hungry eyes

I was at the Collective meet-up in Menlo Park this week (this was the 3rd time I’ve attended and it’s always a great way to connect with investors and just amazingly bright people. I always feel like an ape in this group, but that’s better than the opposite). Shannon, faciliator extraodinaire, gives guest prompts beforehand so they are prepared, including some fun ones like this icebreaker:

share a song that lifted their spirits and why

My answer is Hungry Eyes.

The backstory:

My friend Matt’s bachelor party was in Costa Rica in the early 2010s. We rented a dope house right on the beach. About 15 guys flew in for it. On arrival day, the first fellas claim the best rooms and all that. There’s that dynamic y’all know. Mixing your childhood friends with your college friends, work friends and so on. We’re pregaming before going out for the night and it just feels kinda tense.

Everone down’s the parting shot, the van’s here. We file out, take our seats. It’s quiet as we pull onto a bumpy road. Matt connects his phone to the van’s sound system and throws on a playlist.

That unmistakable sound of 80s kitsch.

Hungry Eyes. Vocals kick in, mood starts to change.

By the time we get to the hook, it’s a full-blown Almost Famous bus scene.

All was copacetic from that point. One of my favorite memories period.

the real Y2k event

About 15 years ago, I read Drew Magary’s sci-fi novel The Postmortal. The book imagines a society that has created a pill of immortality. Your aging stops at the moment in time when you take the pill although it’s still possible to get hit by a car and die.

Civilization reorganizes around this new technology. Marriage contracts have a shelf life of 20 years. This reminded me of Larry David and Cheryl’s tiff, where Larry gets yet another self-induced cold shoulder from his wife, pressing his case that “til death do us part” means he’s free to see other people in the afterlife.

I went to the internet for a reminder of other outputs from the Postmortal world:

  • The Rise of “End Specialists”: Due to severe overpopulation and the lack of natural deaths, the government creates specialized roles to handle population control, with characters like the protagonist, John Farrell, working as “End Specialists”.
  • Widespread Violence and Dystopia: Society breaks down as “Greenie” environmental terrorists and pro-death protesters target those who have taken the cure.
  • The “Cycle” Trend: People adopt hedonistic lifestyles, traveling excessively or changing careers, as they anticipate centuries of life ahead.
  • International Reaction: Countries like China ban the cure and tattoo citizens with their birthdates, while others, such as Russia, militarize their “postmortal” population.
  • The “Correction”: The novel, told through diary entries, news reports, and blog posts, follows the decline of civilization into a “pre-apocalyptic” state, culminating in the “Correction”.

I’m not a regular sci-fi reader, but I should be since I find this recipe of change one major assumption about how the world works and then see how it propagates quite fun. (I am about to re-read Brave New World!)

In the vein of that recipe, there’s a short story I’ve had swirling in the back of my head for a decade. It’s never gonna see the light of day because

a) it’s not a priority and

b) its premise is probably going to happen, spoiling the story

It’s the story of everyone’s private info being leaked on the web. Tax returns, bloodwork, nude photos, Nest footage, emails, DMs, location history. The real Y2K event.

The Postmortal model strongly influenced how I thought about it. There would be a minority of people, like the pro-death protesters who opted out of taking the pill, who were viewed as some anti-progress hippie. It would be the group of people who opted out of looking at other’s private data.

Think of it as a voluntary non-proliferation of grievance. I value whatever privacy remained as of 2026, I assume you do too. We are all adults. We agree to just not look. And society cleaves between the lookers and the ostriches. There’s a whole sci-fi book to be written about every aspect of this.

One of my favorite movies did a skit that would resemble dating in such a world. I love the moment when it “hits” Steve Guttenberg, “It says all that?”

The idea of a non-looker might have been remotely possible when there was friction to sorting and searching through petabytes of files.

But when it’s all leaked, that friction will be gone.

“Hey Claude, have any good friends talked shit about me?”

About a year ago, my family went on a CA gold rush tour at Marshall Gold Discovery Park in Coloma. Strong recommend by the way. The guide is an absolute treasure of historical knowledge. Anyway, you see how the indigenous lived in those lands before the settlers arrived. Touring the site, I was viscerally struck by the lack of privacy that their way of life entailed. Large families coexist in tight tent-like structures. I had to be the one who asked, not quite in these words but with a mix of diplomacy and subtle gestures, “Where did they screw?” As you might guess, tribes didn’t need to do a birds and bees talk. It’s more of a show without the tell.

