In this issue:

• AI leaves the hardest problems to humans
• The triggering implication of arbitrage theory
• options rapid fire
• Nine Inch Noize

Friends,

A thought sparked by the digital id known as X…

AI anxiety takes many forms. Doomerism, FOMO, a sense that the value you may have associated with your efforts is now solved by power cycles, or simply being overwhelmed by its usefulness, making it difficult to triage.

AI forces us to price even more tradeoffs, mostly in the form of explore/exploit problems. In other words, lots of tasks became easier, leaving diabolically hard ones to focus on, namely, “what should I be doing?”

My answer is mostly to be doing more of what I’m doing faster. I admit this is incremental and I’m a little ashamed of that, but I’ve already told you I feel like I’m the American in 1920 who saw a car and thought, “I could use that to go buy food for my horse”.

If you do your work faster, you can do more work. I heard this is called Jevon’s Paradox, which is some economic idea that caught fire like “Baumol’s disease” or “network effects” or “EBITDA”.

Gemini defines Jevon’s paradox:

The Jevons paradox is an economic observation that increased efficiency in using a resource tends to increase, rather than decrease, its total consumption. Proposed by William Stanley Jevons in 1865 regarding coal use, it occurs because higher efficiency lowers the cost of using the resource, driving higher demand that outweighs the initial savings.

Well, ain’t that the truth. Don’t mind me, I’m just over here paying off “intention debts” when I should be…[trails off]. If you feel the same, I see you.

Money Angle

As I expected, the post how to get arbed with perfect info would trip people up. I didn’t expect confusion because I thought Professor Doug Costa, whose explanation is featured in that post, was itself confusing. But because the concept of replication is hard and feels like it violates the good. It’s triggering. It means you can know the truth and still get arbed. Again, this is why I call it the pons asinorum of finance.

A reader brought it up in our Discord so I’m going to share the discussion here as he felt like our back and forth helped.

Before getting to the conversation, let’s refresh the problem Doug set up:

A company issues contracts based on a provably fair coin. The contract pays $150 on heads, $75 on tails. It trades at $100. Interest rate is 0%.

You calculate the true expected value of the 110 call using the true probability of 50%.

It’s worth $20 because it has a 50% chance of being $40 in-the-money.

You pay $20 for it (but even if you paid a bit less for an unambiguously positive EV trade, this analysis will hold. I just want to stay with Professor’s example)

The dealer sells it to you, hedges with 8/15 of the underlying contract, and locks in $6.67 profit in both states. Pure arb.

You had perfect information about the true probability and you still got arbed. The dealer made money in all scenarios, trading the call at fair value with you.

Doug is showing how the real-world probability doesn’t matter to the derivatives trader if they can also trade the underlying. In this case, the underlying is mispriced, but the dealer doesn’t know that. All the dealer cares about is whether the relationship between the derivative price and the underlying price is mispriced. In this contrived example, the mispricing was more profitable than knowing the true probabilities.

And to add something Doug doesn’t mention…if the investor knew the stock was underpriced and bought that instead, they’d have a positive EV trade (the fair price of the stock is $112.50) but they are still worse off than the dealer who knows the relative value of the 2 securities is wrong and gets to make a profit in all scenarios.

This is a good place to insert the chat.

Reader: I see, so the main point is we can converge a spread by trading two things instead of betting on one.

Kris: In a world with no derivatives, you’re left with having to be good at guessing real-world probabilities, but derivatives are their own source of possible edge that doesn’t inherit from knowledge of the future but from relative mispricings between the derivative and the underlying.

It’s obvious that being able to handicap probabilities would be a source of edge, but it’s quite subtle that once you introduce derivatives and the idea of replication, there becomes a source of profit that doesn’t rely on such an ability.

Reader: Right, so it’s instructive in giving one more spread to look at. If you used a put in your example, then the dealer would lose because they’d be too short. Then a dealer that actually has no information and sells both sides ends up $0. This example is picking the (long) side where it wins.

Kris: Yeah, the underlying in this example is too cheap RELATIVE to the call option.

If the call option was $13.33, then from the vantage point of real-world probability, both the underlying and call are too cheap, but they are priced correctly with respect to each other.

Which makes the point — if a derivative and underlying are correctly priced to each other, then the real-world probability is not important to the dealer. The dealer only cares about the relative values.

You can just compute the Sharpe of buying one vs the other I suppose to see which is better (that’s one lens). The call is more underpriced in % terms, 3.33 when it’s worth 20. But it’s more volatile as it will lose all of its value when it loses.

I’d just stick them both in a Kelly calculator in Claude or something and whichever one it says bet more on is the better one lol.

There are some important implications here. And brain damage — investor brain and derivatives brain collision.

The goal is that derivativesbrainskill.md becomes something one calls as needed, like Neo downloading kung fu. But you don’t wanna get carried away with it and shoot it at everything in life. It’s this weird artificial thing that works in a replication context, but it’s also not artificial in that its violation presents hard cash arbitrage!

That’s the end of the chat, but let me add one more thing to make you feel better if it’s still foggy.

I’ve seen this subtlety trip up seasoned options traders where they take B-S pricing to mean that the forward for a stock is stock grown at the risk-free rate (RFR), but this is ONLY true in a world where you can trade the underlying AND the options. Outside the context of replication, you cannot make that assumption.

Struggling with this idea is entirely forgivable. I mean, the realization that you could use RFR as the discount rate was a revolutionary breakthrough. Bachelier figured out option pricing in the early 1900s, but he and his contemporaries were stumped by what rate to discount the payoffs.

Later academics wondered if you should use something like the required return from CAPM or something, but it was the whole idea that if you trade a derivative vs the underlying against one another, then you can have equivalent payoffs and therefore it’s riskless to go long one and short the other. If it’s riskless, then RFR is the appropriate discount rate.

Warren Buffett sees the necessity of agnostic dealers using the RFR to price options in arbitrage-free ways as an opportunity. He asserts that put options are overpriced because they use too low of a discount rate, but the dealers don’t care so long as they can trade the underlying, they can arb any other rate assumption. Again, so long as “they can trade the underlying.”

This single idea allows derivatives traders who know nothing about the fundamentals of securities to make money in a sea of people who do. It’s quite profound and not a small part behind why I think vol trading is easier than directional trading.

Money Angle for Masochists

Rapid-fire format today:

1) A reminder that trading vol is not trading a line on a chart

Selling vol when it’s high because it’s mean-reverting is not like selling a stock that is going to fall. Option performance depends not just on what happens to implied vol but on how much the stock moves. If it were as simple as selling an IV number before it went down, just sell equity options just before earnings come out. I’m 99.9% sure the implied vol is going to fall after the announcement.

Just remember:

If you are trading near-dated option just think “I’m not trading implied vol I’m trading straddles”. The further you go out in time, the more it’s like trading implied vol since those options are dominated by vega, not gamma and theta.

2) Avis stock

Ticker CAR has been squeezing higher as activist owners with locked up float collide with heavy short interest.

As you might guess, I’m getting messages about the positive delta puts post.

Refreshing a perma-disclaimer: I’m not an advisor. You are responsible for your own actions.

3) ICYMI

Thursday’s post was especially well-received perhaps because it’s highly relevant for option sellers. Just to bring it to your attention again:

A devilish question for option sellers: Which VRP is higher?

It is a fuller response to the quote-tweet from a month ago:

To be blunt, if it were as easy as “sell vol when IV is high” you’d need to believe that option traders, a cohort known for being stupid, never noticed the obvious.

And finally, a reminder of the Moontower Review of option-based ETFs ISSB and ISBG:

• IncomeSTKd: Anatomy of a Next-Generation Options-Income ETF

This Week In The Options Trench

From My Actual Life

My wife tells me the internet is calling the Nine Inch Noize set last weekend the best in Coachella history. Nine Inch Noize is a mash-up of Nine Inch Nails and German DJ Boyz Noize

These are subjective things, of course, but I’m not surprised by the sentiment. I’ve seen NIN 3x in the past 3 years and the last 2 were with Boyz Noize on the Peel It Back Tour. I’m tired of raving about them. I don’t listen NIN regularly (well, more so now), but the recordings don’t do the in-person experience justice. You can watch YT clips to get a sense of the lasers and effects which are impossibly creative. The Coachella show was different than the tour shows so that’s something to appreciate of its own.

The tour shows have sections where it’s just Trent, sections with Trent and the band without the drummer (who by the way the alien Josh Freese), the full band, and then the tracks with Boyz Noize which thump real hard.

On Friday they dropped the first Nine Inch Noize album. The Pitchfork review is worth a read if any of this is interesting to you. It gives a lot of context not just to the album but the Peel It Back Tour as well.

🔗Pitchfork Album Review of Nine Inch Noize

The song I’m currently obsessed is an old one from the With Teeth LP. He opens his shows with it solo on the piano, which has a different feel than the recorded version. The recorded version has that velcro static fuzz sound that I f’n love, but it’s not for everyone.

Recorded version:

Live:

And my favorite cover of it has a beautiful orchestration and recording:

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• IncomeSTKd: Anatomy of a Next-Generation Options-Income ETF
• A devilish question for option sellers: Which VRP is higher?

