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For K-12 Students · Efficient Frontier

Efficient Frontier for a mortgage

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a mortgage live below — adjust the inputs and watch it respond, right in your browser.

Efficient FrontierLive

Markowitz portfolio theory

Controls

Presets

Asset A return

Asset A volatility

Asset B return

Asset B volatility

Correlation

Combining two assets traces a curved frontier of risk versus return. Because they are not perfectly correlated, some mixes have lower risk than either asset alone — the power of diversification. The pink point is the minimum-variance portfolio. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Min-var weight A0%

Min-var return0.0%

Min-var volatility0.0%

Governing equation

σ_{p}^{2} = w^{2} σ_{A}^{2} + (1 - w)^{2} σ_{B}^{2} + 2 w (1 - w) ρ σ_{A} σ_{B}, ρ = 0.20, w^{*} = 0%

Reading this result: The assets differ sharply in volatility, so the minimum-variance blend leans heavily toward the calmer one to hold total risk down.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Efficient Frontier for a mortgage" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.