CAPM and beta

Portfolio and Risk, lesson 5

How much of a return the market explains.

Beta as the slope of a regression on the market, from Statistics and Regression, and the tangency portfolio from Mean-variance.

Part 1. Beta against return

Ten simulated portfolios of stocks, grouped by beta, over twenty years. The line is a prediction of what each should earn. Tap the dots.

Ten portfolios and a lineLive

The line says a portfolio's return above cash should be its beta times the market's. The highest returns came from the highest betas, and that was pay for market risk, not skill. A dot's distance from the line is the part beta doesn't explain. In the CAPM world it was luck, and its t-statistic said so. In the flatter world, low-beta portfolios beat the line and high-beta ones fell short.

Alpha and the security market line

The line of expected return against beta is the security market line. A return's distance above it, what's left after paying for market risk, is its alpha. Measured over a few years, alpha is mostly noise, so it needs a standard error next to it.

Your turn

A fund has a beta of 0.8. It beat cash by 6% a year while the market beat cash by 5%. What's its alpha?

The line expects 0.8 × 5% = 4% above cash. The fund made 6%, so its alpha is 6% − 4% = +2%. Comparing it with the market's 5% directly forgets that the fund took less market risk.

Show the answer

B. The line expects 0.8 × 5% = 4% above cash. The fund made 6%, so its alpha is 6% − 4% = +2%. Comparing it with the market's 5% directly forgets that the fund took less market risk.

Part 2. Why only beta is paid

Keep going with Pro

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

Still to come

Why only beta is paid
Two kinds of risk
A worked problem
The same thing, for real

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Next lessonFactor modelsValue, size, momentum and the few drivers behind many stocks. Start lesson 6

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05 · CAPM and beta