collar shopping

At the end of July, Dean Curnutt tweeted:

The thread should sound familiar. Weeks earlier, Dean tweeted about SNDK vols presenting attractive collar pricing for hedgers.

From high implied vol can work for or against you?:

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

A non-technical way to appreciate how high vol creates this opportunity in upside call vs downside put differentials: Imagine a stock starts at $100. It gets to $125. From $125 to $150 is only 20%. But if the stock fell to $75 the distance from $75 to $50 is 33%. Both $50 and $150 are 50% from the initial price, but in a compounding sense 150 is much “closer” to the starting value than $50. The higher the vol the less “distance” a fixed dollar move represents. As implied vol increases OTM calls grow faster in value than OTM puts. This is the source of the attractive pricing you see in the risk reversal (ie option collar).

That pricing falls out of the risk-neutral world that rests on “no-arbitrage” assumptions. In fact, the lognormal return process, described in the quote without ever using the word “lognormal”, is only one of many assumptions. The forward price of the stock is also assumed to be a function of the risk-free rate, which pushes the price that the options are based on higher than the spot price. This, of course, pushes up calls and puts down by their respective deltas. These assumptions conspire to make calls look quite expensive relative to puts to someone comparing the risk-reward of options intuitively.

Intuition would likely lead to very different prices, but present an arbitrage in the process because you live in the real world not the risk-neutral world.

A few examples from that post:

  • Warren Buffett sells the long-dated puts because he believes the no-arbitrage assumption of the risk-free rate underestimates real-world forward prices. The option trader he faces is quite content to buy those puts since they are looking for an easy flip in the vol market.
  • FX carry. The speculator holds the future for the risky but generous profit the risk-neutral price creates. The derivatives trader is content to make a penny of arbitrage profit.

This is an admittedly mind-bending state of affairs, but it creates disagreement because of different horizons. This is the basis for trade!

The collars (also known as risk reversals or fences depending on the trading floor you grew up on) are another example of risk-neutral assumptions presenting wacky prices to those who don’t require arbitrage to trade.

The arbitrageur prices the collar like a contractor bidding a job. The daily hedges are materials and labor. The replication price is a manufacturing cost. Call it $500 per square foot. But the client trading the collar is looking at the finished house represented by the payoff of where the stock lands. They are happy to pay $500/ sq ft if the final product is worth $800/ft. The derivatives trader is not underwriting the final value but operating a cost plus business. They have no view on the value of the final product. It’s literally none of their business.

If you want to tangle with this deeper, you are welcome to revisit how to get arbed with perfect information (again) but take heart that you aren’t alone if you struggle with the idea of no-arbitrage replication. I always say it’s the “bridge of asses” for finance.

Collar Shopping

Dean’s tweets highlighted stocks where the calls you overwrite can finance a fairly high strike put, creating an attractive hedge and therefore risk-reward to a long position.

Consider an example where you buy a $100 stock and a 1-year 20% out-of-the-money put while selling a 1-year 40% out-of-the-money call at the same price as the put. In other words, a “zero-cost” collar. The most you can lose is 20% in the case where the stock tanks. Your upside is capped at 40% before your shares would be called away. If you think the stock has a symmetrical distribution where it’s going up or going down are the same probability this looks like a good bet because you are getting 2-1 odds.

If the collar costs $2 or 2% of the stock price, we can roll that into the basis (so $102). Now you are risking 22% to make 38%, a risk reward (R:R) of 1.73 to 1.

This is a snapshot from the Moontower Collars Workflow on 8/11/26 for options with about 3 months to expiry.

Every row on the screen prices the package of buying the .25 delta put, selling the .25 delta call, and buying the stock.

You can restrict your universe to certain sectors and re-sort. You can filter for stocks a certain threshold above their moving average or stocks that are strongly correlated to each other to hunt for the best bang for your buck for a given beta, or just any number of screens to narrow your candidates.

