Portfolio Volatility Calculator

A portfolio volatility calculator measures the overall risk of a multi-asset portfolio, taking into account not just the individual volatilities of each holding but also how they move in relation to each other. It is used by investors and portfolio managers to understand total portfolio risk and the diversification benefit of combining different assets.

How to Use the Portfolio Volatility Calculator

1. Enter the weight of each asset in your portfolio as a percentage.
2. Enter the annualised standard deviation (volatility) for each asset.
3. Enter the correlation coefficient between each pair of assets.
4. The calculator applies the portfolio variance formula to produce an overall portfolio volatility figure.
5. Compare the result to the weighted average of individual asset volatilities to see how much risk diversification reduces.

The Formula

For a two-asset portfolio:

Portfolio Variance = (w1^2 x sigma1^2) + (w2^2 x sigma2^2) + (2 x w1 x w2 x sigma1 x sigma2 x correlation)

Portfolio Volatility = Square root of Portfolio Variance

Where w1 and w2 are the portfolio weights of each asset, sigma1 and sigma2 are their individual volatilities (standard deviations), and correlation is the correlation coefficient between the two assets, which ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation). For portfolios with more than two assets, the formula extends to sum all pairwise variance and covariance terms.

Real-World Example

Your portfolio has two assets: equities with a weight of 60% and a volatility of 16%, and bonds with a weight of 40% and a volatility of 7%. The correlation between equities and bonds is -0.2.

Portfolio Variance = (0.6^2 x 0.16^2) + (0.4^2 x 0.07^2) + (2 x 0.6 x 0.4 x 0.16 x 0.07 x -0.2) = (0.36 x 0.0256) + (0.16 x 0.0049) + (2 x 0.6 x 0.4 x 0.0112 x -0.2) = 0.009216 + 0.000784 - 0.001075 = 0.008925

Portfolio Volatility = Square root of 0.008925 = 9.45%

The weighted average volatility would be (0.6 x 16%) + (0.4 x 7%) = 12.4%. The diversified portfolio has a volatility of only 9.45%, demonstrating that the negative correlation between equities and bonds significantly reduces total portfolio risk.

The Role of Correlation in Diversification

Correlation is the most powerful lever in portfolio construction. Assets with low or negative correlation provide the greatest diversification benefit. Equities and government bonds have historically shown negative or low positive correlation, which is why the classic 60/40 portfolio has been such an enduring allocation. However, correlations are not stable. During severe market stress events, previously uncorrelated assets can move together, reducing diversification precisely when investors need it most. This phenomenon is known as correlation breakdown and is a critical risk in any diversified portfolio during crisis conditions.

Frequently Asked Questions

What is a typical volatility for an equity portfolio? Diversified equity portfolios have historically exhibited annualised volatility of around 15-20% for global equities. Single-country or sector-concentrated portfolios can be significantly more volatile. Bond portfolios typically show volatility of 5-10% depending on duration.

What is the difference between portfolio volatility and standard deviation? They are the same measure. Portfolio volatility is the annualised standard deviation of the portfolio's periodic returns. Standard deviation measures how much returns deviate from their average over the measurement period.

Can correlations change over time? Yes, significantly. Correlations between asset classes shift with market conditions, economic cycles, and policy changes. Historical correlations provide a starting point but should not be assumed to be stable, particularly over short horizons or during market crises.

How does adding more assets reduce volatility? Each new asset added to a portfolio contributes its own variance and its covariance with all existing assets. If the new asset has low or negative correlation with existing holdings, it tends to reduce total portfolio variance. Beyond around 20-30 well-diversified holdings, the diversification benefit of adding more assets diminishes rapidly.

Why does a three-asset portfolio need three correlations?

Every pair of assets needs its own number. Two assets have one pair. Three assets have three pairs: equity with bond, equity with property, and bond with property. Ten assets need 45 pairs, which is why portfolio risk models work in matrix form rather than as a single formula. Plug your own figures into the calculator above.

Should I use annual or monthly volatility?

Either, as long as every asset in the same calculation uses the same period. Mixing a daily figure for one asset with an annual figure for another produces a portfolio number that means nothing. Convert first, then run the formula, and state the period with the answer.

How correlation moves the answer

Hold the weights and the two volatilities from the example above and vary only the correlation. The mix stays at 60% equities at 16% volatility and 40% bonds at 7%.

At a correlation of +1 the portfolio is exactly as risky as the weighted average of its parts, and diversification adds nothing. Everything between is the diversification benefit, and it shrinks as the correlation rises.

Three assets, three correlations

The two-asset formula extends by adding a covariance term for every pair of assets. Take a 50% equity, 30% bond, 20% property mix with volatilities of 18%, 8%, and 12%, and correlations of -0.1 between equities and bonds, +0.7 between equities and property, and +0.2 between bonds and property.

Portfolio volatility is the square root of 0.012074, which is 10.99%. The weighted average of the three volatilities is 13.80%, so the mix gives up 2.81 points of risk. The property sleeve does most of the work against the portfolio: its +0.7 correlation with equities all but cancels the diversification the bonds bring.

Turning daily or monthly figures into annual ones

Volatility is quoted over a period, and the period has to be stated before the number means anything.

The square-root rule assumes returns are independent from one period to the next. It overstates annual risk when monthly returns are negatively correlated and understates it when they are positively correlated. Quote the period you started from alongside the annual figure.

Getting the two inputs from a return series

Both inputs come from the same return history, and the arithmetic is short enough to check by hand. Six monthly returns for an equity sleeve and a bond sleeve, in percent:

The equity sleeve deviates from its 1.000% mean by +1.0, -2.5, +2.0, -0.5, -3.0, and +3.0 points. Squaring those gives 1.00, 6.25, 4.00, 0.25, 9.00, and 9.00, which sum to 29.50. Divide by five, one less than the number of observations, for a variance of 5.90 and a standard deviation of 2.429% a month. Six observations is far too few to rely on. This is the arithmetic, not a usable estimate.

The correlation comes from the same paired series. Multiply the two sets of deviations month by month: 0.20, 0.00, -1.00, -0.15, 0.30, and 0.30, which sum to -0.35. Divide by five for a covariance of -0.0700.

Dividing by one less than the number of observations is the sample convention. A population version divides by six and returns a slightly smaller figure for both sleeves. Pick one convention, apply it to every input in the portfolio, and annualise once at the end.

Sources

• NIST/SEMATECH e-Handbook of Statistical Methods, measures of scale. https://www.itl.nist.gov/div898/handbook/. Accessed 2026-09-13.
• Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77 to 91. The original mean-variance treatment of portfolio risk.

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