Moontower #331

Note of an Instagram Experiment

I’m trying something new that has become much easier with Meta’s personal AI assistant Muse: turning Moontower posts into Instagram Stories and Reels.

Math and personal finance ideas, one frame at a time. Muse handles the heavy lifting of reading the posts and synthesizing the arc. I then edit the frames and add music.

This week so far:

Why Godzilla can’t exist (stories)
You already trade options. You just call it a car lease. (stories)
Selling your 3% mortgage incinerates $188,000 (stories)

The feedback has been encouraging!

Follow @kris_to_the_max.

In this issue:

the Farmer’s Almanac for Investing
the “iron condor destroyer” tool

Friends,

Just a few fun things up here since the bulk of today’s letter is heavy on investing stuff.

I Was the Wedding Planner for the Guns N’ Roses “November Rain” Ceremony and Reception | 4 min read

Oh McSweeneys. I knew your writers must be jaded hipster millennials.

“Uh, no”

And here’s a clip I’m very, very late to, but making up for lost time by replaying it 20x in a row.

I just love how the announcer who gets caught off guard is so quick to come up with the most charitable interpretation of the question. Also that voice?! He was engineered in a lab to do that job.

Money Angle

Exponential Wealth: Centuries of Stock and Bond Returns free PDF · 380 pp.

In 1976, Roger Ibbotson and Rex Sinquefield published “Stocks, Bonds, Bills, and Inflation” (SBBI), the first long-run total-return history of the major asset classes. Economists had talked about the equity risk premium for years but as Ibbotson puts it, “SBBI gave us a measure of it.” The data became the standard reference for historical return assumptions, from asset allocation to cost-of-capital work.

This is the 50th-anniversary update, rebuilt from CRSP after Morningstar discontinued the original indices, with the dataset now spanning a full century, 1926–2025.

It recaps what stocks, bonds, bills, and inflation have delivered, then widens out to global markets since 1900, the US before 1926, commodity futures since 1871, bubbles and crashes since 1792, and a forecast to 2050.

It’s a free, encyclopedic reference I recommend adding to your favorite LLM’s investing project folder. It’s like the Farmer’s Almanac for money.

It’s also a great reference for methodologies since the studies entail constructing price series and indices, measuring their statistical features, and addressing pitfalls such as survivorship bias, float vs full-cap weighting, shifting size definitions, overlapping observations, and effective sample sizes.

A sprinkling of fun facts:

$1 in US large caps in 1926 → $14,751 by end of 2025; $814 after inflation. Long Treasuries: $117 nominal, under $8 real. T-bills: $25 nominal, under $2 real.
Real compound returns: stocks 6.9%, long Treasuries 1.9%, bills 0.3%.
About a third of the century was spent below a prior real high: 1929–WWII, 1966–82 (16 years of zero real growth), 2000–2012.
A 50% three-year run-up was followed by another 50% run-up ~3x as often as by a full reversal (144 vs 50 of 394 episodes, 1792–2024). Crashes were followed by full recovery even more reliably.
Top 25 companies are ~50% of US market cap, a level last seen in the 1930s. Tech is ~40% of cap.
This is a non-obvious logical bit: Index total return is attainable by any investor but not all investors, for example dividend reinvestment can’t scale to everyone. Reminds me of these fallacy of composition peculiarities like “paradox of thrift” or treating government finances as if they are a household.
Investors had the least cash when expected returns are highest.
Micro cap: 16.5% arithmetic, 11.1% geometric, σ = 37%. Mid cap matches micro on compound return with σ = 24%. Post-1976, micro had the lowest compound return of any size bucket.
October 1987 was a 1-in-10¹²⁸ event under lognormal i.i.d. The chapter links fat tails to the persistent apparent overpricing of OTM S&P puts.

The book closes with a forecast for 2026–2050, using the same approach Ibbotson and Sinquefield used in 1976. It has 3 steps:

They anchor interest rates and inflation to today’s Treasury yield curve.
Resample historical risk premiums.
Simulate thousands of possible paths.

How did this method fare from 1976 to today?

Pretty well, actually. Although the composition of the return wasn’t quite what they expected.

From 1976 to 2025, the forecast called for a median of ~13.3% a year, but stocks only returned ~11.9%. However, it assumed ~6.7% inflation (it was the 70s after all) when actual inflation was only a bit more than half at 3.6%. Which means nominal returns fell short of the forecast while real returns beat it (~8.1% vs ~6.2%).

At this time, inflation and rates are closer to their 100-year averages, so the yield curve isn’t pushing the forecast much in either direction. What does it say about 2026–2050?

On raw US history: 9.5% nominal, 7.0% real per year.
The authors think that bakes in an unusually fortunate US century, so they pull the mean toward the global historical experience.
Preferred forecast: 8.0% nominal, 5.6% real, implying an equity risk premium of about 4.7% over cash. In their words, a premium “very close to what it always has been.”

Seems rosy. We’re not allowed to be this optimistic. Let’s get a second opinion. This one comes from the market itself as translated by Elm Wealth. Their capital markets assumptions, out this week, are implied from current bond yields and valuations (a cyclically adjusted earnings yield) instead of historical premiums.

[Whether CAPE is a more or less reliable forecasting tool is up for debate, but any attempt to forecast returns feels about as ill-fitting as using a vacuum to pull out a splinter. I’m in the camp that it’s a pointless exercise, while vols are more predictable and therefore a sounder basis for “know nothing” sizing, which I need because I know nothing.]

Elm reports as of September 30:

US stocks: 2.92% real, 5.30% nominal
Non-US stocks: 5.78% real, 8.15% nominal
10-year TIPS: 2.91% real
US equity risk premium over TIPS: 0.01%

Where do Elm and the authors agree?

Both take the rate and inflation pieces from market yields.
Both lean away from projecting the US past forward. Ibbotson adjusts toward global history.

Where do they depart from each other?

The equity premium. History says ~4.7% over cash. Today’s valuations say roughly zero over TIPS. Measured against the same TIPS yield, Ibbotson’s forecast is still ~2.7 points above it.
Ibbotson does address valuation. The chapter flags P/E expansion as inflating the historical record and tests stripping it out, but that actually lowered the forecast less than the global adjustment did. In other words, using global historical valuation was more conservative.
There’s some timing mismatch. Ibbotson uses the end-2025 curve while Elm’s publishing 9 months later when we know 10-year real yields are up over a full 100 bps.

Caveats both sides attach

Elm: the risk premium is a poor predictor of near-term direction; momentum is positive and its risk indicator reads low.
Ibbotson: a forecast is the center of a wide distribution, “not a guarantee.”

A lazy man’s framing

Ibbotson forecasts 5.7% real equity returns for a couple of decades. The CAPE method is close to 0. Split the difference, and you are close to the current 2.90% 10-year TIPS yield you can lock in now (for reference, Treasuries returned 1.9% real over the last 100 years.)

The market in general doesn’t appear to be especially frothy, but the risk-reward in bonds has gotten far more attractive with the latest surge in yields. If AI turns out to be deflationary and hurts employment at the same time that housing rolls over because the cost to own and finance has skyrocketed, then bonds will have looked like insurance policies with ex-ante positive carry. In English, a pretty sweet deal.

But I get it, it’s no spaceship outta the underclass.

It’s funny, when you learn about investing, you associate greed with bullishness. Turns out the textbooks have it exactly backwards in the context of our modern economic ~~pathology~~ psychology.

Money Angle For Masochists

Workflows are Moontower’s screeners organized around what you’re trying to do: sell premium (Income), buy protection (Defensive), finance that protection with your upside (Collars).

We just released a new one to help directional traders scan across the market for the best payoff for a given move: Verticals

About the Verticals Workflow

It starts from a simple need:

How do I compare payoffs across tickers in volatility-adjusted terms?

You don’t want to screen across names for the best bang-for-your-buck on a 10% rally because 10% means something very different in SPY vs MU or TSLA.

Instead we use standard deviations computed from the name’s own surface. Pick a move, say +1 SD by the November expiry, and ask the same question of every name: what’s the cheapest vertical that pays in full if the stock gets there?

The Verticals workflow returns the answer in a grid based on the watchlist you care about.

Let’s see how it works (and learn some option math in the process).

Two knobs

You set two things:

An expiry. The picker lists every expiry any name in your list carries, with a count of how many names list it. Every row in the grid is the same maturity, so you’re comparing like with like.
A signed move. ±0.5, ±1 or ±1.5 SD. Positive means call spreads, negative means put spreads.

For each name, the grid shows the tightest vertical that is fully in the money at that move. Tightest means adjacent listed strikes. Fully in the money means if the stock lands exactly on the target at expiry, you collect the whole strike width.

Finding the breakpoint

The target strike for a z-SD move is:

Then pick strikes:

Calls: the short strike is the closest listed strike at or below K_z. The long strike is the next one down.
Puts: the short strike is the closest listed strike at or above K_z. The long strike is the next one up.

Both rules keep the whole spread inside the target, so a stock that gets to the breakpoint maximizes the max spread value (ie it pays the width of the strikes.)

Marking the spread

The obvious price is the spread’s mid, but it’s far too noisy if each leg is 40 cents wide and the spread is worth 30 cents.

Collecting an accurate mark for a spread is a bit of an art, combining curve fitting and option pricing. In the app, the Price you see for the spread is not mid but a Moontower fair value which lives within the bid-ask.

Reading the grid

The headline number is Payout:

A 1-point spread priced at $0.20 pays 4 to 1 if the stock gets to the target.

Payout is the first column your eye goes to, but we include several columns to judge how much to trust a mark.

Filtering for confident markets

Spread bid / ask: the spread’s own market.
Mkt width: the legged market, both legs’ bid/ask widths added together. It’s what you’d pay to cross both legs.
Mkt / strike width: Mkt width as a share of the strike width. A 20-cent-wide market on a $1 vertical might be hard to execute nearfair value.
Leg width / vol: the wider leg’s bid/ask expressed in vol points, as a share of its IV. It puts a 20-cent market on a $400 stock and a 20-cent market on a $30 stock on the same footing.
Mid: Compare with Price. When these two sit close together, the market and the model agree. When they’re far apart, the Moontower fair value is probably more reliable.
Liq: the name’s liquidity tier, which we provide in all our filters. It’sa function of how wide the markets as a percent of vol allowing us to compare across names.

The grid also drops names whose markets are too wide to mark at all. They’re counted in the “N names excluded” line under the grid, so you can see what got left out.

A few screens to start with

Tight markets only. Mkt / strike width under 20%, Liq High, sorted by Payout. This is the honest version of the leaderboard.
Where the market and the model agree. Add the Mid column and keep rows where Price is within a few cents of it.
Cheap upside: +1 SD, Call skew %tile low, sorted by Payout.

Everything filters, groups and sorts like the other workflows, and your choices persist between visits.

This tool will let you look at the market and answer where the cheapest put spread or call spread to bet on a .5 or 1 standard deviation move by some expiry date.

You can also just reverse sort if you’re looking for spreads to sell. Knowing how much people love to sell options, I should probably rebrand this as the iron condor destroyer (an iron condor is a package of 2 OTM vertical spreads typically marketed as a less risky way to sell a strangle).

Stay groovy

☮️

Moontower Weekly Recap

Moontower #330

In this issue:

academic acceleration
wrapping up Kelly
option topics from the RH Summit
game and food recs

Friends,

One of my close friends runs an advisory for HS students applying to college. He wrote this guest post years ago: Moneyballing College Admissions.

He lives in the Bay Area and told me he’s seeing more parents complaining about the lack of acceleration options in the public school. He said outside CA it’s becoming far more common for high schoolers to take AP Calculus BC before senior year. My 8th graders’ goal is to take it by junior year, giving himself a chance to take Multivariate Calculus by senior year at a local college. This is already offered in some high schools across the nation, including some on the peninsula. Just this week, I talked to someone whose 9th grader was in Calc BC. That only sounds crazy if you haven’t been paying attention to what I’ve been sharing about Math Academy students (my 8th grader says his 5th grade little bro is already doing the same stuff his “advanced” math class is doing.)

In our local school district, we are finally seeing the pendulum swing the other way on math instruction. A few years ago, they got rid of “tracking” in 6th grade, forcing all kids, regardless of their interest/aptitude, into the same class. Well, the seeds of change are obvious in this survey I just filled out, as I don’t think we could have even had this conversation 5 years ago:

That #7 offers choices besides “supportive” and “very supportive” tells me these 2 articles are as important as I think they are.

Smarter Than Yesterday (6 min read)

Pamela Hobart argues “the academic acceleration community needs a viable brand”. Co-sign. Terrific post. I’ve had many of the same thoughts, especially as my kid’s schoolwork will leave me wondering, as Pamela has, “what are we even doing here?”

Everyone Wants a Child Like Eileen Gu (10 min read)

”almost nobody today wants the childhood that produced her.”

Violet Gordeljevic spitting truth in this one. I’ll share a few excerpts that resonated with me. You should read it to see what lands or doesn’t for you.

On Discipline and Exceptionalism

“So when people say she sounds and talks so disciplined, and that she knows her own mind—well, yes. That is what a decade of being asked to do your best looks like from the outside.”
“Nobody arrives at exceptional by accident. It doesn’t turn up later as a nice surprise because the child was left alone and bored for long enough.”

On Passion and Competence

“Passion doesn’t usually come first and then get supported. Usually exposure comes first, then competence (from actually having gone through practice), and passion tends to arrive somewhere after that, because human beings mostly love the things they are good at.”
“What is important to understand is that she could not have fallen in love with skiing, or Mandarin, or Olympiad maths, if nobody had ever put her in front of these things…A child who is never introduced to numbers will not reveal unusual mathematical ability. A child who never sits at an instrument will not discover she has an ear.”

On Modern Parenting and “Full Schedules”

“We didn’t lighten the load at all. We drive our children to more things than any generation in history. We just stopped asking them to become good at any of it.”
“If we are honest, the schedule is full but the demand is zero. It’s honestly like we have swapped skill for entertainment.”
“Underneath every version of this conversation sits the same line: I don’t need my child to be exceptional, I just want them to be happy. … But being the parent who stretches a child—who asks for one more go, who expects them to learn to write something properly or figure out that math equation, who holds the line at six when she wants to quit ballet—doing this is harder and considerably less pleasant than being her friend.”

On Warmth, Adversity, and Long-Term Value

“Protecting a child from effort is not the same as protecting a child.”
“What separates people with more demanding childhoods from those with easy, low demand ones, isn’t how much or even what was asked. It’s rather whether the asking sat inside enough warmth to be survivable.”
“The choice was never between pressure and love. It was always meant to be both.”

And then my 2 favorite:

“I have met a great many people who regret being allowed to quit”
“The thing is, children are not good judges of what they will be glad to be good at at thirty.”

Money Angle

Wrapping up Kelly

I know I’ve published a few articles on the Kelly Criterion recently, but if you prefer other mediums:

🤳🏼 This is the IG story version

If you prefer a more in-depth lesson, the lecture version with Matt Zeigler dropped this week:

📊Accompanying Kelly Slides

Robinhood Summit 2026

I was in Houston this week for the Robinhood Summit to help with 2 sessions.

A “trading lab” class where Mat Cashman and I gave a lesson on buying options.
I was also invited to play the role of “trader” on a panel featuring a few of the data providers on RH’s new agentic trading platform. You can think of it like an app store, where users can subscribe to have vetted providers’ data accessible within RH’s trading agent.

