hurst

In a random walk where trials are independent, variance scales linearly with time. Since standard deviation is the square root of variance, volatility scales with sqrt(T).

This sublinear power law scaling gets smuggled into option math that answers practical questions. For example, assuming implied vol is constant, a 12-month ATF straddle is twice the price of a 3-month ATF straddle because sqrt (12/3) = 2.

This scaling is commonly used to convert raw vega into weighted vega. Raw vega is an extremely low-resolution number. If you own 50k 12-month vega vs being short 40k 3-month vega then it appears like you are long vol. But 12-month IV doesn’t whip around as much as 3-month IV, so this position will not act like it’s long vol on a large move higher in vol as the term structure will not “parallel shift” higher. The 3-month will increase faster as the term structure steepens into a downward sloping shape. A shape referred to as “inverted” or “backwardated”.

A simple way to modify raw vega is to scale all your monthly vegas by 1/sqrt(T) by normalizing them to a fixed DTE, for example 3 months. In that case, using the same math we did above, a 12-month vega is cut in half relative to the 3-month.

So your re-weighted vega is now short 15k vega instead of being long 10k vega!

12-month vega x scaling factor relative to 3m vega = +50k * 1/sqrt(12/3) = +25k

3-month vega x scaling factor relative to 3m vega = -40k * 1/sqrt(3/3) = -40k

Net: -15k

That volatility changes should move in proportion to 1/sqrt(T) is not a commandment brought down from Moses. It’s a convenient scaling factor that corresponds better, even if imperfectly, to empirical vol surface behavior. It also has a handy interpretation. If IV’s change in proportion to 1/sqrt(T) then ATM time spreads are unchanged (net of theta). In other words, the 3m/12month straddle spread is unchanged in such a regime.

Again, this scaling doesn’t need to hold. Sometimes we have parallel shifts in term structure and sometimes term structures steepen faster or slower than sqrt(T) scaling would predict. But the scaling is still a better prediction than the raw vega measure, which would have you believe IVs from all months are directly comparable without adjusting for how slow long-dated IVs change or how fast a weekly IV can move.

Random walks and the derivative pricing theory built upon them assume returns are independent. In hindsight, random walks still exhibit stretches that can be labeled “trend” (like a run of heads) or “mean reversion” (period of frequent alternating). But it’s one thing to label these stretches and hindsight vs predict them.

It should be self-evident that being able to predict trends or reversion would be marvelously profitable for a directional trader. But, direction aside, it would be a gift to volatility traders as well. It would influence not only how they priced vertical spreads and time spreads but the deltas in their models and their delta-hedging strategies. In other words, it would change everything if you had an edge on the probability of the next move being up or down, even if you did not have an edge on the fair value of the stock (this would occur if you had an edge on probability but not on the magnitude of up move vs down move). Option structures allow fine-grained bets that can isolate probability from magnitude.

If an asset trends over weeks or months, you will underestimate its volatility by scaling its daily volatility by sqrt(T). That makes sense. If it trended, that’s similar to saying the moves were auto-correlated and therefore dependent. Again, this is descriptive, not predictive, but relating measures of volatility to this interdependence lets us see how sensitive option pricing is to the random walk assumption. A few articles I’ve written in this vein:

These articles have a unifying concern. If prices are random, then sure, the power function that specifies how volatility scales is the familiar:

But if prices trend or mean-revert, the exponent is no longer 1/2.

Over any historical sample, H can be observed to be something other than 1/2. For it to be 1/2 would mean that annualized volatility over 2 different sampling windows was identical. In hindsight, that will rarely occur. But it’s also true for any exponent you pick. It’s hard to make the persistent case for a value other than 1/2, especially when it carries the financial totem of randomness.

In Retail Options Trading, Euan Sinclair says markets aren’t random, but they’re close to random. The question of whether there’s enough life growing in the gap between “random” and “almost random” for a skilled hunter to eat is existential professional investors’ careers.

We need to examine randomness.

Returning to the context of volatility scaling and its relationship to randomness, Euan reaches for a popular quant tool. The Hurst exponent. That’s why I picked H for the exponent in the general version of the volatility power law.

Euan’s definitions:

  • H = 0.5 is a random walk. No memory.
  • H < 0.5 is mean-reverting. Up tends to be followed by down.
  • H > 0.5 is trending, or “persistent.” Up tends to be followed by more up.

It’s time to do some learning moontower-style and start with the basics.

What The Hurst Exponent Actually Measures

Our Favorite Starting Point: Coin Flips

Flip a fair coin 100 times. Score +1 for heads, −1 for tails, and keep a running sum.

After 100 flips, how far from zero is that running sum?

Three stylized regimes to compare:

  • Perfectly correlated flips (every flip copies the last one): the running sum after 100 flips is ±100. It grows linearly with N.
  • Perfectly anti-correlated flips (+1, −1, +1, −1, …): the running sum never escapes ±1. It doesn’t grow with N at all.
  • Independent flips: the running sum lands around ±√N or in this case ±10.

Think of these as regimes that correspond to three scaling exponents:

  • Correlated (trending) N^1
  • Anti-correlated (mean-reverting): N^0
  • Independent (random walk) N^0.5

The exponent is the answer to “what power of N does the cumulative range scale with?”

Strip out the step size to isolate the regime

The ±1 coin gave a running sum with range around √N. If the coin paid ±10 instead, the range would be 10·√N. Bigger steps, bigger range. We want to strip out that distortion. If we measured price range on raw market data, a jumpy stock would always look more “trending” than a calm one, just because its steps are bigger. We’d be measuring volatility tangled up with regime, when we want regime alone.

The fix is to divide the range by the standard deviation of the steps: R/S

For the ±1 coin, R ≈ √N and S = 1, so R/S ≈ √N.

For the ±10 coin, R ≈ 10·√N and S = 10, so R/S ≈ √N. Same answer. The step size cancels out.

That’s the rescaled range. R/S only cares about the regime of the series, not its scale.

From coins to assets

Now we can adapt this to asset returns.

So we have two measurements over a window of T days of log returns:

  • S = the standard deviation of the returns (the step size in the coin example)
  • R = the range (max − min) of the cumulative sum of the de-meaned returns. How far the running total wandered between its high and its low.

We de-mean before computing R, so we strip out drift. We don’t care that the thing went up over the window, we care how it wandered around that trend. We divide by S to strip out the volatility scale.

The √T Benchmark

If returns are independent, R/S also grows like √T for the same underlying reason:

The variances of independent things add, so the spread grows by √T.

Now generalize it. Instead of forcing the exponent to be 0.5, let the data tell you:

R/S ~ T^H

  • H = 0.5: matches √T. Independent.
  • H > 0.5: R/S grows faster than √T. Trending. Moves reinforce each other.
  • H < 0.5: R/S grows slower than √T. Mean-reverting. Moves fight each other.

Reading H Off A Plot

The scaled range takes the functional form of a power law. If we take logs of both sides, the power law becomes a straight line, and the exponent H becomes the slope of the line.

log₂(R/S) = H · log₂(T)

Compute R/S at a few different T’s, plot them log-log, and the slope is H. It doesn’t matter which type of log we use. We could choose log₁₀ or ln, but using log₂ gives a clean way to narrate it: every time you double T, R/S multiplies by 2^H.

  • H = 0.5: each doubling multiplies R/S by √2 ≈ 1.41
  • H = 1.0: each doubling doubles R/S
  • H = 0.0: each doubling leaves R/S untouched

The Implementation Recipe

  1. Pick several T’s (say 5, 10, 20, 40).
  2. At each T, chop the sample into non-overlapping chunks. (see appendix)
  3. For each chunk: de-mean, cumulative sum, R = max − min, S = std dev, then R/S.
  4. Average R/S across the chunks at that T.
  5. Fit a line through the (log₂T, log₂(R/S)) points. The slope is H.

Worked Examples

Computing one R/S by hand

Take a single 5-day chunk of returns, in %: +1, +3, −2, +4, −1.

  1. Mean: (1 + 3 − 2 + 4 − 1) / 5 = +1%
  2. De-mean (subtract the mean from each): 0, +2, −3, +3, −2
  3. Cumulative sum (running total of the de-meaned series): 0, +2, −1, +2, 0
  4. R is the range of that running total: max − min = (+2) − (−1) = 3
  5. S is the standard deviation of the original five returns ≈ 2.28 (population stdev, STDEV.P)
  6. R/S = 3 / 2.28 ≈ 1.32

That 1.32 is one chunk’s R/S.

Notice that since √5 ≈ 2.24, this little stretch wandered less than a random walk would, so it reads mean-reverting

We just repeat this for several windows.

Say you’ve got 80 days of returns.

Compute R/S at T = 5, 10, 20, 40:

The Hurst exponent, H ≈ 0.43, is extracted as the slope from the log-log plot, which is is linear transformation of a power function.

H<.50 corresponds to mean-reversion. Every doubling of T multiplies R/S by 2^0.43 ≈ 1.35, a hair under the 1.41 you’d get from a pure random walk. The wandering is growing slower than random diffusion would predict.

Applications of H

If H isn’t 0.5, then √T annualization is wrong for that asset. H > 0.5 means your long-horizon vol is higher than √252 × daily vol claims. H < 0.5 means it’s lower.

The articles I linked to in the intro wrestle with this same idea but in a simpler point-to-point manner in the form of a trend ratio (ie vol sampled weekly ÷ vol sampled daily).

If you assume the asset is “self-similar,” then the exponent H governs the scaling at every horizon then besides looking for trend or mean reversion strategies you can now research a world of option relationships that are potentially mispriced if the assumption of independence is strongly embedded in volatility scaling models.

To be reductionist, my trend ratio calcs were a two-point estimate of H. Autocorrelation patches function as a lagged estimate of the same thing. Hurst is the version that uses the whole curve instead of two points or one lag.

The assumption that markets are self-similar is wrong. The more wrong it is, the less you have to gain from Hurst vs point-to-point extrapolations, but all of this is dominated by the biggest elephant in the room. Can past data help you predict trend or mean-reversion at all? Which just circles back to Euan. If you are going to bother trading, you must believe, at worst, they are merely “almost random”.

A Sense Of Proportion

H looks like a number between 0 and 1, so a move from 0.50 to 0.55 feels insignificant. The vol-annualization lens is the cleanest way to debunk that.

Consider a stock with 1% daily vol.

  • At H = 0.50: 1% × 252^0.5 = 15.9% annual
  • At H = 0.55: 1% × 252^0.55 = 19.4% annual

A 0.05 bump in H means a 22% increase in annualized vol. This obviously affects your opinion of option prices but it’s also meaningful for position sizing and risk or VaR.

Most equity-index Hurst estimates sit in a narrow-looking 0.45 to 0.55 band, but that “small” band obscures significant differences.

The Catch: The Naive Number Lies

Now go back to Sinclair’s warning, because this is where it earns its keep.

Classic R/S — the recipe above, the one in his book, the one everybody reaches for first — is biased. Run it on a series you know is a memoryless random walk, at a 252-day window, and it does not hand you back 0.5. It hands you back something noticeably higher. The estimator manufactures a little fake memory all on its own, before the data even gets a vote.

So when SPY’s rolling H sits below 0.5, you have to ask how much of that is the market and how much is the ruler. This isn’t a fringe complaint. Lo built a modified R/S statistic back in 1991 precisely because the classic version confuses genuine long memory with garden-variety short-range stuff like volatility clustering, and equity returns are drowning in volatility clustering.

The fix is not exotic. Simulate a big pile of random walks the same length as your estimation window, run the exact same R/S recipe on them, and see what H the estimator coughs up on data you built to have none. Whatever offset it shows is the lie. Subtract it. Now a true random walk reads 0.5, and a reading that survives the correction is one you can actually look at.

This is the same humility you already preach about your own VRP work. A single rolling-window H is one draw. Treating it as gospel is exactly the “sample size of 1” trap. Calibrate it or don’t believe it.

Sandbox

I’ve heard of many traders, including option traders using Hurst in their research. It feels like it’s accelerated in the past 5 years. I didn’t take a harder look at it until Euan gave a brief intro to it in Retail Options Trading and LLM’s made it easier to tutor yourself on a quant method. It’s a technique that’s well-known, but anecdotally I’ve heard a wide range of mileage from it (I’m guessing every pro option trader in a seat today has at least heard of it in trading contexts).

