Compare allocations, model covariance risk and plan dollar rebalancing with explicit assumptions.
Current and target weights
Normalization is an explicit edit; no weights are changed automatically.
AssetCurrent (%)Target (%)
US Stocks
International Stocks
Bonds
REITs
Gold
Commodities
USD inputs use whole cents. Percentages accept up to 10 decimal places for weights and 8 for model assumptions.
Modeled annual return
Annual standard deviation (%/year)
Sharpe ratio
Equity blend mean (%)
Modeled volatility reduction (pp)
Normal 5% lower return
Normal 95% loss magnitude
10-year constant-factor value (USD)
Illustrative defaults reviewed 2026-10-20; edits are your model assumptions, not verified market data or forecasts. Cash earns the entered risk-free rate with zero modeled volatility.
Standard deviation measures dispersion. The normal 5% lower return is mean minus 1.645 standard deviations; the loss magnitude is max(0, minus that return). Neither is a maximum loss or a guarantee. Normal tails can imply losses beyond 100%; this is a limitation of that approximation.
Rebalancing ledger
Dollar allocations use largest-remainder whole-cent rounding in asset order. Buys minus sales equals new cash. Taxes, fees, spreads and brokerage execution are excluded.
Editable model assumptions
Illustrative defaults reviewed 2026-10-20; edits are your model assumptions, not verified market data or forecasts. Cash earns the entered risk-free rate with zero modeled volatility.
Correlation pair editor
Each pair updates both symmetric entries. The diagonal is fixed at 1.
Allocation comparison
All allocation comparisons use the same entered returns, volatilities, correlations and risk-free rate. These are scenarios, not recommendations.
Before / after assumptions, with current weights fixed
Correlation matrix
Covariance inputs (%²/year)
Return-assumption sensitivity
Asset return means shift by −4, 0 or +4 percentage points; covariance, weights and the cash rate stay unchanged. These are illustrative assumptions, not bear/base/bull forecasts.
Asset details
Seeded simulation
Annual-moment-matched lognormal
Independent monthly lognormal draws; seeded pseudorandom samples; empirical P10/P50/P90 use linear interpolation. Sample percentiles differ from analytic quantiles. The middle 80% band excludes tails and is not a forecast or the full range of outcomes.
Ready to simulate.
Projection settings
The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.
Legacy illustration uses (1 + mean − SD²/2)^(1/12). It preserves the earlier deterministic convention and does not match the simulation distribution.
Projection
Value (USD)
Contributed (USD)
Gain / loss (USD)
Inflation-adjusted value (USD)
Constant-factor projection and contributions
Allocation comparison
Reviewed share link
Review the allocation and assumptions below before copying a link. Dollar amounts are omitted unless you explicitly include them.
US StocksInternational StocksBondsREITsGoldCommoditiesResidual cashCurrentTargetBuy / sellAssetAnnual arithmetic mean (%)Annual standard deviation (%/year)Sharpe ratioNormal 5% lower returnNormal 95% loss magnitudeModeled volatility reduction (pp)Undefined at zero volatilityUnavailableCheck the highlighted fields and model assumptions.Choose a total of exactly 100%, use Normalize, or select residual cash.Weights exceed 100%. Leverage is not enabled.Weights must be 0–100%, with at most 10 decimal places.This correlation matrix is not positive semidefinite. Risk outputs are unavailable; valid allocation arithmetic remains available.Correlation must be between −1 and 1, with at most 8 decimal places.Enter a risk-free rate from −100% to 1000%, with at most 8 decimal places.Returns must be −100% to 1000%; standard deviation must be 0–200%, with at most 8 decimal places.Enter USD amounts from 0 to 1,000,000,000, in whole cents.Projection years must be an integer from 1 to 50; inflation must be −99% to 100%.Check the projection assumptions.A −100% arithmetic mean with nonzero standard deviation cannot define this lognormal model.The legacy growth factor must be nonnegative.This scenario exceeds the supported numerical range.Use 100–5000 simulations and a whole-number seed from 0 to 