Correlation & Diversification Analyzer

Frequently Asked Questions

What does correlation mean for a portfolio?

Correlation ranges from -1 to +1. Two assets with correlation below 0.7 add meaningful diversification. Most US stocks correlate around 0.5-0.8 with the S&P 500, so adding more US stocks adds little real diversification.

Why does correlation rise during crises?

In sharp drawdowns, investors sell whatever is liquid, and previously uncorrelated assets fall together. In March 2020, even gold and Treasuries briefly fell with stocks. Diversification reduces but does not eliminate tail risk.

What are the lowest-correlation pairs?

Long Treasuries vs. stocks (often -0.2 to -0.4 in normal regimes), gold vs. stocks (near zero long-term), managed futures vs. stocks. Correlations are unstable and shift with the macro regime.

How many stocks does it take to be diversified?

Roughly 25-30 stocks across sectors capture about 90% of the diversification benefit of the full market. Beyond 50 names, marginal benefit is small. Index funds with 500+ holdings are still preferred for cost and tax efficiency.

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Investment Disclaimer: Estimates only. Not investment advice.

This calculator provides estimates for educational purposes only and is not investment advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making investment decisions. All investments carry risk, including potential loss of principal.

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How This Calculator Works

You describe two assets - each with an expected return, a standard deviation (σ, its risk), and a portfolio weight - plus the correlation (ρ) between them. The tool first normalizes the two weights so they sum to 100%, then computes the portfolio's expected return as a simple weighted average. The interesting part is risk: it calculates portfolio standard deviation using the two-asset variance formula, which folds in the correlation term. It compares that figure to the weighted-average risk you would get if the assets were perfectly correlated, and reports the gap as the diversification benefit - the risk you eliminate for free by combining imperfectly correlated holdings. It also reports a Sharpe-style ratio using a 3% risk-free rate.

The Two-Asset Variance Formula

σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ, and portfolio risk is the square root of that variance. Expected return = w₁r₁ + w₂r₂. The third variance term is where diversification lives: whenever ρ < 1, that term shrinks total variance below the weighted average of the individual risks. The Sharpe-like ratio is (portfolio return − 3%) ÷ portfolio σ, rewarding return earned per unit of risk.

Worked Example

Combine US stocks (10% return, 15.5% σ, 60% weight) with 10-year Treasuries (5% return, 7% σ, 40% weight) at ρ = 0.2. Expected return = 0.6×10 + 0.4×5 = 8%. Variance = 0.6²×0.155² + 0.4²×0.07² + 2×0.6×0.4×0.155×0.07×0.2, giving a portfolio σ near 9.7%. If the two were perfectly correlated, the weighted-average risk would be 0.6×15.5 + 0.4×7 = 12.1% - so low correlation cuts roughly 2.4 points, about 20% less risk, with no sacrifice in expected return.

Common Mistakes

Entering weights that do not sum to 100% - the tool normalizes them, but be aware your effective mix may differ from what you typed.

Assuming diversification always works; in the 2008 and 2020 crashes most correlations spiked toward 1, gutting the benefit exactly when it was needed most.

Confusing low correlation with low risk - two volatile assets can still produce a volatile portfolio even when ρ is small.

Using a single historical ρ as if it were stable; correlations drift with regime and time horizon.

Tips & FAQ

Rough long-run correlations: US stocks vs. bonds ≈0.0 to +0.3, vs. developed international ≈+0.85, vs. gold ≈−0.05 (a frequent crisis hedge), vs. REITs ≈+0.65. A ρ of +1 gives zero benefit; 0 gives meaningful benefit; −1 in theory lets risk be eliminated entirely. Harry Markowitz won the 1990 Nobel Prize for formalizing this "free lunch" of risk reduction without giving up return. Treasury bonds and gold remain the most reliable diversifiers in panics. Educational only, not investment advice.

Correlation & Diversification Analyzer

Frequently Asked Questions

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