In this issue:

• Investment Beginnings Class #3 and the game we played
• What if gasoline futures roll up to the current spot price all year?
• Checking in on the TIPs replication trade
• Music for the journey

Friends,

I taught lesson 3 of the Investment Beginnings course this week for 14 middle and HSers. That link includes the materials and video.

I opened the class with a timely story. The day before the class, I found a statement for an account I forgot about. 25 years ago, I spent $800 buying FedEx and Motorola shares. The account value according to the current statement…$14k!

I told them about studies claiming dead investors outperform the living, but I actually think it’s apocryphal. Sometimes it’s spun as “investors who lost their password” made the most money. In any case, it basically happened to me. It gave me an excuse to foist math on them by making them calculate my CAGR. You want those calcs to be second nature. I saw an interview where an investment manager said their target is to return 2 to 4x the fund in 7 years. Immediately, in your head, that’s 10-20% CAGR.

We sprinkle little bits of investing math as we traipse around the day’s lesson, but the heart of this particular class was a game. We broke into teams to construct investment portfolios. I used historical data but changed the names of 15 real companies to local towns and showed various metrics like margins, FCF%, earnings, revenue growth, etc.

We played 4 rounds starting from 2014. The teams lock in their portfolio weights to the different companies. There’s also the choice to invest in T-bills. There’s also a benchmark portfolio that is 20% T-bills and the remaining 80% is equally allocated across the 15 stocks.

Every 3 years, we reveal returns and allow the teams to re-jigger their portfolios. The 4 rounds take us through the start of 2026. Then I revealed the actual companies and we discussed what drove the returns. The most interesting aspect is how the metrics are loaded with pitfalls, so we talk a bit about the nature of the information that is available. The most overpriced stock with terrible margins was the best performer. Wear a helmet kiddos.

Introducing Erdo

Emi, my moontower.ai cofounder and a small team who I have the privilege to chat and work with as well, launched Erdo. I’ve been using it for months connected to the moontower.ai infrastructure. By now, I know enough to just go along with anything Emi’s up to.

Check out his brief post if interested:

Introducing Erdo: The AI Workforce for Business

Money Angle

Trailing 1-year inflation per the CPI index has been ~2.5%

Prompt CME gasoline futures (RBOB) are up 80% this year but the curve is strongle backwardated (deferred futures are trading much lower).

Gasoline is about 3% of CPI. If the futures roll up all year to prompt levels, this alone will add about 2.5% inflation for the next year.

The bond market has added 25 bps to the 10-year yield since the start of 2026. It sits at a 9 month high(via CNBC):

The put skew is also starting to kick in with the risk reversals on IEF making 1-year highs. This is the 1-month maturity for reference:

Bonds are in a weird spot. If the economy sputters, you usually want bonds as a hedge but not if it sputters because of supply-side inflation. Kinda makes me want to sell bond vol as they are might whip around but not really go anywhere but even though IEF vol is relatively pumped, how much fun is it to sell 9 vol?

Anyway, all the commotion did get me to pull up TIPs. The 10-year yield is 2%. The purple checkmark is the last time I bought them (and I wrote a big post on that decision and how to understand TIPs generally).

10-year breakevens look a tad elevated but not especially compelling so if you don’t like bonds, TIPs don’t look like an extra cheap alternative.

Been a while since I pulled this up. My TIPs replication “symphony” on Composer comprised of oil + bonds, inverse vol weighted:

The replicator has been underperforming TIP (the TIPs ETF) for years but just “caught up” on cumulative gain thanks to the recent oil surge.

Explained here:

💡Inflation Replicator | 8 min read

Finally, for the yield hogs with a stomach for swings, M1 WTI trades about >3% premium to M2, so if you think the futures keep rolling up, that’s a 36% annualized roll return if a prompt barrel maintains a market premium (formally called a “convenience yield” in futures parlance).

Money Angle for Masochists

Put skews normalizing and then some

We already saw IEF put skew coming to life.

Silver put skew is coming back. The 25d risk reversal on 30d options has been grinding back toward zero and is now turning positive.

Gold put skew is ripping higher.

Apparently, no asset is safe. Maybe those private ones that don’t have prices. Oops, scratch that…

Energy and the dollar vs everything else (Street Fighter voice) Ready, FIGHT!

And for the metals enjoyyyers…gold vols are way off the curve after prices crashed 15% in a month (that’s ~52% annualized realized vol but who’s counting?)

Erik (Outlier Trading) and I record a podcast each week. We usually discuss an evergreen idea but we also sprinkle in topical episodes based if something current is on our minds. This is one of those:

I step through my thinking and the price of oil call spreads on the pod but here’s a summary:

If CPI trends toward 5%…

My market on real yields: somewhere between 0 and 1%.

→ That puts the 10-year at ~5.5%, or about 100 bps higher than today’s 4.4%

→ IEF (duration ~7) drops about 7% — which is in line with current higher implied vols in IEF.

→ Jan IEF 90/89 put spread: ~6-to-1 payout

Now the equity side.

Current SPX forward earnings yield: ~5%. If investors accept just 50 bps of risk premium over a 5.5% 10-year, then the earnings yield needs to be ~6%, which implies a P/E of ~16.7. That’s roughly 17% lower from here, assuming forward earnings don’t contract.

→ Jan SPX put spreads at those levels: also ~6-to-1

Both trades land in the same neighborhood.

(You could go to lower strikes for fatter payouts if you think the market is genuinely asleep at the wheel on inflation risk.)

Oil call spreads suggest that the chance of the oil prices rising to current levels through the end of the year are about 25% so you can take or lay 3-1 odds. Steeping through the chain, if there’s a 25% chance of dropping 20% and the current price is fair then the upside to SPX is:

.75*SPX_up – .25*20% = 0

.75*SPX_up = .25*20%

SPX_up = 6.66% which would take the market back to unchanged for the year.

It’s quite reductionist to think this is binary and to reduce the valuation of equity to inflation —> higher interest rates —> multiple falling, but the art of market-making is essentially sense-making between prices and probabilities quickly.

If there are aspects you disagree with, I’ve shared what some of the prices are in the market so let me know what the trade is.

In the vein of Thursday’s post, you could think about stuff like “Buy IEF put spreads and buy SPY shares on a ratio of X” if you think SPY has more upside because its current pricing is coming from a >20% downside (do you see how that math works?). Trading is like a sudoku puzzle with prices as the given numbers. It’s like you have to find the hedge ratios that solve the grid.

I thought this thread was interesting, but not to scare you, it thinks my downside scenario is quite conservative if gasoline prices stay stubbornly high:

If SpaceX and OpenAI want to go public, I wonder if Elon and Sam call Trump…”bruh you’re ruining our picture”. And then they could all sit down and work something out. Art of the Deal.

You know how in Monopoly when you are a bystander to 2 other people trade you are sad? It’s because regardless of who got the better of it, you know YOU are worse off.

From My Actual Life

I discovered the band King Buffalo while watching the Lost In Vegas guys…

…and now I’m obsessed. Spacy, bangin’, psychedelic grooves. If you’ve heard of Elder or All Them Witches, you’re familiar with the style. It’s kind of like Tool’s last album, but more chill. Built for journeys.

I’m not the only one feelin it…

There’s no band called Otter and it sounds like the name of a band that would make music like this. I gotta get the kid on this, I’m stretched too thin.

(I’m playing with the music school band class today actually. Setlist is Your Love by Outfield, Complicated by Avril, and Yellow by Coldplay).

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• a market-making project you can do today
• how to get arbed with perfect information

In this issue:

• AI scheduled task example
• A rare, honest trading post-mortem
• Sorting through the bluster of the SpaceX IPO controversy

Friends,

⏰Claude can now run scheduled tasks | 3 min read

Khe explains how laypeople can easily schedule cron jobs. Put your “daemons” to work.

I used the scheduler to create a morning brief from my emails. For the past several years, I’ve been using autofilters in gmail that star (⭐) and apply a “Newsletter Subscriptions” label to senders I sub to.

At 6:30 am, I have a new gmail draft (Claude is not authorized to send emails so it’s stored as a draft):

 

By the way, anyone else notice that AI means we work even more? I think there’s something to that and it’s underdiscussed relative to the clickbait extremes of “post scarcity” utopia and a Skynet uprising.

The “something to that” is a mix of 3 things:

1. fomo
2. being busy “paying off our intention debt”
3. something we can’t see yet

I suspect both #1 and #2 are temporary and characteristic of a transition period on a compressed timeline.

#3 is a force that is probably positive and appears once our intention debts are paid. Which means the place to look for answers regarding #3 is young people embracing AI (although not in a Cluely, hollow your humanity, spirit). Young people have less intention debt, less to “renovate”, less to backfill, and a smaller corpus to consolidate. More of their use should be moving forward.

I like watching people like Nat use AI because they are plugged into the right layer of abstraction. The layer of recursion where every action is coupled with instructions to learn from the action so next time the action is improved. Infinite loop until you find a limit of perfection that would satisfy Zeno himself.

