Moontower #205

Friends,

One of the Substacks I never fail to read is Range Widely by David Epstein, author of Range (my notes on his interview about the book) and The Sports Gene: Inside the Science of Extraordinary Athletic Performance.

David is a journalist by trade. His writing is well-researched. Social science research, especially the kind of pop-sci stuff that climbs the heap to find itself in airport bookstores, should require a “grain of salt” rating (G: “germane”, PG: “possibly garbage”, R: “rumored at best“). David’s process and intellectual demeanor indicate care — he resists the temptation to oversell conclusions.

Personally, I rarely read social science books — I’ll just listen to a podcast with the author if I care. The insights in such books feel like they have an asymmetrical yield — if they confirm what you already thought then the opportunity cost of reading that book is high (I’ll be lucky if I read 500 more books before I’m dead) and if the book has a ground-breaking insight it’ll almost certainly be out of fashion within a decade (“the game theory of getting published in social science” is a comically fractal idea. If you google that phrase, you’ll see why).

Anyway, David’s history of intellectual care makes him an ideal candidate to interview other social science authors about their books — critical enough to ask good questions but friendly enough that he can get the interviews in the first place.

Enough preamble…some excerpts I enjoyed from David’s Q&A with psychologist Adam Grant on his new book Hidden Potential: The Science of Achieving Greater Thing (emphasis mine):

  • Many people believe that if you’re not precocious, it’s a sign that you lack potential. But potential is not about where you start — it’s a matter of how far you’ll travel. And the latest science reveals that we shouldn’t mistake speed for aptitude. Our rate of learning is driven by motivation and opportunity, not just ability. Think of all the late bloomers who weren’t lucky enough to stumble on a passion, or to have a parent, teacher, or coach early on who recognized and developed their hidden potential.

    This doesn’t mean we should ignore “gifted” students. We need to think differently about how we nurture their potential too. Empirically, the rate of child prodigies becoming adult geniuses is surprisingly low. I suspect one of the reasons is that they learn to excel at other people’s crafts but not to develop their own. Mastering Mozart’s melodies doesn’t prepare you to write your own original symphonies. [Kris: this is exactly the point Trent Reznor made to Rick Rubin as he wrestled with his own potential]. Memorizing thousands of digits of pi does little to train your mind to come up with your own Pythagorean theorem. And the easier a new skill comes to you, the less experience you have with facing failure. This is a lesson that chess grandmaster Maurice Ashley drove home for me: the people who struggle early often build the character skills to excel later. We need to start investing in character skills sooner.

  • Because Glennie is deaf, she had to find nontraditional ways to learn, like using different parts of her body to feel vibrations that correspond to different pitches. She and her teacher were constantly trying different ways to do that, and different ways to do everything, really. As you write: “Continually varying the task and raising the bar made learning a joy.” I’ve long been fascinated by this issue of variable practice. Mixing things up constantly might seem counterintuitive, but it turns out to be better for learning.
  • You note that concert pianists who reach international acclaim by age 40 typically were not obsessed early on, and that they usually had a slow but steady increase in their commitment to music. It just made me think of the first page of Battle Hymn — in which the author promises the secrets to raising stereotypically successful children, and recounts assigning her daughter violin and soon she’s supervising five hours of deliberate practice a day. That part was excerpted in the Wall St. Journal, and it was the Journal’s most commented upon article ever! It really seeped into the public consciousness, I think. What didn’t make as much of an impression was the part later in the book where the author (to her credit) recounts her daughter turning to her and saying: “You picked it, not me,” and more or less quits. [Kris: I’m very careful riding our kids in areas that they are naturally drawn to because of such “reactance”. I don’t want to turn “their thing” into “my thing”. You have an extra gear to give for those things that you discover independently.]
  • The issue of “learning styles.” This is the very popular idea that some people learn best by listening, others by reading, others by looking, etc. Maybe someone prefers podcasts to books because they style themself an “auditory learner.” Trouble is, a mountain of research has failed to back this idea up [Kris: Veritasium calls this “the biggest myth in education”. Although I suspect the testing design for experiments that dismiss the idea might be strawmanning the contention or interpreting it too narrowly].People may indeed have a style of learning that feels most comfortable, but that doesn’t mean they’re actually learning more that way. In fact, to use a line from Range, in many cases, difficulty is not a sign that you aren’t learning, but ease is [Kris: I’ve found that many teachers I respect agree with this so it’s not as bold a statement as it might appear even if this is the first time you’ve heard that. I remind my kids — if it’s easy it’s just review, not learning. Non-superficial learning hurts. I might even go as far to say that learning and pain are nearly synonyms. To be clear, such a statement is more useful as a reminder than a universal truth. Experiential learning is an easy counterexample]. As you write: “Sometimes you even learn better in the mode that makes you the most uncomfortable, because you have to work harder at it.” I was just reading a study (“Measuring actual learning versus feeling of learning”) which showed that Harvard physics students preferred lectures from highly-rated instructors to active learning exercises. But they learned more from the latter. The main difference in the active group was that students had to try to solve problems in groups before they really knew what they were doing, and so they would discuss, generate questions, and hit dead-ends, all before seeing correct solutions. We know that forcing learners to try to generate solutions before seeing them enhances learning (the so-called “generation effect”), but it doesn’t feel great, so we may avoid it.
  • Back in December, you helped me get in touch with RA Dickey, and he was every bit as stellar of an interview as you promised. His story helps to illuminate why so many people fail to try new methods when we get stuck. It’s not so much that we’re stubborn or resistant to change. We hate the thought of giving up the gains we’ve already made. We forget that sometimes, the best way to move forward is to go back to the drawing board. [Kris: Feeling seen] If your fastball is slowing down and your career is stalling, you have nothing to lose by tinkering with the knuckleball. We shouldn’t be so afraid of failing that we fail to try. 

Money Angle

Let’s moan about the reality of realty today.

My quick take when I saw that tweet and the comments:

This tweet is getting a lot of hate but…it’s exactly what I did for every place I’ve bought. Got an agent from the same firm so they can double dip. I mean the whole options market revolves around understanding the dynamic of billing both sides.

You’ll get better allocations when there’s a judgment call (there usually is) on the splits if you are a regular client of the broker. Give up a half-cent commission on a 5k lot a couple times a month lot so you can get 1/2 instead of 1/4 allocation on the 10k lot good by a dime.

In the options world, the analytics and nerd stuff get s a lot of attention but it’s also the most democratic aspect. The highest edge (although least scalable) part of the game is relationship maintenance. There’s an equilibrium of tit-for-tat that resides within a snapshot of time that is defined by prevailing technology and the split of predator/prey populations. Large shifts in either the tech or the populations alter the parameters of the equilibrium pecking order. There is one constant — middlemen “control” the flow. Flow is the plankton at the bottom of the food chain.

I think as a metaphor for many businesses — AI is gonna handle the calculus. But getting close to the people who wake up in the morning with opinions that lead them to buy and sell will always be the job to be done. The nerd stuff is satisfying. But making money is just grimy work.

It’s important to have the right expectations lest you cry when you find out who makes the most money (especially per unit of risk).

[A prior riff on the idea: The Juicy Stuff Doesn’t Hit The Pit]

One last thing…if the persistence of 6% broker commissions in our Zillow-enabled world has you puzzled, it seems like times might be changing. A recent settlement seems watershed:

🔗The Middleman Economy: Why Realtors Just Took a Big Loss and Homebuyers Might Benefit (9 min read)
by Matt Stoller

A shocking $1.8 billion antitrust decision by a jury against the National Association of Realtors for price-fixing could rearrange housing markets.

Money Angle For Masochists

🔗New post: A Simple Demonstration of Return Vs Volatility

  • Expected return for a bet is the simple probability-weighted average of outcomes.
  • If there is a 50% chance of a bet making 21% and a 50% chance of it returning 19% this it’s a good bet that is also not volatile. You expect to make 20% on average (despite the fact that you can’t ever make that on any single bet since you can only earn 19% or 21%).
  • Your expected terminal wealth after a single trial is 1.2x what you started with.
  • Since we took a simple average of the outcomes we computed an arithmetic mean return of 20%

Compounded returns

For multi-period investing where we do not take any distributions or “money off the table” we cannot use simple arithmetic means to compute an expected return.

Consider the same bet after 2 trials. These are the 4 possibilities each equally likely:

  • Best return, best return
  • Best return, worst return
  • Worst return, best return
  • Worst return, worst return

If we look at the summary table, there is no difference between the mean expected return and the median.

Let’s keep the mean return the same but raise the volatility. An investment that is equally likely to:

  • go up 100%
  • fall by 60%

Even though this is more volatile than the first investment, the mean expected return is still 20% per trial. You can compute this in 2 ways:

50% * +100% + 50% * -60% = 20%

or

Terminal wealth  = 50% * 2 + 50% * .4 = 1.2 or 20% return

But let’s see what happens when we look at the compounded scenario where we fully re-invest the proceeds of the first period into a second period.

Now the mean compounded return has dropped from 20% to just 4.72% and the median outcome is a loss of 10.6%!

The divergence between mean and median returns comes from the compounded effect of volatility.

Investing Is a Multiplicative Process

When it comes to investing, we are usually re-investing rather than taking our profits off the table each year. We hope to grow our wealth year by year like this:

1.10 * 1.10 * 1.10 … or 1.10n where n is the number of compounding intervals (typically years).

Therefore, we want to look at compounded not mean rates of return. To compute them we simply take the n-th root of our terminal wealth where n is the number of years.

If you doubled your money in 5 years then your CAGR = 21/5 – 1 = 14.9%

Note that if you took the naive average return you could say you earned 100% in 5 years or 20% per year. But this defies reality where you re-invested a growing sum of capital every year.

CAGR is a median return

It’s important to note that the expected mean return of these investments is still 20% per year. It’s just that the median is much lower. In the high volatility example, your lived experience usually results in a loss of 10.6% but the mean 2-period return is still positive 4.7%. The complication is that the avergae is driven by the 25% probability that you double your money in 2 consecutive year. In every other scenario, you lose money.

Volatility is altering the distribution of your outcomes not the mean outcome. 

Mathematically the median is the geometric mean. In a multiplicative process, you care more about the geometric mean. After all, you only get one life.