A thread for the masochists

The strikes here are delta-defined, so the vol gap between names is already baked in. You could imagine beta-adjusting the strikes to go a step further (although you’d need to use the API/MCP).

Beta is correlation times the vol ratio. So if correlation < 1.0, beta-adjusting pulls the call strike in toward at-the-money. You’re short that call in a collar, so a nearer strike prints fatter making the risk-reward look better. But it’s a trade-off. The result comes from truncating idiosyncratic upside that is not captured in beta.

Defensive-minded investors should take note (as Dean clearly has). The multi-year highs in deferred interest rates (pushes up forward prices) and the fact that high-flying stocks that have made concentrated investors quite rich are also relatively high-volatility presents those of us in the real (not risk-neutral) world an attractive menu of hedges.

A final puzzle for the masochists

Collared stock has the same hockey stock diagram as owning a call spread of the same strikes but the total cost will vary by some amount. How much is the amount and why? The hint lies in put-call parity. Solving this should feel like a puzzle and is a step on the “bridge of asses”.

the sound of inevitability

The market is 12-15.

12 bid. 15 offer.

The broker sizes up the offer.

“How many you got there? How about you? And you?”

A couple of the market makers get flakey once they see him counting.

“You know what, I’m 17 now.”

“Fine, but can you fill the size there?”

“This second, no more shopping.”

“Mine.”

A few minutes pass.

The broker comes back around. “How now?”

“Go fuck yourself. 20-40. Small.”

And that’s it.

It’s a liquidity-clearing trade. The market’s version of punctuated equilibrium.

Small lot sizes from here on out.

The price drifts higher over time. The same amount of volume moves the price by larger increments. The least-capitalized shorts who are also the smallest in the trade begrudgingly cover. Better to live another day. The larger ones lay off some of the headline greeks in related assets, but the basis leaks against them the whole way. At least it’s not a fresh flesh wound every day. Paper cuts aren’t mortal risks, but the job will be demoralizing for a while. We’re gonna do this again? Why don’t I learn? I’ve done well enough. Right? I don’t need this shit I say as I fire up loopnet on yet another chrome tab hoping to find a cap rate in the shape of an eternal palm tree.

Weeks pass. Maybe longer. Who’s counting?

You see the price. 63. Numb. Doesn’t mean anything anymore. You can’t taunt a ghost.

More time.

Wait, 56?

“Anybody doing anything in this?”

“Nah, maybe just recent sympathy with hawkish Fed chatter.”

“You think this thing being up 300% has anything to do with basis points. C’mon.”

“Yea, I don’t know. I’m trying to book Odyssey tickets on IMAX for 3am, can we do this later.”

“Neverm—”

[Ringing. The hoot flashes.]

[Groans and picks up.]

“Sal, I thought I told you to cut the line. The fuck you want?”

“How is it today?”

“I don’t know, Saaaal, why don’t you tell me how it is?”

“At 45”.

“We’re 5 minutes from the close, I can’t show.”

“At 33. They’re gonna trade”.

“I’ll round you out just to be social.”

Next day.

How?

“15-25. Your move, Sal.”

Leo

Matt Levine:

[On the modern AI thesis] Aschenbrenner was early and smart and articulate about it. This allowed him to raise money, and the fact that it has been basically correct allowed him to return 270% through May.

Leopold Aschenbrenner’s fund, Situational Awareness LP (SALP) started in late 2024 when he was 23. He raised $225mm and, through the use of leverage and being right as hell, rode a legendary heater with assets at peak over $25B about a month ago.

His portfolio concentrated heavily on hardware and chip shares of CoreWeave, Nebius, Bloom Energy, Iris Energy, Micron and the Korean company SK Hynix, as well as a sizable private stake in Anthropic. Meanwhile, he was shorting traditional software companies. You only need to pull up the charts of his longs and shorts to explain how his returns had been so stellar.