Since this panel was on the “main stage” the recording is available here:

The kids were able to watch the live stream before school

Money Angle For Masochists

2 examples from the Summit.

Mat Cashman and I did a teach-in session to a large audience of conference-goers who use options. Here’s one idea from that session.

What does optionality actually buy you?

The simplest way to understand the value of buying an option for directional reasons is to benchmark it to the counterfactual: how do I perform relative to “if I just bought the stock?”

If you buy a call, you do better in the large up move OR the large down move vs just buying the stock. You have more upside leverage, and if the stock craters, you only lose your premium. The tradeoff is that the option strategy underperforms owning the shares on intermediate-sized moves. That’s why we say owning an option is “long volatility” even if someone resists thinking in such admittedly abstract terms.

The chart subtracts the P/L of 100 shares from the P/L of ~2.2 calls on the 1-year 110 strike, at expiry. The calls cost $2,194 and carry the same delta as shares that cost $10,000 (100 shares of a $100 stock).

🔨Exercise: Solve for what delta the calls are

The shares win between roughly $78 and $137. The gap is widest at $110, where the calls expire worthless and the shares are up $1,000, a $3,200 difference. Below $78, the calls lose $2,194 at most while the shares keep falling. Above $110 the calls behave like 217 shares instead of 100.

If you buy a call and lose your premium, you can’t evaluate if this is a good or bad outcome without considering the counterfactual.

The INTC calls and a possible Micron sympathy trade

This was one of the examples I discussed in the live stream session where we talked about combining sources of data to reason through trade ideas.

The print. On Sep 28th, there was notable size buying in INTC October 16 130 calls.
An odd expiry. It was a lot of premium spent on high gamma & theta calls which expire a week ahead of Intel’s October 23 earnings call. Why spend that much premium on a short-dated bet that rolls off before the stock’s own catalyst?
The sympathy hypothesis. Micron was reporting on the day I was talking after the close, Sep 30th. Maybe the buyer was using INTC as a semis proxy, owning short-dated calls to catch a sympathy move off Micron’s print. It’s one possible story, not something I can confirm.
Did the seller make a mistake? A seller may think “these don’t capture earnings, so they don’t deserve a premium,” or INTC shouldn’t move much in the quiet blackout period before an earnings report, ignoring possible spillover effects from MU’s bellwether report and guidance.
The next question. Is Micron earnings even a big deal? Look at Micron’s earnings straddle. If the implied move is small, the market isn’t expecting Micron to move much. Then the sympathy thesis loses most of its appeal, since there’s less distance for INTC to get dragged along. Turn out MU earnings were priced cheaply compared to the last few years.
Then look at what INTC vol already costs. Implied vol was middle-of-the-road but high cross-sectionally (ie relative to other stocks in the current market regime). Call skew was rich, though not extreme.
Put it together. Rich vol plus a firm call skew, the primary market for MU volatility saying earnings are going to be a non-event, and a possible story for putting the INTC buyer “on a hand” adds up to making me more inclined to want to fade the INTC call buyer. Possible trades are selling INTC straddles or, if you already own the stock, writing calls against it.
You don’t have to sell the 130s to fade the 130 buyer. Heavy buying in one strike lifts vol across that whole expiry. Strikes near each other move together, so the bid in the 130 calls shows up in the 125s, the 135s, and the at-the-money options too. Selling the straddle, or whatever structure fits your book, still takes the other side of this buyer. Don’t anchor on the exact strike that printed. Put-call parity ensures the entire surface gets richer.

Finally, an analogy I didn’t make at the conference, but notice how much like poker the chain of thought is. The cards you can see (ie the flop) are the measurables like IV rank or call skew. The quantity of options purchased is the bet size. The expiry is like thinking about the position they bet from (ie “under the gun” or right after the button to last position or “dealer”). One of the market-makers’ advantages is that they keep tabs on notable flow, like a poker bot which examines online players’ hand histories and tendencies.

From My Actual Life

Once the RH Summit ended, I was rewarded with some nice personal moments. I took Mat Cashman to Camaraderie in the Heights area of Houston for an exceptional meal by super chef Shawn Gawle.

Shawn is a friend of mine. He lived with Yinh and I for a couple of months when he first moved to SF to be the pastry chef at Saison. If you are in Houston, do not miss Camaraderie.

Finally getting to experience what I fully expected to live up to the hype.

Then on Friday, Yinh and I celebrated our 17th wedding anniversary. (We’ve been together for 23 years in total).

We both played hooky and went hiking up in Fairfax (Marin County) before an exceptional dinner at Vin in San Rafael. It’s both casual (we were still in hiking clothes) and worth going out of your way for. Unbelievable eating week. Might as well. I have a colonoscopy later this week, so I need to follow some dietary restrictions for the next few days.

We also did a bit of shopping in downtown San Rafael. Picked up some used vinyl at Red Devil and also went to one of the best game shops I’ve ever been in:

This Gamescape has a shared lineage with the classic one on Divisadero in SF but the San Rafael one is much larger. Their game wall is immense and ordered from least to most complex.

I picked up these 2:

Acquire is one of my favorite games and while I have it already, this newer edition has irresistible plastic buildings. I must support this.

Brass Birmingham has been at or near the top of the BGG rankings for nearly a decade, which is Nigel Richards’ level of domination. My favorite boardgame is the first edition of Brass released in 2007, but supposedly the 2018 Brass Birmingham is much better. Time to find out.

Stay groovy

☮️

Moontower #329

In this issue:

soulcraft
grab a coffee and derive this with me

Friends,

My second favorite thing after a piece of art, writing, music, movie, and sport that I love is watching someone else gush over things they love. It’s why the Lost in Vegas guys are so endearing, especially when the channel first started. You were watching hip-hop heads not only discover but unpeel the layers in Tool’s music.

One of my dad friends recently bought a 1979 Jeep to restore with his son and asked if my son Zak (13) would like to help. Zak’s “hell yea” beat the sound of my last syllable when I asked him. He started watching YouTube, and we landed on a channel where these obsessed details comb the U.S. looking for “barn finds” to clean for the owners. For free! It’s free because the channel has almost 2 million subscribers clamoring to watch an impossible cleaning.

I watched a few videos. I get it. Renewal of beauty, just like the objects of renewal never goes out of style. The process is as timelessly rewarding as the result.

Caitlin’s tweet is an appeal to our spirit of obsession and craft.

Article content — https://x.com/KrisAbdelmessih/status/2102392847676637227?s=20

Which brings me to a luxurious reading experience:

I like ‘em thick (Adam Mastroianni)

This essay not only feels good but is an important lens on the fast-approaching experiment of whether infinite electric monkeys will pound out Shakespeare.

Normally I might apologize for extensive excerpting but they are the point. I can do no better than this.

It opens:

I owe an apology to every English teacher I ever had. I always assumed that so-called “great” literature was a hoax, a punishment inflicted upon adolescents for the crime of being young. These books did not have anything special about them, and covering up that fact was simply a make-work exercise for former English majors, a sort of “jobs for snobs” program.

I was wrong about this. There is such thing as greatness. More specifically, there is such thing as thickness. Great works of fiction—for that matter, great works of any art—unfurl in response to your attention. The more time you spend with them, the more you get out of them. That kind of responsiveness is so addicting that it can lead people to do crazy things, like try to teach literature to high schoolers.

But thickness is tricky, because rewarding the careful reader often means repelling the casual one. And this is where I would like an apology in return from my English teachers, because while this might have been obvious to them, they never made it obvious to me.

I was presented with art and literature as if it was self-explanatory, and that everything wonderful about it was plainly visible from the outside. But those works were much more like dark, winding caves with treasure stashed inside of them. My teachers were like, “Right, well, into the cave you go!” and I was like “But there’s nothing in there” and they were like “Entering the cave is 30% of your grade” and so I took a few steps into the darkness and I was like “Just as I suspected: an empty cave” and then I came trudging back out and pretended that I saw something.

It goes on to describe spectacular examples of “thickness”. You won’t want to miss the The Garden of Earthly Delights painting and its unintended invitation to hear “butt music”.

Adam presents 4 qualities that make something thick with examples from a children’s book, the “ears” in Hamlet, and Penn (of Penn and Teller fame) eating fire.

There’s an amazing takedown of what passes for popular non-fiction.:

Reading a book like this feels like wandering through a Potemkin village. Touch any of the ideas, and they tip over.

He contrasts gilded examples of non-fiction with solid gold:

Thickness comes from surfacing a few facts well, and in such a way that you realize the existence of entire universes of additional facts that could be known….[Jane Jacobs book] is pointing out a fact that millions of people observe every day, but almost none of them notice.

He addresses an easily anticipated objection, which you’ll be familiar with if you have read any of deBoer on “poptimism”:

If you allow for the existence of secret treasures that can only be accessed with effort and analysis, then you empower the elitists and the snobs. “Buddy, don’t even talk to me until you’ve been in the cave!”

But look around. The snobs are in full retreat. We have swung the pendulum so far toward poptimism, toward the blinkered idea that all art is equal because all humans are equal, toward the ethos that guilty pleasures are simply pleasures, that I’m not sure if we can ever swing it back.

And finally, Adam addresses the elephant:

Erasing the line between the thick and the thin has left us defenseless against slop at the exact moment of its onslaught. Everyone can sense there’s something amiss with the prose that comes out of the machines, but we lack the language to talk about it, and so we’ve converged on the idea that slop simply means using too many em dashes, bullet points, and line breaks.

What separates substance from slop is thickness. Slop holds no secrets; it signifies nothing. Under scrutiny, it evaporates. All it can offer is bottomlessness—sure, there’s nothing on, but at least there are infinite channels!

That’s why I’m neither surprised nor dismayed when studies find that people prefer AI art to human art. Of course they do! In the short term, thinness prevails. When people are making snap judgments, they want pretty flowers, poems that rhyme, pleasing pablum, the simulacrum of thought. But none of these last…

About once a week, I get a pitch from some AI startup that wants to automate some part of my writing. The most recent one says it’s “built for credible thinkers who have a book’s worth of ideas but not the time it typically takes to write one”.

I’m sorry, but if you’re building or using a tool like this, then you’ve got slop for brains. There is no such thing as having a “book’s worth of ideas” that are all ready to go except for the small matter of choosing the right words and putting them in the right order.

I know exactly the feeling that these slop-trepeneurs are preying on, because I feel it all the time: I’ve got these thoughts in my head, and boy oh boy they’re good ones, all-timers, really, and it’s so annoying that I have to spend all this time making the words sound good, when the ideas behind the words are already so good!

But this is an illusion. The ideas are not already good. They need to be thickened. I understand why it’s tempting to force a machine do the hard part for you, but it can’t, and the hard part is the only part worth doing anyway.

Money Angle

People seemed to like the post I wrote 2 weeks ago teaching readers how to compute Kelly optimal bet sizes in their heads. A lot of people reached out saying that despite learning Kelly in the past, this treatment not only made it clearer but also helped them appreciate how its approach informs risk-taking in wider contexts.

Panoptica graciously asked me to republish it under their own banner:

After this post you will be sizing bets in your head (Panoptica)

Just to put a bow on it, I’ll restate what I think are the most crucial lessons without dwelling on the formula:

Even educated people are terrible at sizing bets. It’s not because it’s so complex, but I guess it’s like squatting. It seems like you should just know how to do it, but it’s actually something you need to learn the mechanics of.
Overbetting is incinerating money. This is something that’s hard to appreciate until you see the math. The reason you size smaller is because of the asymmetry of being wrong on your edge. If you underbet, you slow your growth rate but slow risk even faster. At least you’re exchanging lower returns for a better risk/reward. But if you overbet, you lower your growth rate AND increase your risk even faster than you reduce your reward. Both the numerator and denominator of your risk/reward move in the wrong directions!

If interested, Matt does this neat meta series “Notes on Notes”. It’s a short chat about how and why a particular article comes together in the first place. You can watch it here:

via Matt Zeigler@CultishCreative

A short yet broad-ranging talk with @KrisAbdelmessih on @Panoptica_ai for his @EpsilonTheory: Unplugged essay, “After this post you will be sizing bets in your head” Kelly bets, using AI to learn math, creativity… NEW Notes on Notes!

To round out this Kelly sprint, I have 2 more bits that are again overtures to curious learners who may find math intimidating.

1) Slides

The first is a condensed slide version, which I hope makes this accessible. It was born out of teaching Kelly to my 8th grader at breakfast this past Tuesday. “Zak, I wanna see if I can teach you something neat in 5 minutes.” He rolled his eyes, but at least he humored me while scarfing down his cereal.

📊Moontower Kelly Slides

2) An empowering derivation

The derivation of the Kelly formula is so fun because as it rolls downhill, a number of concepts we talk about in this letter stick to it, so when we get to the end it feels like something grand, but it’s so damn compact.

Another teaching experiment. Let’s see if I can narrate the derivation in a way so that as you follow along it never feels “hard”. I want to prove that this is fun to do and while I don’t expect to convert everyone, I do think there’s a bunch of you who’d like to be able to learn this but feel blocked because you have gaps in your foundations or can’t remember HS math, or just lack some confidence.

Screw all that, I’ll lay my jacket over the puddles so you can see that it’s not so bad out here. Just come along.

Money Angle For Masochists

Deriving Kelly From Scratch

Stating the question

You have a bet. You win with probability p and lose with probability q = 1 − p. If you win, you get paid B times what you risked. If you lose, you lose what you risked. B is also just a return. So if you double your money on a bet, B=1=100% return.

You’re going to bet the same fraction f of your bankroll every time and let it ride.

What’s the f that yields the highest compounded return?

Step 1: What one bet does to your wealth

If your wealth is W and you bet the fraction f:

Win: W → W(1 + Bf) Lose: W → W(1 − f)

Example:

Your starting wealth is $100 and you bet 50% of it on a coin flip. Remember B =1 because when you win you make 100%. When you lose you always lose f which is your bet size.

Win: 100 → 100(1 + 1*.50) = $150 Lose: 100 → 100(1 − .50) = $50

You keep the part you didn’t bet no matter what. A win adds B times your stake. A loss takes your stake away.

Step 2: What many bets do to your wealth

Play n bets. You win h of them and lose the other n − h. Each bet multiplies whatever the last one left you, so the multipliers stack:

Wₙ = W₀(1 + Bf)ʰ(1 − f)ⁿ⁻ʰ

The order of wins and losses doesn’t matter. Only the count does.

Example:

I bet 50% of my wealth each turn on the coin. I play 4 times and I win 3 of them.

100(1+1*.5)3(1-.5)1= 168.75

Order doesn’t matter. If I lost 50% on the first flip, then won 3 in a row:

Start: 100 Lose (×0.5): 50 Win (×1.5): 75 Win (×1.5): 112.50 Win (×1.5): 168.75

Step 3: Turn total growth into a growth rate

Wₙ is where you end up. We want a per-bet growth rate.

You already know how to do this. If an investment grew by a factor of (1 + 8%)¹⁰ over 10 years, you take the 10th root to get the CAGR back. Same move here: take the nth root of this equation: Wₙ = W₀(1 + Bf)ʰ(1 − f)ⁿ⁻ʰ

Note that W₀ can be divided out, just as if your starting identity was 150 = 100(1+8%)¹⁰ and you turned that into 1.5 = 1.08¹⁰ before taking the 10th root to get to annual growth rate.