A note on log returns

A logreturn is a compounded return where we assume continuous compounding. So instead of every year, it’s more like every second. Of course, if our wealth grows from $1 to $2 in 5 years but we assume tiny compouding intervals, then the rate per interval must be small. After all the start and end of our journey ($1 to $2) is the same, we are just slicing it into smaller sections.

Computing an expected logreturn is simple. Using the volatile example:

.5 * ln(2) + .5 + ln(.40) = -11.2%

Note that this is slightly worse than the geometric mean return (aka median) we computed earlier of -10.6%

Volatility’s effect on compounded returns

The following table presents different investments that each have an expected arithmetic return of 20%. Just like the examples above. But the various payoffs are altered to proxy different levels of volatility. An investment that can earn 21% or 19% is much less volatile than one that can return 100% or -60% even though the average return is the same.

We use the simplest measure to represent the volatility — the ratio of the best return to the worst return.

The stable investment volatility proxy is 1.21 / 1.19 = 1.017

The volatile investment above is 2 / .4 = 5.00

Table snippet:

These charts show the divergence between arithmetic and median returns as we increase the volatility (the ratio of the best return to the worst return):

An investment that is equally likely to return 60% as it is to lose 20% has a 20% expected return but if you keep re-investing your long-term median outcome is closer to a 12-13% CAGR.

What if we raise the volatility further to a ratio of 5 (terminal wealth of 2x vs .4x):

At a ratio of 3.5 (1.87x vs .53x) our median result is zero. At a ratio of 5, the average return remains 20% but the median return is losing 10%. Almost all the paths are losing they are just being counterbalanced by the unlikely event that you keep flipping heads.

Takeaways

  • Investing is a multiplicative process so we want to look at compounded or log returns not simple returns
  • Compounded returns ask “what growth rate when multiplied from period to period gets us from the start point to the end point?”
  • Compounded and logreturns are always less than arithmetic returns
  • Compounded and log returns are better measures for what you expect to find in your bank account after volatility has taken its toll. Remember if you lose 50% on an investment you need 100% to get back to even. If you earn 50% on an investment you only need to lose 33% to be back at even.
  • If there was no volatility there’d be no promise of return, but volatility is a quadratic drag on returns. The sweet spot for your portfolio likely falls in the realm of the volatility of broadly diversified portfolios. By rebalancing you can reduce concentration risks that threaten to turn your entire nest egg into a coin flip. Even if this coin has positive expectancy, remember you can’t eat theoretical edge.

Pitbulls (Formerly StockSlam) Testimonial

One of the most fortuitous decisions I made in my career was accepting a job from SIG out of college. Back in 2000 going to Silicon Valley or I-Banking was all the rage. While trading was a coveted job, the idea of going to an exchange floor to sling options was not a mainstream career choice. And SIG was not a well-known company outside this narrow world.

The job offer I got from them was the lowest paying, but the interview process stood apart from the banks and other firms I talked to. It was clear that working for SIG meant a serious education in decision-making commensurate with the objective — to take responsibility for risking the partners’ own money after as little as 9 months of training.

I was placed at the American Stock Exchange where I would learn from senior traders including their head of education in NY, Mike Steiner, simply known as Steiner.

Steiner was a natural teacher, able to communicate complex ideas with simplicity and frankly, joy. It was no surprise when I discovered 20 years later he retired to become a physics teacher in public school.

In 2022, we reconnected and he showed me the prototype for what would become Pitbulls. Pitbulls is a game distilling the essence and mechanics of the mock trading program we used in training. Pitbulls is a fast-paced game requiring players to think quantitatively while building intuition and understanding investor psychology. Steiner focused on making it fun — it’s a game first. But when I saw it I was immediately struck by its potential to bring investing principles to life!

Skills that will immediately develop from the very first game:

  • market making in an open outcry market
  • tracking multiple quotes from competitors
  • managing a rudimentary portfolio
  • reacting to new information

Deeper concepts embedded in Pitbulls:

  • arbitrage pricing, inter-dependent pricing
  • expected value and probability
  • the concept of edge as the foundation of a business
  • how you can be profitable without relying on prediction
  • making trading decisions under uncertainty
  • risk and diversification
  • the role, wisdom, and conditions of a healthy market
  • an introduction to derivatives
  • a bridge from trading to investing principles

Steiner has been hosting in-person playshops for years and I helped organize larger events in NYC, SF, and Chicago to overwhelmingly positive feedback. Unsurprisingly, the most universal suggestion was “give us an online version”. People wanted to play on their own and host their own sessions.

Starting now, you can play online!

I’ve been writing about financial education topics for years. These posts go into how Pitbulls and its underpinnings can improve your thinking in powerful ways.

The Midpoint From 1 to 9 is…3?

For the past 3 years, the Berkeley Chess School has done a weekly lesson in our backyard. About 15 kids attend. They are mostly 2nd and 5th graders because we know the families through our kids.

I walk home from school with all the kids on chess day. I usually throw out a math question or riddle and by now the kids just ask for them on our strolls. Lately, the questions deal with rates, percentages/fractions, exponents/roots, or some basic number play stuff (“How do you know if a number is divisible by 9?”)

Some examples:

  • Start with $100. If you earn 10% then lose 10%, how much money do you have?
  • What’s larger 3⁴ or 4³ and similar questions?
  • If you travel 5 miles in 12 minutes, how fast are you going?[I haven’t dropped this one on them: “If I drive around a one-mile track and average 30 mph for the first lap, how fast do I have to drive the second lap to average 60 mph for both laps combined?” (Solution)]
  • If you have 5 kids on your team and only 4 kids start how many possible starting lineups are there?
  • If you lose 25%, how much do you have to make to get back to even?[I like that one because it’s a useful elasticity idea. If X is the loss percentage, you need to earn back X/(1-X).

    If you are selling lemonade and you cut your price by 20%, you need to sell 25% more cups to be revenue-neutral.]

I started giving these questions because, well it’s just play. Riddles are inherently satisfying. But I’m also conscious of imparting some durable concepts. It’s not quite as deliberate as hiding the dog’s pill in the peanut butter but there’s some overlap. Honestly, the main motivation is keeping the kids who aren’t into sports engaged. There’s about 40 minutes between the kids getting to my house and the start of chess. The 2nd graders usually play soccer and the 5th graders hoop it up. A few kids aren’t into either but they gravitate to the riddles (my boys just wanna play sports and my 5th grader, Zak, with sass tells his friends “This is the stuff I deal with all the time”).

Lately, I’ve been doing more exponent stuff because I know they aren’t doing that yet in 5th grade but it’s reachable for them. Zak is taking the online Pre-Algebra I course on Art of Problem Solving which is comprised of 7 chapters. He just wrapped chapter 2 which is all about exponents so that’s been top-of-mind for coming up with the questions.

The challenge question to end the chapter was to solve for the 2 possible values of X (see below). But keep in mind, they haven’t learned how to compute square roots or any other kind of roots. You can do this without any involved computations and without roots. You can find the solution at the end of the post.

Find the 2 possible values of x:

Anyway, I didn’t give the kids that question but by this past week, they understood the basics of computing a simple exponent or taking a square root. So I took a stab at base 10 logarithms. I just explained it as the power you need to raise 10 to get to the target number.

“So if our target is 100, what do you have to raise 10 to? How about a target of 1,000?”

They had no trouble with this. So I explained how both the Richter and decibel scales were log scales that compressed a wide range into a smaller ruler. A 6 on the Richter is not twice the energy of a 3 but 1000x more energy. Every integer increase in the scale is just a higher order of magnitude.

The most pleasant thing happened. The kids that gravitated to this stuff were stoked. As it it settled in their brains they were all Keanu Reeves “Whoa, that’s so cool”.

I texted one of the parents:

Putting aside the pure joy of watching a kid unlock, exponents and logs are fundamentally important operations like adding and subtracting. Our first formal introduction to them outside a math class is usually science (exponential growth/decay) but more prosaic to this audience is the topic of investing, specifically the idea of compound growth. It’s an idea you’d love to see people internalize as young as possible.

Typically when someone (and I’ve done this too) writes about compounding they reference Einstein’s 8th Wonder of the World quote or talk about how our minds think linearly and find exponential growth unintuitive. [This was a common conversation at the start of the COVID pandemic with VCs patting themselves on the back for lateral thinking about how coefficients of virality applied to…the domain where exponential growth is usually people’s first contact with the topic. Like twisting a eulogy into a chance to talk about yourself. I’m not even mad, it’s the whole wheel of cheese].

With that in mind, I’ll leave you with an excerpt from Grant Sanderson, the mathematician behind the 3Blue1Brown YouTube channel. This is from his appearance on

Dwarkesh Patel

excellent Lunar Society Podcast:

Have you come across those studies where anthropologists interview tribes of people that are removed enough from normal society that they don’t have the level of numeracy that you or I do? But there’s some notion of counting. You have one coconut or nine coconuts like you have a sense of that. But if you ask what number is halfway between one and nine, those groups will answer three whereas you or I or people in our world would probably answer five and because we think on this very linear scale.

It’s interesting that evidently the natural way to think about things is logarithmically, which kind of makes sense. The social dynamics of as you go from solitude to a group of 10 people to a group of 100 people have roughly equal steps in increasing complexity more so than if you go from 1 to 51 to 102 and I wonder if it’s it’s the case that by adding numeracy in some senses we’ve also like lost some numeracy or lost some intuition in others, where now if you ask middle school teachers what’s a difficult topic to teacher for students to understand they’re like logarithms. But that should be deep in our bones right so somehow it got unlearned

What a cheeky observation. Gives a second entendre to the expression “natural log”.

2 ways I came up with to solve the AoPS question

Method 1:

x could also be -243 since it’s being raised to an even power.

Method 2:

Moontower #204

Friends,

For the past 3 years, the Berkeley Chess School has done a weekly lesson in our backyard. About 15 kids attend. They are mostly 2nd and 5th graders because we know the families through our kids.

I walk home from school with all the kids on chess day. I usually throw out a math question or riddle and by now the kids just ask for them on our strolls. Lately, the questions deal with rates, percentages/fractions, exponents/roots, or some basic number play stuff (“How do you know if a number is divisible by 9?”)

