A second value ratio is not a second factor until it adds association that the
first ratio does not already carry. The weights that maximise the composite
information ratio are derived in the multifactor alpha model, and the translation from information
coefficient to information ratio sits in the fundamental law. This note decides what is
allowed to enter that combination for the running book-to-price case: a raw
cheapness score, a residual after profitability, or a second ratio that failed
its own test.
Learning objectives. By the end of this note you should be able to:
- connect a dollar-neutral book's excess return to the cross-sectional correlation of weights and relative returns;
- distinguish value (the raw ratio) from valuation (the residual after a profitability regression);
- refuse an equal-weight blend of book-to-price with a significant cash-flow ratio;
- state the linearity and time-independence assumptions a single composite weight vector imposes, and the contextual evidence Qian cite against both.
In this lesson
- The correlation the book actually earns
- Do not blend a failed ratio into a passing one
- The composite is a model of the cross section, and it is rigid
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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