This equation took our simple total growth equation and turned it into a growth rate equation:

Step 4: Let probabilities take over

We can clean up our new growth equation with several handy notation substitutions.

Ps and Qs

h/n is the share of bets won

(n-h)/n is the share of bets lost

Over a long run, the fraction of bets you win settles down to your win probability:

h/n → p and (n − h)/n → q

Wₙ/W₀ is just a wealth multiple. If you made 200% on your investment portfolio over a decade, your wealth multiple is 3 because you started with $1 and ended up with $3.

We’ll call that wealth multiple G (for “gross multiple”)

So the per-bet growth factor becomes:

G = (1 + Bf)ᵖ(1 − f)ᑫ

G = 1.05 means your bankroll grows 5% per bet on a compounded basis. In traditional investing, we’d substitute the word “year” for “bet”. Each flip is like a year.

Our job is to find the f that makes G (the gross multiple of our wealth) as big as possible.

Step 5: Take the log to make the math easy

Maximizing G means taking its derivative with respect to f and setting it to zero.

It’s 2026, you don’t need to know how to actually differentiate an equation. You just have to awaken that part of your brain that knows:

a) a derivative is the slope of a function at a given point on a curve

b) when the slope of a curve is 0 this is a maximum or minimum

c) intuitively, we can reason that this is a growth curve is a hill with no bumps. Its slope starts positive and only ever gets smaller as you bet more, so it can hit zero exactly once, and when it does, you’re at the top. (the jargon version: this growth curve is concave: it bends downward everywhere from the max, with no inflection points)

We are still here:

G = (1 + Bf)ᵖ(1 − f)ᑫ

But G is a product of powers, which is nasty to differentiate.

But remember from simple pleasures, logs fix this. They are the inverse of exponentiation, allowing them to turn multiplication into addition!

Push the cobwebs away to recall that this works:

log(100) = log(10 × 10) = log(10) + log(10) = 1 + 1 = 2

That’s not all logs do.

They pull exponents down in front: log(xᵖ) = p · log(x).

We can prep that equation for differentiation by taking the log of both sides and using both of those sexy log features:

log(G) = p · log(1 + Bf) + q · log(1 − f)

Maximizing log(G) gives the same f as maximizing G, because log always rises when its input rises.

There’s another little bonus.

Log(G) is the log return per bet, the same quantity as ln(S₁/S₀).

It re-expresses a compounded, multiplicative growth factor as a continuously compounded rate, and rates add cleanly.

Step 6: Differentiate and set to zero

Once you know this is a derivative problem because you are trying to maximize then we can rely on crutches (Claude) for thing that’s hard to remember.

Namely that:

the derivative of log(x) is 1/x.
If there’s something inside the log, also multiply by the derivative of that inside piece (the chain rule)

So we have our equation:

log(G) = p · log(1 + Bf) + q · log(1 − f)

then we differentiate our terms to be added with respect to f:

p · log(1 + Bf) → pB/(1 + Bf) (the inside, 1 + Bf, has derivative B)
q · log(1 − f) → −q/(1 − f) (the inside, 1 − f, has derivative −1)

Set the sum equal to zero, which is where the growth curve is flat at its peak:

pB/(1 + Bf) − q/(1 − f) = 0

Step 7: Solve for f

Move the second term across and cross-multiply:

pB(1 − f) = q(1 + Bf)

pB − pBf = q + qBf

pB − q = pBf + qBf

pB − q = Bf(p + q)

But don’t turn your pattern recognition noggin off!

Since p + q = 1, this collapses to:

f = (pB − q) / B

f = p − q / B

Can you reproduce this right now on a blank sheet of paper?* Probably not. But go through it once the way you used to trace when you learned the motions for drawing comic book characters or flowers or in my case TMNT. After a single reproduction by hand, I assure you some neural pathways will re-open that have had construction signs in front of them for years.

And to tie this back to the beginning, that is the joy of thickness.

[Get your mind back over here, this is a family letter.]

*You will be able to reproduce it on your own after 2 or 3 attempts. I don’t know why the motion of the pencil is a 10x better instructor than reading it a bunch of times (generation effect maybe?). But this is one of those learning principles I take seriously and impress on my kids.

The world will seduce you with ease where you’d be better served by friction. It is a 21st-century skill to have a point of view on the difference.

Moontower #328

In this issue:

blindsided
“end behavior”

Friends,

Blindsided

My cousin Nicole just had her first child in the past year and is now compiling resources for new parents in light of where her attention has obviously been.

In our family chat, she asked:

When you became a new parent, what blindsided you the most?

I’ll share my answer, which I qualify with both the awareness that having a child is a gamble on many levels and that conception itself is a miracle and should never be taken for granted. What was I blindsided by?

[9:16 AM, 9/16/2026] Kris Abdelmessih: that they were gonna be so awesome

[9:17 AM, 9/16/2026] Kris Abdelmessih: that last one is important when we live in times where people have less kids and talk about it as though it’s a chore (it is) but not the amazing upside

The most transcendent single moment of my life thus far was to hear my son’s voice the day he came into the world. I don’t know if that’s every parent’s experience, but immediately I felt the joy and clarity of purpose. Before that cry, I don’t think I would have said I had no purpose, but the moment revealed that I didn’t believe I did. The speed and intensity of this rush of belief was a novel feeling. Thus, irreparably blindsided.

Share your own answers in the comments and I’ll share them with Nicole. Thank you!

I offered a couple of less serious answers to her question as well.

On that last one, I wrote about that 2 years ago in our minds love to betray us:

When I was at the Sphere with my family over Spring Break, I wouldn’t ride the long, exposed escalators. I took the elevator where I found the rest of the scaredy-cats.

If there’s anything good about having a phobia, it’s empathy for the range of what can go on in people’s minds and bodies.

I’m watching this poor guy thinking, don’t do it man, it’s not worth and all he wants is a glimpse:

Man crawls through his phobia of heights to get a view of the Atlantic Ocean from the edge of a cliff. 😅

1:44 PM · Sep 12, 2026 · 36.9M Views

2.99K Replies · 5.3K Reposts · 131K Likes

The comment section understands, and based on the number of “likes”, many others do too.

Anyway, I blame my kids for my embarrassment when I go to the Sphere to see Metallica with a group of guys next month and have to explain that I’ll meet them at the seats.

Money Angle

A couple of Option Trench episodes to share:

📺Terminal vs Path-Dependent Value Explained Using Collars | 39 min

📺The (Not So) Efficient Market Hypothesis? | 59 min

The first one will be useful for anyone wanting to learn more about option collars, which I’ve been writing a lot about. A video might be a gentler format so check that out.

The second one applies to investing broadly. I also use the Paradox of Provable Alpha at the end to answer a good question Erik asks.

Money Angle For Masochists

Alex is an options trader you should follow in case he ever tweets a lot. Because he doesn’t, when he posted the question below a year ago, it got few responses. I took the liberty of posting it myself this week.

This was fun because it led to a lot of discussion on the timeline and DMs. I was told it sparked a bunch of quant debate on one trader’s desk.

The most popular answer, which was still less than 1/3 of the responses, was the correct answer.

Why?

The maximum value of a put is the strike. The maximum value of a call is the stock price.

Straddle is C + P so $100+$100 = $200

Notice how this means all call spreads go to zero since the calls are worth the same — the stock price. All put spreads go to their max value— the distance between strikes because the puts themselves are worth the strikes.

Logic for delta:

Delta is the change in option price per change in stock.

But the put’s strike is fixed, so the value of the put doesn’t depend on the stock price. The put has zero delta. It’s always worth $100. Which means it has no gamma either 🙂

The call is $100 because the max value of the call is the stock price. The call value moves 1-to-1 with the stock, so it has a delta of 1 or 100%

The max value of a straddle is therefore the stock price plus the strike price.

If you sell the straddle or either option at max value and hedge on its delta one time (this is known as a static hedge in contrast to dynamic hedging where you would rebalance as your hedge ratio changes), you cannot lose. It is that simple fact of arbitrage that makes it the upper bound.

To address the second most popular response in the poll, those who said the straddle is $100 (wrong) and has a 1.00 delta (correct), we will demonstrate why this is incorrect.

What’s your p/l if you sell 1 straddle at $100 and buy 100 shares against, if the stock goes to $300?

The straddle will be worth $400, so you lose $300 but make $200 on your long share.

Hmm, maybe I’m just underhedged. Fine, what if I hedge on a 200 delta?

In that case, you actually make money; you win $400 on your 2 shares more than offsetting the $300 straddle loss. But what if the stock went to zero?

Your straddle p/l is unchanged, but you lost $200 on the long stock position. Arbitrage max value means you cannot lose if you sell at that price. Since we found a losing scenario, the price is not the maximum arbitrage bound. If you sell the straddle at $200 and buy a single share of stock, there’s no scenario where you lose. It is the lowest straddle value for which this no-lose scenario is true, thus it’s the arbitrage bound.

Of course, this is but a toy problem where the call and put go to their maximum values because it’s a degenerate case of infinite time or vol. But learning how a function (an option price is just a function) behaves by observing its boundaries is good for intuition. You did this in 9th grade. Khan Academy can jog your memory:

In the real world, you can fleetingly find options that trade beyond their arbitrage values:

Earlier in the week, @DeepDishEnjoyer aka p4 wrote a thread about a dividend mispricing.

It led to some back and forth with passersbys who use options but appear to have large gaps in the fundamentals.

Between the maximum value poll and p4’s dividend lesson, it’s worth saying it:

In a proper option education, you spend a lot of time on arbitrage relationships, cost of carry, and synthetics before you ever hear the word “volatility”.

I didn’t study formal math but I imagine there’s a lot in common with the process of proofs. Arbitrages rest heavily on assumptions. So to understand the relationships, you are forced into an intimate familiarity with the assumptions. And in the extremes of everything, it’s the failure to examine assumptions that leads to being blindsided. But also, when things get extreme, to go on the attack means asking yourself, “Who’s on autopilot? Is this price resting on a stale assumption?” The arbitrage relationships give you the highest conceptual ROI that derivatives offer, you never learn the most useful thing derivatives can teach…passage over the “bridge of asses”.

If you want to see more examples of why option basics are so key to understanding assumptions and opportunities when things get weird:

From My Actual Life

I leave you with another pic from our family chat where my wife posted a photo of where she was walking.

I don’t know how many Egyptian Arabic speakers we got in the crowd but “shib-shib” is like a slipper. Mom’s weapon of choice. Apparently this is a broader thing:

Mothers and shoes

Stay groovy

☮️

Moontower Weekly Recap

Moontower #327

In this issue:

slow burn
mental bet sizing for everyone
sizing for real-life decisions

Friends,

Riddle me this:

Reading moontower makes me feel…

⏹️Smart

⏹️Stupid

(read the article on substack to actually submit an answer)

Over the years, I’ve administered 2 reader polls to take the pulse of why you bother reading this newsletter. Both times I’ve asked the above question but with an open-ended fill-in-the-blank template. The answers come back in all shapes and sizes, but most of them can be boiled down to “smart” or “stupid”.

My reactions to the “stupid” responses:

My writing has a style that can be, at times, counterproductive. It’s often unfiltered and parenthetical. My wife constantly tells me that if I write more clearly, I’d have a bigger audience, and she’s, of course, right. The writing is not optimized for clarity. Scott H Young is my canonical example of such writing. I’m a big fan, but my lack of self-control forbids this common-sense approach.

My writing is aspirationally in the spirit of a Pixar movie where it serves 2 masters: the child and the adult who brought them to the theater. I’m trying to teach relatively basic or intermediate concepts while leaving Easter eggs for readers who arrive with more finance/trading context. This will leave the more basic readers feeling like they are missing a joke.

Fellow trader and writer RobotJames, once told me that Moontower is a “slow burn”. There’s no single banger that you could send to someone and say “this is why you should read this”, but reading it week in and week out leads to something more than the sum of its parts. My lament over never having a truly massive hit notwithstanding, I will not complain about the “slow burn” status. Many of my favorite things often took time to warm up to. Acquired tastes are rewards for crossing rugged terrain. (Except when they’re status cosplays. Our wants are even opaque to ourselves. There’s a thin line between appreciation and snobbery and its placement is up to the onlookers, not the admirer.)

To feel stupid when reading moontower would be natural. There’s technical or domain-specific minutiae mixed in with the meat and potatoes. This is further exacerbated by the cohort of readers who only show up for the personal sections and whose interests lie especially far from any of the material I cover. But if I read the blog of a doctor friend because it’s a way to follow along their life, the object-level material is gonna make me feel stupid.

And of course sometimes you feel stupid because I fail. The sequence of words fails to unlock the concept. Today I’m actively trying not to f this up. I want to teach you a neat topic. My goal is to really cement it for you. To make it accessible in real life for you in the same way multiplication tables are at your disposal.

If you don’t regularly read Money Angle, maybe see if today works for you. It’s long, but that’s because we are going to drill the concept. If you succeed in walking away with a new mental tool to practice, then the ROI on the reading time will look like a steal. If you’re not interested, then I’ll channel one of my college roommates whenever I tried to bail on hitting the gym, ”That’s cool man, I’ll just take you off my list of successful people for today” and leave you one of the OG memes that deserves annual visitation.

Commencing demystifications now…

Money Angle

One of the most important concepts in risk-taking is bet sizing. Which is unfortunate because people are quite bad at it, while the effort to be way above average is quite low.

A jarring and famous demonstration of this is the Haghani-Dewey Coin Flipping study, which showed how even college grads with business, economic, and technical backgrounds incinerated their capital or massively underperformed the expected profits presented to them by a game they knew was rigged in their favor.

You can read my synopsis in Bet Sizing Is Not Intuitive.

For a binary wager (ie win or lose), if you know the payoffs and the probability of winning, both of which were known to the participants, the solution is to use the Kelly Criterion.

The tragedy is that it is incredibly simple to compute and applies to many conventional gambles and decisions (the examples in the quiz will span various life situations!).

If something is both easy and widely relevant, it should be common knowledge. So let’s fix that today. I’ll show you how easy it is to use, and you’ll forever be able to do it in your head.

First, a succinct definition:

Kelly is the bet size, as a fraction of bankroll, that maximizes the long-run compounded growth rate of your wealth. It’s a mathematical solution to bet size that doesn’t seek to maximize expected profit per trial, but the size that optimally balances compounding rate and survival.

If you want to go deep on this, see Moontowerquant’s Kelly Criterion Resources, but today’s focus is on getting straight to usability.

We will use this formulation of Kelly because it’s general:

f* = p − q/b

where:

p = probability of winning

q = 1−p or probability of losing

b = the odds you’re getting → what you win divided by what you risk

The easiest way to learn it is just jump right in with a few worked examples:

Fair coin wager (even odds style bet)

p =50%

q= 50%

b =1 (ie even money, for a $1 bet you either lose a $1 or make a $1 profit)

f* = 50% – 50% / 1 = 0 → bet nothing, zero edge

Coin biased in your favor (even odds style bet)

p =60%

q= 40%

b =1 (ie even money, for a $1 bet you either lose a $1 or make a $1 profit)

f* = 60% – 40% / 1 = .20 → bet 20% of your bankroll

Roll a 6 on a die (underdog bet where you get odds)

p =1/6

q= 5/6

b =8 (for a $1 bet, you either lose a $1 or make an $8 profit)

f* = 1/6 – (5/6) / 8

f* =8/48 – 5/48 = 3/48 → bet 6.25% of your bankroll

If f* is 0 or negative, you have no edge, so not betting is prescribed

Sports moneyline (betting as a favorite where you lay odds)

A −200 favorite. You risk $2 to win $1, and the line implies 2/3, but you think it’s closer to 3 in 4.

p = 75%
q = 25%
b = 0.5 (getting 50% return on the amount you risk)

f* = 75% − 25% / 0.5 = 75% − 50% = 25% → bet 25% of your bankroll

Wait a minute, these are large bets?!!