Many of his longs peaked in late June. On July 24th, he sent a memo to investors stating that the fund “has not been immune” to recent market volatility. He invited existing investors to commit fresh capital effective Aug 1, citing the most attractive opportunity set since early 2025.

Within the week, SALP would proceed to lose 2/3 of its assets and liquidate its public portfolio to Citadel.

Back to the pit

Trading is about pricing liquidity. Handicapping the price to move a chunk of risk in a particular period of time.

Leopold was very right on his security selection. So right that even net of the liquidation, the fund is still up 80% on the year! That’s got to be unprecedented. But being liquidated in the first place was inevitable.

Let’s go back to the stylized story from the opening.

When an asset rips higher as quickly as these longs did, it exhausts the supply of offers that maintain a sensible relationship to a concept of fair value. For the sake of legibility, we’ll call those sellers the natural investors. The ones whose bids and offers are tied to some semblance of a fundamental model.

If a stock you sold when it 3x’d continues on its way to a 10x in a short window of time, like on the order of months, there is a paradigm shift in its liquidity. In a squeeze, there is a shortage of supply, but those episodes are faster and less mysterious. In the opening example, it’s not a supply squeeze but reluctance.

With the “naturals” long taken out of the stock, the marginal liquidity provider on the offer is an atheist. In other words, a trader. They have no religion about the short. It’s an HFT, a market maker trading some low-capacity intraday basis they discovered in a linear regression, or some passive mechanism with a rebalance toggle.

What do these sellers have in common?

They’re hyper-tuned to the risk. They have a volatility number somewhere in their trade lifecycle.

Fine, who’s buying when the stock is now twice the price that itself was twice the price of anything sensible?

For starters, the original fanatic, especially if they are receiving inflows based on the marks they are reinforcing. Who else is buying? The momos and fomos. Weak hands. The momos are executing a simple bandwagon python script. This is a weak hand by design. The fomo weak hands come in 2 forms. The ones who haven’t had an original thought in their life and the ones chasing a benchmark because they devoted their life to mimicry with just enough leeway to preserve the illusion that their creativity matters. There’s a price for everything, so no shade, but calling a spade a spade, this is the weakest hand.

The stock is in a liminal zone. Levitating on the echo flows from the original disturbance. The stock market’s microstructure always presents a wash of back-and-forth trading. The withdrawal of real liquidity is less visible than the example in the opening sequence, which caricatures a market in a derivative or obscure contract that trades on Clearport by appointment but lacks a DOM. But make no mistake, the liquidity of the super stock is broken just like the fake derivative example.

The liminal zone, to quote Kindergarten Cop, “lacks discipline”. The sellers are atheists, the buyers are momos, fomos, and the original mover gathering flows, literally “high on his own supply”, with a mandate to trade on a thesis he publicly telegraphed in an adversarial game. The marketing effect of this strategy was powerful but not free. Why not? Because it rings the dinner bell which reverberates with the sound of inevitability.

Mordecai

When I graduated college in 2000, my mother took my sis and me to visit our family in Sydney and travel Australia for 3 weeks. In Darwin, we took one of those boat tours on the Adelaide River where they hang massive slabs of meat over the sides so us tourists can watch the crocs coil below and then leap high for their meals. Once you get on the river, the swarm of eyes comes out of the weeds as the sound of the motor signifies meal time. I’ll never forget the sheer size and thus the name of the croc they told us was the river’s alpha — Mordecai.

Leo’s wild success summoned Mordecai.

Crocs don’t need to chase. They don’t waste energy. The strike happens in a muddy thrash, and shortly after, the ripples of water slow as the trees and surrounding fauna relax in the wake of violent awe.

And even if the alpha crocs turns over, replaced by a new alpha, this species lives forever.

If I can prove how apt this analogy is, you will believe, like I do, that this liquidation was inevitable.

If you’ve been following this saga, you will notice I haven’t yet introduced the true culprit — Leverage + Concentration. The crocs aren’t the villains. In the words of Jack White, “if you’re headed to the grave you don’t blame the hearse”.