If autocorrelation adnrealized vol ratios at different frequencies are worth looking at then Hurst is worth at least “spaghetti on the wall”. I built a Jupyter notebook to tinker using yfinance data. You can use it, fork it, whatever:

https://colab.research.google.com/github/Kris-SF/data-pipelines/blob/main/quant-analysis/hurst_analysis.ipynb

If I were to bring this “in the lab” to see how it can become a metric or even signal I’d start with tinkering to see how it its output jives with my intuition of how a certain asset behaved over a particular period.

Once I had a feel for it, I’d throw the metric up on a scatterplot against other metrics to develop a sense of what is normal. Are there any correlations between H and IV skews or IV term structures? How do changes in Hurst coincide with changes in realized vol (rv is an input to R/S therefore and ultimately H so maybe we are hunting for a residual variable to track?)

If you have organized data, in the world of LLMs all of this work is more fun and faster. For now, I hope this primer on Hurst was a digestible first step for explaining the theory behind it and why it can be relevant.

You can find additional notes below.

Appendix: What “chop into non-overlapping chunks” really means

T is a window length, just how many days of wandering you measure at once. You pick several because H isn’t a property of any single window. It’s the rate at which R/S grows as the window lengthens. A handful of T’s gives you points to fit a slope through.

You have 251 daily returns. You want one number, H. That’s the entire goal.

Pick a few window sizes: 5, 10, 20, 40.

For each window size you do the exact same thing:

  • T = 5: chop the 251 days into back-to-back groups of 5. You get 50 groups. Compute R/S for each group, then average all 50. That’s your R/S at 5.
  • T = 10: chop into groups of 10. You get 25 groups. R/S for each, average them. R/S at 10.
  • T = 20: groups of 20, so 12 groups. Average. R/S at 20.
  • T = 40: groups of 40, so 6 groups. Average. R/S at 40.

Now you have four points: (5, R/S@5), (10, R/S@10), (20, R/S@20), (40, R/S@40). Plot them log-log, draw the best-fit line, and the slope is H.

You want enough windows to fit a line, but longer windows are comprised of fewer blocks (like the T=40 window) so they’re shakier sample from which you are computing an average R/S.

Appendix: Bias

The body said classic R/S reads high on a random walk.

The finite-sample problem

Even on a true coin-flip walk, R/S over a short window doesn’t average to exactly √T. It sits a little above. Hurst, Anis, and Lloyd worked out the expected R/S of a random walk in closed form back in the 70s, so one fix is to divide your measured R/S by that expected value at each T before you fit. It’s conceptually similar to the familiar Bessel n−1 adjustment done to sample variance since we don’t know the true population variance.

Claude suggested 2 ways to apply a correction:

  • Use the closed-form expected R/S directly
  • Simulate a pile of random walks and measure what your exact regression spits out.

They differ because the log of an average isn’t the average of a log (Jensen’s inequality). The closed-form route leaves a residual bias of a few hundredths. The simulation route, because it runs the identical regression you use in practice, lands a true random walk back at 0.5.

After much back-and-forth, I took Claude’s rec and had the notebook use the simulation route.

The nice thing about LLMs is they know a lot of the academic history of a measure. Like I said this is a starting point for your own exploration.

Better estimators exist.

Classic R/S is the cleanest to teach and the weakest to trade. Lo’s modified R/S (1991) is built to ignore short-range dependence like volatility clustering, which plain R/S happily mislabels as memory. Detrended Fluctuation Analysis (Peng et al., 1994) is the workhorse in the econophysics literature. If you ever size a position off an H, cross-check it with one of those rather than lean on R/S alone.

what new grads should focus on

In light of graduation season, this week’s material has been focused on a mix of inspiration and general course of action to what I would characterize as an overarching sense of thriving.

When I’m not yapping about trading or options, much of my writing or curation revolves around learning, motivation, and creativity. These 3 factors are in a continuous conversation with each other. That internal conversation has far-reaching effects because it guides our actions which in turn feed back to this internal conversation. We’re these complicated black boxes hosting billions of hormonal and electrical collisions that mean on some level we’re all the same in that we can be described generally as such a machine, but profoundly different since the infinite combinations of those reactions make us unique as, well, precious snowflakes.

Any perspective that fails to appreciate both how general and specific we are is an incomplete description of our condition. Which brings us to the fundamental tension of advice. It’s tempting to give it because on one level we’re not that different, but on another level it’s impossible for any general advice to be right-sized for any individual.

It is with this uneasy marriage of humility and hubris that I dare to offer a few thoughts for those pulling up to the staging areas of their careers. It is the same answer I give to those insistent enough to figuratively sign a waiver acknowledging all the disclaimers that an honest person would give before proffering advice.

The magical words that indicate such an insistence, an insistence which places earnestness above omniscience, which may be the best we can do in wicked domains, are “what would you tell your kids to do?”

In the face of such an approach, I’m cornered. But since I know that you know my kids are not your kids, I can trust you will be able to adapt the advice to your own or your loved ones’ situation.

What should a new grad pursue?

The number one thing a new grad should optimize for is rapid learning.

Womp, womp.

Kris, you put that behind a paywall?

Hang on.

It’s quite clear to me that this is either not as obvious as it appears OR people don’t even know what rapid learning means.

Let’s start with what it means to learn.

Actually, let’s start with what it is not.

Learning is not trivia. It’s not most of what you ever did in school. To be as charitable as possible to the institution of school, it is a survey of the pu pu platter of subjects that have achieved a depth of scholarly history for which the degree of specialization required to contribute to our collective understanding offers an ample capacity to absorb a motivated student’s talent. There is no end to biology. If it has grabbed your imagination, there is a lifelong pursuit awaiting you.

However, most people will not become academics, scholars, or scientists. Most will not chase anything formal school is instrumental for, or for which access to leading professors is important. The learning you get from school beyond the years of arithmetic and reading acquisition is mostly trivia.

[This is not a knock on trivia or, by implication, the subject of history. Thinking needs raw material to operate on. There are extreme points of view that don’t see the benefit of learning anything, since you can look stuff up. If I had to steelman that position, I’d argue that basic knowledge should be reclassified as something to acquire on demand since there’s an opportunity cost of onboarding knowledge you’ll never actually need.

But I think the extreme view is a bridge too far because there’s an irreducible arbitrariness in what will turn out to be useful knowledge. The project known as humanity seems to be an instance of a cosmic explore/exploit problem. I think there’s plenty of room to update curricula to better balance pragmatism and imagination, but as we get to the steep part of any learning ROI curve, the risk of premature optimization would overwhelm the gain in local efficiency. But insofar as I think curricula can use an OS upgrade, we’re pretty far from that point.]

So for most people, school mostly teaches trivia that they will mostly forget. The forgetting part is neither the student or the school’s fault. It’s actually a symptom of the uselessness. Knowledge is use it or lose it. If you’re losing it, it’s because you’re not using it. What odds are you willing to lay on your ability to do long division with 3-digit numbers? Can you multiply the year the Magna Carta by the atomic weight of oxygen? That “Are you smarter than a 5th grader?” was a fun show that proves the point. You might not know what a 5th grader knows, but you can still multiply 2 numbers. Use it or lose it.

Great, we’ve established that most of what we were told is learning, is actually not learning, at least according to any definition of learning worth having. Ok, here’s a definition worth having:

The assimilation of information that leads to adaptive changes in behavior

It’s only a few words, but it orients “learning” towards identifiable goals.

To go all 5th grader on you, subject:

“Assimilation of information” is not just about onboarding but also about accessible retention. You need to be able to draw the arrow from your quiver when appropriate.

Predicate:

“Leads to adaptive changes in behavior” implies that the knowledge is applied towards growth which is something that happens in the physical world, even if it starts internally. Growth is a goal. It can be as fuzzy as imagination or brain fodder, but these remain intermediate steps to change.

That change should be in the direction of desire.

This deserves a couple of comments:

  1. Getting better at crime is a desire and anti-desire depending on who you ask, so the notion of growth is neutral from a non-moral master view.
  2. The recursive nature of learning is also on display. Our desires are inputs that dictate where we spend time to learn, but also outputs that can change based on learning.

Learning is ultimately about outcomes. The concept, being morally neutral, is compatible with any metaphysical view. But being as we are literal material composed of nature’s Legos, our bodies and minds have maintenance requirements throughout our lives. Those requirements should include a surplus capacity for growth in the early years of our lives and a surplus to slow the decay in our back nine.

Rapid learning is the abstract foundation of this surplus. You can modify the terms based on context. Make it more concrete if you prefer. Savings. Redundancy. Time. All of which return to the abstract. To a benevolence at a human scale. A nest for babies, children, and the next generation to grow. To learn.

[It’s possible that this value-neutral concept of learning would not lead to benevolence but annihilation. Perhaps the pace of advance into god-like technology intercepts nature’s learning algorithm, evolution, at a time scale in which it cannot recover its goal of replication. We don’t even know if passive investing is a Taleb turkey problem, good luck with “was the die cast on our own demise when a proto-human first used a stone as a bludgeon?”]

We defined learning. We established why it’s important. It follows that, given its importance and our finite time, that faster is better (holding quality constant). We laid all this out but did not talk about how.

How do we learn?

Well, the how is critical because it’s the advice for new grads follows very naturally from the how.

We learn from risk. From bearing the cost of trial-and-error. School trains us to appease. Generally, the expedient way for a student to meet there 2 biggest goals, namely to get good grades while minimizing the teacher’s interference in the student’s affairs, is to flatter whatever dogmatic attachments the teacher harbors.

In elementary school, the answer the teacher wants and the right answer are aligned. Spelling, remedial comprehension, basic math operations. As children mature, the classes become more subjective. Risk becomes more inconvenient for the student as there is no marginal payoff vs reciting the “acceptable” answer since the ceiling is an A+ and is designed to be accessible. In real life, separation requires a combination of excellence and risk. I suspect many reading this will find it self-evident from experience that good grades had such steep conditions.

When you graduate, you want to optimize for learning and learning velocity. You want to prioritize for:

  1. Risk and accountability
  2. Working with exceptional people

The problem is these are not always straightforward to evaluate from the outside and the shortcuts that help evaluate don’t often work where you want them to.

Risk and accountability

You want responsibility quickly. In fact, this single fact was a major factor in choosing SIG over a bank when I graduated, despite far less up front pay. I wanted acceleration not a tantalizing y-intercept.

But zooming out a bit, I wanted trading more than banking because the whole field meant the chance to sink or swim sooner. I can’t explain it better than Paul Graham does in his classic essay How To Make Wealth:

Economically, you can think of a startup as a way to compress your whole working life into a few years. Instead of working at a low intensity for forty years, you work as hard as you possibly can for four. This pays especially well in technology, where you earn a premium for working fast…

Companies are not set up to reward people who want to do this. You can’t go to your boss and say, I’d like to start working ten times as hard, so will you please pay me ten times as much? For one thing, the official fiction is that you are already working as hard as you can. But a more serious problem is that the company has no way of measuring the value of your work.

Trading is not technology, but it’s similar in that you aren’t spending your time stapling and copying. But say you are not in trading or a start-up, how fast do you get to be at a client dinner or? How fast do you get to make decisions that impact the company’s p/l by choosing from a set of possibilities where there is a dispersion of value over the replacement or default decision? You want to ask the interviewer these questions, although I might try being more indirect unless you think impatience will reflect well.

Tactically, this means either trying to work for a smaller company, a startup in the limit case, or a company whose functional work teams are lean such that its members’ contributions are critical. Whatever the equivalent of a pod is in the industry you are entertaining.

Finally, there’s the canonical case in trading of someone getting fired and the boss tapping the trading assistant who is most familiar with the book to step up to manage the position. If you are talented and hang around the rim of any position where talent matters, you’re a 1 night away from all the responsibility you can handle.

My favorite such story is my friend Tony thrust into hosting Around The Horn for the first time when Max Kellerman suddenly left the show. That day was the start of an almost unheard-of 21-year run as an ESPN host. Talk about being thrown into the fire, that was the day after the Janet Jackson nipplegate Super Bowl.

Working with exceptional people

This one is hard to judge from a few rounds of interviews. The more experience you have with people, the better your judgment gets. You’ve seen how first impressions cash out, you recognize red flags, and the reps build intuition. But job-matching is naturally adversarial since the stakes are high. You’re trying to find who you’ll apprentice under, and that person who emerges as your eventual mentor might never have been in the room during interviews.

