Portfolio Diversification Calculator

MPT-based expected return, volatility, Sharpe ratio, Monte Carlo simulation & correlation analysis

PRESET PORTFOLIOS
ASSET ALLOCATIONTotal: 100%
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$
EXPECTED ANNUAL RETURN —
Portfolio Volatility—
Sharpe Ratio—
All-Stocks Return10.00%
Diversification Benefit—
1-yr 95% VaR—
10-yr Projected Value—
E(Rp) = Σ(wᵢ × Rᵢ)
Sharpe = (Rp − Rf) ÷ σp

Portfolio vs. Benchmarks

Expected return & volatility compared to classic benchmark portfolios

PortfolioExp ReturnVolatilitySharpe

Asset Class Details

AssetWeightExp ReturnVolatilityCorr vs US

Correlation Matrix

Lower correlation = better diversification. Green = low, Red = high.

Risk Assessment

Risk Score —
Concentration Risk—
Largest Position—
Bond / Equity—
Sharpe vs 60/40—

Scenario Analysis

Monte Carlo Simulation —

300 simulations showing P10 (conservative) / P50 (median) / P90 (optimistic) outcomes over your projection horizon

Projection Settings

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Projection Results

Projected Portfolio—
Total Contributed—
Investment Gains—
Inflation-Adj Value—

Portfolio Growth vs. Benchmarks

Model Portfolio Comparison

PortfolioExp ReturnVolatilitySharpeProjected Value

How to Use This Calculator

1
Set Your Allocation

Enter weights for each asset class — they must sum to 100%. Start with a preset (60/40, All-Weather, etc.) then customize. The total badge turns green when your allocation is valid.

2
Review Risk Metrics

Expected return, volatility, and Sharpe ratio quantify your portfolio's risk-adjusted performance. Explore the Risk & Analysis tab for Monte Carlo simulation and correlation breakdown.

3
Project Long-Term Wealth

Use the 30-Year Projector tab to model your portfolio growth with monthly contributions. Compare against the S&P 500 and 60/40 classic to see the long-term impact of your allocation.

Key Formulas

E(Rp) = Σ(wᵢ × Rᵢ) — weighted average return
σ²p = Σ Σ (wᵢ × wⱼ × σᵢ × σⱼ × ρᵢⱼ) — portfolio variance
Sharpe = (Rp − Rf) ÷ σp
VaR (95%) ≈ Rp − 1.645 × σp

Key Terms

Sharpe Ratio — Return above risk-free rate per unit of risk. >1.0 = excellent; 0.5–1.0 = good; <0.5 = acceptable.
Volatility — Standard deviation of annual returns. Measures how much the portfolio swings year to year.
VaR (95%) — Value at Risk: worst-case 1-year loss at 95% confidence. A −12% VaR means you'd expect worse only 1 in 20 years.
Correlation — How two assets move together (−1 to +1). Lower = better diversification. Bonds/stocks near 0 is ideal.
HHI (Concentration) — Herfindahl-Hirschman Index. Sum of squared weights. >4000 = high concentration; <2500 = well diversified.
Monte Carlo — Thousands of random simulations to model probability distribution of outcomes, showing optimistic/median/pessimistic paths.

Portfolio Diversification: The Only Free Lunch in Investing

Nobel Prize winner Harry Markowitz famously said that diversification is "the only free lunch in investing." By combining assets with low correlations, you reduce portfolio risk without proportionally reducing expected returns. This calculator implements the core mathematics of Modern Portfolio Theory (MPT) to show exactly how different allocations trade off risk and return.

Understanding Expected Return and Volatility

A portfolio's expected return is the weighted average of each asset's expected return. Volatility, however, is NOT simply the weighted average of individual volatilities — it's lower when assets have low correlations. A 60/40 portfolio has roughly 10–12% volatility vs. ~16% for 100% US stocks. That 4–6% reduction in volatility with nearly identical long-run return is the mathematical proof of diversification's value.

The Sharpe Ratio and Risk-Adjusted Performance

The Sharpe ratio measures return per unit of risk: (Return − Risk-Free Rate) / Volatility. The S&P 500 has historically achieved Sharpe ratios of 0.4–0.5 over long periods. The 60/40 portfolio often achieves 0.5–0.7 because bonds dramatically reduce volatility. Higher is better, but Sharpe should always be paired with absolute return consideration — a very low-risk, low-return portfolio can have a high Sharpe but won't build meaningful wealth.

Monte Carlo Simulation Explained

Deterministic projections show one possible outcome. Monte Carlo simulation runs hundreds of randomized scenarios using your portfolio's expected return and volatility, revealing the full distribution of outcomes. The P10 line represents the pessimistic 10th percentile; P90 the optimistic 90th. Real portfolios follow a random walk — this range is a far more honest picture than a single line.

