Finance & Investment · Risk & Portfolio
Portfolio Volatility Calculator
Enter your assets' weights, expected returns and volatilities, plus how they move together, to get the portfolio's expected return and volatility — and see how much risk diversification removes compared with simply averaging the assets' volatilities.
Your inputs
Quick start — try a typical case
Weights should add up to 100 %. Volatility = annualised standard deviation.
Used for every pair not listed below. 1 = move together, 0 = unrelated, −1 = opposite.
Your result Live
Portfolio Volatility
10.62%
Expected return 10.00% a year — 0.94 units of return per unit of risk
- Expected Portfolio Return
- 10.00%
- Weighted Average of Volatilities
- 13.40%
- Risk Removed by Diversification
- 2.78% (21% less)
- Typical Bad Year (−1 std dev)
- -0.62%
- Rough Worst Year in 20 (−1.65 std dev)
- -7.47%
- Indian equity — share of risk91%
- Bonds / debt funds — share of risk3%
- Gold — share of risk1%
- International equity — share of risk5%
Assets
4 rowsHow this is calculated
σₚ = √(Σᵢ Σⱼ wᵢ wⱼ σᵢ σⱼ ρᵢⱼ) · E[Rₚ] = Σ wᵢ E[Rᵢ]
- wᵢ, σᵢ
- Weight and volatility of asset i
- ρᵢⱼ
- Correlation between assets i and j (1 on the diagonal)
A portfolio's risk is less than the average of its parts unless everything moves together. The lower the correlations, the bigger the diversification benefit — that's why mixing equity with bonds and gold can cut risk sharply for a modest fall in expected return. The table shows which assets drive the portfolio's risk.
Assumptions & sources
- Inputs are long-run annual estimates; correlations rise in crises, so real diversification can be smaller when you need it most.
- Returns are roughly normally distributed for the 'bad year' figures — real markets have fatter tails.
- 1Portfolio Selection (Markowitz, 1952) — Journal of Finance
- 2Investments (Bodie, Kane & Marcus), chapters on returns, compounding and the time value of money — McGraw-Hill
- 3CFA Program Curriculum — Quantitative Methods: The Time Value of Money — CFA Institute
Calculator ID FIN-RISK-PORTVOL-001 · version 1.0.0
Common questions
Where do I get volatilities and correlations?
Fund factsheets give 3-year standard deviation. Correlations can be computed from monthly returns (the Beta & Correlation Calculator shows them) or taken from long-run asset-class studies.
Why is portfolio risk lower than average risk?
When assets don't move in lockstep, their ups and downs partly cancel out. Only with perfect correlation (1.0) is portfolio volatility equal to the weighted average.