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Portfolio Risk Calculator

Two investments can be risky on their own and less risky together. Change their relationship, move your allocation, and see why — with hypothetical assumptions, free and without signing in.

Switching models opens a separate example. Returns, risks and correlation alone do not specify a unique set of possible outcomes.

Perfect positive correlation: splitting between these two assets does not reduce volatility. Two names do not necessarily mean two sources of risk.

Same allocation. Different relationship.

Same assets. Different relationship.

A · Asset AB · Asset B

Scroll sideways to see the full chart.

Two-asset risk–return opportunity setVolatility increases to the right; expected return increases upward. The line follows allocations to A in increasing order. Filled circle: selected allocation. Selected: 50.00% in A; expected return 8.0000%; volatility 20.000%. Open circle: correlation +1 at the same allocation. Every supplied allocation has the same return and volatility, so all points overlap.0.0%7.0%5.6%7.5%11.2%8.0%16.8%8.5%22.4%9.0%Expected returnVolatility (standard deviation)A, B
Teal: the full supplied allocation path, not just efficient portfolios. Filled circle: your allocation. Open circle: correlation +1 at the same allocation. All allocations overlap at one point; they have not been spread out artificially.

Your selected allocation

Expected return
8.00%
Volatility
20.00%

If correlation were +1: 20.00% volatility at this allocation.

−1: perfectly opposite · 0: uncorrelated · +1: perfectly together

Link to this view

With JavaScript, sliders update the chart immediately, without animation. Without it, move the sliders and submit to calculate. Apply them to update the address bar and assumption form.

This allocation has the same volatility as it would with perfect positive correlation. A different asset name alone does not guarantee diversification.

What happens at 50/50?

Keep these same assets and split equally. Only their correlation changes.

Correlation -1
0.00%volatility
Correlation 0
14.14%volatility
Correlation +1
20.00%volatility

Every permitted allocation has the same modeled volatility. There is no unique minimum-risk allocation.

Read the numbers
Quarter-step comparisons, your selected allocation and the grid minimum when risk is not constant. All results are rounded; the chart samples at 1% steps plus the minimum.
Allocation to AExpected returnVolatilityNote
0.00%8.00%20.00%
25.00%8.00%20.00%
50.00%8.00%20.00%Selected
75.00%8.00%20.00%
100.00%8.00%20.00%

Set the assumptions

Use hypothetical expected returns and volatilities for the same period. Apply edits to update the chart; the sliders above use the last applied assumptions.

Asset A
Asset B

Works without JavaScript or an account. The submitted assumptions appear in the address bar, so use example names rather than private financial information.

A model for learning, not an investment recommendation

Volatility is the standard deviation of returns, not the chance of losing money. Expected return is not a promised outcome. These calculations do not assume a normal distribution and do not estimate either input from market prices.

This is a two-asset, single-period, long-only model: weights total 100%, with no borrowing or short selling. It leaves out transaction costs, taxes and changes in correlation. A zero modeled variance in an idealized example does not make a real investment risk-free.

See the calculation

Let w be the fraction in A, μ the expected return, σ the volatility and ρ the correlation. B receives 1 − w.

Expected return = w μA + (1 − w) μB

Variance = w² σA² + (1 − w)² σB² + 2w(1 − w) σA σB ρ

Volatility is the square root of variance. Computation uses decimal rates; the display converts back to percentages. The minimum is over allocations in steps of 0.01%, not a recommendation or a search over other investments. Values shown are rounded.

For the underlying ideas, see MIT’s Portfolio Theory lectures and Wharton’s Mechanics of Diversification. These are independent teaching resources, not endorsements of this tool.

Teaching the topic? Explore the finance classroom library. This calculator does not yet create a live portfolio lesson.