I’ve been burying you with investment material, including an analysis of the TIPs + oil portfolio I strapped on this week. There’s also a tail option piece to it that I’ll write about this coming week. Remember I share what I do for educational purposes only, and while the pieces are detailed, they also make for great seeds to put in an LLM for you to augment your learning by discussing the risk and execution with your favorite bot.
This is the epitome of random, but after I wrote my piece, I called 2 friends who run commodity funds before I executed the trades I laid out. Both of them told me that, independently, a couple of their trader friends who only reach out when something gets interesting raised the idea on the same day. I don’t independently know the people who reached out (one of them is both famous- he was played in a movie- and anonymous, so I know of this individual).
Both managers took it as a sign to look a bit closer.
In AI
Noah Tye
@noahlt
Lately I’ve been learning math with ChatGPT (Astra) as my tutor, using this document scanning camera and a vibecoded tool that pastes the captured image right into the chat.
This way, I just work problems on paper and ChatGPT gives feedback. It’s really nice.
I feel like I’m getting a big hug when my readers tagged me in the replies to this amazing post by Noah because this is the exact kind of wishlist item I wanted in Socrates 2026: how to use highlights
Noah hacked this together for ~$100:
Why the experience of AI feels so different between people
This puts some numbers on it.
Andrej Karpathy
@karpathy
Dusting off this tweet from April because this gap in shared understanding of LLM capability is *widening*. It's now less "two groups of people speaking past each other" and more a sharp funnel.
– Napkin math somewhere around 6B people (~75% of the population) have barely come…
Andrej Karpathy @karpathy
Judging by my tl there is a growing gap in understanding of AI capability.
The first issue I think is around recency and tier of use. I think a lot of people tried the free tier of ChatGPT somewhere last year and allowed it to inform their views on AI a little too much. This is
I’ve said it in a number of posts this year, but I’m in the camp that you won’t recognize knowledge work as you’ve come to know it soon enough. I dislike fear as a marketing tactic, but I also think this is true. And if you feel FOMO, you are right to be rethinking how much of your work will be automated and what you would do to move up the value-creation chain in the role.
I’d be very concerned about any well-paying job that looks like a computer jockey, particularly if you can’t immediately name what makes you uniquely special at it.
This doesn’t even account for how much work will be outright commoditized or immediately copied. My friend Fonz was over this week and playtesting a game I’m developing called Market Maker.
If it’s any good, it will be instantly copied. It’s a discouraging thought, but there’s no point in lingering on such a helpless feeling. Instead, you have to identify and orient towards what stays scarce and therefore valuable in the future: trust and distribution. Plus costly signals, like spending time with people in person and all the things that come with that.
[And of course essential attributes like courage, reliability, and self-efficacy or discipline or whatever you want to call it. That thing where, when you need to get something done, you do it excellently and instill confidence amongst other high performers. In a way, I think this is just the plainest advice to give to a young adult. Point to someone who’s like that as a model for quality and tell the young adult that you must become someone who would have a similar reputation. Stick to your word and be accountable. This is what betting on yourself looks like.]
It recently came to my attention that fellow contributor to the upcoming How I Invest Volume 2, Drew Dickson, wrote the following in his essay:
Buy many copies and give them out to the clients or investors in your life! → Pre-order link (Ships Tuesday, Oct 20th).
Drew is very nice, ridiculous, if we care about the meaning of words actually, to be so glazy. I’ve thought a bit about why I can be regarded in this way when I know that I’m no smarter than anyone else on that list.
My thinking patterns just seem different and those differences are probably seen as some variant perception when they’re really just the output of doing a niche job like trading options. The job rewired my brain. It’s going to sound ridiculous, but I’ve had so many readers ask me how to adopt a similar way of seeing. Well, I don’t know, trade ten of millions of options contracts for 20 years and nothing else and see what happens. You might not like what happens. If you had a rosy outlook before, say goodbye to that shit. Paranoia is your new mind loop. But then you know you’re paranoid, so you have to tell yourself that’s an illusion, and before you know it, you are in mental exile in that triangle phantom zone in Superman II.
Ok let me be serious for a beat here.
I’ve said it repeatedly. To understand options requires understanding arbitrage pricing theory, which means crossing the “bridge of asses” in the field of investing. The underpinning of that theory makes concepts like opportunity cost, value over replacement, the idea of an equilibrium, higher-order effects (ie greeks) and a humbling appreciation for counterfactuals explicit and visceral. Notice how central these concepts are to decision-making generally. Jeff Yass minces no words on the topic. He doesn’t think a person can have sound judgement and decision-making skills without an understanding of option theory. Of course this is a maximalist claim, but the point is that being soaked in this stuff will make you think differently. And those differences are what I think are being, for better or worse, perceived as “smart”.