4294967295.Simulation unavailable. No simulated results have been substituted.Simulation cancelled.Ready to simulate.Simulations completedfinish at or above nominal contributionsYearContributed (USD)Gain / loss (USD)Inflation-adjusted value (USD)Value (USD)Weight (%)Risk contribution (pp)Marginal volatility (pp per unit weight)Before assumption editCurrent assumptionsPortfolioHypothetical allocationAssumptions reviewedCurrency: USDSummary copied.Copy failed. Select the reviewed text to copy it.Complete valid inputs before using this action.Seeded simulationConstant median-factor illustrationLegacy illustrationSample P10Sample P50Sample P90SeedSimulation countAllocation policyExactly 100%Residual cashTotalNormalization is an explicit edit; no weights are changed automatically.Illustrative defaults reviewed 2026-10-20; edits are your model assumptions, not verified market data or forecasts. Cash earns the entered risk-free rate with zero modeled volatility.Standard deviation measures dispersion. The normal 5% lower return is mean minus 1.645 standard deviations; the loss magnitude is max(0, minus that return). Neither is a maximum loss or a guarantee. Normal tails can imply losses beyond 100%; this is a limitation of that approximation.Dollar allocations use largest-remainder whole-cent rounding in asset order. Buys minus sales equals new cash. Taxes, fees, spreads and brokerage execution are excluded.The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.Independent monthly lognormal draws; seeded pseudorandom samples; empirical P10/P50/P90 use linear interpolation. Sample percentiles differ from analytic quantiles. The middle 80% band excludes tails and is not a forecast or the full range of outcomes.Legacy illustration uses (1 + mean − SD²/2)^(1/12). It preserves the earlier deterministic convention and does not match the simulation distribution.Inputs stay in this browser by default. No financial input values are written to the URL automatically. A reviewed share link is public to anyone who receives it. No account or holdings connection is used.Review the allocation and assumptions below before copying a link. Dollar amounts are omitted unless you explicitly include them.All allocation comparisons use the same entered returns, volatilities, correlations and risk-free rate. These are scenarios, not recommendations.Selected assetProjection settingsAllocation and rebalancingRisk and assumptionsProjectionEditable model assumptionsCorrelation pair editorRebalancing ledgerAllocation comparisonProjection ledgerCurrent, target and required dollar tradesModeled volatility versus expected returnConstant-factor projection and contributionsSeeded simulation percentilesCurrent allocation including residual cashCovariance inputs (%²/year)Correlation matrixPortfolio scenario reportInclude portfolio value, new cash and projection dollar amountsCopy reviewed linkCancel sharingReviewed share linkNormalize target to 100%Normalize current to 100%Use current as targetNew cash to invest (USD)Portfolio value (USD)Risk-free rate (%/year)Run seeded simulationCancel simulationUse these assumptions as before-edit baselineAsset detailsBefore / after assumptions, with current weights fixedNet trades (USD)Buys (USD)Sales (USD)Model limitationsUSD inputs use whole cents. Percentages accept up to 10 decimal places for weights and 8 for model assumptions.How to handle unallocated weightProjection conventionAnnual-moment-matched lognormalLegacy deterministic illustrationInitial investment (USD)Month-end contribution (USD)Projection yearsInflation (%/year)Reset inputs to defaultsExpected return = Σ(wᵢ × μᵢ); volatility = √(wᵀΣw); Sharpe = (mean − risk-free rate) / volatility.Return-assumption sensitivityAsset return means shift by −4, 0 or +4 percentage points; covariance, weights and the cash rate stay unchanged. These are illustrative assumptions, not bear/base/bull forecasts.Allocation concentration index (sum of squared percentage weights)Input format: 1,234.56Input format: 1.234,56Equity blend mean (%)10-year constant-factor value (USD)
Weights change only when you edit them or choose Normalize. Choose exactly 100% or explicitly treat unallocated weight as cash.
