market maker privilege

Trader is a broad term. Uselessly broad if it encompasses jobs from the Vanguard employee who sends the rebalance order 4x per year to keep VOO in line with SP500 weights to the oil trader who flies into contested lands to broker cargos to a warlord. The word “trader” flatters a healthy share of W2 earners while underselling big-stakes dealmakers. Trading itself is a business, capable of being traded, bought and sold, while the soldiers within the business themselves are also called traders.

The trading decision to bother at all with this project we call “trading” is more important than the trades you make if you do bother. This is why it’s important to understand the nature of the various careers that count as “trading”.

Market Makers

“Market-maker” is a weird word. The first time I ever heard the alliterative phrase was being asked in an interview to “make a market” on some quantity like “how many McDonald’s are in Philadelphia”.

Eyes just glazed over. Like what does that sequence of words mean? Like you want me to go make a market? Like set up a McDonald’s in Philadelphia? The words did not compute at all.

When I see a Asian HS kid with a swag tee that includes Jane Street’s logo in the sponsorship roll, I promise you that 16-year-old knows what a market-maker is. Times have changed. The job literally pays 21-year-olds the same amount a doctor makes by the time they are in their prime only after not sleeping in their 20s during the institutional hazing period known as residency. It’s the same pool of high achievers, but one group got the memo that being a millionaire by age 27 is better than just starting to chip away at a million dollars of debt if we count in pre-tax dollars.

There’s no twist here. Ball don’t lie. The market-makers have a sweet gig. That’s why it’s hard to get. Also, the kids they hire to become market-makers…well, they’re smarter than you. You can get all triggered and start the whole EQ or “street smart “ song and dance and you wouldn’t be totally wrong, but you’d be wrong. Those kids get hired because they’ve outcompeted many other kids who, unlike in my day, are aware of the job, aware of what it takes to get the job, and really, really want the job.

Now, if your goal is to be financially successful and you found this in any way to be discouraging, then you have told on yourself. Your powers of observation and creativity are holding you back more so than your brains. You’re also a quitter and may not have a claim to even a single original thought. Since nobody in their right mind would surrender to these charges, I assume nobody feels discouraged. We’ll proceed.

The point is, it’s a job with a honed criteria. On average, you must be tall to play basketball. No controversy. But this job of market-maker is just that. A job. You’re not an entrepreneur. You’re not consumer-facing. You aren’t a deal-maker. You’re a polar bear. Adapted to a specific environment. I’m not saying these people couldn’t adapt in another one, I’m only saying that they are specialists, which is a neutral statement.

The job doesn’t require as many hats as one that must constantly interface externally or with clients, suppliers, or investors. You just talk to other nerds and maybe, if you have a Chicago or Brooklyn accent, some brokers.

Which is all to say — it’s a weird thing to fetishize. If you’re going to fetishize a job just because it makes money, what happened to rockstars or center fielders or Scott Disick.

The fetish with market-makers or almost all professional traders is misplaced. Most professional traders have exactly what the dreamers don’t want. A job. They have a job in a system. With a boss. They are highly specialized at piloting that lucrative system, but it’s not their system. A fighter pilot is a decent analogy. You have an exceptional person tuned to commanding a complex, cutting-edge machine. You want a great pilot to maximize its potential. But if we’re being honest, the machine matters more. If you have a 2.5 standard deviation pilot instead of 3, I suspect that doesn’t matter as much as having the best jet. If you’re a market maker whose machine can’t win a race, it won’t matter that you’re smarter than the trader at Jump.

Unless…

You’re not entering the battles or the races where the machine is the showcase. The traders who have the biggest p/l’s don’t necessarily get to keep the most, because they are the same traders who had the fastest plane. Well, a lot of that performance is credited to the tech. The seat.

Since I left institutional trading, I’ve had a chance to meet traders I didn’t think existed. I’ve been paid to simply be a sounding board for people who have more money than they have any idea what to do with. Money piled high by trading for themselves in active strategies. Sums that pods would be thrilled with, but this is personal capital. Those are the traders I’d think would be in the mind’s eye of the aspiring trader. No obligations to investors. Very few or even no employees. The trading versions of Phil Ivey.

[I don’t think I’d be stepping out of turn to share some commonalities I noticed in my conversations with these traders. They were all under 35. They were almost all obsessed, although some were leaving that phase. Having more loot than you can spend in a few generations is probably demotivating to anyone who isn’t a megalomaniac.

Which leads me to what I did not expect…they were all humble. It wasn’t an aww shucks humility. It came across in the way they listened. Sponges. Parsing everything. When I say humility, I mean low ego, as in they didn’t bring assumptions to the way they listened. It felt out of the ordinary and yet they all shared this quality. It left a mark on me. Since meeting them, the absence of this quality is now more noticeable.

Oh, one amusing contrast. There was this recent Pmarca bit where he shit all over introspection, meanwhile, I recall this group of traders being way out on the right tail of introspection and self-awareness. Could be a selection effect as I was approached by a 3rd party about meeting them, so I wouldn’t meet the people who didn’t agree to it.]

Anyway, back to the market-makers toiling away in their getting-paid-like-a-doctor-in-the-80s job. They’re not raising a flag, but by virtue of their academic excellence and persistence, have successfully landed, at least a temporary inheritance, of a lucrative seat. The seat is a legacy from a process I outlined in A Former Market Maker’s Perception of PFOF:

What’s absent from the narrative is how tall the pile of bodies these firms stand atop. I should know. I used to be able to work five hours a day (NYMEX alum holla) and make a lawyer’s wage. And in some years, a law partner’s carry too. Well, if you were smart you saved your money and realized it wasn’t going to last. The days of “locals” (ie wildcat market-makers) is long gone.

Many of the small firms, who saw the writing on wall and had an appetite for the long game, plowed money back into massive technology capex. Most of them just earned the right to say they lost to the best. In some cases they found small, profitable niches where they play the role of suckerfish. Respect to them, even this was not easy.

How about the remaining firms? The private giants the media likes to call “shadowy”. They were the ones who were most adept at assembling teams of software and hardware engineers working with game-theory geniuses to devise algos in a cat-and-mouse battle with competitors. The ones who stayed step-for-step with the exchanges who themselves were experimenting with matching engine rules, data, product listings and connectivity in their own battles for market share.

The truth is progress is cutthroat.

It started with skill and luck. The early big bets on talent and technology meant they were bringing guns to a knife fight. SIG wasn’t know as the “evil empire” on the Amex just because of the black jackets we wore. They understood the risk-reward was completely outsized to what it should be 25 years ago. They were amongst the first to tighten markets to steal market share. They accepted slightly worse risk-reward per trade but for way more absolute dollars. They then used the cash to scale more broadly. This allowed them to “get a look on everything”. Which means you can price and hedge even tighter. Which means you can re-invest at a yet faster rate. Now you are blowing away less coordinated competitors who were quite content to earn their hundreds of percent a year and retire early once the markets got too tight for them to compete.

SIG was playing the long game. The parallels to big tech write themselves. A few firms who bet big on the right markets start printing cash. This kicks off the flywheel:

Provide better product –> increase market share –> harvest proprietary data. Circle back to start.

The lead over your competitors compounds. Competitors die off. They call you a monopoly.

Option market-making is not a monopoly but an oligopoly since a handful of firms control a vast majority of the market share. Oligopolies tend to emerge in industries where high fixed costs are a barrier to entry.

Options market-making derives its high fixed costs from technology capex and the need for extensive market coverage. You can’t price options competitively in a thin margin game if you cannot see and connect to flow. You need both speed and breadth. If you can’t price well and access uninformed orders, then you only get filled when you’re wrong.

All the talent, pipes, compliance, quoting infrastructure, data, and regulatory overhead have to be procured and maintained whether you trade one contract or a million. Whether the VIX averages 9 or 29 for the year.

This is all easily apparent to anyone who’s been around the industry. But I’ll add a more editorial thought. Exchanges are the archetype for a business with “network effects”. They are expensive to build and maintain, but the biggest hurdle is the chicken-or-egg problem of attracting liquidity.

Unfolding today, in the wake of Hyperliquid’s great success, there’s a swath of perp exchanges trying to grab a foothold. 10 exchanges aren’t gonna make it…but it’s a lotto payoff for the winner(s). Spoils to the victor of the tournament. Spoils in the form of excess profit. Network effects mean wide moats for incumbents. These are businesses that are closer to monopolies.

I was at the NYSE and the NYMEX before they each “demutualized”. They went from being member-owned organizations that were thought of as utilities to public companies. The incentives shifted from the desires of member firms who had trading permits to public shareholders listening in on quarterly earnings calls.

This is America. What have you done for me lately? Where’s my 15% annual growth? And not only do I want the growth, I want the put. Give me consistency. Well, conveniently for exchanges, some of their biggest customers are those steady oligopolies. You want them to be happy. You want them to be good credits.

At some point, the marginal benefit of allowing an additional market maker’s ability to effect pricing in hopes of growing the pie is not worth destabilizing the symbiotic equilibrium the exchange maintains with its existing market-makers, especially as volumes hum along.

In the past 25 years, we’ve gone from 4 option exchanges to 18. Some of these have been spinoffs from incumbent exchanges. Some have been backed by the market makers themselves. You can make Friedman-esque justifications for these investments such as “customer choice”, but it’s also the standoff at a drug deal. Every investment is another gun drawn, maintaining both the tension and stability of the current equilibrium.

As we zoom in from the industry point of view to the day-to-day business of filling orders, we find the rules of engagement which inherit from the higher-level negotiated equilibrium. A mix of privilege and obligation. This is the environment in which those who become market-makers slot into when they accept their “trader” job.

From this point, we launch deeper into the privileges that accrue to these market-maker seats regardless of who sits in them.

On The Trading Floor

I started on the American Stock Exchange (AMEX) on Trinity Street. It was one of the 4 option exchanges back in 2000. The AMEX was a “specialist” system. Specialist is a technical title granted to a firm on a per-symbol basis by the exchange. It confers a set of rights and obligations to a primary market maker. For example, SIG was the specialist on the AMEX for IBM options.

The specialist was in charge of broadcasting electronic quotes to the world. Market makers would “stand in the crowd” in front of the IBM post and announce their own markets, ie bids and offers, for the different option series.

If a market-maker and specialist disagreed, they could trade with each other. If there are no disagreements, the broadcast market was the aggregation of the best bid and ask from the market-makers and specialist. In the case of a multiple-listed option, for example, IBM trading on the CBOE, the agglomeration of best bids and asks is known as the NBBO (national best bid/offer).

It is hard to find a picture of what this looks like on the web, I had to dig this up from the AMEX Alumni Group on Facebook.

Floor brokers would receive orders from trading desks and investment funds, walk over to the post, and either request a quote or expose their bid/offer. If they announced a bid or offer, this is now legally public information. It was not public before it was vocalized. Similarly, an electronic order is not public until it routes to the exchange and is represented on the order book. A specialist had a waterfall view of the orders arriving and had to represent it to the crowd so that the market-makers, the specialist, and any broker in the crowd had an opportunity to fill it inside the NBBO. If they chose not to, the order if it could, would be matched with any customer bid or offers resting on the order book. At those prices, the resting customer orders had priority over market-makers but any imbalance could be filled by the traders, routed to another exchange, or if there was no marketable opposing order, it is left to rest unfilled, assuming it had a limit. Market orders, of course, always find a price.

