Without even checking, I can think of a bunch of assets which 7x'ed since Jan 2020. (BTC/general crypto, TSLA, GME/AMC etc).

I figured that's the first thing someone would think of upon hearing "7x" which is why I mentioned "This was done using a variety of strategies across a large number of individual names" in the OP. Just to further clarify, I have some exposure to crypto but I'm not counting it for this post, I bought some TSLA puts (forgot whether I made a profit overall), and didn't touch AMC. I had a 0.1% exposure to some GME calls which went to 1% of my portfolio and that's the only involvement there.

Personally, I have seen enough people claiming to outperform, but then fail to do so out of sample.

Can you please give some examples of such people? I wonder if there are any updates or lessons there for me.

Either way, I think it's very hard to convince me with just ~1.5 years of evidence that you have edge. I think if you showed me ~1k trades with some sensible risk parameters at all times, then I could be convinced.

I don't think I've done that many trades (depending on how you define a trade, e.g., presumably accumulating a position across different days doesn't count as separate trades). Maybe in the low hundreds? But why would you need ~1k trades to verify that I was not doing particularly high variance strategies? I guess this is mostly academic though, as it would take a lot of labor to parse my trade logs and understand the underlying market mechanics to figure out what I was doing and how much risk I was taking (e.g., some pair/arbitrage trades were spread across several brokers depending on where I could find borrow). I don't supposed you'd actually want to do this? (I also have some privacy concerns on my end, but maybe could be persuaded if the "value added" in doing this seems really high.)

Or if in another year and a half you have $300mm because you've managed to 7x your small HF AUM, I will be convinced

I'm definitely not expecting such high returns going forward. ("600% return" was meant to be Bayesian evidence to update on, not used to directly set expectations. I thought that went without saying around here...) Obviously there was a significant amount of luck involved, for example as I mentioned the market was particularly inefficient last year. One of the hedge fund managers I follow had returns similar to mine this year and last year, but not in the years before that. I'd guess 20-50% above market returns is a realistic expectation if market conditions stay similar to today's, and I hope I can still outperform if market conditions go more "out of sample" but I currently have no basis to say by how much.

Also, I'm already starting to feel diminishing returns (is there a more technical term for this in the investing world?) kick in at my AUM level, as I now have to spend multiple days accumulating some positions to the sizes that I want (and they sometimes take off before I finish), or ignore some particularly illiquid instruments that I would have traded in the past.

NOTE: Don't believe everything I said in this comment! I elaborate on some of the problems with it in the responses, but I'm leaving this original comment up because I think it's instructive even though it's not correct.

There is a theoretical account for why portfolios leveraged beyond a certain point would have poor returns even if prices follow a random process with (almost surely) continuous sample paths: leverage decay. If you could continuously rebalance a leveraged portfolio this would not be an issue, but if you can't do that then leverage exhibits discontinuous behavior as the frequency of rebalancing goes to infinity.

A simple way to see this is that if the underlying follows Brownian motion $dS/S=\mu dt+\sigma dW$ and the risk-free return is zero, a portfolio of the underlying leveraged k-fold and rebalanced with a period of T (which has to be small enough for these approximations to be valid) will get a return

On the other hand, the ideal leveraged portfolio that's continuously rebalanced would get

If we assume the period T is small enough that a second order Taylor approximation is valid, the difference between these two is approximately

In particular, the difference in expected return scales linearly with the period in this regime, which means if we look at returns over the same time interval changing T has no effect on the amount of leverage decay. In particular, we can have a rule of thumb that to find the optimal (from the point of view of maximizing long-term expected return alone) leverage in a market we should maximize an expression of the form

with respect to k, which would have us choose something like $k=\mu /{\sigma }^2+1/2$. Picking the leverage factor to be any larger than that is not optimal. You can see this effect in practice if you look at how well leveraged ETFs tracking the S&P 500 perform in times of high volatility.

I think the two mutual funds theorem roughly holds as long as asset prices change continuously. I agree that if asset prices can make large jumps (or if you are a large fraction of the market) such that you aren't able to liquidate positions at intermediate prices, then the statement is only true approximately.

That's not the key assumption for purposes of this discussion. The key assumption is that you can short arbitrary amounts of either fund, and hold those short positions even if the portfolio value dips close to zero or even negative from time to time.

Leveraged portfolios will of course have a higher EV if they don't get margin called. But in an efficient market, the probability of a margin call (and the loss taken when the call hits) offsets the higher EV - otherwise the lender would have a below-market expected return on their loan. Unfortunately most theoretical accounts assume you can get arbitrary amounts of leverage without ever having to worry about margin calls - a lesson I learned the hard way, back in the day.

In general, if leveraged portfolios have higher EV, then we need to have some explanation of why someone is making the loan.

Maybe the weirdness is that you are assuming all investors have linear utility? (I don't know what the symbol V_t means, and generally don't quite understand the theorem statement.) Or maybe in your theorem "E" is an expectation that weights worlds based on the marginal value of $ in those worlds, whereas in other places we are using "probability" to refer to the fraction of worlds in which an event occurs?

Nope, not linear utility, unless we're using the risk-free rate for r, which is not the case in general. The symbol V_t is a lazy shorthand for the price of the asset, plus the value of any dividends paid up to time t. The weighting by marginal value of $ in different worlds comes from the discount rate r; E is just a plain old expectation.