You’ll need to reach for heuristics. Unfortunately, the good ones are weak and the convenient ones are broken. Credentialism has some signal. I don’t think I’ve ever met an MIT grad who wasn’t smarter than me. But the error bars on the signal path from even honest credentials to efficacy are wide. The Stanford PhD who can’t reason out loud and the state-school kid who dismantles your argument in five minutes are data points your priors lack.

In fact, the state-school stud example is a common version of the credential trap. Berkson’s paradox tells us that inside any selected pool, the visible signals stop telling you what you think they tell you. If you see a short kid start on one of the best varsity basketball teams in the state, get ready to watch an absolute savage. The population correlation will correctly predict that taller people are better basketball players, but when you restrict the range to people already on a basketball team, the correlation loses predictive value and can even invert at the extreme. The Taleb version of this idea is that you don’t want a surgeon who looks like someone who plays a surgeon on TV. I say it a lot, but once you are familiar with Berkson’s, you see it everywhere. When you are in a wicked info landscape knowing these little anomalies can counteract the System 1 snap judgements trained on population-level observation.

Let’s move to company reputation. Reputation, the literal outside view, is a convenient heuristic. With enough samples can sketch a reasonable portrayal of a company. But it won’t work where my first piece of advice sends you — (not AI dash, sigh) to a lean team where your contribution is critical. Not enough samples. You’d be lucky to find even one. The places everyone has opinions about are, almost by definition, big and legible ones, therefore the least likely to give you the responsibility you actually want.

Unfortunately, there’s no shortcut to spotting exceptional colleagues. It is the bane of employers and job-seekers alike and it’s not for lack of effort. There is tremendous leverage not only in hiring well, but in the spirit of all this advice, to learning extremely fast if you find the right mentor.

An exception

We’re giving preference to going to a small company where you are pressured to learn fast and compress your timeline. But there’s a specific class of bigger institutions that earns an exemption. These are the places that have managed to formalize their the hard-won, domain-specific practical wisdom, or metis, that usually lives only within individuals. The default in companies, especially those that have a star culture, is that knowledge stays tacit and exits when good people leave.

Most organizations cannot or will not invest in the preservation and transfer of knowledge because it’s expensive. Some companies may see training as a box to check, while those with a long-term view will see it as an investment in a compounding edge. If you are talking to a firm in the second category, you are at the doorstep of rapid learning even if the org chart is a pyramid.

A few concrete examples of orgs known for their training:

  • Navy SEALs are experts in decentralized command under pressure. They fuse a culture of risk assessment and extreme preparation. The government spares no expense in manufacturing these soldiers. (My favorite book during every man’s signature special ops rabbit hole is Lone Survivor which my older kid also loved.)
  • SIG and Jane Street fancy themselves the SEALs of discretionary and quant trading, respectively.
  • Goldman is in the fancy client business. I imagine it’s hard not to walk away without some durable closing skills and a smidge of dark arts.
  • P&G built the academy that trained a generation of CMOs in brand management with their alumni in leadership roles across hundreds of giant consumer companies. The playbook for selling a commoditized product existed well before the era of digital marketing.
  • Finally, Disney Institute and Chick-fil-A are widely considered the template for customer service.

Blood from a stone

It can’t be overemphasized. The purpose of a new grad’s job is rapid learning. Hopefully, in the field they want to be in (although the messy process of learning can also mean self-discovery and detours which are fine if not expected). But in the very real possibility that the field isn’t for them, it’s more important that the rapid learning is for skills that mesh with their talents and can find purpose in whatever direction their careers evolve.

Since it’s unlikely that one’s first job is their last, let me offer a final bit of advice. It’s time to change roles or companies once you feel your learning rate slow to a crawl. When professional gains feel like blood from a stone, it’s time to poke around. Explore. Maybe develop new skills at night while you bide your time. There’s even a chance these explorations rejuvenate your current role as AI has done for many.

I mention this because there can be a disconnect between learning rate and how things are currently going for you. This is definitely a trap. Results are a lagging indicator of effective learning. The cost of slow growth shows up in the future, delayed by the comfortable harvest seeded by your previous high learning rate.

I leave that as a warning. I will tell my kids the same.

Wrapping up

  • Optimize for learning rate. Not pay, not prestige, not the y-intercept. You want acceleration.
  • Actual learning requires risk and accountability
  • When you find an exceptional colleague, help them and if you can learn from them you’ll compress time
  • If opting for a big company, focus on those who make serious investments in training that will serve your career especially since you are unlikley to stay at the first big company you work for
  • When the learning becomes blood from a stone, you need to make a change. Your own stagnation follows on a lag.

When in doubt, ask yourself where you will learn the fastest.

stacking carry: an inflation hedge you get paid to own

US bond yields are rising as inflation re-enters the conversation. The 10-year yield is up to 4.65% and 30-year bonds have just crossed 5%, a nearly 20-year high.

This isn’t surprising. 6 weeks ago, in Trading As A Sudoku Puzzle With Prices As The Given Numbers, I talked about how 1-year gasoline futures were trading at a 1/3 discount to prompt pricing, but if gasoline prices remain high, this will roll up. If spot prices stay high for a year, those back-month futures will converge to current prices. Even though energy is only about 5% of CPI, the size of such a sustained move would easily transmit 1.5% to inflation indices and that is just due to direct energy effects and ignoring indirect effects on food, construction, and transport.

We’ll switch the conversation to crude oil just because it’s more widely tracked and the specifics of the contracts aren’t critical to where we’re going. Prompt oil is roughly in the same place vs 7 weeks ago, but the contract that was 12-months out and is now 11-months out has rolled up >6%. Meanwhile, another month of sustained high oil prices has pushed the 10-year yield up 30 bps from 4.3% to 4.6% with IEF price returning about -1.6% a bit better than what’s expected by its duration.*

*There’s some leeway since I’m using an index for the yield which may have a different set of weighted maturities than IEF holds. Also, IEF total return is closer to -1.1% because you earn interest for 7 weeks.

So far, so good. The reaction function in bonds makes sense. But my Sudoku post claimed that an inflation-induced yield bump would transmit to real equity risk premiums. In other words, I would expect equities to sell off with bonds, or heck, at least not have such a sharp rally.

This is not quite the puzzle it appears to be. The equity exuberance is actually quite limited if you look under the hood of the index.

From Shannon’s substack:

The internals are doing something the people who watch this for a living have never seen. The S&P is up 4.2% month-to-date with 209 stocks up and 295 down. The NASDAQ is up 8% month-to-date on a near-even split (51 up, 50 down). The index is 9% above its 50-day moving average while only roughly half the components are above their own 50-day; at that distance you’d normally expect 80% breadth. Four days running, more S&P stocks hit new 52-week lows than 52-week highs, with the index at all-time highs and up 30% year over year. Yesterday 9% of the index hit new lows. None of this happens together in a healthy tape.

I’ve noticed many market people interpret these “internals” as bearish. I’m not sure this is bearish for the index. It just is. A few companies are eating everything else. We get it. At this point, the low cross-correlation of the components is common knowledge (isn’t this what managers call a “stock pickers market”?).

Rather than use the term “bearish” which has a predictive slant I can’t justify, we can just accept that the sustained oil price, inflation jitters, and rise in yields are being reflected in prices broadly. SMH (semis ETF) is near 1-year highs while XHB (homebuilders) are near one-year lows.

The AI story is in a parallel vacuum, indifferent to relics like discount rates or identities such as spending = income, but stocks overall are not being indiscriminantly bid. SPY has returned nearly 2x RSP, the equal-weighted SP500 index, over the past year. So the loving arms of our cap-weighted benchmarks hold us tight, shielding our eyes from the turmoil within. Trepidation over supply-side inflation is confirmed by bond and non-AI stocks alike.

Concerned with inflation, I dust off some old posts, like What I Learned About TIPs which I wrote when I bought when breakevens shrunk to about 2.2% (green box).

(When breakevens are skinny, TIPs are relatively cheap compared to nominal bonds, and when they are fat, they are relatively expensive. The way to think of that is if you buy TIPs at say 2% breakevens, then you are better off with the TIPs if CPI realizes more than 2% and vice versa.)

Breakevens are currently matching 3-year highs so TIPs don’t look attractive on a relative basis, but that’s only one lens. The real driver of my decision to buy TIPs in Oct 2023 was the absolute real rate which was ~2.45% which still stands as the peak for most investors under age 40’s working life.

Remember that’s 245 bps of return above inflation for no risk and if you hold them in an IRA, no tax drag. Historically speaking, equity real returns have been in the range of 3-6%, but recent years have been quite a run of heads. Whether the coin is biased now is a question for someone smarter than I. But I digress.

The point is I’ve started once again to consider inflation-aware trades. 10-year TIPs don’t stand out as a bargain relative to nominal bonds. I’m wary on gold and silver because of how well they’ve performed recently, but also historically, they have not been great to own when real rates increase and we can see from the absolute TIPs rate that, despite breakevens not breaking out, real rates are crawling higher, approaching an 18-month high.

So I dust off yet another post, this one from 2 years ago: Inflation Replicator. I show how a portfolio of oil futures plus nominal bonds mimics the behavior of inflation-indexed bonds like TIPs. I constructed it in Composer using USL, which holds a strip of oil futures maturing within the next 12-months, plus TLH, a bond ETF holding bonds with 10-20 year maturities. The portfolio is inverse-vol weighted, rebalanced quarterly.

This is the out-of-sample performance since I published the post (green line).

That portfolio is a set-and-forget inflation hedge if you don’t like TIPs.

[Speaking of “tips”, here’s a general one. If you have a portfolio that rebalances, it is often selling winners to re-invest in losers. This keeps you diversified and avoids the volatility tax that comes from concentration, but it’s not tax-friendly unless you do it in a sheltered account. To do it in a regular account, you can consider a tax-loss overlay where instead of buying more of the losing position, you actually sell the losing position and another ETF that has a highly correlated exposure. So, for example, if TLH is the losing side and you need to add more on the rebalance, you actually tax-loss harvest the TLH and replace it with TLT length. It’s a similar exposure, but you can now use the TLH capital loss to offset the gain on the USL win you trimmed.]

The specific inflation replicator I composed was TLH + USL. But if we abstract it to “bonds + oil”, it invites us to think about risk premia that exist in both asset classes in the current market.

In the remainder of this post, I’ll narrate layering a couple of edges onto a core portfolio idea. By following along, you’ll get concrete ideas for measuring and managing risk and open your mind to the different Legos available to build the portfolio and ultimately express the trade while targeting the carry embedded in the asset’s pricing complex.

Inflation Replicator with positive carry

Let’s talk about our baseline exposures: oil + bonds

Instead of building the inflation replicator portfolio with the USL ETF, we want to isolate a carry-rich version of “oil”.

The oil leg

As I write on 5/20/26, the prompt WTI future, CLM6 (expires in May), is $98.

CLZ6, expiring in November, is $81.75.

If the spot oil market is unchanged over the next 6 months, CLZ6 will “roll up” nearly 17% (~34% annualized).

The bond leg

Long TLT shares. You collect the ~5% annual yield as carry. That’s the simplest expression and what we’ll size against.

Reiterating the core idea of the inflation-protected bond we are creating

We are pairing oil and bonds together because high oil prices are a major driver of inflation and the accompanying weakness in bonds. In other words, the bonds and the oil hedge each other if we own both.

They are coupled antagonistically. Look at the correlation of TLT (longer-dated bond ETF) and USO, which holds prompt WTI futures.

moontower.ai

Before the war, the rolling 21-day correlation of returns between TLT and USO ranged from about zero to -.50, spending the bulk of the time between 0 and -.25.

Since the war, the correlation range abruptly shifted lower, recovered a bit and has now collapsed to -.75.

💡Does it matter that we are comparing TLT with prompt WTI via USO when we want to express crude length with the deferred Z26 contract? The vol of the two contracts is very different, which matters for sizing reasons and would show up in the beta, which is vol ratio * correlation. But correlation alone is still tight across the futures strip with M1 to M6 easily above 0.90. It’s safe enough to infer the correlation of TLT to Z6 futures from its relationship with USO.

You will see how the inflation replicator portfolio benefits from the negative correlation when we get to sizing. Understanding the correlation range will also be key, as it’s a critical input to risk management.