Notice how much optionality there is in standing on the floor. You get the right of first refusal. Even more subtly, you get access to tells. If a broker buys IBM calls, then approaches the crowd again, you might guess she’s a buyer. You see the same people every day. You start to notice patterns. Today, people program computers to spot patterns. Then you could see the order urgently sprint or leisurely stroll into the crowd. The benefit of all this is bundled into the general term “time/place advantage”. We will come back to this, to see how it persists today.

This advantage is not free, but it was available to anyone with sufficient capital (low 6 figues was sufficient but not advisable) to fund a margin account with a clearing firm and either buy or lease a seat. You also had to pass a membership exam to make sure you knew the floor rules. There are lots of rules about how orders have to be handled, communication conducted, and general compliance. The test was about as hard as the Series 3 but not nearly as hard as the 7.

In addition to time/place advantage, specialists were entitled, depending on conditions to 30-40% of the volume that traded on the published markets after any customer orders were satisfied. The market-makers in the crowd had to split the remaining 60-70% (I might be a bit off on those percentages; it’s been a while). Some crowds were chill. Some were cutthroat. It wasn’t common, but things could be fisticuffs tense over whether that 40% meant rounding up or down a single contract of an order in something as juicy as an index option that trades by appointment. Also, where you physically stood in the trading crowd could easily mean the difference between hundreds of thousands of dollars per year. Standing close to brokers or being cozy with the specialist was the original co-location.

[Random aside: I met a buddy of mine who had a similar career path, although he came up through Knight/Citi back in the MSFT crowd on the Amex. Really nice guy, a year younger than me, also Cornell. He got assigned to market make in that crowd a few months after I joined it. We were both pretty young in that group and looked out for each other as much as we could in the context of working for competing firms. Somewhat recently, he told me a story of how I got into a nose-to-nose shouting match with a broker who tried to bully him when he was new and he never forgot that I stood up for him. I don’t even remember it. Which goes to show that confrontation, despite being uncommon, was still way more routine than most jobs.]

In exchange for time/place and allocation advantages, specialists were expected to maintain “orderly markets”. This means being willing to quote all the option chains for each name assigned to your post (this could easily be 40 stocks). All the strikes, including the deep-in-the-money high delta strikes, where you are more likely to get picked off if your model has the wrong underlying price because the bid-ask in the stock goes wide. There were guidelines about how wide you needed to quote based on how risky the stocks were. The privileges outweighed the burden provided you had enough know-how to price options and navigate different market conditions.

If you were too weak or meek in your liquidity provision duties, the exchange could re-assign your specialist post to another firm. The exchange was sensitive to market share. They wanted strong traders who could price tightly to lure flow away from competing exchanges once options became listed on multiple venues, breaking any single exchange’s monopoly.

The upshot of this storytelling is that option market makers exist at the intersection of statutory privilege in exchange for obligations set at a high bar. If the bar is too low, privileges are granted without a commensurate improvement in market quality, however you care to define that. If the bar is too high, then the privileges are not worth pursuing.

Wherever that bar is set, one thing is certain — the fairness or anti-competitiveness of its product will be debated. Which is fine, but as you’re about to see, the statues are esoteric. It’s not discourse you are used to hearing about. And behind every rule, there is a winning and losing lawyer, both of whom were paid by extremely rich clients.

Let’s examine some privileges, shall we?

[A note on the research: I relied on Claude’s Research Mode to surface citations, but I only chose to focus on items that were salient to my business. I pre-applaud your masochism. This is like reading Warhammer rulebooks.]

I’ll classify the privileges into 2 categories

Moats: Barriers that keep non-MMs from competing away the margins. These barriers have costs.

Time/place advantage: execution advantages that directly generate P&L

Moats

The Professional Customer Classification (The 390-Order Threshold)

If you are a market-maker looking to leave the mothership and start a hedge fund that tries to be a market maker, you might wanna be aware of the “390 rule”.

Any non-broker-dealer customer who averages more than 390 orders per day during a calendar month loses “Priority Customer” status and gets treated as a “Professional”. You are then queued behind Priority Customers and stripped of customer-level fee treatment.

💡Why 390? That’s an order a minute for the 6.5 hours the market is open.

In addition, cancel/replaces count as new orders, complex multi-leg orders may count each leg separately, and brokers must review customer activity at a minimum quarterly and reclassify within 5 business days, while ISE requires aggregation of “obviously connected” accounts to prevent splitting orders across multiple accounts.

The practical implication:

Most obviously, you cannot just stream a 2-sided quotes as if you are a market maker. More subtly, being cast a “Pro cust” loses Priority Customer allocation priority and are treated the same as broker-dealer orders. For the people who did trade on the floor, you might remember the provision that allowed you to not honor your quote for an order that came from a professional broker dealer. The “390 rule” rhymes a bit.

Also, the 390 threshold hasn’t been adjusted since inception despite the explosion in order volume.

Fast pipes

Market makers pay for and receive preference for faster pipes. This enables effective market maker “protections”. For example, if you get filled on too many contracts over a small time interval, or take on too many deltas too quickly, the protections kick in and “panic” your quotes (ie widen them way out) because there’s a good chance you’re getting picked off by. Lots of execution software have the ability to tune these settings but they’re only as good as the pipes they operate on.

Portfolio Margining & Capital Relief

Risk-based margin using OCC’s TIMS framework. Qualified traders get roughly 6.6-to-1 leverage vs Reg T’s 2:1. For registered MMs, FINRA Rule 4210(a) allows margin on whatever basis is “satisfactory to both parties,” with the binding constraint being net capital haircuts under Rule 15c3-1.

Ultimately this rule gives prime brokers room to innovate on how they account for risk and feels less heavy-handed and more market-based. But it’s something outsiders are less aware of.

DMM Seat Concentration & The PFOF Loop

This is one I wasn’t aware of exactly but Claude surfaced. Would love if any readers can verify. It’s esoteric but important since the most desirable flow to trade against is usually less than 15 contracts or so.

DMMs receive the first 5 contracts of any order at exchanges where they hold designation. Exchanges almost never reassign DMM seats. This combines with PFOF to produce a self-reinforcing loop: the DMM pays PFOF to brokers, brokers direct flow to exchanges where that firm is DMM, and the DMM captures the guaranteed allocation on that flow.

I thought there were internalization mechanisms that would supersede this but again open to learning.

Reg SHO Locate Exemption

When an options market maker needs to sell stock short to delta-hedge, they are exempt from the requirement to first locate shares. Instead market makers receive an extended close-out window of T+4 under Rule 204.

If the market-maker fails to deliver:

on a standard short sale, it must be closed out by the beginning of trading on T+2 (one settlement day after the T+1 settlement date).
in the course of “bona fide” market making, they receive an extended timeline of T+4 (three settlement days after the T+1 settlement date).

FINRA has intensified scrutiny on this issue. The 2025 Annual Regulatory Oversight Report warns that merely having an exchange’s market making designation does not per se qualify for the exception. A new reporting requirement as of Dec 2025 will give regulators order-level visibility into which short sales invoke the MM exemption.

Claude identifies the “locate exemption is the single most economically significant MM privilege”.

There used to be a time when the window before your shares were “bought-in” was 13 days. I was strictly in the futures markets in those days but I heard of strategies where MMs would cover then short again to reset the clock. You can basically get away with buying synthetic stock via combos way at big discounts in hard-to-borrow names without getting hit with the big financing fee on the short leg of the arbitrage.

No first-hand experience here, so treat this like gossip.

Position Limit Exemptions

This one was a pain in the butt as a large option trader in USO but without market maker status.

Standard position limits are tiered at 25,000 to 250,000 contracts based on the net delta option positions.

When USO was a $20 stock, 250,000 contracts amounted to about 5000 WTI futures options contracts which isn’t a huge position when you trade a few thousand lots a day. I can remember needing to build a tool that wpuld compute how many USO options I could trade on one side of the market if a broker showed me a deal. “Well, I got this many expiring Friday, so next week I’ll be able to do the trade, sorry”. I’d even look into trading rev/cons just to free up capacity in case a juicy trade came along I would have enough regulatory lot overhead to do it.

Meanwhile exchange-registered MMs are exempt from the limits.

Time/Place Advantage

Guaranteed Allocation / Priority in Order Matching

On most options exchanges, designated/primary market makers receive a guaranteed percentage of incoming order flow when quoting at the best price — independent of how many others are also at that price. This is reminiscent of the specialist or designated market maker system (the CBOE doesn’t have specialists; it has DMMs).

Current allocation rates by exchange (again according to Claude):

Nasdaq ISE: PMM receives 60% (one other participant at best price), 40% (two others), 30% (more than two). Precedence on all orders of 5 contracts or fewer.
NYSE American Options: Specialist guarantees of 40–60% depending on the number of controlled accounts on parity.
MIAX Options: PLMM receives the entire allocation of orders of 5 contracts or fewer when quoting at NBBO.
Nasdaq PHLX: Directed Order Flow Program allows up to 40% participation when quoting at NBBO.
Cboe Options: DPMs/LMMs receive priority through pro-rata allocation combined with the marketing fee pool.

Exchange crosses and “QCC”

The time/place advantage that makes upstairs traders throw their turret through their monitor is the floor market-makers’ right to “break up a cross”.

This is best explained with a scenario.

Let’s say the consolidated screen market for the USO June 100 put is $6.20-$6.90 25×25.

The screen is only “25 up” meaning that’s the full displayed size on the NBBO.

A broker has a customer who wants to pay $6.75 for 1,000 lots.

The broker “shops” the order, calling upstairs option traders, funds he knows are active in the name, or even some commodity market makers.

He gets a hold of me.

I agree to sell 1,000 at $6.75. The client is happy, the broker gets to charge both me as the “solicited order” and the original client commission (the broker is said to have “double billed”— at $1 per contract the broker makes a quick $2k).

High fives all around.

Just one more step. The trade has to be “printed” on an exchange to go on the public tape before it can be submitted for clearing.

Well, the market-makers on the floor know I was solicited to “cut” the market. Even though they are offered at $6.90 on the “wire”, they want to sell at $6.75, especially knowing that the “solicited seller” who is probably a vol trader is offered there. It’s a pretty good trade to sell on someone else’s offer!

So the market makers have a few choices. They can wait until the broker starts announcing the trade, remember the broker needs to represent the bid and offer aloud by announcing “$6.75 bid for 1000, at $6.75. Trades”. Then, market makers pounce, hitting the bid when he announces it. My solicited offer goes unfilled, the broker only gets to bill the original client, and has an unhappy seller on his hands.

This is all quite adversarial and risky. It goes down like this in fiercely competitive crowds. But the normal way this happens is in the context of a repeated negotiated game. The broker understands the market makers have the right to “break up the cross” and the market makers understand that if the broker doesn’t bring flow to this floor as opposed to another, they’ll never eat.

So they haggle.

The market makers might say we’ll let you cross 600 contracts but we want to sell 400. The broker says his solicited seller won’t go for that and he’ll “take the order away to another floor to cross”. The market makers relent, “fine we’ll settle for 20%” and the deal prints.

The market makers have a large advantage. They get the last look. They get to know the solicited trader’s intent. And finally, they get a crazy “free roll”. Let’s say USO tanks in the window of time between when I agree to sell the puts and the broker representing the orders to the floor. The put fair value might jump up to say $7.00 and the market makers not only pass on selling puts but they decide to jump in front of the original customer order and lift my offer paying $6.80. This would be a disaster for the broker. The original client is unfilled and now the puts have run away from them, while I, the solicited offer whom the market makers perceive as a competitor, get picked off. The broker has 2 unhappy customers. Realistically, the broker wouldn’t open themselves up to such a fiasco (although sometimes they happen…there is an amount of money where an iterated game becomes worth sacrificing for single windfall).