[I know many an option wizard whose decision-making leads them to disaster in relationships, addictions, or any number of objectionable choices. Are they “smart”? In a pointy sense, yes. But when we talk about smart in the general sense, photographic memory ranks far below “I am getting what I want out of life.” A lot of god-given horsepower is a party trick to be fetishized by Mensa members who can’t wait to advertise their membership in said club. You all get a yellow star sticker. But in case you haven’t noticed, the thing you hang your hat on is now commoditized by electricity, and if we’re getting to the root, it’s sunshine and black rocks. “Smart” is great, but we have plenty of it in isolation. For a short window in the 20th century, a nerd might have been able to have a great life with just ore and trading it for wheat, brick, and lumber at the port of “STEM job”. But the island is flooding with ore with each passing day.]
What does this all mean?
If you learn option theory, I can’t promise it will make you smarter, but it will make you think differently in ways that make people think you’re smart. That doesn’t hurt (unless you’re trying to hustle someone).
But I have a better pitch.
It’s fun! It’s a bicycle for the mind. It’s a puzzle.
Whatever draws you to it, you should know about THIS:
Kris
@KrisAbdelmessih
This will become the Options 101 reference for the Internet.
Totally free.
Stoked to be a contributor.
Agustin Lebron @AgustinLebron3
Excited to announce Options 101!
It's a site that provides free, no-ads, no-shill education on financial options (calls + puts).
The first course is one I'm now teaching this fall at Charles University in Prague. Lecture notes, videos, assignments.
I’m putting together a bunch of the 201 materials which will come out next year but the 101 materials are starting to be available, including Agustin’s lecture videos and slides at Charles University in Prague.
Some background
The course teaches options the way professional trading firms train new people. Agustin trained as an electrical engineer, joined Jane Street as a trader in 2008, and by 2011 was running all EMEA options trading out of London. He later wrote the excellent Laws of Trading.
The content is nearly identical to the intern and new-hire training they ran for years at Jane Street. And since Jane was born from SIG, I’m not surprised to see the overlap in how this material was covered in my own training.
Why you should care: options and option-like payoffs show up all over finance and daily life, the math ties together probability, calculus, optimization, and economics, you may need to value stock options you get as compensation, and it can become a career.
Learning goals. By the end, students should be able to:
Explain what options are and how they’re used
Relate options to each other and find value bounds with arbitrage arguments
Price vanilla options with both closed-form and numerical methods
Manage the risks of an options portfolio
Build and use volatility models of option curves and surfaces
Non-goals The course explicitly won’t teach profitable trading strategies. The slide says anyone hoping for “how to make money trading” should take a different course.
Prerequisites
Basic single-variable calculus
Basic Python programming
No prior experience with markets or trading is expected
Format One lecture a week plus one supervision session a week.
Syllabus
What Is an Option? Contracts, payoffs, exercise rights
The Value of Optionality: Uncertainty, distributions, time value
Put-Call Parity and Synthetic Equivalence: Synthetic positions, static arbitrage
Pricing by Replication: Binomial hedges, cash, fair price
Black-Scholes: Dynamic hedging and the pricing argument
Implied Volatility: Turning option prices into vol quotes
Delta and Directional Hedging: Hedge ratios, changing exposure
Gamma, Theta, Vega, and P&L: Convexity, decay, volatility risk
Volatility Curves and Surfaces: Smiles, skew, strike, expiry
No-Arbitrage and Distributions: Bounds, convexity, implied probabilities
Financial Time and Variance-Time: Trading time, calendar time, events
Stochastic Volatility Models: Random volatility, jumps, calibration
Random but related
My mother recently called to tell me she’s taking an options course at a local college in NJ. Her sister (my aunt) is trading the “wheel” strategy and has encouraged her to learn about options. My mother will never trade as she’s very skittish about anything that looks like gambling, but she enjoys math and puzzles and is always wanting to make sure her brain health is ok so she’s using options as her latest challenge. Plus she knows someone who can help when she’s stuck.
Separately, my uncle, my mother’s brother, has actually been a retail options trader for over 20 years (he was on an fx desk in the late 80s or early 90s) but has been a self-employed tax accountant and trader since.
If you’re wondering whether we talk shop at gatherings…nope. I say my boilerplate “don’t bet more than you are comfortable losing” as I’m in violent agreement with Victor Haghani when he says you can’t change minds.
From the team behind the Arbor Trading Bootcamps which I constantly say are so good they should not exist:
Join us at Metagame, November 6–8 at Lighthaven in Berkeley, for a weekend of games, puzzles, and immersive play. Explore tabletop games and RPGs, discover cryptic clues, and take part in a weekend-long Megagame connecting puzzles, games, and stories across the event.