As tech zooms forward, do social norms loop back to prehistory?

N² – n: why shorting is mathematically cursed

Recall the levered silver flows post where we see the quick math of levered ETFs. For a fund to maintain its mandated exposure, the amount of $$ worth of reference asset they need to trade at the close of the business day is:

x(x - 1) * percent change in the reference asset * prior day AUM

where x = leverage factor

examples of x:
x=2 double long 
x=-1 inverse ETF
x= 3 triple long
x= -2 double inverse

This isn’t just a levered ETF thing. The -1 leverage factor is exactly the same as just a vanilla short position. It’s a sneaky reason why the shorting is mathematically challenged.

The easiest way to think of this as an individual investor is to imagine you have an account value of $100. The account is holding $100 in cash, but it’s the proceeds from shorting a $100 stock (assume you don’t need any excess margin to maintain the short). If the stock falls to $50, your account value is now $150 (your cash + $50 mark-to-market profit on the short). You earned a 50% return on a 50% drop in the stock.

Now what?

If the stock falls another 50%, you make $25.

$25/$150 = 16.7%

If you want to maintain the same exposure so that you make 50% on your account on that second 50% drop, you would have needed to short more shares at $50.

How many more dollars’ worth of stock?

-1 (-1 -1) x -50% x $100 = -$100

You needed to sell an additional $100 worth of stock or 2 more shares at $50. Then on that last leg down, you would have made $25 on 3 shares total or $75.

$75 profit /$150 account value = 50% return

Learn more:

🔗 The difficulty with shorting and inverse positions.

Moontower #310

In this issue:

  • post-privacy: musings as we hear more about Mythos and quantum computing
  • N² – n: why shorting is mathematically cursed
  • math shortcuts traders know by heart
  • almost famous

Friends,

Post-Privacy

About 15 years ago, I read Drew Magary’s sci-fi novel The Postmortal. The book imagines a society that has created a pill of immortality. Your aging stops at the moment in time when you take the pill although it’s still possible to get hit by a car and die.

Civilization reorganizes around this new technology. Marriage contracts have a shelf life of 20 years. This reminded me of Larry David and Cheryl’s tiff, where Larry gets yet another self-induced cold shoulder from his wife, pressing his case that “til death do us part” means he’s free to see other people in the afterlife.

I went to the internet for a reminder of other outputs from the Postmortal world:

  • The Rise of “End Specialists”: Due to severe overpopulation and the lack of natural deaths, the government creates specialized roles to handle population control, with characters like the protagonist, John Farrell, working as “End Specialists”.
  • Widespread Violence and Dystopia: Society breaks down as “Greenie” environmental terrorists and pro-death protesters target those who have taken the cure.
  • The “Cycle” Trend: People adopt hedonistic lifestyles, traveling excessively or changing careers, as they anticipate centuries of life ahead.
  • International Reaction: Countries like China ban the cure and tattoo citizens with their birthdates, while others, such as Russia, militarize their “postmortal” population.
  • The “Correction”: The novel, told through diary entries, news reports, and blog posts, follows the decline of civilization into a “pre-apocalyptic” state, culminating in the “Correction”.

I’m not a regular sci-fi reader, but I should be since I find this recipe of change one major assumption about how the world works and then see how it propagates quite fun. (I am about to re-read Brave New World!)

In the vein of that recipe, there’s a short story I’ve had swirling in the back of my head for a decade. It’s never gonna see the light of day because

a) it’s not a priority and

b) its premise is probably going to happen, spoiling the story

It’s the story of everyone’s private info being leaked on the web. Tax returns, bloodwork, nude photos, Nest footage, emails, DMs, location history. The real Y2K event.

The Postmortal model strongly influenced how I thought about it. There would be a minority of people, like the pro-death protesters who opted out of taking the pill, who were viewed as some anti-progress hippie. It would be the group of people who opted out of looking at other’s private data.

Think of it as a voluntary non-proliferation of grievance. I value whatever privacy remained as of 2026, I assume you do too. We are all adults. We agree to just not look. And society cleaves between the lookers and the ostriches. There’s a whole sci-fi book to be written about every aspect of this.

One of my favorite movies did a skit that would resemble dating in such a world. I love the moment when it “hits” Steve Guttenberg, “It says all that?”

