How all of it works.
Portfolio Lab is built on institutional-grade portfolio construction techniques. This page explains every method, data source, and assumption behind the platform in plain English, with enough detail for practitioners who want to know exactly what's happening under the hood.
1. Data Sources & Assumptions
Where the default return forecasts come from
The default is Current benchmark models: dated market observations combined with explicit growth, valuation, financing and fee assumptions. Equity, bond, cash and alternative models use the method appropriate to their exposure. Assumptions is the shared workspace for inspecting those calculations and changing their supported inputs.
Choose a three-, five- or ten-year forecast horizon and a central, lower or upper sensitivity. These are annual planning assumptions, not guaranteed returns or probability bounds. Your selected rates feed portfolio analytics, optimization, simulation and reports; historical backtests continue to use historical observations.
Published forecasts from J.P. Morgan, BlackRock, Research Affiliates and AQR remain separate comparisons. You can select a reference source or enter your own final returns. In the current model, changing a building block recalculates its forecast and clears that asset’s final-return override. Existing results need a rerun. See the exact method, source dates and limitations for every asset class.
What the shared assumptions contain
For each of the 57 asset classes, we carry:
- Geometric (compound) expected return: an annualized growth assumption for the selected horizon. A current cash-flow scenario, a published reference estimate and a user forecast have different evidence behind them; none is a guaranteed outcome.
- Arithmetic expected return: the simple average of annual returns, and the input our Monte Carlo sampler consumes. At least as high as geometric under the same distribution; equal when returns do not fluctuate. We derive a reference arithmetic mean from the selected compound assumption and volatility using the lognormal moment identity. This conversion is exact for that reference distribution; it is not an empirical estimate of the source model’s arithmetic mean. The published source columns remain reference forecasts.
- Annualized volatility: the standard deviation of annual returns, measuring how much the asset bounces around its expected path.
- Skewness: whether the distribution of returns leans left (negative skew, more crash risk) or right (positive skew, more upside surprise). Most equities have negative skew.
- Excess kurtosis: how “fat” the tails are compared to a normal distribution. Higher kurtosis means more extreme events than a bell curve would predict.
- Correlations: a full 57×57 matrix describing how assets move together, estimated from the available return series, adjusted for different histories and regularised into a valid matrix. Private-asset appraisal smoothing and benchmark differences limit those estimates. This is the foundation of diversification math.
Average return and compound growth
Fourteen additional local bond classes use current issuer portfolio observations in sterling, euros or Canadian dollars: UK gilts and short gilts; euro-area, Italian and German government bonds; sterling and euro corporate bonds; euro high yield and covered bonds; Canadian short, universe and long bonds; and a plain euro aggregate. German government inputs match their historical fund proxies. The covered-bond row uses a German Pfandbriefe proxy, so it does not claim to represent the whole euro-area market. Source benchmark names and dates are checked on each daily refresh.
These local bond forecasts subtract rating-based credit allowances from current yield. Euro-area national sovereigns use S&P’s foreign-currency default convention; UK and Canadian federal debt use local-currency priors. Aggregate funds publish separate rating and sector totals. Their central allowance assumes independence, while a range shows every possible pairing of those totals. Other aggregate sectors and covered bonds retain conservative corporate-rating proxies; these are unresolved calibration limits, not cover-pool or issuer-level models. Canadian and State Street inputs are reported as yield to maturity, without claiming they are yield to worst. All fourteen have an unhedged flat-exchange-rate case and a separately calculated hedge using the bond portfolio’s actual currency and dated financing rates. No second house FX adjustment is added.
A cash-flow IRR or an annualised scenario is not automatically a statistically estimated average return. Our current cash-flow and terminal-value models supply conditional compound-growth assumptions. We calibrate a lognormal reference distribution to that growth rate and the selected volatility; this is a modelling assumption, not proof that the scenario is the expected outcome. Factor models instead build average annual returns and convert them to compound growth once. Published-reference and user-entered compound forecasts are not given a second volatility deduction.
For a portfolio, average annual returns are weighted across holdings. Portfolio variance includes their correlations. We then convert the basket’s average return and volatility to a compound-growth approximation. Averaging individual compound returns would miss diversification’s effect. A basket of assets is not exactly lognormal: the displayed figure assumes constant weights and moment matching. Simulations can differ with rebalancing schedules, fat tails, withdrawals and changing conditions. The displayed growth estimate is not a guaranteed return or the mean of every possible finite-horizon CAGR.
