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Portfolio Results
Solid diversification - meaningful risk reduction
Formula Breakdown
Understanding the Results
Variance vs Volatility
Variance (σ²) is the squared measure of risk. Volatility (σ) is the square root of variance and is expressed in percentage terms, making it easier to interpret.
Diversification Benefit
The difference between weighted average volatility and actual portfolio volatility. Lower correlation = greater benefit.
Diversification Benefit Ratings
| Risk Reduction | Rating | Interpretation |
|---|---|---|
| 40%+ | Excellent | Outstanding diversification |
| 25-40% | Good | Meaningful risk reduction |
| 10-25% | Moderate | Noticeable improvement |
| 0-10% | Minimal | Limited benefit |
| < 0% | No Benefit | Consider different assets |
Understanding Portfolio Variance
What is Portfolio Variance?
Portfolio variance (σₚ²) measures how portfolio returns disperse around the expected return. Unlike individual asset variance, portfolio variance accounts for:
- Individual asset volatilities (σ₁ and σ₂)
- Portfolio weights (how much you allocate to each asset)
- Correlation (how the assets move together)
Portfolio volatility (σₚ) is simply the square root of variance, expressed in the same units as returns (percentage).
The Power of Diversification
Consider two assets, each with 20% volatility, held in equal weights (50/50):
- 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 = -0.5: Portfolio volatility ≈ 10% (substantial benefit)
- If ρ = -1.0: Portfolio volatility = 0% (perfect hedge)
The Formula Explained
The two-asset portfolio variance formula has three components:
- w₁²σ₁² - Contribution from Asset 1's variance
- w₂²σ₂² - Contribution from Asset 2's variance
- 2w₁w₂ρσ₁σ₂ - The "interaction" term (covariance contribution)
When ρ is positive, the interaction term adds to variance. When ρ is negative, it subtracts - hence the diversification benefit.
Extending to More Assets
For portfolios with more than two assets, the formula becomes a matrix calculation. Each pair of assets contributes a covariance term. With N assets, there are N variance terms and N(N-1)/2 unique covariance terms.
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only and does not constitute financial advice. Portfolio variance calculations assume normal distribution of returns and constant correlation, which may not hold in practice. Always consult with a qualified financial advisor before making investment decisions.