Moontower readers receive $50 off regular tickets.
I’ve been burying you with investment material, including an analysis of the TIPs + oil portfolio I strapped on this week. There’s also a tail option piece to it that I’ll write about this coming week. Remember I share what I do for educational purposes only, and while the pieces are detailed, they also make for great seeds to put in an LLM for you to augment your learning by discussing the risk and execution with your favorite bot.
This is the epitome of random, but after I wrote my piece, I called 2 friends who run commodity funds before I executed the trades I laid out. Both of them told me that, independently, a couple of their trader friends who only reach out when something gets interesting raised the idea on the same day. I don’t independently know the people who reached out (one of them is both famous- he was played in a movie- and anonymous, so I know of this individual).
Both managers took it as a sign to look a bit closer.
Anyway, instead of burying you more ahead of more investing posts, I’ll use today’s letter to share some useful, interesting or fun hits that grabbed my attention.
In AI
Noah Tye
@noahlt
Lately I’ve been learning math with ChatGPT (Astra) as my tutor, using this document scanning camera and a vibecoded tool that pastes the captured image right into the chat.
This way, I just work problems on paper and ChatGPT gives feedback. It’s really nice.
I feel like I’m getting a big hug when my readers tagged me in the replies to this amazing post by Noah because this is the exact kind of wishlist item I wanted in Socrates 2026: how to use highlights
Noah hacked this together for ~$100:
Why the experience of AI feels so different between people
This puts some numbers on it.
Andrej Karpathy
@karpathy
Dusting off this tweet from April because this gap in shared understanding of LLM capability is *widening*. It's now less "two groups of people speaking past each other" and more a sharp funnel.
– Napkin math somewhere around 6B people (~75% of the population) have barely come…
Andrej Karpathy @karpathy
Judging by my tl there is a growing gap in understanding of AI capability.
The first issue I think is around recency and tier of use. I think a lot of people tried the free tier of ChatGPT somewhere last year and allowed it to inform their views on AI a little too much. This is
I’ve said it in a number of posts this year, but I’m in the camp that you won’t recognize knowledge work as you’ve come to know it soon enough. I dislike fear as a marketing tactic, but I also think this is true. And if you feel FOMO, you are right to be rethinking how much of your work will be automated and what you would do to move up the value-creation chain in the role.
I’d be very concerned about any well-paying job that looks like a computer jockey, particularly if you can’t immediately name what makes you uniquely special at it.
This doesn’t even account for how much work will be outright commoditized or immediately copied. My friend Fonz was over this week and playtesting a game I’m developing called Market Maker.
If it’s any good, it will be instantly copied. It’s a discouraging thought, but there’s no point in lingering on such a helpless feeling. Instead, you have to identify and orient towards what stays scarce and therefore valuable in the future: trust and distribution. Plus costly signals, like spending time with people in person and all the things that come with that.
[And of course essential attributes like courage, reliability, and self-efficacy or discipline or whatever you want to call it. That thing where, when you need to get something done, you do it excellently and instill confidence amongst other high performers. In a way, I think this is just the plainest advice to give to a young adult. Point to someone who’s like that as a model for quality and tell the young adult that you must become someone who would have a similar reputation. Stick to your word and be accountable. This is what betting on yourself looks like.]
Elm Wealth’s most recent post is, like mine, harping on TIPs.
Key quotes:
This illustrates an important point: while the inflation-adjusted market price of long-term TIPS can fluctuate significantly, they’re remarkably stable when measured using what really matters: the long-term spending they can support…
A boat tied to a floating dock rises and falls with every tide. If you measure it against the seabed it never stops moving, but measure it against the dock, where you’ll step aboard, and it barely moves at all. Long-term TIPS are like that boat: volatile in today’s dollars, but remarkably steady measured against the real spending they’ll support.
Seen this way, most of the confusion about TIPS disappears. They do exactly what they were designed to do. And as the safest asset going, their real yield is the natural benchmark against which to judge the stock market’s expected real return when you decide how much to invest in stocks.
“Moontower, how do the options look”?
Speaking of automation earlier…the original post I’m quote-tweeting below is an example of how the future is going to increasingly be bots reading for you, and of course bots writing for bots. Considering I write a letter for humans, this does not bode well, and I expect a bear market in reading probably for the rest of my life. I have no plans to stop writing, but I suspect it becomes an increasingly niche thing to do, like being an upholsterer. I have no quarrels with that outcome, but intend to be adaptable to whatever medium helps people learn and ultimately flourish.
Kris
@KrisAbdelmessih
For investing applications route the letters directly to pipeline to MCPs for your data or market analytics and have the summaries intersect with the quantitative.