The idea of a non-looker might have been remotely possible when there was friction to sorting and searching through petabytes of files.

But when it’s all leaked, that friction will be gone.

“Hey Claude, have any good friends talked shit about me?”

About a year ago, my family went on a CA gold rush tour at Marshall Gold Discovery Park in Coloma. Strong recommend by the way. The guide is an absolute treasure of historical knowledge. Anyway, you see how the indigenous lived in those lands before the settlers arrived. Touring the site, I was viscerally struck by the lack of privacy that their way of life entailed. Large families coexist in tight tent-like structures. I had to be the one who asked, not quite in these words but with a mix of diplomacy and subtle gestures, “Where did they screw?” As you might guess, tribes didn’t need to do a birds and bees talk. It’s more of a show without the tell.

As tech zooms forward, do social norms loop back to prehistory?

Money Angle

I made this joke a couple weeks ago. Except for it wasn’t a joke. I really multiplied 25×35 this way while sitting at my desk.

To spell out the link to investing math:

What did we notice?

a * b = Mean² − MAD² (where MAD = mean absolute deviation)

As soon as numbers deviate from the mean, their product is dragged down, even if the mean is unchanged. More deviation, more drag. And what is deviation? Volatility.

Bridging middle school math to investing math

In investing, we compound, or multiply returns. So even if the mean of two returns is identical, the dispersion between them matters. Not just matters. It matters quadratically.

No dispersion: The arithmetic mean of (8, 8) is 8. The geometric mean of (8, 8) is √(8×8) = 8.

With dispersion: The arithmetic mean of (5, 11) is still 8. But the geometric mean of (5, 11) is √(5×11) = ~7.4.

If you earn 10% on an investment and then lose 10%, your mean return is 0, but your actual compounded (geometric) return is 1 − √(1.1 × 0.9) = −0.50%.

Now increase the volatility: earn 40%, lose 40%. Mean return is still 0. Compounded return? 1 − √(1.4 × 0.6) = −8.3%.

The drag on your returns is a function of squared deviation. Put simply:

Compounded Return = Average Return − σ²/2

How many unique pairs from N items?

N² – n shows up in investing as well!

Recall the levered silver flows post where we see the quick math of levered ETFs. For a fund to maintain its mandated exposure, the amount of $$ worth of reference asset they need to trade at the close of the business day is:

x(x - 1) * percent change in the reference asset * prior day AUM

where x = leverage factor

examples of x:
x=2 double long 
x=-1 inverse ETF
x= 3 triple long
x= -2 double inverse

This isn’t just a levered ETF thing. The -1 leverage factor is exactly the same as just a vanilla short position. It’s a sneaky reason why the shorting is mathematically challenged.

The easiest way to think of this as an individual investor is to imagine you have an account value of $100. The account is holding $100 in cash, but it’s the proceeds from shorting a $100 stock (assume you don’t need any excess margin to maintain the short). If the stock falls to $50, your account value is now $150 (your cash + $50 mark-to-market profit on the short). You earned a 50% return on a 50% drop in the stock.

Now what?

If the stock falls another 50%, you make $25.

$25/$150 = 16.7%

If you want to maintain the same exposure so that you make 50% on your account on that second 50% drop, you would have needed to short more shares at $50.

How many more dollars’ worth of stock?

-1 (-1 -1) x -50% x $100 = -$100

You needed to sell an additional $100 worth of stock or 2 more shares at $50. Then on that last leg down, you would have made $25 on 3 shares total or $75.

$75 profit /$150 account value = 50% return

Learn more:

🔗 The difficulty with shorting and inverse positions.

Money Angle for Masochists

People like little tricks. I published this article on X and it got over a thousand likes which is 3 standard dev engagement for me (probably. I’m going off feel.)

🧠Math Shortcuts Traders Know By Heart

A random smattering from it:

Straddle to Vol

Implied Correlation

Implied correlation ~ index variance / weighted average stock variance

Using implied vols instead:

Implied correlation ~ (index volatility / weighted average stock volatility)²

Example:

If the SPX is 15% vol and a typical stock in the index is 30% vol, implied correlation is (.15/.30)² = .25

The Moontower Rule of 70

This is related to the Rule of 72 but allows you to solve for the CAGR if you know how much your money has grown in X years.

CAGR = 70% * (doublings/years)

Example:

Your home is up 8x in 50 years.

What’s the CAGR?

