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Comment by kgwgk | Hacker News Reader

What do the volatility and return of the market have to do with anything?

Are you calculating the probability that he did achieve these returns by luck timing the market? That's obviously not what he did.

Picking and holding a stock that did extremely well by over the period is not a one in a quintillion event.

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For a fund like this, more volatility = more opportunities to make money. Doing 25% when the benchmark does 15% is less impressive than when it does 10, 5, or is down over the same period.

(Not GP.)

This statement is correct, but doesn't address the problem with the OP's calculation.

This fund is up basically entirely on the strength of TSLA being up 700%. OP is basically considering two possibilities:

1. TSLA stock is a driftless geometric Brownian motion with a volatility matching that of the general market, and happened to get a 700% return purely by chance, or

2. The fund manager, due to his exceptional skill, knew that TSLA was going to be up 700%.

The OP is rejecting option (1) and then concluding that option (2) must be the case.

Of course in reality neither is the case and the OP's calculation is totally irrelevant.

But what matters is not the volatility of the market as much as the cross-sectional dispersion of stocks. If correlation was high and all the stocks hade beta one and were almost identical to the market there would be little opportunity for a stock-picking fund like this, whatever the volatility of the market.

The market's only moved in one direction over the period; the fund can make money on moves in both directions.

So the more volatile (within a period) the more money making moves there.

If this is the benchmark:

     _   _/\  /
    / \_/   \/

at a dollar per slash, it's up $2. A fund that bet (and realised) a $1 per slash made $8.

(Even with only long bets, they could make $5.)

The market has moved a lot. But the point is that if the fund goes 100% TSLA at the beginning and does nothing else it would have outperformed massively and the volatility of the market would be completely irrelevant.

What point is that? You're moving the goalposts, why would/should/do you think this fund did go '100% TSLA at the beginning and [do] nothinig else'?

That seems closer to what they did than timing the market, don't you think?

My point was that to "test" if a concentrated stock-picking fund can get that result by luck you don't look at how often the market with such and such return and volatility gets that performance or how often randomly trading the market would you get this performance.

You look at how rare is it that a concentrated portfolio of random stocks has a very good performance. The answer is "not that much".

you look at a normal distribution of returns using SPY mean return and SPY stdev as the parameters and then calculate the chance of his returns or better 6 years in a row.

There's a lot of things wrong with my calculation, but it was illustrative of how P < 0.05 in this case, no matter how you calculate it.

We agree at least that there are a lot of things wrong with your calculation.

Null hypothesis is: he is not generating alpha given the assumption the underlying distribution of his returns are the same as SPY. How would you calculate the chance of him generating alpha using only the fact (and no other data) that he generated an annualized return of ~37% (iirc) over a six year period?

So you’ve rejected the hypothesis that his portfolio has the same distribution of returns as the SPY. Looks reasonable, because his portfolio does not track the S&P 500. Congratulations!

The QQQ (Nasdaq 100) also generates alpha without any doubt then, as does the SPUU (leveraged S&P 500).

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