@citrini is bullish abc, moontower how do the options look?
Brent Beshore @BrentBeshore
As of a month ago, I started having AI sort my inbox every 5 minutes, including collecting all the newsletters and summarizing them into a master newsletter every morning.
Been fantastic for me. Not great for the newsletter business.
It recently came to my attention that fellow contributor to the upcoming How I Invest Volume 2, Drew Dickson, wrote the following in his essay:
Buy many copies and give them out to the clients or investors in your life! → Pre-order link (Ships Tuesday, Oct 20th).
Drew is very nice, ridiculous, if we care about the meaning of words actually, to be so glazy. I’ve thought a bit about why I can be regarded in this way when I know that I’m no smarter than anyone else on that list.
My thinking patterns just seem different and those differences are probably seen as some variant perception when they’re really just the output of doing a niche job like trading options. The job rewired my brain. It’s going to sound ridiculous, but I’ve had so many readers ask me how to adopt a similar way of seeing. Well, I don’t know, trade ten of millions of options contracts for 20 years and nothing else and see what happens. You might not like what happens. If you had a rosy outlook before, say goodbye to that shit. Paranoia is your new mind loop. But then you know you’re paranoid, so you have to tell yourself that’s an illusion, and before you know it, you are in mental exile in that triangle phantom zone in Superman II.
Ok let me be serious for a beat here.
I’ve said it repeatedly. To understand options requires understanding arbitrage pricing theory, which means crossing the “bridge of asses” in the field of investing. The underpinning of that theory makes concepts like opportunity cost, value over replacement, the idea of an equilibrium, higher-order effects (ie greeks) and a humbling appreciation for counterfactuals explicit and visceral. Notice how central these concepts are to decision-making generally. Jeff Yass minces no words on the topic. He doesn’t think a person can have sound judgement and decision-making skills without an understanding of option theory. Of course this is a maximalist claim, but the point is that being soaked in this stuff will make you think differently. And those differences are what I think are being, for better or worse, perceived as “smart”.
[I know many an option wizard whose decision-making leads them to disaster in relationships, addictions, or any number of objectionable choices. Are they “smart”? In a pointy sense, yes. But when we talk about smart in the general sense, photographic memory ranks far below “I am getting what I want out of life.” A lot of god-given horsepower is a party trick to be fetishized by Mensa members who can’t wait to advertise their membership in said club. You all get a yellow star sticker. But in case you haven’t noticed, the thing you hang your hat on is now commoditized by electricity, and if we’re getting to the root, it’s sunshine and black rocks. “Smart” is great, but we have plenty of it in isolation. For a short window in the 20th century, a nerd might have been able to have a great life with just ore and trading it for wheat, brick, and lumber at the port of “STEM job”. But the island is flooding with ore with each passing day.]
What does this all mean?
If you learn option theory, I can’t promise it will make you smarter, but it will make you think differently in ways that make people think you’re smart. That doesn’t hurt (unless you’re trying to hustle someone).
But I have a better pitch.
It’s fun! It’s a bicycle for the mind. It’s a puzzle.
Whatever draws you to it, you should know about THIS:
Kris
@KrisAbdelmessih
This will become the Options 101 reference for the Internet.
Totally free.
Stoked to be a contributor.
Agustin Lebron @AgustinLebron3
Excited to announce Options 101!
It's a site that provides free, no-ads, no-shill education on financial options (calls + puts).
The first course is one I'm now teaching this fall at Charles University in Prague. Lecture notes, videos, assignments.
I’m putting together a bunch of the 201 materials which will come out next year but the 101 materials are starting to be available, including Agustin’s lecture videos and slides at Charles University in Prague.
Some background
The course teaches options the way professional trading firms train new people. Agustin trained as an electrical engineer, joined Jane Street as a trader in 2008, and by 2011 was running all EMEA options trading out of London. He later wrote the excellent Laws of Trading.
The content is nearly identical to the intern and new-hire training they ran for years at Jane Street. And since Jane was born from SIG, I’m not surprised to see the overlap in how this material was covered in my own training.
Why you should care: options and option-like payoffs show up all over finance and daily life, the math ties together probability, calculus, optimization, and economics, you may need to value stock options you get as compensation, and it can become a career.
Learning goals. By the end, students should be able to:
Explain what options are and how they’re used
Relate options to each other and find value bounds with arbitrage arguments
Price vanilla options with both closed-form and numerical methods
Manage the risks of an options portfolio
Build and use volatility models of option curves and surfaces
Non-goals The course explicitly won’t teach profitable trading strategies. The slide says anyone hoping for “how to make money trading” should take a different course.
Prerequisites
Basic single-variable calculus
Basic Python programming
No prior experience with markets or trading is expected
Format One lecture a week plus one supervision session a week.