8 is 3 doublings

70% * (3/50) = 4.2%

Doublings might sound like a complicated measure, but you should get up to 2¹⁰ as quickly as you know your multiplication table for 12s.

If something is up 50x, that’s somewhere between 2⁵ and 2⁶ or about 5.5 doublings.

And just like that, you can estimate log base-2 fairly quickly for any number up to 1024!

Finally I published this tool on the website to estimate slippage:

📱Square Root Impact Calculator

This Week In The Options Trench

Last week, we talked about trading as a business. This week, we talk about options market making.

Some of the topics here were covered in further depth in Thursday’s half rant/half insider look: market maker privilege

From My Actual Life

I was at the Collective meet-up in Menlo Park this week (this was the 3rd time I’ve attended and it’s always a great way to connect with investors and just amazingly bright people. I always feel like an ape in this group, but that’s better than the opposite). Shannon, faciliator extraodinaire, gives guest prompts beforehand so they are prepared, including some fun ones like this icebreaker:

share a song that lifted their spirits and why

My answer is Hungry Eyes.

The backstory:

My friend Matt’s bachelor party was in Costa Rica in the early 2010s. We rented a dope house right on the beach. About 15 guys flew in for it. On arrival day, the first fellas claim the best rooms and all that. There’s that dynamic y’all know. Mixing your childhood friends with your college friends, work friends and so on. We’re pregaming before going out for the night and it just feels kinda tense.

Everone down’s the parting shot, the van’s here. We file out, take our seats. It’s quiet as we pull onto a bumpy road. Matt connects his phone to the van’s sound system and throws on a playlist.

That unmistakable sound of 80s kitsch.

Hungry Eyes. Vocals kick in, mood starts to change.

By the time we get to the hook, it’s a full-blown Almost Famous bus scene.

All was copacetic from that point. One of my favorite memories period.

Such a great prompt Shannon!

Stay groovy

☮️

 

Moontower Weekly Recap

Posts:

not all averages are created equal

What did we notice?

a * b = Mean² − MAD² (where MAD = mean absolute deviation)

As soon as numbers deviate from the mean, their product is dragged down — even if the mean is unchanged. More deviation, more drag. And what is deviation? Volatility.

Bridging middle school math to investing math

In investing, we compound, or multiply returns. So even if the mean of two returns is identical, the dispersion between them matters. Not just matters. It matters quadratically.

No dispersion: The arithmetic mean of (8, 8) is 8. The geometric mean of (8, 8) is √(8×8) = 8.

With dispersion: The arithmetic mean of (5, 11) is still 8. But the geometric mean of (5, 11) is √(5×11) = ~7.4.

If you earn 10% on an investment and then lose 10%, your mean return is 0, but your actual compounded (geometric) return is 1 − √(1.1 × 0.9) = −0.50%.

Now increase the volatility: earn 40%, lose 40%. Mean return is still 0. Compounded return? 1 − √(1.4 × 0.6) = −8.3%.

The drag on your returns is a function of squared deviation. Put simply:

Compounded Return = Average Return − σ²/2

From Text ➡️ Dashboards

We’ll start with some useful resources for the learners, then move to material for traders ready to do stuff.

CME Trading Simulator

While looking up data on CME’s website I came across this amazing, 100% free learning environment with live ticking data:

https://www.cmegroup.com/education/practice/about-the-trading-simulator

My demo vid:

Implied Forwards and Jensen (not Huang)

As I mentioned a few weeks ago, I’ve been re-publishing educational posts on X Articles which serves as spaced repetition practice for long-time readers or just bringing them to the attention of new readers who would be better served by a steady IV drip (no pun) of archival posts than attempting to raw dog the compendium.

These are 2 I think you’ll like:

From Text ➡️ Dashboards

I bought silver a year ago because of Alexander Campbell’s substack. He does a great job showing his thinking behind ideas with data and charts. This alone is helpful because it reveals “these are the datasets a smart guy pays attention to”.

AI tools are shortening the distance between “Hey, that’s neat, I should add that to my dashboard” and like actually adding it to your dashboard. Even if you stink at the world’s most popular coding tool —- Excel (see Will Claude Eat Excel?)

I used one of Alexander’s recent posts to whip up a silver dashboard. I’ll explain what I did, what I added, and share it with you so you can duplicate it as your own starting template. But the broader lesson is that agents are going to make all content “interactive”, we’re just not used to those patterns. Yet.