If these bet sizes seem surprisingly large for the given advantages, then your senses are well-tuned. For most people, “full” Kelly is too big!

Kelly maximizes long-run growth on the assumption your probability is correct. Well, it probably isn’t because the world is messy. We can inject some humility by using a fraction of Kelly:

“Half Kelly” gives up about a quarter of the growth rate and roughly halves the drawdowns. If you invert that, you see that the Kelly scaling law means as you bet bigger, you get diminishing returns per unit of risk. Extrapolating that logic, betting more than “full Kelly” is incinerating compounded wealth even if the individual bet has positive EV.
“Quarter Kelly” or less is far more common in practice.

Please don’t let the equation scare you, it’s intuitive and easy to remember

Look at the equation again:

f* = p − q/b

It’s just “how often you win” minus “how often you lose.” It’s just that the second term incorporates the payoff. The loss term gets divided by b, which represents the return you collect when you’re right.

When b = 1, you’re getting even money. A 100% return. Dividing by 1 leaves q alone, and the equation collapses to pure hit rate: p − q. That’s the coin case where you bet $1 to make $1.
When b > 1, you’re getting long odds. The division shrinks the loss term. This is why the die works. You lose 5 out of 6 rolls. Straight subtraction says you’re down 66 cents on the dollar and should never play, but you’re paid 8-to-1, so that 5/6 becomes 5/48, and suddenly the 1/6 win percentage is the bigger number. Long odds forgive a bad hit rate.
When b < 1, you’re laying odds. Now division stretches the loss term. The moneyline: you only lose a quarter of the time, but at −200 each loss costs you two units to earn back one, so that 25% loss percentage behaves like 50%. Being right three times out of four barely clears the bar. Lay enough odds and even a very good record is a losing proposition.

The graphic shows how you can think of the odds (the denominator) as shrinking or inflating q, as you collapse your thinking to a comparison of p vs q.

A word on b

b trips people up because “odds” is loaded gambler jargon. A wider interpretation of b is that it’s a percent return.

It’s what you make divided by what you risk. Even money is b = 1: risk a dollar, make a dollar. That’s a 100% return on the amount at stake. 3-to-1 is b = 3, a 300% return. Laying −200 is b = 0.5 because if you risk two to make one, it’s a 50% return.

[Return is a profit, while multiples don’t subtract your initial risk. It’s the difference between “I 2x’d my money” vs “I made 100%” or “I 10x’d my money” vs “I made 900%”. The percent return is the multiple minus one because we subtract our initial risk.]

The reason it’s a return and not just “the odds” is that Kelly assumes a loss wipes out the whole stake. The denominator is always the same number: everything you put up. b is comparable across a coin, a die, and a moneyline because it’s the return on risk, always measured against a total loss.

b = 1 is a natural reference point. At 100% return, a win exactly cancels a loss, so you need to win more than half the time. The breakeven hit rate changes with b.

Set f* = 0 and you get p = 1/(1+b).

Read the table as a menu of the hit rates you’re allowed to have. At b = 24 you can be wrong 24 times out of 25 and still be flat. At b = 0.25 you can be right four out of five and still be flat

Applying to real life: when is Kelly the right tool?

Kelly needs a few inputs: a bankroll, a payoff you know, and a probability estimate.

Which of these is a Kelly problem?

A prediction market contract trading at 30¢. You think it’s worth 45¢.
You’re all-in-or-fold on the river with a read that you’re good 40% of the time, getting 3-to-1 from the pot.
How much of your 401(k) to put in equities.
Writing checks as an angel investor across 30 startups.
Buying a weekly call on a biotech ahead of an FDA decision date.
Whether to take the new job.
Your buddy offers you 5-to-1 that it rains in Oakland tomorrow. The forecast says 30%.
Buying homeowners insurance. The premium is clearly more than the expected loss — that’s how the insurer stays in business.
Your neighbor doesn’t carry homeowners coverage. She banks the premium instead.
Your auto policy offers a $500 deductible or a $2,500 deductible, for a $340/yr discount on the premium.
You’ve got vested startup options. Exercising costs $40k out of pocket in strike, and you think there’s maybe a 15% chance the company gets somewhere that makes them worth $1M.
A merger arb spread. Target’s at $46, deal price is $50, and it trades back to $38 if the deal breaks. You think it closes 90% of the time.
Your agency spends 20 hours of unbilled time on a speculative pitch. You win about a quarter of them, and a win is worth 80 billable hours.

Money Angle For Masochists

Solutions to Kelly Problems

Yes. Cleanest case there is. Binary, known payoff, and the price provides b directly. Risk 30¢ to make 70¢, so b = 2.33. f* = 45% − 55%/2.33 = 21%.
Yes. This is the canonical one. p = 40%, b = 3, f* = 40% − 60%/3 = 20% of your stack. The wrinkle is that in poker your stack isn’t really your bankroll. There’s a whole literature on pros using Kelly for bankroll management across sessions rather than for a single river decision.
No. Not this version of it. Stock returns aren’t generally binary so there’s no p, q, or b. There’s a continuous analog called Merton’s Share, which is similarly rooted in reward vs variance. What Gamblers Can Teach the Buy-and-Hold Crowd can get you started.
Sort of. The structure is right: repeated, roughly binary, long odds. The problem is that p is a guess and b is a bigger guess, and Kelly is violently sensitive to overestimating your edge. Garbage in, garbage out.
Approximately. If you treat it as approve/reject it’s binary enough to size with. If the expiry aligns with the date such that you are betting strictly on the terminal intrinsic value, the option piece will inherit the binary modeling you imposed on the stock.
No. The variables are too opaque.
Yes. p = 30%, b = 5, f* = 30% − 70%/5 = 16%. Note, you’ll lose this bet more than twice as often as you win it, so your most likely scenario is losing 16%. You can shrink the Kelly fraction if this makes you uncomfortable.
Wrong side of the equation. Run f* on this and you get a negative number, because you’re buying a negative-EV bet.
Yes. It’s the same policy, so notice that the bet only exists on the insurer’s side of it! Every year your neighbor doesn’t buy, she collects a premium and writes a tail. Rebuild cost $500k, premium $3,000, call it a 1-in-500 chance of a total loss.
p = 99.8%
q = 0.2%
b = 3,000 / 500,000 = 0.006 (risk $500k to win $3,000)

f* = 99.8% − 0.2%/0.006 = 99.8% − 33.3% = 66.5%

Positive, as expected since insurers price premiums well above fair value. In this case, her bet size is the $500k house. If the house is most of her net worth, she’s at 100% on a bet capped at 66%. Rather than overbet, she should buy the policy. If she’s worth $5M, she’s betting 10% when she’s allowed 66%, which puts her near quarter Kelly (~14%), and she could skip the insurance. If she’s worth $1mm, it’s a 50% bet, which is more than half Kelly. I’d say take the insurance but I’m a wimp. There are other considerations (would she have the liquidity to rebuild the home or maybe taking the insurance with a high deductible is a better fit), but just doing this exercise gives you a sense of how risky or conservative your choices are relative to the bet share that maximizes long-term wealth.
Yes. Raising the deductible is like you writing a $2,000 policy and collecting $340 a year for it. You’re the insurer again, so work out what you need to believe. Take the high deductible and save $340. Have a claim, and you’re out $2,000 more, but you already banked the $340, so the loss is $1,660.
b = 340 / 1,660 = 0.205

f* = p − q/0.205 = p − 4.88q

Set that to zero, and you get p = 4.88q, which, with p + q = 1, means q = 17%. Your breakeven is a claim every 5.9 years. Anything less frequent and you’re the one with the edge.

Let’s say real-world collision frequency is more like 6%. So p = 94%:

f* = 94% − 6%/0.205 = 94% − 29.3% = 64.7%

Which says risk at most ~65% of your bankroll. The risk here is $1,660. That clears as long as you have about $2,600 in liquid savings, which is to say the sizing check is trivially satisfied for almost everyone so you should generally opt for the higher deductible. For quarter Kelly, we’d need savings of $1,660/(.647 * .25) = $10,262.
Approximately. It’s not truly binary, but if you frame it in a way where you are comfortable with the no consolation prize of a medium outcome, you can see it as paying $40k for a 15% shot at $1M. b = 24, so f* = 15% − 85%/24 = 11.5% of your liquid net worth. This is quite sensitive to your estimate of p of course.
Yes, a classic example of binary-type risk in markets. You risk $8 to make $4, so b = 0.5 — you’re laying odds, same as the moneyline. f* = 90% − 10%/0.5 = 70%. That number is only as good as the 90%. Revise p to 75% and f* is 25%.
Yes, in a subtle way! Your bankroll is capacity, not cash. b = 80/20 = 4, so f* = 25% − 75%/4 = 6.25%. Twenty hours has to be 6% of what you’re working with, which means you can’t run this pitch out of a 100-hour month. If you’re the manager, you can put it in dollar terms by converting to wages.

Finally, I strongly recommend William Poundstone’s book Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street

Description:

In 1956, two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein’s. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory—the basis of computers and the Internet—to the problem of making as much money as possible, as fast as possible.

Shannon and MIT mathematician Edward O. Thorp took the “Kelly formula” to Las Vegas. It worked. They realized that there was even more money to be made in the stock market. Thorp used the Kelly system with his phenomenally successful hedge fund, Princeton-Newport Partners. Shannon became a successful investor, too, topping even Warren Buffett’s rate of return. Fortune’s Formula traces how the Kelly formula sparked controversy even as it made fortunes at racetracks, casinos, and trading desks. It reveals the dark side of this alluring scheme, which is founded on exploiting an insider’s edge.

Shannon believed it was possible for a smart investor to beat the market—and William Poundstone’s Fortune’s Formula will convince you that he was right.

And this is from my notes, Insights From Fortune’s Formula:

a gripping narrative full of 20th century trivia that ties together the birth of information theory, some of the greatest scientific minds of the 1900s, the rise of quantitative finance, and the role of organized crime. These topics come alive in a fresh, memorable way when discovered through the lens of its colorful characters.

It chronicles the history of the efficient market hypothesis (MIT, U Chicago, Paul Samuelson). You can organize its conclusion around this excerpt:

There is much truth in the efficient market hypothesis. The controversy has always been over just how far the claim can be pressed. Asking whether markets are efficient is like asking whether the world is round. The best way to answer depends on the expectations and sophistication of the questioner. If someone is asking whether the world is round or flat, as fifteenth-century Europeans might have asked, then “round” is a better answer. If someone knows that and is asking whether the earth is a geometrically perfect sphere, the answer is no.

Stay groovy

☮️

Moontower Weekly Recap

Moontower #326

In this issue:

energy as the ultimate currency
“middle manager” fiction

Friends,

A year ago I wrote a piece called Capitalism Is a Temporary Condition. Buried in it was a thought:

An investor in an age of acceleration watches as commodity prices, real things, hover in familiar territory while “future cash flows discounted” reward attention — in some cases because of optimistic stories, in some cases because the company exchanges cash for BTC (an act which adds no economic value), and in some cases for nostalgic lolz.

Today, it’s embarrassing to think of actual value. The most basic form is stored energy**. An obvious example is oil. Slightly more abstract —a building is a collection of atoms that took energy to arrange and provides utility. It’s proof of work. Same with a good reputation.

The ** footnote:

I increasingly think that a durable concept of a risk-free or least-risky rate is more likely to come from Vaclav Smil than U Chicago.

I knew about Smil from a profile piece that celebrated his suffer-no-fools rigor in making sense of the world.

I’m finally getting around to How the World Really Works, and I dig how quickly it’s zeroing in on what I anticipated to be the biggest muscle movement of all. I’ll let it unfold as he does the book’s intro.

Smil asks us to imagine an alien probe watching Earth, programmed to wake up whenever something important changes in the way energy is captured or used.

For a very long time, it sleeps.

Then life figures out photosynthesis: sunlight can be captured and stored as chemical energy. Much later, humans learn to control fire. Then agriculture. Draft animals. Wind and water.

The gaps are enormous. Billions of years. Millions. Thousands.

Then they start collapsing.

Coal gives humans access to immense stores of ancient solar energy. You can see a parallel to wealth in that phrase alone. Steam will turn that energy into mechanical work, replacing what he calls prime mover energy (human and animal labor). Oil makes enormous amounts of energy portable while electricity makes it transmissible and almost infinitely adaptable.

Smil puts numbers on this.

In 1800, the world had access to roughly 0.05 gigajoules of useful energy per person each year. By 1900 it was 2.7. By 1950, about 10. By 2000, 28. By 2020, roughly 34.

In a little over two centuries, useful energy per person increased nearly 700-fold.

The average person today commands roughly the energy equivalent of 60 adults working continuously, day and night. In affluent countries, the equivalent is closer to 200–240 permanent laborers.

And the averages hide enormous differences.

Measured in primary energy, someone in one of the world’s poorest countries may use less than 10 GJ a year. India is around 20–30. The global average is roughly 75–80. China is above 100. Western Europe and Japan generally sit around 120–160. The United States is closer to 250–280.

It sounds a lot like how GDP per capita is distributed. We measure GDP in dollars, but money can be printed, thus distorting its exchange rate versus the stored value of work. In that sense, energy may be civilization’s only uncorruptible currency.

If we continue pulling on the thread, wealth might be thought of as an account from which we can spend to hold entropy at bay.

A 72-degree house in Scottsdale.
Mango salad in during a Minnesota January.
Clean water pumped up the Hollywood Hills.
A sterile operating room.
Skyscrapers defying gravity.
Data centers (I couldn’t resist).

Much of the AI commotion revolves around what it means for humans to directly turn electricity into intelligence. That the product is intelligence which can recursively accelerate knowledge instinctively unsettles us because it violates our sensibilities around balance. Like energy is somehow not being conserved, leading to the type of divergence we associate with chain reactions.

I’m actually struggling to put my finger on the right analogy, which validates another point Smil makes. He argues that at precisely the moment when we have become capable of commanding extraordinary quantities of energy, most of us have become almost completely detached from how any of it happens.

Smil calls this our “comprehension deficit.”

Modernity is a black box. Light comes from a switch, and meat comes from a carton lined with a maxi pad. It’s all so effortless. Students of economics read I, Pencil to appreciate how capitalism’s profit-motive and competition actually lead to complex chains of cooperation. The side effect of the story is a (demoralizing?) inference that the world is so invisibly complicated now that you should feel good in your choice of major because it’s strategic to be a symbol-pusher since details are hopelessly infinite. (Sorry, did I go to far here? I’m an econ major, so it’s kind of like Chappelle using the n-word. Kinda? Nevermind.)