[My mathematical metaphor would be doing a Newton search, a common technique for estimating implied volatility, except the ε tolerance term isn’t predefined but shrinks as the calculation itself gets more efficient.]

In contrast, when I use AI, I feel like I’m living during the debut of the automobile and thinking, “Wow, I could drive that to the granary to buy food for my horse.”

 

I’m doing old things faster which is now par, but if you stop there it’s a failure of imagination.

Anyway, as I keep an eye on Nat’s quest, I’m curious how he breaks through this plateau.

Money Angle

📺”Ben Lost Everything”| 15 min

A few issues ago, I pointed out Ben’s YT channel, which is equal parts educational and hilarious. My wife is even working through the catalog. She and I were both very impressed with his most recent video, which continues to teach despite a brutal context. Ben blew his account up.

The post-mortem, reflection and honesty on display is rare. Given what I’ve seen from him, I expect him to bounce back stronger and wish him the best.

The follow-up to building an option chain in your head

🔗A Deeper Understanding of Vertical Spreads | 12 min read

 

If you are interested in prediction markets, that post’s discussion of binary probability is fertile soil for cross-pollination. Enjoy.

Money Angle for Masochists

From at least make the conspiracy make sense, we acknowledge an enduring difficulty between information and infohazards. In that issue, I called out Zerohedge for a disenguous conclusion based on NVDA earnings. But chastizing Zerohedge might as well be a pro wrestling ref admonishing the Macho Man for grabbing a folding chair.

Even as you move up the chain of credibility, it can be hard to distinguish degrees of expertise. Hell, even the idea of expertise itself has been in retreat. Freddie deBoer’s recent post Overlearning ($) collects several examples where a justifiable backlash to putting too much faith in expertise has led to its own form of blindness:

Each of these examples of overlearning began with a real grievance and a defensible insight, and each got driven by the normal human hunger for clean conclusions one or two steps further than the evidence actually supported. The result was backlashes to backlashes. The trouble with overlearning is that it inoculates people against correction. Because the original observation was right, any challenge feels like an assault on hard-won clarity, like a regressive attack. The overlearner has usually endured some version of being fooled (by the audiophile YouTuber, by the diet industry, by institutions that failed them) and so they’re constitutionally committed to not being fooled again. That commitment becomes its own kind of blindness, arguably more intractable than ordinary ignorance because it comes armored with a legitimate grievance.

Today I have an example of famous professional investors touting viral views that seem to be more smoke than fire.

I’m not an expert on the topic at hand, but an important skill in a complex world is being able to identify who is.

Let’s start with the scene.

In February, Nasdaq opened a public consultation on changes to its Nasdaq 100 methodology. The subtext being SpaceX’s plan to IPO at a $1.75 trillion valuation. There were two proposed rule changes.

1. a “fast entry” provision letting large new listings join the index after just 15 trading days
2. a multiplier that inflates how low-float stocks are weighted

This struck observers as suspiciously tailored to the occasion.

Fund manager George Noble called it “the most SHAMELESS structural manipulation of a major index I’ve ever seen.” Michael Burry called Noble’s piece a “Must Read” and sent it to his >1 million followers. The posts went viral, sparking the latest outrage: Musk bends yet another institution to serve his interests, and your 401(k) is the exit liquidity.

I don’t know who Noble is, but apparently, he’s a famous investor with all the credentials and job history.

My perception of Burry is that he has that autistic cocktail of persistence, intelligence, and disinterest in norms that enabled him to make a fortune betting the Don’t Pass (and got lucky enough on the timing which famously bedeviled a wider pool of investors who saw the same thing but were early).

Since the GFC, it’s been a bear market for bear outlooks, and from what I can tell with some googling Burry has done just fine since securing his bag over 15 years ago, so I’m not throwing tomatoes here. In fact, that he is such a smart guy devoted to the craft of investing, but has not performed notably one way or the other since his big score, illuminates how difficult alpha is.

But the bar to say stuff is simply lower. Their outrage is the kind of message built to travel, while expertise and nuance are boring and, in this case, going to throw cold water on the outrage festival.

I happen to know that when it comes to anything related to the details of index constitution, from arbitrage to legal frameworks, you find out what the account I call the “sensei” has to say.

Sensei gave a masterclass on this topic on my X timeline, then decided to resurrect his sleeping substack to publish a full rebuttal to Noble and Burry.

This Is Not The NASDAQ 100 Consultation Fight You Are Looking For | 20 min read

This is sensei. His pushbacks in descending levels of importance from my point of view.

1. Fast entry isn’t new. MSCI, FTSE, TOPIX, and most major global indices already have fast entry rules for large IPOs, some even faster than 15 days. It’s not a Nasdaq invention.
2. The “up to a year” claim is wrong. Nasdaq 100 already allows entry with as little as 16 weeks of trading history under existing rules.
3. The 5x multiplier actually lowers the index weight. Under current rules, a 10%-float stock is weighted at its full market cap. Under the proposed rule, it’s weighted at 50% of market cap. The math runs the opposite direction from what Noble and Keubiko claimed.
4. Keubiko’s lockup-expiry conspiracy doesn’t calendar out. He argued Musk engineered the IPO so a 180-day lockup would expire at the December reconstitution. For that to work, the IPO would need to be in late May, not the mid-June date Keubiko himself cited.
5. Noble misread S&P 500 methodology. He wrote that S&P weights a 5%-float stock at 5% of market cap. A stock with less than 10% float is simply ineligible for the S&P 500 entirely.
6. They ignored the Russell consultation. Russell US Indices was running an identical consultation on fast entry and float rules at the exact same time. None of the three mentioned it.
7. They complained after the window closed. Both Noble and Keubiko published their pieces weeks after the consultation period had already ended on February 27th, too late to actually influence the outcome.

Bau acknowledges the legitimate underlying grievance that Nasdaq uses total market cap weighting at all rather than free-float weighting like the S&P 500. But that objection predates this whole consultation.

You could take a consequentialist position that the ricochet effect of these folks’ rage-laundering brings a warranted, overdue wider awareness of Nasdaq’s weighting bugs, but I’m old-fashioned and think intentions do matter even if they sometimes backfire in effect. Let’s be clear, the intention here was to rile you up with a villain story, not emphasize Nasdaq or apparently many index providers’ methodologies.

I’m not one to strain to make an apology for Elon. But if you call fouls where there aren’t any, you lose credibility.

Baus exist. There’s credibility out there. But it often sounds like a whisper because it gets drowned out by what’s built to travel. Nuance is heavy and takes up lots of space. It’s the first thing to get thrown overboard when you want to get somewhere fast.

This Week In The Options Trench

Erik and I talk options earnings:

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• Fair…I can see how you might think I lied
• does revenue seasonality translate to vol seasonality?
• a cleaner way to compute seasonal vol

In this issue:

• math in the car with kids
• trader quick math
• from straddle to gamma

Friends,

My older kid is getting braces in a few weeks. Based on the expected time he has to wear them, it’ll cost about $350/month. That’s a car lease. I’m not complaining (God: “he’s complaining”), I just suffer from chronic numeraire substitution. I’ll come back to the braces thing in a bit, but let’s chat some other stuff for a bit.

My sons are in 4th and 7th grade. A nuisance I will one day miss is shuttling them and their friends all around. We talk about lots of stuff, but stuff is often made of numbers, so I end up teaching them how to reason numerically about real-life stuff in an organic way in the context of things they find interesting. Yay. Except they groan because they know it’s coming. But I believe in osmosis and their future selves will be thankful. Or at least have endearing stories at my funeral about their old man being a crank who also happened to love them. And since they might have kids of their own one day, appreciate, just as I do now when I think about my parents, that we’re all just making shit up as we go.

Where were we before my inner monologue took over, ah yes, car convo. I got the boys in the car with another friend headed to practice. The 7th graders said they were learning scientific notation. Shouldn’t have told me that. Immediate quiz. Represent 1/50th in scientific notation.

I was impressed. I listened to his friend reason aloud for about 20 seconds before getting 2 x 10⁻²

Zak got the answer faster than I did. The Math Academy lessons are paying off.

Why is scientific notation useful?

To torture us.

Besides that.

“I don’t know, [proceed to fumble around for explanations before landing on something that tracks]. Because we need to measure stuff in micrograms? Is there even such a thing as micrograms?”

Very good. That makes sense. From the stars to bacteria and atoms scientists deal with things that are really big or really small. It’s right there in the name: SCIENTIFIC notation. We talked about how insane the idea of a light year is for a bit before arriving at the gym but not before I told them next time they watch YouTube, instead of watching Jesser we’re gonna learn about the Fermi Paradox which they theorized naturally but didn’t realize it was a famous contradiction.

On the way home from practice, the kids started talking about IQ. I forget what the comment was, but it indicated that they did not understand that an IQ of 100 is normalized to be the average. Sweet. We get to learn about bell curves right now.

I explain that 15 points is 1 standard deviation which encompasses 68% of the population. So to be greater than 1 standard deviation means being in the top 16%, since the 32 remaining percent have to be split between the lower and upper parts of the population, leaving 16% ABOVE 1 standard deviation.