Some examples:

  • Start with $100. If you earn 10% then lose 10%, how much money do you have?
  • What’s larger 3⁴ or 4³ and similar questions?
  • If you travel 5 miles in 12 minutes, how fast are you going?[I haven’t dropped this one on them: “If I drive around a one-mile track and average 30 mph for the first lap, how fast do I have to drive the second lap to average 60 mph for both laps combined?” (Solution)]
  • If you have 5 kids on your team and only 4 kids start how many possible starting lineups are there?
  • If you lose 25%, how much do you have to make to get back to even?[I like that one because it’s a useful elasticity idea. If X is the loss percentage, you need to earn back X/(1-X).

    If you are selling lemonade and you cut your price by 20%, you need to sell 25% more cups to be revenue-neutral.]

I started giving these questions because, well it’s just play. Riddles are inherently satisfying. But I’m also conscious of imparting some durable concepts. It’s not quite as deliberate as hiding the dog’s pill in the peanut butter but there’s some overlap. Honestly, the main motivation is keeping the kids who aren’t into sports engaged. There’s about 40 minutes between the kids getting to my house and the start of chess. The 2nd graders usually play soccer and the 5th graders hoop it up. A few kids aren’t into either but they gravitate to the riddles (my boys just wanna play sports and my 5th grader, Zak, with sass tells his friends “This is the stuff I deal with all the time”).

Lately, I’ve been doing more exponent stuff because I know they aren’t doing that yet in 5th grade but it’s reachable for them. Zak is taking the online Pre-Algebra I course on Art of Problem Solving which is comprised of 7 chapters. He just wrapped chapter 2 which is all about exponents so that’s been top-of-mind for coming up with the questions.

The challenge question to end the chapter was to solve for the 2 possible values of X (see below). But keep in mind, they haven’t learned how to compute square roots or any other kind of roots. You can do this without any involved computations and without roots. You can find the solution at the end of the post.

Find the 2 possible values of x:

Anyway, I didn’t give the kids that question but by this past week, they understood the basics of computing a simple exponent or taking a square root. So I took a stab at base 10 logarithms. I just explained it as the power you need to raise 10 to get to the target number.

“So if our target is 100, what do you have to raise 10 to? How about a target of 1,000?”

They had no trouble with this. So I explained how both the Richter and decibel scales were log scales that compressed a wide range into a smaller ruler. A 6 on the Richter is not twice the energy of a 3 but 1000x more energy. Every integer increase in the scale is just a higher order of magnitude.

The most pleasant thing happened. The kids that gravitated to this stuff were stoked. As it it settled in their brains they were all Keanu Reeves “Whoa, that’s so cool”.

I texted one of the parents:

Putting aside the pure joy of watching a kid unlock, exponents and logs are fundamentally important operations like adding and subtracting. Our first formal introduction to them outside a math class is usually science (exponential growth/decay) but more prosaic to this audience is the topic of investing, specifically the idea of compound growth. It’s an idea you’d love to see people internalize as young as possible.

Typically when someone (and I’ve done this too) writes about compounding they reference Einstein’s 8th Wonder of the World quote or talk about how our minds think linearly and find exponential growth unintuitive. [This was a common conversation at the start of the COVID pandemic with VCs patting themselves on the back for lateral thinking about how coefficients of virality applied to…the domain where exponential growth is usually people’s first contact with the topic. Like twisting a eulogy into a chance to talk about yourself. I’m not even mad, it’s the whole wheel of cheese].

With that in mind, I’ll leave you with an excerpt from Grant Sanderson, the mathematician behind the 3Blue1Brown YouTube channel. This is from his appearance on

Dwarkesh Patel

excellent Lunar Society Podcast:

Have you come across those studies where anthropologists interview tribes of people that are removed enough from normal society that they don’t have the level of numeracy that you or I do? But there’s some notion of counting. You have one coconut or nine coconuts like you have a sense of that. But if you ask what number is halfway between one and nine, those groups will answer three whereas you or I or people in our world would probably answer five and because we think on this very linear scale.

It’s interesting that evidently the natural way to think about things is logarithmically, which kind of makes sense. The social dynamics of as you go from solitude to a group of 10 people to a group of 100 people have roughly equal steps in increasing complexity more so than if you go from 1 to 51 to 102 and I wonder if it’s it’s the case that by adding numeracy in some senses we’ve also like lost some numeracy or lost some intuition in others, where now if you ask middle school teachers what’s a difficult topic to teacher for students to understand they’re like logarithms. But that should be deep in our bones right so somehow it got unlearned

What a cheeky observation. Gives a second entendre to the expression “natural log”.

Money Angle

I’m using this space to invite you to play PitBulls (formerly StockSlam) online this coming Friday evening. It’s totally free but space is limited.

Reserve your spot (choose Friday November 3rd if you want to play with me)

This is my testimonial for the game:

One of the most fortuitous decisions I made in my career was accepting a job from SIG out of college. Back in 2000 going to Silicon Valley or I-Banking was all the rage. While trading was a coveted job, the idea of going to an exchange floor to sling options was not a mainstream career choice. And SIG was not a well-known company outside this narrow world.

The job offer I got from them was the lowest paying, but the interview process stood apart from the banks and other firms I talked to. It was clear that working for SIG meant a serious education in decision-making commensurate with the objective — to take responsibility for risking the partners’ own money after as little as 9 months of training.

I was placed at the American Stock Exchange where I would learn from senior traders including their head of education in NY, Mike Steiner, simply known as Steiner.

Steiner was a natural teacher, able to communicate complex ideas with simplicity and frankly, joy. It was no surprise when I discovered 20 years later he retired to become a physics teacher in public school.

In 2022, we reconnected and he showed me the prototype for what would become Pitbulls. Pitbulls is a game distilling the essence and mechanics of the mock trading program we used in training. Pitbulls is a fast-paced game requiring players to think quantitatively while building intuition and understanding investor psychology. Steiner focused on making it fun — it’s a game first. But when I saw it I was immediately struck by its potential to bring investing principles to life!

Skills that will immediately develop from the very first game:

  • market making in an open outcry market
  • tracking multiple quotes from competitors
  • managing a rudimentary portfolio
  • reacting to new information

Deeper concepts embedded in Pitbulls:

  • arbitrage pricing, inter-dependent pricing
  • expected value and probability
  • the concept of edge as the foundation of a business
  • how you can be profitable without relying on prediction
  • making trading decisions under uncertainty
  • risk and diversification
  • the role, wisdom, and conditions of a healthy market
  • an introduction to derivatives
  • a bridge from trading to investing principles

Steiner has been hosting in-person playshops for years and I helped organize larger events in NYC, SF, and Chicago to overwhelmingly positive feedback. Unsurprisingly, the most universal suggestion was “give us an online version”. People wanted to play on their own and host their own sessions.

Starting now, you can play online!

I’ve been writing about financial education topics for years. These posts go into how Pitbulls and its underpinnings can improve your thinking in powerful ways.

Money Angle For Masochists

Quant legend Peter Muller wrote a candid, somewhat irreverent post 20 years ago that holds timeless wisdom.

🔗Proprietary trading: truth and fiction (Link)

Excerpts:

  1. But the most important risk is the possibility of our models not working correctly. To minimize that risk, we set loss targets for strategies — if we lose more money than the pre-specified target then the strategy is re-evaluated and shut down for a while (perhaps forever). This is not that different from the old school of proprietary trader management: ‘Go ahead and trade, don’t do anything too risky, and if you lose more than $x we’re going to shut you down. ’Our strategies are evaluated by looking at reward/risk measures. For symmetric, market-neutral strategies without significant tail events, the Sharpe Ratio (SR) is probably the best ex-ante measure. SR is defined as the portfolio annual excess return divided by the annualized standard deviation of that return. Our benchmark is cash, hence measuring excess returns is appropriate for our portfolio. For long-only managers, the Information Ratio—which measures excess returns relative to a benchmark—is more appropriate. When we evaluate past performance, we also look at peak-to-trough drawdowns (a measure of the maximum drop between consecutive maximum and minimum values of return over the life of the strategy) as an additional risk variable. This can help pick up serial correlation in portfolio returns that the Sharpe Ratio doesn’t capture. Also of interest is the fraction of expected gross profits consumed by expected transaction costs. The higher this number, the more money we expect to lose if our model stops working. At least some of our edge comes from opportunities that are created in the market by institutional managers who trade too much. Their trading is usually based on either an exaggerated view of how well they can predict investment returns or a misunderstanding of how trading costs increase with size. The strategies of institutional managers can still be perfectly rational despite providing us with opportunities through over-trading, simply because of the huge agency issues in portfolio management.
  2. In Grinold and Kahn’s book on Active Portfolio Management, the authors describe the ‘FundamentalLaw of Active Management’: a strategy’s Sharpe Ratio is proportional to the number of independent bets taken by the strategy multiplied by the correlation of those bets with their outcome. To get a higher SR, you need to increase the number of your bets or increase the strength of your forecasts. In my opinion, it is far better to refine an individual strategy by increasing both the number of bets within the strategy and the strength of the forecasts made in the strategy, than to attempt to put together lots of weaker strategies. Depth is more important than breadth for investment strategies…I would much rather have a single strategy with an expected Sharpe Ratio of 2 than a strategy that has an expected Sharpe Ratio of 2.5 formed by putting together five supposedly uncorrelated strategies each with an expected Sharpe Ratio of 1. In the latter case, you’re faced with the risk that the strategies are more correlated than you realize (think Long Term Capital). There is also the increased effort of ascertaining whether each individual strategy really has a Sharpe Ratio of 1.
  3. An important choice for many proprietary traders is whether to focus on shorter or longer-horizon strategies. Typically, shorter horizon strategies get their edge from providing temporal liquidity to a marketplace or predicting short-term trends that arise from efficient trading. Longer-term models focus on asset pricing inefficiencies. How does the implementation of these strategies compare? Shorter-horizon investment strategies are desirable because they tend to create higher Sharpe ratios. If your average holding period is a day or a month, you have the opportunity to place many more bets than if you hold positions for three months to a year or longer. On the flip side, shorter horizon strategies tend to have capacity issues (it’s easy to make a small amount of money with them, but harder to make a lot of money). Shorter horizon strategies also require serious investments in trading infrastructure, since quick and inexpensive execution is much more important than for longer horizon strategies. Risk management for shorter-horizon strategies tends to occur through position trading rather than portfolio construction. Assets are not held for long periods of time and portfolio characteristics change quickly. The biggest risk for shorter horizon strategies model risk, or the risk that the trading strategy deployed has stopped working. Since even the best trading strategies experience periodic drawdowns, the hardest challenge for the short-term model-based trader is to figure out whether his model is going through a regular drawdown or has stopped working altogether. Longer-horizon model-driven investment strategies have different issues. Since assets are held for longer periods of time, execution costs (although still important) are not the primary focus. Statistical inference becomes more difficult and the danger of overfitting or mining data becomes larger. Risk management for longer-term strategies happens in portfolio construction: since rebalancing occurs less frequently, more care needs to be taken to ensure the portfolio is not exposed to unintended sources of risk. Because they tend to have lower Sharpe ratios, longer horizon strategies have a different kind of capacity issue—the capacity for pain. However, there is one advantage: because trading occurs less frequently it’s possible to lead a much better lifestyle than if you’re running shorter horizon strategies!