Return targets and growth projections use compound growth. Sharpe ratios use average annual excess returns. Simulations start from average annual returns so fluctuations enter compounding through their generated paths rather than through a second manual deduction. All asset classes, including local and currency-hedged variants, use this same convention.
Asset universe
The dollar table holds 57 asset classes spanning global equities (27), fixed income (16), alternatives (13), and cash (1). The equity count includes 14 value and growth sleeves, which only Research Affiliates forecast and which are carried as a style spread against their parent index rather than as standalone levels.
The available catalogue depends on the investor currency. The sterling view carries 73 asset classes, including UK Gilts, UK All Cap, UK Cash and UK Inflation-Linked Bonds. Currency and hedge choices affect the forecast and risk inputs, not just the symbol beside the amount. Current models, published-reference rows and source coverage have different currency treatments, documented in the currency methodology. Unsupported forecasts are labelled rather than silently substituted.
Bitcoin
Bitcoin is not forecast in the published CMA comparison rows used here. Its return is Portfolio Lab's own adoption scenario, not a consensus or a calibrated probability. The reference USD row carries 15.0% geometric expected return (21.8% arithmetic, lognormal-consistent), 42.5% annualized volatility, positive skew (0.80), and excess kurtosis (2.0). The reference USD correlation matrix has 0.35 to US large cap, 0.11 to bonds and 0.10 to gold. These describe a model, not fixed relationships that markets must follow. Bitcoin is also available in other investor currencies. Your selected currency, model settings and return override determine the active figures shown in Assumptions.
Historical currency-hedge financing
Monthly hedged histories add the previous month's short-term interest-rate differential to the underlying asset return. For April 2020, the USD source has no financial commercial paper observation. We use the Federal Reserve's published 90-day AA nonfinancial commercial paper rate, 0.98% a year, for that month only. This has the same currency, maturity and credit rating but different borrowers, so it is a financing proxy, not an observation of the missing series. It restores the May 2020 hedge calculation without interpolating share or bond returns. Other missing observations are not automatically filled.
How correlations are estimated, and what is inferred
Correlations combine observed public-market returns and explicitly modelled private-fund risk histories within the calibration window, 2006-07 to 2025-06. The assets do not all have that much history: Bitcoin's usable series starts in 2010, China A-shares in 2013, and the unlisted alternatives are valued by appraisal once a quarter rather than daily.
Unhedged histories include exchange-rate changes in the selected investor currency. Private quarterly returns use consecutive quarter-end rates; any appraisal adjustment is applied in the source currency first. Missing exchange-rate observations shorten the usable history. The six private-fund models use institutionally anchored volatility and benchmark correlation together, with empirical residual dependence. Full appraisal reconstructions remain comparison cases. QAI is a liquid hedge-fund backtest proxy, not the broad fund risk source. Model-implied histories are not historical investment performance. Private currency hedges use quarterly funding differentials known at the previous quarter end; missing rates are not automatically filled.
Estimating each pair over whatever window its two assets happen to share sounds like the careful thing to do, and it produces a table that is not a valid correlation matrix. There is no single set of returns behind an estimate built that way, so nothing forces the cells to agree with each other, and ours did not: every base arrived with 15 to 24 impossible relationships that had to be repaired before an optimiser could use it.
We use Stambaugh's method (1997) instead. Assets are grouped by when their history begins. The longest-running group is measured directly and sets the sample. Regime weights enter the means, factor extraction, fitted relationships and residual risk consistently. Each later group is then regressed on the assets already placed, over the years they do share, and that relationship is carried back across the full sample. The assembled matrix is positive semidefinite by construction. A final eigenvalue floor and diagonal rescaling provide numerical stability for optimisation.
The honest caveat. This means a short-history asset's correlations for the years before it existed are inferred, not observed. Bitcoin has no 2008 return, and no method can invent one. What the method does is ask how Bitcoin has related to assets that were around in 2008, and carry that relationship back. Other estimators and shorter common samples make different trade-offs. A short private-market sample can produce sensitive fitted relationships, even with a valid matrix. Positive semidefiniteness establishes mathematical consistency; it does not prove forecast accuracy or stable future correlations. You should know which rows rest on inferred history. The rows that do are the ones whose series start late, which the assumptions table shows for every asset.
Risk-free rate
Sharpe ratios measure average annual return above the cash assumption in force, divided by portfolio volatility. The workstation uses the cash row from your active assumptions and investor currency. That rate can change with the model inputs or your edits, so there is no single permanent cash number for every portfolio. Check the active cash assumption and the captured result basis alongside any Sharpe comparison.
