Achieving Higher Information Ratios: The Fundamental Law of Active Management
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The fundamental law is additive in the squared IRs:

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Overall IR^2 = IRA^2 + IRB^2 + IRC^2
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IC common:

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?: the correlation between the two information sources or managers ICcom: the skill level of the combined sources
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3 assumptions of the fundamental law:
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(1) the manager has an accurate measure of his or her own skills and exploits information (2) the sources of information are independent (3) the skill level (IC) involved in forecasting each active bet (BR) is the same
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