2 standard deviation outperformance means top 2%.

I note that my scientific notation quiz asked for 1/50. Your father is psychic.

[Between that and the fact that I predicted that Axl Rose, who’s friends with AC/DC and lives in LA is probably at the Rose Bowl concert we were at last May, only to have him walk out from backstage about 60 seconds after I said that, they might think I’m a witch.]

Then we do 3 standard deviations. That encompasses 99.73%. For just the upper, it’s about 1.3 per 1000; let’s call it 1 in 750.

Given the size of your middle school, there are probably 2 kids that smart.

Except for that your school isn’t a random draw from the population.

We’re a long way from where I grew up. That night I explained to them that the test they took in 3rd grade, where they got 2 standard deviations above the mean, wasn’t even close to getting accepted to the local GAT program. Sorry boys, you’re not Asian enough and that’s on me.

Wanting to change the topic from IQ, I brought up height. After all, we just left hoops. I invented some numbers. The average adult American male is 5’9 with a standard deviation of 3”.

We stepped through the progression.

A 6’0 man is taller than 5 out of 6 men. (1 st dev)

6’3 and you’re 1 in 50. (2 st dev)

6’6 and you’re 1 in 750. In the running for the tallest boy in H.S. (3 st dev)

(Although selection effects need another nod here).

7-footers are 5 sigma. Using just the right-tail probability that’s 1 in 3.5 million.

This was a chance to apply their newfound knowledge of scientific notation.

How many 7-footers do you expect in the world if there are 3.5 billion adult men?

A million is 6 zeros. 10⁶. A billion is 9 zeros.

9 zeros divided by 6 zeros leaves us with 3 zeros.

We expect 1,000 7-footers.

Google says it’s estimated that there is “2,800” 7-footers in the world which the CDC statistically extrapolated using a standard deviation of 2.9 to 3. Small differences add up when you start adding sigmas such that our final estimate is off by a factor of 3. But hey, the right order of magnitude.

While we were countin’ sigmas the 9-year-old wants to know how Wemby exists. Wemby is officially listed as 7’4. There’s online debate as to whether his height is underreported and if it’s really 7’5. We’ll use that since it’s 6 standard deviations.

Siri, what’s the probability of an event beyond 6 standard deviations? 1 in 500mm. One-tailed, 1 in a billion. Wemby.

Statistically speaking you wouldn’t expect to have enough 7’4 mutants to assemble a starting 5 lineup but in reality you there’s enough of them to at least field a football team. Waves hand in the shape of epsilon.

Anyway, in service of handy takeaways, it’s useful to remember that a 3 standard deviation extreme on 1 side of a bell curve occurs about 1 in 750. For quick math, call it 1 in 1,000 or 10³. So if you’re talking about the American population of 3 x 10⁸, the number of 3 sigma people on a particular trait would fit in an MLB stadium.

Or about the same number of people who subscribe to moontower. See, you’re all 3 sigma! ❤️

Speaking of…

Moontower is 7 years old.

The first issue was March 17, 2019. This is Moontower #307, Munchies is up to #146, there’s been 96 paywalled posts, plus possibly the single largest archive of options blog posts on the internet. (ChatGPT mentions Larry McMillan and Kirk DuPlessis as being similarly if not more prolific.) Fyi, nearly everything I’ve ever published is indexed here and religiously updated so when robots erase me it is in totality. Thanks for following. I never expected to be writing this long. I didn’t expect anything.

Addendum on braces:

I wore braces from freshman to senior year of high school. My son will get his off about a month into freshman year. How’s that for generational progress.

The braces thing conjures something of a subway platform riddle for demographics where I can’t tell if the world is moving or me. My little guy got “spacers” in 3rd grade and will wear a retainer for 2 years. I’m like, is getting braces twice a new thing, or something I just never would have seen in my strata growing up?

I’ve noticed 2 other versions of this demographic subway platform riddle.

The older kid is now past the halfway point of middle school and I still never hear of fistfights. Growing up, at least every other week, the beacon went up, “FIGHT!!!”. Social class or changing times?

Finally, skiing. This one isn’t a riddle but it’s so jarring. I was 20 years old the first time I stepped on a mountain. Here’s school in the winter feels optional. Everyone has a cabin in Tahoe, all the dads are metereologists, and an expert on MTN stock.

Cold, heights and ski lifts, driving on dangerous roads?

I think I’ll just binge Nelly & Ashanti: We Belong Together thank you very much.

[We did knock this out in 2 nights. Plenty of time to cancel the 1-week Peacock subscription it required. I friggin’ love Nelly and so much more after watching the show. He comes off as an amazing father, raising both of his own as well as his sister’s kids when she passed at a young age. The only thing that bugs me is how good he looks at age 50. Save something for the rest of us bruh.]

Money Angle

Dean Curnutt graciously invited me to be on his outstanding podcast. His prompts led the conversation towards useful stuff. The description:

We begin with developments in commodity markets, particularly crude oil, and silver, where geopolitical tension and speculative flows have led to sharp changes in volatility surfaces. Kris explains how option skew in underlyings like oil can reprice rapidly during shock events, leading to inverted termstructure and a well bid call skew. These dynamics create unusual behavior in vertical spreads and probabilities implied by option prices.

Kris describes how the relationship between spot moves and volatility changes across market environments, emphasizing that traders must continually recalibrate their models. What appears to be a stable relationship—such as the familiar beta between the S&P 500 and the VIX—can shift quickly depending on positioning and market structure.

A major focus of our conversation is on the mental math traders use to interpret option prices without relying on models. Kris walks through several shortcuts that allow traders to move quickly between volatility, straddle prices, and probability estimates. These approximations help traders identify when prices look unusual and whether options markets imply probabilities that diverge from other markets.

Finally, we discuss the work Kris is doing on financial education. Inspired by teaching his own children about investing and compounding, he has begun running small classes for students and sharing the materials publicly. The goal is simple: introduce younger investors to concepts like time value of money and long-term compounding earlier in life.

If you are interested in a step-by-step breakdown of how I found an estimate of an out-of-the-money put like I did in that interview this post is for you:

🔗building an option chain in your head

Money Angle for Masochists

A topic I could have rattled on for much longer in that interview with Dean is trader mental math devices. By now y’all know option traders have the ATM straddle approximation burned into their retina:

straddle ≈ .8 Sσ √T

A useful approximation I did not explain in the interview is the similar-looking ATM gamma formula for a Black-Scholes straddle:

Γ ≈ .8 / (Sσ√T)

The three things that shrink gamma are in the denominator:

Higher S (price): The same $1 move is a smaller percentage move on a more expensive underlying.

Higher σ (vol): The option is already “priced for action.” The curvature of the price function gets spread over a wider range of expected outcomes. More vol → flatter curvature near the money → less gamma.

Higher T (time): Same logic as vol. More time spreads the curvature out. The more time to expiry the less a given move influences the delta of the option. The delta of 10-year option is not going to change much based on how the underlying changes day-to-day.

A couple of educational points:

• Take note of the scaling. Double the vol, gamma roughly halves. You need to quadruple DTE to get the same effect.
• As always, a good habit when trying to understand greek levers, is to take examples to extremes. If you raise DTE or vol to infinity, all options go to their maximum value. For calls, that’s the spot price itself. For puts, it’s their strike price. That means calls go to 100% delta since they move dollar-for-dollar with the spot. Puts go to 0 delta. It doesn’t matter where the spot price goes, the option is already at its max value. It doesn’t change. If a call is 100% delta and a put is 0% delta, the option has no gamma. Its delta doesn’t change with respect to the spot.

Going back to those formulas for a moment:

straddle ≈ .8 Sσ √T

Γ ≈ .8 / (Sσ√T)

The denominator of gamma = straddle/.8

Substituting:

Γ ≈ .8 /(straddle/.8)

Γ ≈ .8 /(straddle/.8)

Γ ≈ .64 /straddle

So when you want to do mental math you take “2/3 of the inverse of the straddle.”

This might sound obtuse, but taking inverse or “1 over” some number should be one of the fastest mental math operations anyone dealing with investing does. After all, when you see any ratio like P/E or P/FCF you are immediately flipping that to a yield where it can be compared with things like interest rates or cap rates.

If a straddle is $5, the gamma is 2/3 of $.20 or ~.13

And we know that doubling the straddle halves the gamma so you can just memorize that a $10 straddle has ~6.6 cents of gamma and linearly estimate gamma for any straddle price relative to that (ie $20 straddle is about 3.3 cents of gamma and $15 straddle is in the middle of 3.3 and 6.6).

And of course there’s time scaling. To find an option that has double the gamma you need to cut the DTE by 1/4.

Keep flipping this stuff over in your head, it’s satisfying, and it thickens the myelin around whatever brain cells you sacrifice to options damage.

If the 9-year-old can do it, so can you.

(I’m kidding. I just found this moment of deep thought cute. Between both kids’ basketball lives, the gym has become my office. Max does his Math Academy after his practice while waiting for the bro to finish. He recently discovered my Kindle is a scratchpad which has made my “no math without scrap paper” rule less of a nuisance. I adopted that rule from Math Academy’s recommendation, my affinity for mental math notwithstanding.)