Smil’s punchy take on specialization:

You could meet real Renaissance men on Florence’s Piazza Signoria in 1500, but not for too long after that…By the middle of the 18th century, Diderot and d’Alembert could still assemble a group capable of summing up much of their era’s knowledge in the Encyclopédie…In 1872, a century after the appearance of the last volume of the Encyclopédie, any collection of knowledge had to resort to the superficial treatment of a rapidly expanding range of topics…today, it is impossible to sum up our understanding even within narrowly circumscribed specialties…experts in particle physics would find it very hard to understand even the first page of a new research paper in viral immunology …Highly specialized branches of modern science have become so arcane” that many practitioners must train into their thirties “in order to join the new priesthood.

All I’ve done is read the introduction to the book, but the “comprehension deficit”, which he’s fixin’ to remedy with respect to how the world works (at least from a physics/chemistry macro point of view), is just a fascinating idea of its own. Before the printing process and hyper-connectedness, it was hard to learn much of what was a relatively small body of knowledge, but since then, even though you could learn more in a lifetime, it was a smaller percent of what could be known.

But that I can sit here in an air-conditioned house on a 90-degree day typing contemplations about abstractions like how wealth is really the temporary abatement of nature’s randomness and how the accounting of such wealth should be denominated in units of work, which is traditionally measured by money and its continuously leaking exchange rate to said work is itself a wild collective achievement fueled by eons of carbon remnants from lives I never knew.

I guess I feel like I owe it to the universe to be curious about its ways even if it’s a Sisyphean fantasy to close the comprehension deficit. Looking forward to continuing:

A thought worth sharing more widely from hemispheres this week’s post about discretionary trading:

In this AI era, brains and consciousness are major topics du jour. I increasingly see us as technology centaurs with both a meat and silicon brain mediating structured and unstructured data, which in turn can be private or public.

On the private side, I have Claude connected to:

my personal knowledge management or PKM (Notion)
MCP to moontower.ai data
git repos across work and personal
email (which means it can access all my writing)
project management software (Linear)
Google drive
Google calendar

And of course, the entire world of public info lives in the model’s training data and ability to go online.

You can be taking a walk with voice mode on spec’ing a prototype that will connect to data with nearly any context you want to provide from your private knowledge, the internet, or what’s in your head that moment.

The future is here for anyone who feels haunted by dozens of ideas a day that they previously couldn’t or wouldn’t act on.

And a discretionary trader is nobody if not someone who starts 50 sentences a day with “I wonder what happens if…”

Money Angle

I ask for your indulgence, for what follows is an informal word-wall connecting conversations I’ve had with some W2 friends.

Pick your favorite gospel on disruption. Schumpeter’s creative destruction, Christensen’s innovator’s dilemma. Most companies, sometimes even industries, will eventually recognize themselves as a melting ice cube.

In a great talk back in 2009, media investor Peter Chernin warned:

One of the things I always used to say to the people who work for me is that you can’t protect your business, and your job is not to protect your business. Your job isn’t to protect. Your job is to maximize your business at any given time, but your real job is to grow new businesses faster than the old ones decay.

He uses record labels as the cautionary example. They set out to protect their business, but “to the degree you’re going to try and do it you’re going to get killed because technology is going to liberate audiences in such a way that they’re going to get what they want regardless.”

It feels like there are only bad choices for companies that are now run-off businesses. Re-investment feels too speculative, but panic will preclude any chance of a soft or at least dignified landing. Navigating these moments well is a sign of grace, but if grace were easy we’d call it something else.

Instead we get to witness corporate pathology.

The ice cube is melting. But it started as a very big ice cube. Big enough to bridge a middle-aged middle-manager’s soft landing into an early retirement if they can claim a larger share of a shrinking cube. Welcome to corporate hunger games on steroids.

The middle manager is a risk-averse incrementalist. That’s WHY they are middle managers. They will do no such thing as grow new businesses faster than the old ones decay. They need an accomplice to secure their spot on the life raft. This accomplice comes from an unexpected place. The partners.

You see, entrepreneurs have deranged brain chemistry. My friend Jason Buck and I were drinking coffee in my backyard on Wednesday when he described an entrepreneur as someone who works 100 hours a week for themselves to not have to work an hour for someone else.

The entrepreneur, the founder, the partner is a delusional optimist. A melting ice cube can be refrozen if you just find the right segment to sell to, the one that somehow eluded you when things were going well. The middle manager latches on to this hope.

He crafts a business plan to do things “radically” differently. Of course, radical in this context is a mere gesture in comparison to the extinction-level shift in the business environment. The partners, never ones to back down from a fight, support this can-do attitude from the manager who stepped up.

The manager, energized and enabled, moves to consolidate influence. By promoting their plan, any plan, doomed as it is, they portray unsupportive colleagues as quitters by virtue of their dissent.

“If you’re not on board with my [dumb] plan, you clearly hate the company and are not a team player.”

There’s no serious appraisal of the dissenting argument’s merit. And that’s probably because the dissenting argument is “Umm, we’re f’d, so we should focus on retention, not growth, because [insert analysis that actually makes sense]”. Any analysis that maximizes EV in a losing game will be hard to sell against a bad strategy employed with hope. We gamble to get back to even and we’re risk-averse when we’re ahead.

Our middle-manager doesn’t just knife out the dissenters. They fully larp optimism with expansion. They hire loyalists, veterans of this obsolete-but-not-yet-obviously-so strategy. The loyalists are relieved. They, themselves, were cooked seeing the same writing-on-the-wall, but they just got thrown a lifeline by the last firm running the old plays. The only plays they’re familiar with. The reunion with their middle-manager buddy is as predictable as you expect, complete with brown liquor and nostalgia for those nights during training when they were chasing tail in Murray Hill and scarfing khati roll together if they struck out that night. Ah, Indian food before bed. To be young again.

The loyalist cluster is pragmatic. Every year of health insurance and private school tuition extends the polyester harmony that is their home life. But for the middle manager, the loyalist cluster is strategic. He’s like an old piece of tile covering himself in linoleum. It’s all wrong but a bigger nuisance to remove. Become hard to kill by entangling yourself deeper in a hierarchy that you created and from which you are a convenient buffer between partners and minions whose names they never want to know.

The misalignment, politics, and the waste of human life force in the name of self-preservation of an artificial environment (that’s a big one to unpack, but y’all might have to come have coffee or maybe something a bit stiffer for that convo) are regrettable.

But you know what I find worse?

That our middle-manager protagonist was not as cunning as he seems. That his primary offense was stupidity. That he sincerely mistook the situation for something he could fix instead of a noble impulse towards calculated self-preservation.

Stupidity is uncivilized. It’s unpredictable. “Say what you want about the tenets of national socialism, at least it’s an ethos. These guys are nihilists.” That’s how I feel about our manager if he is stupid. That’s a barbarian. It might be unpleasant, but you can reason with the merely deceptive.

I’m not sure if our middle-manager character (whose likeness to any real-life individual is purely coincidental) is sincere and stupid or just trying to survive, but those accomplices on high, blinded by desperate optimism, channeled the old guy at the club instead of having the courage to reinvent or the grace to just go home.

Then again, being who they are is what got them to giant ice cube status in the first place.

Money Angle For Masochists

A recommendation

Besides writing, part of my role here is to find good stuff to share with you.

One of my favorite online discoveries this year has been the X account of @SowingAlphaSeed. It’s an anonymous account that goes by “Farmer”.

The bio says:

Retail investor w/ a stretch goal of 2 Sharpe + 30% CAGR. Please DM me if you have fund recommendations. Live portfolio and track record on my website.

The main draw is that this account has steadily been learning and doing “in public”. It’s a constant source of interesting and smart ideas. It’s also focused on what it says in the bio, so the percentage of useful posts to total posts is extremely high.

Tip of the hat to Farmer (who I never met and don’t know).

An observation:

1-year collars in MU are close to the cheapest they’ve in the past year. If you’re bullish you can budget a trade that can offer multiples of return per dollar bet. If MU already made you rich, the cost to hedge is actuarially small.

Then again, you didn’t get rich by hedging amirite

This week:

Zooming in:

Moontower Weekly Recap

Moontower #325

In this issue:

for when the world slows down
family investing webinar
futures premium cell

Friends,

I’m in Vegas with friends to see GnR this weekend. 36 hours of noise bookended by 1-hour flights of peaceful purification in the form of flight reading.

Most of what I read on the regular is work-related and instrumental. I save appreciative reading for when the world slows down. Flights are a reliable example of such a time.

Here is both a short article and a long one for when you’re in the mood to actually read every word.

The Real Meaning of the “Road Less Taken” | 2 min read

I love this message and agree with the author about it being the one we need. It’s also the message I closed last year’s trading bootcamp talk with, so I’m biased.

Letter from Wendell: How a poet and farmer and a guitarist and teacher connected across time and space | 36 min read

A friend of my wife who reads my stuff sent her this to pass along to me. There is no summarizing an article like this. It would completely miss the point. That’s why I recommend reading it when you are in the mood to read every word. The friend has a good read on me (or my aspirational self anyway).

Money Angle

This summer I scheduled a lab to help kids in the Investment Beginnings Class buy their first portfolios.

I scheduled the lab during market hours so I could help with the execution. Between vacations and camps, a lot of kids were unable to make the lab, so it turned into rolling office hours. I ended up doing 8 sessions, sometimes just with one student on Zoom (one of the kids called from sleepaway camp!)

Parents sat in on some of these. Word spread, so I ended up getting a bunch of students who didn’t come to the 5-week course, but the parents are friends, so I put together a super abbreviated version of the course.

Actually, it wasn’t really a review because that’s hard to have people engage with if they never went through the course in the first place. It evolved into a spiel that overlapped with key ideas from the course. I’ve done it a bunch of times now so it’s more like a 2-hour seminar.

The whole experience makes me wanna try something.

Let’s do a “family investing webinar” where a kid and their parent(s)/guardian(s) join a Zoom call that I host.

2 hours in one shot is too long. We’ll break it up into 2 1-hour sessions.

There won’t be any charge for it, but I will limit it to paid subs to this newsletter.

Money Angle For Masochists

First, a heads-up that Thursday’s using tick data for spot-vol correlations was enough masochism that I was told to back off:

On to today’s masochism…

The futures-premium cell

Back in my SIG days, every trader had a cell on their spreadsheet showing the SPUs (the name for SPX futures back in the day; it’s derived from the September symbol) premium or discount to the “cash”.

A little background

The cash is the SPX index price based on its components’ spot prices. You can compute the index value from the stock bids, and that would be the “SPX cash bid”. You can do this for the offer as well. The average of the bid and offer is SPX mid-market.

Futures contracts, based on no-arbitrage pricing, have a fair value based on what you gain or give up by owning the future instead of the cash basket. Since you save the interest on the cash it would cost to own the basket but forgo any dividends you would have received that offset the drop in the shares when they are paid the futures are valued as

SPX + (interest – dividends)

The interest and dividends are estimated from today until the futures’ expiry date.

Assume:

SPX cash mid market: 7,800

RFR = 3.5%

annual dividend yield =1.5%

t = 1 year

The 1-year future fair value is approximately 7800e^{(3.5% – 1.5%)*1}= 7957.57

The basis between the future and the cash index was known as the EFP (“exchange for physical”). In our example, it equals 157.57

If the future was trading 7977.57, we’d say “the futures are trading over”. In this case, it would be 20 points or about 25 bps rich as a percent of the cash index.

This is an arbitrageable difference as a trading firm can sell the future, buy all the components, and book a theoretical profit that will become a real profit if their carry assumptions hold true. As a market-maker on the floor, I was not involved in index arbitrage this directly (although most of my clerking experience was much closer to these strategies).

S&P Futures and Fair Value. | The Blue Collar Investor — You have probably seen this kind of graphic on CNBC

The futures are more liquid than the cash index so the basket price lags. If systematic bullish news hits the tape, you cross the tiny bid/ask on the futures. In fact, the ES or e-mini future actually leads the big SPUs, so ES was used for computing the premium or discount.

All of the market-makers had a cell on the spreadsheet on their handheld tablets that showed the futures’ premium/discount to fair value (FV = cash index + EFP). Those premiums or discounts were typically small, 10 bps or less, as the market bounced around. But huge news could catapult the futures 300 bps before much of the basket could blink. As you can imagine, index arbs get very uneven fills on the baskets they try to execute to close the gap. That’s because everyone making markets has not only pulled their stock offers, but lifting resting customer offers, often several levels through the NBBO that was posted a split second ago.

You can beta-weight the “amount over” or premium the futures are trading to estimate a new fair value for the stock. If the stock you trade has a 1.2 beta, then you might think its new fair value is 3.6% higher than the pre-news price if the futures are trading at a 3% premium. Of course, beta is just a statistical quantity so you have a confidence interval around the beta, which is pretty much life as a market maker. Futures are trading 300 bps over, what’s your 2-way on XYZ stock? Maybe I’m “2% over” bid, offered “4% over”. Then, you’d need to be quick to remember what bids and offers on the option chain are resting that you should race to lift (all the calls should increase by their delta * your beta-weighted change in fair value) and hit (all the puts will decrease by the same factor and this is not even considering the effect of gamma).

Today, all the quotes being streamed by traders will get pulled while they simultaneously blast all the resting orders in a flash, but this process happened a bit more at human speed 30 years ago (although you still weren’t gonna beat the floor…the competition for the resting orders would be market-maker on market-maker).

I’m mostly sharing this because it’s fun for the stragglers who read this far into the masochists section, but it’s worth mentioning the context that made me think of it.

This phenomenon sometimes leads to anti-data or an interpretation of data that is exactly the opposite of the typical inference.

Why?

If a contract or security trades on the offer, the assumption is generally that “paper” (trader language for customers) is buying and the market-maker is selling. But in the example above, the market-makers are the aggressors because they know the market is much higher than last sale. They are lifting calls and hitting puts, so your read on flow sentiment is exactly the opposite of a normal market condition.

Just another example of reality having a surprising amount of detail.

Moontower Weekly Recap

Moontower #324

In this issue:

a showdown with yourself
unique job opening
real-returns
trading stock-bond correlation
confidence intervals on bounded ranges

Friends,

Earlier this summer, while still in the midst of reading, I recommended this book:

I wrote:

My wife and I are both reading this. It’s laugh-out-loud funny. Gary is an excellent writer. The novel is written from the point of view of an elite school’s endowment CIO. It presents as a series of meetings with prospective managers, deals with politics within the endowment but also with the external culture of the investing world. If you are in finance, Gary’s sharp eye will delight you til no end.

I’m less than halfway through it and already I can’t recommend it enough. It was recommended to me by an allocator (thanks Tom!) and I saw in a recent Byrne Hobart letter that one of Byrne’s friends physically accosted him for not having read this book yet.

You can see Matt Levine’s endorsement in the screenshot. I wouldn’t have articulated what Matt wrote, but once he said it, I noticed that’s the exact feeling I get reading it.

The CIO’s banter, verbal chess, and inner monologue reveal a fox-like savvy honed by years of battle with both the market and the managers who make convincing cases for how they’ve mastered them. It gave me a tremendous appreciation for the difficulty of the job. If you are not a professional investor and have confused the most generous market run in anyone’s living memory for your own brilliance, then considering the CIO’s constraints will update your context for the pro version.

I’m done with the book. So what do I have to say now?

Go read it this second if it sounds even remotely interesting to you.

I was so enamored of the protagonist’s wit, smarts and integrity…but it is all a setup. It’s not a twist like he turns out to be Marty Bird or something like that. The twist is subtle enough that not everyone would notice there even is one, and yet it knocked me right over.

