The efficient frontier

Portfolio and Risk, lesson 4

Every best mix at once, and where it breaks in practice.

The tangency portfolio from Mean-variance, and the standard error of an average, σ / √n, from Statistics and Regression.

Part 1. Four assets

Four simulated asset classes. The grey cloud is every mix of them. Move the sliders to place yours.

Every mix of fourLive

Mixes inside the cloud are beaten by mixes on its upper edge: the same risk, more return. The edge is the menu of sensible portfolios, and where you sit on it depends only on how much risk you want.

Efficient frontier and minimum-variance portfolio

The upper edge, the most return for each level of risk, is the efficient frontier. Its left tip, the lowest-risk mix of all, is the minimum-variance portfolio. Add cash, and the steepest line from Mean-variance touches the frontier at one point: the tangency portfolio.

Your turn

Your portfolio sits inside the cloud, below the frontier. Which is true?

A point below the edge has a point directly above it, with the same volatility and more return. Nobody who cares only about return and risk should hold it.

Show the answer

C. A point below the edge has a point directly above it, with the same volatility and more return. Nobody who cares only about return and risk should hold it.

Part 2. Where it breaks

Keep going with Pro

You've done the first part. Pro opens the rest of this lesson, and every other one.

Still to come

Where it breaks
A worked problem
The same thing, for real

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Next lessonCAPM and betaHow much of a return the market explains. Start lesson 5

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04 · The efficient frontier