The moment Leo chose 4x leverage on a concentrated book, he splashed loudly into the river. From there, crocs just do what they do.

Byrne Hobart, in the Diff:

When there’s an economic actor whose day job is to identify forces that will lead to short-term flows in and out of particular stocks, and whose long-term model is to periodically pounce on distressed companies, these models will tend to converge into a model where they trade in advance of the blowup, and then exit and reverse that trade in the rescue.

The economic actor Byrne is referring to specifically is Ken Griffin’s Citadel, but generally, it is the dealer. The primary function of a dealer in any market, whether it’s securities, art, cars, or even being a link in a supply chain, is to price liquidity and manage inventory. SALP’s performance was a confession of Leverage + Concentration. Crank the virtuous loop of momentum and flows into thin liquidity, and those dead eyes surface for a look. If understanding liquidity was easy, then market-making would be less profitable. It simply would not be as valuable a service. So we can forgive Leopold for not realizing his gross market value was in shallower waters than he thought.

Market-making is a psychological grind. Again, go to the story from the open. You get paid $10 to flip million-dollar coins, and every now and then you find out you’re on the wrong side of a rigged coin. But even rarer than getting picked off is the chance to feast on fat prey. Now, to be fat, they must have been doing something right, but the weight makes it harder to maneuver than it used to be, and in Leo’s case, “used to be” was quite recent. It only takes a moment of indiscretion to show your belly. Markets are unforgiving because you’re only as sturdy as your worst mistake.

The crocs are always there. Griffin was also there to buy Amaranth out of their positions. Citadel has been in nat gas since the Centaurus era, and with John Arnold retired, Citadel has been an alpha croc in gas trading for well over a decade. If you search my writing, you’ll see a recurring theme of “what equity traders can learn from commodity futures markets”. Futures are zero-sum, so not all the lessons apply, but the ruthlessness will let you borrow a healthy amount of paranoia.

This is @LepoulpePoulpo:

So this was the view I always had wrt equities before
Vs commodities where a lot of shady stuff happens all the time but everyone knows about these games

On the other hand, I’m really less sure now. “It wasn’t certain how close SALP were to a margin call. Wasn’t certain they would have to liquidate in a block” -> I think if you had an idea of their leverage, and saw the price action on all his names, significantly worse than other semis, you could anticipate he would be close to force unwind/liquidate and try to squeeze him.

I admit I don’t know any equities trading team where people would do this kind of thing, but it happens often in commodities.

The word liquidity is a reminder that this is a biological system. Leo priced his trade as if the distribution were exogenous. He would never admit that, but his actions suggest his understanding was purely academic.

Byrne Hobart again:

AI people obsess about existential risk in theory and Leopold has publicly spoken about being aware of it, from a financial standpoint, in practice. But if you want someone who really feels existential risk in their bones, you’re better off talking to a hedge fund manager in Miami.

A mental model for the commodity market I’ve at times lamented and at times celebrated is that for the most part it’s a boring business of blocking and tackling. But now and then a well-capitalized outsider hops Chesterton’s Fence to see if he can force the market to cry uncle. If they’re especially crafty, it can work for a while. You can always beat a dealer on the way in. But you need liquidity to get out and now you don’t have the element of surprise on your side. Eventually, the old illuminati of the business lock arms to go on a hunting expedition. We used to call this “running them in”. If you are forced to cover, there’s little risk to me to bid ahead of you. (That’s not to say the “clean up” isn’t competitive. This is a good thread.)

When the Hunt Brothers cornered silver, the exchange eventually disallowed opening buy orders and raised margin requirements, depleting all the fuel. The exchange used to be owned by traders. They were literally called “members”. You can imagine their position at the top.