Sizing the core portfolio

We begin with a risk target expressed as a fraction of a portfolio. We’ll choose $100k of annualized volatility allocated to this trade. Feel free to pick your own number, the method is what matters.

A $100k annual vol target is easier to reason about if I convert it to a daily number, because daily P&L swings are what I actually watch on the screen. Annual vol scales with the square root of time, so:

$6,300 of daily swings is for the portfolio of oil futures + TLT. We need to size the individual legs of the trade.

Step 1: convert each leg’s vol to a daily number

Again, we are converting annual vols to daily by dividing by √252

CLZ6 has 43% implied vol → daily vol ≈ 2.71%

TLT has 11.5% implied vol → daily vol ≈ 0.72%

Oil is about 3.7x as volatile as TLT on a same-dollar basis.

Step 2: inverse-vol weight the two legs

Inverse-vol weighting means I want each leg to contribute the same daily dollar volatility to the portfolio. Not the same notional, the same risk. The high-vol leg (oil) gets less notional, the low-vol leg (bonds) gets more, until they pull equal weight in risk terms.

Mechanically:

The daily dollar vol due to either asset should be equal. We’ll set that dollar vol equal to S.

Step 3: solve for the portfolio vol as a function of S and correlation

This is the two-asset portfolio variance formula:

 

The w’s are dollar weights, the vols are in daily percent, ρ is correlation.

Inverse-vol weighting forces w₁σ₁ = w₂σ₂ = S, therefore every term becomes a multiple of S²:

 

That’s the engine. Portfolio daily $ vol is just the per-leg $ vol scaled by √(2(1+ρ)).

Note how correlation has such a large impact on the portfolio vol. At today’s ρ = −0.75, the multiplier √(2(1−0.75)) = √0.5 ≈ 0.71. The portfolio is less volatile than a single leg.

Step 4: invert to find the leg size

I want σ_p = $6,300. Solving the formula above for S gives S = $6,300 ÷ √0.5 ≈ $8,900. So each leg should carry about $8,900 of daily dollar vol.

Convert that back to notional: oil notional = S ÷ daily oil vol = $8,900 ÷ 2.71% ≈ $328,000.

  • CLZ6 is $81.75 and each contract is 1,000 barrels, so one contract is ~$81,750 of notional. $328,000 ÷ $81,750 ≈ 4 contracts.
  • TLT is .72% daily vol, so we need $8,858/.72% or ~ $1.22mm of notional or about 14,500 shares because TLT is $84

[$8,858 instead of the $8,900 we solved for comes the fact that we need 4 contracts that are not divisible any further. Note how the bond notional is ~3.7x the oil notional, exactly the inverse of the vol ratio.]

And the resulting portfolio daily vol at ρ = −0.75 is σ_p = $8,858 × √0.5 ≈ $6,263. Right on our $6,300 daily risk target, which corresponds to $100k of annual vol.

The beauty and danger of correlation

Let’s appreciate what’s happening here by considering monthly risk and reward.

Let’s start with risk.

Scale daily risk to monthly:

$6,300 *√(252/12) = $28,870

Now for the expected reward.

Oil: 2.5% roll up * $327,000 notional = $8,175

TLT: 5% yield * $1.22mm / 12 months = $5,083

Total expected return = $13,258

Monthly sharpe ratio = $13,258/$28,870 = .46

Annualize the SR:

.46 * √12 = 1.59

This is possible because we get to be long quite a bit of assets in notional terms, but the volatility of the portfolio is small.

The reason it’s so small is that the correlation is very negative.

But ρ = −0.75 because the war pushing oil up is adding a risk premium to bonds (ie pushing their price lower).

To understand the risk, we must stress-test correlation. We fix S and vary ρ.

[Risk should really be treated like a matrix since changes in the correlation will coincide with the vol of the legs moving, thus changing the vol ratio between them. For example, if the war relaxes and the correlation heads back towards 0, oil prices likely fall, bonds likely rally. That’s ambiguous for the p/l, but since oil’s vol is the one that’s more stretched from “normal” you are underweight the falling asset which is good. However, the increased correlation means total portfolio risk is more than you intended]

Your portfolio risk doubles if corr goes back to 0.

Juicing the bond leg with options

So far the bond leg is plain-vanilla long TLT shares earning the ~5% yield. But given the sell-off and inflation fears, the bond option market is also offering risk premia as vols have increased and put skew has steepened.

Let’s talk about the vol first.

VRP

As I write on 5/20/26, the ATM 1-month put is around $1.20, corresponding to 11.5% IV. TLT’s realized vol has been running below its implied. 1m realized vol is ~8%, 1-week rv is closer to 9% and median 1-month rv for the past year is about 10.5%.

Call it a 15% vol risk premia:

  • Put premium: $1.20/share
  • Fair value: $1.20 ÷ 1.15 ≈ $1.043/share
  • VRP edge: $1.20 − $1.043 ≈ $0.157/share, or 15.7 cents per share

The practitioner’s way to carry that number in your head is per contract. Each contract is 100 shares, so the VRP per contract is $0.1565 × 100 = $15.65 per contract per month.

The bond leg’s delta target was the equivalent of +14,556 shares of TLT. An ATM put has a delta of about −0.50, so selling one put gives you +0.50 deltas per share, or +50 deltas per contract (100 shares × 0.50). To replicate the share position’s delta: contracts = 14,556 deltas ÷ 50 deltas/contract ≈ 291 contracts.

291 × $15.65 ≈ $4,555 per month, or ≈ $54,700 annualized.

If you sell ATM puts to express the same long-delta exposure. You collect the put premium, and the portion of that premium above fair value is vol risk premia stacked on top of the yield carry.

💡It’s never that simple when it comes to options. The yield carry is the yield * notional but as TLT moves around, you are short gamma so as the stock falls you are longer TLT and as it goes up, you become less long TLT, so the yield due to bond income is a moving target.

Be careful. 291 contracts on an $84 stock is $2.44mm of gross notional, even if it’s still $1.22mm share-equivalent notional. The local delta exposure is identical, but by swapping the expression to pick up VRP we added non-linear risk to the position.

Skew

TLT’s 1-month risk reversal is at the 94th percentile of the trailing year. The put skew is rich, call skew is depressed.

montower.ai skew percentiles (puts on x-axis, calls on y-axis)
moontower.ai

You can express the delta by selling OTM puts, which will make the risk non-linearities even more concave. You can also sell put/buy call on risk reversals to take advantage of the stretched skew in both directions. All of this is changing the shape of the p/l and risks dramatically. The best way to get your arms around it is to construct a matrix of scenarios.

Oil options

The bond leg harvests rich skew by selling puts but the oil leg can do the same thing in the opposite direction.

Oil call skew has a war premium. That makes a call spread an attractive way to express the long oil leg: buy a closer-to-the-money call and sell a further-OTM call at a stretched IV against it, financing part of your long with the fat skew you’re selling.

For example, instead of buying 4 Z26 futures, you could buy the Z26 88/98 call spread. With the underlying at $81.75 this OTM structure costs ~ $2.35. It has a .12 delta, so to get 4 contracts worth, you’d need to buy ~33 call spreads (4/.12).

You’re long the rollup-and-supply-scare upside, but you’ve capped your gain to $7.65 (about 3.2-1 odds on your premium), but your downside is limited to the debit if Hormuz de-escalates and oil pukes.

Trade management

It’s well understood that when it comes to options your risk is changing as assets move around, as time passes, and as implied vol fluctuates.

A more subtle risk is how your exposure changes on the oil leg even without options. The oil future becomes more volatile it approaches maturity ages. The 6-month oil future currently has a 43% implied vol but the near-dated future can be twice the vol in times of stress. So even if nothing moves, the oil leg’s daily dollar vol creeps up over the life of the trade. This might be partially mitigated by the roll-up amount becoming steeper as you approach the front of the curve.

The 1-month rollup from M2 to M1 is twice as steep as the 1-month rollup from M6 to M5.

CL futures via TradingView

 

The good news: the same risk framework that sized the trade also manages it. Re-run σ_p = S·√(2(1+ρ)) with fresh inputs whenever the market moves:

  • Oil vol rose? Each leg’s S is no longer balanced. Trim oil contracts (or tighten the option overlay) and add bonds to re-equalize the legs and pull portfolio vol back to the $6,300 daily target.
  • Correlation drifting toward zero? The shock table prescribes how to proportionally hold both legs to maintain the vol target.
  • If you use options and your total risk or relative leg risks get out of tolerance bands, you can reassess to see if you should roll, add, or even close.

Because the trade is a living position, you may want to treat the target risk as an upper bound, and initiate the trade at smaller sizing giving you wiggle room to rebalance less often.

A summary of stacked edges

The bond leg is long carry because the position has a net long delta (yield) and short rich puts (VRP).

The oil leg is long carry (rollup) and short rich calls (skew).

You’ve taken a simple “buy oil, buy bonds” inflation replicator and layered distinct edges onto it, each one sourced from a risk premium in the pricing complex:

  1. Oil rollup carry (term structure)
  2. Bond yield carry
  3. Bond VRP + put skew
  4. Oil call skew

On the carry side, you are monitoring VRPs, term structure, and coupons, while on the risk side you are monitoring the volatility of the legs as well as the correlation which has a major impact on the portfolio risk.

How big a portfolio does this need?

I sized everything to $100k of annual vol, but I never said what size account sits behind this trade. Vol targets don’t specify a portfolio on their own — they specify a portfolio once you decide what fraction of your risk budget the trade gets. If you want this to be a 10% vol sleeve, you’re implicitly running it against a $1mm book. A 5% sleeve implies $2mm.

You’ll immediately notice a problem if you consider the 10% / $1mm case. The bond leg alone is $1.22mm of TLT shares, which exceeds the entire account. You can’t fund it with cash, you need leverage. Futures are inherently levered as you only need to post initial and possibly variation margin. For the equity portion, portfolio margin can allow you to post even less than a 50% haircut.

But leverage introduces path risk. Your position is changing with market conditions, especially if you use options. But this portfolio sizing is resting on a large position in a low-vol asset as well as a negative correlation. The simplest way to appreciate the risk is to notice that a mere $100k of annual vol rests on ~$1.5mm gross exposure. If you run this portfolio at $100k annual vol with only a $1mm account, you are managing both risk and margin closely.

Recall the portfolio expected Sharpe was 1.59. So for $100k annual vol, we expect $159k in profits or 15.9% on a $1mm account. The expected return halves to ~8% if you run it in a $2mm account.

The best but most complicated choice is to run a strategy like this in a diversified account where the other moving parts interact with the portfolio margining computations such that the required haircut is small and therefore efficient.

Let’s leave it there for today.

what I want my kids to know

I went to Catholic school for K-12. Public schools were less than good where I grew up. My kids go to public school. The K-8 schools here are fine. Better than where I was raised but still nothing special.

The biggest difference is demographics. This is an upper-class area, the student body on average has a natural head start academically. You can attribute it to nature or nurture but it’s true. The mean OLSAT scores, which determine if your kids get into gifted programs, are a full standard deviation higher than the CA mean. Since the test is approximately an IQ test, that places the mean public school student at around 115 in this area. You need to be somewhere around 1.5-2 standard deviations higher than that mean to make the gifted programs here.

There are children of founders, scientists, artists, doctors, lawyers and athletes. Several are legit famous (Steph Curry lived here at the start of his career and there are a number of NBA, MLB, and Olympians who call our area of the East Bay home. Alanis Morrissette lived a few blocks away from the first house I lived in here, but has since moved, and the Chevron CEO’s house is on the best block for trick-or-treating. I think he’s not here anymore either, though). There are many more famous in their fields. But it is a deeply understated area as I can think of at least 3 billionaires in town and probably 2 dozen centimillionaires, but you are not going to find a 30k sq ft house anywhere in the vicinity. It is the opposite of Miami. It is what my friend Jason Buck calls, “stealth wealth”.

Beneath the fancy folk, there’s a thick sedimentary layer of unmemorable overachievers (like yours truly) ranging from white collar workers to the type of entrepreneur who calls themself a businessperson, not a founder. You own a construction company or a few burger joints that sell boozy shakes.

And then there’s the strata of wage earners with the honest jobs. The kind you find in Richard Scarry books. Nurse, firefighter, teacher, cop. They almost all grew up here. Nobody subjects themselves to the financial punishment of moving here if they make their money the hard way.