Excerpts From Grant Sanderson on The Lunar Society Podcast

Dwarkesh Patel interviews Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about:

  • Whether advanced math requires AGI
  • What careers should mathematically talented students pursue
  • Why Grant plans on doing a stint as a high school teacher
  • Tips for self teaching
  • Does Godel’s incompleteness theorem actually matter
  • Why are good explanations so hard to find?

Watch on YouTube. Listen on Spotify, Apple Podcasts, or any other podcast platform. Full transcript here.

Kris: I snipped several excerpts for future reference. Emphasis mine. I cut up the excerpts as I want to remember them which means there are missing sections so I encourage you to listen to the whole episode or read the sections of transcript I’m pulling from if you want a closer look.

On the future of education 

[key ideas: reducing distance to students, educator’s role is not just explanation but more importantly “bring out knowledge” not put it in, the non-linear influence of a teacher on a student’s future, and the chaotic concept of “sensitivity to initial conditions”]

Dwarkesh Patel 0:44:44

Should the top 0.1% of educators exclusively be on the internet because it seems like a waste if you were just a college professor or a high school professor and you were teaching 50 kids a year or something. Given the greater scale available should more of them be trying to see if they can reach more people?

Grant Sanderson 0:45:01

I think it’s not a bad thing for more educators who are good at what they’re doing to put their stuff online for sure. I highly encourage that even if it’s as simple as getting someone to put a camera in the back of the classroom. I don’t think it would be a good idea to get those people out of the classroom.

If anything I think one of the best things that I could do for my career would be to put myself into more classrooms…

One of the most valuable things that you can have if you’re trying to explain stuff online is a sense of empathy for what possible viewers that are out there. The more distance that you put between yourself and them in terms of life circumstances. I’m not a college student so I don’t have the same empathy with college students. Certainly not a high school student, so I’ve lost that empathy. That distance just makes it more and more of an uphill battle to make the content good for them and I think keeping people in regular touch with just what people in the classroom actively need is necessary for them to remain as good and as sharp as they are…

The other thing I might disagree with is the idea that the reach is lower. Yes, it’s a smaller number of people but you’re with them for much, much more time and you actually have the chance of influencing their trajectory through a social connection in a way that you just don’t over Youtube.

You’re using the word education in a way that I would maybe sub out for the word explanation. You want explanations to be online but the word education derives from the same root as the word educe, to bring out, and I really like that as a bit of etymology because it reminds you that the job of an educator is not to take their knowledge and shove it into the heads of someone else the job is to bring it out. That’s very, very hard to do in a video and in fact, even if you can kind of get at it by asking intriguing questions for the most part the video is there to answer something once someone has a question.

The teacher’s job, or the educator’s job, should be to provide the environment such that you’re bringing out from your students as much as you can through inspiration through projects, through little bits of mentorship and encouragement along the way. That requires eye contact and being there in person and being the true figure in their life rather than just an abstract voice behind a screen.

Anytime I chat with mathematicians and try to get a sense for how they got into it and what got them started, so often they start by saying there was this one teacher and that teacher did something very small — like they pulled them aside and just said, “Hey. You’re really good at this. Have you considered studying more?” or they give them an interesting problem.

And the thing that takes at most 30 minutes of the teacher’s time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets them on this whole different trajectory.

Two examples of this come to mind. One is this woman who was saying she had this moment when she got pulled aside by the teacher and he just said, “Hey, I think you’re really good at math. You should consider being a math major.” which had been completely outside of her purview at that time. That changed the way she thought about it. And then later she said she learned that he did that for a large number of people. He just pulled them and was like, “Hey, you’re really good at math.” So that’s a level of impact that you can have as a figure in their lives in a way that you can’t over screen.

Another one which was very funny. I was asking this guy why he went into the specific field that he did. It was a seemingly arbitrary thing in my mind but I guess all pure math seems to be. He said that in his first year of grad school he was sitting in this seminar and at the end of the seminar the professor, who was this old professor who he had never met him before, they didn’t have any kind of connection. He seeks this guy out and comes up and he says, “You. I have a problem for you. A good research problem that I think I think might be a good place for you to start in the next couple months” and this guy was like “Oh, okay” and he gets this research problem and he spends some months thinking about it and he comes back and then it later came to light that the professor mistook him for someone else that was someone he was supposed to be mentoring. He was just the stereotypical image of like a doddering old math professor who’s not very in tune with the people in his life that was the actual situation but nevertheless that moment of accidentally giving someone a problem completely shifted the research path for him, which if nothing else, shows you the sensitivity to initial conditions that takes place when you are a student and how the educator is is right on that nexus of sensitivity who can completely swing the fences one way or another for what you do.

For every one of those stories there’s going to be an unfortunate counterbalancing story about people who are demotivated from math. I think this was seventh grade. There was this math class that I was in and I was one of the people who was good at math and enjoyed it and would often help the people in the class understand it. I had enough ego built up to have a strong shell around things. For context, I also really liked music and there was this concert that had happened where I had a certain solo or something earlier in that week.

There was a substitute teacher one day who didn’t have any of the context and she gave some lesson and had us spend the second half of the class going over the homework for it. All of the other students in the class were very confused and I think I remember like they would come to me and I would try to offer to help them and the substitute was going around the class in these circles and basically marking off a little star for how far down the homework people were just to get a sense are they progressing. That was kind of her way of measuring how far they were. When she got to me I had done none of them because I was spending my whole time trying to help all of the others and after having written a little star next to the same problem like three different times she said to me like, “Sometimes music people just aren’t math people.” and then keeps walking on.

I was in the best possible circumstance to not let that hit hard because one, I had the moral high ground of “Hey, I’ve just been helping all these people. I understand it and I’ve been doing your job for you.” This was my little egotistical seventh grade brain. I knew that I knew the stuff. Even with all of the armor that was put up, I remember it was just this shock to my system, she says this thing and it just made me strangely teary-eyed or something.

I can only imagine if you’re in a position where you’re not confident in math and the thing that you know deep in your heart is actually you are kind of struggling with it, just a little throwaway comment like that could completely derail the whole system in terms of your relationship with the subject.

So it’s another example to illustrate the sensitivity to initial conditions. I was in a robust position and wasn’t as sensitive. I was gonna love math no matter what but you envision someone who’s a little bit more on that teetering edge and the comment, one way or another, either saying you’re good at this you should consider majoring in it or saying, “Sometimes music people aren’t math people” which isn’t even true. That was the other thing about it that niggled at my brain when she said it.

All of that is just so important for people’s development that when people talk about online education as being valuable or revolutionary or anything like that, there’s a part of me that sort of rolls my eyes because it just doesn’t get at the truth that online explanations have nothing to do with all of that important stuff that’s actually happening and at best it should be like in the service of helping that side of things where the rubber meets the road.

On explanations 

[key ideas: not everyone responds to the same explanations so explanations that scale well are difficult to conjure. There’s room for multiple approaches and ways to communicate]

Dwarkesh Patel 1:02:22

Why are good explanations so hard to find, despite how useful they are? Obviously, other than you, there’s many other cases of good explanations. But generally, it just seems like there aren’t as many as there should be. Is it just a story of economics where it’s nobody’s incentive to spend a lot of time making good explanations? Is it just a really hard skill that isn’t correlated with being able to come up with a discovery itself? Why are good explanations scarce?

Grant Sanderson 1:02:47

I think there’s maybe two explanations.

The first less important one is going to be that there’s a difference between knowing something and then remembering what it’s like not to know it. And the characteristic of a good explanation is that you’re walking someone on a path from the feeling of not understanding up to the feeling of understanding.

Earlier, you were asking about societies that lack numeracy. That’s such a hard brain state to put yourself in, like what’s it like to not even know numbers? How would you start to explain what numbers are? Maybe you should go from a bunch of concrete examples. But like the way that you think about numbers and adding things, it’s just you have to really unpack a lot before you even start there.

And I think at higher levels of abstraction, that becomes even harder because it shapes the way that you think so much that remembering what it’s like not to understand it. You’re teaching some kid algebra and the premise of like a variable. They’re like, “What is X?” It’s not necessarily anything but it’s what we’re solving for. Like, yeah, but what is it? Trying to answer “What is X?” is a weirdly hard thing because it is the premise that you’re even starting from.

The more important explanation probably is that the best explanation depends heavily on the individual who’s learning. And the perfect explanation for you often might be very different from the perfect explanation for someone else. So there’s a lot of very good domain specific explanations. Pull up in any textbook and like chapter 12 of it is probably explaining the content in there quite well, assuming that you’ve read chapters one through 11, but if you’re coming in from a cold start, it’s a little bit hard.

So the real golden egg is like, how do you construct explanations which are as generally useful as possible and generally appealing as possible? And that because you can’t assume shared context, it becomes this challenge. And I think there’s like tips and tricks along the way, but because the people that are often making explanations have a specific enough audience, it is this classroom of 30 people. Or it’s this discipline of majors who are in their third year. All the explanations from the people who are professional explainers in some sense are so targeted that maybe it’s the economic thing you’re talking about. There’s not, or at least until recently in history, there hasn’t been the need to or the incentive to come up with something that would be motivating and approachable and clear to an extremely wide variety of different backgrounds.

