inamerrata

(Random topic courtesy of Dressy Bessy)

A couple more thoughts on Sunday’s post. In comments, Brendan Scott asks “Why would a trader extrapolate against their estimate v valuation?” But there’s actually a broader question — why would anyone trade at all? The initial scenario provided infinite supply at $500 per item, and gave a randomly chosen demand at $500 per item, which was then naturally fully satisfied. If they thought it was a good idea to buy more at more than $500, they should have bought upfront, and why would they want to sell something they just paid $500 for, for less than $500? Worse, the only difference between the traders is the input they get from the random generator: their strategies are explicitly the same. So no trader can potentially be smarter than another, and profit from their stupidity, they can only profit if the random number generator gives them a lucky number, and someone else an unlucky number. So I don’t think there’s a good answer to “why would they do this?” — participating in this market is fundamentally a mistake, the way most people view the world. For instance, it ends up with a 74% chance that you’ll have less money than you started with, and starts off with perfectly equal wealth amongst all the participants, and ends up with the wealthiest individuals having over $60,000 while the poorest have less than $10.

In a real market, as JD points out you have different people having different information — though of course you’d have to actually have something to have information about. If you decided the assets were batches of ten barrels of oil ready for delivery in twenty-four months time, different people would have better or worse estimates of the value, and depending on other changes in the economy, the underlying value would change too (maybe someone discovers a cheap oil replacement and it drops, maybe there’s a war and it rises).

An interesting theory that I’d never heard of until David Pennock posted about it the other day is the “Kelly Criterion”. Given an estimate of your odds of success, and how much you’ll make, it will tell you the optimal amount to risk to get the biggest advantage from compounding returns. The idea is if you’ve got an almost sure thing, and you only risk a few dollars on it, you won’t make much; but if you continually risk everything, even on sure things, you’ll eventually lose it all, and that’s no good either. The Kelly criterion makes that idea precise, telling you exactly how much of your resources you should commit, assuming you can come up with a reasonable estimate of your odds.

The original paper was from 1956 byJohn Kelly, apparently in collaboration with Claude Shannon, and as you might therefore expect, came from an information theoretic approach, rather than an economics one. The idea was that you have a secret channel that tells you exactly what to bet on, but unfortunately it’s not a clear channel, and sometimes you mishear what you’re being told and thus bet wrong. Fortunately you’re clever enough to figure out how often this is likely to happen, and thus you can work out when to follow the tips and how much to invest in them, which gives you the aforementioned Kelly criterion. But the signal you get doesn’t have to actually be from the future, it just has to be correct predictably often. If you want to apply that to your intuition, your astrologer, or a groundhog’s shadow, that’s fine, though the lower your odds of success, the lower the amount you’ll be encouraged to invest, and thus the lower your optimal returns will be.

But that’s only relevant if you’ve got an actual meaningful signal and a chance to actually profit, which isn’t what I gave my poor automated traders. If I had, an optimal system would’ve rewarded folks with the best signal, provided useful information for someone, and transferred physical wealth from people who wanted information to people who had it. Redoing the marketplace so that was actually possible would provide a much more interesting endgame.

Nevertheless, it’s interesting to me that even without any fundamentals at all, or any complicated trading techniques, you can pretty easily get behaviour that looks like a bunch of otherwise intelligent people bidding themselves into bubbles and then crashes. If you looked at those graphs as the price of oil or milk or similar, you’d naturally go looking for a cause for the price changes: but at heart, there actually wasn’t one in that case, it was just a combination of coin flips, that happened to be more or less likely, due to trader’s habits, and how much they could happen to afford at the time. You can only reasonably fix that by changing habits, and probably the only way to do that is to bankrupt folks with bad habits so they stop it…