Portfolio Volatility Calculator
Estimate your portfolio’s overall volatility using asset weights, individual volatilities, and a simple correlation assumption. See total risk and each asset’s contribution to that risk.
Portfolio volatility formulas
Portfolio volatility is the standard deviation of portfolio returns. In a multi-asset portfolio, it depends on asset volatilities, weights, and correlations. This calculator uses a three-asset approximation with a single average correlation to keep the math accessible while still showing diversification effects.
1. Inputs and conversions
Weights (decimal):
w1, w2, w3
Volatilities (decimal per year):
σ1, σ2, σ3
Average correlation:
ρ (between -1 and 1)
Check:
w1 + w2 + w3 = 1
2. Portfolio variance with average correlation
Portfolio variance:
Var_p = w1² σ1² + w2² σ2² + w3² σ3²
+ 2 ρ (w1 w2 σ1 σ2 + w1 w3 σ1 σ3 + w2 w3 σ2 σ3)
Portfolio volatility:
σ_p = √Var_p
The first part of the formula is the weighted sum of individual variances. The second part adds the covariance terms, using a single average correlation ρ for all pairs. When ρ is low, the covariance terms are smaller, and diversification reduces overall volatility.
3. Weighted average volatility and diversification effect
Weighted average volatility:
σ_w = w1 σ1 + w2 σ2 + w3 σ3
Diversification effect:
Diversification = σ_w − σ_p
The weighted average volatility is what you’d get if there were no diversification benefits. The difference between this and the actual portfolio volatility shows how much risk reduction you gain from combining assets with less-than-perfect correlation.
4. Risk contributions (approximate)
Approximate contribution of asset i:
RC_i ≈ (w_i σ_i / σ_p) × 100%
These percentages sum to roughly 100% and show which assets drive most of the portfolio’s volatility.
Risk contributions help you see whether one asset dominates portfolio risk. Even a small weight in a very volatile asset can contribute disproportionately to overall volatility.
Understanding portfolio volatility and diversification
Volatility is one of the most common ways to describe investment risk. A portfolio with high volatility tends to experience larger swings in value, while a low-volatility portfolio is more stable. The key insight of modern portfolio theory is that combining assets with imperfect correlations can reduce overall volatility without necessarily reducing expected return.
How this calculator models your portfolio
You enter weights and volatilities for up to three assets, along with an average correlation. The calculator converts weights and volatilities into decimals, checks that weights sum to 100%, and then applies the portfolio variance formula with a single correlation parameter. From there, it computes portfolio volatility, the weighted average volatility, and the diversification effect.
Worked example
Suppose you have:
- Asset 1 (stocks): 40% weight, 15% volatility
- Asset 2 (bonds): 40% weight, 10% volatility
- Asset 3 (alternatives): 20% weight, 25% volatility
- Average correlation: 0.3
With these inputs, the calculator shows the portfolio’s volatility, the simple weighted average volatility, and how much risk reduction you get from diversification. It also estimates each asset’s contribution to total volatility, highlighting whether the alternatives slice is punching above its weight in terms of risk.
Using the results
The summary helps you see whether your portfolio’s volatility matches your comfort level. If the diversification effect is small, your assets may be too correlated, and you might consider adding more diversifying exposures. If one asset contributes most of the risk, you can experiment with lower weights or less volatile alternatives.
Remember that this is a simplified model. Real portfolios often include many assets, and correlations can change over time. Still, the core intuition—weights, volatilities, and correlations jointly determine risk—is powerful and useful for everyday portfolio decisions.
Frequently Asked Questions
Do my weights have to sum to 100%?
Yes. The calculator expects weights to represent your full portfolio. If they don’t sum to 100%, it will warn you.
Where do I get volatilities?
You can estimate volatilities from historical data or use approximate values from research reports or fund fact sheets.
What correlation should I use?
If you don’t have detailed data, use a rough estimate (e.g., 0.2–0.4 for stocks and bonds). Run multiple scenarios to see how sensitive your risk is to correlation assumptions.
Is this the same as Value at Risk (VaR)?
No. Volatility is a building block for risk measures like VaR, but this tool focuses on standard deviation, not tail risk.
Can I export the risk contributions?
Yes. Use the Export CSV button to download the contribution table and analyze it in a spreadsheet.
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Information on this site is for educational purposes only and is not financial, tax, or legal advice. Calculations are estimates and may not reflect actual results. See our Privacy Policy and Disclaimer.