Portfolio Volatility Calculator
Portfolio volatility (standard deviation) captures the total risk of combining two assets, taking into account how they move relative to each other. The key insight of Modern Portfolio Theory, developed by Harry Markowitz, is that combining assets with less-than-perfect positive correlation reduces total portfolio risk below the weighted average of the individual risks. This is the mathematical basis for diversification. This calculator uses the two-asset portfolio variance formula to compute overall portfolio volatility from each asset's individual volatility (annualised standard deviation of returns), their portfolio weights, and the correlation coefficient between them. A correlation of 0 means the assets are uncorrelated; -1 means perfectly negatively correlated; +1 means no diversification benefit.
Portfolio volatility formula
Portfolio Variance = w1^2 x s1^2 + w2^2 x s2^2 + 2 x w1 x w2 x s1 x s2 x rho
Portfolio Volatility = sqrt(Portfolio Variance)
Weighted Average Vol = w1 x s1 + w2 x s2
Diversification Benefit = Weighted Avg Vol - Portfolio Volatility
Where w = weight (as decimal), s = standard deviation (as decimal), rho = correlation coefficient.
Diversification benefits at different correlations
- Correlation = +1.0: no benefit; portfolio volatility = weighted average volatility.
- Correlation = 0: partial benefit; assets move independently.
- Correlation = -1.0: maximum benefit; can achieve zero portfolio variance with the right weights.
- Stock-bond correlation has been approximately -0.2 over the past 25 years (as of 2023).
- Diversification only eliminates unsystematic risk; systematic risk remains regardless of correlation.
Portfolio volatility: frequently asked questions
What is portfolio volatility?
Portfolio volatility is the standard deviation of portfolio returns, measuring the dispersion of outcomes around the average return. It quantifies total risk. Higher volatility means greater uncertainty in returns, both positive and negative.
How does correlation affect portfolio volatility?
Correlation measures how two assets move together. A correlation of +1 means perfect co-movement; combining them provides no diversification benefit. A correlation of -1 means they move opposite to each other, potentially eliminating volatility entirely. Correlation between 0 and +1 provides partial diversification benefit.
Why is portfolio volatility lower than the weighted average of individual volatilities?
Unless assets are perfectly correlated (correlation = +1), combining them reduces total risk through diversification. The portfolio variance formula subtracts a term based on the correlation, which lowers the overall variance below the weighted sum of individual variances.
What is the two-asset portfolio variance formula?
Portfolio Variance = w1^2 x sigma1^2 + w2^2 x sigma2^2 + 2 x w1 x w2 x sigma1 x sigma2 x correlation. Portfolio standard deviation (volatility) is the square root of this variance. This is the standard Modern Portfolio Theory (Markowitz) formula.
What correlation should I use for stocks and bonds?
The stock-bond correlation is not fixed and changes over time. During the 1990s and 2000s it was often negative (-0.2 to -0.4), which is why the classic 60/40 portfolio worked well as a diversifier. During periods of rising inflation (like 2022), the correlation can turn positive, reducing the diversification benefit.
Official sources
- SEC: Mutual Funds and ETFs - Diversification.
- Federal Reserve Bank of Chicago: Financial Conditions Data.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.