You can see how powerful this market maker time/place advantage is. It’s so strong that in the last few years, Citadel started putting market makers on at least the CBOE. SIG always had market makers on every floor so the broker cannot threaten to “take the order away”. SIG is going to make sure it gets its tribute.

Now there are mechanisms for crossing option trades electronically. It’s known as a Qualified Contingent Cross (QCC). It allows the broker to cross the trade without exposing the options leg to the normal auction process, but it must meet specific criteria:

The order must pair the customer’s options order with a stock order; delta-neutral ratios are common.
It must be at least 1,000 contracts on the options side.
The package is crossed at a price that’s at or between the NBBO.

The rule was designed for large institutional hedged trades where breaking up the package would create execution risk, as I described above. The idea is that the stock and options legs are economically contingent. You wouldn’t do one without the other.

The QCC mechanism eliminates the floor traders’ last look advantage but only for orders that meet the criteria. For a live (ie unhedged) option order, you are forced to expose it to either an electronic auction or a trading crowd.

Going from memory, most QCCs print on the PHLX, as they targeted this volume with rebates or monthly fee caps, but again, don’t quote me on that. Even when this is your job, it’s a task to stay on top of all the changing fee schedules.

If you want even more detail, I stepped through some examples in a chat with Jason:

Wrapping up

The romantic notion of being a “trader” exists, but it’s a small percentage of those who identify with the title. Market makers are traders who are deeply embedded in a system of privilege and obligation. They operate within an optimization and constraint function that is relatable only in the abstract and incomplete way that any business you are not fully in is.

If you put different people in the same seat, you’ll get different results. But it’s not the absolute p/l that matters, but the VORP. There’s a y-intercept to that seat’s p/l that derives from technology and access that wouldn’t exist at another firm. You can think of the y-intercept of profits like operating margin instead of p/l.

If you don’t believe me, eavesdrop on a manager giving his trading pod henchmen a year-end review. You’re a special snowflake when they recruit you, but a commodity when they pay you.

Hey, at least you didn’t have to take the MCAT.

how to get arbed with perfect information (again)

In this issue:

cross the “bridge of asses”
scaling laws of risk reduction
“research collector” skill

The “Bridge of Asses”

📺Option Pricing Explained: No Arbitrage + Financial Mathematics from a Quant | 52 min watch

Doug Costa (SIG quant, former math professor, and the teacher I learned Black-Scholes from 25 years ago) builds no-arbitrage derivatives pricing from scratch using a binomial tree. No calculus, pure replication.

The thing I want to point you to is the profound role of the no-arbitrage axiom. It is the basis of derivatives replication and, by my assertion, represents the “bridge of asses” in investing education.

As a reminder, since nobody clicks links, Wikipedia says the pons asinorum or “bridge of asses” is:

used metaphorically for a problem or challenge which acts as a test of critical thinking, referring to the “ass’ bridge’s” ability to separate capable and incapable reasoners

The notion of replication is the pons asinorum of investing education because it is:

the conceptual rails of looking at a web of branching future payoffs, seeing how they could be replicated, and measuring the cost of that replicating portfolio today. It is the formalization of finance’s deepest truth — you cannot eradicate risk, but only change its shape.

You could make an even stronger claim that it lies at the core of decision-making itself, as it formalizes opportunity cost.

And I say this without being able to appreciate its deeper impact. Doug pauses for a moment in the video to marvel: when you add no-arbitrage condition to the standard axioms of mathematics, he says, the entire field of financial engineering “blossoms” out.

His colleague frames the no-arbitrage axiom joyfully:

Either we get a formula [so we win mathematically]. Or it’s violated and we make free money. Either way, we win.

Towards the end of the video, Doug discusses reflexive pushbacks he’s encountered after teaching this.

“One piece of pushback is typically, well, maybe it’s just that with stock prices, you don’t really know the probabilities. So it’s just a matter of knowing the right probabilities— if you could really discover somehow what the true probabilities were, then it would be better to use them [than the risk neutral probabilities].”

Doug’s rebuttal shows how you would still be arbed.

“I’m going to give you an example to debunk that idea. And I call this example the coin flip contract. So I’m going to postulate that there’s a company, a corporation, that finances itself, not by selling stock, but by selling what they call coin flip contracts. And the corporation has gone to great trouble and expense to manufacture a perfect coin, meaning a coin that is exactly 50% to be heads and 50% to be tails every time it’s flipped. So the probabilities are always 1 half and 1 half guaranteed…

You can watch the video, but I paraphrased it here as well. Here’s how it works.

A company issues coin-flip contracts based on a provably fair coin. The contract pays $150 on heads, $75 on tails. These trade in a secondary market at $100. Interest rate is 0%.

So we know everything. The probabilities aren’t hidden or estimated. They’re printed on the coin: p = ½.

Now: what’s the no-arbitrage price of a 110-strike call on this contract?

p̂ = (100 − 75) / (150 − 75) = ⅓

Call value = ⅓ × $40 + ⅔ × $0 = $13.33

Delta = (40 − 0) / (150 − 75) = 8/15 of a contract

Now suppose you say: I know better. The real probabilities are ½ and ½, and I’m not going to ignore them. Expected payoff is ½ × $40 = $20. So you buy the call from me at $20.

Here’s what I do next. I’m short the call. I immediately buy 8/15 of a contract to hedge.

Heads: My 8/15 position gains 8/15 × $50 = $26.67. Plus your $20 premium, I have $46.67. I owe you $40 (I have to buy the contract at $150 and sell it to you at $110). Net: +$6.67.

Tails: My 8/15 position loses 8/15 × $25 = $13.33. But I have your $20 premium. Net: +$6.67.

Every time. Both states. Guaranteed $6.67. I haven’t predicted anything. I don’t care what the coin does.

What did you get? Heads: gain $40 on the option, paid $20, net +$20. Tails: lose your $20 premium, net −$20. You’ve turned a coin flip into a coin flip — a $20 bet where you win or lose based on what the coin does.

If you try to hedge back? Doesn’t matter how you move delta. Win more on heads, lose more on tails. Move it down: vice versa. The best you can do is lock in a guaranteed $6.67 loss.

You had perfect information about the true probability….and you still got arbed buying the calls (you should have bought the contract!).

The market-maker doesn’t need a view on the coin, just the ability to trade the underlying and the derivative simultaneously. And acquiring the knowledge to cross the “bridge of asses.”

A random personal thought:

I suspect is kind of triggering for some people. It offends one’s sensibilities to think

that understanding derivative pricing ends up trumping knowledge about the true odds of things.

It’s like you spend all this time researching and learning and at the end of the day some market-maker knows just enough to not trade at the wrong price with you anyway. I’m overstating that reality, getting picked-off is real and market-makers are rightfully paranoid. But I guess that’s why I’m drawn to replication as a way of thinking. A trader is just looking for some free money when your bid or offer presents a contradiction. And that hunt makes all prices a little smarter, which, is a public good (but also a frustrating result for traders themselves, which is why the job is always uphill. A byproduct of your success is a smaller TAM).

Just to be thorough, this replication thing applies mostly to derivatives. The arb needs to be able to trade the derivative and the underlying and all advantage comes from the relationship between the two. The arb is useless without relative value.

Related learning:

🔗 Understanding Risk-Neutral Probability | Moontower

🖥️Moontower Presentation on Black Scholes “As a Trading Strategy” | Slides

The slides for that presentation are based on this post: The Intuition Behind The Black-Scholes Equation
There’s also a video where I do this as a presentation for the Moontower Community. This is an unlisted vid so please don’t share widely:

The Scaling Laws of Risk-Reduction

In a misconception about harvesting volatility, you learn that you do NOT need to scalp the gamma to isolate the vol of an option trade.

If you buy options implying a daily vol of 2% per day and it moves 4% per day, your expectancy is positive regardless of whether you hedge or not. That doesn’t mean you will win any more than it means you will win if you flip a fair coin and receive 2-1 odds. You have made Sklansky bucks, not necessarily real bucks.

RIP Sklansky

Hedging reduces the p/l variation around the expectancy.

In Financial Hacking, Philip Maymin explains

The inability to hedge perfectly continuously impacts your trading by introducing random risk. This risk decreases if you hedge more frequently, but only as fast as the square root. Therefore, if you want to halve your risk, you have to hedge four times as often.

He makes this tangible and practical when he says:

Noise from hedging a one-year option on a daily basis instead of continuously is about the same as one volatility point. If you make one volatility point in expected profit and the standard deviation of your profit is one volatility point, then your Sharpe ratio is about one.

His final point echoes my argument that a requirement to hedge to isolate vol is a misconception:

The risk from not hedging continuously can be diversified away.

I built a simulator so you can see this scaling law in action.

An oblique insight can be witnessed if you set up the simulation with negative expectancy, ie pay 24% vol for a stock that realizes 20%. The more you hedge the more certain you lock in negative expectancy.

Doug Costa actually showed that happen in the toy example above. The investor who bought the 110 calls based on the real-world probability but then hedged by shorting the mispriced security actually assured themselves of a loss.

If you have no edge, variance is your friend. Not financial advice.

🎮Moontower Discrete Hedging Simulator

Research Collector Skill

With LLMs lowering the effort on info-gathering I figured why not include citations to literature on this topic for those who think purely in math.

I had Claude devise a Research Collector Skill.

Its purpose:

When building an interactive tool or educational artifact that demonstrates a quantitative concept, this skill gathers the academic and practitioner literature behind the concept and produces a research lineage panel — not a flat bibliography, but a structured narrative showing how ideas built on each other.

This is what it produced and what you can find in the dropdown at the end of the tool:

Foundation — The 1/√n Result

When Is Time Continuous?

Bertsimas, Kogan & Lo — Journal of Financial Economics, 2000

The foundational paper. Characterizes the asymptotic distribution of replication errors from delta-hedging in discrete time. Introduces “temporal granularity” — a measure of how well discrete hedging tracks a derivative’s payoff. Proves that for European options under GBM, the hedging error standard deviation scales as 1/√n where n is the number of rebalancing intervals. Derives closed-form expressions for calls and puts.

web.mit.edu/lkogan2/www/Papers/WITC.pdf (free PDF)

Extensions — Generalization & Irregular Payoffs

Evaluating Hedging Errors: An Asymptotic Approach

Hayashi & Mykland — Mathematical Finance, 2005

Generalizes Bertsimas et al. (2000) from one-dimensional diffusions to continuous Itô processes driven by multidimensional Brownian motion — covering stochastic volatility models, non-Markovian settings, and data-driven hedging strategies where the true model is unknown. Shows the hedging error converges to a time-changed Brownian motion.

galton.uchicago.edu/~mykland/paperlinks/hedgeerrors.pdf (free PDF)

↳ addresses a limitation of the foundation paper…

Discrete Time Hedging Errors for Options with Irregular Payoffs

Gobet & Temam — Finance and Stochastics, 2001

Shows the convergence rate depends on payoff smoothness. For standard European calls/puts (smooth payoff), the L² error converges at rate 1/√n. But for digital options (discontinuous payoff), the rate drops to n^(1/4). This matters practically — hedging binary options is fundamentally harder than hedging vanillas, and more frequent hedging buys you less improvement.