It is just another staple in my belief that as the cost of inference approaches zero the value of unique data increases. At one time oil was used for light and warmth. But when the automobile was born it claimed the largest cut of the barrel. If data is oil, more people everday are unlocking the ability to “refine” it by transforming it, building new logic and visualizations.

Let’s get to creating the dashboard.

One giant disclaimer:

Expectations are everything. AI is not going to one-shot this project. I’d estimate it reduced a 6 hour task to 90 minutes. Indulge my parental tone for a sec. It would be a mistake to permit this to let you work less in the spirit of that stupid Genspark AI Super Bowl ad. Instead, you should see this as “I can do 4x as many projects as I could before.” This may sound like hustle-porn (you know it when you see it, right?) but if that’s your attitude I offer 2 observations:

  1. You probably don’t like your work. If you do, then giant increases in productivity allow you to get even closer to the the best parts of your work.
  2. Regardless, this goldilocks period will end, everyone will know how to use the 21st century calculator, and 4x as productive will become the new baseline. Red queen. A very smart guy who used to work with me (he was the one who did a lot of the math and technical stuff that we’d need) works in real estate now. I suspect he’s in the top 1% of nerd in that industry. He recently applied for a job and failed a test that was intended to deomonstrate how resourceful he was in the context of AI tools. Knowing him as well I do, I found this shocking because he’s the kind of person that always does well on formal exams. Granted, he admits he’s not not using AI as much more than a google replacement. That this exam exists and a person like him failed, suggests the goldilocks period may already be drawing to a close. It’s not like real estate companies are living on the bleeding edge either.

On a positive note, I think you learn just as much in the compressed time as if you spent 6 hours. Instead of fumbling around with semicolons and syntax you learn how the internet is stitched together and how technologies talk to each other. Embrace manager mode.

Enough of that, moving on to the meat.

Step 1

Give Claude Alexander’s post Silver Moon.

Tell Claude to generate a dashboard in Google sheets inspired by all the arguments in the article. Examples include:

  • SOFR Rate — funding cost baseline for carry trades
  • Funding Rate — broker-specific borrowing cost (SOFR + spread)
  • ETF Prices — SLV, GLD, UUP, SIL, SILJ for cross-asset context
  • Derived Spot — London silver price via SLV ÷ oz/share
  • Futures Curve — next 5 liquid contracts with live prices
  • Expiry & DTE — days to expiration for roll timing
  • Basis — futures premium/discount to spot ($, %)
  • Annualized Carry — implied yield from contango/backwardation
  • Shanghai Premium — China price vs COMEX (arbitrage signal)
  • COMEX Inventory — registered/eligible silver (physical supply)
  • COT Positioning — commercial vs speculative positioning (sentiment)
  • SLV Shares Outstanding — ETF creation/redemption flows
  • SLV Oz in Trust — physical silver backing
  • Implied Volatility — options market fear/complacency

There are 2 key features that operate the sheet

Control Tab

We include a control tab for sourcing the relevant data. All of Alexander’s sources were public but whether you can automatically connect to them is another matter.

That’s why I like ot have a control tab which triages which sources are MANUAL, API, or SCRAPED.

Google App Scripts

This is the equivalent of VBA behind Google Sheets but it’s in Javascript which Claude will happily write for you whether you want to wire the sheet up to APIs or scrape.

Step 3

Troubleshoot. Claude’s sheet gets you 75% of the way in moments and then you spend 90 minutes on this step.

Most of the scraping failed. Sometime because Claude referenced a stale website. But even when you update the correct URL you quickly find that financial data websites tend to lockdown the ability to scrape.

I worked through each data source, iterating with Claude to find automatic (and free) solutions or writing AppScripts usually falling back to “manual” when necessary.

Finally, as I made changes to the spreadsheet there’s the expected debugging and tracing of formulas that happen whenever you delete stuff from a sheet someone else (in this case a bot) made. Pound ref and N/A always show up for a gangbang.

Step 4

Add spice to taste.

Alexander + Claude leapfrogged a lot of work. But there’s still plenty of room for your own judgement and creativity.

For example, when it comes to COT I use the fantastic tools on the CME website which aggregate both futures and options positioning.

I also added leveraged ETF tickers and logic that estimates how much silver there is to buy/sell based on their daily rebalances and even a first pass at computing market impact (see appendix).

