The phrase "information ratio" names two different quantities in this program and in the literature, and confusing them produces predictions that are wrong by an order of magnitude.
What are the two kinds of information ratio?
The portfolio information ratio is the one the performance-measurement work already taught, and the one the fundamental law predicts: active return divided by active risk, both measured on a portfolio's return series. It is a ratio of a percentage to a percentage, so it is unitless, and for real long-only equity managers it runs from about minus 0.5 to about 1.0. A sustained value above 1.0 should send you to check the benchmark before you congratulate the manager.
The signal information ratio is the one the factor-construction work uses: the mean of a factor's period-by-period information coefficient divided by the standard deviation of that same series. It measures whether a signal's edge is reliably positive rather than occasionally large. It is also unitless, and it also tends to land between 0.5 and 1.0, which is exactly why the collision is so easy to miss.
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Why can't a signal's information ratio predict a portfolio's?
The two are not convertible into one another, and here is what happens when someone tries. Take a momentum signal whose mean monthly information coefficient measures 0.1209 with a standard deviation of 0.1255 across 48 monthly cross-sections. Its signal information ratio is 0.9633. That number tells you the signal's mean information coefficient is reliably positive, and the associated t-statistic, 0.9633 x sqrt(48) = 6.674, says the edge is not a fluke of the sample.
It does not say the portfolio built on that signal will have an information ratio of 0.9633. To get a portfolio prediction you must feed the mean information coefficient of 0.1209 into the fundamental law with an honest breadth. Feed it a dishonest one and watch what happens: 60 names scored every month for twelve months looks like 720 independent forecasts, and 0.1209 x sqrt(720) = 3.244. No equity manager in recorded history has sustained an information ratio of 3.2.
The correction is the breadth section's, and it is brutal. If the 720 forecasts carry a pairwise correlation of just 0.039268, the effective breadth collapses from 720 to 24.63 and the predicted information ratio falls to 0.60, which is a very good real-world number. A correlation of under 4 percent between forecasts destroys 81.5 percent of the naive prediction. Stocks in one month's cross-section share sectors, factor exposures and a market; a correlation of 4 percent between their forecast errors is an optimistic assumption, not a pessimistic one.
State which information ratio you mean, every time, in the sentence that carries the number. When a factor paper quotes an information ratio of 0.96 and a consultant quotes an information ratio of 0.45 for a manager, those are not comparable quantities and putting them in one table is a category error.