Syllabus
What Is an Option? Contracts, payoffs, exercise rights
The Value of Optionality: Uncertainty, distributions, time value
Put-Call Parity and Synthetic Equivalence: Synthetic positions, static arbitrage
Pricing by Replication: Binomial hedges, cash, fair price
Black-Scholes: Dynamic hedging and the pricing argument
Implied Volatility: Turning option prices into vol quotes
Delta and Directional Hedging: Hedge ratios, changing exposure
Gamma, Theta, Vega, and P&L: Convexity, decay, volatility risk
Volatility Curves and Surfaces: Smiles, skew, strike, expiry
No-Arbitrage and Distributions: Bounds, convexity, implied probabilities
Financial Time and Variance-Time: Trading time, calendar time, events
Stochastic Volatility Models: Random volatility, jumps, calibration
Random but related
My mother recently called to tell me she’s taking an options course at a local college in NJ. Her sister (my aunt) is trading the “wheel” strategy and has encouraged her to learn about options. My mother will never trade as she’s very skittish about anything that looks like gambling, but she enjoys math and puzzles and is always wanting to make sure her brain health is ok so she’s using options as her latest challenge. Plus she knows someone who can help when she’s stuck.
Separately, my uncle, my mother’s brother, has actually been a retail options trader for over 20 years (he was on an fx desk in the late 80s or early 90s) but has been a self-employed tax accountant and trader since.
If you’re wondering whether we talk shop at gatherings…nope. I say my boilerplate “don’t bet more than you are comfortable losing” as I’m in violent agreement with Victor Haghani when he says you can’t change minds.
A great Munchie today. As usual, I highlight the parts I want to keepsake and inject my own comments here and there.
LTCM Co-founder Victor Haghani: “Taking Risk Is Always a Negative” | 1 hr 12 min watch
LTCM: right and ruined (01:27)
It’s good to think about investing as being two decisions: what to invest in and how much. And almost all of the focus of financial media, training, education, financial education is on what we should invest in… And at LTCM, we found some really good whats to invest in. But the sizing decision, how much of those good things is the right amount of good things, is equally critical, and is actually an easier decision to get right. But you have to realize how critical it is and that it deserves focus, and enough focus. And I think at LTCM, that’s where the mistake was, was on the sizing. It wasn’t on the selection of the trades, it was on the sizing.
EV ≠ risk-adjusted value (03:00)
Consider a 60/40 coin in your favor, but you must play 20 flips. This is a great “what” to invest in. But how much? Betting everything on every flip maximizes expected wealth, but you almost certainly end up broke.
The strategy that gives you the highest expected wealth at the end is actually to bet all of your money on heads each of the 20 flips. You have almost no chance of coming out of it with any wealth left… People don’t realize that’s the highest expected value thing to do, but it really shows you that expected value and risk-adjusted value are two different things. And it’s this risk-adjusted value that we want to maximize.
Risk-adjusted value is another way to say compounded return. Compounding naturally incorporates risk because the math of compounding is highly sensitive to variance. We’ll get to that later.
How the coin-flip players blew it (05:15)
Players came from graduate finance programs and Wall Street PM seats
They treated independent flips as dependent: bet heads after a run of tails, bet tails after five heads
Some people just bet a dollar every time. They just figured, “Well, if I bet a dollar, I’ll never go bankrupt”… and they really didn’t maximize the opportunity that they were given. And then other people were too aggressive and actually went bankrupt. They got their $25 down to like $3 and then they just started to YOLO it, out of impatience or whatever.
A good way to play this game is to bet a constant proportion of your bankroll on each flip. Bet on heads every time. Bet as fast as you can, like hit the buttons as fast as you can. And what should that constant fraction be? …between 10 and 20%. Like 20% is Kelly, and maybe you want to be a bit less…
And once we told people that, everybody accepted it. It was beautiful to see. It was like, “Oh gosh, I just wish somebody had told me that before.”
Sizing is non-zero-sum (08:20)
I really like this point:
Getting your sizing right is not a zero-sum activity. For you to be right, nobody needs to be wrong. We can all be correct together. But if you want to beat the market, you can only beat the market by choosing investments that you find that other people have not found and are doing worse than the market. The only way to beat the market is for somebody to underperform the market. It’s zero-sum.
Risk as an internal fee (12:55)
I plan to write a bit more on this idea myself. The “fee” framing Victor uses is fantastically plain, which I love, but I suspect people don’t believe this. I’m working on a post to step readers through the idea. As we’ll see later in this interview, my hopes aren’t high that it will convince anyone. Still, I believe it’s a profoundly worthy idea to flesh out.
