A signal has an information coefficient of 0.03 against next month's returns, is applied to 1500 roughly independent bets a year, and constraints give a transfer coefficient of 0.6. What information ratio should you expect, and what would double it?

A signal has an information coefficient of 0.03 against next month's returns, is applied to 1500 roughly independent bets a year, and constraints give a transfer coefficient of 0.6. What information ratio should you expect, and what would double it?

Approach: Apply the fundamental law of active management, then compare the sensitivity of the result to each of its three inputs.

0.70. The fundamental law of active management gives IR = TC*IC*sqrt(BR) = 0.6*0.03*sqrt(1500) = 0.6*0.03*38.73 = 0.697. The unconstrained version would promise 1.16, so position limits, turnover caps and the borrow list cost 40% of the ratio, and lifting them is often cheaper than finding new signal. Doubling the information coefficient doubles the ratio while doubling breadth adds only 41%, so research effort belongs in signal quality first. Breadth means independent bets, so 1500 names driven by one common factor have a breadth in the tens and the formula flatters any strategy whose positions all express the same view.

Follow-up: How would you estimate the effective breadth of a book of 1500 names with an average pairwise return correlation of 0.25?

Key concepts: information coefficient, breadth, transfer coefficient, information ratio.