Putting in work with calculations

Dwarkesh Patel 1:20:44

If you’re self teaching yourself a field that involves mathematics, let’s say it’s Physics or some other thing like that, there’s problems where you have to understand how do I put this in terms of a derivative or an integral and from there, can I solve this integral? What would you recommend to somebody who is teaching themselves quantum mechanics and they figured out how to put how to get the right mathematical equation here. Is it important for their understanding to be able to go from there to getting it to the end result or can they just say well, I can just abstract that out. I understand the broader way to set up the problem in terms of the physics itself.

Grant Sanderson 1:22:00

I think where a lot of self-learners shoot themselves in the foot is by skipping calculations by thinking that that’s incidental to the core understanding. But actually, I do think you build a lot of intuition just by putting in the reps of certain calculations. Some of them maybe turn out not to be all that important and in that case, so be it, but sometimes that’s what maybe shapes your sense of where the substance of a result really came from.

I don’t know it might be something you realize like “Oh, it’s because of the square root that you get this decay.” And if you didn’t really go through the exercise, you would just come away thinking like instead of coming away thinking like such and such decays but with other circumstances, it doesn’t decay and not really understanding what was the core part of this high level result that is the thing you actually want to come out remembering.

Putting in the work with the calculations is where you solidify all of those underlying intuitions. And without the forcing function of homework, People just don’t do it. So I think that’s one thing that I learned as a big difference post college versus during college.

Post college, it’s very easy to just accidentally skip that while learning stuff and then it doesn’t sink in as well. So I think when you’re reading something, having a notebook and pencil next to you should be considered part of the actual reading process.

And if you are relying too much on reading and looking up and thinking in your head, maybe that’s going to get you something but it’s not going to be as highly leveraged as it could be.

The “failure to disrupt”

[key ideas: learning is not bottlenecked by good explanations but by social incentives. Deeply resonant. Reading between the lines — we are aspirational and good at copying others or trying to impress them, so if we know that we should provide good models for learners to emulate]

Dwarkesh Patel 1:23:39

What would be the impact of more self teaching in terms of what kinds of personalities benefit most? There’s obviously a difference in the kind of person who benefits most. In a situation where it’s a college course and everybody has to do the homework, but maybe some people are better tuned for the kind of work that’s placed there versus all this stuff is available for you on youtube and then textbooks for exercises and so on but you have to have the conscientiousness to actually go ahead and pursue it.

How do you see the distribution of who will benefit from the more modern way in which you can get whatever you want but you have to push yourself to get it.

Grant Sanderson 1:24:17

There’s a really good book that’s actually kind of relevant to some of your early questions called Failure to Disrupt that goes over the history of educational technology. It tries to answer the question of why you have these repeated cycles of people saying such and such technology that almost always is getting more explanations to more people, promises that it’ll disrupt the existing university system or disrupt the existing school system and just kind of never does.

One of the things that it highlights is how stratifying these technologies will be in that they actually are very very good for those who are already motivated or kind of already on the top in some way and they end up struggling the most just for those who are performing more poorly.

And maybe it’s because of confounding causation where the same thing that causes someone to not do poorly in the traditional system also means that they’re not going to engage as well with the plethora of tools available.

I don’t know if this answers your question, but I would reemphasize that what’s probably most important to getting people to actually learn something is not the explanation…but instead, it’s going to be the social factors. Are the five best friends you have also interested in this stuff and do they tend to push you up or they tend to pull you down when it comes to learning more things? Or do you have a reason to? There’s a job that you want to get or a domain that you want to enter where you just have to understand something or is there a personal project that you’re doing?

The existence of compelling personal projects and encouraging friend groups probably does way way more than the average quality of explanation online ever could because once you get someone motivated, they’re just they’re going to learn it and it maybe makes it a more fluid process if there’s good explanations versus bad ones and it keeps you from having some people drop out of that process,which is important.

But if you’re not motivating them into it in the first place, it doesn’t matter if you have the most world-class explanations on every possible topic out there. It’s screaming into a void effectively.

And I don’t know the best way to get more people into things. I have had a thought and this is the kind of thing that could never be done in practice but instead it’s something you would like write some kind of novel about, where if you want the perfect school, something where you can insert some students and then you want them to get the best education that you can, what you need to do is — Let’s say it’s a high school. You insert a lot of really attractive high schooler plants as actors that you get the students to develop crushes on. And then anything that you want to learn, the plant has to express a certain interest in it. They’re like, “Oh, they’re really interested in Charles Dickens.” And they express this interest and then they suggest that they would become more interested in whoever your target student is if they also read the dickens with them.

If you socially engineer the setting in that way, the effectiveness that would have to get students to actually learn stuff is probably so many miles above anything else that we could do. Nothing like that in practice could ever actually literally work but at least viewing that as this end point of “Okay, this mode of interaction would be hyper effective at education. Is there anything that kind of gets at that?”

And the kind of things that get at that would be — being cognizant of your child’s peer group or something which is something that parents very naturally do or okay, it doesn’t have to be a romantic crush, but it could be that there’s respect for the teacher. It’s someone that they genuinely respect and look up to such that when they say there’s an edification to come from reading Dickens, that actually lands in a way.

The natural extension of this:

Encourage people to mentor or teach on the side!

Grant Sanderson

I think there are two things I would want to get out of teaching in a school setting. One of them, as I was emphasizing, I think you just lose touch with what it’s like not to know stuff or what it’s like to be a student and so maintaining that kind of connection so that I don’t become duller and duller over time feels important.

The other, I would like to live in a world where more people who are savvy with STEM spend some of their time teaching. I just think that’s one of the highest leverage ways that you can think of to actually get more people to engage with math

And so I would like to encourage people to do that and call for action. Some notion of spending, maybe not your whole career, a little bit of time. In teaching, there’s not as fluid a system for doing that as going through a tour of service in certain countries where everyone spends two years in the military

Shy of having a system like that for education, there’s all these kind of ad hoc things where charter schools might have an emergency credential system to get a science teacher in. Teach for America is something out there.

There’s enough ways that someone could spend a little bit of time that’s probably not fully saturated at this point that the world would be better if more people did that

A Simple Demonstration of Return Vs Volatility

Arithmetic returns

  • Expected return for a bet is the simple probability-weighted average of outcomes.
  • If there is a 50% chance of a bet making 21% and a 50% chance of it returning 19% this it’s a good bet that is also not volatile. You expect to make 20% on average (despite the fact that you can’t ever make that on any single bet since you can only earn 19% or 21%).
  • Your expected terminal wealth after a single trial is 1.2x what you started with.
  • Since we took a simple average of the outcomes we computed an arithmetic mean return of 20%

Compounded returns

For multi-period investing where we do not take any distributions or “money off the table” we cannot use simple arithmetic means to compute an expected return.

Consider the same bet after 2 trials. These are the 4 possibilities each equally likely:

  • Best return, best return
  • Best return, worst return
  • Worst return, best return
  • Worst return, worst return

If we look at the summary table, there is no difference between the mean expected return and the median.

Let’s keep the mean return the same but raise the volatility. An investment that is equally likely to:

  • go up 100%
  • fall by 60%

Even though this is more volatile than the first investment, the mean expected return is still 20% per trial. You can compute this in 2 ways:

50% * +100% + 50% * -60% = 20%

or

Terminal wealth  = 50% * 2 + 50% * .4 = 1.2 or 20% return

But let’s see what happens when we look at the compounded scenario where we fully re-invest the proceeds of the first period into a second period.

Now the mean compounded return has dropped from 20% to just 4.72% and the median outcome is a loss of 10.6%!

The divergence between mean and median returns comes from the compounded effect of volatility.

Investing Is a Multiplicative Process

When it comes to investing, we are usually re-investing rather than taking our profits off the table each year. We hope to grow our wealth year by year like this:

1.10 * 1.10 * 1.10 … or 1.10n where n is the number of compounding intervals (typically years).

Therefore, we want to look at compounded not mean rates of return. To compute them we simply take the n-th root of our terminal wealth where n is the number of years.

If you doubled your money in 5 years then your CAGR = 21/5 – 1 = 14.9%

Note that if you took the naive average return you could say you earned 100% in 5 years or 20% per year. But this defies reality where you re-invested a growing sum of capital every year.

CAGR is a median return

It’s important to note that the expected mean return of these investments is still 20% per year. It’s just that the median is much lower. In the high volatility example, your lived experience usually results in a loss of 10.6% but the mean 2-period return is still positive 4.7%. The complication is that the avergae is driven by the 25% probability that you double your money in 2 consecutive year. In every other scenario, you lose money.

Volatility is altering the distribution of your outcomes not the mean outcome. 

Mathematically the median is the geometric mean. In a multiplicative process, you care more about the geometric mean. After all, you only get one life.

A note on log returns

A logreturn is a compounded return where we assume continuous compounding. So instead of every year, it’s more like every second. Of course, if our wealth grows from $1 to $2 in 5 years but we assume tiny compouding intervals, then the rate per interval must be small. After all the start and end of our journey ($1 to $2) is the same, we are just slicing it into smaller sections.

Computing an expected logreturn is simple. Using the volatile example:

.5 * ln(2) + .5 * ln(.40) = -11.2%

Note that this is slightly worse than the geometric mean return (aka median) we computed earlier of -10.6%

Volatility’s effect on compounded returns

The following table presents different investments that each have an expected arithmetic return of 20%. Just like the examples above. But the various payoffs are altered to proxy different levels of volatility. An investment that can earn 21% or 19% is much less volatile than one that can return 100% or -60% even though the average return is the same.

We use the simplest measure to represent the volatility — the ratio of the best return to the worst return.

The stable investment volatility proxy is 1.21 / 1.19 = 1.017

The volatile investment above is 2 / .4 = 5.00

Table snippet:

These charts show the divergence between arithmetic and median returns as we increase the volatility (the ratio of the best return to the worst return):

An investment that is equally likely to return 60% as it is to lose 20% has a 20% expected return but if you keep re-investing your long-term median outcome is closer to a 12-13% CAGR.

What if we raise the volatility further to a ratio of 5 (terminal wealth of 2x vs .4x):

At a ratio of 3.5 (1.87x vs .53x) our median result is zero. At a ratio of 5, the average return remains 20% but the median return is losing 10%. Almost all the paths are losing they are just being counterbalanced by the unlikely event that you keep flipping heads.