There is a cost of risk which is the same as paying a fee. So when you’re paying an investment management fee to somebody, you pay that fee and you see that fee… And so if somebody turns up to most investors and says, “I’ve got this S&P 500 fund and the fee is 75 basis points,” people are like, “Come on, give me a break.” …Taking risk, you should think about taking risk as also paying a fee… The problem is that it’s kind of like you’re paying it to yourself. There’s nobody charging it to your account and it’s going out. It’s an internal accounting metric that you need to have.
For typical degrees of risk aversion for people, I would say you could think of that charge as just being equal to the variance of your portfolio. So if you have a portfolio that has 15% standard deviation… then I’m saying that you should be thinking that the cost of risk that you’re paying is 0.15 squared, is 15% squared, which is 2¼%.
His rule of thumb: cost of risk = γσ²/2.
This formula comes from something called the “Merton Rule” and it’s basically Kelly adapted for non-discrete-style betting, more akin to typical investing contexts in stocks and bonds.
A typical investor (γ ≈ 2) pays σ² while a Kelly bettor (γ = 1) pays σ²/2. Remember prescribed Kelly sizing is optimal for maximizing long-term CAGR, but it’s also very risky.
The Kelly bettor is a bit of a mythical being out there… I think that the typical guy is somewhere between what I described and 50% more risk averse actually.
Concentrated stock math (16:30)
If you have this concentrated stock portfolio that has 30% volatility, then you should be charging yourself, what’s 30% squared? It’s unbelievable. It’s 9%, right? It’s four times as much as 15 squared.
I’m willing to accept that the idiosyncratic risk is 50/50. Of course, there’s somebody on the other side of your hopeful 50/50 bet, and probably that other person is smarter than me anyway. So I don’t want to do it. I don’t want to have D. E. Shaw or Renaissance or whatever on the other side of my trades… Once I recognize that, it’s like, “Wait a second, I’ve got to make an extra 7% on those trades, an extra 7% just to break even and get a higher risk-adjusted return.”
That’s quite a hurdle considering that in a relatively efficient market you’re a coin flip to have bet right.
He talks a lot more about this in the interview so you can check that out on your own.
“How do I become a billionaire” is the wrong question (22:20)
When young people at a VC firm that invited them in to talk about his book…
It’s the right answer to the wrong question. That’s what’s going on here, right? If the question is, “How do I become a billionaire?” The right answer is take a lot of risk. Take a ton of risk… What do I need to do to become a billionaire is the wrong question. That’s the wrong objective.
The right objective for people is that you want to have the highest smooth, risk-adjusted, or we call it sustainable, lifetime spending and giving of money, adjusted for inflation, cost of living… The objective is not whoever dies with the most wealth wins. The objective is not I want to maximize the probability of having enough to retire. It’s not I want to die broke. Well, dying broke is easy. You spend all your money tomorrow and take a pill.
A few of the people said like, “But if I do what you’re saying to do, how am I ever going to become a billionaire?” And it’s like, that’s not the right question.
The only thing in a bear market is risk-aversion lol.
Crystal Ball, humans (27:25)
Victor saw a Taleb tweet:
He tweeted that if you gave people the front page of the Wall Street Journal one day ahead of time, they would all go bust in a year… They would be so overconfident. They would be so greedy. They wouldn’t size the trades right. They wouldn’t recognize that sometimes the employment report is hot and bonds go up.
The Elm team hired an intern to build a program to test this idea.
Business-school round: about 100 players staked $50 each, about $5,000 total. Elm paid out about $5,300, so with the next day’s news they eeked out a small profit. About 1/6 went bust, and the hit ratio was 52%. Some players ran 20x leverage.
In the web version: about 50k players with $1M of play money. The results were predictably unimpressive.
Six macro pros averaged about a 60% hit ratio and +70%, and all six made money:
Most of them were very selective. Like they only bet on six or seven of the 15 days. They didn’t always bet on stocks and bonds… They were just looking for something that they were really confident in and then they bet pretty big.
Totally different experience because all you want to do is beat the AI. So you lose your mind… It’s like, “How can I beat Grok? I’ve got to at least be able to beat Grok.” Like Claude gets ahead, but it’s like, “Okay, I’ve got to at least get ahead of Grok.”
The paper confirmed his hunch. Head-to-head players used 30x average gross leverage versus 25x solo, and maxed their leverage on 10% of plays versus 6%
All of them are too aggressive and risk-taking… Claude is getting like just over a 60% hit ratio.
This doesn’t mean that they can beat the market, but it does mean that they’re doing better than the average human that comes to play the game… Most of what’s going on right now is people are running AIs to see if they can beat the market, but they’re not really comparing it to the average investor.