↳ extends to delta-gamma hedging…

The Tracking Error Rate of the Delta-Gamma Hedging Strategy

Gobet & Makhlouf — Mathematical Finance, 2012

Shows that adding gamma hedging (hedging with a second option) can improve the convergence rate from 1/√n to 1/n for smooth payoffs. The tracking error is driven by the third derivative of the price function rather than the second (gamma). Gives conditions on trading dates to achieve optimal convergence.

hal.science/hal-00401182/document (free PDF)

Practitioner — Volatility Arbitrage P&L

Which Free Lunch Would You Like Today, Sir?

Ahmad & Wilmott — Wilmott Magazine, 2005

The practitioner bridge. Derives closed-form expected profit and variance of profit for delta-hedging mispriced options. Key insight: hedging with implied vol gives path-dependent but always-positive daily P&L when on the right side (RV > IV for longs). Hedging with realized vol gives path-independent total P&L but wild daily swings. Also covers optimal portfolio construction across multiple mispriced options.

spekulant.com.pl/…/DeltaHedgingVolatility.pdf (free PDF)

Trading Volatility

Colin Bennett — Santander, 2014

Comprehensive practitioner reference. Page 95 states the normalization coefficient for the hedging error formula is √π, giving the full result: σ(P&L) ∝ ½ S² σ² T Γ × √(1/N). Covers the full landscape of volatility trading — skew, term structure, and practical hedging mechanics. The standard desk reference for vol traders.

trading-volatility.com/Trading-Volatility.pdf (free PDF)

Hedging Errors & Options PnL

Lihong — The Logbook (Substack), 2024

Clear, modern walkthrough of the hedging error framework. Connects the discrete hedging variance to the diffusion scaling intuition (price variance ∝ √time, so hedging error ∝ √(1/frequency)). Also covers the impact of return autocorrelation on optimal hedge frequency — negative correlation (mean-reversion) reduces the benefit of frequent hedging, while positive correlation increases it. References Ahmad & Wilmott and Bennett.

freeportlogbook.substack.com/p/hedging-errors

Code — Open Source Implementation

QuantLib: DiscreteHedging Example

QuantLib Project (C++)

Production-grade C++ implementation of the discrete hedging Monte Carlo in the QuantLib open source library. Simulates replication error across random scenarios, directly implementing the Bertsimas-Kogan-Lo framework. Useful reference for verifying simulation logic against an independent codebase.

github.com/lballabio/QuantLib/…/DiscreteHedging.cpp

a cleaner way to compute seasonal vol

Vivek emailed me a simple question after reading yesterday’s does revenue seasonality translate to vol seasonality? post:

Why not just compute volatility from the daily returns within each calendar month instead of using a trailing 20-day window?

Um, well, eh. I don’t know. I guess just had a blind spot. I think of rolling realized vol instinctively. But for a seasonality study, it has a problem I already flagged in the post: a big earnings move in August gets recounted ~20 times as the window slides over it, smearing that vol into September.

It’s just unnecessary. So I added a section to the notebook that computes calendar-month realized vol directly: take each month’s daily log returns, compute √(mean(r²)) × √252, and you get one clean RV number per month per year without overlap.

Did the calendar month realized vol (CMRV) method change the story?

The earnings effects and their seasonal patterns does look sharper.

May, June, August, and November are now the clear relative-vol peaks. Feb earnings are not important as the May and Aug earnings are capturing the bulk of the year’s revenue recognition.
September, which looked like a peak in the rolling version, drops to a trough. It was borrowing August’s earnings move through the sliding window. Once you measure September’s own returns, it’s quiet.
The late-year volatility surge now concentrates in November, an earnings month, where the rolling method showed strong effects in December.

August is now the single largest effect size, the only month exceeding the “medium” threshold. June is close.
September flips to a quiet month once you stop smearing.
The scatter plot confirms it’s not one wild year: August dots are consistently elevated across the sample. All 3 of these charts are controlling for IWM.

A few more charts just to round it out:

The updated notebook is here: 👉 HRB Seasonality Study

Thanks again to Vivek for the feedback. Vivek was one of the senior quants at SIG when I was there. He’s also a chess genius if you’re into that.

does revenue seasonality translate to vol seasonality?

Last month H&R Block (NYSE: HRB) sold off hard on AI fears.

Implied volatility soared to a new 1-year high.

I wouldn’t have noticed if I wasn’t prepping materials for the kids’ Investment Beginnings Class. In the class, we learn how growth expectations as embodied by P/E multiples combined with what earnings materialize to generate a return that is some mix of reality and how those expectations are revised as investors “see the flop”.

HRB is a low P/E, high earnings yield company whose growth days are a distant memory. It doesn’t have a lot of upside but if it can maintain its current earnings and multiple its earnings yield of 16% (P/E ~ 6) looks like a super, super distressed bond. I know bonds and stocks have different hockey stick diagrams, but stay with me.

Selling a cash-secured put has similar risk characteristics as buying a bond. You collect some yield, your upside is capped at the yield, and you risk the notional amount of the strike if the stock zeroes. With the implied vol jacked, my thinking is all that vol belongs to the left of the distribution. I’m not bullish on the company. I’m not really anything as I’m not studying the company in any fundamental depth but my sling-from-the-hip trading attitude is:

This company has survived every existential threat thrown at it — the transition from brick-and-mortar to internet filing, the rise of TurboTax, and a significant increase in the standard deduction. Looks like a cockroach.

And they don’t fancy themselves more than that. Between buybacks and dividends, their shareholder yield is similar to their earnings yield. They are distributing all the cash back to shareholders so those earnings aren’t trapped inside a melting ice cube.

With implied vol jacked, I decided instead of buying the stock outright I’d skim the yield by “selling my own version of a bond”. I sold some 40 delta puts and sized it such that if I were assigned on them, it would not amount to more than 1% of my portfolio.

That’s all storytime background. I’ve written about seasonality in the context of commodities and futures spreads but HRB is a dramatic example of seasonality in an equity.

Today:

We’ll explore how to even observe the pattern and consider how it influences option pricing.
The post will include 2 Jupyter notebooks you can fork and let Codex or Claude Code run the same analysis on any tickers you like. They will automatically pull yfinance. One notebook is focused on stocks and another is focused on commodity ETFs.

A seasonal business

For as long as I can remember, I’ve heard that there are many retailers that make most of their earnings during the holidays. I’ve never verified the numbers but it makes sense. This suggests to me that much of a retailer’s annual volatility should be concentrated around Q4 results.

I never thought about how a company like HRB would also have extremely lumpy earnings. HRB’s fiscal year ends June 30. FQ3 (Jan–Mar) and FQ4 (Apr–Jun) together account for roughly 90% of annual revenue. FQ3 alone, peak tax season, is about 60% while FQ1 (Jul–Sep) is a rounding error.

Revenue has been stable around $3.4B since recovering from a 2022 restructuring. Net income sits around $554M. EPS has grown from $3.08 to $3.51 over the last few years despite flat earnings (shrinking share count).

The natural question: does the stock’s realized volatility reflect this extreme business seasonality?

Vol Has A Tax Season Too

I computed 20-day realized volatility (annualized) for HRB from 2016–2025 and broke it out by calendar month. I used SPY and IWM as control groups.

The green-shaded bands are tax season. I only show that chart for larger context but I find it hard to see clearly in that view.

Instead, I will show charts with more granular groupings with the observations that pertain to each.

Not suprising, but HRB’s median RV20 runs about 10 to 20 points above IWM in every month. This stock is always noisier than the market.
The most excess vols occur in May/Jun, Sep, Nov/Dec. This makes sense. Earnings are reported in Feb, May, Aug, Nov and the subsequent realized vol is much higher than non-earnings months.

What about March? This one is curious. Perhaps there are possibly real-time tea leaves that fundamental PMs might look at during the heart of tax prep that can lead them to trade. Or maybe this is when analysts write about tax season. For now it’s a puzzling observation.

The IQR band widens in June, Sep, and Dec meaning not only is the ratio higher, but the variance of the ratio is higher. More uncertainty about the uncertainty. Dec isn’t explained by earnings, so that’s another strange observation to note.

We can observe higher volatility related to earnings. But I would expect this for any stock. I’m suprised the earnings/post-earnings period in May-Jun doesn’t stand out as far more volatile since that report contains the bulk of the year’s earnings information.

I asked Claude for some statistical treatment even though I don’t really think “doing stats” on this little data beyond casual inspection provides marginal informational warrants raising your confidence. Turns out just asking the question did lead to some education but not how I intended.

I asked Claude to hypothesis test and generate z-scores for each month vs the mean mean log ratio of HRB to IWM vol for the entire sample. It went off and performed a t-test that generated 5 sigma z-scores in the most volatile months.

From what we’ve seen so far, that just sounds ridiculous. When I pushed back on Claude it explained that the standard error denominator in the z-scores as shrunk by √n.

Do you see the problem?

For 10 years of data, if you compute 20d trailing RV for each day in the month you will have about 200 observations per month which shrinks the denominator by a factor of √200 ~ 14. But 19/20 days overlap in the data from one day to the next. You really only have about 10 samples. Basically, one month per year when your window is 20 days.

Instead of totally putting the breaks on a statistical output, I was curious how Claude would deal with this.

It computed a stat called Cohen’s d which treats N as 10 for each month.
June (d = 0.50) is the only month approaching a “medium” effect size. December (d = 0.42) is close.
The percentile chart: a typical June sits at the 69th percentile of all month-medians. September at the 67th.
The scatter plot is a sanity check. Each dot is one year. June and September have consistently elevated dots, not one crazy year pulling the mean.

Finally, we use a heatmap to look under the surface. We can visually inspect trends or outliers, and can even be a launch point for specific inquiries like “Gee, what happened in Spring of 2020?”

The first chart, which doesn’t control for IWM, shows the impact of Covid. The second chart invites you to say, “Let’s toss 2016 and 2017, and see how the seasonality would reveal itself”. Small sample size, but May through Sep, Nov and Dec do seem more volatile.

That said, I’m not sold on May earnings being even more significant than later earnings, which is to say seasonality embedded in HRB’s revenue calendar does NOT seem to bleed into one of its earnings being that much more special than the others.

As December goes, I sparred a bit with ChatGPT on possible causes for elevated HRB volatility, even controlling for benchmarks and it gave 5 reasons that me groan. This was the best one and it feels meh:

Tax names can be unusually sensitive in December because investors are thinking about rule changes, credits, deductions, IRS readiness, and filing complexity for the coming season. Even when nothing dramatic happens, the possibility of change can raise uncertainty around demand for assisted prep versus DIY.

Wrapping up with stock seasonality

As promised, here’s the notebook to replicate the study or apply to another ticker of your choice

👉 HRB Seasonality Study

It pulls data from yfinance, computes 20-day realized vol, and generates all the charts you’ve seen here.

It also partitions return analysis by month. Example charts:

I didn’t go into that here since my bias is that seasonal features of volatility are more reliable than return seasonality, but you’re free fork it and play around.

Extensions

I measured realized vol, not implied vol. None of this pretends the option market isn’t aware of the seasonality. I didn’t study IV at all so the questions are green space.
The title of this post is “does revenue seasonality translate to vol seasonality?” I looked at one relatively small company in the grand scheme of things. Lots of cross-sectional green space to examine. Hopefully, there’s some inspiration in this post that you can extrapolate to broader studies.
Commodity ETF seasonal volatility

I forked and modified the notebook into one more tuned for ETFs (for example, it doesn’t control for equity benchmark volatility).

