High skill, modest breadth: what information ratio?

Question

A strong forecasting signal has an information coefficient (IC) of 0.10, and you make 64 independent bets per year. What annualized information ratio does this imply?

Accepted Answer

The Fundamental Law. The information ratio is skill times the square root of breadth: IR = IC 	imes \sqrt{BR}. Plug in the numbers. With IC = 0.10 and BR = 64: IR = 0.10 	imes \sqrt{64} = 0.10 	imes 8 = 0.8. Interpretation. A high skill level (IC of 0.10 is exceptional in practice) over just 64 bets gives an information ratio of 0.8. Compare with a weak signal (IC 0.03) that needed 400 bets to reach 0.6: strong skill buys a high IR with far fewer bets. There is a real trade-off between depth (skill per bet) and breadth (number of bets), and the same IR can be reached by many combinations, …

High skill, modest breadth: what information ratio?

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