It’s not a spoiler to say that the story is all a set-up for a showdown with a character named Michael Hermann. Which is, depending how much you hate yourself (in my case apparently a whole lot), a showdown with yourself.

I’ll leave things a tad vague as I don’t want to ruin anything, but this book’s mark of greatness is that you are left to tangle with a particular instance of the Witch illusion.

You might never unsee the possibility that free-thinking and excellence might be exclusionary of all else.

I posted a bunch of screenshots from the book on X, but I won’t link to them. Better to go in raw. But in case that weren’t enough to frighten you

Seriously.

Money Angle

A grab bag of topics.

Unique job opportunity

Old Mission is a large derivatives market-maker founded by SIG alum nearly 20 years ago. Mike Suh is their head of education amongst other things. Mike was a colleague at SIG and as my friend Tina says, he’s not just smart like “smart smart” which says so much with so little.

He is hiring an Associate Head of Trader Education. If you are qualified and live in Chicago this is worth checking out. OM is a very impressive firm (and lured Mike out of early retirement) and this is a rare opportunity.

→ Job description

Goat Risk

Speaking of SIG, here’s a headline you don’t see often…a reference to literal goats:

Goat herding hedge: How Susquehanna and Kalshi are helping this company offset a change in California law

You’re welcome to read that article but the Matt Levine post Bilateral Goat Hedge unpeels the most interesting angles which come down to the evolving legal architecture of betting in the U.S.

Excerpt of note:

Trading vs Gambling

Speaking of betting, Erik and I published this episode in early August.

📺Is Trading Just Fancy Gambling? | The Options Trench

The question has never been more relevant considering this story which made the rounds all over social media this week and opens with a doozy:

More than half of Gen Z investors redirected money for investing toward sports betting in the past year, according to Betterment‘s 2026 Retail Investor Survey released this week.

Real Returns

This is from you can ONLY eat risk-adjusted returns:

There’s a question bandied around Twitter every now and then…What would the TIPs yield need to be for you to plow all your savings into it and not concern yourself with investing anymore? In this interview, Corey and Victor frequently speak in terms of real returns and what sticks out to me is how much higher people think equity real returns are above TIPs but in reality that number over long periods is ~ 3% give or take 2%, maybe 3%. If the TIPs yield were 4% you could really live by the 4% rule without worrying.

Well, dust off the discussion.

10-year bond yields are near 20-year highs.

but also…TIPs breakevens are on the skinny side of their 5-year range, meaning the TIPs yield is relatively attractive versus the nominal bond yield. If that’s confusing, just imagine they both had the same yield (ie the breakeven inflation were 0)…in that case you’d definitely prefer the TIPs.

Here’s Nick’s post from a few weeks ago regarding the 30-year:

I focus on the 10-year because my bias is that the term premium for the 30-year isn’t enough to consider.

Current 10-Year TIPS Yield: ~2.40% Recent 10-Year Nominal Treasury Yield: ~4.65% Implied 10-Year Breakeven Inflation Rate: ~2.25% (calculated as the difference between the nominal yield and the TIPS real yield)

And this is Elm Wealth’s most recent model update:

I have my eye on more TIPs for my IRA. I know it’s boring stuff. If you want more excitement, remember all the collar stuff I published this week. The high rates improve the collar risk-reward profiles.

We are not in a TINA environment. There are reasonable prices to diversify out of equities if you feel defensive. Elm expects historically low compensation for taking equity risk, but that’s been the story for years. That’s why this isn’t easy. I just know that diversification is my best ex-ante strategy so I’m thankful for the alternatives.

Learn more:

🔗What I Learned About TIPs | 10 min read

Money Angle For Masochists

Reading Correlation Through RSSB Options | 12 slides

Return Stacked’s RSSB gives you a dollar of global equities and a dollar of Treasuries on the same dollar of capital. They just listed options on it this week. It will be a useful option market to watch if it gathers liquidity because its implied vol allows you to back out an implied stock-bond correlation since we know the vol of the legs.

Risk-parity funds and strategies are diversified, which gives them cover to use leverage but also means they are structurally short stock-bond correlation. In theory, they should be natural buyers of RSSB vol. If they actually did that, I’d expect the implied vol to trade at a healthy risk premium since it’s a one-way risk. There’s no real natural seller of that correlation.

I asked the Moontower Agent to work out the details and generate a deck (which is also a heat check on its abilities.) It produced a deck I could download, walking through the variance identity, a IEF-for-GOVT proxy swap, a scenario table for implied ρ across RSSB IV levels, and the noise associated with realized correlation.

The deck is short and educational:

Reading Implied Correlation Through RSSB Options

Confidence Intervals on Correlation

This made me look up a time series of the correlation between stocks and bonds using VTI and IEF as respective representatives of the asset classes. The 30-day came back +0.43, the 1-year at +0.28.

The agent volunteered the following statistical insight:

N=22 daily returns is a small sample. The 95% confidence interval on a correlation of +0.43 with N=22 is roughly [+0.02, +0.72] — wide. You cannot confidently distinguish +0.43 from +0.20 or +0.60 at that sample size. The 1Y number (N=251) is statistically much tighter — CI roughly [+0.16, +0.39].

Normally, when you compute a confidence interval, you effectively make a market by scaling the standard deviation to your desired confidence (so 1.96 or “2 sigma” for ~95% confidence)

But take notice of the first interval: +0.02 to +0.72 isn’t centered on +0.43. The upper tail runs 0.29 above, the lower tail 0.41 below. Weird. You wouldn’t see lopsided error bars if the math was something like “estimate ± 1.96 × standard error”.

Agent teach me what you did and why.

The problem is that the error bar’s width depends on the answer

Correlation lives on [−1, +1]. Bounded. If the true ρ is 0.9, your sample estimates can’t overshoot by much (the ceiling is 1.0) but they can undershoot plenty.

That boundedness shows up in the standard error of r itself, which runs about (1 − r²)/√(N − 1). Look at what that does. At r = 0.43 with N = 22 the SE is 0.177. At r = 0.9 with the same 22 observations it’s 0.042, four times tighter. Not because you learned more, but because you got squeezed against the wall.

The agent used something it called Fisher’s fix to move to a coordinate system where the standard error stops depending on r, do the easy symmetric thing there, and come back.

The recipe

1. Transform the point estimate: z = arctanh(r) = ½ · ln[(1 + r) / (1 − r)]

2. Take the standard error in z-space: SE = 1/√(N − 3). Note what’s missing. No r. Sample size is the only input.

3. Build the interval symmetrically, the boring way you already know: z ± 1.96 · SE

4. Recover each endpoint separately: tanh(z_low) and tanh(z_high)

Broadly educational bits to notice

Step 1 does almost nothing to the estimate.

0.4332 becomes 0.4635. The transform is only there to get the r out of the standard error in step 2.

Step 4 is where the lopsidedness comes from.

Both 30-day endpoints sit exactly 0.4497 away from the center in z-space. Perfectly symmetric. But tanh squashes hard once you’re out past 0.5 but does almost nothing near the origin, so the top end at 0.9131 gets crushed down to +0.72 while the bottom end at 0.0139 is nearly untouched at +0.014. What matters is each endpoint’s distance from zero, not its distance from your estimate.

Step 2 accounts for sample size

Ten times the sample and the standard error only comes down by a factor of 3.6. At large N the confidence grows by √N scaling, but at small N, subtracting 3 makes the confidence grow slower than square root scaling.

2 lessons

The object-level lesson: Correlations are volatile and because they are bounded from [-1,1] we need to recenter our point estimates before cuffing their ranges
The meta-lesson: LLMs are great math tutors so when they volunteer info of the “I don’t know what I don’t know” variety they can hold your hand. I’ve shared how I use LLMs as a tutor before in Socrates 2026: how to use highlights

Moontower Weekly Recap

Moontower #323

Friends,

I’m visiting my family in NJ so Moontower will return August 12th.

That said, today is a longer essay.

the sound of inevitability

The market is 12-15.

12 bid. 15 offer.

The broker sizes up the offer.

“How many you got there? How about you? And you?”

A couple of the market makers get flakey once they see him counting.

“You know what, I’m 17 now.”

“Fine, but can you fill the size there?”

“This second, no more shopping.”

“Mine.”

A few minutes pass.

The broker comes back around. “How now?”

“Go fuck yourself. 20-40. Small.”

And that’s it.

It’s a liquidity-clearing trade. The market’s version of punctuated equilibrium.

Small lot sizes from here on out.

The price drifts higher over time. The same amount of volume moves the price by larger increments. The least-capitalized shorts who are also the smallest in the trade begrudgingly cover. Better to live another day. The larger ones lay off some of the headline greeks in related assets, but the basis leaks against them the whole way. At least it’s not a fresh flesh wound every day. Paper cuts aren’t mortal risks, but the job will be demoralizing for a while. We’re gonna do this again? Why don’t I learn? I’ve done well enough. Right? I don’t need this shit I say as I fire up loopnet on yet another chrome tab hoping to find a cap rate in the shape of an eternal palm tree.

Weeks pass. Maybe longer. Who’s counting?

You see the price. 63. Numb. Doesn’t mean anything anymore. You can’t taunt a ghost.

More time.

Wait, 56?

“Anybody doing anything in this?”

“Nah, maybe just recent sympathy with hawkish Fed chatter.”

“You think this thing being up 300% has anything to do with basis points. C’mon.”

“Yea, I don’t know. I’m trying to book Odyssey tickets on IMAX for 3am, can we do this later.”

“Neverm—”

[Ringing. The hoot flashes.]

[Groans and picks up.]

“Sal, I thought I told you to cut the line. The fuck you want?”

“How is it today?”

“I don’t know, Saaaal, why don’t you tell me how it is?”

“At 45”.

“We’re 5 minutes from the close, I can’t show.”

“At 33. They’re gonna trade”.

“I’ll round you out just to be social.”

Next day.

How?

“15-25. Your move, Sal.”

Leo

Matt Levine:

[On the modern AI thesis] Aschenbrenner was early and smart and articulate about it. This allowed him to raise money, and the fact that it has been basically correct allowed him to return 270% through May.

Leopold Aschenbrenner’s fund, Situational Awareness LP (SALP) started in late 2024 when he was 23. He raised $225mm and, through the use of leverage and being right as hell, rode a legendary heater with assets at peak over $25B about a month ago.

His portfolio concentrated heavily on hardware and chip shares of CoreWeave, Nebius, Bloom Energy, Iris Energy, Micron and the Korean company SK Hynix, as well as a sizable private stake in Anthropic. Meanwhile, he was shorting traditional software companies. You only need to pull up the charts of his longs and shorts to explain how his returns had been so stellar.

Many of his longs peaked in late June. On July 24th, he sent a memo to investors stating that the fund “has not been immune” to recent market volatility. He invited existing investors to commit fresh capital effective Aug 1, citing the most attractive opportunity set since early 2025.

Within the week, SALP would proceed to lose 2/3 of its assets and liquidate its public portfolio to Citadel.

Back to the pit

Trading is about pricing liquidity. Handicapping the price to move a chunk of risk in a particular period of time.

Leopold was very right on his security selection. So right that even net of the liquidation, the fund is still up 80% on the year! That’s got to be unprecedented. But being liquidated in the first place was inevitable.

Let’s go back to the stylized story from the opening.

When an asset rips higher as quickly as these longs did, it exhausts the supply of offers that maintain a sensible relationship to a concept of fair value. For the sake of legibility, we’ll call those sellers the natural investors. The ones whose bids and offers are tied to some semblance of a fundamental model.

If a stock you sold when it 3x’d continues on its way to a 10x in a short window of time, like on the order of months, there is a paradigm shift in its liquidity. In a squeeze, there is a shortage of supply, but those episodes are faster and less mysterious. In the opening example, it’s not a supply squeeze but reluctance.

With the “naturals” long taken out of the stock, the marginal liquidity provider on the offer is an atheist. In other words, a trader. They have no religion about the short. It’s an HFT, a market maker trading some low-capacity intraday basis they discovered in a linear regression, or some passive mechanism with a rebalance toggle.

What do these sellers have in common?

They’re hyper-tuned to the risk. They have a volatility number somewhere in their trade lifecycle.

Fine, who’s buying when the stock is now twice the price that itself was twice the price of anything sensible?

For starters, the original fanatic, especially if they are receiving inflows based on the marks they are reinforcing. Who else is buying? The momos and fomos. Weak hands. The momos are executing a simple bandwagon python script. This is a weak hand by design. The fomo weak hands come in 2 forms. The ones who haven’t had an original thought in their life and the ones chasing a benchmark because they devoted their life to mimicry with just enough leeway to preserve the illusion that their creativity matters. There’s a price for everything, so no shade, but calling a spade a spade, this is the weakest hand.

The stock is in a liminal zone. Levitating on the echo flows from the original disturbance. The stock market’s microstructure always presents a wash of back-and-forth trading. The withdrawal of real liquidity is less visible than the example in the opening sequence, which caricatures a market in a derivative or obscure contract that trades on Clearport by appointment but lacks a DOM. But make no mistake, the liquidity of the super stock is broken just like the fake derivative example.

The liminal zone, to quote Kindergarten Cop, “lacks discipline”. The sellers are atheists, the buyers are momos, fomos, and the original mover gathering flows, literally “high on his own supply”, with a mandate to trade on a thesis he publicly telegraphed in an adversarial game. The marketing effect of this strategy was powerful but not free. Why not? Because it rings the dinner bell which reverberates with the sound of inevitability.

Mordecai

When I graduated college in 2000, my mother took my sis and me to visit our family in Sydney and travel Australia for 3 weeks. In Darwin, we took one of those boat tours on the Adelaide River where they hang massive slabs of meat over the sides so us tourists can watch the crocs coil below and then leap high for their meals. Once you get on the river, the swarm of eyes comes out of the weeds as the sound of the motor signifies meal time. I’ll never forget the sheer size and thus the name of the croc they told us was the river’s alpha — Mordecai.

Leo’s wild success summoned Mordecai.

Crocs don’t need to chase. They don’t waste energy. The strike happens in a muddy thrash, and shortly after, the ripples of water slow as the trees and surrounding fauna relax in the wake of violent awe.

And even if the alpha crocs turns over, replaced by a new alpha, this species lives forever.

If I can prove how apt this analogy is, you will believe, like I do, that this liquidation was inevitable.

If you’ve been following this saga, you will notice I haven’t yet introduced the true culprit — Leverage + Concentration. The crocs aren’t the villains. In the words of Jack White, “if you’re headed to the grave you don’t blame the hearse”.

The moment Leo chose 4x leverage on a concentrated book, he splashed loudly into the river. From there, crocs just do what they do.

Byrne Hobart, in the Diff:

When there’s an economic actor whose day job is to identify forces that will lead to short-term flows in and out of particular stocks, and whose long-term model is to periodically pounce on distressed companies, these models will tend to converge into a model where they trade in advance of the blowup, and then exit and reverse that trade in the rescue.

The economic actor Byrne is referring to specifically is Ken Griffin’s Citadel, but generally, it is the dealer. The primary function of a dealer in any market, whether it’s securities, art, cars, or even being a link in a supply chain, is to price liquidity and manage inventory. SALP’s performance was a confession of Leverage + Concentration. Crank the virtuous loop of momentum and flows into thin liquidity, and those dead eyes surface for a look. If understanding liquidity was easy, then market-making would be less profitable. It simply would not be as valuable a service. So we can forgive Leopold for not realizing his gross market value was in shallower waters than he thought.