Common Model Portfolios Compared

The 60/40 portfolio is the classic balanced allocation with ~150 years of data. The 80/20 targets higher long-term growth for investors with 20+ year horizons. Ray Dalio's All-Weather portfolio (30% stocks, 55% bonds, 7.5% gold, 7.5% commodities) is designed to perform acceptably in all four economic quadrants (growth, recession, inflation, deflation). The three-fund portfolio (US stocks + international + bonds) is the Bogleheads' passive investing cornerstone.

Frequently Asked Questions

How many stocks do I need for a diversified portfolio?

Research shows 20–30 stocks across different sectors eliminates most unsystematic risk. However, a single low-cost index fund providing 500–3,000 stock exposure is the simplest and most cost-effective approach for most investors.

What is the best asset allocation?

There's no universal answer — it depends on your time horizon, risk tolerance, and goals. A common rule: "110 minus your age" in stocks. For 20+ year horizons, 70–90% stocks has historically outperformed. Shorter horizons benefit from more bonds.

What is a good Sharpe ratio?

Above 1.0 is excellent, 0.5–1.0 is good, 0.2–0.5 is acceptable. The S&P 500 has historically achieved 0.4–0.5. The 60/40 portfolio often achieves 0.5–0.7 due to the significant volatility reduction from bonds.

Should I include international stocks?

Yes. US stocks represent ~60% of global market cap. International diversification has historically reduced volatility and captures returns in markets that outperform the US in certain periods. Most target-date funds include 20–40% international exposure.

How often should I rebalance?

Annual or semi-annual rebalancing is sufficient for most investors. Some use a "threshold" approach — rebalancing when any asset class drifts more than 5% from target. Tax-efficient rebalancing uses new contributions and tax-advantaged accounts to minimize taxable events.

What is Value at Risk (VaR)?

VaR estimates the maximum likely loss over a given period at a specific confidence level. A 1-year 95% VaR of −12% means you'd expect to lose more than 12% only 1 in 20 years historically. It helps calibrate whether you can emotionally handle the portfolio's downside risk.

Why does the All-Weather portfolio include gold?

Gold has historically had low or negative correlation with stocks (around −0.05) and moderate positive correlation with bonds in inflationary environments. Ray Dalio's All-Weather portfolio uses gold as an inflation hedge that performs when both stocks and bonds struggle simultaneously — particularly during stagflation.

Is the 60/40 portfolio dead?

The 60/40 had its worst year in decades in 2022 when both stocks and bonds fell simultaneously due to inflation. However, over long periods, the diversification benefit of bonds remains statistically sound. The portfolio returned over 15% in 2023. Most financial economists still recommend bond allocation for investors within 10–15 years of retirement.

What happens to diversification in a market crash?

In severe crashes, correlations typically rise — assets that normally move independently tend to fall together as investors sell everything. This is called "correlation breakdown." The 2008 crisis demonstrated that even diversified portfolios fell significantly. Only cash, short-term treasuries, and gold reliably maintained value.

How do I know my risk tolerance?

Risk tolerance has two components: capacity (how much loss you can financially absorb) and willingness (how much volatility you can emotionally handle). Test: if your $100,000 portfolio dropped to $65,000, would you stay the course or sell? If you'd sell, your equity allocation may exceed your actual risk tolerance.

Do REITs improve portfolio diversification?

REITs have moderate correlation with stocks (0.6–0.7), providing some diversification while offering higher dividend yields. A 5–15% REIT allocation can improve risk-adjusted returns, though REITs are highly sensitive to interest rate changes and may underperform in rising-rate environments.

What is factor investing?

Factor investing tilts a portfolio toward characteristics historically associated with higher returns: small cap, value, profitability, momentum, and low volatility. Academic research (Fama-French model) supports these as risk premiums. Factor ETFs allow investors to systematically capture these tilts at low cost.

Should I use target-date funds?

Target-date funds automatically shift from aggressive to conservative as you approach retirement. They're excellent set-it-and-forget-it solutions. Expense ratios are low (0.05–0.15% at Vanguard/Fidelity), rebalancing is automatic, and they implement sound diversification theory without requiring active management.

How does Monte Carlo simulation work?

Monte Carlo runs hundreds of random simulations of your portfolio using the expected return and volatility. Each simulation draws random annual returns from a normal distribution matching your portfolio's parameters, then compounds them over time. The result shows the full range of possible outcomes — not just the average.

What correlation between bonds and stocks should I expect?

Historically, bonds and stocks have had low or negative correlation (−0.1 to +0.2), which is why 60/40 works so well. However, in 2022, both fell simultaneously due to inflation, showing correlation can turn positive in certain regimes. This is the key risk of bond diversification — it's not infallible.

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