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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.

A lower-risk asset and a higher-return asset with correlation 0.25. Which allocations have more expected return at the same risk? Minimum variance alone does not settle that question.

Same allocation. Different relationship.

Risk, return and the relationship between assets

A · Lower-risk assetB · Higher-return asset

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 8.5000%; volatility 14.577%. Diamond: minimum-risk grid allocation. Open circle: correlation +1 at the same allocation. Different allocations can share the same plotted position.0.0%3.7%7.0%6.1%14.0%8.5%21.0%10.9%28.0%13.3%Expected returnVolatility (standard deviation)AB
Teal: the full supplied allocation path, not just efficient portfolios. Filled circle: your allocation. Diamond: minimum-risk allocation on the 0.01% weight grid. Open circle: correlation +1 at the same allocation. Overlapping marks can represent different allocations.

Your selected allocation

Expected return
8.50%
Volatility
14.58%

If correlation were +1: 17.50% 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.

2.92 percentage points less volatility than the same allocation with perfect positive correlation. Expected return does not change when only correlation changes.

What happens at 50/50?

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

Correlation -1
7.50%volatility
Correlation 0
13.46%volatility
Correlation +1
17.50%volatility

Lowest volatility on the 0.01% allocation grid: 9.88%, with 93.75% in Lower-risk asset. Minimum risk does not mean maximum expected return.

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%12.00%25.00%
25.00%10.25%19.53%
50.00%8.50%14.58%Selected
75.00%6.75%10.90%
93.75%5.44%9.88%Grid minimum
100.00%5.00%10.00%

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.