What I envision as maybe a more representative analysis (but impractical for our purposes, taking too much work) would be to consider the effects of adding each individual fund to a baseline portfolio. Then we can say something like "X% of large blend funds improved portfolio outcomes, Y% made portfolios worse, Z% improved outcomes by a Sharpe ratio boost of more than 0.05 for the optimal ex-post allocation." Then compare that to funds in different categories. But something like that might not answer the questions you were looking at.
I completely agree that that something like that seems like the analysis one would like to make.
However, there's a simple-minded, and, I think valid way to look at results like the ones above, when the results that are as plain as the nose on your face. It is that takes some
really extraordinary combination of high volatility and robust, persistent, reliable negative correlation, for an otherwise crappy investment (low return) to improve a portfolio with much higher return. With results like the ones above, I don't think you need to do the math. However, let's look at one. We're looking this time at the mutual fund itself, the blue line, because I can analyze mutual funds in PortfolioVisualizer, and I can't put the Morningstar averages into PortfolioVisualizer.
For example, in the managed futures category: MHFIX, Equinox MutualHedge Futures Strategy Fund.
Source

This is a fund that
beat its category average. The category average would be
worse. If this fund doesn't help a portfolio, the category average won't.
And if we use Vanguard LifeStrategy Moderate as a good example of a "traditional" 60/40 stocks-and-bonds portfolio, well, look at the low correlation.
So do you
really believe that this fund, which earned a
cumulative total of only 14% over a period of 8-1/2 years, would have improved Vanguard Lifestrategy Moderate?
Because it wouldn't have. The red curve is 80% LifeStrategy moderate, 20% MHFIX. By all means play with the percentages if you think 20% an unreasonable number.
Source
MHFIX, because it had such low return, dragged down VSMGX's return. Because it had such low correlation, it
did reduce volatility. But... overall... it lowered the Sharpe and Sortino ratios.
Are you interested in the averages themselves or in the behavior of funds? I definitely understand not wanting to focus on individual funds, especially those known ex-post to have been the best. But I wonder about the applicability of the averages to whatever questions you're trying to answer, which I'd like some clarification about.
I'm interested in funds for a number of reasons. One is that as a low-sophistication retail investor, not a "qualified" investor, funds and the Investment Company Act of 1940 are suitable for me.
Another is that funds force realism. You can't hide behind cost-free academic indexes. People say, "well, of course the fund performed poorly, look at the expense ratio." I say "well, why is the expense ratio so high?" (1.70% for MHFIX!) Maybe there is a high intrinsic cost in trying to invest in this asset class.
Another is that funds force transparency. I don't know what to make of assertions that some strategy or another has been used and working magnificently for advisors or hedge funds. I just have no way to verify them. With funds, there is a huge wealth of information... and a lot of help from Morningstar.
The interesting thing is how many strategies that look great in presentations, have fallen down just about the time they were implemented as mutual funds. I don't know if that's real or just my biased perception. "Rekenthaler's Rule" is "if the bozos know about it, it doesn't work any more." Perhaps "getting mutual funds that implement them" is a good marker for "the bozos know about it."
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.