Ralph Melton (ralphmelton) wrote,
Ralph Melton

Big Round Number

My AAPL-heavy portfolio is very close to a Big Round Number. This is very exciting, but it's also quite meaningless. I can hit that Big Round Number easily if I include other assets. My portfolio would have hit that Big Round Number before if I had not sold some Apple stock. Even if it hit that Big Round Number soon, I'm likely to drop below that number when a charitable donation goes through. Even if that happens, I'll hit the Big Round Number if the stock price goes up another $10 or in April when more RSUs vest.
I won't even see a number with a lot of zeroes; the chances of me seeing a moment when my portfolio has really hit the Big Round Number are pretty low.

But even so, Big Round Number! Woo!


My financial advisor has noticed a tone to some articles about Apple that smells of overconfidence. I'd seen the same article and I smelled it too.

This leaves me full of uncertainty and doubt. I feel that Apple has tremendous upside potential, and I'd hate to miss out on that. On the other hand, I know that I'm likely to be optimistic about Apple even when that optimism is not justified, and one of the things I pay this financial advisor for is to balance me on that and be sensible when I am not.

So my general strategy is to be pretty conservative with the money that I know I need. And then for the money I don't yet know what to do with... well, I'm not sure. I don't believe that I have any significant ability to predict the market, either for Apple or the market in general. I think my best way of finding happiness with my investments is to pick a strategy that adequately covers the possibilities, execute that strategy, and accept the results without fussing too much about what could have been.


Back in October, I got bluelang to help me think through a vast oversimplification of this sort of problem.

Consider this game: you bet as much or as little money as you want. 50% of the time, you win 3 times the amount you bet; otherwise, you lose what you bet. This is a repeated game; you play it over and over.
Three things are obvious to me about this game:
- This is a game worth playing; you'll generally profit by putting some money in this game.
- The more you put in, the more you make.
- If you put in all your money each time, you will almost certainly lose it all.
So what's the right strategy?

The strategy that maximizes the expected money you have after N repetitions of this game is to bet all your money every time. You only have a 1/2^N chance of winning anything, but if you do you end up with 3^N.

But that really seems like a wrong strategy intuitively, because you're almost certain to lose it all. So maybe the value I'm placing on money is nonlinear. (It's really hard to measure how I value money. I suspect that my valuation is monotonically increasing, vaguely differentiable, and its derivative is generally decreasing.)

So I reanalyzed this game, but instead of trying to maximize Exp(money), I tried to maximize Exp(log(money)). It turns out that this particular game is simple enough that it can be solved analytically: you maximize Exp(log(money)) by betting 25% of your money at any time.

This is very interesting, because it gives a basis for diversifying. The 25% is clearly just an artifact of this particular game, and I mustn't get hung up on that. But trying to maximize Exp(log(money)) suggests strategies that make a tradeoff between safety and opportunity, which matches my intuition that I do need to make some sort of tradeoff between those two.

I mentioned all this to my financial advisor, and he pointed out that studies show that people in general are more unhappy about losing half their portfolio value than they are happy if it doubles - which would disprove a log valuation. So my strategy may well be wrong for maximizing my happiness. This sort of thing causes me no end of second-guessing.


Since I began this article several days ago, my portfolio has surpassed that Big Round Number and then dropped back below it.
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