👉 ETF Seasonality Study

The US Natural Gas Fund (UNG) regales us with its wildly seasonal behavior:

Go run it on WEAT.

It makes sense. Commodities make sense. I don’t know what to make of stocks. Maybe that makes me crazy for being short those HRB puts.

They were originally May puts, but I rolled them forward to April. Don’t want the earnings risk and because giant sell-off was recent the April’s still had a fat bid.

Let’s leave it there.

Greg Newman of Onyx on Odds On Open podcast

📺How the World’s Largest Oil Derivatives Trading Firm Is Navigating the Iran War | Odds on Open

I’m biased considering I traded oil options for nearly 20 years but this interview is pure heat. Ethan Kho’s sat for a lengthy interview with Greg Newman, co-founder of Onyx, the world’s largest liquidity provider in oil.

Let’s go right to the excerpts (emphasis mine).

Interviewer: The oil markets have been crazy recently. How do I make sense of it all?

Greg: Honestly, I’d argue to begin with that it’s not like you should know something. There have been many crises, but this is unprecedented, and as a trader in particular it’s been very, very difficult.

There are so many oil contracts and so many liquidity pools out there. Brent and WTI are the key contracts that most traders and finance people know — that’s really the pool people dip into to hedge. But even that market, which is normally super liquid, has had its basis completely break down for a lot of these hedges. We’re used to at least one, two, three cents bid/offer, deep liquidity, lots of high-frequency traders, all that. We’re now talking 50 cents per barrel bid/offer minimum. And as you’re hedging, the price swings dollars per barrel at a time. It just breaks the whole system, because so many things in the oil world — all the contracts for every different product around the world, every region — ultimately link back to those core liquidity pools. When everything is broken from that sense, it’s incredibly hard to get a handle on it. So speculation has, to some extent, been out of the water. It’s been very difficult to do… What’s actually going on in the physical market gets reflected in these more niche contracts, of which there are many, many more, but they’re less liquid. That’s our specialty. Unless you’ve had exposure to those, it’s probably been very difficult to get an accurate reflection of what you should really be trading to profit from this.

How Onyx manages process when liquidity breaks down

Greg: We are market makers. There’s obviously a proprietary element to that, as you and your audience know very well. The temptation always is to combine your market making, look for some arbitrage-type opportunities, and then layer a discretionary element on top of that — ride momentum, things like that. But to begin with, it was really about getting to grips with the fact that you’ve got to take that discretionary overlay off the table. It just doesn’t serve you, because you’ve got people defaulting, people who can’t finance their positions. There are people whose only job is to take risk off the table because they’ve either blown up or they need to hedge, and it’s just not an orderly move. So you go back to your core business model — and you have to ask whether your core model is even suitable for that regime. The discretionary, hedge-fund-style approach is just not going to fare well in this scenario, certainly not at the beginning.

All the high-frequency traders looked like they were out of the game, to some extent. Maybe in the last couple of days they’ve been back in, bits and pieces, but certainly nowhere near the kind of medium-frequency trading they usually do. That’s been blown out of the water, and you can see it in the volatility. So you go back to your core model. Any model you had, any automation you had — it just doesn’t mean anything in this market. You go back to manual. You’ve got to be fully on top of it. It’s kind of basic in its process: you have a month-one price, you add your time spread, you infer the rest of the curve, then you keep adding differentials. That’s not too hard to see how to do. But they’re all moving so aggressively that just keeping everything in line is 90% of what we focused on. Because then what you’re able to do is spot the things that are so far offside that you can take them on — not to hold a proprietary view, but to back out of the liquidity with a correlated contract, something traded a bit further down the forward curve. Just going back to basics — fair value, trading what’s in front of you.

[Kris: This is exactly what I meant in Timing the Market when I describe taking off the discretionary trader pipe and glasses and putting on the market-maker boots and scrubs:

Trading is compensation for a service. In other words, a role. Don’t lose sight of the role. The easiest way to remember that is to ask yourself, “If I’m buying X at this price, what is it cheap against?”

The mantra stops you from drawing lines in the sand. From turning a relative value game into a…timing game. That’s what an outsize position relative to your business is — a timing bet.]

As you build infrastructure and a brand for liquidity and people come to you because you’re reliable, that’s when it pays off, because they’re not really looking for a good economical price — they’re looking for liquidity, and that’s what we do. So it was a good test of our business model. If you didn’t have that, honestly, the only move was to stay out of it until you could spot something not obvious but where you felt relatively safe — and that was just very, very dangerous to do.

Pricing fair value on Sunday night with no precedent

[Kris: I love this. Mock traders only need apply. Back to basics in a fast market. Snap judgements born from reps.]

Greg: Breaking it down — you have the Friday-night indications, and it’s our job to be completely 100% in the know. It cannot be partially in the know. So the moat we’ve got is our relationship with the brokerage firms around the world and the dark pool of liquidity we’ve got great visibility over. It’s not like other markets where it’s all electronic. It’s barely electronic, and in a time like now, electronic trading basically goes out the window, apart from the core one or two contracts. So this is where the niche expertise comes in.

Number one: you did know where it was Friday night. That’s not going to be completely irrelevant — you’ve at least got your starting point. We’ve also got traders who’ve been doing this long enough that they have a general sense of the relationship between big moves in the outright contracts — WTI and Brent — and Middle East wars, and generally what should happen to the refined products, how the curve should behave, how the time structure should behave, how clients tend to behave. And if you’re in our game with the kind of market share we have — 20–30%, sometimes 50% of some of these contracts — you’ve got a very good sense of how people are positioned. You know the weak spots in the curve, the strong parts in the curve. That’s not going to change, because at the very least people are going to sell what they own and buy what they don’t own. So you at least know where those things are going to come in.

So it becomes about having a very good feel for how the curvature started and how the relationships were working before, overlaid with analysis. You’ve got a weekend in oil, thankfully, where nothing trades, and you can use that time to look at previous times — what’s happened before. For example — it’s getting a little niche — naphtha, which we use for cracking to make petrochemicals, is a really key contract with Iran. They produce so much of it and send a lot of it to China, and China makes a lot of petrochemicals. So that’s a real sweet spot for Iran when an Iran situation kicks off. You’re expecting a reaction there.

Physical market participants and the reflexivity of hedging behavior

Greg: And then you’re expecting — okay, if all these things were to get higher, we know the behavior of, say, refiners is going to change. That’s the other thing about this market that’s different to maybe every other asset class. In a way it’s relatively illiquid, but so sophisticated. What that means is, for most contracts around the world, when there’s a big price move of any differential or time spread — let alone the outright price — it can reveal or destroy someone’s economics very quickly.

For example, a refiner says, “okay, I’ve got to hedge what I produce versus what I buy” — what we call the margin. They’re selling this kind of diff. And if it suddenly goes up $5, some of these bigger refiners have made an extra $5 billion on paper for the rest of the year. So they want to lock that in. Their behavior changes at certain price levels. The producers change their activity. And again, going from $80 to $120 oil, you’ve gone from maybe pretty good economics for a producing country to suddenly the best budget they’ve had in five years. So if they can lock that in, that’s what they’re going to do.

Another thing that’s unprecedented: how involved governments and producing countries have been in the futures market. Usually they’ve said, “look, we’re too big, we don’t want to hedge everything, it’ll just mess things up.” But we saw the US Treasury sell WTI — or at least it was reported that way — selling WTI swaps throughout the year, 11 million barrels, which isn’t a huge amount, but in a market like this it’s huge. You’ve got Saudi Aramco, BP, Shell — these guys who own a lot of the oil infrastructure in the world — they’re hedging. In real time you’re seeing their economics change, them trying to lock it in on paper, then suddenly those economics flipping on their head and deteriorating, and then the reverse.

Shipping companies are like, “look, this is great for my economics.” Airlines have done incredibly well from their hedges because they’re long, and they’re very active hedgers, and suddenly the hedge is way in the money. They’re going to want to lock it in. The airlines are a good example, because they hedge based on predetermined travel and fuel usage — that’s what determines the size of their hedge. So suddenly the price skyrockets as much as it does, and then you have disruption for airlines — there have been reports of something like a thousand flights a day cancelled around the Middle East. Suddenly they don’t have that physical consumption anymore. So they’re like, “well, we’ve just got a long position then, we’re just speculators now.” So they rush to take profit.

The jet fuel market in particular got most of the talk in our game, and there was some serious blood in the streets. It found its way onto X if you want to check it out, because it went in a straight line from probably about $90 a barrel — it carries a premium to Brent, so let’s say $10–15 above Brent — and it just went bang. And when I say bang, I mean no trades, all the way up to $200, and messing around since. How can that happen? It’s an example of the market being unbelievably short that trade — taking on airline trades, thinking the market’s not too volatile, “I’ll just wear this as a carry trade” — then bang. Some of the biggest oil traders in the world have the biggest position on. They can’t just go and buy it back; if they buy it back, it’s probably going to move another $100 a barrel, maybe more. So they just have to wear it. And so you’re hearing about oil traders in the market having huge margin calls — but these businesses are $10–15 billion-a-year businesses, and they’re getting margin called. This is the kind of craziness I’m talking about.

Voice brokers, people talking their book, and where the information actually lives

Greg: Why is it so incredibly difficult to replicate and do yourself? Because oil still has some very interesting dynamics — inter-dealer brokers and voice brokers. People hear that and say, “what, voice brokers?” Yeah — 80% of the volume is through voice brokers. If they don’t know you, if they don’t like you, if they don’t give you information about who — or not even who, just what — is buying and selling, you’re just in the dark. Literally a dark pool. The exchanges hate it, but it’s a very well-protected industry, because it’s a community, and these guys get paid a ton of money. There are huge companies that see the edge in having relationships with these brokers and probably keeping it that way. So unless you’re plugged into that game, it’s going to be very, very difficult to have the kind of visibility I’m talking about — who’s positioned where.

And then you could say, “well, look, I’ve got some friends, I’ve got some good information.” But that’s classic — we laugh about it all the time. That used to be a thing: go to a Mayfair pub and talk about who’s doing what. But the whole time, they’re talking their book. And unbelievably, people still fall for it. They go, “oh, I know this guy at this company, he said everyone’s buying, it’s going to be bullish.” He’s probably on the offer. You cannot rely on that information whatsoever. People talk their book. We’ve gone from traders talking their book to OPEC talking their book — they’re always out in the market feeding information, they know the headline sensitivity. Now you’ve got Trump talking the US book. It’s actually crazy.

Prediction markets as an information signal — and why Onyx stopped using them

Greg: It’s like the financial market — it’s so financialized, and the world’s governments know that and are more familiar with that than ever before, so they use it. They spoof the market, feed information, see how it reacts. That adds another layer. In that sense, there have been scenarios where huge option trades go through the night before Iran kicks off — huge, huge — someone clearly knows something. And even Polymarket being pretty useful. Something’s kicking off in Polymarket, an event that would clearly have a big impact on oil, and there’s now a dark area of oil where you’re saying, “someone might come in and do something pretty serious now.” And it’s not the oil traders, not people with physical information — it’s people with government information. So the dynamics are getting super interesting, but like any other financial asset class, I guess.