2
Editable model assumptions
Illustrative assumptions reviewed 2026-10-20 are editable and are not live forecasts. All allocation comparisons use the same entered assumptions.
3
Rebalancing ledger
Whole-cent dollar allocations use largest-remainder rounding. Buys minus sales equals new cash; taxes, fees and brokerage execution are excluded.
4
Risk and assumptions
Annual standard deviation measures dispersion. Normal 5% lower return is mean minus 1.645 standard deviations. This percentile is not a maximum loss.
5
Projection
The default lognormal model matches annual arithmetic mean and SD. Deposits occur at month end; the constant median-factor line is an illustration, not a forecast.
Standard deviation measures dispersion. The normal 5% lower return is mean minus 1.645 standard deviations; the loss magnitude is max(0, minus that return). Neither is a maximum loss or a guarantee. Normal tails can imply losses beyond 100%; this is a limitation of that approximation.
Projection
s² = ln(1 + (σ/(1+μ))²); m = ln(1+μ) − s²/2
The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.
Reviewer: Calculover Editorial Review - Source and limitation review
Last reviewed: 2026-08-10
Last verified: 2026-10-20
Data effective: 2026-10-20
Methodology
Expected return = Σ(wᵢ × μᵢ); volatility = √(wᵀΣw); Sharpe = (mean − risk-free rate) / volatility. The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.
Assumption: Illustrative defaults reviewed 2026-10-20; edits are your model assumptions, not verified market data or forecasts. Cash earns the entered risk-free rate with zero modeled volatility.
Assumption: All allocation comparisons use the same entered returns, volatilities, correlations and risk-free rate. These are scenarios, not recommendations.
Assumption: USD inputs use whole cents. Percentages accept up to 10 decimal places for weights and 8 for model assumptions.
Assumption: The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.
Assumption: Independent monthly lognormal draws; seeded pseudorandom samples; empirical P10/P50/P90 use linear interpolation. Sample percentiles differ from analytic quantiles. The middle 80% band excludes tails and is not a forecast or the full range of outcomes.
Assumption: Legacy illustration uses (1 + mean − SD²/2)^(1/12). It preserves the earlier deterministic convention and does not match the simulation distribution.
Limitations & guidance
Standard deviation measures dispersion. The normal 5% lower return is mean minus 1.645 standard deviations; the loss magnitude is max(0, minus that return). Neither is a maximum loss or a guarantee. Normal tails can imply losses beyond 100%; this is a limitation of that approximation.
Dollar allocations use largest-remainder whole-cent rounding in asset order. Buys minus sales equals new cash. Taxes, fees, spreads and brokerage execution are excluded.
Inputs stay in this browser by default. No financial input values are written to the URL automatically. A reviewed share link is public to anyone who receives it. No account or holdings connection is used.
Professional guidance: Portfolio Diversification Calculator is for investment math education only and is not investment, tax, legal, or financial advice. Consider risk, fees, taxes, and suitability before acting.
Weight (%) ↗Weights change only when you edit them or choose Normalize. Choose exactly 100% or explicitly treat unallocated weight as cash.
Annual arithmetic mean (%) ↗Illustrative assumptions reviewed 2026-10-20 are editable and are not live forecasts. All allocation comparisons use the same entered assumptions.
Annual standard deviation (%/year) ↗Annual standard deviation measures dispersion. Normal 5% lower return is mean minus 1.645 standard deviations. This percentile is not a maximum loss.
Sharpe ratio ↗Sharpe is modeled annual excess return divided by annual standard deviation. It is undefined at zero volatility and does not establish personal suitability.
Correlation matrix ↗The correlation matrix must be symmetric, have a unit diagonal and be positive semidefinite. Invalid matrices block risk results, while valid allocation arithmetic remains.
Constant median-factor illustration ↗The default lognormal model matches annual arithmetic mean and SD. Deposits occur at month end; the constant median-factor line is an illustration, not a forecast.
Seeded simulation ↗Seeded monthly lognormal draws run in a cancellable worker. Sample P10/P50/P90 use linear interpolation; they are not exact analytic quantiles or the full range of outcomes.