Finally, there are the villains of CA. Retired boomers living in $2mm houses, paying $2k a year in property taxes with 2 vacant bedrooms plus a 3rd for their golden-doodle. As an abstract class, I understand the venom, but also these are my neighbors who I mostly get along great with. If I went on Nextdoor maybe I’d feel differently but I choose not to look.

[Everything I said above is likely taken up 1 to 10 notches, depending on if you are in Marin or the peninsula. The East Bay, for all its unrelatability to much of the U.S., is still the most relatable. Much of my surrounding area towns remind me of where I grew up, but parallel shifted higher simply because CA cost-of-living and incomes have a higher Y-intercept. The slope of experience is likely very similar. For Mother’s Day my wife’s extended family of ~50 people visited from various parts of the East Bay and I feel like this is the normal I grew up around, except everyone has straight hair and knows how to use their indoor voice when they’re 12 inches from your face.]

Back to public school. The system itself is incrementally better than home, but the kids are generally pulling from a more talented, competitive, and driven baseline. Life’s not fair and it’s indifferent to your pleas otherwise. I tell my kids this.

On Monday, on the way home from track, I took the 7th grader to Safeway. We were in there for odds and ends. Bagels, sunflower seed butter, milk, berries. 2 paper bags worth of stuff. There was a $30 tub of protein. All-in, $120.

I gave Zak a lecture he didn’t ask for or see coming. “Did you see how little stuff we just bought? 120 bucks, including about 10% sales tax. If you work as that check-out person in the grocery store for $15/hr, that haul is a day of work.”

Then I go on my dad rant about not getting fooled by your surroundings. What school says is an A is nothing but basics. The basics of showing up and executing on what they told you to do. If inflicted by an uninspiring teacher, it’s compliance training.

[I’m not saying everyone should feel this way, you know your own kids. The only way I would not have gotten As growing up was if I were negligent and that certainly happened sometimes, but again, the bar of not being negligent is ground zero executive functioning. If you can’t do that, then it makes sense to track down the reason and decide what the cost/benefit of trying to remedy it or not is. These are personal battles to choose.]

The gears were turning. Both he and his 4th-grade brother were taking this in. I’ve explained this to them before but they were listening now. We chatted for about 45 minutes meandering through several related topics. One question took me off guard because it’s a sharp reminder that their frames of reference are so different that their minds go to places that surprise me. They asked if I had that paper they give people when school is over.

A diploma?

Yes. They asked if everyone gets one if they finish school or if you have to go to a “good” school? A bit of a strategic moment here. I need to simultaneously encourage education without tricking them into placing it on a pedestal. Education at its best is useful knowledge and deep inquiry, but at its worst, the exact opposite — propaganda and conformity (I hate using the “—” but I assure you that was me).

I told them I had a diploma. In fact, it’s framed, a gift to me from their grandma. They asked why I don’t hang it up like the orthodontist does. It was time for real talk.

I explained that I’m not especially proud of my degree. But take full responsibility for my disappointment. I took a non-technical econ degree. It was an easy 4.0 because it relied on me writing persuasive-sounding bullshit on blue-lined pamphlet paper. This didn’t push me to grow.

Then I found myself in a technical career where I wish I had studied what I tried to study at first but gave up on. Computer science. It would have empowered me to go faster. But even more important is the confidence. I was always insecure about not applying myself growing up and therefore having no real skills. Attached to what I was told about my potential for longer than maturity should permit.

Possessed by the ghost of my adolescent guile, I asked Zak if he thought he was actually good at the tasks given to him at school or if he was good at guessing the teacher’s password. By whose standards is your grade an A?

My correction (overcorrection?) now is that I tell my kids the world doesn’t need nor give a smouldering turd about another smart person. Dime a dozen. What you need is nerve. Courage. What’s the point of smart if you can’t get what you want out of life? In fact, nothing is more embarrassing than watching a person who thinks of themself as smart complain. If you’re so smart, figure it out. If you can’t, then your smarts are either not useful, not real, or a party trick. If they are a party trick, find a way to get the trick rewarded so you have less to complain about.

So what is school good for? What can you salvage from the private school or the better school district? It’s a hard question. And I’m at least a little concerned that my impulsive but deeply sincere reply below represents the bulk of my answer.

I’m not trying to manufacture contempt in my kids for their smuggest peers, but I assure you I’m going to look the other way while their mom does.

The excerpt below from author Devon Erikson articulates a phenomena we all see. It’s also deeply related to trading which I’ll explain afterwards.

There are two types of intelligence tasks: answer tasks and result tasks.

A result task is graded by the reaction of the environment to your work. Either your software runs, or it doesn’t. Either your rockets fly, or they don’t. Customer buy millions of your product, or none.

You have unlimited tries unless you run out of money, but there’s no partial credit, and you can’t talk the universe into accepting your answer if it doesn’t.

Result tasks typically require a lot of work, are data-intensive, and have lots of sub-problems, because the ones that didn’t are already solved.

Result tasks are why we care about smart at all. Because smart people are the ones who can do this. And every human advancement or achievement ever was a result task.

Answer tasks are quite different. They are artificial problems created by a human being for another human being, whose goal is to produce the known answer.

Tasks like this have useful features. They can be tightly calibrated for appropriate difficulty. They are easy to grade. They can be used to teach particular subjects or skills.

But there are certain things they don’t teach.

How to do the boring parts that don’t impress anyone with how talented you are.

How to fail and try again.

How to change the question instead of answering it, because the question itself was wrong.

How to absorb from others what they had to learn the hard way, instead of reinventing the wheel.

How to deal with problems that have no solutions, only tradeoffs.

How to work with others and pass the ball.

How not to adapt instead of freezing when the universe gives the exam before the lesson.

How to substitute the adequate you can afford for the ideal you can’t.

How to prioritize what is needful over what is elegant or cool.

Without this learning, and other similar lessons, the talent child turns into an adult with an unbalanced intellectual development, like a bodybuilder who skipped far too many leg days.

You’ll find a lot of men like this in academia because it provides them with a sheltered, tightly controlled environment, where the problems are abstract if not utterly fake, and the persuasiveness of a solution trumps its workability.

They tend to scorn achievers, especially achievers with modest academic credentials or none, and this invites scorn in turn from people with real jobs.

But really what they are is victims. Entire campuses and networks full of what was potential greatness, crippled in it youth by bureaucracies that claim to serve it.

Homeschool your children.

Give them projects, not puzzles.

Teach them to build things.

The bridge to picking better advisors, doctors and agents in life

Devon’s argument is generally about what developers call “acceptance criteria”. The predefined requirements by which a solution is deemed a success.

“Does it fly?” versus “Would leading experts agree that this would fly?”

In a non-fake field, these acceptance criteria would be strongly correlated.

Short-term trading based on high sample sizes has an acceptance criterion of “does this reliably make beyond a narrow slice of world states?”

Investing, the further it strays from the principles that drive trading (for example, deal flow is a universal alpha), becomes faker. It becomes more consensus-seeking. More “nobody gets fired for buying AAPL” than “what have you done for me lately?”. Long feedback loops, loops that can last a career, shield its actors from dispositive resolutions of acceptance criteria.

Investing, like medicine, is a minefield because it’s a complex domain that even bona fide experts have limited, even if deep, knowledge. What is a consumer to do when tasked with finding a trustworthy agent in such a hazardous info landscape?

The trick is at the meta level. To consider the acceptance criteria that their agent uses to make judgments. Shut up and listen to people and they will unknowingly confess their epistemology. In fact, many will outright proclaim faulty acceptance criteria as a sales pitch without a hint of awareness that they are themselves fooled by standards (“I’m 30 under 30”) so fraudulent that those standards are unironically acknowledged countersignals by anyone with basic survival instincts. It’s like advertising alignment with hall monitors and the hopelessly dense.

Another red flag is the equivalent of waving your diploma on social media. An appeal to an authority that is disconnected from relevant questions like “will it bear weight?” or “does it make money”? Here’s an example. I didn’t want to call out the individual who was not only wrong about option theory but superciliously so:

“So and so is great on F&O” and “look at my degrees” are appeals to authority when the topic at hand is only answerable to arbitrage or not. This is a breathtaking juxtaposition of opposing epistemologies. Arbirtage is mathematical proof while a degree is conferred upon completion of fake obstacle courses. Arbitrage is gravity. Its equations exist whether or not someone in a robe approves.

The tweet digs into a defensive posture. Revealing. You don’t make it out of the first 5 minutes of a phone interview in trading with this reflex.

The right reflex is “I raised into a bettor, who has re-raised and I now have to reevaluate my hand.” You didn’t raise in the context of something subjective like religion or philosophy. Your opponent could be and very likely might be holding the “nuts” given this is a public forum with embarrassment at stake AND the right answer is very knowable. I can’t even process how broken your reasoning skills must be to not recognize the nature of information. This is what it looks like to be captured by the fake standards that Devon wrote about. The charitable take is to bemoan a definition of education that permits this as passable thinking. Devon would call this person a victim.

Screening for traders is tough because you have to sort through people that have spent much of their life being right, but are dropped into a game where other smart people raise into you knowing that you are smart too.

It’s hard to tell if someone would be good at trading, but it’s much easier to tell if they wouldn’t. One of the things I’d look for is the type of intellectual humility that you immediately recognize when someone seems to make very few assumptions once they are in a situation where they are confronted with a bet or claim. They have a debugging mindset as they checklist through what assumptions are material to the decision. They have an imagination that survived the weathering effects of formal education’s emphasis on what Devon called “answer tasks”.

If you ever watch a 3-card Monty hustle or even a magic show/sleight of hand, it should remind you that there’s a lot of profit lurking for someone who painstakingly examines the territory where your confidence in appearances stretches further than it should.

Just as it’s hard to tell if someone is good at trading but easier to rule out those whose reasoning machinery is stunted, you should be able to at least rule out bad agents in complex domains by inviting them to talk too much. Go forth and listen.

[Twitter is amazing for countersignals because its incentive structure encourages people to talk too much. I think a lot of famous investors have revealed themselves to be trash investors but good business builders by streaming their thoughts. Unless they are reaping some rewards from manipulation, it also indicates poor risk management. You benefited from mystery and sold it for ego strokes from simping strangers.]

face-ripper

If you reside in the quark-sized intersection of people who read this letter but don’t follow the market, I’m informing you that shares of corporations are up sharply in the past 5 weeks.

The magnitude and speed of the rally have been “hellacious” to use a mentor’s favorite way to describe the face-ripping bear market rallies. Not that this is a bear market rally. As you know, bears are extinct and all the degeneracy you see is their normal diet flourishing without a natural predator.

Now, about that face-ripper…my turn to cherry-pick. It turns out selling calls that carry a high implied vol but were in the 0th percentile of skew wasn’t really “income”.

The green line is a portfolio of 75% SPY, 25% cash rebalanced monthly which is a more proper comparison to JEPI which sells OTM calls. Rough month for the home team.

If curious here is 75% SPY vs JEPI since it launched:

 

The rally has people confused. What about the war? What about oil? What the f is happening in this chart:

TradingView chart
Created with TradingView

It’s not even a single stock. It’s a sector. A sector with a big market cap already!

Two thoughts wash over me.

Thought 1: Is any of the news we see reliable? Do we have perceptions that are unlinked to reality, causing the market behavior to look so dissonant?

Thought 2: Horse said it best and this was only 2 weeks into the up-flush:

Let me save you some grief. Causality and stories are for historians, novelists, brand strategists, politicians, and grifters.

Traders are agnostic. Markets are Sudoku puzzles with prices in place of digits and risk/reward comes from the strain of contradiction. It can’t be otherwise. I saw Horse’s tweet after midnight when I couldn’t sleep so figured I’d pop off on why I agree.

Paradox of skill…the smarter markets are the more random it feels.

If lines to a game are well set you win some, you lose some and either way you pay the vig

The market not making “sense” …makes sense

Your making money shouldn’t depend on it making sense, because if it did, it would violate the idea that most people cannot make money trading (assuming the notion of sense was something shared)

This feels like some corollary to trading broadly…trading is about making money in the absence of knowing what is going to happen.

Trading is a practice that be adapted to any environment. Sometimes you inherit a departed trader’s position. You deal with it. You manage the risk. Your ability to do this shouldn’t depend on the market behaving according to your opinions.

