Practice Second Gear Thinking

A theme I harp on is that investing is biology not physics. It’s a competitive game. You figure something out, the game adjusts. When people say “X happens in Y-year cycles” they are thinking like an astronomer who notes the fixed periodicity by which the Earth orbits the sun. This is physics thinking.

But markets price in common information.

Housing has been an inflation hedge. But if everyone knows that, will they bid it up until it’s not? If someone pays 2x the Zestimate for your house, then is this “investment” still an inflation hedge?

Absolute statements in the world of investing without any consideration of price are a red flag that the speaker doesn’t understand the difference. We know the Celtics are good. But what matters to a bettor is their record against the point spread. The point spread is why investing will never be QED’d.

You can learn more about investing from games and betting than books that have “investing” in the title. The investing books are fine for glossaries and knowing the mechanics of a bond just as the rulebook is imperative to play Scrabble. But the rulebook, like the textbooks, teaches you nothing of how to be good at the game at hand.

In an adaptive game, you need to see the next level. Let’s look at 2 types of second-level.

“Theory of Mind”

Wikipedia defines “theory of mind” as the “capacity to understand other people by ascribing mental states to them.”

In poker, when you bet, you know your cards and some sense of how they might rank at the table. But the key piece of information, is “when I make a bet, what hand do my opponents think I have?” Without considering such second-order knowledge how do you weigh the information you receive when they call your bet? You must inhabit your opponent’s mind. It’s the same skill you need to interpret market prices (see Staring Out The Window). What expectations and beliefs are in the price? This is second-order thinking.

Second order sensitivities

Besides second-order thinking, we must identify second-order effects. In the options world, the “greeks” are sensitivities. Delta is the option’s sensitivity to the underlying. Gamma is a second-order sensitivity that describes how an option’s delta changes with respect to the underlying.

But this topic is everywhere. If a company sells more widgets it makes more profit. But second-order effects mean attracting more competition or saturating a market. Every satisfied customer is one less customer that needs satisfying. So if I build a model of profitability based on units sold, when does the function inflect? When does opportunity fade into unsold inventory?

[A fun way to think about second-order sensitivities is playing “engine builder” boardgames like Dominion or Wingspan where synergies between your cards lower the marginal costs of later actions2. In essence, the cards have gamma based on how you stack them. Every time I use a card it might increase my odds of winning by X. That’s the delta or “benefit per use”. But the delta itself increases with synergy, so as the game progresses, you get more delta or benefit/use ratio, from the same card]

An exercise in thinking about second-order sensitivities

Commercial real estate investor Bill Lenehan on Invest Like The Best:

Here in Marin County, where values have gone up substantially and having a small house in Montana, where that market has similarly boomed post-COVID is that it is unquestionable that these property values are not sustainable…As someone who’s trying to build a business, which includes recruiting people, training them, compensating them, et cetera, doing that in this housing market is substantially more challenging. Well, I guess it feels good that the house is worth more than you paid for it. Net-net, I would welcome a decline in housing to a more normalized level.

Bill is looking at second-order effects. What would it look like if we translated bits of this quote to “greeks”?

Bill’s personal net worth sounds like it had an uptick because he owns a home in Marin. But he knows it would go up even more if it didn’t go up by residential home appreciation. That’s because he knows he has a larger delta to his business than his home.

Define delta as a change in Bill’s net worth with respect to real estate prices

What does this depend on?

For our narrow example, we will limit this to 2 sources of his net worth.

  • The weight of his home as % of net worth
  • The (delta of his business to RE prices) x (his ownership of the business)

But delta of his business to RE prices decomposes further:

  1. There’s the value of his company’s real estate
  2. The expected growth of the business which depends on operating margins amortized into a current valuation.

Bill recognizes that the growth of the business is the largest driver of his net worth and the rise in value of his Marin home represents a slowdown on this larger (albeit nebulous) factor.

First-order thinking is delta. “What happens to my income if I work more hours?” That’s a simple line with a slope of “pay per hour”. Suppose the extra work means you need to employ a babysitter. The slope is just “net pay per hour after paying the sitter”. But if the sitter is a student who can only work an additional 5 hours per week, then the delta or net pay per hour changes because you need to find a higher-priced sitter at some threshold of hours. That’s gamma – the change in your delta. What if there are no other sitters? Then you hit a wall. Your payoff function is abruptly halted. Or what if it inflects because now you need more massages because work makes your body hurt? These are all second-order effects on your delta (slope = net pay per hour) with respect to an increase in hours.

