Actually, I would argue that for the purpose of what the article was trying to convey, they used the right statistic.
Let me illustrate by running with your own suggestion of trying to find out whether there are actively managed funds that consistently produce better compound returns than indices over 5 year periods. How would you actually do that?
Certainly we agree that a fund outperforming an index over one 5 year period is irrelevant to answer that question. To check whether there is a fund that consistently outperforms an index over 5 year periods, you would look at several such periods, e.g. 5 consecutive 5 year periods (for a total of 25 years of data [1]).
This is exactly analogous to the statistic used by the article, and somebody could then make the argument (like yourself) that a misleading statistic is used, and that people should instead look at the compound return over the entire period of 25 years.
There is nothing wrong in principle with the statistic used by the article.
However, it is reasonable to argue that looking at compound return over a 1 year period is too short (because typical investment time horizons are longer), and I would agree. Unfortunately, there's [1].
[1] And obviously, using such a long timespan is itself problematic for many reasons.
Right, that's absolutely a problem, but it's orthogonal to the supposed problem that OP was mentioning (e.g., it could be that those funds are so bad that even the top quartile doesn't outperform the index in a particular period).
Or perhaps OP intended to refer to this problem, and it just wasn't done very clearly.
Let me illustrate by running with your own suggestion of trying to find out whether there are actively managed funds that consistently produce better compound returns than indices over 5 year periods. How would you actually do that?
Certainly we agree that a fund outperforming an index over one 5 year period is irrelevant to answer that question. To check whether there is a fund that consistently outperforms an index over 5 year periods, you would look at several such periods, e.g. 5 consecutive 5 year periods (for a total of 25 years of data [1]).
This is exactly analogous to the statistic used by the article, and somebody could then make the argument (like yourself) that a misleading statistic is used, and that people should instead look at the compound return over the entire period of 25 years.
There is nothing wrong in principle with the statistic used by the article.
However, it is reasonable to argue that looking at compound return over a 1 year period is too short (because typical investment time horizons are longer), and I would agree. Unfortunately, there's [1].
[1] And obviously, using such a long timespan is itself problematic for many reasons.