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Empirical Asset Pricing and Factor Investing / Testing asset-pricing models

Factor construction

The time-series pass needs a factor return, and a characteristic such as book-to-price is not yet a return. The arbitrage pricing theory and the risk-model factor structure already say why a linear factor model prices assets. This note builds the portfolio whose return stands in for the characteristic: a zero-net-investment book with unit exposure to that characteristic and, where the test requires it, zero exposure to the other factors in the model.
Learning objectives. By the end of this note you should be able to:
  • distinguish a firm characteristic from a factor return, and state the three ways a test obtains the loadings;
  • read the APT price of risk as the excess return on a portfolio with unit exposure to one index and zero exposure to the others;
  • write the Fama–French size and book-to-market portfolios as zero-net-investment books, including the breakpoint rule that keeps market capitalisation in the small side;
  • state the weighted least-squares factor-mimicking portfolio and the optimisation problem it solves.

In this lesson

  1. Characteristic, loading, factor return
  2. A portfolio return for size and for book-to-market
  3. Named characteristics and named macro factors
  4. The minimum-variance unit-exposure book

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