Paper companion numbers:
Base models ended at Claude $2.59M, ChatGPT $1.47M, Grok $968k, Gemini $492k
Stock sizing averaged 7–12x, and the market has moved more than 5% on 23 days since 2000
Merton share implies 7.5–15% daily σ; the AIs ran 20–40%
Gemini and Grok had positive Sharpe ratios and still lost money from overbetting
All four knew Kelly from the coin flip but didn’t connect it to stocks and bonds
After reading the book, sizing became far more appropriate and prediction skill stayed the same
Elm’s sizing question (47:40)
The main question we’re asking people is saying like, imagine that stocks have an expected return 4% higher than safe bonds. How much of your wealth do you want in stocks if that were the case? So that answers the risk aversion question and their view of the riskiness of stocks all in one go… And then we say, “Well, if stocks only have a 2% expected return above bonds, what do you want to do then?” And they’re like, “I’m happy to have 37.5% in stocks.”
Notice that the 4% → 75% allocation answer implies γ ≈ 2 at about 16% equity vol. This is the “typical guy” as his σ² rule.
Remember Merton: w = ERP / (γσ²)
ERP is “equity risk premium”
(Just fyi: Elm charges 12 bps; its ETF runs a 75% equity baseline)
You can’t change minds (1:02:45)
I’ve got similar stories up the wazoo:
One thing I’ve learned in doing what we’ve been doing for the last 15 years is that you just don’t change anybody’s mind about anything.
My mother day trades stocks. She’s 92 years old… She’s only been day trading since commissions went to zero. But for 20 years, I’ve been telling her to invest in index funds, that she’s a nonprofessional investor, that she should just own index funds and not worry about it. But every day she’s day trading now, in the morning, in the evening. It’s taking up a couple of hours of every one of her days. She loves it. She thinks she’s doing well. And nothing that I could say, no amount of time I could spend with her, would convince her to not be a day trader and would convince her that she’s not doing well.
And she thinks that I’m intelligent. Like she doesn’t think I’m her stupid son. She thinks that I’m intelligent. She knows I work in finance. She knows that some people listen to me. She knows I wrote a book, right? So she knows that, and she knows that there’s no conflict of interest, that I want to help her. Like, she knows that I don’t benefit in any way from her not day trading. So it’s really hard to change anybody’s mind.
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.
moontower.ai
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.
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).
Exponential Wealth: Centuries of Stock and Bond Returnsfree 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.
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.
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 Returnsfree 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.
moontower.ai
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.
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).
At the Robinhood Summit last week, Mat Cashman and I hosted a “Trading Lab” emphasizing that options are surgical tools. You only want to reach for them when you have a specific view. While their payoff is highly levered to nailing a particular timing, they are unforgiving to vague forecasts like “I generally want to be long this stock”. If you buy the stock instead, you know your exposure. Your delta is 1.00 and doesn’t change.
If you buy an option, your exposure changes due to time passing alone. So that initial decision thrusts you into a series of future decisions, each one challenging you to tighten your thesis and face yet another bid/ask spread.
To demonstrate an appropriate use of options we stepped through a highly specific example during the lab and even executed the trade live!
I’m going to walk you through it here today.
Setup
The session was on Wednesday, September 30th. Nike (NKE) reports earnings after the close Thursday, October 1st.
Some context:
✔️NKE is down ~75% since its lifetime peak which occurred 5 years ago. While falling short of the peak, it did stage a large rally from late 2022 into 2023, before resuming its downward March which accelerated this year with the stock down >40% YTD at the time of the session.
✔️NKE typically pays about $1.40/yr in dividends or greater than 4% yield at recent stock prices. However, it can no longer fund the dividend from current cash flows. They could fund it from balance sheet assets (ie dip into their savings) to be able to pay it for several more years. I learned this from Brett Caughran’s tweet:
✔️I used moontower.ai’s MCP (which is now included with individual plans 😉) to ask Claude if the options market was anticipating a cut. It turns out the implied dividend about 1 year out is 50% of what NKE has been paying. NKE’s woes are out in the open, the stock and options markets see them.
With such a backdrop, we expect this to be an important earnings call. After all, if a plane is nosediving, we expect the captain to say something. (We know the content of the words will be reassuring, but we’ll listen to the tone of his voice to infer how scared or optimistic we should be.)
Pulling up the option chain
With the above context in mind, we load the October 2nd option chain. This is clean as a market gets around an earnings move since the options expire 24 hours after the earnings call.
During the session, I reason aloud through what I’m looking at.
The stock is ~$36. The 36 straddle, which can be interpreted as the average expected move size, is ~$3 or 8% of the stock price. Earnings are a big deal.
I gracefully elide the question of whether you should be bullish or bearish. If I was privy to such information, I’d be a Market Wizard. But many people have views and wanna bet. I can help you reason through your choices given you have a view. So let’s get specific.
