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Typical Correlations
- Stocks vs Bonds: ~0.0 to 0.3
- US vs International: ~0.6 to 0.8
- Stocks vs Gold: ~-0.1 to 0.2
- Same Sector Stocks: ~0.7 to 0.9
Correlation Result
Formula Breakdown
Understanding Correlation
What is Correlation?
Correlation (ρ) measures the linear relationship between two assets. It ranges from -1 to +1, where -1 means perfect inverse movement, +1 means perfect tandem movement, and 0 means no linear relationship.
Diversification Benefit
Lower correlation provides better diversification. When assets are negatively correlated, gains in one can offset losses in another, reducing overall portfolio risk.
Correlation and Diversification Benefit
| Range | Benefit | Interpretation |
|---|---|---|
| -1.0 | Maximum | Can enable a perfect hedge with appropriate weights |
| -1.0 to -0.7 | Excellent | Strong inverse movement |
| -0.7 to -0.3 | Good | Often move opposite |
| -0.3 to 0.3 | Moderate | Little relationship |
| 0.3 to 0.7 | Limited | Often move together |
| 0.7 to 1.0 | Minimal | Strong co-movement |
| 1.0 | None | Identical movements |
Understanding Correlation in Portfolio Management
What is Correlation?
Correlation (ρ) is a statistical measure that describes how two assets move in relation to each other. It ranges from -1 to +1:
- ρ = +1: Perfect positive correlation - assets move in lockstep
- ρ = 0: No correlation - movements are unrelated
- ρ = -1: Perfect negative correlation - assets move in opposite directions
The formula divides covariance by the product of standard deviations: ρ = Cov(X,Y) / (σ_X × σ_Y). This standardization makes correlation unitless and easy to compare across different asset pairs.
Why Correlation Matters for Diversification
Correlation is the foundation of portfolio diversification. When you combine assets with low or negative correlation, the portfolio's overall risk can be less than the weighted average of individual asset risks.
Consider two assets, each with 20% volatility:
- If ρ = +1.0: Portfolio volatility = 20% (no diversification benefit)
- If ρ = +0.5: Portfolio volatility ≈ 17.3% (moderate benefit)
- If ρ = 0.0: Portfolio volatility ≈ 14.1% (significant benefit)
- If ρ = -1.0: Portfolio volatility = 0% (perfect hedge possible)
This is why institutional investors spend considerable effort finding assets with low correlation to their existing holdings.
Historical Correlation Examples
Here are typical correlations between major asset classes (historical averages, which can vary over time):
- U.S. Large-Cap Stocks / U.S. Small-Cap Stocks: ~0.85 (high - similar risk factors)
- U.S. Stocks / International Developed Stocks: ~0.75 (moderate-high - increasing globalization)
- U.S. Stocks / U.S. Treasury Bonds: ~0.0 to -0.3 (low/negative - classic diversifier)
- U.S. Stocks / Gold: ~0.0 to 0.1 (low - alternative asset)
- U.S. Stocks / REITs: ~0.60 (moderate - some equity-like behavior)
Limitations of Correlation
- Linear relationships only: Correlation measures linear dependence. Two assets could have a strong non-linear relationship but zero correlation.
- Not causation: High correlation doesn't mean one asset causes the other to move - both might respond to a common factor.
- Time-varying: Correlations change over time and across market regimes. Historical correlation may not predict future correlation.
- Sensitive to time period: Correlation calculated over 1 year may differ significantly from 5-year or 10-year calculations.
- Tail dependence ignored: Standard correlation doesn't capture how assets behave during extreme events (tails of the distribution).
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only and does not constitute financial advice. Historical correlations may not predict future relationships. Always consult with a qualified financial advisor before making investment decisions.
