Monday, May 3, 2010

Einstein was right.

Albert Einstein was once asked what he thought was the most powerful force in the universe. He replied, "compound interest."

And it's true (of course it's true, you condescending git, bloody Einstein said it) that exponential growth -- compound interest being a type of exponential growth -- can produce effects that are utterly counter-intuitive. Like that old Indian story about the sage who beat a king at chess and asked as his reward "merely" for a grain of rice on the first square of a chessboard, two on the second, four on the third, etc. The king thought he'd gotten off lightly, but by the time he'd reached the 64th square, there wasn't enough rice in the kingdom to meet the demand.

(I put this story into This Private Plot. In more detail. You'll have to wait.)

It's like the betting tactic called an accumulator, where you place all your winnings from one horse race onto the next, and so on. The Economist once had an article (which I couldn't find before writing this, so the details are fuzzy and probably fabricated) that calculated what would have happened if you'd started with a dollar in the 1920s and, by good fortune, switched your accumulated investments at the beginning of every calendar quarter into the sector of the economy that was going to perform best during that quarter -- gold, or real estate, large-cap stocks, etc. Of course, the final number was some ludicrous sum, probably greater than GDP of the entire solar system.

And, of course, nobody did it. Because nobody can reliably predict the economy, especially economists. If they could, they wouldn't stick around being economists. They'd be Grand-Dukes or Hugh Hefner or something. Anything but an economist. Even a mystery novelist, and we don't make any money.

The Economist followed this up with an alternative calculation -- what happens if you switch your accumulated earnings into the sector that was the best performer in the previous calendar quarter? In other words, if your investment strategy is, like most people's, just a little reactive. You can't predict the future, but you move as quickly as you can to catch the rising tide. It's once a quarter -- surely the trends will keep going just for a few weeks more?

Uh-uh. In this scenario, if I recall, you end up with a net loss over the years. Or perhaps about a hundred bucks, the price of a Starbucks coffee in, oh, 2012. In other words, if you hear about a good-performing investment, it's already too late for you.

Now with this in mind, suppose I'm a shyster (not too great a stretch). I pick, say, 1,024 likely millionaire investors and write them a letter, boasting of my prowess at foretelling investment performance. (Why 1,024 and not a round 1,000? Pay attention.) And to prove it, I'll predict which way Apple's share price will go by the end of the week. But to half of those investors, I say it'll go up; the other half get a letter saying it'll go down.

At the end of the first week, in which Apple has increased in value, I forget about the 512 investors who got the "Apple goes down" letter -- and they'll forget about me long before the next scam -- and I send the other 512 another letter. Again, one half get the upswing prediction, the other half the downswing.

Well, you see where this is going. After just six weeks, I'm down to a mere sixteen potential investors. Ah, but those sixteen people have just watched me predict, with uncanny accuracy, the performance of a leading stock for six weeks in a row. So by now, they've probably taken the bait, and I can stop -- I don't even need to go the full ten weeks that would bring me down to my last surviving (but hugely impressed) millionaire.

Hang on, why did I get started on this? Oh yeah, that exponential growth thing also works in reverse. Numbers get smaller very quickly if you keep halving them, instead of doubling like the chessboard conundrum. From about a thousand* investors, we're down to a mere sixteen in only six weeks, and only one remaining if I'd gone for ten weeks.  But the point about my shysterdom is that, somewhere along the journey -- likely, long before even six weeks are up -- I only need one or two of those astounded and greedy millionaires to hand over their fortunes to me to, er, manage, and it's next stop Bimini.

(Where is Bimini? And do they have extradition orders?)

And that's what I want to write about: family trees. But another time, because this is quite long enough.

*It was 1,028 because it's an exponential of two.

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