Alexey,
Thank you for your reply. It is clear and widely known that clients mostly or always lose with active equity funds. It also makes sense, that if the time period, over which you compare the results of actice equity funds, does not matter statistically. Because their cyclicality is probably rather similar to each other due to their similar benchmark hugging, minimizing their risk of negative tracking error, but also eliminating their chance for any positive alpha for clients after fees. Thus, the time period of the comparison is only irrelevant if the cyclicalites of all compared funds are similar.

However, the cyclicalities of active and passive equity funds is usually rather different from each other as you stated: "...active managers underperform in rising markets (such as -150bp per year) and then add relative value in bear markets (such as +250bp per year)".

Thus, if you compare active equity funds vs. their passive equity fund benchmark over less than the last market cycle, you systematically bias the result of the comparison against active funds. Because you omit the last bear market phase from 2007-2009, when active funds outperformed their benchmark on average, as shown in the third figure entitled "Actively Managed Large-Blend Mutual Funds vs. The S&P 500". I.e., you make the average performance of active equity funds appear worse against the benchmark than it actually is. 

This is like comparing the average temperatures of certain cities only from Jan. until Sept. and not from Jan. until December. If you are only interested in the difference of the average temperatures, this would ONLY be OK, even though not perfect academically, IF both cities are located on the SAME hemisphere, north or south, with the same cyclicality or rather seasonality!

However, IF they lie on OPPOSITE hemispheres, i.e. north and south like London and Sidney, this is plainly WRONG due to different cyclicalities/seasonalities and would produce biased results. Namely that London has a relatively higher average temperature than Sidney as is the case when compared correctly over one whole year, taking into account all seasons in both cities completely.

As extreme investment example to make this more obvious, just take the (intended) extreme differences in cyclicality of a time series momentum managed futures fund or trendfollower (TF) and a passive equity fund. Let's assume both of them achieved the same absolute return and risk values over the (assumed) last market cycle, i.e., from the market peak in 2007 until the last market peak in 2019. 

If you compared them only over the last ten years from 2009 until today, the TF performance would appear to be much worse than the equity fund by several 100 bps p.a. Because you omitted the phase of the highest gains of TFs but included the phase of the highest gains of the equity funds. Because most TFs achieved them in 2008 due to their highly negative correlation to stocks during drawdowns, their main USP! In turn, this due to going short during pronounced drawdowns, exploiting the downward trend! As you correctly stated, real alpha can only be earned of going short, which TFs ideally do in bear markets.

Thus, such a comparison of funds with extremely different cyclicalities over less than one whole market cycle is just plainly wrong. But it can often be observed even with many professionals for whatever reason!? Not so seldomly this even leads to dumb bashing of well managed TFs, which intend these differences to diversify equity dominated portfolios in the first place! See: awealthofcommonsense.com/2017/04/managed-futures-dealing-with-uncorrelated-assets/

Thus, comparing active and passive equity funds - certainly differing much less in their cyclicality but usually still differing as you mentioned - only during a boom phase, as you have done since 2010, you also make the performance of active equity funds appear worse than they actually are by some ten bps p.a. vs. their passive benchmark.

Thus, I think that your statement "On average, active managers underperformed by -1.7% per calendar year. The results are even worse for the most recent decade. Since 2010, active managers have failed to keep pace with the S&P 500 every year, lagging by -2.1% a year on average." is misleading. Because most probably the observed decrease in performance is mainly due to the biasing comparison over less than one whole market cycle and not due to further decreasing active fund manager performance or increase of fees. Or what else can explain the apparent decrease in performance of active equity fund managers during the current decade?

Actually, due to the immense pressure from low cost passive equity funds, you would rather expect that they really try hard to reduce their poor performance after fees mainly by lowering fees.

Sorry for the length of my post. I just felt it needs some more details to make my point.