“Buy low, sell high.”

For what it’s worth, everyone’s heard this old Wall Street mantra. Unfortunately, it ain’t worth very much.

If there were a 100% chance that the stock market would go up tomorrow, you’d probably buy some shares. In fact, there’d be no reason not to buy as many shares as you could, because you’re getting what’s essentially free money. That’s pretty obvious.

But in case you didn’t know, this doesn’t ever happen. Instead, what really happens is more like, “there’s a 51% chance that the market will go up in the next week.” And it wouldn’t make much sense to go crazy and buy all the shares you can if these are your measly odds.

The question, though, is how much should I buy — or sell — when the probabilities are complex and hard to decipher? Professionals know that this decision-making under uncertainty is what investing is all about. But professionals also know their personal limitations.

Man vs. Machine

We’ll just come out and say it: Humans, naturally, are really bad at investing. So bad, in fact, that even if you have the raw intellect to get over the first hurdle to investment success, you still have no chance of getting over the second.

The first hurdle is that we humans have no intuitive idea of how much money to bet on something simple. Even if you’re not the kind of person who buys lotto tickets (which are, in case you didn’t know, a bad investment!), you probably won’t be able to figure out how many dollars you should bet on a simple game of chance like this:

Bill flips a weighted coin. There is a 60% chance it will land heads. You have $100. For every dollar you bet, Bill will pay out a dollar if you’re right. You can play as long as you like, and you want to make as much money as possible without bankrupting yourself.

Now, obviously, you’ll bet heads, since the probability is way better. (Stupid Bill.) But less obvious is how much money you’ll bet on each throw.

Most people will say $1. Some say $5. And if they play the game until they have $100 in winnings ($200 total), the $1 people might start betting $2. Eventually, many of them will get too confident and start betting $20-50 at once, then some of the less lucky ones will double down until they literally lose everything. That’s just what humans do.

Fortunately for professional investors, there are ways to avoid our emotions here — there are actually correct mathematical answers to these types of problems. In the case of this coin-flip game, the correct answer is 20% of your money, or $20 to start. If you had a different answer, your answer was wrong. And we really mean that! Objectively, mathematically wrong!

All of the stuff above was still just the first hurdle to decision-making under uncertainty. Are you ready for the next part? The second hurdle is exponentially more complex, and nobody who isn’t a cyborg can overcome it. Let’s keep Bill around, but this time he’s your broker.

Bill gives you a call and tells you that by next Friday, the S&P 500 has a 20% chance of going up between 0% and 0.5%, a 10% chance of going up between 0.5% and 1.2%, a 2% chance of going down 4% to 6%, a 0.2% chance of going down 10% to 18%…

Now, assuming that Bill’s even right about all of this, how do we go about determining how much money we ought to have in the market? How seriously should we take that 2% chance of the market crashing 4% to 6%? What about a 0.2% chance of 10%+ losses? Remember, choosing the right answer means the difference between gaining or losing $100,000 this year. No pressure!

Professionals know that our brains do not have the capacity to make a decision on this type of information — at least not a good decision. This second hurdle is where the idea of “volatility” finally enters the picture, and this is why people talk so much about “market volatility” as a scary thing. Whereas in the coin-flip game, there were only two outcomes (and that was hard enough!), now there are quite literally millions, and some of them are really scary and really hard to quantify.

A “volatile” stock market has a whole lot of possible outcomes. It could go up 50% or down 50%, and land anywhere in-between. And no one is ever certain what will happen next. When we talk about investing as decision-making under uncertainty, this is really where it gets hard, and this is where the human professionals rightly throw up their arms and turn to computers — because our brains just can’t do it.

Unlike humans, computers are designed to find the right answers to questions like those above. Not that the answers always come quickly (we run nearly an hour of computer simulations every day to get you the “correct” allocation numbers for the S&P 500), but the answers come eventually, and the computers do a million times better than we humans could ever do on our own.

This, and this alone, is why we believe that we can invest a substantial portion of our retirement savings onto the stock market without being scared all the time. Most people just push the button and hope for the best. We don’t want that for you — and that’s why there’s a small army of computers figuring out the ideal stock allocation for someone with your risk tolerance.

Thanks to the miracle of cheap computing power, all of this costs you a grant total of $7.99 a month. (And that’s a no-brainer!)

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