The Size Tilt — Portfolio Simulator

US large-cap: The biggest US companies — the S&P 500. The bulk of the US market by value.

US small-cap: Smaller US companies. Historically a touch higher return with bigger ups and downs.

Developed large-cap: Large developed-market companies outside the US.

Developed small-cap: Smaller companies in developed markets outside the US.

EM large-cap: Large companies in emerging markets.

EM small-cap: Smaller companies in emerging markets — the widest swings of the stock group.

Bonds: US investment-grade bonds — loans to the government and solid companies that pay interest. Lower return, but far steadier than stocks.

Real estate (REITs): Real Estate Investment Trusts — companies that own income property (apartments, warehouses, malls). Real-estate exposure you can buy like a stock.

Gold: Physical gold. It pays no income, but often holds its value when stocks or the dollar are struggling.

Crypto (Bitcoin): Bitcoin, as the representative crypto asset. Very large swings in both directions. Its expected return here is a long-term estimate, set well below its short early history.

Each simulated month, your portfolio earns a random return based on its blended expected return and volatility. We do that 2,000 times and report the range.

1. Blend your mix into one return + volatility (assuming annual rebalancing): μₚ = Σ wᵢ·μᵢ, σₚ = √(ΣΣ wᵢwⱼσᵢσⱼρᵢⱼ).

2. Annual → monthly: m = (1+μₚ)^(1/12) − 1, s = σₚ/√12.

3. Each month, draw a random return from a lognormal calibrated to (m, s).

4. Grow and add contributions: Bₜ₊₁ = (Bₜ + contribution) × (1 + rₜ), until the "keep investing for" cutoff.

5. Repeat 2,000×; sort the ending values; report the 10th / 50th / 90th percentiles. "Today's dollars" divides by (1.025)^years.

The numbers used (nominal annual return + volatility, ~30-yr history where available):

Asset	Proxy	Return	Volatility
US large-cap	S&P 500	10.3%	15.5%
US small-cap	Russell 2000	11.0%	19.5%
Developed large-cap	MSCI EAFE	5.9%	16.4%
Developed small-cap	MSCI EAFE Small Cap	7.5%	18.5%
EM large-cap	MSCI EM	6.5%	22.2%
EM small-cap	MSCI EM Small Cap	8.5%	25.0%
Bonds	Bloomberg US Aggregate (BND)	4.0%	4.2%
Real estate (REITs)	FTSE NAREIT (VNQ)	8.0%	18.0%
Gold	Spot gold (GLD)	5.0%	15.0%
Crypto (Bitcoin)	Bitcoin (BTC)	15.0%	65.0%

• Method: each figure is the long-run average from roughly 30 years of history (about 1996–2026 for US, developed, emerging, bonds, REITs and gold; Bitcoin uses ~10 years, deliberately moderated well below its short history).
• Sources: index total-return series (VTI, EFA, EEM, BND, VNQ), spot gold and Bitcoin via lazyportfolioetf.com, cross-checked against S&P 500, MSCI and Bloomberg index fact sheets.
• Small/large and growth/value sub-classes are estimated from the matching Russell and MSCI indices; correlations are approximate long-run values.
• Home-country tilt: ~30-year USD total returns (unhedged, so they include currency moves): Canada 8.6% / 20.1%, UK 6.5% / 16.6%, Australia 7.6% / 21.7%, Europe 7.3% / 18.0% (via lazyportfolioetf.com).
• These are historical assumptions, not forecasts.