Mathematically, deltas are the slopes of lines. The cause-effect relationship of anything important is rarely so simple. It is convenience that compels us to describe how things work by pointing to lines. The deltas themselves change reminding you that linear thinking is just a snapshot in time. In fact, that’s all a calculus derivative is — zooming in so close to a function that its slope at that point describes a line.

When you listen to explanations, try to fill in the gaps of logic that the speaker understands but are unsaid. You are making the “greeks” or sensitivities explicit. Then you are only one step away from asking “what other greeks are at play?” and what is the “shape of their functions?”

To ponder:

What does a “too much of a good thing” function look like?

How about a hormesis (ie “a little of bad” thing) function?

What does a discontinuous phase transition(ie “gas > liquid> solid”) look like?

What does a logistics or S-curve function signify?

What phenomena follow a convex function? A concave function?

What’s a “winner-take-all” function look like?

Sell Your Textbooks For Boardgames

My bias is traders should study gambling, not investors and definitely not macroeconomics. I feel trading requires self-awareness and unique mix of humility and confidence. Humility demands questioning how you know what you think you know. But this is also a description of a cat chasing its epistemological tail. This needs to be balanced with the confidence to make a decision before you are comfortable, otherwise, you will be too late.

This brings me to Aaron Brown’s article in Bloomberg (paywalled):

Want to Succeed on Wall Street? Learn Poker, Not Economics

These excerpts will save you a click.


The Federal Reserve Bank of New York in conjunction with researchers at the University of Southern California and University College London for a paper titled Strategic Sophistication and Trading Profits: An Experiment with Professional Traders. The authors recruited 56 professional traders, plus an equal-size sample of students for controls, and evaluated their performance in a computer-simulated trading game. They then tested their subjects on a wide range of specific skills to see which skills were correlated to trading success.

Main findings

  • Among students, the only useful predictor of trading success was general intelligence.
  • Among professional traders, though, neither intelligence nor other personality traits and cognitive skills mattered much. Success did not depend on any fundamental insight about value. What mattered was strategic sophistication in the sense of taking an analysis of other people’s behavior to high levels. This calls to mind the folk wisdom found in poker, which is that “beginners think about their cards. With a little experience, they start thinking of the other guy’s cards. Poker begins when you think about what the other guy thinks about your cards.” The Fed paper suggests that professional traders are playing poker, while the students are playing games like chess, backgammon, or blackjack that depend on intelligence rather than guessing what other people are thinking.
  • The paper’s finding goes well beyond the claim that strategy is valuable for trading. It suggests that other things such as intelligence, risk strategies, personality traits or knowledge of fundamental value do not matter — or at least are evenly distributed among traders that they can’t be used to predict success.

Murky interpretations

  • The Fed paper did not find any advantage to years of education or experience or other indicators of trading. Who should you believe? The Turtle experiment and Wall Street folk wisdom have one great advantage, in that they are based on real people trading large amounts of money in real financial markets. Unfortunately, that makes controlled experimentation prohibitively expensive. Formal studies and other academic work conducted under laboratory conditions make the results much more scientific but at the cost of being one layer removed from reality.
  • If you are not a trader but want to be one, either for your own account or for an institution, the study suggests you should play poker rather than attending class and take game theory courses over economics…but
  • Conventional wisdom says you should develop your comparative advantages, whatever they are, and study successful traders. If your interest is to understand the economic function of trading, the study suggests it is a game that rewards aggregating information from others’ bids and offers and using that information to provide liquidity. Conventional wisdom suggests trading is a broader skill that combines fundamental and technical information to produce an equilibrium, with many different types of traders performing different functions.

Practical upshot (emphasis mine)

If you like poker more than class and game theory more than economics, it’s good news. You may lose in trading competitions with fellow students, but you have a bright future on Wall Street. On the other hand, if you’re counting on traders to assess fundamental economic value, the study is bad news. It suggests they’re focused on outsmarting each other, not on investigating reality.

Whatever you think about the study and possible implications, it’s always good to see a careful, controlled, rigorous analysis in an area where opinions tend to be much stronger than the foundations for those opinions.

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