Finally, I included a placeholder picture to compute the implied term structure from the SLV options term structure by backing out hard-to-borrow rates.

from moontower data infra

The google sheet is mostly self-explanatory but even if you get stuck just use Gemini in sheets or the Claude extension in a browser to mentor you along.

Here ya go:

🔗silver_dashboard

vega’s finishing move

“Vega wounds, gamma kills” is an esoteric expression that’s still common enough that you can google it and return a bunch of hits. It’s a reasonable acknowledgement of realized vol p/l being quadratic with respect to how large a stock move is.

I’ve recently been cross-posting my writing on how this works on X since they’ve been pushing their Articles functionality.*

* A lot of people (and bots) are boosting these. I am treating these releases as a spaced repetition exercise for long-time readers. Analytics show very high engagement so X must be signal-boosting them. This is a 1-year chart. The recent spike is Articles:
A lot of people cry about the growth of Articles longform on X but twitter is a long way from the community it used to be anyway, so don’t really care as much if I’m burning the house for warmth in the eyes of diehards. Although I don’t think I am since the reason I came to twitter in the first place was to find stuff to read and learn not hot takes. It's different things to different people and when they suppressed Substack it shifted the appeal for me. This is some re-alignment, albeit on their terms. Fine. It's a reasonable negotiation.

The Articles I’ve posted on the theme of non-linearity in options

This last one is about the “gamma” of vega. For OTM options, the vega of the option, its sensitivity to changes in IV, itself changes. We call that second-order sensitivity volga. Volga is to vega as gamma is to delta.

I don’t have a dedicated post on vanna I’ll cover it briefly right now.

Vanna

The definition of vanna you are most familiar with is change in delta due to change vol. You have heard of this because of dealer flow discourse. For example, if dealers are long calls and hedged with short shares, as vol declines on a rally, their long option deltas shrink. If this happens faster than their long gamma increases their net delta, then they will have stock to buy to rebalance to neutral.

But vanna has an alternate definition. One that dominates our understanding of trading skew:

the change in vega for a change in underlying

If you are short puts on a risk reversal as the stock falls, you get shorter vol and vice versa. Your vega changes as the spot moves.

I suspect the “gamma kills” idea is popular because it’s a common experience. Option volume is dominated by near-dated expiries where gamma and theta dominate the p/l. Most people will simply never feel what it’s like to be wrecked or celebrated by volga or by a delta-hedged skew position. They might know what it’s like to get crushed to vega directly, but even that will be less familiar than realized vol-driven performance, given typical trade duration.

But I can tell you that my most memorable p/ls have all had vanna and volga at the scene. 2020 was especially dramatic in this regard as an explosion in vols led to position sizes exploding and finding myself sitting on a growing pile of vega that varied from “increasing in demand” to “panic bid”.

Qualitatively, the repricing of vega is significant because vega is illiquid. You can delta-hedge your way to a replication of a relatively short-dated option. In a sense, the volume in the underlying itself is a form of liquidity for options even if the options themselves are illiquid. But this idea extending to a long-dated option is only theoretical. In practice, if you are short a long-dated straddle that doubles in value, the mark and its accompanying hit to your capital may leave you in a forced position. You don’t have the luxury of manufacturing that vol via delta-hedges for a year.

This will be exacerbated if you were short, say 100k 1-year vega, but because of vol exploding you find that you are now short 200k vega. Maybe you can stomach the p/l hit due to vega, but you might not be able to hold the new position size. If Street Fighter’s Vega had Mortal Kombat finishing moves, they would be called vanna and volga.

The recent silver move has been so crazy that vega p/l has dominated realized p/l (realized p/l is the tug of war between gamma p/l from the equation at the opening of the post and theta). It’s an outstanding case study in how higher-order effects are fundamental to understanding options.

We’ll begin with a classic “trap” trade.

Imagine back on Dec 31st, with SLV at $64.44, you bought put and sold call on the 60/100 risk reversal delta neutral with the plan to hedge the delta at the close each day.

This position starts:

  • Long vega
  • Long gamma
  • Paying theta (you laid out extrinsic option premium)
  • The 60 put you buy is 59.6% IV, the 100 call you sell is 78.7% IV

The risk reversal would have cost you $2.89 of option premium since the put is much closer to at-the-money.

💡I used the Moontower Attribution Visualizer to compile data for this article

What happens between when you opened the trade and the snapshot I took this past Tuesday, 1/27/26, when the stock has risen to $97.09 and the options still have over 3 weeks to expiry?