Takeaways

  • Investing is a multiplicative process so we want to look at compounded or log returns not simple returns
  • Compounded returns ask “what growth rate when multiplied from period to period gets us from the start point to the end point?”
  • Compounded and logreturns are always less than arithmetic returns
  • Compounded and log returns are better measures for what you expect to find in your bank account after volatility has taken its toll. Remember if you lose 50% on an investment you need 100% to get back to even. If you earn 50% on an investment you only need to lose 33% to be back at even.
  • If there was no volatility there’d be no promise of return, but volatility is a quadratic drag on returns. The sweet spot for your portfolio likely falls in the realm of the volatility of broadly diversified portfolios. By rebalancing you can reduce concentration risks that threaten to turn your entire nest egg into a coin flip. Even if this coin has positive expectancy, remember you can’t eat theoretical edge.

Further reading

The Creep of Arbitrage Means Investing Is Mostly A Faith Exercise

The intellectual force-of-nature Byrne Hobart publishes a widely-read daily letter that I often pull from called The Diff. It’s in the same league as Stratechery or Matt Levine which is to say GOAT-level.

Byrne also publishes an educational post on Wednesdays in a letter called Capital Gains.

This week’s Capital Gains was one of my favorites. I’ll leave you with excerpts even though it’s pretty short. It’s one of those irreducible posts that should just be excerpted in full (said otherwise — just read it). There’s no waste.

[As usual, emphasis mine]

Risk and Returns, Before and After the Fact (Capital Gains)

There are two ways to talk about long-term returns from investing in a given asset class. One is easy because it has limited utility, and the other is a useful intellectual exercise, but impossible to get right.

  • Long-term returns are, in a simplistic model, the current dividend yield plus long-term growth in dividends per share—where “long-term” is very long-term, like a lifetime or longer. And growth in dividends per share is, also in the very long term, a function of growth in revenue per share: margins tend to be surprisingly stable over long periods, and multiples can only go so far in one direction or another…This model looks too easy, and in some ways it is. For example, it’s correct over a timescale long enough to be irrelevant to individuals; there can be long swings towards lower margins, like the one that took place in the US from the 60s through the 90s. And there can be swings in the opposite direction, like the rise in corporate margins that’s taken place since then. But these trends can’t go on forever—each one of them could easily be the majority of the lifetime of a specific individual investor. Swings in valuation can happen, too; P/E ratios went from ~20x in the late 1920s (on low-quality earnings that were increasingly from financial engineering) to the mid-single digits in the late 1940s, back to 20+ in the 60s, back to single digits by the late 70s, and so on
  • The discussion of fundamental drivers of equity returns hammered home the idea that valuation is not a driver of returns, because it moves so slowly. Even if the market switched from trading at ~10x earnings in the early 20th century to ~25x today, that’s 70 basis points per year of annual return. But the flip side of this is that over shorter periods, valuation’s role as a return driver goes way up. Year to year, the market’s moves are typically the result of multiple expansion rather than earnings growth or dividends…Over even shorter periods, valuation becomes even more important; an intraday swing or the change in price from one trade to the next are, almost by definition, overwhelmingly driven by valuation multiples rather than some tiny incremental update to a company’s fundamentals.
  • In the very long run, stocks tend to go up. But that’s only sustainable if that long-term gain is compensation for some shorter-term variability. You can know roughly what you’re getting into by looking at broad valuation metrics, which tell you that stocks are fairly expensive right now, especially in the context of higher rates. But you can’t get much more information than that—the difficulty of timing the market is a function of how all the easy ways have been arbitraged away, and what’s left is a bedrock of uncertainty that, over short timescales, dominates fundamental drivers and long-term trends.

Money Angle for Masochists

I just want to attach a thought to Byrne’s post that seems cruel to dump on casual investors. Hence its home in the Masochism section.

If valuation is a limited return driver except over a long-run period, a period nobody knows anything about 1

AND you are invested in managers who have valuation-based strategies, then Byrne’s post has Shrodinger’s cat vibes. There’s a duality of epistemology between the description of “what happened” with “what will happen” that really doesn’t seem to overlap in any pragmatic context. And the assumption of that overlap is the rationalization that underpins all long-term investing sales pitches.

Let’s back up and consider the problem of the long-term generally.

The best we can do is have sound frameworks for decision-making. Being probabilistic thinkers, understanding incentives, etc etc. All the stuff you hear on podcasts, Mungerisms, yadda yadda. It’s all sound even if it’s hard to implement in a messy world.

I feel that our frameworks have limited potential in outperforming the wisdom of crowds for long time horizons. Those frameworks help but their value is more in avoiding stupidity rather than aiding one in outperforming unemotional benchmarks that already incorporate intelligent portfolio construction logic — diversification, cutting losers (ie following trends) and rebalancing.

Everybody would love to hide behind “we are good at this in the long run and until that long run happens you shouldn’t judge us” while they collect nonrefundable fees. I don’t think there is data that you can look at that solves the problem of “who is good at beating benchmarks over the long term” for a price that doesn’t negate the advantage. But even price aside, how do you say “this buy-and-hold approach is better than a benchmark”? You need to believe they know something about the far future that other smart people do not. And the type of people that are good at that (if “that” exists) do not strike me as the same imaginations that are drawn to value investing.

The longer you hold an investment, the less your entry price matters. The most important driver of the investment will be the rate at which it compounds invested capital. A company that has the promise to do this is unlikely to be cheap. Everyone understands the math and understands that getting the entry price wrong is okay if they:

a) get business returns roughly right

and

b) don’t sell

The re-rating of the multiple matters more for the short to medium-term investor.

Doesn’t this put long-term investing at odds with the extreme couponing personas that value investors project?!

These other ideas make sense:

  • Buffet preaches buying great businesses at fair prices
  • Trader types are cool to buy a crap business they think is oversold but will re-rate when flows stabilize or there’s capitulation or whatever short-term thesis they envision materializes. They are just focused on beating the spread on the new slate of volatile stocks each week (or month).
  • The growth investor appears to have internalized the idea that you can pay up for the best businesses and you’ll do great in the long run.

It’s the long-term value investors trying to buy pristine ROIC for bargain prices who appear to be spitting on the laws of investing gravity. Value investing seems like a mean reversion trade. “Trade” being the operative word here not “investing”.

The premise of long-term value investing appears logically incoherent when you try to marry “cheap” with “good business” in transparent public markets. Shorter-term strategies attract more competition (if you can “buy well” you’d like to exploit that skill 1000x a year rather than 5x a year) but they are at least possible to evaluate.

You could ask a manager, “What kind of things I should look at to figure out if your strategy is getting worse?” Tell me how to judge you. Tell me how to judge whether it even makes sense to try to get alpha in your space. There’s an old interview with an option guy Wayne Himelsein where he discusses strategy evaluation:

Are you achieving your premise? So you’ve said yourself, I know where I want to neutralize, and I know where I want to get my alpha. And if that’s where you get your alpha, you have to know that number one, you have alpha there. So if you look at your growth tilt and measure that against Fama growth factor, do you beat it? If not, you’ve got no edge.

He talks about mapping a strategy. Comparing the exposures to a time series of different exposures to see how it behaves.

“I don’t ever listen to what [the manager] tells me. I just run it versus we have in here about 180 different exposures that we have time series for factors or exposures [to find out] “what is inside this thing?”

How intentional are the exposures?

Managers will tell you that they’re doing something but don’t even know what they’re exposed to. “Did you know you have a 30% exposure to momentum? Oh, no, I didn’t. I’m actually a value investor.”

This is an older interview, but it’s increasingly common knowledge today that these lines of questioning inform pod shops’ risk and compensation frameworks.

This doesn’t work for choosing long-term investors.

The problem feels intractable.

You might convince me there are some weirdos who have first-hand tinkered with things that inform a vision of the far future. But they wouldn’t balk at the ticket price to board that ride anyway. They believe.

VC makes sense because overpaying doesn’t matter if you are truly drawing from a power law distribution (that’s a big “if” though).

And trading oriented managers can be evaluated. Just ask them the terms they want to be evaluated, hang them on their own inconsistencies, and choose from whoever’s left.

But long-term investors who want cheap prices? I don’t know if that job is even doable ex-ante and if it is I don’t think you wear a suit to do it.

I’ll let Byrne’s post provide the closing thought:

In the very long run, stocks tend to go up. But that’s only sustainable if that long-term gain is compensation for some shorter-term variability. You can know roughly what you’re getting into by looking at broad valuation metrics, which tell you that stocks are fairly expensive right now, especially in the context of higher rates. But you can’t get much more information than that—the difficulty of timing the market is a function of how all the easy ways have been arbitraged away, and what’s left is a bedrock of uncertainty that, over short timescales, dominates fundamental drivers and long-term trends.

Explorables

In Wednesday’s Munchie Generative Instincts, there was talk of representing data visually.

I quoted Eugene Wei:

The reason the book [Tufte] influenced me so deeply is that it is actually a book about the pursuit of truth through knowledge. It is ostensibly about producing better charts; what stays with you is the principles for general clarity of thought. Reading the book, chiseling away at my line graphs late nights, talking to people all over the company to understand what might explain each of them, gave me a path towards explaining the past and predicting the future. Ask anyone about any work of art they love, whether it’s a book or a movie or an album, and it’s never just about what it’s about. I haven’t read Zen and the Art of Motorcycle Maintenance; I’m guessing it wasn’t written just for motorcycle enthusiasts. A good line graph is a fusion of right and left brain, of literacy and numeracy. Just numbers alone aren’t enough to explain the truth, but accurate numbers, represented truthfully, are a check on our anecdotal excesses, confirmation biases, tribal affiliations.

I wanted to share a few places where you can see visuals expertly used to teach or bring the user through a story.

🧪Math and Science Interactive Essays

🔭Explorables

  • Nicky CaseNicky’s work bursts with brilliance and creativity.

    The archive is loaded with explorables.

    Don’t miss: An Interactive Introduction to Attractor Landscapes

    If you have ever heard the word “sticky” in a trading context that explorable is a must. It’s a fascinating lens for articulating option regimes.

    Nicky also has one on the Wisdom/Madness of Crowds.

    Nicky is incredibly transparent and the work is 100% open-source. I find it insanely inspirational.

