Estimates only — not financial, tax, or professional advice.
100% private — every number you enter is calculated in your browser and never sent to our servers.
What it calculates: Portfolio volatility, Weighted-average volatility, Diversification benefit.
Updated 5 June 2026 · Transparent assumptions
A weighted average says 14%; the portfolio actually carries 12.15%
Sixty percent at 18% volatility and forty percent at 8% average to 14% if you simply weight them. The portfolio\u2019s actual volatility is 12.15%, because the two assets do not move together — a correlation of 0.3 means their movements partly offset. The 1.85-point gap is the diversification benefit, and it is free.
This is the one genuinely free lunch in investing, and it is why the portfolio variance formula has a third term. Returns combine linearly; risk does not, and the cross term is where the entire benefit lives.
The same two assets give 14% at ρ = 1 and 7.2% at ρ = −1
At perfect positive correlation the assets move in lockstep and there is no benefit at all — portfolio volatility equals the weighted average, 14%. At zero correlation it falls to 11.5%. At perfect negative correlation the movements cancel to the greatest extent the weights allow, giving 7.2% here.
Real asset pairs sit between, usually well above zero. The practical implication is that adding a second asset with similar correlation to what you already hold does far less than adding one that behaves differently, even if the second looks riskier on its own volatility.
Which is why judging a holding on its own volatility is the wrong test
It is entirely possible to add an asset with volatility above the portfolio\u2019s own and reduce total risk, provided its correlation is low enough. The condition depends on the correlation, the weights and the relative volatilities, and it is why assets that look reckless in isolation — commodities, managed futures, long-dated bonds in an equity portfolio — can be risk-reducing in combination.
The corollary is that a holding should be judged by its marginal contribution to portfolio risk, not by its standalone volatility. That is a different and often opposite conclusion, and it is the main reason risk is a portfolio-level question rather than a security-level one.
A stable correlation, and volatility that describes the future
Correlation is estimated from history and is not stable. The most damaging property of asset correlations is that they tend to rise in crises — precisely when the diversification benefit is most needed, the assets start moving together and the benefit shrinks. A portfolio built on calm-period correlations is less diversified than it appears in exactly the conditions that matter.
The model also covers two assets. Extending to more requires the full covariance matrix, and the number of correlation pairs grows with the square of the holdings — ten assets need forty-five of them, each estimated with error. The two-asset case shows the mechanism cleanly; a real portfolio needs the matrix.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Returns are assumptions, not guarantees. Actual results may vary because of market performance, taxes, fees, inflation, and timing. This is an educational projection, not investment advice.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified that portfolio volatility equals the weighted average at perfect positive correlation and falls below it everywhere else, which is the diversification benefit the page quantifies.
Add this calculator to your site
Responsive embed — and private: nothing your visitors type leaves their browser.