Interviewer: You brought up Polymarket, and this was something I was curious about before our conversation. I haven’t looked too closely into the types of contracts on these prediction markets related to the conflict in Iran, but I’m sure you have because of its implications in your industry. In general, how accurate a forecast do these prediction markets tend to bring? Is there enough volume on them? And more importantly, how do you think about them as a source of information?

Greg: To begin with, it was great. There really was nothing like it. Funnily enough, it was the Iranian situation last year — I forget exactly which month — but it was very useful then, because it was a new concept. A lot of people were betting on whether the Strait of Hormuz would be closed. People have talked about the Strait being closed as a hypothetical — you put it in your scenario analysis, you talk about it as a hypothetical — but no one ever believed, one, that it was even possible, and two, that it would happen. We even had a research guy, adamant, been in the game for 50 years, saying, “you cannot close the Strait.” So it was really interesting to see people actually believing it would. For a time in Polymarket, we were watching it live, going up to 80% yes, and we’re like, “come on, someone knows something.” And then you get all these messages of people saying, “I’m literally on a ship in the Strait, it’s fine.” That kind of transparent information, in real time, you can’t beat it. This is the good part of capitalism — using people’s greed for transparency, for the better functioning of markets and day-to-day life. No one in any other way would be incentivized to tell you what’s really going on. So suddenly you have something like Polymarket, and someone has information and wants to trade it, and that finds its way into the ecosystem of information.

So I thought it was a really good thing to begin with. Then what started happening, unfortunately, is it got more and more popular, and we started to realize the way it settles is just not ideal. Even with that Strait example, some people felt it had technically closed — ships slowed down for a time. How do you define “closed”? The settlement matters. It’s funny, because in our market in particular, with so many of these contracts, the big thing is to let contracts expire — which is actually quite unusual. A lot of us take these contracts to expiry. You might hold things against it, but expiry is incredibly important — how the contract expires and to what methodology. So we’re very used to studying these underlying methodologies, and that’s where relative-value opportunities — maybe not arbitrage, but relative value — can become very important.

So when we studied that from a Polymarket perspective, we lost confidence very quickly in what the game was all about. You have to own the tokens — you have to own a big portion of it — to be able to decide. So who decides is as important as anything else. And then — I’m not even saying it’s rigged — it’s just inefficient. So to use it as a reliable source of information, it kind of lost its gravitas quite quickly. So then we stopped looking at it.

Options flow as the real tell

Greg: …when someone has good information — and you can empathize — if you have good information, you don’t know when it’s going to kick off. So you just want the straddle, you want some good convexity. An option is a great thing to use. The interest in options became so overwhelming that it’s been a better indication of information being out there than anything else. So we kind of moved from Polymarket to options open interest and options activity at key times, right around the moment.

[Kris: Umm yea. The oil options market has been smart af for a long time]

And just to finish on that: the oil market historically has been quite orderly around its market hours. But after 7:30pm our time — which is the US close, up to maybe 6pm their time — that window is meant to be dead. It’s meant to not really trade, and it’s been very, very active around these times. So now we’re doing the hours later on, to see what’s going on, because the order book will reveal things. If you’ve got the visibility of all the contracts, that’s where you’re in the best position to know: has someone selected something in particular, and what could that mean? Because there’s no other reason why you would trade at that time. If you want to hedge, you go for the peak times. If you want to speculate, you want liquidity, so again you go for peak times. So why are you trading in these evening-to-nighttime trades? It makes no sense, other than maybe you’ve just got the information. And I think Trump knows that as well, because he makes a lot of his announcements either on the weekend — when the market will gap up or down — or at night. And we’re forced to be very ready up until the actual close of the exchange now, rather than the close of the market day.

That’s my favorite stuff because it’s about the nitty-gritty of trading but the rest is full of good business talk and a bit more on trading:

Regime-break risk: when the exchanges themselves are the risk. Greg’s worst moment last week wasn’t market risk but a flashback to 2022 TTF, when the EU floated capping the European gas futures price. A delta-flat book against expiry administrative volume becomes a billion-dollar naked short the instant nobody can sell you the futures to close on. He puts it in the same family as the Treasury basis trade.
What it’s like running the book through it. Sleeping bags in the office, WhatsApp blaring, the fighter-pilot bit.
The 26-hour evacuation. 55 people and 9 dogs chartered out of Dubai because the office was being bombed. Flight paths changed five times. They traded the next morning.
Countercyclical hiring during the lull. 2024 and 2025 were horrendous; that’s when they bought a team from a competitor, set up Dubai, and did the cultural reformation.
Why Onyx hasn’t taken outside capital, despite being asked repeatedly. Energy at the hedge funds has seriously underperformed outside of, say, Citadel. Capital isn’t the constraint; deployment and conviction are.
From prop shop to liquidity infrastructure. The flywheel: data, training, single-dealer platform, retail brokerage, credit/mini-bank. All of it leveraged off the core engine of being the most-liquid price.
The Glassdoor review that turned Greg into a LinkedIn presence. And the Hamilton line about who tells your story.
What’s surprised him most after 14 years. Spoiler: it’s not technical.

Finally, I was chatting with an oil trader about this interview and he recommended a book I immediately lifted:

the singularity trade

Not to deter any stubborn bears, but just understand your history. In 1999, the Nasdaq returned 86%.

If we ignore the small 3.2% down year in 1994, that run looks even crazier and capped with an insane blow-off top.

The 1999 blow-off top is pretty interesting from a how-do-I-reconcile-option-pricing-with-real-world lens.

I’ve written a bunch on how volatility measures are sensitive to sampling periods.

See:

Volatility scaling can feel unintuitive.

If an asset’s annual standard deviation (ie volatility) is 16%, then its daily standard dev is ~1%

Well, from that, it’s clear that you can have say a 10 sigma move in a day, but not in a year. That alone seems to point to a weakness in how we scale volatility through time.

But this is mostly resolved by measuring distances in lognormal space correctly. When you do that, you find that +86% is MUCH closer than -86%.

Just screenshot the formula in the post and treat Gemini like a calculator:

This explains why calls that are 50% OTM calls are worth more than puts that are 50% OTM (even if the spot and forward were the same).

To consolidate knowledge, it’s why collars can look so attractive in high vol stocks:

“Stock pickers market”

I’m old enough to remember when investment managers complained that the Fed drove the market, everything was correlated, and there was little reward for discerning between companies.

Well, we’re in the opposite world.

This is showing put skew falling and call skew rising in QQQ:

This is front-and-center to the options market:

There’s a record disconnect unfolding in the trading pits right now

A chart from the article shows the spread between the weighted avg stock vol in the SPX vs the index vol. It’s another proxy for cross-correlation as the index vol is dampened relative to the stock vols because the stocks are doing a great job diversifying each other.

A stretched relationship can get more stretched. But as it stretches, there is a mathematical reason why the spread would revert. Think of the limit. If 1 company achieved singularity and ate all the other companies, its weight would increase relatively as each dollar it made was a dollar less for the others until it was the index. This is NOT a tradable idea. That is a make-believe world. I’m only being pedantic to help you move the pieces around in your brain to help you see how they fit together.

But the price action of anything related to AI ripping vs everything else is a giant singularity trade, and from that context, the low correlation makes superficial narrative sense for now…a handful of companies are expected to eat the rest.

But I’ll pose this one…if instead this handful of companies are becoming the COGS of all other companies, wouldn’t that look more like the stories we’ve heard that I had Claude reconstruct by asking it to describe the circular revenue phenomena in bubbles:

Company A buys ads on Company B’s site. Company B uses that revenue to buy servers/software from Company C. Company C buys ads on Company A’s site. Everyone books revenue, everyone’s growth numbers look great, valuations rip higher — but no net new money is entering the system from outside customers. It’s just the same dollars chasing themselves around a closed loop, with each pass inflating reported revenue.

The poster children were the late-90s telecom and dot-com names. Global Crossing and Qwest got nailed for swapping fiber capacity with each other and booking both sides as revenue (”capacity swaps”). AOL was accused of round-tripping ad deals. A lot of dot-coms were essentially selling ads to each other, with VC money funding the ad budgets — so the “revenue” was really just recycled venture capital.

The concern isn’t fake deals today, but the circularity possibility means index vol will have its revenge. Good luck with timing though.

SpaceX

It’s interesting to hear Mitchell step through the numbers of how much day 1 shares need to be absorbed and how unprecedented this is. Recall in PTJ’s interview on Invest Like The Best:

2000 was the easiest bear market I’ve ever seen in my whole life. It’s got so many similarities to right now, in the sense that the bear market of 2001 and 2002 were a consequence of all the IPOs in ’99 and 2000. And then as they unlocked, you just had this never-ending cascade of selling, that’s a great way of putting it. And we’re getting ready – I want to say that the contemplated IPOs for next year are going to be five or six percent of market cap. So why are we where we are right now? Because we’ve been retiring two or three percent of market cap, probably a little less than 2% of market cap, every year without fail for the past 10 years [through buybacks.]

And so now all of a sudden, you’re gonna completely reverse that math. And so, I don’t think it necessarily happens instantaneously with the IPOs, but then there’ll be the unlocks. So you can see a situation where, okay, maybe we go through some kind of rolling top. And then 18 months from now – six months, we’ll have to look at the unlock schedule. But you’re going to want to watch those because that’ll just be adding equity supply. And you’ve already gonna be diminishing the buybacks because of all the commitment to capex from the hyper-scalers. They’re already gonna be eating into their cash flow.

The current set-up feels very strange. It seems too easy to think it’s going to be a local top right? But it’s a hard idea to resist. It feels like it’s a negative for gross returns and then under the hood, possibly chaotic for sector flows (like to absorb the IPO do people rebalance out of what went up the most recently? That feels like a pretty natural idea).

You have pockets of extreme bullishness manifesting in options with cheap put skew and risk reversals and left-for-dead implied correlations but the bearish factors are also common knowledge:

IPO issuance
Midterms (assuming Dems are the bear choice)

polymarket on 5/29/26
elevated bond yields

In other words, current prices are NET of everyone knowing about these factors. By the way, this is always the problem with markets. If you see something on the horizon and think it’s bearish, whose to say the current market wouldn’t just be higher if that thing you’re latching on to is observable by others.

What’s the more contrarian position right now, to be bullish or bearish?

The option point spreads have shifted in a way that suggest bullishness is consensus.

Moontower agent

The moontower agent has been in the wild for a month now, and it’s been an awesome companion to help you reason through trading questions. It’s connected to the data we buy and process, and it’s tuned and under ongoing reinforcement learning for trading contexts.

=> Ask the agent a question

It’s powered by AI harnesses, of course, so the output is non-deterministic, so it’s helpful to report back on what it does well and poorly so we can keep course-correcting.

a delightful conclusion to the Investment Beginnings Series

This week I taught Class 5 of the Investment Beginnings series I’ve been doing with the 12+ year olds.

It’s the last class in the series before we do “labs” in July. During lab, we’ll convene when the market’s open and I will give each kid individual attention as they execute an investment. I want to make sure they know how to read the screen, navigate their broker site, see the confirmation of the execution etc.

This last class was special. I’ve been posting all the materials online and there are families following along remotely. One dad sent me an app that consolidated and vibecoded the slides and games. He and his son worked on the project together:

https://investment-class.vercel.app/

And this next part blew people’s minds in the class, not to mention my own. A mom brought her son from Miami because he’s been obsessed with the class and wanted to be here in person with the other kids. I’m speechless. Supermom and superkid.