  • Explorable Explanations…a hub for learning through play! We’re a disorganized “movement” of artists, coders & educators who want to reunite play and learning.

    Straight into the veins.

🍮Pudding posts

The Pudding is a digital publication that brings cultural stories to life using interactive visualizations. They highlight some of their favorites in this introduction.

Their recent newsletter featured several fun ones. I often check out the articles even if the topic doesn’t interest me just because the design and tech used to create them is always fresh:

Romance Novels (Link)

What does a happily ever after look like? We look at over 1,400 romance covers to find out what visuals are used.

Invisible Epidemic (Link)

Watch 24 hours of an American day, and the invisible crisis hiding in plain sight

A series of experimental clocks that connect data to time

A clock where the time is…

  1. in a song title
  2. mentioned on YouTube
  3. made of news headlines
  4. the population of a US place

Moontower #203

In Wednesday’s Munchie Generative Instincts, there was talk of representing data visually.

I quoted Eugene Wei:

The reason the book [Tufte] influenced me so deeply is that it is actually a book about the pursuit of truth through knowledge. It is ostensibly about producing better charts; what stays with you is the principles for general clarity of thought. Reading the book, chiseling away at my line graphs late nights, talking to people all over the company to understand what might explain each of them, gave me a path towards explaining the past and predicting the future. Ask anyone about any work of art they love, whether it’s a book or a movie or an album, and it’s never just about what it’s about. I haven’t read Zen and the Art of Motorcycle Maintenance; I’m guessing it wasn’t written just for motorcycle enthusiasts. A good line graph is a fusion of right and left brain, of literacy and numeracy. Just numbers alone aren’t enough to explain the truth, but accurate numbers, represented truthfully, are a check on our anecdotal excesses, confirmation biases, tribal affiliations.

I wanted to share a few places where you can see visuals expertly used to teach or bring the user through a story.

🧪Math and Science Interactive Essays

🔭Explorables

  • Nicky CaseNicky’s work bursts with brilliance and creativity.

    The archive is loaded with explorables.

    Don’t miss: An Interactive Introduction to Attractor Landscapes

    If you have ever heard the word “sticky” in a trading context that explorable is a must. It’s a fascinating lens for articulating option regimes.

    Nicky also has one on the Wisdom/Madness of Crowds.

    Nicky is incredibly transparent and the work is 100% open-source. I find it insanely inspirational.

  • Explorable Explanations…a hub for learning through play! We’re a disorganized “movement” of artists, coders & educators who want to reunite play and learning.

    Straight into the veins.

🍮Pudding posts

The Pudding is a digital publication that brings cultural stories to life using interactive visualizations. They highlight some of their favorites in this introduction.

Their recent newsletter featured several fun ones. I often check out the articles even if the topic doesn’t interest me just because the design and tech used to create them is always fresh:

Romance Novels (Link)

What does a happily ever after look like? We look at over 1,400 romance covers to find out what visuals are used.

Invisible Epidemic (Link)

Watch 24 hours of an American day, and the invisible crisis hiding in plain sight

A series of experimental clocks that connect data to time

A clock where the time is…

  1. in a song title
  2. mentioned on YouTube
  3. made of news headlines
  4. the population of a US place

Money Angle

The intellectual force-of-nature

Byrne Hobart

publishes a widely-read daily letter that I often pull from called The Diff. It’s in the same league as Stratechery or Matt Levine which is to say GOAT-level.

Byrne also publishes an educational post on Wednesdays in a letter called Capital Gains.

This week’s Capital Gains was one of my favorites. I’ll leave you with excerpts even though it’s pretty short. It’s one of those irreducible posts that should just be excerpted in full (said otherwise — just read it). There’s no waste.

[As usual, emphasis mine]

Risk and Returns, Before and After the Fact (Capital Gains)

There are two ways to talk about long-term returns from investing in a given asset class. One is easy because it has limited utility, and the other is a useful intellectual exercise, but impossible to get right.

  • Long-term returns are, in a simplistic model, the current dividend yield plus long-term growth in dividends per share—where “long-term” is very long-term, like a lifetime or longer. And growth in dividends per share is, also in the very long term, a function of growth in revenue per share: margins tend to be surprisingly stable over long periods, and multiples can only go so far in one direction or another…This model looks too easy, and in some ways it is. For example, it’s correct over a timescale long enough to be irrelevant to individuals; there can be long swings towards lower margins, like the one that took place in the US from the 60s through the 90s. And there can be swings in the opposite direction, like the rise in corporate margins that’s taken place since then. But these trends can’t go on forever—each one of them could easily be the majority of the lifetime of a specific individual investor. Swings in valuation can happen, too; P/E ratios went from ~20x in the late 1920s (on low-quality earnings that were increasingly from financial engineering) to the mid-single digits in the late 1940s, back to 20+ in the 60s, back to single digits by the late 70s, and so on
  • The discussion of fundamental drivers of equity returns hammered home the idea that valuation is not a driver of returns, because it moves so slowly. Even if the market switched from trading at ~10x earnings in the early 20th century to ~25x today, that’s 70 basis points per year of annual return. But the flip side of this is that over shorter periods, valuation’s role as a return driver goes way up. Year to year, the market’s moves are typically the result of multiple expansion rather than earnings growth or dividends…Over even shorter periods, valuation becomes even more important; an intraday swing or the change in price from one trade to the next are, almost by definition, overwhelmingly driven by valuation multiples rather than some tiny incremental update to a company’s fundamentals.
  • In the very long run, stocks tend to go up. But that’s only sustainable if that long-term gain is compensation for some shorter-term variability. You can know roughly what you’re getting into by looking at broad valuation metrics, which tell you that stocks are fairly expensive right now, especially in the context of higher rates. But you can’t get much more information than that—the difficulty of timing the market is a function of how all the easy ways have been arbitraged away, and what’s left is a bedrock of uncertainty that, over short timescales, dominates fundamental drivers and long-term trends.

Money Angle for Masochists

I just want to attach a thought to Byrne’s post that seems cruel to dump on casual investors. Hence its home in the Masochism section.

If valuation is a limited return driver except over a long-run period, a period nobody knows anything about

1

AND you are invested in managers who have valuation-based strategies, then Byrne’s post has Shrodinger’s cat vibes. There’s a duality of epistemology between the description of “what happened” with “what will happen” that really doesn’t seem to overlap in any pragmatic context. And the assumption of that overlap is the rationalization that underpins all long-term investing sales pitches.

Let’s back up and consider the problem of the long-term generally.

The best we can do is have sound frameworks for decision-making. Being probabilistic thinkers, understanding incentives, etc etc. All the stuff you hear on podcasts, Mungerisms, yadda yadda. It’s all sound even if it’s hard to implement in a messy world.

I feel that our frameworks have limited potential in outperforming the wisdom of crowds for long time horizons. Those frameworks help but their value is more in avoiding stupidity rather than aiding one in outperforming unemotional benchmarks that already incorporate intelligent portfolio construction logic — diversification, cutting losers (ie following trends) and rebalancing.

Everybody would love to hide behind “we are good at this in the long run and until that long run happens you shouldn’t judge us” while they collect nonrefundable fees. I don’t think there is data that you can look at that solves the problem of “who is good at beating benchmarks over the long term” for a price that doesn’t negate the advantage. But even price aside, how do you say “this buy-and-hold approach is better than a benchmark”? You need to believe they know something about the far future that other smart people do not. And the type of people that are good at that (if “that” exists) do not strike me as the same imaginations that are drawn to value investing.

The longer you hold an investment, the less your entry price matters. The most important driver of the investment will be the rate at which it compounds invested capital. A company that has the promise to do this is unlikely to be cheap. Everyone understands the math and understands that getting the entry price wrong is okay if they:

a) get business returns roughly right

and

b) don’t sell

The re-rating of the multiple matters more for the short to medium-term investor.

Doesn’t this put long-term investing at odds with the extreme couponing personas that value investors project?!

These other ideas make sense:

  • Buffet preaches buying great businesses at fair prices
  • Trader types are cool to buy a crap business they think is oversold but will re-rate when flows stabilize or there’s capitulation or whatever short-term thesis they envision materializes. They are just focused on beating the spread on the new slate of volatile stocks each week (or month).
  • The growth investor appears to have internalized the idea that you can pay up for the best businesses and you’ll do great in the long run.

It’s the long-term value investors trying to buy pristine ROIC for bargain prices who appear to be spitting on the laws of investing gravity. Value investing seems like a mean reversion trade. “Trade” being the operative word here not “investing”.

The premise of long-term value investing appears logically incoherent when you try to marry “cheap” with “good business” in transparent public markets. Shorter-term strategies attract more competition (if you can “buy well” you’d like to exploit that skill 1000x a year rather than 5x a year) but they are at least possible to evaluate.

You could ask a manager, “What kind of things I should look at to figure out if your strategy is getting worse?” Tell me how to judge you. Tell me how to judge whether it even makes sense to try to get alpha in your space. There’s an old interview with an option guy Wayne Himelsein where he discusses strategy evaluation:

Are you achieving your premise? So you’ve said yourself, I know where I want to neutralize, and I know where I want to get my alpha. And if that’s where you get your alpha, you have to know that number one, you have alpha there. So if you look at your growth tilt and measure that against Fama growth factor, do you beat it? If not, you’ve got no edge.

He talks about mapping a strategy. Comparing the exposures to a time series of different exposures to see how it behaves.

“I don’t ever listen to what [the manager] tells me. I just run it versus we have in here about 180 different exposures that we have time series for factors or exposures [to find out] “what is inside this thing?”

How intentional are the exposures?

Managers will tell you that they’re doing something but don’t even know what they’re exposed to. “Did you know you have a 30% exposure to momentum? Oh, no, I didn’t. I’m actually a value investor.”

This is an older interview, but it’s increasingly common knowledge today that these lines of questioning inform pod shops’ risk and compensation frameworks.

This doesn’t work for choosing long-term investors.

The problem feels intractable.

You might convince me there are some weirdos who have first-hand tinkered with things that inform a vision of the far future. But they wouldn’t balk at the ticket price to board that ride anyway. They believe.

VC makes sense because overpaying doesn’t matter if you are truly drawing from a power law distribution (that’s a big “if” though).