Our own equity forecasts
Assumptions is the home for Portfolio Lab's active return forecasts and their editable building blocks. Current equity models use benchmark income, per-share growth assumptions and a terminal valuation. Published house forecasts remain separate reference choices. The historical CAPE research and valuation sensitivities do not turn those references into current institutional forecasts. The asset-by-asset methodology identifies each active model, its sources and limitations.
2. Optimization Methods
Portfolio optimization is the mathematical process of selecting asset weights that maximize expected return for a given level of risk, or minimize risk for a given return target. It uses expected returns, volatilities, and correlations to find the combination of assets that sits on the efficient frontier.
Portfolio Lab offers five optimization methods. Each approaches the problem from a different angle. No single method is universally best, and the right choice depends on your confidence in the inputs and your investment philosophy.
Maximum Sharpe Ratio
What it does: Finds the portfolio with the highest risk-adjusted return, the best return per unit of risk. This is the classic “tangency portfolio” from Modern Portfolio Theory, sitting at the point where a line from the risk-free rate is tangent to the efficient frontier.
How it works: The optimizer uses projected gradient descent to search the space of allocations, subject to your constraints, for the combination that maximizes (average annual return − risk-free rate) / volatility. Regression scenarios are checked against scipy's independent SLSQP solver, with additional closed-form and constraint checks. These tests cover representative cases; they are not a proof of optimality for every possible set of inputs.
When to use it: When you trust the return assumptions and want the mathematically optimal risk-return trade-off.
Key insight: This method is sensitive to return estimates. Small changes in expected returns can produce large changes in allocations. That's why Portfolio Lab also offers methods that don't rely on return forecasts.
Minimum Variance
What it does: Finds the portfolio with the lowest possible volatility, regardless of expected return. This is the leftmost point on the efficient frontier.
How it works: The same projected gradient solver, but the objective is simply to minimize portfolio variance (the weighted sum of all pairwise covariances). Return assumptions are used only for reporting, not for the optimization itself.
When to use it: When you want the smoothest possible ride and are willing to accept lower returns. Good for defensive portfolios or when you distrust return forecasts entirely.
Key insight: Because it ignores returns, minimum variance is more stable than Max Sharpe, because the output changes less when assumptions are revised.
Risk Parity
What it does: Allocates so that every asset contributes equally to total portfolio risk. Instead of equalizing dollar amounts (like equal-weight), it equalizes risk contributions.
How it works: Cyclical coordinate descent, following Griveau-Billion, Richard and Roncalli (2013): each asset's weight is solved in turn so that its marginal contribution to portfolio volatility matches its target, holding the others fixed, and the sweep repeats until nothing moves.
When to use it: When you want true diversification across risk sources, not just across dollar amounts. Risk Parity typically results in higher bond allocations than traditional 60/40 because bonds are less volatile.
Key insight: Like Minimum Variance, Risk Parity uses only volatilities and correlations, with no return assumptions needed. This makes it robust to the biggest source of estimation error in portfolio optimization.
Hierarchical Risk Parity (HRP)
What it does: A machine learning approach developed by MarcosLópez de Prado (2016). It clusters assets by how similarly they behave, then allocates within and across clusters using inverse-variance weighting.
How it works: Three steps: (1) compute a distance matrix from correlations, (2) apply hierarchical clustering to group similar assets into a tree structure, (3) allocate by recursively splitting the tree and weighting branches by inverse variance. No quadratic optimization is needed.
When to use it: When you want a method that's robust to estimation error and doesn't suffer from the instability of traditional mean-variance optimization. HRP handles noisy correlation matrices better than any other method here.
Key insight: Traditional MVO requires inverting the covariance matrix, which amplifies estimation errors. HRP avoids matrix inversion entirely, making it more stable in practice. It also produces more diversified portfolios.
Black-Litterman
What it does: Starts from market equilibrium, the implied returns that would make current market-cap weights optimal, and blends in your personal views with a specified confidence level.
How it works: A Bayesian framework. First, reverse-engineer “equilibrium returns” from market weights using CAPM. Then combine these with your views (e.g., “I think emerging markets will return 2% more than the model suggests”) using the precision of each estimate. The result is a blended set of returns that tilts toward your views in proportion to your confidence.
When to use it: When you have specific views about certain assets but want a stable starting point. Black-Litterman solves the biggest practical problem with MVO: that small changes in return inputs cause wild swings in allocations.
Key insight: With no views, Black-Litterman produces the market portfolio. With 100% confidence views, it converges toward Max Sharpe on your custom returns. It's a dial between “trust the market” and “trust my analysis.”
