Active risk exists in two versions and they get confused constantly. Ex-ante active risk is a forecast, produced by a risk model from current holdings and an estimated covariance matrix. Ex-post active risk is a measurement, the realised standard deviation of the active return series. They are different statistics about different time periods and there is no reason for them to agree exactly.
They should agree approximately, though, and a persistent gap is information. On the twelve-quarter series in Worked Example 2 the realised annualised tracking error is 4.515 percent. A risk system reporting 3.50 percent ex ante throughout gives a ratio of 1.29, and only three things explain it. The covariance estimates are stale against a changed regime, the holdings moved intra-quarter in ways the month-end snapshot missed, or the model is missing a factor the portfolio is loaded on. Ask which. A ratio persistently below 1.0 is equally informative and usually means the model is over-fitting a calm sample.
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How precise is a realised information ratio?
The harder point concerns the realised information ratio, and it is the one candidates get wrong. A realised information ratio is an estimate with a standard error, and over any horizon a client will tolerate, that standard error is enormous. For roughly independent returns the standard error of a Sharpe-type ratio over T periods is about sqrt((1 + IR^2/2) / T). On the twelve-quarter series the quarterly information ratio is 0.1846 with a standard error of 0.2911, so the annualised figure of 0.3691 carries a standard error of 0.5822. The 95 percent interval runs from minus 0.7721 to plus 1.5104. That interval contains zero, contains every mediocre manager and contains several excellent ones, and the t-statistic on the active return is 0.639.
The years required to do better are the power calculation from the process capstone, and they are worth quoting rather than softening. The t-statistic on a track record grows as IR x sqrt(T), so the years needed to clear t = 1.96 are (1.96 / IR)^2: 3.8 years at an information ratio of 1.00, 15.4 at 0.50, 42.7 at 0.30. On the twelve-quarter record above, at its realised information ratio of 0.3691, bare significance would arrive in 28.2 years.
Does a three-year manager ranking mean much?
None of that makes performance measurement useless. It makes it weak evidence to be combined with other evidence rather than a verdict. And it means that when a consultant presents a three-year ranking of forty managers, the first question is not who is at the top. It is how much of the ranking would survive being re-drawn on a different three years, and the honest answer is: very little.