio Management 35(1), 40–51, 2008.
The effective number of bets, counted over uncorrelated principal portfolios rather than over holdings: A. Meucci, "Managing Diversification." Risk, 2009.
The correlation breakdown in crashes, and why a calm-window estimate is the wrong one for the day you need it: F. Longin and B. Solnik, "Extreme Correlation of International Equity Markets." The Journal of Finance 56(2), 649–676, 2001.
The same asymmetry measured on US portfolios — correlations rise in down markets and not in up ones: A. Ang and J. Chen, "Asymmetric correlations of equity portfolios." Journal of Financial Economics 63(3), 443–494, 2002.
Why the two solved allocations under the table are estimates and not targets — the sampling error in a covariance matrix: O. Ledoit and M. Wolf, "Honey, I Shrunk the Sample Covariance Matrix." The Journal of Portfolio Management 30(4), 110–119, 2004.
And the measured consequence: out of sample, the optimised weights often lose to equal weights: V. DeMiguel, L. Garlappi and R. Uppal, "Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?" The Review of Financial Studies 22(5), 1915–1953, 2009.
Estimating a covariance is hard; estimating a mean return is much harder, which is why nothing on this page uses one: R. C. Merton, "On estimating the expected return on the market: An exploratory investigation." Journal of Financial Economics 8(4), 323–361, 1980.
The standing objection to reading any of this off one observed market proxy: R. Roll, "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory." Journal of Financial Economics 4(2), 129–176, 1977.

By the 42Math team · Updated 2026-08-19

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

60/40 portfolio - Two holdings, so three terms: one variance each and a single covariance between them. It is the smallest portfolio where diversification can do anything at all, and the worked problem below takes this exact pair apart.
Tech growth - Four tickers, so four variance terms against twelve covariances. The catch is in the holdings rather than the count: QQQ already contains AAPL, MSFT and NVDA, so three of the four names are being bought twice.
Crypto-heavy - BTC and ETH are the position; COIN is a leveraged bet on the same thing, since an exchange earns from crypto volume. Three of the four holdings move on one story, which is concentration wearing four tickers.
All-weather style - Five assets chosen to fail at different times: equities, long Treasuries, gold, commodities and property. That gives twenty covariance terms against five variances, and the twenty are the whole design.
Europe balanced - Six holdings, four of them European equity. VGK and IEUR cover nearly the same market, and EWG and EWU are Germany and the UK, which sit inside both. Six names, and far fewer than six independent bets.
60/40 since 1928
When bonds hedged, 2000-2012