Friends,

You can’t swing a cat these days without hitting a prediction of what AI means for humanity. Insofar as it’s possible for someone writing for a wide audience, I’ll share what amounts to some half-baked thoughts that I keep coming back to.

“YOU GET A UI, YOU GET A UI”

I say this as someone who feels some dissonance building an analytics product with charts and tables. The future is just APIs talking to each other. In the future, Zillow’s UI is a mere suggestion. You want the data in a different format? You want inference beyond what Zillow decided goes into a Zestimate? All of that is getting cheaper and accessible to non-technical people.

You’ll go to a site. Maybe. Instead it wil be Siri or Jarvis or Alexa or whatever “I want to see XYZ” and your client-side listener will construct it but it’s going to need access to API that has the data. The data is increasingly all the value while rigid presentations become pointless.

Again, the future is APIs talking to each other. Data becomes increasingly locked down.

On Data Lockdown…

Scarce or exclusive data’s value increases as its complement, inference, gets cheaper. The big futures and stock exchanges are some of the original 2-sided platform businesses. Can see them flexing their quasi-monopolistic might on the data side.

…which might get dark

The fight over data will intensify as well. If you place a bid, the exchange claims that’s their data. But is it yours? Well, it’s of little value to you but whose gonna galvanize the white-collar movement around “hey AI trained on all this data that had little value in isolation, but so much value in aggregate then used it to disrupt US”. It started with the Hollywood writers guilds, but is it crazy to imagine rolling protests as automation eviscerates industry by industry? To see picketers with dystopian slogans like “my data, my choice”.

It’s a different argument than p(doom) objections to AI. It’s not “you shouldn’t have built this” but you had no right to cut me out. It seemed like a bargain when we got “free” email or “free” social media. The tone deaf tech mogul will undoubtedly claim it was fair at the time and maybe that can fly intellectually. But it’s not the clawback by court that will decide. That one happens by pitchfork.

AI Immune

As SaaS gets wrecked, we wonder retains value in the singularity. My working model is:

trust and accountability

Maybe AI can sell my house but realtors have survived fee compression and technology far longer than anyone expects. I think this hints at a still-valid truth. People want to have someone to yell at, appeal to, or simply talk to when it comes to lumpy, rarely repeated transactions.

It’s the “shit umbrellas” theory. The human’s value is not in doing the work but in retaining liability. AI can read the tax code, but my accountant will stand by his work in court.

If you travel extensively for work your relationships are hard-earned. The proof of work is miles traveled or other exclusionary behavior where there was no substitute. Relationships are repos of accumulated, unfakeable work.

The more you can position yourself as accountable the more value you can retain. Being trustworthy and reliable don’t go out of fashion. They will get even more valuable as so much else can be faked.

A strange corollary to this:

Things that were always fake but valuable will stay that way. Like astrology.

A final thought in this thread:

Anyone burning their reputation to the ground thinks either the world is ending or the tides won’t ever turn. Hmm, how would you act if you couldn’t afford for the tides to ever turn?

Art

Art is a big question. There’s will always be a positional scarcity component of it and there will always be genius. The question of whether there will be a surplus of robot genius around as well. We may finally get an answer to would a million monkeys write Shakespeare.

Live performance and sports will stay important. At least until everyone over the age of 10 today is dead. Then all bets are off. I never thought watching people play video games would be popular. I’m now open to the possibility that future people may perfectly prefer robots playing video games or anything for that matter over people playing.

I leave you with this interview with the creator of Open Claw. Listen specifically from 8:30 to 10:17

107 seconds and I quote, “Holy fuck”

If you are hanging your hat on cleverness for its own sake or rigid definitions of intelligence, your time is over. I’m not saying intelligence is losing value, but that its truest definition will become obvious — the ability to get what you want out of life. This is the only definition that will matter and the bright side of that is that its more inclusive than whatever school thinks it is.

I was at a local book fair last week where you dump as many books as you can fit into brown shopping bag for $8. It was an epic haul and a great incentive to just snag boogs that seem even remotely interesting.

I picked up this 1957 classic by C. Northcote Parkinson. I was familiar with his eponymous law, which states “work expands so as to fill the time available for its completion”.

This entire book is an extraordinary, laugh-out-loud, pull-no-punches satire. Parkinson would have been an absolute master at Twitter. The law itself is satire wrapped around a specific observation. The way he formalizes the argument is pure art, even ending with an insane equation (he constructs hilarious equations throughout making the book feel like a tongue-in-cheek treatise on social physics).

Satire, notwithstanding, it sure feels like the very thing Parkinson’s Law pokes fun also holds the key to our salvation if AI just does all the work. So that’s where I am now. Placing humanity’s hope on a joke by a British naval man whose skill with the pen is such that I want to vibecode a Parkinson writing voice app.

Money Angle

As an example of “everyone gets their own UI” I whipped up a Dashboard page where I can add modular tools.

The first tool I added is something I call the “Financial Analyzer”. The seed of the idea came from an education POV. I’m teaching this Investment Beginnings Class, but I myself am a novice at reading balance sheets and income statements.

Pre-AI I would want a teacher sitting next to me explaining what sticks out to them. In minutes I was able to make a site where I give it a ticker and range of years and it pulls the filings from the SEC’s Edgar database. But the best part is Claude can act as the teacher and write its own summary of what it sees from year to year. I’m not saying this is going to be human expert level analysis but that is not the bar. I’d just like to pull up a stock and get a quick orientation through the years.

I could even feed the analysis back into an LLM to have it explain it to me even simpler.

I happened to pick up Neal Stephenson’s Diamond Age from that book fair I went to. You can build your own “Young Lady’s Illustrated Primer” now. It’s a bull market for learners out here.

The video below shows how the tool works. I’m not sharing the tool publicly because the analysis layer uses Anthropic tokens but this description is from Claude and is probably a good enough prompt to make it yourself:

A browser-based tool that pulls structured financial data for any US public company directly from the SEC’s EDGAR XBRL API — the same data companies are required to submit with their 10-K and 10-Q filings. No third-party data providers, no API keys.

• Enter a ticker, pick a year range, and get collapsible income statement, balance sheet, and cash flow tables going back to 2005.
• Toggle between annual and quarterly views.
• Every line item shows the exact XBRL concept tag it maps to, so you can trace any number back to the original filing. A “Raw XBRL Data” tab exposes the complete set of concepts the company filed — not just the ~40 our template covers — with search and filtering. Remainder rows flag where our template’s sub-items don’t sum to the reported total, so nothing silently disappears.
• An AI-generated analysis summarizes trends across the full time series.

Stack

• Single HTML file (no framework, no build step)
• Vercel serverless functions for the SEC proxy and Claude API calls, hosted on Vercel’s free tier.

Data endpoints

• www.sec.gov/files/company_tickers.json for ticker lookup
• data.sec.gov/api/xbrl/companyfacts/ for filing data.

Money Angle for Masochists

My new podcat series with Outlier Trading is up. The first is a short one just to set the stage for what to expect from weekly episodes.

We released a second one on Friday because, well, oil is interesting.

Visual Derivations

This week I re-published a foundational option post on X articles.

🔗👿The MAD Straddle👿

It’s a beast of a post that I orginally published in the format of a Socratic homework but in the X format you can basically read straight through it.

It covers:

☑️The relationship between MAD (mean absolute deviation) and standard deviation
☑️how to approximate a straddle value without a model
☑️a visual derivation of the approximation
☑️see how the straddle is the MAD
☑️gain an intuition for how skew and fat-tailed distributions distort the relationship between straddle prices and volatility
☑️see practical situations where ATM straddles and therefore volatility misrepresents risk

Sometimes these learning posts go over a lot of material so I think it’s helpful to point out what parts of them are most interesting to me personally. In this post it’s the section Lessons from a Skewed Coin and how standard deviation and in turn straddles are deeply misleading representations of risk when a distribution is highly skewed such that the mean is balancing many frequent events in one direction verse rare but large events in the other. I talk about how this shows up in familiar investing scenarios.

The other concept in here I like to emphasize, in no small part, because it’s legit fun is the visual derivation of the straddle approximation that states the straddle is 80% of the vol.

The derivation:

The mean of the distribution

We want to estimate the straddle. The mean of the underlying stock distribution is centered around the forward price not the at-the-money price.

We will estimate the at-the-forward (ATF) straddle.

This means we are estimating the straddle struck at the ATF strike.

The ATF strike occurs at the ATF price:

Approximating the ATF call option

This is the meat of the work.

[It requires no more than pre-algebra.]

Let’s go.

While we want the straddle, let’s start with the ATF call option.

We established 3 identities that occur at-the-forward:

Now we just plug these back into the B-S formula for the call.

Hmm, this looks fairly docile. Stare at it hard. The next section will feel good if you like geometry!

The underlying distributions for B-S is that stock prices are lognormal. The prices are lognromal but logreturns are normally distributed.

This is handy because normal distributions are familiar to work with.

d1 and d2 are like Z-scores on a Gaussian (bell) curve of logreturns!