I’m guessing that the needs-to-make-sense crowd sees the market like a physics or cause and effect problem rather than what it is. Positions and flows

(In the long run whatever that means it probably does make sense but nobody wants long run edge because it has long feedback loops and doesn’t maximize throughput of an actual edge like higher turnover, better sharp strats. But short term movements have no reason to make sense in any economic or textbook ways)

The market is just positions and flows.

Why does it go up? There’s a lot of savings in America seeking a return and not enough issuance that it desires to satisfy it.

I’ll use the overrated phrase “first principles” to describe what I think of the market when I zoom out:

Laws and governance matter because they modulate the rights of managers to extract, influence, and enhance both the paid and retained claims that shareholders own. And then those rules and incentives determine capital allocations to generate returns that hopefully justify spending our cells’ ATPs on these projects instead of killing each other in a world of scarcity. This is all crucially important and their fulfillment or lack thereof will make sense in the story of humanity. But they operate on a different time scale than trading or short-term returns.

The only way the short-term stuff will make any sense is from the vantage point of knowing what people’s orders are. But the reason their orders are what they are will remain opaque (excluding of course, forced or recipe-based strategies — which is why arb-minded traders think a lot about what Euan calls “inefficiencies” as opposed to risk-premia.)

Implications

1) Specialize

In a finance context, this is what I call “matching your strategy to your dashboard”. Warren Buffet doesn’t do technical analysis to evaluate a business. The input of charts is not relevant to what determines his outcomes. Likewise, a trader focused on an opening range breakouts strategy doesn’t care about free cash flow. If you listen to traders and investors talk, listen for how things that wouldn’t be critical metrics in their dashboard seep into their thesis.

Remember the Paul Slovic study where experienced horse handicappers are given a few pieces of data of their own choosing. Armed with their preferred data, they are able to not only make good bets, but also to be well-calibrated about their accuracy. Their confidence and accuracy were in agreement. However, as the bettors are given increasing amounts of data their accuracy falls, but their confidence shoots up. No bueno. Presumably, they were less experienced in weighing the additional data, which turned it into noise for their handicapping process.

Just to broaden this section for a moment. With the success of David Epstein’s Range and the internet’s vague references to the “world belongs to generalists”, it’s probably contrarian to recommend specialization. The generalists get all the attention. Who doesn’t want to be the macro Neo seeing through the matrix of green digital rain to pull money out of connections nobody else sees?

It’s not just macro. VCs are seen as generalist extraordinaires studying up on a wide spectrum of technologies. Just enough to “be dangerous” as the self-aware ones will admit. But the trader in me doesn’t see a group of people with any special ability to see the future (painting with a broad brush, if you’re a VC reading this, you’re special, don’t worry). I see a social game with the goal to buy “below the bid”. The ability to buy in a dark market and sell in an efficient lit one requires specialization in something (probably marketing). And if you get that right, you have an edge. And that edge accumulates more advantage until you are free to tell any fancy story that sounds better than whatever their actual specialty is.

I’m not saying be one-dimensional. But becoming very pointy in a single area is a better beachead from which to launch the various campaigns in your life. Those may eventually lead you far away from where you started which is almost certainly a sign of victory.

The world actually belongs to the obsessed. Talk to parents. They know. The whole extracurriculars pu-pu platter is a fallback plan to Operation: Optionality because their kid has not found their obsession.

[Related thought: Being hot, super-charismatic, or any number of things we would think of more as a talent are all forms of speciality that can confound how we see the success of a “generalist”. But even then, there’s no ceiling for someone who applies their natural gifts to a craft that benefits directly from them. This is the dream. Talent and interest synchronously rowing in the same direction.]

2) Should you care about market plumbing?

I’ve seen this sentiment several times over the last couple years:

The Seawolf guys (they were portrayed in The Big Short as the disagreeable investors in the weeds of bank accounting) have said something similar after a short tenure as pod PMs at Citadel. They said it’s important to understand how the pods move capital, even if they don’t think whatever they are doing is really investing. It’s more like trading with a focus on the coming quarter instead of intraday scalping.

If the pods are the marginal price setters, then understanding their behavior is important for traders or any investor whose investors judge them on the basis of months, not years. Nobody wants to be judged on the months of course, but not everyone can pick the investors best aligned with their horizon.

Speaking of horizons, if you care about short-run market behavior (days and weeks) but don’t have a dashboard tuned to flows, then day-to-day activity will remain inscrutable. If you care about intraday, then you are either in the same pool as HFTs OR you are staring for hours at illiquid order books to divine the story. Where can you compete?

Finally, these voodoo market movements can create opportunities for investors willing to underwrite a long-term thesis. This is admittedly tricky. Long-term investing is weirdly a difficult place for professional investors (it kinda feels like it’s a place that individual investors should have a better chance to prevail since they don’t answer to LPs, don’t need to benchmark, or worry about looking stupid).

Besides fickle LPs, professional long-term investors face feedback loops that can last a career, making them a) difficult to learn from and b) fertile landscapes for confirmation bias. Those types of edges are never provable. And when they exist, the horizon means less throughput…you aren’t getting thousands of at-bats to put the edge to work.

Insofar as a professional investor is able to convince investors to stay the course, this ability need not have anything to do with investing skill. In fact, a patient investor base paying an AUM fee is an arrangement that might make all but the most competitive investors a tad lazy.

The lack of feedback, throughput, and competitive pressures rooted in predictive performance metrics is a set of conditions that would not predict the best investors are looking to underwrite the long-run. This is a place to potentially compete. Of course, every silver lining has a cloud. Those near-term dislocations driven by the glorified day-traders might offer a better entry but the longer your holding period, the less your entry price matters. If you find a compounder for 15 years, it won’t matter much if you bought it for $80 instead of $100 because a bunch of pods got tapped to shed a factor.

get a mortgage from the option market

I sold a house in the DFW area in 2022. Instead of a mortgage, the buyers financed the purchase via a margin loan against their stock holdings held in a Morgan Stanley account. A bit unusual. That was the year mortgage rates spiked so maybe the margin rate looked relatively more palatable. But there could be other reasons too. For example, getting a loan or HELOC is much harder these days without a fat W2 income, so maybe the buyer was an entrepreneur or retiree.

[I remember the aftermath of the credit crunch, an oil option trader I knew just had an 8-figure year as an independent trader, couldn’t borrow even $2mm of the $5mm loft he bought because his income was deemed so variable. I’m not saying bankers should use a sortino ratio, but damn that was broken. The contrast of today, when every risk gets underwritten with little premium, to that era when banks wouldn’t touch cash-good risks is stark. Do what you want with that.]

We are going to start construction on an ADU so I’ve been thinking about financing at a time when there are more options (a pun that doubles as foreshadowing). Last week, I wrote a guide to option margin. While a post like that was overdue, the timing of it was not an accident. It is deeply entwined with today’s topic of disintermediated borrowing.

Box Spreads Go Mainstream

If you’re here, you probably know a box spread is a way to borrow or lend cash via the options market. A quick refresher from the lender’s point of view:

It’s a very vanilla option trade where you buy a synthetic long at one strike, sell a synthetic short at another strike, same expiration, and you’re left with a position whose terminal payoff is just the difference between the two strikes. Since you are both long and short the underlying for a known differential at expiry, that’s a profit guaranteed in the future. That future profit trades at a discount today because of the time value of money.

Since the profit is guaranteed, the discount rate is approximately the risk-free rate. In other words, it looks like a bond. You might pay $9.60 today for a riskless $10 in one year. In this case, you are lending $9.70 to the options market. The credit risk is minimal because, just like any option trade, you are facing the Options Clearing Corporation (OCC), not a counterparty or brokerage.

You can find a fuller treatment of mechanics in my post BOXX: Access Options Funding Rates In An ETF. BOXX was born around the time I wrote that article. Today, there is over $10B of assets in BOXX (I own some as well). Its success has had a ripple effect for consumers, creating an entire new financing market that is cutting out high-overhead banks by leveraging 2 innovations that are sadly not often recognized as innovations unless you work in finance:

  • better risk-management
  • liquidity

We jeered when the head of a vampire squid said he was doing god’s work, but Lloyd was being both cheeky and observant at the same time. But I agree, it’s hard to concede credit to a band of traders who somehow got made whole on their CDS while everyone else was forced to take medicine after the credit crisis. (This felt like Epstein class cronyism between gov’t and private industry revolving doors even before the unaccountability of elites became the issue it is today. In fact, that period felt like it got the ball rolling not to mention spread the ashes from which BTC would emerge. My crank sense of recent history is that the GFC is probably still underrated as far as what it did to any sense that we animals are created equal. Private gains with socialized losses probably revealed a US class system that hid for a long time behind a shared story. So long to that fairy tale. The spirit of the day is more like picking through the salvage bins for your own family’s needs while you watch the elites loot the trust that dies hardest because it’s rooted in desperate hope. Oops, that got out of hand fast.

Where were we? Ahh, yes, risk management and liquidity. The risk management part comes from the portfolio margin framework adopted by exchanges for margin accounts that opt into it. It’s explained in last week’s post, but it’s ultimately about looking at portfolios holistically and allowing for sensible offsets for analogous instruments. A call spread is a combination of 2 options, but the risk is well-defined if you recognize them as a single chunk. Asking for reserves that exceed the maximum loss is inefficient. Which means we can make the world more efficient by measuring better. I think we have enough computers to do that in 2026. Low-hanging fruit.

It’s hard to appreciate productivity gains like this because it’s not visible in the same consumer-friendly way as a phone with a camera in it. This goes for liquidity as well. If the inputs to pricing any risk become more transparent and measurable, then someone will require less premium to underwrite the risk. Pricing gets tighter, attracts more volume, more transparency and a virtuous loop repeats. It’s the gist of not needing to come to terms with finance guilt.

[As financial innovation goes, I’m not sure if the last PhD hired to provide best-in-class liquidity services has low societal ROI but the first one has a high one, and we can’t really know the limits. As freedom and competition go, the argument is best reserved for dorm rooms smoke-outs instead of pre-policy dossiers with a red hammer on the cover.]

Anyway, once a giant “lender” like BOXX pokes its beak in the options market, it attracts borrowers. Liquidity begets liquidity. For decades, box spreads have been a quiet financing tool for market makers and hedge funds operating under intelligent margin frameworks. They are now shaping a two-sided retail banking function. Without the banks.

 

The emergence of a retail box market

In early 2024, just months after BOXX launched the average daily notional volume on SPX box spreads was over $900 million. A year later, it had grown by 30% to over $1.2B. The CBOE has built an entire suite around the popularization of box spreads.

In addition to all the education (these are options after all), they’ve greased access to the box market via the Quoted Spread Book, launched June 2024. Cboe calls it QSB; I’ve always heard it as the “COB” or complex order book, which is the general way to interact with package orders in SPX.

Before QSB, market makers were not allowed to rest orders in SPX option COBs during regular hours forcing boxes and other complex orders to trade open outcry in the pit. Chicago is a gangsta town son. This effectively gated the market to those with a broker. Now, MMs can post electronic quotes in designated box spreads, box swaps and jelly rolls (calendar spreads of boxes used to roll from one expiry to another).

Each trading day CBOE designates roughly 10 box spreads and 25 box swaps as quotable with strikes in 1000-point increments. Since the option multiplier is 100, a 1 lot box spread corresponds to $100k value at expiration. You can think of that as the standard face value of the “bond”. A 10-lot would correspond to $1mm.

The borrower side of the trade

Pre-existing market participants create both the supply and demand for spreads in response to their cash management needs while BOXX is a structural buyer of boxes (a lending transaction) so long as it enjoys inflows.

The market is now seeing a new breed of borrower via sellers of box spreads. Historically, that borrower was a dealer financing options inventory. Increasingly, it is a wealthy household financing a house, a tax bill, or consumption. Given the endless bull run of equity markets, being wealthy almost certainly means sitting on a pile of unrealized capital gains. The economic impact of deferring or ultimately avoiding taxes is likely an order of magnitude higher than earning more market alpha. Eeking out an extra 200 bps of return per unit of risk is just not that interesting if you have to pay taxes on it every year, especially if you live in CA, NY, or Chicago, where somewhat ironically many alpha-obsessives tend to gather (notwithstanding large recent migrations to FL, TX, NV, and of course PR).