Market-making is a psychological grind. Again, go to the story from the open. You get paid $10 to flip million-dollar coins, and every now and then you find out you’re on the wrong side of a rigged coin. But even rarer than getting picked off is the chance to feast on fat prey. Now, to be fat, they must have been doing something right, but the weight makes it harder to maneuver than it used to be, and in Leo’s case, “used to be” was quite recent. It only takes a moment of indiscretion to show your belly. Markets are unforgiving because you’re only as sturdy as your worst mistake.

The crocs are always there. Griffin was also there to buy Amaranth out of their positions. Citadel has been in nat gas since the Centaurus era, and with John Arnold retired, Citadel has been an alpha croc in gas trading for well over a decade. If you search my writing, you’ll see a recurring theme of “what equity traders can learn from commodity futures markets”. Futures are zero-sum, so not all the lessons apply, but the ruthlessness will let you borrow a healthy amount of paranoia.

This is @LepoulpePoulpo:

So this was the view I always had wrt equities before
Vs commodities where a lot of shady stuff happens all the time but everyone knows about these games

On the other hand, I’m really less sure now. “It wasn’t certain how close SALP were to a margin call. Wasn’t certain they would have to liquidate in a block” -> I think if you had an idea of their leverage, and saw the price action on all his names, significantly worse than other semis, you could anticipate he would be close to force unwind/liquidate and try to squeeze him.

I admit I don’t know any equities trading team where people would do this kind of thing, but it happens often in commodities.

Bushels 🌾 Barrels 🛢 & Bullion 💰@BuBarrelBull

Everyone is amazed by the ruthlessness / cunning of Citadel on this Situational (lack of) Awareness trade. Every day shit in physical commodities trading.

12:11 PM · Jul 30, 2026 · 31.9K Views

4 Replies · 5 Reposts · 97 Likes

The word liquidity is a reminder that this is a biological system. Leo priced his trade as if the distribution were exogenous. He would never admit that, but his actions suggest his understanding was purely academic.

Byrne Hobart again:

AI people obsess about existential risk in theory and Leopold has publicly spoken about being aware of it, from a financial standpoint, in practice. But if you want someone who really feels existential risk in their bones, you’re better off talking to a hedge fund manager in Miami.

A mental model for the commodity market I’ve at times lamented and at times celebrated is that for the most part it’s a boring business of blocking and tackling. But now and then a well-capitalized outsider hops Chesterton’s Fence to see if he can force the market to cry uncle. If they’re especially crafty, it can work for a while. You can always beat a dealer on the way in. But you need liquidity to get out and now you don’t have the element of surprise on your side. Eventually, the old illuminati of the business lock arms to go on a hunting expedition. We used to call this “running them in”. If you are forced to cover, there’s little risk to me to bid ahead of you. (That’s not to say the “clean up” isn’t competitive. This is a good thread.)

When the Hunt Brothers cornered silver, the exchange eventually disallowed opening buy orders and raised margin requirements, depleting all the fuel. The exchange used to be owned by traders. They were literally called “members”. You can imagine their position at the top.

The sound of inevitability

In Jurassic Park, Michael Crichton folded an introduction to the field of complexity into the story. The park’s creators’ overconfidence in linear scientific thinking led to disaster. Complexity focuses on chaotic systems like weather (the proverbial butterfly flaps its wings and causes a hurricane across the globe) where models resist equations. There’s a greater emphasis on simulation and higher-order effects. A popular analogy from complexity science is the sandpile. Eventually the sandpile collapses but nobody would say the nth grain of sand causes the avalanche. It simply reveals that the pile angle had become unstable.

When observers consider the timeline (SALP’s peak was likely in late June) they are trying to label the nth grain. Fully embracing the butterfly, here’s my list:

the SpaceX IPO
the World Cup
the uptick in long-term yields
box spread rates reflecting funding costs rising as demand for leverage increased, with those costs passed straight through to levered ETFs
a slowing trend increasing chop, which increases drag in levered ETFs, which wears down the momos’ patience faster
the Knicks winning
Kris visits Rome for the first time

Inevitability means none of these matter.

So why was a liquidation inevitable? Why was at least one croc guaranteed a meal?

I already said it. It’s for the same reason LTCM, Hwang, Alameda, and Brian Hunter remain cautionary tales:

Leverage + Concentration.

But what’s so lethal about this combination? Why must it lead to liquidation?

Stated as plainly as possible:

As soon as you assert leverage, you are saying not only am I right, I’m right on timing AND path.

It’s a continuous time parlay. Even if he is right on the destination within the time frame of his choosing he can’t tolerate a large drawdown in the interim.

There’s just no give in the math.

Here’s quant Richard Craib:

But the outcome was never about being right or wrong on AI. At ~150% vol, variance drag alone is ~113%/yr, and risk of ruin is roughly a coin flip over the fund’s life. A child can do the math on a napkin (Claude did it for me: “ruin wasn’t unlikely, it was roughly even money”).

Volatility that high pierces every other fact about a portfolio: the thesis, the timing, the talent. The initial success and the margin call are draws from the same distribution.

And this isn’t really conditioning on the reality that a market’s price discovery function means they will push to a clearing price on a faster schedule than your lender would like. If you didn’t have a lender, this is not a concern!

Martin Shkreli had great coverage on the SALP story on TBPN. But thrown in at the end of the interview is this terrific section:

Kelly famously came up with what is now called the Kelly Criterion. It started as a gambling concept before becoming a finance concept, and it mathematically proves the optimal bet size. The formula is your edge minus the reciprocal of the odds. So, if you have a 55% edge, your optimal bet size is about 10%.

Even that is quite volatile for most people, which is why many investors use half-Kelly or quarter-Kelly sizing. The reality is that most traders don’t actually have an edge, yet they trade as if they have a four- or five-times Kelly edge.

That might sound like they’re simply taking a lot of risk, but if you run the simulation, you’ll go to zero almost every time. The simulator is a really powerful tool because it shows that even if you had a 60/40 edge on every trade—which nobody has in the stock market—you’ll still go bust if you overbet.

That’s a real eye-opener. Position sizing matters just as much as having an edge. It’s something I had to learn the hard way over many years: I was almost always overbetting. I think most hedge funds do it to some extent, and certainly most retail investors do. Very few people actually simulate their portfolios to understand what the appropriate position sizing should be.

After I left the Tiger Cub fund where I worked, I spent a short time in the office of a former SAC Capital (now Point72) portfolio manager. He was one of the best managers I’d ever seen—a quiet guy that almost nobody has heard of, now retired. I had the chance to watch him for a few months before launching my own hedge fund, where I proceeded to do the exact opposite and massively overbet everything.

I group LTCM in with other victims of the Leverage + Concentration poison. As a quant fund, their business was actually to lever diversified edges. But once the correlations of their positions converged, their cocktail was spiked with mathematical Concentration. On the surface, you might say what does a position in corn have to do with Treasury basis, but when a single commingled fund cross-collateralizes its leverage, then their size in the market imports a temporary synchronization of price returns.

Horse@TheFlowHorse

Leo knew… H/t @QuiteMidlife

7:45 AM · Jul 30, 2026 · 149K Views

20 Replies · 42 Reposts · 1.08K Likes

Elm Wealth’s Victor Haghani has done a public good by commuting his pain as LTCM partner to teaching the necessity of sound bet sizing. His famous coin-flipping studies show how econ and finance professionals manage to continuously blow up 60/40 advantages by betting far more than what Kelly prescribes.

It gets better. In Fortune’s Formula, I learned that someone betting the prescribed Kelly fraction of their bankroll (which btw implies they have an edge in the first place) has a 50% chance of experiencing a 50% drawdown and a 1/3 chance of experiencing a 50% drawdown before doubling up. In other words, the Kelly fraction is not even conservative. Many traders and gamblers I know will max their betting at half-Kelly.

[The book points out that halving your Kelly fraction will cut your drawdown risk in half but your return only by a quarter so even though your long-term wealth compounds more slowly, the risk-reward is better. That fact alone tells you that the scaling law is extremely punitive if you overbet at all nevermind overbet at the rate Leo was.]

Why Leo, why?

I’m not attacking Leo. I mean he’s very rich, and a bona fide genius. But if the goal is to learn from what we see, I can’t shy from documenting the mistakes despite the optics of seemingly picking on someone half my age.

[His defenders are quick to point out that he’s still up 80% for the year, but all this does is highlight the thin line between zero and hero. We overfit narratives with a comfort that is comically out of tune with what is warranted by circumstance. If Leo loses an extra 25%, an utter blip given his vol, at 4x leverage his investors are zeroed. He made a great call to liquidate, but the presence of liquidity to do so is never a given. In the final hours of a deeply fragile situation, every routine event, hell a Trump tweet, has butterfly potential. Putting yourself in a situation where there is no margin for error is itself a mistake. Leo’s future will revise and buff down the pointy edges of the story’s path dependence, but honesty demands acknowledging that no matter what he becomes, today he is neither lion nor lamb but liquidation was inevitable. He is a man alternating as we do between grace and folly, with neither ever being our full legacy.]

Let’s proceed.

Structure Mistakes

Matt Levine:

If you are all-in on this thesis, you might be more than all-in on this thesis. You won’t put 100% of your money (and your investors’ money) into the AI boom. You’ll put, like, 300% of your money into the AI boom. You’ll borrow money to lever up your bets on the AI boom. As your AI stocks go up, you’ll borrow more to buy more. Getting a 200% return on your money by buying SK Hynix stock is great, but getting a 1,000% return on your money requires borrowing more money to buy more stock. This is a naturally long-term trade. Aschenbrenner’s famous June 2024 essay series is titled “Situational Awareness: The Decade Ahead.” The point is not, like, “SK Hynix will beat earnings expectations next quarter”; the point is stuff like “by the end of the decade, we are headed to $1T+ individual training clusters, requiring power equivalent to >20% of US electricity production.”

You have a vision of the future and want to make a fortune; you need to match your funding to the duration it will take to see the thesis play out. The use of recourse leverage, subject to daily revaluation, is wholly inconsistent with the horizon.

He must know this.

That’s why companies issue equity. They don’t want to worry about the next loan payment. The duration of the financing and vision are aligned. A business that cannot fund ops from cash flows is depleting capital and will need to issue more equity. In that sense, its leverage is not reevaluated every day its beholden to investor appetites at discrete points when it refinances. Meanwhile, a self-sustaining profit machine is more like permanent capital. If it doesn’t like investor bids, it can create its own liquidity by buying itself back.

There was a failure in appreciating structure. The vehicle you use to express a vision is no less important than the vision itself. Founders Fund is Peter Thiel’s GOAT-level investing vehicle, which uses locked-up capital to invest in private companies. Meanwhile, Clarium, his hedge fund that invested in public markets, lost 90% and closed in the wake of the GFC. That a hyper-opinionated genius could succeed and fail so loudly in seemingly similar tasks should alert you to the nature of edge, its prerequisites, and limitations with respect to how you express it.

Hubris?

The most famous Leopold I knew of before Aschenbrenner was another genius.

Nathan Leopold.

In bullet form:

First words at four months and three weeks
Studied fifteen languages, claimed five fluently.
Graduated in his teens Phi Beta Kappa at Chicago, headed for Harvard Law.
A nationally recognized ornithologist at nineteen

Enamored with Nietzsche’s Übermensch (“supermen”) as transcendent individuals with superior intellect, Leopold wrote to his a precocious friend Loeb, that such a man is “exempted from the ordinary laws which govern men.”

They conspired to get away with the perfect murder as proof and tribute to their superiority. They spent 7 months planning the abduction, disposal, and even a ransom demand purely as misdirection.

All this only to be caught by eyeglasses dropped near the body. While the glasses had an ordinary prescription and an ordinary frame, they featured an unusual hinge sold to three customers in Chicago. One was Leopold.

Kelly math would have been trivial to Aschenbrenner by the time he was 10. He probably would have used the word “trivial”.

Ed Thorp, another genius, was able to connect the dots from John Kelly’s equation to its use in investing, effectively inventing the world’s first quant fund (which incidentally seeded Ken Griffin when Thorp shut down and gave Ken all his documents since he saw Ken knew what to do with it all). But I’m increasingly of the mind that Thorp’s genius also included suppressing his own ego enough to take Kelly seriously. It’s an intersection of classical genius and wisdom which itself needn’t be so rare. It’s neither here nor there, but I think the public recognizes that the type of genius we are getting out of Silicon Valley is far narrower than the Thorpian variety.

[Related: The connection and friendship between Thorp and Buffett, whose approach to investing was vastly different, was one of the audience’s favorite parts of the talk I gave at Arbor].

Back to Shkreli referring to a trader he once worked with:

What amazed me was that he managed roughly $300–400 million of his own capital but almost never used it. Eighty to ninety percent of the portfolio was simply cash. He would make these tiny trades—little nibbles—and over more than 20 years, I don’t think he ever had a down quarter. He generated 20–30% annual returns while barely putting capital at risk.

It was an incredible lesson. Then, of course, the moment I got the opportunity to manage capital myself, I was running eight times leverage. Looking back, it was one of the dumbest things I could have done. You live and you learn.

Apparently, you can’t learn risk management. You can only live it. Allocators take note.

The allocator’s mistake

Speaking of allocators…why do they keep falling for this grand thesis routine?

I mean, what makes us human, right?

We love stories. We need stories. We want to see athletes fly. We want the impossible dream. We love that truth is stranger than fiction, after all, fiction is restrained by its need to make sense.

The optimism required to back the impossible is the same optimism required to attempt the impossible. Leopold’s investors were not teachers’ pensions and bean counters. It was his singularity-pilled entrepreneur brethren.

Even if he zeroed the damage would be contained to those who can afford it, so my view is no harm, no foul.

Just to share a personal thought.

I’m deeply uninterested in whiz kids that are too cool for the mundane. I strayed from this once and was burned by giving money to some hotshot who I have no doubt is a genius. It wasn’t a fraud or blowup. Hell, it’s still operating as a respectable, institutionally-approved fund. It’s just expensive mediocrity. If I wanted that, I could find some value fogies quoting Cicero.

I went against my better judgement.

Where is the repurposed crusty trader who’s been turned upside down a few times but never had a losing year, even if sometimes it’s a T-bill? I don’t need him originating the ideas, but I need him to call you an idiot and ask hard questions because he’s just as dubious of smart kids as he is of the government. When you use all your brilliance to dress a pump-and-dump in new tech and memes, he reminds you the tail you’re selling is tied to a statute of limitations, and anything like that is a non-starter.

Gimme the corny words. A warden of capital. A trustee. A fiduciary. At least they have a chance of not being a grift. I still need to figure out if they’re made of what I want at the point of sale and for monitoring the books. Steady hands. Paranoid. Path-aware. Fat Tony. If it leads with sexy, get me outta here.

I want the C in CAGR because I want to minimize drag.

I want the C in curmudgeon because you’ve heard the line:

There are old pilots and bold pilots, but no old, bold pilots.

We have been in a regime where many of the people who can raise money have built returns and stories in a boom environment, but those environments paper over bad habits, which increases the allocator’s adverse selection risk.

If you’re giving someone money for the long run, you want a battle-tested framework honed by the drudgery of risk monitoring, outtrades, system outages, and the paranoia from the memory of a hardcoded number in a spreadsheet getting you picked off.