This daily hedged risk reversal has lost $.82 net.

You are short gamma albeit less gamma than you were long when you initiated the trade because the ATM vol is so much higher!

More things to note:

The IV on your long strike: 59.6% → 99.6% or 40 vol points!

The IV on your short strike: 78.7% → 99.4% or 25 vol points.

You won on the vega spread between the options.

So why did you lose money? Was it the realized vol? That seems suspect, after all, you were long gamma at the start of a big move. You’re short gamma now, yes, but it’s not even that much.

The clue is right there in the table:

You went from long 5 cents of vega to short almost 14 cents of vega as your short strike is now at-the-money.

Yes, the vol on your short strike went up much less than the IV of your short strike, BUT it went up when the vega of that strike was much larger than the vega of the strike you were long.

In short, you were getting shorter vol as vol was ripping higher. The vega p/l totally swamps the realized p/l:

from a long option holder point of view of a daily delta-hedged position

Here’s a snapshot from the interim on 1/13/2026, when the stock had rallied almost to the midpoint of the 60 and 100 strikes.

The 60 put you own has gone up over 7 points, and the 100 strike you are short barely budged from the elevated vol from the original skew. You are up $.37 on the hedged position…but your risk is changing quickly. You are now short vega, flat gamma, and collecting theta.

Wait, you are collecting theta without being short gamma.

Technically your gamma is very slightly short, but the point stands — in fact, if the 60 put IV was a bit lower you could even be long gamma and collecting theta.

New option traders will brag about such a favorable greek profile. An experienced trader knows that the ratio is an indication that you are simply short a premium IV and premium IVs happen near the prices where hell breaks loose. As I’ve said many times…the skew just tells you where the bodies are:

In sum,

Despite these options not being “long-dated” their performance has been dominated by IV. In this case, mostly through vanna which is best seen at the interim.

  • Despite the 60 put vol increasing 7 points, the vega of the option halved as it was now much further from ATM (it went from being a -33 delta put to -9 delta by 1/13/26)
  • Meanwhile, the 100 call’s vega doubled due to it becoming closer to ATM (it went from a 9 delta call to 21 delta).
  • Note that volga is not playing much of a role in 100 call vega doubling. The change in option vega can’t be due to IV increasing. Why? Because IV didn’t change on the 100 strike during the rally from $64.44 to $78.60!

From the vol convexity article, we know ATM options have no volga. In fact, ATM vega is insensitive to vol level and holding DTE constant, it only depends on the spot price!

But OTM options have a lot of vega to gain if IV increases since IV ripping higher makes all OTM options look closer to ATM as they are “less far away”. Their delta increases (vanna) and their vega increases (volga). In the above example, the 100 call IV did not rip higher by 1/13/26, so we couldn’t see volga in action. The vol only roofed on the strike once the option was close to ATM.

To give volga its due, we should zoom in on Monday when Feb SLV vol ripped higher on silver popping 10% (before giving back nearly half its gain).

We’ll look at a call nearly 14% OTM with less than a month til expiry.

The $1.33 of hedged option p/l for that call is only partially explained by the initial vega of .033 and a vol change of 26 points. The difference could be explained by the fact that the average vega of the call as vol (and stock) increased was probably closer to .05.

26 vol points x .05 vega = $1.30

Since the stock only rose by 6%, we can safely guess that the 50% increase in the vega of the option is mostly driven by volga.

Gamma is not the only killer. Any position that grows faster than the underlying changes contains risk that is not seen in a snapshot. That delta hedged vertical spread or risk reversal might look gamma, theta, and vega neutral today but that profile gets battered as soon the clock ticks and the waves start coming in. The snapshot neutrality is dangerous because it can easily lull you into thinking your risk is smaller than it really is.

Ask anyone who bought an SLV and nat gas 1×2 call spread because “the skew was fat” or because they are “long gamma, collecting theta” how that’s working out?

trading as a sudoku puzzle with prices as the given numbers

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).

RBOB futures curve on 3/26/26 via TradingView

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?

3/26/26…IEF vols up over a full click to about 10% IV

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).

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.

moontower.ai

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:

https://x.com/firstlawofvol/status/2037665294400020889?s=20

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.

Moontower #309

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).

RBOB futures curve on 3/26/26 via TradingView

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?