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Scenarios
Real-World Examples
2 worked examples▸
P1
Hypothetical allocation 1
60/40
US Stocks 60%Bonds 40%Risk-free rate (%/year) 4.5%Portfolio value (USD) 100000 USD
μ = 7.8%; σ = 9.8954535%; Sharpe = 0.3334865; q₀.₀₅ = −8.4780210%. Illustrative assumptions reviewed 2026-10-20 are editable and are not live forecasts. All allocation comparisons use the same entered assumptions.
P2
Hypothetical allocation 2
50/50
US Stocks 50%Bonds 50%Risk-free rate (%/year) 4.5%Portfolio value (USD) 100000 USD
μ = 7.25%; σ = 8.5440037%; Sharpe = 0.3218632; q₀.₀₅ = −6.8048862%. Illustrative assumptions reviewed 2026-10-20 are editable and are not live forecasts. All allocation comparisons use the same entered assumptions.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
All allocation comparisons use the same entered returns, volatilities, correlations and risk-free rate. These are scenarios, not recommendations.
Allocation and rebalancing
▸
Normalization is an explicit edit; no weights are changed automatically.
Illustrative defaults reviewed 2026-10-20; edits are your model assumptions, not verified market data or forecasts. Cash earns the entered risk-free rate with zero modeled volatility.
Risk and assumptions
▸
Standard deviation measures dispersion. The normal 5% lower return is mean minus 1.645 standard deviations; the loss magnitude is max(0, minus that return). Neither is a maximum loss or a guarantee. Normal tails can imply losses beyond 100%; this is a limitation of that approximation.
Projection
▸
The default lognormal model matches entered annual arithmetic mean and standard deviation: s² = ln(1 + (SD/(1+mean))²), m = ln(1+mean) − s²/2. Monthly log returns use m/12 and s/√12. Deposits occur at month end. The deterministic line applies the constant median growth factor; with contributions it is not the exact median of terminal wealth.
Independent monthly lognormal draws; seeded pseudorandom samples; empirical P10/P50/P90 use linear interpolation. Sample percentiles differ from analytic quantiles. The middle 80% band excludes tails and is not a forecast or the full range of outcomes.
Rebalancing ledger
▸
Dollar allocations use largest-remainder whole-cent rounding in asset order. Buys minus sales equals new cash. Taxes, fees, spreads and brokerage execution are excluded.
Model limitations
▸
Inputs stay in this browser by default. No financial input values are written to the URL automatically. A reviewed share link is public to anyone who receives it. No account or holdings connection is used.
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Questions
Frequently Asked Questions
8 questions▸
Allocation policy?+
Weights change only when you edit them or choose Normalize. Choose exactly 100% or explicitly treat unallocated weight as cash.
Risk and assumptions?+
Annual standard deviation measures dispersion. Normal 5% lower return is mean minus 1.645 standard deviations. This percentile is not a maximum loss.
Editable model assumptions?+
Illustrative assumptions reviewed 2026-10-20 are editable and are not live forecasts. All allocation comparisons use the same entered assumptions.
Projection?+
The default lognormal model matches annual arithmetic mean and SD. Deposits occur at month end; the constant median-factor line is an illustration, not a forecast.
Seeded simulation?+
Seeded monthly lognormal draws run in a cancellable worker. Sample P10/P50/P90 use linear interpolation; they are not exact analytic quantiles or the full range of outcomes.
Legacy illustration?+
Legacy illustration uses (1 + mean − SD²/2)^(1/12). It preserves the earlier deterministic convention and does not match the simulation distribution.
Rebalancing ledger?+
Whole-cent dollar allocations use largest-remainder rounding. Buys minus sales equals new cash; taxes, fees and brokerage execution are excluded.
Reviewed share link?+
Inputs stay in this browser by default. Sharing opens a disclosure preview; dollar amounts are excluded unless explicitly selected. No brokerage connection is used.
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