What are you paying for?
We arbitrarily side with the bulls, but the analysis that follows works for bears as well if they substitute different contracts.
If the 36 straddle is at-the-money, meaning the stock is also $36, then the 36 call is half the straddle or $1.50.
If the stock experiences the expected move to the upside those calls will double your money as they will be worth $3 of intrinsic value at expiry. In the language of odds, you get paid 1-1 on an 8% up move.
But if this is our specific bet, can we find an expression of the trade with more octane?
We load up the 38.5/39 call spread. It’s marked for $.12 and if NKE expires $39 or higher, it will be worth $.50.
You risk $.12 to make $.38 so you are getting just over 3-1 odds for the same $39 outcome.
Why does this sound so much better than getting 1-1 if we just buy the 36 call for $1.50?
Because the outright call continues to pay off if the stock climbs more than 8%. You are paying for the extra profit potential if NKE goes up 10, 15, 20 percent. Being vague leads you to pay for more margin of error. But if you’re specific, you can get extra leverage on being right. Of course, this is risky because if you’re wrong most scenarios lead to total loss.
Let’s deal with the risk
The setup of the session was that we have $5,000 of capital.
If we are wrong on the vertical spread and the stock doesn’t clear $39 then we likely lose our entire premium.
We get a 3-to-1 payoff when we are right.
This type of binary outcome is a perfect setup to use Kelly sizing. The nice thingabout Kelly is that it assumes you have a total loss when you are wrong, so the sizing itself is the risk management. You’ve already budgeted for the maximum risk.
We’ll get to the sizing in a second but just for building fluency in thinking probabilistically, let’s acknowledge a few heuristics:
1. We know from the derivation of the straddle approximation, that the straddle is 80% of 1 standard deviation. Therefore, it encompasses ~79% of the distribution assuming normality. Therefore the upper tail, where NKE goes up more than $3, is expected 21% of the time. To get 3-1 odds would require a minimum probability of 25% to be a positive EV bet. But, normality is doing a lot of lifting in that sentence. Earnings are more likely a binary outcome, and while it’s too simplistic to say there’s a 50/50 chance of the stock going up or down 8% (which would make this vertical spread seem irresistibly cheap), it’s not unreasonable to think the probability of that spread hitting is greater than 25% (or for that matter, for the symmetrical downside put spread for those with a bearish view).
In the name of walking you through sizing GIVEN you already have the bull view, we’ll presume you believe there’s a 40% chance the stock pops higher by the amount of the straddle or $3 to $39.
How much should we bet on the vertical spread if we are getting 3-1?
Kelly:
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
Plug and chug:
f* = .40 – .60/3 = 20% or $1,000 of the allotted capital
Converting to contracts:
Each option contract is $.12 or $12 once we adjust for the 100 share multipler.
$1,000/$12 ~ 83 contracts
We don’t want to risk overbetting if we overestimate our p (i.e., probability of winning), so let’s size to about half Kelly and only buy 40 contracts.
We actually bought the vertical spreads live during the session.
Postscript
NKE ended up falling after earnings. The equivalent put spread on the downside would have been the 33.50/33 put spread, looking to get paid if NKE fell $3.
NKE closed Friday at $33.90, so the put spread would have expired worthless. At one point, the stock touched $32.09, so the spread would have been deep in-the-money, but because there was still some time value remaining, you wouldn’t have been able to capture its maximum value, although you probably could have flipped out of it and tripled your money, from $.12 to $.36
But it would have been hard to do since, with the stock sitting around $32 you have theta on your side, and you’d probably be thinking, “even if the stock rallies $1 or 3% intraday, I’ll have turned my $.12 into $.50.”
Alas, the stock ripped 6% intraday after bottoming, leaving the put spread worthless!
Notice how tricky this is for everyone. If you were short the spreads, you ended up collecting the full $.12 of premium, but the path would have greyed your hair as it looked like you’d face maximum loss or feel forced to cover only to later watch NKE stage a heroic rally.
Closing words
Options are surgical. I think of them like term life insurance. I have a specific thing I’m trying to mitigate or take advantage. If I buy them and lose, it may or may not have been a good outcome depending on what the counterfactual would have been. The term life analogy is an obvious demonstration of benchmarking to the right outcome.
The more tightly you can wrap an option expression around a terminal value thesis, the easier the risk management is because you can budget for total loss and let sizing do the heavy work.
Thinking probabilistically is a habit of mind. Reasoning between what’s in a price and your own confidence intervals around scenarios will develop not just discipline but it gives you metrics, even if they are finger-in-the-air estimates, to journal or track, allowing you to get a bit more calibrated with each rep.
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.
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.
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.”