3. Constraints
Maximum Sharpe, Minimum Variance and Black-Litterman apply the custom rules below. Risk Parity and Hierarchical Risk Parity ignore those custom rules and produce unconstrained comparisons; their results should not be read as satisfying your mandate. All methods keep weights non-negative and fully invested.
- Per-asset minimum and maximum bounds. Default is 0-100% for each asset. You can set custom minimums (e.g., “at least 5% in gold”) or maximums (e.g., “no more than 30% in any single equity region”).
- Group constraints. Limit total allocation to a category, for example, cap total equities at 60% or total alternatives at 20%.
- “Require All Selected” toggle. When enabled, every asset you've selected receives a minimum 0.5% allocation. This prevents the optimizer from zeroing out assets you specifically chose to include. Custom per-asset minimums take priority over this default.
- Weights sum to 100%. All methods enforce full investment, no cash drag unless you explicitly include cash as an asset.
4. Monte Carlo Simulation
Monte Carlo simulation is a technique that generates thousands of random future scenarios for a portfolio by sampling from a statistical model of asset returns. Instead of projecting a single average outcome, it produces a distribution of possible outcomes, showing the range of what could happen and the probability of each result.
Portfolio Lab's Monte Carlo engine accounts for the randomness of returns, the drag of inflation, and the impact of contributions or withdrawals over time.
Return generation
Each simulation path samples annual returns from a lognormal distribution, the standard model in finance, which ensures returns can't fall below −100%. But real-world returns aren't perfectly lognormal: they have fatter tails (more extreme events) and asymmetry (crashes are more common than equivalent rallies).
To correct for this, Portfolio Lab applies a Cornish-Fisher expansion to each sampled return. This adjusts the normal Z-score using the asset's skewness and excess kurtosis, producing more realistic tail behavior without the complexity of a full fat-tailed distribution model. Most free Monte Carlo calculators skip this step entirely.
Correlated sampling
Assets don't move independently. A stock crash typically coincides with a flight to bonds. Portfolio Lab models this using Cholesky decomposition of the correlation sub-matrix for the assets you actually hold, taken from the full 57×57 matrix. Each year's returns are drawn as a correlated vector, preserving the diversification structure (or lack thereof) between every pair of assets.
Two-phase lifecycle
Simulations model two distinct phases: accumulation (you're contributing monthly, growing the portfolio) and decumulation (you're retired, withdrawing monthly). The transition happens at your specified retirement age. Contributions and withdrawals are distributed proportionally to target weights each month.
Inflation
Inflation is modeled stochastically, not as a fixed number. Each simulation path generates its own inflation trajectory, with 30% correlation to portfolio returns. This captures the real-world relationship between inflation and asset prices, since periods of high inflation tend to coincide with poor equity returns.
Spending strategies
Two withdrawal strategies are supported:
- Fixed: Withdraw a constant inflation-adjusted amount regardless of portfolio performance. The classic “4% rule” approach.
- Guardrails: Dynamically adjust withdrawals based on portfolio performance. If the portfolio grows beyond an upper threshold, spending increases. If it drops below a lower threshold, spending is cut. A floor prevents spending from falling below a minimum.
Configuration
Default: 1,000 simulation paths with annual rebalancing, 0.5% management fee, and 0.1% transaction costs per rebalance. Users can increase to 10,000 paths for smoother percentile estimates. A deterministic seed ensures reproducibility.
5. Backtesting
Portfolio backtesting is the process of applying a portfolio allocation strategy to historical market data to see how it would have performed. It reveals how the portfolio would have behaved through real market crashes, recoveries, and regime changes, providing context that forward-looking models cannot.
Portfolio Lab replays your allocation against actual monthly returns reaching back to1926 for the longest-running asset classes, covering the Great Depression, the 1970s inflation, the GFC, the COVID crash, the January to September 2022 sell-off, and multiple recovery cycles.
How it works
- Monthly returns applied to each asset based on its weight in the portfolio.
- Rebalancing on your chosen schedule: monthly, quarterly, semi-annually, or annually. Alternatively, drift-threshold rebalancing triggers a rebalance only when any asset drifts more than a specified percentage from its target.
- Management fees and transaction costs deducted at each rebalance event.
- Cumulative return, annual returns, drawdowns, and rolling metrics computed for the full period.
Rolling metrics
Two rolling metrics are calculated across the backtest period: trailing 12-month return and trailing 36-month Sharpe ratio. These show how performance and risk-adjusted return evolved over time, rather than collapsing everything into a single number.
