Portfolio Risk Calculator
Calculate portfolio volatility from asset volatilities, weights and correlation.
Please note: For information only, not investment advice. Projections assume constant rates; real markets fluctuate and capital is at risk.
What the Portfolio Risk Calculator does
Portfolio risk is not the average of the individual risks. Because assets do not move in lockstep, combining them produces volatility below the weighted average — the diversification benefit. The lower the correlation, the larger that benefit.
Formula
Two assets: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ)Many assets: σp = √(ΣΣ wᵢwⱼσᵢσⱼρᵢⱼ)Diversification benefit = Weighted average σ − Portfolio σ
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Portfolio type | one of 2 options | Yes | — |
| Weight of asset 1 | % | In some modes | Shown Portfolio type is Two assets (exact correlation). |
| Volatility of asset 1 | % | In some modes | Shown Portfolio type is Two assets (exact correlation). |
| Volatility of asset 2 | % | In some modes | Shown Portfolio type is Two assets (exact correlation). |
| Correlation between assets | number | In some modes | Accepts -1 or more, up to 1. Shown Portfolio type is Two assets (exact correlation). |
| Weights (%) | text | In some modes | Separate values with commas, spaces or new lines. Shown Portfolio type is Multiple assets (average correlation). |
| Volatility of each asset (%) | text | In some modes | Separate values with commas, spaces or new lines. Shown Portfolio type is Multiple assets (average correlation). |
| Average correlation | number | In some modes | Accepts -1 or more, up to 1. Shown Portfolio type is Multiple assets (average correlation). |
How to use it
- Choose Portfolio type.
- Fill in the remaining inputs the form shows for your choice.
- Select Calculate.
Worked example
60% equities at 16% volatility, 40% bonds at 6%, correlation 0.2.
- Weight1
- 60
- Vol1
- 16
- Vol2
- 6
- Correlation
- 0.2
Portfolio volatility about 10.3%, against a weighted average of 12% — roughly 1.7 points of diversification benefit.
Frequently asked questions
What correlation should I assume?
Equities and high-quality bonds have historically run between −0.2 and 0.4. Equities within the same market often exceed 0.7, which limits the benefit of holding many similar stocks.
Does more holdings always mean less risk?
Only up to a point. Once you hold enough assets, the remaining risk is market-wide and cannot be diversified away.
Method and sources
Method. Portfolio standard deviation from the component volatilities, weights and their correlation — for two assets, σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ).
Assumptions
- The volatilities and correlation supplied describe the future, which is the assumption the whole calculation rests on.
- Returns are adequately described by their standard deviation, implying a roughly symmetric distribution.
Limitations
- Correlation is not stable, and it rises toward one precisely when diversification is most needed — the historical figure that made a portfolio look diversified is often the first thing to fail in a crisis.
- Standard deviation treats upside and downside alike and understates tail risk, because real return distributions have fatter tails than the normal one this implies.
- Volatility measured over a calm period is not a forecast of volatility over a turbulent one.