The probability density function (PDF) for a bell curve:

The center of our distribution is an expected logreturn of 0 corresponding to the forward Seʳᵗ

The peak of a bell-curve at that forward price corresponding to a logreturn of 0. For the standard normal curve we can assume σ = 1

Plug 0 into x of the PDF:

Let’s bring this all together into a picture:

Understanding the picture

The value of the ATF call is the integral of the PDF between d1 and d2 but we can estimate it!

height x base x forward price

Note: This will slightly overestimate the value of the call (see the overestimated region in the picture

To go from call price to the straddle, we remember that at-the-forward strike the call and put are equal because of put-call parity!

The rest is easy:

The straddle is the MAD!

The volatility, which is computed just like a standard deviation, gives large moves extra weight. But the straddle is a better reflection of what move size we typically see.

It will cost you .80 of the standard deviation to buy a fairly priced straddle. Let’s plug that into a normal curve’s cumulative distribution function:

💡Theoretically, if the straddle is fairly priced:

• it will expire in-the-money ~ 42% of the time
• despite the low “hit rate”, it’s fairly priced because the payoff on larger moves balances the expectancy

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• at least make the conspiracy make sense
• how a high implied vol can be cheap
• Welcome to The Options Trench Podcast

In this issue:

• white rabbit
• a downside of trading careers
• oil options, Iran, Polymarket

Friends,

I’ll be short up top here today as the Money Angle sections are longer than usual. This is just something fun.

My adult ensemble band played a short set at Norm’s in Danville on Thursday night for “rock band karaoke”. Our set list was High and Dry from Radiohead, You’re Love by The Outfield, and finally White Rabbit via Jefferson Airplane and written by Grace Slick.

White Rabbit is one of my favorite songs because of how it builds, a signature feature of just one of its many eclectic influences, the Spanish bolera. If you’re into song origins this was a great watch.

Apparently, Slick wrote the song after listening to a Miles Davis record for 24 hours during an acid trip. The lyrics reference Alice in Wonderland:

One pill makes you larger
And one pill makes you small
And the ones that mother gives you
Don’t do anything at all
Go ask Alice
When she’s ten feet tall

And if you go chasing rabbits
And you know you’re going to fall
Tell ‘em a hookah-smoking caterpillar
Has given you the call
He called Alice
When she was just small

When the men on the chessboard
Get up and tell you where to go
And you’ve just had some kind of mushroom
And your mind is moving low
Go ask Alice
I think she’ll know

When logic and proportion
Have fallen sloppy dead
And the White Knight is talking backwards
And the Red Queen’s off with her head
Remember what the dormouse said
Feed your head
Feed your head

Money Angle

Ex-SIG quant trader, friend of the Moontower, fellow Substacker Whirligig Bear and prediction market enjooooyer Andrew Courtney went on the Odds On Open with Ethan Kho.

(Ethan’s pod is totally catching fire with his great guests and interviews. He works hard as hell on this project as well as school so I’m stoked he’s getting such traction).

Not surprisingly, it’s a terrific conversation, but I want to zoom in on an idea that resonated deeply for me and easy to overlook for aspiring traders.

Ethan: You left the firm with I think you said only around 40 or so real professional connections. You said that that was one of the other defining things of being a trader — you’re with the same group of people, obviously making lots of money, but it’s not the place for someone who wants to be wants to have this insane network of a lot of different people. Talk to me a bit about the culture.

Andrew: Let’s frame it as who might this fit or not fit. Let’s contrast it with some other high leverage elite type careers. Say you’re a consultant and you’re meeting C-suite people from all different kinds of clients, you know, and you’re only a year out of college. Or you’re an investment banker and you’re doing deals with all these different firms. You’re gathering this wide network of people, a

lot of different information sources. You are working with many people versus my primary relationships were my co-workers. These were fantastic people but that was the most of my network. When you’re a quant trader, you’re not out there at conferences telling people what you’re doing or networking. You’re not talking to anybody about what you’re doing.

So I had a pretty tight network and and good relationships with a lot of these people, but it’s not it’s not like I can the C-suite or get career advice or something like that. It was much more narrow and concentrated and dense network. So it’s a different type of career definitely.

This is very rarely talked about. But the trader career will not leave you with much of a usable business network if you change careers compared to a more sales-oriented job (I say sales because high leverage careers only fall into 2 camps — being on the road selling/deal-making or being a 99.5 percentile solo-player in front of a computer. And the latter is very much under threat right now).

I am always urging early career traders to take the effort to be outward before they need to. You have to overcompensate for the narrow network. After all, you’re going to make a lot of money, right? Well, you want to have people to invest with or raise money from if you decide to become an entrepreneur one day (if you’re trading for a living, there’s a misfit inside you that probably doesn’t want to be an employee forever).

I was fortunate to be on the trading floor which does expose you to lots of people. That network was critical. It led to my next job after SIG, it created most of my broker connections when I left the floor, and it has helped me connect people with firms. But my network didn’t really ramp until I became far more outward. Reaching out on Twitter to learn, starting this letter, and adopting a more sharing posture in general. There is a zero-sumness in trading that leaks into your mindset. It has its purpose to be sure, but don’t let it creep beyond its usefulness.

One last bit that Andrew alludes to…if you want a lunch break or lunch meetings, trading isn’t for you. You never get your full attention. Want to code or do any deep work without one eye scanning screens? Tough luck. Even your basic needs take a backseat.

I forget which comedian made the joke about the weird life of pro athletes. They are rich and influential. But they still have to chase a ball around.

There is no self-aggrandizing story to tell about trading. You serve money. If you’re not there to pick it up when it presents itself why’d you even come in?

Money Angle For Masochists

Oil vols and calls skews were up a lot this week as the expectation of the US striking Iran increases. A few pictures:

Polymarket implies only 38% chance that the U.S. does NOT strike Iran by March 31.

Risk reversals, which measure the premium of puts to calls, in USO have shot sharply negative this month.

USO vols are elevated and strongly inverted across the term structure.

Implied vols until late March are ~53%.

You already know to use the free event volatility extractor to compute trading day volatility by removing an expected earnings move from an expiration. Let’s use the calculator in reverse. If we assume a typical trading day volatility of 30%, then if we were certain a strike were to occur, we guess-and-test our way to an 11.3% move size to make the term vol fair at 53%

But this is not earnings. We don’t know if the “event” will occur. We can use the Polymarket probability of 62% that an attack will occur before the end of March. We’ll need to expand the equation we normally use to account for p.

We recall the basic identity:

Term variance = expected event variance + accumulated daily variance.

In math:

where:

DTE = business days til expiry =26

p = probability of strike = 62%*

TermVol = ATM IV from March 27 expiry = 53%

EventVol = annualized vol of strike day = 224%

DailyVol = annualized vol of regular business day = ❓

*Notice in the case where P =1, the equation would be exactly the same as the one behind the calculator.

Solving for DailyVol:

DailyVol = 40.7%

But, wait, we want to fix the DailyVol to be 30%. We need the event vol that generates a DailyVol of 30% assuming that event only happens 62% of the time, not 100%, as our first calcs assumed.

It turns out to be 14.4% or 285% annualized

💡Annualizing a move to a vol

• 14.4% x 1.25 x √251
• Why 1.25? Because a straddle or move size is only 80% of the volatility or standard deviation. See The MAD Straddle

In sum, if we treat an Iran strike that satisfies Polymarket’s definition AND we believe the Polymarket odds AND we think it manifests as one large single-day move, then 53% IV suggests that oil will move as normal at ~30% vol but have a single-day shock of ~14%.

This is a highly skewed way of decomposing 53% vol. To assume there’s a bunch of variance concentrated in just a single day. But that 53% vol is also not the market assuming we move ~ 3.25% per day either. It’s some mix of:

• “realized vol is elevated right now because there’s uncertainty”
• “at some point in the near-ish future there’s going to be a lump of variance as oil either relaxes lower (which could easily be 10%) or much higher. The current price of oil is a compromise between 2 states of the world but it’s not the right price in either of them and we don’t know which state it’s going to be”

Thoughts on the Polymarket price

Here’s a more up-to-date snapshot (Substack has a Polymarket integration!)

I have zero insight on geopolitics so I’m just going to offer thoughts on prices:

EDIT: The Polymarket prices updated from when this email post sent (a Sunday) and when I wrote it (Friday night)

• The market thinks a strike is coming soon. March 31 is 64% and June 30 is only 68%. Conditional on a strike happening, the market implies 64/68 ~94% chance it happens before the end of March. You can buy June, sell March and only risk $4.
• The dollar volume on these things is small but there are many papers supporting the “marginal trader hypothesis” that it only take a handful of active, well-informed traders to make a market more efficient. This is not suprising. If we played a mock trading game for even zero stakes it wouldn’t take long for you to see how quickly a market converges to a reasonable fair value.
• The volatility risk premium across many liquid markets isn’t abnormal. The market either doesn’t care what oil and Polymarket says or a strike on Iran is not expected to have a material effect on the volatility of equity shares. However, defense names have implied vols in high percentiles (while PLTR vols are tanked btw)

  

Here’s my off-the-cuff impression of the 64% price:

The real odds are probably higher. If this contract were trading for say 10% I’d guess it was overestimating the true probability because of lotto-ticket bias but also because there needs to be a healthy risk premium for seller to enter a highly negative skew trade.

