Advent of Alpha Day 9: Delta T

A few days back I mentioned William Poundstone’s Fortune’s Formula as a great narrative non-fiction telling of Kelly criterion’s creation.

Another book Poundstone wrote that I’ve enjoyed is How to Predict Everything (this was its title in the UK, I believe it has another title in other markets). It is on the surface an introduction to how Bayesian probability can help you predict anything (we’ll return to this another day, perhaps).

The part of the book that really made me sit up and take notice however was his description of J. Richard Gott’s temporal version of the Copernican principle: when you observe a phenomenon in progress, your observation does not occur at a special time.

Gott’s account goes like this, from his time when he was stood in front of the Berlin Wall:

Standing at the Wall in 1969, I made the following argument, using the Copernican principle. I said, Well, there’s nothing special about the timing of my visit. I’m just travelling—you know, Europe on five dollars a day—and I’m observing the Wall because it happens to be here. My visit is random in time. So if I divide the Wall’s total history, from the beginning to the end, into four quarters, and I’m located randomly somewhere in there, there’s a fifty-per-cent chance that I’m in the middle two quarters—that means, not in the first quarter and not in the fourth quarter. Let’s suppose that I’m at the beginning of that middle fifty per cent. In that case, one quarter of the Wall’s ultimate history has passed and there are three quarters left in the future. In that case, the future’s three times as long as the past. On the other hand, if I’m at the other end, then three quarters have happened already, and there’s one quarter left in the future. In that case, the future is one-third as long as the past. … (The Wall was) eight years (old in 1969). So I said to a friend, “There’s a fifty-per-cent chance that the Wall’s future duration will be between (two and) two-thirds of a year and twenty-four years.” Twenty years later, in 1989, the Wall came down, within those two limits that I had predicted. I thought, Well, you know, maybe I should write this up.

Breaking this down, he’s saying there is a 50% chance that you’re in the middle 50% of a period of time of something happening. You can do the maths for any confidence interval you like, he just chose 50% - the maths work for 80%, 90% or 99%, you just assume you’re in that middle piece, nothing special.

The key here is that nothing special is happening. In most markets, they evolve as time gets closer to an event starting, or an event finishing. These are not special times, this method doesn’t work then.

But let’s suppose you’re watching a 10-second swing an hour before an event. Can you state that this might be a random walk, and it might be useful to state with 90% confidence how long that random walk will last, and trade accordingly?

I think it might be interesting to look at.