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06 · Factor models

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Portfolio and Risk, lesson 6

Factor models

Value, size, momentum and the few drivers behind many stocks.

Alpha from CAPM and beta, and regression on several inputs from Statistics and Regression.

Part 1. A fund that looks skilled

A simulated fund beat cash comfortably for twenty years. Measured against the market alone, it has a large, significant alpha. Add more explanations and see what's left.

Explain the fundLive

The fund's apparent skill was two tilts: towards cheap stocks, and towards recent winners. Both earned a premium over these twenty years, and a market-only regression booked those premiums as alpha. Once the regression included them, nothing was left. Size changed nothing, because the fund had no tilt towards small companies.

Factor model

A factor model explains a return as the sum of its exposures to a few common drivers, plus a part of its own: R − r = α + β₁F₁ + β₂F₂ + … + ε. Each F is a factor's return, each β is the loading on that factor, and ε, read "epsilon", is the part left over.

Your turn

A fund's alpha against the market alone is 4% a year, with t = 3. After adding value and momentum factors, it's 0.5% with t = 0.4. What's the best reading?

The return was real, but it came from exposures to known factors. Those can be held more cheaply in other ways, so paying for them as if they were skill makes little sense.

Part 2. Where factors come from

Keep going with Pro

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

Still to come
  1. Where factors come from
  2. Fewer numbers for many stocks
  3. A worked problem
  4. The same thing, for real
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