We took them to dinner with my family and brought along my son’s good buddy so our visiting friend would know a few people before stepping into the class. I can’t gush enough about how nice this all was.

When Class 5 ended, a lot of parents came to talk to me and said all this kind stuff and gave me totally unnecessary, generous gifts (I would have done the same so I get it but also just feels like too much). The most important thing is how all these kids’ gears are turning. It feels like a no-brainer to really clean this up (I learned a lot from doing it and know how I’d mod it in the future) and turn it into something. Maybe a well-produced YT thing, but I’m stretched pretty thin. We’ll see, I guess. Famous last words.

Anyway, here’s the outline of class 5 and link to all the materials from the classes.

Class 5 — Making Trades & Reading Markets

Different kinds of auctions and how markets are continuous auctions
The order book: bids, asks, spread, and what “depth” actually looks like
Price discovery as consensus — the price aggregates what everyone knows
Market hours, plus what pre-market and after-hours really are (and why beginners should avoid them)
Public vs. private markets, with real estate as the bridge example
How an IPO turns a private company into a publicly traded one
Why baskets exist: the easy button for diversification (callback to Class 4)
Three kinds of baskets — index, themed/sector, manager-picked
ETF vs. mutual fund: same idea, different checkout (auction all day vs. one daily NAV)
Index construction math: cap-weighted vs. equal-weighted, with four real stocks
Why SPY and RSP — the same 500 names — can produce materially different returns
Homework: talk to parents about a brokerage account, ahead of the July lab where students place their first real trades

We spent much of the class doing a mock trading game:

How the game worked

There are 16 kids.

Each gets 2 cards — that’s private info
There are 3 “stocks”: Hearts, Spades, and Red
At the end of the game, each stock settles to the sum of the cards held collectively in that category across all 32 dealt cards
Card values run 1 to 13 (ace to king)

Kids bid, offer, and trade with each other based on what they think final settlement will be. They log transactions on index cards they carry.

Every few minutes, news hits — I reveal some of the remaining 20 cards. These are cards that will NOT contribute to the value of the 3 stocks.

The Teaching Moments

Basic valuation

What’s the maximum value of each of the 3 stocks? (Also a fun way to teach someone to quickly compute the sum 1 to N.)
What is the fair value of the stocks at the start of the game, when no common information has been revealed?

Information and private signals

What is the fair value of Hearts if you’re holding the 9 of Hearts?
Ask the kids: what’s a good hand to be dealt, and why? (A very simple exploration of what “information” actually is.)
After news is revealed, how do you update fair value? Walk through the exact math.

Reading flow

Your fair value is always subject to adjustment based on flow. What is Alice’s bid generally saying about Spades? What is Mike’s offer suggest about Red?
At the end, computing P/L is a big exercise — marking trades to settlement.

We didn’t go into crazy depth on any of these. Just getting a basic understanding easily takes a group of 16 kids an hour, and even then some are lost. Totally expected. Honestly, many adults are too.

It’s super interesting to see who gets it very quickly though.

The origin of the game

This was the first trading game I remember doing as a trainee at SIG. All the new hires in NYC played while the trainees who had been around for 3-9 months traded options on these “stocks.” Their hedge orders would get sent into our trainee market!

high implied vol can work for or against you

Here’s how high vol works against you

It’s too expensive to buy puts to trade directionally once an asset has already made a giant move higher.

When you are 100+ vol, it’s not surprising the market puts your odds of getting cut in half at 1 in 3 proposition.

It’s hard to make money in a reasonable risk-adjusted away once an asset is already high vol since it’s hard to size it without risking your neck.

It is well within the meat of the distribution for SNDK to get cut in half this year. That’s just a good baseball player’s chance of getting a hit or a typical NBA player hitting a 3 in a game (or missing a 3 in practice).

How high vol works for you

The high vol is a gift to the natural holders. Millennial employees can lock in their unborn grandkids’ inheritance.

A non-technical way to appreciate how high vol creates this opportunity in upside call vs downside put differentials:

Imagine a stock starts at $100. It gets to $125. From $125 to $150 is only 20%

But if the stock fell to $75 the distance from $75 to $50 is 33%

Both $50 and $150 are 50% from the initial price, but in a compounding sense 150 is much “closer” to the starting value than $50. The higher the vol the less “distance” a fixed dollar move represents. As implied vol increases OTM calls grow faster in value than OTM puts. This is the source of the attractive pricing you see in the risk reversal (ie option collar).

That tweet comes from Dean Curnutt of The Alpha Exchange Podcast. He’s a partner in an option brokerage firm I’ve known for a long time. I told him he needs to buy an SF realty company, since risk reversal-financed $10mm SF Victorian pipeline is unmanned!

Speaking of, if you wanted to bet on AI without access to private shares, real estate on leverage would have worked. See Redfin economist Daryl Fairweather’s Is the Bay Area in an AI Housing Bubble?. I hear from locals who own a bunch of SF RE that the bid is mostly in single-family and multi-family rental units are not getting the hockey stick treatment. The rents have been exploding higher, however. And to think coming out of COVID, you couldn’t give away an SF condo. Super high vol asset. They need options!

appreciating diversification

This week, I hosted class #4 of the Investment Beginnings for local kids aged 12+.

The series’ materials are here:

https://notion.moontowermeta.com/investment-beginnings-course

This is the specific material for class #4:

Slides
Spreadsheet Game (File:duplicate to have your own editable copy)

I also created a web version of the game:

☀️🌧️Sun/Rain Game

While I’ve been doing the series for kids, I think a lot of adults could even benefit. The overall arc of the presentation:

Last class’s game ended with a humbling but common result, hinting at a key pillar of investing.
We use a few facts to dispel the recency bias that all investors carry with them.
They learn what the fundamental nature of stocks predicts about their individual and group behavior.
We widen the meaning of diversification beyond stocks, which was extremely easy to do in light of March 2026.
We play a game that makes the implications for portfolios concrete.

While moontower readers span a wide range of investment experience (although overall quite interested in investing and money), here are a few ideas that I hope are presented in ways that might augment even your understanding or at least help you explain to learners in your life.

The most naive strategy is hard to beat

The kids spent Class 3 picking stocks based on a bunch of variables they could sift through, only for the equal-weight benchmark to beat everyone except the team that contrarily concentrated in the highest momentum company that is very much still an enigma to the market (TSLA).

The equal-weight strategy which I just called a monkey (although it’s not random, just dumb) beat 2/3 of the 15 individual stocks themselves.

The reason you shouldn’t be surprised that the naive strategy is hard to beat

Companies eventually die, but indexes shed them before they are in hospice.

Only 17% of the original S&P 500 companies from 1957 survived 50 years. The average company lifespan on the index was 33 years in 1964 — it’s now under 20. Kodak invented the digital camera in 1975 and buried it because of the innovator’s dilemma.

In a crash, stocks remember they’re all stocks.

Diversification works differently in good years than bad ones. In the class data, stocks spread widely in bull years. Then we looked at Jan 2022 to Jan 2023: 13 of 15 stocks fell together, the spread collapsed.

I didn’t want to lean into the word correlation, but I noticed a different way to convey the same idea. The inter-quartile range (IQR) of annual returns was smallest in the worst years. This chart is rich with insight. Notice the IQR’s visually but also how the equal-weight portfolio performed relative to the individual stock and median stock returns each year:

These observations are non-CAPM ways to arrive at the familiar language of diversifiable risk (company-specific stuff you can eliminate for free) and systematic risk (market-wide stuff you can’t diversify away but do get paid to carry). The crash revealed which was which.

If we zoom out from stocks alone, we see a race where the leaders change each year

The Novel Investor quilt shows 15 years of annual returns ranked best to worst across 9 asset classes. The diversified portfolio, that gray-ish bar, never wins a year nor comes in last. Note commodities, gold and BTC are absent from the series.

How do you think they would influence the gray portfolio?

The Sun/Rain Game

This leads to a game where we can build some intuition about the role of non-stock assets in a portfolio.

If you look at the sheet you can see how the kids actually did (I changed the kids names to letters):

Spreadsheet Game

The game’s punchline is that owning the anti-correlated asset despite it having a worse expected return than the “good” asset leads to a better long-term portfolio.

But this is so unintuitive that I got a student’s question wrong during the discussion!

I’ll explain the mistake here.

A student asked if we played the game for 100 years instead of just 20 years, if owning the good asset ONLY would have led to the best return. I initially said no, then corrected myself and said yes because it has the higher expected return.

But I was right the first time. The answer is definitely NO.

It comes down to the fact that the good asset has an expected arithmetic return of +5%, BUT it has a negative expected CAGR or geometric return.

The math:

The company is 50/50 to return+40% or -30% in any given year.

.5 x 40% + .5 x -30% = +5%

But over 2 years, you expect 1 up, 1 down. Compounding math:

1.4 x .7 = 98%

You expect to lose 2% over a 2-year sequence of about 1% per year.

Formally, we compute the expected CAGR by multiplying (note how the arithmetic or single period return is added):

1.4^(1/2) * .7^(1/2) – 1 = .9899 -1 = -1%

[The exponents represent the probability of each outcome. If there were 3 outcomes, you’d have 3 terms and the exponents sum to 1.]

In the long run, the good asset destroys value. So you do not want to concentrate in it despite its superior expected arithmetic return.

The CAGR is being killed by volatility drag, which is the asymmetry of the fact that if you lose 30% you need to return 42.9% to get back to even, but the “up” years only return 40%. You are falling behind over time.

The bad asset returns -10% half the time and +8% half the time. It’s a “worse” asset, but it’s less volatile. Taking this quality to its extreme, isn’t this what cash is?

In arithmetic terms, our average return if we allocate to each asset equally is +2% (50% x 5% + 50% x -1%). But that portfolio is less volatile because one stock zigs when the other zags. The diversification cuts the volatility MORE than it cuts the expected return, leading to a better risk/reward!

If we rebalance each year back to an equal-weight portfolio, we “pull” the expected CAGR closer to the expected arithmetic return. It’s the only way we can get close to eating those expected arithmetic returns. Otherwise, they don’t really exist for you over time.

This table is worth staring at:

Here’s a message one of the dads sent me after the class:

Measure Your Own Diversification

I made you a tool to compute your portfolio vol and see how much the cross-correlations between your holdings have been reducing total vol from the vol that the individual assets contain. You can tinker by adding ETFs of other asset classes to your equities (ie GLD or USO or TLT etc) to see how they affect the volatility.

If you just want inspiration for an idea, use the tool to compare the Mag 10 index (MGTN) realized volatility with the average realized volatility of its holdings. The index is conveniently equal-weighted, 10% in each name.

Two ways to try this on your own portfolio:

🌐To run in your browser

https://colab.research.google.com/github/Kris-SF/data-pipelines/blob/main/portfolio-vol/portfolio_analysis.ipynb

⚠️Just push through the warning it spits off

The output will includes metrics and charts:

🖥️To run locally

git clone <https://github.com/Kris-SF/data-pipelines.git>
cd data-pipelines/portfolio-vol
pip install -r requirements.txt
jupyter lab portfolio_analysis.ipynb

Either way, edit the WEIGHTS dict and the START / END dates, then Run All.

how a high implied vol can be cheap

EWY, the South Korea ETF, was an interesting source of disagreement in our Discord about whether the vol was expensive or not. This is the IV vs trailing RV:

Based on realized vol calcs using daily sampling, IV approaching 50% looks rich.