I wouldn’t guess that a bunch of yolo-punting puts a price to 64% for lolz. When someone bids 64%, they are laying odds. Betting nearly $2 to win $1. The price of this contract has doubled in a week…it’s the buyer who likely brings more caution to the order book now.

I could imagine someone buying these as part of a relative value trade against selling oil options but the dollars available means it would need to be retail size and that kind of trade (oil vega vs prediction market?!) doesn’t seem like the kind of thing that would excite the class of trader who expects 20x leverage on crypto perps to get them outta bed in the morning.

If Polymarket depth was big enough to influence stock markets, there’d probably be some interesting scenarios of incinerating a few million bucks, maybe less, to influence the Poly price so you can influence the price of defense stocks where you could make tens of millions. The informational and liquidity linkages between prediction markets and traditional markets will be fascinating (appalling?) to watch as they continue to grow.

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• square root law
• the bias of hedging on implied delta

   

In this issue:

• more AI use examples
• options primer
• how taxes can influence option trades

Friends,

When I was in NYC a week ago, a friend pushed back our meeting by 90 minutes. I got a text and the calendar update. Didn’t think anything of it.

When we’re hanging out, I mentioned I’ve been tinkering a bit with AI to get more use out of the largest repo in our lives — our email inbox. My friend pulls out his phone and show me this app Poke. It was poke that pushed our meeting back on his command.

When he wakes up in the morning, Poke which is integrated with his Google suite, sends him a brief. It includes a summary of any emails or action items he received that it judges he would prioritize. It shows his schedule for the day. He had to deal with something pressing that conflicted with our appointment so he simply told Poke to notify me that he’d need to push the meeting back. Poke then emailed and texted me. He just treated his SMS like a personal assistant and it handled the rest.

This isn’t an ad for Poke, but just another thing I saw in the wild that previews how automation creep is about to turn into a flood.

Fun aside: When you onboard with poke you negotiate your monthly price with the app! The friend is well-known in investing circles and very online so the app tried to extract a high price arguing that it knew he was a baller. He got the price down 90% and told me he knows people that have gotten it to $0.

Back to email. I was thinking about marketing-related stuff for moontower. Over the years, readers have emailed me saying my content helped them land trading jobs or their boss told them to subscribe, or my post was forwarded to their desk.

[It’s a peacocky thing to say, but in the past year, the feedback is blunt about this letter being read at every market-making shop. The audience I have in my brain when I do the Thursday posts is an experienced trader who probably has juniors that he or she would rather say “go read this” rather than explain the things themselves. They’re busy trading, and I’ve already invested in the words so they can save their breath.]

I wanted to collect all these emails, but keyword search is far too manual. The ultimate crux of the problem is semantic understanding:

“My PM told the desk to subscribe” and “I got the offer at Citadel” are both results of interest, but there are many variations of these phrases and the words that comprise them share a wide range of contexts (“offer”, “desk”)

I asked the Gemini in Gmail to find them. It returned 4 when I’d expect hundreds, so its method lacks depth.

I turned to Claude to build a pipeline. It took some back and forth, but ultimately it worked beautifully. Which is exciting because it’s a reusable workflow for semantic search on any body of work, of which, Gmail is just one instance.

The pipeline is quite simple. This is how it works:

Step 1: Multiple searches using narrow keyword queries

• 14 targeted Gmail API keyword searches instead of 1 semantic query
• Each catches a different flavor: job language + “Moontower”, boss language + “newsletter”, forwarding language + “your post”
• Result: ~4,200 candidates
• Snag: First queries were too broad (13K results). Fix: anchor every query to “Moontower”

⚡AI Deliverable: Python script to push through Gmail API

Step 2 — Fetch the emails via API

• Gmail API pulls full email bodies programmatically — no export needed
• Result: 3,922 emails fetched
• Snag: Rate-limited at email 2,850. Fix: retry logic + caching to disk

⚡AI Deliverable: I actually used Claude extension in the browser to set up my Gmail API access

Step 3 — LLM classifies each one

• Claude Haiku reads each email: “Is this a finance professional affirming Kris’s work?”
• Categorizes matches: job placement, boss recommendation, team sharing, praise
• Result: 585 matches
• Snags: Wrong model string (3,900 silent 404s), API overload, ran out of credits mid-run, Python exception mismatch. Fix: incremental saving + resume flag

⚡AI Deliverable: This is the main AI magic. Classifying the email as something I’m actually looking for based on the context

Results

• 44 team/desk sharing
• 24 job placements
• 8 boss recommendations
• ~$3 API cost, ~8 hours runtime, 370 lines of Python

Now if I could only have my Twitter DMs accessible via this pipeline 🙂

Takeaway

Use each tool for what it’s good at. Search engines are good at retrieval, but LLMs are good at judgment.

Money Angle

It’s been interesting to re-share the evergreen investing/options posts via Twitter articles to see which one are getting lots of resonance now. Circumstances are different since the original publication date. I published quite a bit even when the blog was obscure so stuff that got lots of views or not were based on a smaller sample of readers.

Thus far in this re-publishing experiment, the most popular share has been about the levered ETF rebalance quantities.

On Friday, I re-published a guest post. It is already the most viral article I’ve put on X.

A Visual Primer For Understanding Options

Money Angle For Masochists

I bought June/Feb13 put calendar in SLV a few weeks ago when the vol spread inversion went nuclear.

That was a disaster.

SLV dumped 30% 2 days later.

The Feb puts I’m short are of course 100 delta, so the effective position is long a June OTM call synthetically.

💡If a stock is $80 and you own the 100 put for $25 and 100 deltas worth of the stock, then you are synthetically long the 100 call for $5. If you don’t believe me, look at your p/l payoff for the portfolio of long puts and stock at expiry for stock prices of $90, $103, and $120 vs what it would be if you just owned the 100 call.

We understand the position and the risk. But we don’t talk about taxes much here so I’ll use this example to introduce the complexity of the real-world.

Let’s say I roll my June puts.

Consider the tax implications.

I will realize a gain on the appreciated puts.

The puts I’m short that are now the risk equivalent of being long shares because they are so far ITM. I have a mark-to-market loss on these puts, but it’s not realized. This is a problem. The entire trade has been a loser, but if I roll my June put,s I crystallize a short-term tax gain. Ideally, I need to crystallize the short-term loss on the puts I’m short by buying them back.

If I don’t buy them back and get assigned, I don’t realize the loss. Instead, I acquire shares with a basis of the strike price minus the premium I collected when I sold them. If I sold the 100 put at $5, my cost basis is $95. The shares are $70, but my loss is still unrealized until I sell the shares.

The problem might not be immediately obvious, so let me break it down.

• If I roll my June puts instead of closing the entire position out, I have a trade that has been a loser, but the tax accounting shows a short-term gain + an unrealized loss.
• To crystallize the loss, I must buy my put back or sell the shares once I’m assigned. But, both of these trades sell lots of SLV delta. If my intention is to maintain a synthetic long call position (long stock + long ITM puts) I’m stuck with an accounting gain.

⛔Because of the wash sale rule I cannot sell my SLV shares then immediately buy them back.

• You can envision a scenario where SLV rallies up again, my synthetic call position recovers the economic loss but I have a taxable gain on the rally. My p/l on all the activity is a wash BUT I have loads of short-term taxable income!

Not picking up your matched short-term loss is leaving a dead soldier behind.

(Ok, that was dramatic. I’m sorry enough to say so, but not enough to delete it. I want to imprint it.)

There are a few choices whereby you can roll the puts, achieve the desired risk exposure but I’m not an accountant and this is not advice. There’s no wink here. Talk to an accountant.

Goal: crystallize short-term loss without getting rid of your long silver delta

Possible solutions

1. Once you are assigned, sell your SLV shares and replace the long with a highly correlated silver proxy such as other ETFs or silver futures. From an IRS interpretation of the wash sale rule, the futures are probably safer since COMEX is NY silver and SLV is London deliverable. But again, not an accountant.
2. Replace your length with assets highly correlated to silver, like miner stocks. The basis risk is obvious.
3. Close your puts and buy the stock at the same time, effectively buying a worthless synthetic call.

Let’s talk about #3 a bit more.

If the stock is $70 and the 100 put is only worth intrinsic (ie there’s no time value left in the 100 call), then that package is worth $100. The stock price plus the $30 put. Now you wouldn’t expect a market-maker to fill you at fair value.

I figured a market-maker might fill me for a penny of edge. When I was looking at the quote montage, the 99 strike call was offered at a penny so by arbitrage the 100 call should be offered at $.01

I tried to pay $100.01 for the package.

No dice. Nobody wanted the free money. I didn’t raise my bid, figuring I would try again on expiration day since perhaps a seller didn’t want to bother with the inventory. If they traded it on expiration day, the whole position would offset at settlement, and they would collect their easy penny.