6. Risk Metrics
Risk metrics are quantitative measures that describe how much a portfolio could lose, how volatile its returns are, and how well it compensates investors for the risk taken. They translate the abstract concept of “risk” into specific numbers that can be compared across portfolios.
Portfolio Lab computes 15 risk metrics from the Monte Carlo simulation output. Here are the most important ones:
Value at Risk (VaR)
The loss that won't be exceeded with a given probability over a given time period. Portfolio Lab reports VaR at both 95% and 99% confidence levels, for both a single year and the full simulation horizon. For example, a 1-year 95% VaR of −18% means there's only a 5% chance of losing more than 18% in any single year.
Conditional VaR (Expected Shortfall)
While VaR tells you the threshold, CVaR tells you the average loss when that threshold is breached. It answers: “when things go badly, how badly do they go on average?” CVaR is always worse than VaR and is considered a more complete measure of tail risk.
Maximum drawdown
The largest peak-to-trough decline across all simulation paths. Portfolio Lab reports the median max drawdown (typical bad experience), 5th percentile (near-worst case), and 95th percentile (best case). This is often the most intuitive risk measure, because it answers “how much could I lose from the peak before things recover?”
Sharpe and Sortino ratios
Risk-adjusted return metrics computed from the 25th, 50th, and 75th percentile simulation paths. The Sharpe ratio penalizes all volatility equally; the Sortino ratio penalizes only downside volatility, which many investors consider more relevant since upside volatility is desirable.
7. Withdrawal Analysis
Withdrawal analysis determines how much you can safely spend from a portfolio each year in retirement without running out of money. The safe withdrawal rate (SWR) is the highest annual withdrawal, as a percentage of starting portfolio value, that survives a given time horizon with a specified probability.
Portfolio Lab's withdrawal engine runs a full grid of Monte Carlo simulations across 13 withdrawal rates (2% to 8%) and 6 time horizons (15 to 40 years).
Safe Withdrawal Rate (SWR)
The highest withdrawal rate at which the portfolio survives the full horizon in at least X% of simulations, where X is your chosen confidence level. For example, if 95% of simulated paths survive 30 years at a 3% withdrawal rate but only 90% survive at 3.5%, the SWR at 95% confidence is 3%.
Perpetual Withdrawal Rate (PWR)
The withdrawal rate that preserves the portfolio's real (inflation-adjusted) value at the end of the horizon in at least X% of simulations. PWR is always lower than SWR because it's a stricter requirement: not just survival, but maintaining purchasing power.
Survival heatmap
The signature output of the withdrawal analysis: a color-coded grid showing survival probability for every combination of withdrawal rate and horizon. Green cells (>95% survival) are safe. Yellow (80-95%) is marginal. Orange (60-80%) is risky. Red (<60%) means you're likely to run out of money.
8. Limitations & Caveats
No model is a crystal ball. Portfolio Lab is a rigorous quantitative tool, but it has inherent limitations that every user should understand:
Forward-looking assumptions are not predictions
J.P. Morgan's capital market assumptions represent their research team's best estimate of annualized returns over the next 10-15 years. They have a reasonable track record over 30 years of publication, but actual returns in any given period will differ, potentially by a wide margin.
Correlations are not stable
Correlations between asset classes tend to increase during market crises, precisely when diversification is most needed. Our matrix gives recession months 15% of the total weight and high-inflation months 12.5%, which is more than their share of the calendar, so it leans towards stress rather than away from it. That is a partial answer and not a full one: a single matrix cannot hold both a calm regime and a stressed one, and the weighting moves it towards the stressed end rather than modelling the two separately. Treat a crash scenario as the place to look for that, not the correlation table.
Model risk
The lognormal + Cornish-Fisher return model captures skewness and fat tails better than a simple normal distribution, but it cannot model regime changes (e.g., a shift from low to high inflation), structural breaks, or truly unprecedented events. For those scenarios, historical backtesting provides a complementary perspective.
No tax modeling
Portfolio Lab does not model taxes. All returns, withdrawals, and growth projections are pre-tax. In practice, tax-loss harvesting, asset location, and the tax treatment of different account types (taxable, IRA, Roth) can meaningfully affect after-tax outcomes.
Estimation error in optimization
Mean-variance optimization is notoriously sensitive to input estimates. A small change in expected returns can produce a dramatically different allocation. This is why Portfolio Lab offers five methods: comparing results across Max Sharpe, Risk Parity, and HRP gives a much more robust picture than relying on any single optimizer.
See It in Action
All five optimization methods, Monte Carlo simulation, backtesting, and withdrawal analysis, with current benchmark models, visible assumptions and published-house comparisons.
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