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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.

Before an outcome: the whole distribution

Different outcomes. The same portfolio return.

Teach this scenario model

Review the lesson with these exact outcomes, probabilities and asset returns. The selected outcome becomes the common illustrated reveal; your allocation is a labelled teacher example. Students submit their own answers. Opening the overview does not save or start anything.

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 0.0000%. Diamond: minimum-risk grid allocation. Different allocations can share the same plotted position.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. Diamond: minimum-risk allocation on the 0.01% weight grid. Overlapping marks can represent different allocations.

Lowest volatility on the 0.01% allocation grid: 0.00%, with 50.00% in Asset A. Minimum risk does not mean maximum expected return.

Across all possible outcomes

Expected return
8.00%
Volatility
0.00%

Inspecting one outcome · not an expected return

Your portfolio in A low · B high
8.00%
Asset A return
-12.00%
Asset B return
28.00%

Entered probability: 50.00%. The same outcome applies to every allocation.

Link to this scenario view

With JavaScript, allocation and outcome controls update immediately. Without it, choose their values and submit. Updating the link also refreshes the table editor. No randomness is used.

Expected return and volatility use all outcomes and their probabilities. Selecting a different outcome does not change the ex-ante risk. Asset correlation from this table: -1.0000.

Every entered outcome at your current allocation. These raw returns and probabilities determine the moments above; the selected row is marked “Inspecting.” Values shown are rounded.
OutcomeProbabilityA returnB returnPortfolio return
1 · A low · B highInspecting50.00%-12.00%28.00%8.00%
2 · A high · B low50.00%28.00%-12.00%8.00%

Write the possible outcomes

Each row is one common outcome for both assets in the same period. Probabilities must total exactly 100%; they are never rescaled. Returns may range from −100% to 1,000%. Use up to two decimal places for percentages.

To change the number of rows without JavaScript, set the count and submit once to open the revised table, then fill in the new rows or rebalance the probabilities. A missing, extra or invalid row stops calculation; it is never silently filled in.

Outcome 1
Outcome 2

No account or JavaScript is required. Submitted labels and numbers appear in the address bar. Do not enter private financial information. The controls above use the last applied table, not unsaved edits here.

One outcome is not the whole risk

The selected row is a hypothetical shared event, not a random draw or a forecast. Every allocation faces that same pair of asset returns. Its portfolio return depends on its weights; the probabilities and possible asset returns do not.

Expected return and volatility summarize the whole entered distribution, before an outcome occurs. A favorable realized return is not evidence that an allocation was safe or skillful. This is a finite population, not a sample estimate, and does not assume a normal distribution.

See the calculation

For outcome s, portfolio return Rₛ = w rAₛ + (1 − w) rBₛ. Expected return μ = Σ pₛ Rₛ. Variance = Σ pₛ (Rₛ − μ)²; volatility is its square root.

The same table determines asset means, covariance and correlation. If either asset has zero variance, its correlation with the other is undefined, not zero. Outcomes with probability zero remain visible but do not affect these moments.

The line includes all long-only allocations, not only efficient ones. It samples 1% steps and the lowest-risk allocation on the 0.01% grid. No short selling, borrowing, transaction costs, taxes, prices or investment recommendations enter this model.

For the underlying concepts, see MIT’s Portfolio Theory lectures and Wharton’s Mechanics of Diversification. These independent resources do not endorse this tool.

Explore the finance classroom library. Finite-scenario models can be reviewed as a classroom lesson before you choose to start it.

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