And trading oriented managers can be evaluated. Just ask them the terms they want to be evaluated, hang them on their own inconsistencies, and choose from whoever’s left.

But long-term investors who want cheap prices? I don’t know if that job is even doable ex-ante and if it is I don’t think you wear a suit to do it.

From My Actual Life

I just finished Vice Principals. Lee Russell is so despicable he has to be one of the best characters ever.

I leave you with a playlist-level song that outros one of the episodes:

Stay groovy ☮️

Generative Instinct

Remove the legend to become one (30 min read)
by Eugene Wei

I’ve been reading Eugene’s outstanding blog for many years but he posts rarely these days. I can’t remember how this post got on my reading queue but I’m happy it did. It’s about a topic close to my heart — creating an effective dashboard chart.

I had never used Excel until my first job as a trading clerk. Most of our models and workflows were in workbooks that had dozens of tabs and masochistically linked to workbooks in other drives (“Hey did you save your workbook so I can pull the fresh data into mine?”)

By following the formulas through the gridded labyrinth I learned both Excel and the pricing models. In my second month as an assistant, I started getting the hang of my post, market-making a relatively new ETF spelled es pee wye, so I asked my boss, Reggie Browne (yes, that Reggie) if I could rebuild our spreadsheets from scratch. I was a bit nervous to even ask since Reggie built them but I was the one using them all day as he was in the pit trading. My job was to make sure we had the right pricing of the ETF NAV based on the daily composition of the baskets and the cash/futures basis.

[I was also in charge of calling the Chicago futures pit to hedge our positions and dealing with daily DKs. A DK or “don’t know” is an error — you thought you bought and hedged 1.2 million shares the prior day but your statement in the morning says something different. Doh. You spend a few hours before the open making sure every share and every cent reconciles. Maybe Reggie thought he bought 67,000 shares from some other badge and only 6,700 cleared. Somebody made a mistake, there’s now an “error p/l” that needs to be sorted out. The mistake could have been me keying in the wrong share amount and have nothing to do with the traders or brokers. There was a lot of looking for needles in haystacks so that you knew your position by the time the bell rang. The grunt work of tiny details, communication with so many traders/clerks on the floor, and ultimately negotiating repeated interactions was a lot of the job back then.]

Reggie was totally supportive. He said building the sheet from scratch would be a worthy learning exercise. From then on, I was hooked. I could always be helpful by whipping sheets up for others. Being useful in a determinate way helps at the margins in a career that is heavily given to the whims of chance.

In my last gig, building dashboards and models was a form of therapy in between the steady stream of voice trades. Still mostly Excel and VBA. I was a bit OCD about aesthetics so my sheets were overkill in that department. You could click on a row in my daily volatility monitor table and it would highlight, sort and pop out cells that were relevant to the user. Sliders that would animate dynamic time series. My instincts around charts were to build them in general ways so the user could easily manipulate parameters to visualize data sets from various angles.

But I was leaving a lot on the table. The sheets could bog down or even crash. I was settled on a Swiss Army Knife because I didn’t prioritize yanagi skills. Weak but true.

Eugene’s post confirms what I had felt. Excel, out of the box, was not ideal for charting. His post is both a set of tips and a narrative worth the journey for anyone who has wondered how to visually compress the hallowed metrics that drive key decisions. I’ll share a few excerpts below (I’m also pleasantly stunned that I arrived at many of his conclusions on my own. One of the fun things about reading the post is finding a fellow psycho. If I ever meet Eugene I’ll ask if he does what I do when I open an Excel workbook — immediately uncheck gridlines.)

Excerpts:

  1. Remove the legend; use data labels
  2. In The Visual Display of Quantitative Information, Tufte uses very little color.
  3. Tufte advocates reducing non-data-ink, within reason, and gridlines are often just that.

And this is immediately one of my favorite sets of sentences ever strung together:

The reason the book [Tufte] influenced me so deeply is that it is actually a book about the pursuit of truth through knowledge. It is ostensibly about producing better charts; what stays with you is the principles for general clarity of thought. Reading the book, chiseling away at my line graphs late nights, talking to people all over the company to understand what might explain each of them, gave me a path towards explaining the past and predicting the future. Ask anyone about any work of art they love, whether it’s a book or a movie or an album, and it’s never just about what it’s about. I haven’t read Zen and the Art of Motorcycle Maintenance; I’m guessing it wasn’t written just for motorcycle enthusiasts. A good line graph is a fusion of right and left brain, of literacy and numeracy. Just numbers alone aren’t enough to explain the truth, but accurate numbers, represented truthfully, are a check on our anecdotal excesses, confirmation biases, tribal affiliations.

From My Actual Life

[If you’re in a rush, this is just skippable personal exhaust. I used to do these more but I struggle to be brief hence the fig leaf-shaped warning]

The last few days have been really pleasant. My 10-year-old’s soccer team won their first game at the end of the season. They scored 3 goals and Zak had 2 plus an assist. He scored from both wings, once with the left foot and the other with the right. But the part I was most stoked about was when he pointed that fact out to me after the game because he’s been working on that (he didn’t need to point it out — the left was a great shot from a tough angle). Nothing beats watching someone, especially a kid, feel paid off for effort. Even if it’s a meaningless rec soccer game. As Gucci Mane once said, you either practice quitting or you practice winning.

Later that night I met up with close college friends who were in town. We ate at Rintaro in SF followed by drinks at Charmaine’s. Both spots are great (although the area around the Proper Hotel isn’t fit for a stroll by Satan himself). The highlight of that evening — my friend, a senior engineer at Waymo, taking us on a 30-minute ride around the city in a fully autonomous Jaguar i-Pace. 25 years ago, almost to the day, we were shotgunning beers in our stinky Ithaca apartment just before it burned down (he was the first person to smell the smoke and start knocking on neighbors’ doors) and now he’s getting to answer our questions about the future!

[In hindsight it’s no coincidence that he also happened to be one of the engineering students who built Cornell’s HEV in the late ‘90s and is flat-out one of the smartest and daring humans I’ve ever met. Big surfer — got his Ph.D. in physics in Hawaii, high diver, snowboarder, Muay Thai fighter. Since he was a teen could quite literally rig up any mechanical thingamajig you needed — the most MacGuyver person I’ve ever met so I wasn’t shocked when he was building lasers in grad school. He is so happy to have matched with this career and work with “smartest people he’s ever met”. Don’t worry J, I’m not offended.]

He couldn’t make it to to Napa with the rest of us the following day but we were still high from the experience and appreciating how much joy he’s found at work. And I realized how deeply the rest of our crew silently cradled that same aspiration — to feel like you’re doing the thing you should be doing. We weren’t envious but just so, I don’t know, inspired and happy to know that it even exists. I feel like I don’t see those fits too often and when I do it’s someone I don’t know as well as J so it doesn’t hit quite the same way. I know where he’s been so I know what this means.

And to wrap the cheese parade, Yinh and I went to Vancouver for a date night (14-year anniversary) to see Alice In Chains, my favorite band from my high school years, open for GnR, my favorite band from my middle school years. A rec for Vancouver — the restaurant/bar called the Botanist. We went for lunch. We’d go back.

Also, this bar is opening Nov 1. I talked to the manager because I couldn’t not weasel my way inside. Turns out it’s the former home of the Vancouver Stock Exchange.

Ok, I leave you with a video now. I’m a huge AIC fan and only recently discovered their pre-Dirt era concert at the Moore in Seattle is on YT. It’s a mere 27 minutes.

Never seen/heard a better version Layne.

Stay groovy ☮️

A postscript observation:

When I first started in options trading, I told that friend now at Waymo, that he should leave Silicon Valley where he took his first job out of college at a chip company. You need to come work on the options floor in NYC. He is a brilliant combination of brains, competitiveness (to an obsessive degree), and sheer will. My pitch was rooted in the money.

Poorly played.

He could care less about that.

He didn’t see the point of doing something where you hadn’t physically built something. I dismissed this at the time and about a decade later when I left the floor and went to a HF I understood.

He had, what I have started calling, a strong generative instinct. An instinct I actually shared to a lesser degree but didn’t realize until I started building infra and trading tools and later writing. Synthesis and creation were more rewarding than the video game that trading itself was.

I’ve thought about this distinction quite a bit. Some jobs don’t build anything. It doesn’t mean they aren’t creative. From poker players to teachers, there are creative jobs that don’t leave behind some tangible artifact or physical product. And I can how someone might find that particular form of expression intrinsically rewarding. To see your thing in the world with others using or enjoying it.

This instinct is a sub-dimension of satisfaction that people may not recognize until it’s explained in that way. When I talk to someone early in their career looking for guidance (one of the weird things that this letter has done is had parents ask if I’d talk to their kids — it happened again recently so I’ll probably share my notes from it in case they’re more widely useful), I explicitly mention this just to see if it pulls something from their unconscious up to the level of self-awareness.

Anyway, the whole pull towards being generative is something that we encourage at home. Be a producer not a consumer. If the extent of your intellectual habits is knowing everything about your favorite sports team, then your sense of agency in a world that is quickly commodifying non-creative tasks will feel threatened.

A darker pull on that thread:

Fear comes from lack of agency.

Ask any middle-aged person who chose a “safe” box-checker career at age 22, who has long since forgotten how to learn, how hemmed in they feel right now. Don’t be surprised when the common theme of their politics reduces to “pull the ladder up” under the guise of “I worked hard to get here”.

As you read this, LLMs are solving real-time language translation. The world’s chaos aside for a moment — a world without language barriers is a flattener. A homogenizer. The less equipped you are to differentiate yourself on some value-creating axis the less claim you stake from the bounties of technology. You’ll have a low Kolmogorov complexity score under the gravity of capitalism. Compressed to a token in some grand computation that takes in souls and spits out GDP.

Resisting the paperclip optimizer entails risk. And courage. If you are doing comfortable, safe things in all parts of your life, there’s a form of technical debt building. It’s insidious because you don’t feel it until it’s close. If you’re old and boring but rich you’ll probably outlast a dwindling sense of control but recommending what appears safe and sensible today to a 22-year-old rather than a wider framework for taking risk intelligently feels like guidance malpractice to me.

Also, I have no basis, training, or credentials to guide anyone. I quoted a convicted (yet seemingly reformed) felon earlier.