The Reddit people whose posts are being used here, but I can't be sure it's just a guess. I'm not talking about fund managers that follow strict rebalancing and risk guidelines. The creator of this webapp acknowledges this and says that it's very hard to be at the top of the rankings without this happening.
You're talking about the efficient frontier from Modern Portfolio Theory, no?
I'm referring to the analogous concept from E log X optimisation. (The "Kelly criterion".)
The efficient frontier based on Markowitz' mean--variance optimisation does not help you find a risk level that maximises growth, because it looks at one investment in isolation, not sequential reinvestment over a long period.
The analogous concept I'm referring to is the set of portfolios that are linear combinations of risk-free assets and the E log X optimal portfolio. These are all Kelly optimal under more and more restrictive constraints on allowed variation, but come with slower growth as a trade-off.
To reiterate, the E log X "efficient frontier" talks about how fast your portfolio will grow over time as you reinvest your gains. The Markowitz efficient frontier tells you something about the statistical nature of a single investment opportunit.
Sure, it does. But it does so in the same sense that MPT requires known mean and variance. In either case, we go with estimations.
In many practical cases, the joint distribution of outcomes is easier to estimate safely than the variance. The joint distribution of outcomes can be approximated by something very close to the actual observed distribution of outcomes. However, the variance has, in a sense, to be derived from a fitted model. This is one step further removed from reality which risks introducing more incorrect assumptions.
Other reasons are that the variance doesn't even exist for some assets (too heavy tailed distributions) and that errors in estimating the joint distribution can be smaller thanks to at least some level of central limit theorem.
You're talking about the efficient frontier from Modern Portfolio Theory, no?