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
Every asset class is set to the average of the 4 forecasting houses that publish a view on it: J.P. Morgan, BlackRock, Research Affiliates and AQR. Each house's figures are brought up to today's market prices before they are averaged, because a forecast written last autumn was written against last autumn's bond yields and share prices. Prices were last read on 2026-08-23.
These are forward-looking estimates for 10 to 15 year annualized returns rather than historical averages. The houses build them from current valuations, yield levels, earnings growth and macroeconomic models, and they are the same figures institutional investors, pension funds and endowments use for strategic asset allocation.
You can run the whole tool on any single house instead, or type your own numbers over the top, and whichever you choose is stamped on every projection. The full reasoning, the research behind it and what our own tests showed is set out separately.
What we take from each house
For each of the 42 asset classes, we carry:
- Geometric (compound) expected return — the annualized return you'd expect to earn over a 10–15 year horizon, accounting for the drag of volatility.
- Arithmetic expected return — the simple average of annual returns, and the input our Monte Carlo sampler consumes. Always higher than geometric due to volatility drag. Where a source publishes only a geometric figure, we derive the arithmetic one with a lognormal-exact conversion — approximately geometric + (volatility² / 2) at normal volatilities, but materially less at Bitcoin-level volatility, where the simple formula overstates the gap.
- 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.
- Pairwise correlations — a full 42×42 correlation matrix describing how assets move together. This is the foundation of diversification math.
Asset universe
The platform includes 42 asset classes spanning global equities (25), fixed income (9), alternatives (7), and cash (1). Three UK-only GBP bond classes from the original J.P. Morgan data were removed to keep the universe USD-denominated and globally relevant. 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.
Bitcoin
Bitcoin is not forecast by any of the houses. Its assumptions are Portfolio Lab estimates set at the conservative end of the institutional range (VanEck, Bitwise, CF Benchmarks, ARK, BlackRock, Fidelity): 15.0% geometric expected return (21.8% arithmetic, lognormal-consistent), 42.5% annualized volatility, positive skew (0.80), and moderate excess kurtosis (2.0). Correlations to traditional assets are estimated from empirical data and research literature (e.g., 0.35 to US large cap, −0.05 to bonds, 0.15 to gold).
Risk-free rate
The risk-free rate used for Sharpe ratio calculations follows whichever assumption set is in force rather than being fixed. On the default it is currently 4.19%, which is what the market prices cash to average over the horizon. It used to be pinned at J.P. Morgan's published 3.10%, which meant a maximum-Sharpe optimisation was rewarding risk it was not being paid for by the difference.
Our own equity forecasts
The Asset Class Forecaster produces Portfolio Lab's own ten-year expected return estimates for individual equity markets, built from CAPE valuations published by Research Affiliates and dividend yields from MSCI index factsheets. These sit alongside the J.P. Morgan assumptions rather than replacing them. The full forecaster methodology sets out the arithmetic, every data source, and the limitations of the approach.
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 — 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 (expected return − risk-free rate) / volatility. Every answer is checked against scipy's SLSQP solver in the test suite, so a drift in our solver fails the build rather than reaching you.
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 — 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 — 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
All optimization methods in Portfolio Lab support constraints that keep the output practical and investable:
- 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 42×42 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 — 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 23 years of actual monthly returns (January 2002 to December 2025), covering the GFC, COVID crash, 2022 rate shock, 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 — 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. The correlation matrix used in Portfolio Lab reflects long-term average relationships, not stress-period correlations. This means the model may underestimate downside risk in severe market events.
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 — powered by J.P. Morgan 2026 capital market assumptions.
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