Well, what happened?

My short put got exercised early! I got stuck with the shares and now have to sell the shares to crystallize the loss.

The interesting thing to point out is that paying up a penny to lock in a short-term accounting loss is a type of trade that’s win-win. The market maker sells a worthless synthetic option, I get my tax situation aligned.

This is a screenshare constructing a synthetic call in IB’s strategy builder, then adding it to the quote panel so you can see the bid/ask for the structure.

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• design patterns
• From Text ➡️ Dashboards

Friends,

My reading habits ebb and flow with my general focus. I read very little compared to my baseline in 2024 since I’ve been giving more time to writing, moontower.ai, and tinkering with new tools.

I subscribe to about 150 newsletters, but I read a small fraction of them. In my more focused phase, my filter is extremely tight. The article needs to satisfy one of 3 conditions:

1. Instrumental to something I’m thinking about
2. Someone strongly recommends it as something that I, in particular, would appreciate
3. By a handful of authors who never fail to provoke or entertain even if I didn’t think I’m interested in the topic (ie Reducible Errors, David Epstein, Adam Mastroianni)

A few years ago, feeling more “explore” mode, my filter was much looser. I’ve made my peace with the idea of tightening and the resulting FOMO. There will be a time to loosen it again. Just another example of life physics where “you can have it all just not at once”.

In addition to tightening the filter, the more focused period coincides with triaging articles differently as well. If the article is short and by a high-signal writer, I’ll usually read it right away. Otherwise, if the article seems worth reading (sometimes this is not clear from a topical skim, and nowadays with Gemini and Claude in my browser I can just ask them for the main points of the article in the sidebar and use that to tip the scale), I stash the link on a Notion page. Once I do get around to reading it, I’ll move the link to a dated file which gets archived. I have a running list of every article I’ve read. I started that habit 5 years ago. I also log every new restaurant I’ve been to by location. I’ve been doing that for 14 years. We are all unwell in our own ways, don’t judge.

In the past 18 months or so, the reading queue gets quite long. The days of reading list “zero” are long gone. I just let it grow without anxiety, knowing that the next time I fly, I’ll rip through it. I can’t sleep and rarely watch movies on planes. It’s trapped reading time.

This trip to NYC was no different. 10 hours of reading in the past week, means I have exhaust. Here’s the best of what I read:

The Last Useful Man: On Tom Cruise and the Case for Embodied Knowledge (11 min read)

This was not only a fun read but deals with a question of growing importance that we all sense — Why learn, if you can ask?

Dan Wang’s 2025 Letter (31 min read)

This was Dan’s annual review letter. The mix of writing and observation in this long piece resists summary because the point is the nuance. The way Dan dusts his personal opinions throughout without imposing them is a graceful verbal judo; the net effect is I give them more weight. Dan delivers on both substance and style.

Inherent Vice is PT Anderson’s Best Film (11 min read)

Freddie de Boer is an exceptional writer. He’s an auto-read. Except for that he’s prolific and often writes about things I don’t care about so there’s just a lot of work I must pass on. So when he chooses a topic I’d love to read about, I’m ready to dim the lights and light a candle. I’ve read and watched Inherent Vice. If you have done either, this article is a gift.

Experimental History posts

Finally, I’m not going to link to Adam Mastroianni articles since you can choose any one of them and be delighted. There’s no point in singling out any specific ones which may sound strange, but it’s really the highest compliment.

Finally, a quote I use a lot…

Judge talent at its best and character at its worst — Lord Acton

Which is why I don’t unsubscribe from writers that I deemed worth subbing to but don’t necessarily read often. I even pay for a bunch of them. I know they are doing good work, but for some stretches of time, to use another quote, “it’s not them, it’s me.”

Money Angle

I saved one of the articles for this section. An immediate favorite of the past year. It is a history of how information travels. It’s the kind of thing that should be adapted to a Veritasium video.

Asymmetry is all you need (35 min read)

What drives information markets, and why the transformer is unlike the telegraph, ticker, and terminal

So good.

Money Angle For Masochists

One of the traders in our Discord was discussing exotic options in commodities markets. The topic of APOs or “average price options” came up because of this tweet:

This is spot on.

From CME:

To understand why producers like APOs (also known as “Asian” options*) we should first understand what they are.

*Via wikipedia:
In the 1980s Mark Standish was with the London-based Bankers Trust working on fixed income derivatives and proprietary arbitrage trading. David Spaughton worked as a systems analyst in the financial markets with Bankers Trust since 1984 when the Bank of England first gave licenses for banks to do foreign exchange options in the London market. In 1987 Standish and Spaughton were in Tokyo on business when "they developed the first commercially used pricing formula for options linked to the average price of crude oil." They called this exotic option the Asian option because they were in Asia.

An APO’s payoff depends on the average price of the underlying asset over a specified period, rather than just the spot price at expiration. For example, an APO call option pays max(Average Underlying Price – Strike, 0) while an APO put pays max(Strike – Average Underlying Price, 0)

Asian options are particularly popular in crude oil for a few reasons.

1. Cash flow matching: Oil producers and consumers often transact at monthly average prices, making Asian options a natural hedge
2. Reduced manipulation risk: Averaging prices over time makes it harder to manipulate the settlement price
3. Lower cost: The averaging mechanism reduces volatility, making Asian options cheaper than standard European options with the same strike. An appealing feature in a cost-focused commercial business with tight margins.

Poking around online, this topical information about APOs isn’t hard to find, but understanding #2 and #3 is harder to see, so let’s touch on the actual mechanics of APOs with an example.

Suppose the price of WTI is $75 and it’s January 31. You buy the Feb 75 Asian-style put.

The put payoff will be $75 – (average settlement price of WTI of the prompt future in the month of February)

"average settlement price of WTI of the prompt future in the month of February"

Unless you have traded Asian options you wouldn't know how this is even computed. We'll use Feb 2026 as an example. 

The prompt future is the March 2026 contract until its last trading date on February 20. Then the April 2026 contract is prompt. 

Taking account of weekends and President's Day, the March contract is prompt for 14 business days and the April contract is prompt for 5 business days. 

February average price = average of 14 March futures datapoints and 5 April futures datapoints. 

Notice that each trading day in February contributes 1/19th of the final settlement price. On the last day before expiration, we have a running tally of the final settlement price — the average of the past 18 days’ closing prices. The last day’s price change is weighted by 1/19 to determine the final average for February.

This means that as you approach expiry, the gamma of this option is actually declining! You’ve already seen most of the flop, right? If the average going into the last trading day is $76, you’d need the futures to fall more than $19 on the last day for the 75 put to go in-the-money.

This explains why Asian options are less prone to manipulation and their deltas less sensitive to changes in the futures. It’s hard for the futures to move enough to materially change the average because each day gets a small weight in the calculation. This stands in stark contrast to vanilla options which have extremely high gamma near expiration. A mere 2-cent move through the strike just before expiry can be the difference between the option being 100 delta or 0 delta.

In this February option example, we are already in the “averaging period”. But what if you buy the December Asian-style 75 put on January 31? The averaging period, the calendar month of December, doesn’t start until 10 months have elapsed.

The pricing model will treat the option just like a vanilla option for 10 months, then account for how the last month’s gamma and theta shrink as each day in the averaging period contributes to the final settlement price. Your optionality is declining in that final month. Asian options have cheaper premiums than their vanilla counterparts because they act the same for some period of time, but then lose optionality relative to the vanillas in the averaging period.

In practice, a hedger may buy a “strip” of Asian options. For example, the Cal27 75 put refers to the “75 put Asian style for each month in the calendar year of 2027”. If the hedger buys 100 strips, they have bought 1200 options (100 options in each month). If a bank sells this strip to the hedger, typically in a bilateral OTC form, they could lay off the risk by buying this APO strip from market-makers. While these don’t trade on a centralized order book, the trades can be submitted to CME’s Clearport where the exchange acts as a clearinghouse and margining agent to both sides, removing counterparty risk to the street.

The bank desk does wear a trader hat in the act of facilitating this flow. They aren’t required to “back-to-back” the risk or cover it exactly as they opened it. For example, if the bank thought the vols in the second half of 2027 were expensive, they could just buy options covering the first half of the year effectively legging a short forward vol term structure trade. If they thought put skew was expensive, they could buy a call strip instead of covering the puts. This would neutralize their vega, but leg them into a short skew risk reversal. They could weight their own hedge in a way to express their bias. They could trade plain American or European options if they thought they’d get tighter prices from a wider pool of traders (more traders deal in vanillas then Asian style options) and sweat the Asian vs vanilla mismatch. The menu of possibilities highlights how valuable it is to have deal flow. You know you are getting to sell on the offer on one side of the deal and then you can try to trade mid or better when covering some or all of the risk. Commodity option trading is a fun global boardgame!

I’ll wrap up with this blurb from my friend Mat. I found it interesting because I have sometimes thought that it’s a historical accident that the most popular options are American-style vanillas when you can see how cash-settled European or even Asian-style options would make more sense.

Stay groovy

☮️

Moontower Weekly Recap

Posts:

• do you have to let it linger? (apparently yes)