Nobody is bigger than the market

A lesson we learn again and again, is that nobody is bigger than the market. Not even the crocs. They survive because they respect it. They’ve seen so much in the course of both providing liquidity and also occasionally taking it to manage risk, that they can have no other relationship to it other than respect.

That means keeping concentration away from leverage. There’s no price worth giving up control of your fate.

There seems to be something deep about risk management that eludes genius alone.

Leopold couldn’t have been ignorant of betting math.
Leopold should have been able to understand structure.
Leopold knew growth would require getting thesis, path, and timing right.

I’m left to conclude that the ancient root of most major errors is at hand. Hubris.

I’m even more confident in this because history tells us that being smart doesn’t inoculate you from hubris and, as the murdering Leopold story suggests, can actively fuel it. But since I have never spent a day being a genius, any more than I jump like Jordan or sing like Sinatra, my sense of limitation leaves me unable to empathize with Leopold’s blind spot.

This is a point of encouragement to everyone.

When you are limited, you seek approaches in light of your limitations, which explains the reality we seek all around us. That the quality of our decisions which determines flourishing has no relationship with excessive intelligence.

Since investing and managing money is a decision overlay that sits on top of research and analysis functions, the manager’s efficacy is rate-limited not by brains but by wisdom.

We should be a bit more obsessed with where wisdom comes from than continue to fall for dazzling minds.

If there’s a bit of poetry in this episode, it’s that Leopold’s only out was a singularity bigger than the market’s boring old constructs like liquidity and collateral. Maybe he could have gotten there. And he still has a chance. His mistake was turning it into a race with the crocs.

If you don’t mix Leverage + Concentration, you never have to get in the water.

Money Angle For Masochists

📺Leopold Aschenbrenner’s Probability of Ruin Explained | The Options Trench

Leo might be Neo. The One. Because the fund is still standing. Given the leverage, they only needed to lose a fraction of its vol to be zeroed. If he emerges as a great fund manager, it’ll be a story for the investing ages. This episode goes a bit more into the brutal inevitability of the math.

Launched this week at Moontower.ai

A quick reminder of how option enjoyyyyers are sorted into 2 camps.

Camp 1: Investors who start with an opinion on a stock. They go to the option chain to express it and accept the posted price as fair. This is the vast majority of option users. Using options for delta or possibly “income” which still maintains a delta.

Camp 2: Vol traders invert the process. They’ll concede the stock is priced about right, since that’s not the skill they bank on. Instead, their discernment goes into the derivatives where they search for relative value of contracts on the volatility surface.

Moontower originates from camp #2, but our new Workflows feature is to serve camp #1.

There’s 3 suites, each one is organized around an intent that drives your screening process married to the Moontower lens for finding value.

Income is for selling covered calls and cash-secured puts.
➡️ Introducing Income Workflows

Defensive is for buying protection, or replacing a long position with calls or spreads.
➡️Introducing Defensive Workflows

Collars is for investors willing to finance protection by selling some of their upside.
➡️Introducing Collar Workflows

The posts explain each suite in more detail, but we built them after talking to clients about their specific processes. The interface will be intuitive based on how investors usually screen for these ideas, except our opinionated analytics are quickly narrowing and sorting to accelerate your workflow. Hence the name.

This is the call-to-action part: Sign up

Seriously, it’s bad-ass.

Stay groovy

☮️

Moontower Weekly Recap

Moontower #322

In this issue:

Slop. Counterslop.
What are retail option traders up to?
Hedging is for gardeners

Friends,

As of 7/21, Substack has a Pangram integration to scan for how much of a post is written by AI.

You can use it on the web from the Substack inbox. Click on a post, hit the 3 dots:

And voila:

Well done David.

Pangram is capable of false positives, but I ran it on both posts I published this week and it was accurate. One was 100% human and one it said 20% AI and 8% AI-assisted which sounds about right (my Thursday post included synopsis bullet points from my Scale notes).

I subscribe to 140 substacks. I don’t miss a word of about 5% of them. Another 10% there’s a decent chance I’ll read, and then there’s a steep falloff. Many of these emails have instrumental value that is going unmined.

[I should probably unsubscribe to the ones I ignore, but I’m not an inbox zero guy. Gmail search is solid and with the Claude-Gmail connector being an email bloodhound, organizing mail is a waste of time.]

I have scheduled jobs that “read” every distribution I’m on. One of my side projects is operationalizing this intake to get value out of this material (I’m into another phase of this which I’ll write about eventually). Running the Panagram scanner on a sample of the emails I read this week…well, let’s just say a lot of what’s out here is 100% AI-generated. I don’t agree that 100% AI means slop since I see posts from insightful people who I don’t think would write at all if it meant a lot more work than massaging a robot to wordsmith your thoughts. I wouldn’t call them writers, but I might still want the info. I actually think they should lean into their non-writer-but-have-something-to share-status. Dump your prompt in the post and move on. If the AI can write your post, my AI can read it. I don’t need you to bother. I don’t want to read it if I can’t feel anything, and I cannot feel anything from what a robot wrote.

Adam Mastroianni explained it well:

Words themselves don’t contain feelings—they are a recipe for creating that feeling inside your own head, to assemble the right set of emotions out of the experiences you have at hand. If I do a good job, the subjective experience that results inside you might resemble the one that originated inside me, but it will never be identical, because we’re working with different ingredients.

The computer doesn’t know any of this. It can’t know any of this. It can only read the cookbook; it can’t taste the meal. Objective knowledge can make your sentences true, but it can’t make them alive.

If it’s not obvious, only people who care about writing itself as an act of expression will be left writing without AI. Writing will be seen as an act of arrogance. A sense that your point-of-view is worth transmitting personally because the unique way it travels is itself part of the message. I will be clinging to self-importance thank you very much.

In Socrates 2026, I had this non-sequitur:

Injecting a thought

AI cannot motivate you. It cannot inspire you. AI offers an unbundling of the tutor, not a replacement. The role of humans in the learning loop is going to grow, which might be a contrarian position. Think of coaches. Some are exceptional because they are masters of the Xs and Os. Some are exceptional because of their ability to lead and communicate. These are squishy. The squishy things will not rise in relative importance. They are important and AI doesn’t change that either way. It’s that AI will put a spotlight on the fact that there will be relatively higher yields to focus on the squishy. Whether we will or not (and be able to judge the delta) is an open question. A topic for another day perhaps, but I’m betting on this with my time.

I spent over an hour walking through the local hills while talking to ChatGPT’s voice functionality Thursday evening. It was the easiest way to think through a large automation project. I won’t discuss the project yet but the sense I had while architecting it with ChatGPT was a new one. It was the feeling I know some friends had about 8 months ago and a smaller group of people (but not a tiny group) had 18 months ago and so on. A tiny group had the feeling a decade ago.

I suspect one’s appreciation for the feeling would be correlated to whatever innate ability one would have for chess even if they never played chess. I know I couldn’t have had the feeling much earlier. I just can’t see enough steps ahead. I can only fathom a little bit of abstraction before my mind begs for a physical demonstration of possibility.

The feeling is that much of what you do is nothing but a loop. Once you see the loop well enough to label its parts, you lose something. Mystery. There’s just less mystery about routine. I wouldn’t have thought anything we called “routine” had mystery in the first place, until that was the thing I felt disappeared. I admit, losing some mystery cost a sense of ego. And yet that feeling was totally overwhelmed by a different mystery. The one the techies and rationalist types have been going on about. “What’s coming next?”

We just finished watching the Mandalorian series. I know, I know. The kids were not interested years ago, so we tried again. In the final season, there’s a utopian city run by Jack Black and Lizzo that is captive to the droids who serve it. Automation has led to Brave New World levels of learned, almost embraced, helplessness. They get bailed out by Din Djarin and Bo-Katan Kryze, which undermines the society’s cautionary tale potential, but alas, Disney. Instead, the city is held up as a UBI-paradise where citizens are freed from scarcity to indulge their passions.

I personally don’t believe UBI can be sold to Americans en masse unless it is imposed from the kind of authoritarian control that we have thus far resisted. Thus far. We’re supposed to be the pole that rejects the social credit score for safety bargain. Our culture (again, thus far) is imprinted with the knowledge that UBI is incoherent because our spirits are blind to whether competition is for physical or positional scarcity. We know better than to “exchange a walk-on part in the war for a lead role in a cage?”

If we are not on our knees, UBI may come anyway but in disguise. TBTF equity markets, voluntarily scrolling ourselves into the Matrix, or whatever the grade inflation version of employment is, financed by literal inflation.

I only say these things to acknowledge the singularity backdrop of anything pertaining to our industrial future. I am not dismissing them. I have no clue what’s coming. But my feeling is I won’t recognize the way I worked for much of my adult life in the same way that a recent grad would not recognize the White Pages (yes, there used to be a list of landlines alphabetized by last name for everyone in your town).

I don’t feel a sense of doom but a feeling that technology will free us from the least human parts of our work. If you wonder how, it ties back to the beginning of this 100% organic post. The world we’re heading into will elevate reading because what will remain of human writing, the writing that is actually read by humans, will have no reason to exist other than its humanity.

That metaphor will apply everywhere.

I’m hopeful that we will look back at the past 10-20 years as the terrible twos of a connected world. A transition marked by phone-neck and expectations running ahead of reality. But if our anxiety is peaking just before reality gets significantly better, that would make perfect sense.

Every generation believes it lives in interesting times. It sure beats apathy.

Counterslop

Peter Yang shared his “No AI slop” skill which you can just tell your LLM to ingest.

https://github.com/petergyang/no-ai-slop/blob/main/SKILL.md

Major Ralph and Sam checking into work energy:

Money Angle

Here’s an example of a post that could have been 100% AI written and it would still be useful. I ran it through Pangram’s web app and it’s 100% human.

The Market Impact of Retail Options Trading | Nam Nguyen Ph.D.

The letter summarizes and links to 3 papers. The points below are the ones I found most interesting.

“Retail Trading in Options and the Rise of the Big Three Wholesalers”

Authors: Bryzgalova, Pavlova & Sikorskaya. Last revised Sep 2023.

Developed a novel measure of retail options activity using transaction-level data and new regulatory reporting requirements.
Validated the measure by showing it drops sharply during brokerage outages and trading restrictions.
Retail traders strongly prefer cheap, weekly options.
Those options carry very wide bid-ask spreads — averaging around 12% — making them costly to trade.
Many retail investors fail to exercise call options optimally before ex-dividend dates.
Retail trading now accounts for over 60% of total U.S. options volume.
Nearly 90% of payment-for-order-flow revenue comes from just three wholesalers.

“Retail Option Traders and the Implied Volatility Surface”

Authors: Eaton, Green, Roseman & Wu

Retail activity concentrates in short-dated, out-of-the-money call options.
Retail investors are typically net sellers of long-dated options.
Used 82 brokerage outages (2019–2021) as natural experiments to isolate retail trading effects. During outages, buying volume falls for retail-favored contracts but rises for long-dated options.
Implied volatility declines during outages for short-dated/OTM calls, but rises for long-dated options.
Retail demand affects not just the level of implied volatility but also the term structure, moneyness curve, and call-put spread of the entire IV surface.
Effects held up under robustness checks, ruling out a few heavily-traded options or dataset choice as the driver.

Quant Radio Podcast segment (this is an AI-generated podcast)

The classic signal “high option-to-stock volume = informed institutional trading” has broken down since 2020 as retail flow now dominates volume.

Money Angle For Masochists

Let’s start with this YouTube/Podcast episode where Erik and I discuss hedging.

📺Delta Hedging Cost Benefit Analysis | The Options Trench

What hedging is: reducing or isolating risks you do not want, to maximize exposure to ones you intend to get paid on
The difference between direct hedges and correlated, indirect hedges with basis risk.
Why every hedge has a cost, including premiums, bid-ask spreads, commissions, slippage, and opportunity cost.
Why you will almost always have “ragrets”: if the hedge works, you wish you hedged more; if it does not, you regret paying for it.
How protective puts, put spreads, collars, and covered calls change risk and cost.
The tradeoff between cheaper short-dated protection and more expensive long-dated protection.
How rising stock prices can make an old put hedge less effective by increasing your unprotected “deductible.”
Two ways to manage hedges: rebalance on a fixed schedule or act when risk crosses a predetermined band.
How hedges can preserve capital and buying power during market stress, when the best opportunities may appear.
An introduction to delta hedging, active delta management, gamma scalping, and how these concepts apply to options strategies.

I noticed this tweet a few weeks ago and it reminded me an example of my training days back in my AMEX days with SIG.

You had full discretion to delta hedge against the option orders you’d do. But as you learn in the podcast, hedging is a cost. You don’t want to hedge if the risk is tolerable. “Hedging is for gardeners.”

SIG had a big balance sheet and very tolerant of letting deltas ride so the bias to hedge was to hedge only if you thought the option order was “smart”. For example, if a cust has a pattern of selling puts right before the stock price rips higher, you want to hedge aggressively when you buy the puts. In fact, you might want to “overhedge.” Instead of buying the amount of shares prescribed by the delta you hedge “1-to-1” or “1 up” meaning you buy 100 deltas worth, effectively turning the put into synthetic calls.

Fast forward to 2026:

The screenshot in the tweet is an option flow service announcing the someone bought the 60/70 put spread which is a bearish statement. Bulltard says he was the one who traded 3000 out of 8000 of these spreads and that he was rolling a short up from the 60 strike to the 70 strike.

This is conceptually similar to our point above about how rising stock prices can make an old put hedge less effective by increasing your unprotected “deductible.” You need to roll the position if your exposure strays sufficiently far from the one you intend to have on. In this case, jbulltard who wants to be short puts wants to be shorter more substantial puts than the 60 strike so he “rolled up” either to re-strike his delta or vol position (or both).

In training, we discussed a scenario which the tweet reminded me of, but in the opposite direction. The question posed by an instructor was:

Imagine a customer coming in to roll his or her put down. They will need to sell a put spread as they close the higher strike and buy the lower one. If you are a market-maker providing liquidity to the seller by buying the put spread to hedge, you buy the stock.

Hold it right there.

If this customer is taking a profit by selling the higher strike put and opening a long position in the lower strike, they are actually still bearish. This customer that has been correct is not covering their short. Technically, they are less short than they were before rolling, but the roll is to get more option firepower in the next leg down. Think of the intent.

As a market-maker, you don’t want to hedge when you buy this put spread. The customer has given you the position you want. You’re short deltas, betting on the same side as the smart customer!

The option flow service above seems like it correctly identified that the trade was a put spread, but it presented the trade as someone buying the put spread. Technically, someone did buy it since there’s a buyer and seller on every trade, but the presumption when you say someone bought the spread is that a customer or “paper” bought the spread, not the market-maker.

From My Actual Life

It’s hard to believe, but we have 2 weeks before school starts again. You get some depressingly small number of summers with your kids in the grand scheme of things and they’re just too short. We’re trying to pack it in. We saw The Odyssey this past week and Ed Sheeran last night at Levi’s. Our 13-year-old couldn’t come. He was living the Boys of Summer song…

His friend’s birthday was this weekend so the dad took this crew to Lake Tahoe. He sent us this picture to the parent chat yesterday morning. Yinh and I were in immediate sync. “One of the best photos we’ve ever seen”.

There’s no future and no past in that shot. It’s pure presence with your friends.

I’m going to get it framed today to give to the birthday boy when they return.

Stay groovy

☮️

Moontower Weekly Recap