But EWY had been grinding up since the beginning of the year. (It tanked along with the dollar this week after the Iran strikes.)

It was up 25% in February alone.

If we annualize that to a vol:

25% * √12 = 87% vol

More than 2x the realized vol and significantly higher than the “rich”IV.

The posts below discuss this sampling issue from several angles.

Risk Depends On The Resolution | 4 min read
Volatility Depends On The Resolution | 5 min read
The Option Market’s Point Spread (Part 2) | 11 min read
Thinking In N not T | 6 min read
A Misconception About Harvesting Volatility | 3 min read
The Coastline Paradox in Financial Markets | 11 min read

There’s no single “realized” volatility. Every time you delta hedge you sample a unique volatility such that is possible for a long delta hedger and a short delta hedger to both make or both lose money depending on the timing and size of their hedges.

Because we are cursed with memories, every good trade we do, we wish we did bigger, and every bad one we wish we did none of. Our memories, combined with the noise inherent in delta hedging is a recipe for madness. That’s why all option traders are unpleasant and wish they had chosen a career where they can simply clip a fee from the collective net worth of society, which has been steadily levitating for the past generation, raising (good) but compressing (boring) the fortunes of the clever and the dimwitted alike.😉

Since realized volatility is sensitive to how we sample it, it’s worth looking a bit closer to how it accumulates. This exploration is likely to inspire your own research or even guide your thinking on how to get your head around return behavior that, despite being common and familiar, remains, as my kids say, confuzzling.

In this post:

The Trend Ratio — what the ratio of weekly-sampled to daily-sampled vol tells you about trending vs choppy regimes
The Variance Contribution Ratio — a single number that tells you whether a trend was a slow grind or a one-day event
Broad patterns across 35 liquid ETFs over a decade (~97K observations)
What TR implies for delta hedging — the tradeoff between rebalancing noise and sampling bias
What happens to forward vol after grinding trends, and what that means for pricing
A self-contained Jupyter notebook that fetches from yfinance and reproduces everything

the shape of volatility

EWY had a grinding rally. You can describe this as momentum, autocorrelation, trend. These are all ways to say the stock went on a quite a run. These descriptions mask something even more fundamental that we should make explicit. The notability of this run, even before describing its steady behavior, is that it was volatile.

Even if it’s 1% per day for 20 days this is volatile in the sense that the movement in the stock was unusual. We do not expect EWY to find itself over 20% away from where it was a month ago. Plain and simple. If we tallied all monthly returns, a move of that size would stand out as an outlier.

If a dog is wearing a dress, we would acknowledge that unusual observation before describing the color or material of the garment. Similarly, before describing the shape EWY’s move, we take it in, “That’s pretty remarkable.” You’d need to have a narrow definition of volatility, a definition that is divorced from an honest view of reality, to think otherwise.

It’s settled then, EWY was volatile. Great. Now we can think about the shape of the volatility. I’m going to introduce 2 measures that we can use in conjunction to classify volatile moves.

Trend Ratio

A common way to compute a realized vol for say 20 trading days is to average the sum of squared daily returns, take the square root, then annualize by √251. We’ll call this 20d RV sampled daily or 20d_RV for short.

Now compute the same realized vol but sample weekly instead of daily. The method is the same except for 2 variables:

5-day returns instead of daily returns. Note that means only 4 data points, not 20.
Since you sampled every 5 days, you annualize by √251/20

We will call this 20d RV sampled weekly or 20d_RV_w

The ratio of weekly-to-daily vol captures how much “trend” was present relative to chop. We can call this Trend Ratio (TR).

TR = 20d_RV_w / 20d_RV

When TR > 1, the market has been trending. The point-to-point displacement exceeds what you’d expect from the daily noise. When TR < 1, daily returns have been partially canceling or mean-reverting within the window.

As of the last day of February 2026:

EWY

20d_RV_w = 49.9%

20d_RV = 40.6%

TR = 1.23

Variance Contribution Ratio

Imagine 2 stocks.

Stock A: Moves 1% every day. Its vol annualizes to 16% if you sample daily

Stock B: Moves .60% 19 days, and 3.6277% on 1 day. Its vol also annualizes to 16% sampled daily

Both A and B accumulated the same amount of variance, but for A, each day contributed 1/20 of the variance. Stock B’s most volatile day contributed 65.8% of the total variance!

💡Variance is the square of returns. We care about variance because realized p/l in options is proportional to variance. If you are short gamma, a 6% move costs you more than 2x a 3% move.

We will define a Variance Contribution Ratio (VCR) as the fraction of total variance explained by the single largest squared daily return. Hence, the VCR for a 20d window:

VCR20 = max(r²) / Σ(r²)

If all 20 days contributed equally to variance, VCR would be 1/20 = 5%.

Snooping ahead for a moment, the median VCR across 35 liquid ETFs for the past decade is about 25%. This means one day typically explains a quarter of the whole month’s variance. A major departure from the uniform case. The real world is lumpy.

Boiling vs jumpy frogs

A high TR reading tells you the market trended, but not necessarily how. By filtering TRs by VCR or vice versa, we can distinguish grinding or frog-boiling trends versus a trend characterized by larger jumps. From there, we can study subsequent realized volatility behavior.

I grabbed 10 years of daily return data for 35 ETFs spanning equities, fixed income, fx, and commodities from yfinance (~97,000 observations)

The details of all the calcs and code are in this notebook:

🔗https://github.com/Kris-SF/public_projects/blob/main/vol_ratio_vcr_study1.ipynb

Here’s a high-level summary:

Across all tickers, we can see that the median trend ratio is ~95%. In other words, volatility sampled weekly is about 5% less than if you sample daily. More frequent sampling over the same time window generally leads to higher vol computations, so this is not a surprising result.

If VRPs are typically 10-15%, then VRPs are about 1/2 to 1/3 larger if you sample weekly. An interesting observation for someone debating how often to hedge. The trade-off, of course, is noise. We can see the distribution of trend ratios in the blue histogram. Again, that’s across all tickers. For individual tickers, you can look up the standard deviation of the Trend Ratio. We will look at them graphically below in a bit. The distribution of TR appears well-balanced.

On the other hand, we can see that VCRs have a strong positive skew. The median VCR is ~25%, meaning it’s normal for 1 out of 20 days to comprise 25% of the total variance! It’s never the case that the distribution is truly uniform, but there’s about a 1 in 20 chance that a single day can comprise 50% of the variance. Remember, there are no single stocks in this universe, so earnings are not a factor. If interested, you could change the tickers in the notebook to study single stocks.

What’s normal at the ticker level?

Trend Ratios by ticker:

Commodities seem to exhibit more trending behavior than equities, but the overall feels compact with a range of TRs from .9 to 1

VCRs by ticker:

It seems like SLV and FXY have had about 10 to 20% higher VCRs than the typical name suggesting they are more prone to a single jumpy move in their return stream. Because we are looking at the median VCR I don’t think the recent SLV chaos is skewing the data. If I exclude SLV data from June 2025 until now, the median VCR only drops from 29.5% to 29.4%.

Classification

Split TR and VCR at their medians to get a blunt classification framework:

Summary:

Grinding Trend: 20,744 (21.3%)
Spike Trend : 21,605 (22.1%)
Choppy Grind : 28,046 (28.8%)
Spike Revert : 27,150 (27.8%)
TOTAL : 97,545

EWY’s move was textbook upper-left quadrant grinding trend. High TR, low VCR.

Let’s set VCR aside for a moment. It’s nice that the recent VCR confirms that the variance was not especially lumpy, but we can see that with our eyes. The question that prompted this whole post was whether the elevated TR, the fact that the less frequently sampled vol was much higher than the daily vol, meant anything for future volatility? Is the high IV actually expensive, or does the option’s market somehow balance both measures of realized vol?

Phrased generally:

Does the elevated TR tell you anything about subsequent realized vol?

For every observation, I computed both the current TR and VCR, then looked at what happened to daily realized vol over the next 20 trading days. To be clear, this is the window that is 20 days hence, so there are no overlapping days between the TR reading and the subsequent volatility.

I’m specifically interested if daily sampled vol exhibits any tendencies. I sorted all observations into TR quintiles and measured the median percent change (technically the log change) in RV20d from the current window to the next window.

The pattern is monotonic and the direction of change is what I’d expect.

In Q1 (lowest TR, most choppy) forward daily RV declines. To be fair, I had no expectation about whether it would increase or decline, merely that as we increase the TR, the subsequent RV would increase.

[To articulate the logic: there’s additional information in the less frequently sampled vol at the margin, perhaps uncovered by splitting the data into quintiles. We are looking for benefit in the margins as we accept that there is less total information than more frequently sampled vol. After all, daily vol sample would converge to a good estimate of an asset’s true vol faster than once a year observations. This is also why you would prefer daily data about a trading strategy versus monthly.]

As we ascend quintiles, Q5 (highest TR, most trending) precedes a median increase of +3.4% in RV20d.

The daily estimator was understating the expectation of the next period’s vol if we assume it would be unchanged. The next period, daily RV partially “catches” up.

3.4% isn’t a huge number, but it’s material. If you thought 50% vol is fair, now you might pad that to 51.7% but…it’s highly variable and positively skewed. The mean vol increase is 14.9%, which would mean raising your fair vol from 50% to 57.5%!

This is the histogram of the percent vol increase in the subsequent period for the 5th quintile of trend ratio:

Be careful, the standard deviation of that vol change is huge. This is all the quintiles:

That EWY elevated IV over daily-sampled RV starts making a lot more sense because its trend ratio of 1.23 is in its top quintile.

VCR adds independent information

High VCR predicts vol decline, holding TR constant. This is partly mechanical. To take an extreme example, when one day accounts for half your variance budget, vol drops when it rolls out of the next window. But it’s also real: spike regimes tend to cluster and then subside.

To examine how VCR may interact with TR, we construct a heatmap. Each cell shows the median percent change in daily RV from the current 20-day window to the next, broken out by TR (columns) and VCR (rows).

Reading left to right (TR axis): Higher TR predicts vol increase, and this holds within nearly every VCR row. Look at the 15-20 VCR row: it goes from roughly flat at low TR to +11% at high TR. The pattern repeats row by row.

Reading top to bottom (VCR axis): High VCR predicts vol decline across every TR bin. The bottom row (VCR > 50) is negative across the board, ranging from -30% to -3%.

We would find EWY in the upper right corner (high TR, low VCR) the grinding trend zone. Subsequent vol rises from +8 to +12%.

Recall from the four quadrants that grinding trend is the least common, showing up about 21% of the time. But this is still frequent enough that you can easily bid an IV equivalent to the trailing daily-sampled vol.

I just doubt that the market will give it to you. But at least you know to screen for this and at the very least not be tricked into selling an insufficiently high IV.

It’s trivial to compute a VCR as well, so you can add this filter as confirmation that the trend is boiling a frog not just a jump.

The Notebook

Again, I’ve open-sourced the full Jupyter notebook behind this analysis.

🔗https://github.com/Kris-SF/public_projects/blob/main/vol_ratio_vcr_study1.ipynb

It fetches data directly from Yahoo Finance, constructs all the variables from scratch, and reproduces every chart above. You can change the ticker universe, the window length, or the sampling frequency and re-run the whole thing.

Note the code computes TR and VCR using a zero-mean estimator for realized vol (dividing by N, not N-1). This is deliberate, we’re measuring total quadratic variation including drift so the zero-mean formulation is standard in the vol trading world