3/26/26…IEF vols up over a full click to about 10% IV

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.

moontower.ai

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:

https://x.com/firstlawofvol/status/2037665294400020889?s=20

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

Friends,

I tweeted something the other day that I want to expand on because it’s one of those ideas that’s simple on the surface but points to an exercise that would teach viscerally market-making.

https://x.com/KrisAbdelmessih/status/2035025124102217780

 

Polymarket has a contract “Will crude oil settle above $90?” It was priced around 73 cents. That’s an implied probability. We also know that the value of a tight call spread around the $90 strike represents a tradeable probability.

💡See a deeper understanding of vertical spreads

If you price a 89.5/90.5 call spread in Black-Scholes at 90 IV with a month to expiry, you get a “fair” probability that CL settles above $90. That number moves smoothly as the futures price moves. Technically, it has sensitivity to implied volatility (aka vega) and time to expiry BUT the vega of the spread is negligible and the time to expiry component is mirrored in the poly contract too. Both the contract and the spread are driven by what’s the chance of oil being above or below $90 at expiry with no consideration of how far above or below $90 we are which is more of a volatility question.

The Poly contract tracks the same fundamental question but if it around due to sentiment and order flow faster than what a basic random walk option model places the probability at you have a tradable idea.

You can measure how much it bounces relative to the underlying by computing its implied delta (how many probability points it moves per $1 in CL) and comparing that to the call spread delta.

If the Poly delta is steeper than the call spread delta, the market is overpricing per-dollar sensitivity. You’d sell the Poly contract and hedge with futures (or the call spread). If it’s cheaper, you buy it.

[How you actually manage the risk is part of the market-making lesson. The tradeoff between risk reduction and hedging costs become palpable.]

I do believe this simple example of “market-making around a fair value” is an incredibly powerful way to take the mystery out of what market-making is. It makes it very obvious that the business of market-making has nothing to do with prediction. I vibed a little sim that shows this in action.

The heartbeat chart on the left shows Poly odds bouncing around the call spread fair value as oil moves, and the scatter on the right plots both against the oil price, where the slope of the regression line is the delta. You can see the Poly line is steeper (by my construction). The difference in slopes creates the market-making opportunity. In this case Poly flows overreact to the futures prices.

If you want to build this with live data, you could use the Poly API and a feed for the futures price. I’ll argue that you don’t need a live feed of the call spread market.

Why?

You can just look up the implied vol for a strike near $90 from settlements that correspond to the Poly expiration and reprice the spread analytically as S moves. 2 of the four BSM inputs (T, K) are quasi-static, a third (implied vol) has little impact because it’s canceled out by the spread of long one option and short the other. Just track S in real time and recompute.

I’ve never built a market-making bot so I can’t speak to the execution side, but even building such a monitor would go a long way to teaching you about pricing, delta, and risk. All from one contract on Polymarket, a futures price and the Black-Scholes formula.

Are Traders on Kalshi Being Profiled? | 9 min read

Andrew’s fantastic post uses a simple taxonomy to classify participants on an exchange:

  • squares (uninformed)
  • sharps (informed)
  • dealers (liquidity providers)

Using Kalshi and Poly’s market design choices, he makes the broader point that exchange rules are dials that shift the balance of power among these three groups.

Anonymity and fee structure influence who shows up, who gets picked off, and how efficiently prices incorporate information. Anyone who has dealt with the labyrinth of option exchange fee, allocation, order book priority, and crossing rules will nod along.

Of special note is Andrew’s warning to those trying to “copy-trade” perceived sharps.

Sharp traders could respond to this by fragmenting their trading across multiple accounts. They may have an account that has negative PNL on a certain market type. This account is unlikely to be copy-traded. When building a position, they would prefer to use this relatively anonymous account, rather than suffer the price impact of having their trades copied before they’ve built their position. If copy-traders are too aggressive following the sharp account, this creates an incentive to build the position on the anonymous account, and then trade in the followed account, generating further price impact and increasing profits. Is this manipulation or simply smart situational awareness of the impact of your trades? If the intent was to buy a large position anonymously, then buy on the main account to trigger copy-trading, and then sell at higher prices to those copy-traders in a third account….. that sounds like the kind of thing you eventually read about in an enforcement action, at least if it happened on a regulated market.

I would be cautious about using simple copy-trading strategies. The lesson is not to ignore all counterparty information, but to recognize that sophisticated traders are aware of it and can adapt.