May 25, 2023

Thinking in Probabilities

I was a math major in college. My favorite class was Probability and Statistics, taught by Dr. Wolcin. He warned us from the beginning that the final exam was the grandaddy of final exams—that it was really hard, and he would probably end up curving it. He said that if you got a 90%, you were a total stud. I got an 89%. The highest grade in the class was a 99%. You won’t believe what the guy who got a 99% is doing these days.

I think one of the main problems that people run into while trading is that they don’t think in terms of probabilities. They have a deterministic view of the market. The chart says the market will go up; therefore, the market will go up. But you have to think in terms of probabilities, assign expected values to each outcome, and make your decision on that basis.

Estimating probabilities is hard. Sometimes the computer will do it for you—the World Interest Rate Probability (WIRP) screen on Bloomberg will tell you Fed rate hike probabilities based on where interest rate futures are trading. Other probabilities are hard to handicap. How do you figure out the probability that XYZ company will beat earnings? And even if it did, what is the probability that the stock will go up?

I use a combination of probabilistic and deterministic thinking when trading. As you know, I am a sentiment geek, so when sentiment is one-sided, you pretty much have your answer. But the rest of the time, probabilistic thinking should be your guide.

What is the probability that a stock will go from 10 to 5 when it has already gone from 50 to 10? The answer might surprise you.

Blackjack

We use probabilities all the time in real life. I was in Las Vegas recently and played a terrible blackjack game down on Fremont Street, a progressive game with a Shuffle Master. Probability was no help then. But if you’re playing a genuine six-deck game, then the odds may, at some point, be in your favor.

As a blackjack player, you like face cards—they are good for making 20s and 21s—but you hate small cards because the dealer will continue to hit until they have 17, and small cards will help them get there.

When people think of counting cards, they think it’s a matter of counting all the cards in the shoe. Not at all. You’re just keeping track of how many face cards come out because, occasionally, they are all concentrated in the back of the show. And, as long as you are allowed to vary your bet size, you can bet bigger when all the face cards start coming out. (Note: This is usually what gets people banned from casinos if they do it in any kind of size.)

Really what you are doing is assessing your probabilities. If you know that you have a 70% chance of winning the hand instead of a 49% chance, then you will naturally bet bigger. It’s very simple.

Conceptually, counting cards is not that hard—the hard part is doing it, pretending you’re not doing it, and camouflaging your behavior. And if you’re camouflaging your behavior, that’s going to take your win rate down to the point where it’s not really worthwhile. Nobody wants to do this and risk getting banned for $20 an hour.

Even understanding basic strategy can get you a long way toward understanding probability. Why do you hit a 16 against a dealer 10 upcard? Because you’ve already lost the hand by this point, and you’re just trying to make the best of a bad situation. Why do you always split 8s? Splitting 8s is a defensive split—if you have two 8s, you have a 16, which is a terrible hand.

You are better off with two 8s. And so on.

The Debt Ceiling

Here’s a good one: What is the probability that the US will default on its debt?

Well, it has never happened. The US always works it out in the end. So is the probability zero?

And then you think about what a bunch of coneheads these people are, how ideologically far apart they are, and how the political environment has never been more polarized… and then you think, well, maybe the probability is not zero. Maybe the probability is 5%.

Five percent is big enough that you should think about hedging that possibility. And then you have to do some fancy options math on what puts you can buy that will hedge that 5% probability.

What if the probability isn’t 5% but 40%? That is a whole different ball of wax. Incidentally, I think the probability is closer to 40% than it is to 5%.

None of this is easy. If it was easy, everyone would do it.

Jared Dillian

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