The reluctance to realize capital gains is the root of the “buy, borrow, die” strategy which revolves around funding expenditures with loans against appreciating collateral. Then, at death, the cost basis of the assets is stepped up to current market value when heirs can sell to pay off the loans. Rajiv Rebello’s Eliminating a Large Capital Gain with Tax-Aware Investing explains this as well as other increasingly popular tax alpha strategies. The common theme running through them is the use of borrowing/leverage to delay the tax man, hopefully forever.

Box spreads allow consumers with a healthy asset buffer to borrow at highly attractive rates, especially on an after-tax basis. Box rates typically print within 50 bps or less of treasuries of comparable duration. The “interest” you pay is realized as a Section 1256 capital loss, marked to market each year, 60% long-term and 40% short-term. Meanwhile, a margin loan at Schwab or a securities-backed line at a wirehouse can easily spread 200–400 bps over government rates. Depending on your personal itemization situation, the interest on those loans may be non-deductible.

The catch, of course, is that “all you have to do” to capture this is correctly execute a four-legged SPX option spread on an order book, understand margin against your portfolio, and roll spread before expiry. This is enough to keep most affluent households away, but this is changing.

White-glove vs. DIY

There are now broadly two paths.

White-glove

A handful of providers will run the strategy for you or for your advisor.

  • SyntheticFi is the most aggressive on the retail and RIA side — YC-backed, run by Joseph Wang (ex-Deutsche Bank rates, ex-VRGL). SyntheticFI pitches itself as a sub-advisor that integrates with your existing brokerage rather than asking you to move assets. They handle execution and rolls and charge somewhere in the neighborhood of 50 bps on the borrowed amount
  • Vest’s Synthetic Borrow is on Schwab’s Managed Accounts Marketplace and runs at roughly 95 bps. Managed box spread financing, advisor-distributed.
  • Aptus is an asset manager with both option-based ETF offerings and an option overlay program which now includes box spread financing.

I’m not endorsing any of these but as I’ve seen box spreads awareness grow these commercial programs have made their way into my feeds.

DIY

As I alluded to earlier, if you have a portfolio margin account and feel comfortable executing option packages, you can do this yourself. You can even piggyback on SyntheticFI’s marketing efforts by using boxtrades.com (whose order book data is aggregated via SyntheticFi) to see daily and historical prints and rates by expiration.

The DIY route will save you 50–100 bps in fees in exchange for needing to handle the operations of trading, rolling and monitoring margin.

If you are interested in this route, I vibed up a handy checklist:

🔗Box Spread Borrowing: The Compact Guide

Home-financing angles

CBOE leads with this base scenario:

Instead of a 7% mortgages, borrow at the 5-year box rate of 4.5%. The “interest” on the box accrues annually as a 1256 capital loss, which you can use to offset gains elsewhere in the portfolio. A high-bracket household is financing a house at something with a 3-handle on it. From there, you can stack by taking a conforming or jumbo first mortgage up to the deductible-interest cap, then box-finance the rest.

Additional risk and other considerations

  • The “jingle mail” option. A mortgage does have some unique advantages. It is a non-recourse loan.
  • Margin call risk. Your portfolio is collateral. If SPX drops 30% the day after you buy the house, you may need to add cash, sell something, or roll into a smaller box. SyntheticFi’s published worked example has a borrower at 42% LTV able to absorb a ~40% portfolio drawdown before margin call. You are short a tail. Of course, you could also buy tails to cap your margin risk!
  • Asset-liability mismatch. The box has a fixed maturity that is likely shorter than the duration of homeownership. You will need to roll, and the next box will print at whatever the curve is at that point. You have similar rate risks as an adjustable rate mortgage.
  • Interest-rate risk on early unwind. If you need to close the box before expiration, you mark to current rates, which can be a cost.
  • Realized interest costs. A simple rolling example could mean selling a new 1-year box for 96% of new face to buy back an old box at ~99% of face with 2 months left. The net out-of-pocket of 3% of face is your realized interest.

my little baby is all grown up

Before I go on, I just want to acknowledge how weird it feels to see box spreads become something a normal investor might hear about. When I was a trainee, the first option structures they taught were financing trades:

  1. synthetic futures (or combos in the parlance of our time)
  2. reversals and conversions which are just synthetic futures with an offsetting stock position
  3. box spreads which are just spreads of synthetic futures (later you learn that algebraically they are equivalent to the sum of the call spread and the put spreads between the 2 strikes, an identity which helps you make markets in mock trading much faster!)

Despite some latent pangs of “I liked that band before you even heard of them”, the mainstreaming of box spreads makes a ton of sense.

Lending markets are normally intermediated by banks. The bank takes deposits at one rate and lends them out at a higher rate; the spread is the bank’s margin and the cost of the bank’s existence. The box spread goes around a costly bilateral transaction to let two market participants, one with cash, one with collateral, meet on a regulated exchange and swap exposures at clearinghouse-guaranteed rate.

Wes Gray, who co-created BOXX, told Brent Sullivan in Tax Alpha Insider:

Box spreads might be the ultimate ‘disintermediated’ borrowing mechanism out there.

The CBOE, fintech, and advisor community have found enough forgone bank margin to insert themselves as brokers between consumer borrowers and the liquid funding market entwined in the booming options business.

The wholesale financing rate that has historically been available to a market maker on the SPX floor is now accessible to a household with $2M in a brokerage account. These same households that are sitting on appreciated assets, which they can conveniently sell slowly in a tax-efficient way as the gains wash with the capital losses on the box “interest”.

Financial innovation and competition is notably triumphant in solving high-class problems. You can decide how to feel about that but I gotta figure out how to finance this ADU so you get to learn about stuff like this.

 

Further reading

a guide to option margin

A few quick hits to start

Welcome to Scamerica

I remember on the NYMEX, when certain brokers would mosey into the pit you’d literally hear someone say “watch your wallet”.

Well, here’s a new product from fintwit’s philosopher king:

My reflex was “Hey, here’s another fund using retail marks as exit liquidity before they can stuff the indexes with their low-float IPOs at mature, expensive growth valuations.” Thanks for the look Mr. Positive-Sum Game Preacher.

My expectations are so low for anything sold by the VC crowd on socials, but I still try to be charitable. Like, fine, give people what they want. You’re dying to pay trillion-dollar valuations in a one-way auction (see a recipe for overpaying), someone is going to broker it. Since it’s private and requires herding retail cats, it’s going to be pricey.

I also recognize I’m biased towards cynicism because when it comes to any match-making in finance. It’s a bazaar loaded with adverse selection because there’s so much info asymmetry and persuasive marketing within a competitive landscape that pretty much assures most of its emperors to be sociopaths.

But fine. It’s a market. It’s 2026. I’m inured against disappointment. In fact, flip it. The more fun game is to watch the limbo. How low we gonna go? Bro’s shoulder blades are grazing the turf. See the tweet:

Shout out to these guys for reading the fine print or at least feeding it to Claude. Oh the irony of using LLMs created by the companies in the fund to ask “read this prospectus and tell me all the ways I’m being bent over”.

Speaking of LLMs…

The agent craze has been amazing for getting things done, but in the past week I’ve needed to go back to the classic AI use — research.

A good friend from my local in-person life is raising a few hundred grand to grow a business he started a year ago that’s getting awesome traction. It started with him looking for a local business to buy but ended up with him starting one from scratch. It’s not a venture-shaped business and makes more sense for friends and family, so I am looking at it.

Over the years, I’ve invested in some private stuff friends have done, like restaurants or real estate deals. Some go well, some don’t. Honestly, the whole endeavor doesn’t feel like a great use of time so I’m definitely more disciplined about this stuff, but also I know I have so much to learn about business in general.

I have uselessly broad heuristics. SaaS is high margin. Packaged goods are about distribution. Bars are for vanity. I have a superficial understanding of accounting and financial statements from reading a couple books. But I do like looking at spreadsheets and following the cells to see the levers and sensitivities. It feels like a game.

And I took more interest in this exercise this time around as I looked through my friend’s financials for the past year and the model he built for projections and tracking. I think the extra interest is at least partly because of having to learn more about investing fundamentals for the class I do for the teens, but also because there’s so much less friction in learning.

For example, as I study his business, I can see how the gross margin shrinks down to the contribution margin and finally to a net margin. But then you wonder, how does this progression work in various business models? What are the typical ranges of relationships between the numbers across industries?

The questions come alive when you start from the specific, like a company you are studying, and then zoom out for perspective. You have to spend time on the company to start, but if you don’t have a background in banking, corporate finance, or accounting, you now have to build context. But this is where the LLM comes in. Especially the “deep research” or equivalent setting on whichever you use. The visibility of sources is an effective audit against hallucinations. And voila, you send it to work for an hour and you have a relevant book report customized to your practical interest.

I found its output satisfyingly illuminating for my purpose:

Contribution Margin Vs Net Margin: What Gets Lost Between The Two

My delight with that one renewed my interest in a book I printed out many years ago but never got around to reading:

The Base Rate Book Michael Mauboussin

I, of course, had the LLM create a summary with my interests in mind.

Again, more context for understanding business. On the one hand, stuff like this is high-level enough to only make you dangerous, but you have to build a sense of proportion and, well, base rates to relate narrow explorations, like that of an individual business, to enterprise broadly.

A word on AI book reports

I subscribe to a lot of quant finance substacks. I don’t read them all but the cost of triage with AI summary abilities is so cheap now.

But this is the mirror of the cheapness to produce as well. I have noticed that a lot of substacks with a premium tier are really just baity book reports about trading firms. Like long versions of twitter slop threads which are proven methods for building audiences.

I don’t want to be too negative about them since they do synthesize high-level information at slightly higher than replacement value than what you could wrangle out of an LLM. I usually don’t pay for them because they lack a sharp “point of view”. And even if they do, if it’s hard to tell if it’s an earned one, then it probably isn’t. God knows we’re awash in baseless points of view in general and that’s on the benign side of the spectrum, opposite rage-bait or doomer copywriting predation models.

I don’t have a grand opinion here, but I’m confident the future is going to be a lot more of your AI reading someone else’s AI-produced writing, at least in the world of non-fiction. Our relationship to reading is going to change and the role of email in that world will also transform. I need to think about this a lot more. My bet is that retaining a voice matters. The question is whether it matters the same way live music matters or if it’s looked at the way we see an artisan who makes their own furniture. Pure soulcraft.

Back to practical matters

In professional trading, there are critical functions that are abstracted away from your day-to-day job which cannot be if you are independent. A good example of this is the topic of margin.

If you run a strategy that is relatively small compared to your entire fund or firm so long as your haircut is commensurate with the opportunity size of your specific business, you likely don’t even know what it is. From your point of view, you’re trading with a blank check so long as you are within risk limits. Margin risk is monitored and managed a layer up from market risk which you are keenly aware of.

I’ve discussed this before in When it’s normal to have no idea what your returns are.

On the other hand, experienced retail traders understand margin inside out because it’s a matter of survival. Some retail traders understand it so well I think the margin sometimes wags the trading dog where instead of starting with an edge they start with what is margin efficient.

Margin and options is complicated topic and one I’ve been overdue on diving into. I put together a guide to understanding option margin, shorting details, and Interactive Brokers specifically since that’s my primary broker.

I host this on my Notion site. I used ChatGPT ‘deep research’ to do, well, the research then steered it into a reference, but something that should be read all the way through. Margin isn’t a fun topic but ultimately this is about risk.

Margin, Explained: Reg T vs Portfolio Margin, and Why IBKR Is a Different Animal

What you’ll find:

  • Detailed look at both Reg T and Portfolio Margin (PM)
  • A side-by-side summary of the key differences
  • How each framework can hurt you in ways the other can’t
  • Who each framework is actually best for
  • How Interactive Brokers (IBKR) implements all of this differently from other brokers
  • Short selling mechanics — borrow, SYEP, rebates — where IBKR is the unique retail player
  • A glossary of the IBKR-specific metrics that actually matter (NLV, ELV, SMA, SEM, Excess Liquidity)

A few topics in here that were especially enlightening to me, often because they were discussed by different names than I’m familiar with or were not an issue in a professional setting.

Expiration risk

The first one here is one you will not encounter if you work for a firm but is dangerous for an individual. The idea that you can be liquidated on a long option! This scenario was one of the reasons I prioritized this article. A mutual on Twitter had this happen to them and discussed it on the timeline. There was a pile-on of “duh” but that risk is not something I’d necessarily focus on. Now I know better.

