That's not what the sentence you quoted means. When you say "asset X has never traded down over a 5 year period", it means if you look at any day, and then look at the price 5 years later, the price 5 years later will be higher. For a 12 year old asset class, just taking daily prices that means you have over 2500 pairs of prices (1 day compared to a day 5 years later) to look at, and in this case, in all of those 2500 pairs the later price was higher.

Well sure, but those 2500 pairs aren't exactly independent now are they? In fact you can't identify more than 2 independent pairs.

You'd be better of just pointing out it increased quite a bit those two time periods of 5 years, as that would already imply that those 5-year differences were unlikely to be negative in-between. At least if Black–Scholes is to have any merit.

This is a substantially better way to make the point I tried to make.

Ok, humor me here, you guys are certainly smarter than I am.

This would be based on a flawed assumption that history is a good indicator of future performance. I choose an entry point into Bitcoin somewhere in the last 12 to 5 years. From that point on, 5 years later, the price is always ahead. Those pairs as you said are not independent. How does that matter here?

Edit: And why would that make a bad observation or a bad strategy?

It's not necessarily a bad observation but if you look at a lot of dependent observations then you can't simply count the number of observations.

I mean sure 'it has never decreased' is slightly stronger than just the fact that it increased over 2 independent 5 year time periods, but that's mostly because 'it has increased' is a pretty weak observation. The information it adds is that it must have increased quite a bit, which you already knew.

So rather than a bad observation it just doesn't tell you much, hence my tongue in cheek observation that they're basing decisions on the basis that it has happened 'twice'.

I think what we are saying is mostly just talking about how strong the evidence (how it has gone) is, for the outcome that it will be like that in the future.

I don't think I'm "clearly smarter", I just happen to have taken a class that said a little about stochastic processes, which I think are neat, and therefore jumped at a chance to try to apply it a little bit. I don't have any deep understanding of investment. (contravariant might though, idk.)

It's still a weird thing to note. If the price goes down to 3k tomorrow and stays there forever, they can still make the same claim for 2 more years.

I think he meant at least seven times ;)

If we pretend (which is of course not accurate, which is why I say pretend) that the price follows a Wiener process, so that on each time interval the net change across that interval is a normally distributed random variable with mean 0, where the difference across different disjoint intervals are independent, well, under that inapplicable model, said "7 different times" wouldn't be independent (while the difference across the first 5 years, and across the second 5 years, would be independent, and so that would count as 2 independent observances of that.

I wonder, if you have such a process W, what would the probability of "For all t in [0,7], W_{t+5} > W_t" be? It would of course be less than (1/4) because it would imply W_5 > W_0 , and also W_12 > W_5 , which would be independent events each with probability 1/2 , and so the probability has to be at most 1/4 . But I assume it probably has a much smaller probability than that.

If instead of a Wiener process, we model it as a Wiener process with drift, as X_t = \mu t + \sigma W_t , how does the probability of "For all t in [0,7], X_{t+5} > X_t" vary with \mu ? (well, obviously, as \mu increases, the probability goes up, but I mean stuff like "how big does \mu have to be in order for it to not be unlikely?" and "how quickly does the probability increase as \mu increases?", etc. . )

Isn't the point he tried to make that if you've chosen an entry point into Bitcoin anywhere in the last -12 - -5 years you'd still be ahead 5 years later? So that if your time horizon is at least 5 years and if history is any indicator (here is the real fallacy imho) investing in Bitcoin is a good idea?

(Sure, that's way more than 7 entry points :)

I was mostly just trying to show why the "it happened twice" makes some sense, (though, it is somewhat stronger than "it happened both times". I just don't know how much stronger. I guess that was the sort of thing I was wondering-out-loud about) and also saying some thoughts that that brought to my mind.

But yes, "it working at any time if you wait 5 years" would be relevant. I guess I was trying to think about, "what would the chances be of that happening to have been the case purely by chance?". Like, in order to look at how strongly it suggests it will be the same in the future.