Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A negative or low correlation between two assets can make a combined portfolio's total volatility genuinely lower than either asset's individual volatility alone, which is the actual mathematical mechanism behind diversification, not just a comforting phrase. The math itself shows how combining imperfectly correlated assets reduces risk below what either one carries by itself.
Before you rely on it
What to check
Confirm the correlation input reflects a realistic, current relationship between the two specific assets, since portfolio risk is highly sensitive to that one number.
The common error
Where people go wrong with two-asset portfolio risk calculator
Assuming a diversified two-asset portfolio's risk is simply the weighted average of the two individual asset volatilities. When correlation is meaningfully below 1, the combined portfolio volatility comes in lower than that weighted average, which is the actual point of diversifying.
Sensitivity evidence
How asset a weight changes the portfolio volatility
| Asset A weight | Portfolio volatility | Diversification benefit | Asset B weight |
|---|---|---|---|
| 56.0% | 9.7% | 2.2% | 44.0% |
| 58.0% | 9.9% | 2.1% | 42.0% |
| 60.0%worked example | 10.1% | 2.1% | 40.0% |
| 62.0% | 10.3% | 2.0% | 38.0% |
| 64.0% | 10.6% | 1.9% | 36.0% |
Every input, tested
Which input moves the portfolio volatility most
| Input | Tested from | To | Portfolio volatility at each end | Swing |
|---|---|---|---|---|
| Asset A volatility | 13.0% | 17.0% | 9.0% to 11.3% | 2.3% (22%) |
| Asset B volatility | 6.0% | 10.0% | 9.8% to 10.6% | 0.787% (7.8%) |
| Asset A weight | 58.0% | 62.0% | 9.9% to 10.3% | 0.413% (4.1%) |
| Asset correlation | 0.18 | 0.22 | 10.1% to 10.2% | 0.114% (1.1%) |
Two variables at once
Portfolio volatility by asset a weight and asset a volatility
| Asset A weight \ Asset A volatility | 11.0% | 15.0% | 19.0% |
|---|---|---|---|
| 56.0% | 7.7% | 9.7% | 11.9% |
| 58.0% | 7.8% | 9.9% | 12.1% |
| 60.0% | 7.9% | 10.1% | 12.4% |
| 62.0% | 8.0% | 10.3% | 12.7% |
| 64.0% | 8.1% | 10.6% | 13.0% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Asset A weight | 60.0% |
| Asset A volatility | 15.0% |
| Asset B volatility | 8.0% |
| Asset correlation | 0.2 |
| Portfolio volatility | 10.1% |
| Diversification benefit | 2.1% |
| Asset B weight | 40.0% |
Where the inputs come from
Asset A weight is its share of the portfolio, and Asset B's weight is the remainder. Enter each asset's annual volatility as a standard deviation and the correlation between them from a data source. Typical values: stocks around 15% to 20% volatility, bonds 4% to 8%, with a correlation that has ranged from slightly negative to positive depending on the period. Use figures from the same window.
Using the portfolio volatility in a real decision
That is the case for holding assets that behave differently.
When the result stops applying
The formula covers two assets and assumes constant volatilities and correlation, but both change, especially in crises. It gives volatility only, not the chance of a large loss. A real portfolio has more than two holdings and needs a full covariance matrix. Correlations estimated from a short period can mislead.
What to compare it with
The asset correlation calculator gives the correlation input, and the portfolio weighted return page shows what you expect to earn for the risk. See the maximum drawdown and Sharpe ratio calculators for related measures. Rebalancing keeps the weights, and therefore the risk, near the plan.
People also ask
Frequently asked questions
Why is portfolio risk lower than the average of the two?
Because the assets do not move in lockstep. When one falls, the other may rise or fall less, so the combined swings partly cancel out.
What if the correlation is 1?
Then there is no diversification benefit, and portfolio volatility simply equals the weighted average of the two volatilities, so mixing them only changes the level of risk.
Does adding a risky asset always raise risk?
Not necessarily. A small allocation to a volatile asset with low correlation can lower the portfolio's overall volatility.