It’s an interesting risk because it creates a meaningful limit to how levered you can be on a long option position whose premium you can afford. For example, if you have a big chunk of your account in small delta puts that actually hit, you will likely need to roll or close before expiry and must be ready to trade.

  1. IBKR runs expiration exposure simulations and may liquidate options before expiration if the projected post-expiry exposure is deemed excessive. Pre-expiration liquidations typically happen expiration day afternoon, sometimes earlier. IBKR may also lapse long ITM options that would otherwise auto-exercise if exercising would breach margin.
  2. The truly dangerous case: early assignment on the short leg of a spread. IBKR will not automatically exercise your long leg to cover. Short put assigned Friday night → stock position Saturday morning. If you lack margin for that stock position, IBKR begins liquidating Monday at ~9:40 AM ET, and may liquidate any position in the account, not just the assigned shares. There are multiple documented six-figure retail blowups from exactly this.

Short selling

IB lets you lend your shares through its Stock Yield Enhancement Program (SYEP). You and IB split the lending fee charged to the borrower. But there are risks I didn’t know about:

  • Loss of SIPC protection on lent shares. IBKR posts Treasury/cash collateral as a substitute, but in an IBKR default, this is your only recourse.
  • Payment in lieu of dividends (PIL) when shares are on loan over ex-date: taxed as ordinary income (1099-MISC), not qualified dividend rates (1099-DIV). Practitioners report 50–60% of dividends received as PIL rather than qualified — tax disaster for dividend-focused portfolios.

IB’s advantage over many other brokers is that they pay you interest on the cash from the short sale proceeds (I was relieved to see that IB calls it what I’ve always known it as — the “short stock rebate”). The rebate is not as generous as what you get institutionally but it’s better than I got when I had a backer!

Final thought

The guide is critical for parsing whether you want to be in a portfolio margin or Reg-T margin account.

Unlike most Thursday posts, this one has a good chance of being more enlightening for professional options traders than retail option traders!

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

A well-supported and common belief in the options world is that there is a premium of implied volatility to realized volatility. The implication is that options, on average, are overpriced, so the structural edge in the options market comes from selling them to “harvest the VRP”.

If you put a gun to my head to confess where I stand, I’ll coldly chant “I have no quarrel with that belief” in the cadence of His name is Robert Paulson.

There’s enough evidence to not disagree with the belief. But as a trader who spent 2 decades being long gamma and vega more often than short and not being especially rare among professional option traders in that regard, it’s hard to bang on the VRP desk with fervor.

Aside

It is entirely possible that my trading profits made up for a persistent negative edge in my positioning. That’s plausible because I traded thousands of contracts a day for 20 years in a market-neutral way, but there are facts that cast doubt on the long vol bias being detrimental. My largest p/ls were in years that were most volatile like the late 2000s, 2018, and 2020, and driven by vega. Now vega is a funny thing because people will argue that it’s not real, it’s marks, etc. They are still on their option blue belt and failing to appreciate

a) that vega can be ported through time through calendars, but it’s almost impossible to do this efficiently unless you are organized to trade flow

b) vega is illiquid. You can manufacture a near-dated option through replication so even if the option is illiquid as long as you can trade an underlying against it there is an out. Deferred options can turn into Hotel California quickly, and when they do it’s good to have the keys to the rooms.

In fact, the market for vega (ie longer-dated options) and gamma (near-dated options) is different. Different players, motivations, and execution methods. For the pros reading, have you ever seen a market where one trader deals in the “fronts” and another trader is in charge of the “backs”. This is the most salient demonstration of this bifurcation, but it exists in subtler ways in many markets and there’s money in bridging the liquidity.

We can peel back assumptions about VRP all day. For example, what do you mean by “realized volatility”? But a highly tiresome unpacking would leave us in a predictably unsatisfying duality:

  1. Options are generally overpriced
  2. This is hard to translate into risk-adjusted, opportunity-cost-aware amounts of food on the table

Anyway, I’ve needled you enough. I’m not sorry about that. Part of my self-anointed duty is to test your armor before you march into your Robinhood options tab.

Let’s turn to the “V” in VRP.

I’ve seen it refer to “volatility” or “variance”. In the non-technical context that it’s used, this is fine. In our app, it refers to “volatility”.

But the distinction is absolutely critical when evaluating and sizing trades.

We can examine this by starting with a market observation that points to expensive options. When we pull it apart, there’s so much more than meets the eye. This lesson brings together fundamentally important themes we cover in this letter like:

  • The importance of proper measurement
  • how you want to approach the same idea from multiple angles, because it’s rare that a single measure sees all the facets
  • The math of option risk and p/l
  • Markets being smarter than they seem at first glance

Let’s start with this chart of 30d constant maturity implied vol vs trailing 30d realized vol in HYG.

We can see that absent the Liberation Day period last year and the current Iran stress, IV maintains a steady premium to RV. Also note that realized vol is typically below 5% annualized. This is a low-vol ETF.

Another way to look at this is to turn that relationship into a ratio representing the percent premium of IV to RV and call that the volatility risk premium (VRP). We do that below as a scatterplot with the 30-day RV percentiled over the past year.

It shows the premium is often around 40 to 100%, and it’s fattest when the realized vol is very low. This is indicative of IV’s habit of pricing in mean reversion. When realized vol gets very low, the IV doesn’t chase it all the way down. It’s stickier as the market doesn’t extrapolate the low vol periods to persist. Same when the market gets very volatile. The premium narrows as the market doesn’t bid the IV up “too high” as it expects the elevated realized vol to subside.

How you measure the VRP is a choice. We chose to measure it as a ratio because it makes cross-sectional comparison easier. If a name realizes 5% vol but trades for 6% vol, that is put on par with a 50% vol name trading for 60% IV.

We could have also chosen to measure the premium as a “spread” instead of a ratio. In that case, HYG could be said to have a VRP of 1 (ie 6% IV – 5% RV) and the higher vol name would have a spread of 10 (60% IV – 50% RV).

If HYG was 15% IV and 5% RV, that would also be a 10-point spread, so the spread approach just feels more wrong when you compare assets of different vols. The ratio offers a better comparison.

But remember:

how you want to approach the same idea from multiple angles, because it’s rare that a single measure sees all the facets

The plot is going to thicken considerably because putting on risk and screening are 2 different activities that are related via decision-making but divorced in execution.

Back to HYG. Whether you use a ratio or spread, implied vol is sitting well above trailing realized vol. The ratio is more flattering than the spread, but either way it appears like a structural risk premium. Sell the options, collect the premium, repeat. Right?

As you zoom in, the details start to hint at why this ratio or spread is just sitting there for the taking.

The Gamma-Theta Tug of War

If you are selling options to capture VRP, your intent or thesis is not about IV falling, just that your theta p/l, the option decay you collect as time passes, will outweigh the losses you incur from being short gamma as the stock moves around. We make allowances for path dependence, but on average, if the stock moves around less than what is implied by the option prices, you win.

The net P&L of the position due to realized vol makes the battle of gamma and theta visible. This is from the long option holder’s point of view. For them, if the RV is greater than the IV, this term is positive:

Although this comes back to that letter “V”.

σ² refers to variance not volatility. If you are short options, you make money when realized variance is below implied variance. The distinction between volatility and variance is critical. But we’ll get to that.

We also want to quickly review approximations for ATM options (technically ATF or “at-the-forward”).

This is the straddle and its gamma, respectively:

Focus on the following relationships that fall out of these approximations.

  1. First, the straddle price is proportional to σ. Which means daily theta decay is proportional to σ, since you can think of theta as the diff of the straddle formula on T vs the straddle formula on T-1. A 50-vol name bleeds twice as fast as a 25-vol name.
  2. Γ is inversely proportional to σ. A 50-vol name has half the gamma per dollar of notional as a 25-vol name.

You should notice…

A lower vol name has less theta AND more gamma

Theta-weighting position size

Say you want to sell the same dollar amount of daily theta across two names, a 50-vol name and a 10-vol name. Since theta scales proportionally with vol, you need 5x more contracts in the 10-vol name to collect the same daily premium. That’s the theta-neutral scalar: σ_high / σ_low.

We start with a question:

If both names trade at the same ratio premium, say IV is 20% above RV for each ,does theta-neutral sizing give you the same variance edge?

Holding that ratio premium fixed at 20%, look at what the variance edge (IV² − RV²) does as we down the vol spectrum from our baseline 50% RV name:

[example of variance edge per contract for baseline is 60² − 50² = 1,100 units]

The variance edge per contract collapses as vol falls. When you scaled notional by 5x in the 10-vol name to match theta, you are capturing much less variance edge for the same risk.

To fully equalize variance edge at theta-neutral sizing, you’d need to scale by (σ_high / σ_low)² or the square of the theta-neutral ratio.

Theta-neutral means 5×. Variance-edge-neutral means 25×. If we use theta as a proxy for risk, which is a common and sensible barometer (but again, like all measures, incomplete) for understanding position size, we would need to take far more risk in the low vol name to capture the same amount of edge.

How Rich Does The Low-Vol Name Need To Be?

So a 50-vol name trades at 60 vol for a 20% ratio premium. Variance edge per contract: 60² − 50² = 3600 − 2500 = 1,100 variance units.

You want to find the IV for a 10-vol name such that theta-neutral sizing (5× contracts) delivers the same 1,100 variance units.

Working through the algebra (see appendix), the answer is:

 

Plugging in: IV_low = 10 × √(1 + 1100 / (10 × 50)) = 10 × √(1 + 2.2) = 10 × √3.2 = 17.9

So the 10-vol name needs to trade at 17.9 vol or a 79% ratio premium to RV to deliver the same theta-neutral variance edge as the 50-vol name at a 20% premium.

 

A 10-vol name trading at 12 vol (20% premium) looks identical to the 50-vol name on a ratio chart. In variance-edge terms, it’s delivering less than a tenth of the expected profit, even after upsizing to theta-neutral scaling.

Spread Gets You Closer

Screening by vol ratio might offer sensible comparisons but fails to compare opportunity in a risk-aware way. At the end of the day, a 40% vol premium on a 5-vol name is still just 2 points. You can get a feels for this when you look at selling options on fixed income ETFs. That IEF vol looks high, and then when you look at the premium it just feels like the juice isn’t worth the squeeze.

So what about vol-point spread?

It works quite well for comparing edge, at least until you get to much lower vol names.

The table shows the spread needed for variance-edge equivalence across the vol spectrum. It’s pretty constant from 25 to 100 vol names.

The ratio needed to equate the variance edge went from 20% to 79% to 132%. It makes low-vol names look rich when they’re structurally disadvantaged in variance-edge terms.

Back To HYG

The ratio VRP in HYG looks persistently fat, often 50% or more above realized vol. But even the spread measure doesn’t quite put it on par with the variance edge in higher vol names. A stock priced at 60 vol that moves at a 50 vol has a 10 point spread, which is equivalent variance edge to HYG moving 5 vol but being priced at 11.6. But that kind of differential is extreme. HYG’s median spread in recent data is around 2-3 vol points, not 6 or more, equivalent to say a name that moves 50 vol trading 55 vol.

HYG options really are persistently rich relative to realized vol. But the ratio charts can make hide the fact that on a relative basis, HYG vols at a 2-3 point premium are actually cheap compared to a 50 vol name priced at 60% IV!

Additional consideration on low vol names

The cost of harvesting that variance edge premium in low vol names can be more expensive since theta-equivalence means trading far more contracts of the lower vol name (assuming stock prices are the same).

And of course, for a given level of theta, the lower vol name has far more gamma, which means more trading costs because you will be trading more shares.

If you are selling options to capture VRP, be aware that the V that matters is variance and that the scaling properties of risk and edge make ranking opportunities a bit unintuitive when looking at ratios. Spreads are a more solid footing, but selling a 20 vol name at 30 vol is still better than selling a 120 vol name at 130 vol, even if ratios can be misleading.

Appendix: Deriving the “Required IV” Formula

You provide 3 inputs:

  • RV_low
  • RV_high
  • IV_high

It returns the minimum IV the low-vol name needs to trade at for the trade to be economically equivalent on a theta-neutral variance-edge basis. Anything below that number is a relatively worse trade than the baseline you are comparing against.

I was only able to do the algebra myself until step 6. It was fun to do, like a little puzzle. But then it was depressing to be old and stuck and not even remember quadratic form.

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