The sound of inevitability

In Jurassic Park, Michael Crichton folded an introduction to the field of complexity into the story. The park’s creators’ overconfidence in linear scientific thinking led to disaster. Complexity focuses on chaotic systems like weather (the proverbial butterfly flaps its wings and causes a hurricane across the globe) where models resist equations. There’s a greater emphasis on simulation and higher-order effects. A popular analogy from complexity science is the sandpile. Eventually the sandpile collapses but nobody would say the nth grain of sand causes the avalanche. It simply reveals that the pile angle had become unstable.

When observers consider the timeline (SALP’s peak was likely in late June) they are trying to label the nth grain. Fully embracing the butterfly, here’s my list:

  • the SpaceX IPO
  • the World Cup
  • the uptick in long-term yields
  • box spread rates reflecting funding costs rising as demand for leverage increased, with those costs passed straight through to levered ETFs
  • a slowing trend increasing chop, which increases drag in levered ETFs, which wears down the momos’ patience faster
  • the Knicks winning
  • Kris visits Rome for the first time

Inevitability means none of these matter.

So why was a liquidation inevitable? Why was at least one croc guaranteed a meal?

I already said it. It’s for the same reason LTCM, Hwang, Alameda, and Brian Hunter remain cautionary tales:

Leverage + Concentration.

But what’s so lethal about this combination? Why must it lead to liquidation?

Stated as plainly as possible:

As soon as you assert leverage, you are saying not only am I right, I’m right on timing AND path.

It’s a continuous time parlay. Even if he is right on the destination within the time frame of his choosing he can’t tolerate a large drawdown in the interim.

There’s just no give in the math.

Here’s quant Richard Craib:

But the outcome was never about being right or wrong on AI. At ~150% vol, variance drag alone is ~113%/yr, and risk of ruin is roughly a coin flip over the fund’s life. A child can do the math on a napkin (Claude did it for me: “ruin wasn’t unlikely, it was roughly even money”).

Volatility that high pierces every other fact about a portfolio: the thesis, the timing, the talent. The initial success and the margin call are draws from the same distribution.

And this isn’t really conditioning on the reality that a market’s price discovery function means they will push to a clearing price on a faster schedule than your lender would like. If you didn’t have a lender, this is not a concern!

Martin Shkreli had great coverage on the SALP story on TBPN. But thrown in at the end of the interview is this terrific section:

Kelly famously came up with what is now called the Kelly Criterion. It started as a gambling concept before becoming a finance concept, and it mathematically proves the optimal bet size. The formula is your edge minus the reciprocal of the odds. So, if you have a 55% edge, your optimal bet size is about 10%.

Even that is quite volatile for most people, which is why many investors use half-Kelly or quarter-Kelly sizing. The reality is that most traders don’t actually have an edge, yet they trade as if they have a four- or five-times Kelly edge.

That might sound like they’re simply taking a lot of risk, but if you run the simulation, you’ll go to zero almost every time. The simulator is a really powerful tool because it shows that even if you had a 60/40 edge on every trade—which nobody has in the stock market—you’ll still go bust if you overbet.

That’s a real eye-opener. Position sizing matters just as much as having an edge. It’s something I had to learn the hard way over many years: I was almost always overbetting. I think most hedge funds do it to some extent, and certainly most retail investors do. Very few people actually simulate their portfolios to understand what the appropriate position sizing should be.

After I left the Tiger Cub fund where I worked, I spent a short time in the office of a former SAC Capital (now Point72) portfolio manager. He was one of the best managers I’d ever seen—a quiet guy that almost nobody has heard of, now retired. I had the chance to watch him for a few months before launching my own hedge fund, where I proceeded to do the exact opposite and massively overbet everything.

I group LTCM in with other victims of the Leverage + Concentration poison. As a quant fund, their business was actually to lever diversified edges. But once the correlations of their positions converged, their cocktail was spiked with mathematical Concentration. On the surface, you might say what does a position in corn have to do with Treasury basis, but when a single commingled fund cross-collateralizes its leverage, then their size in the market imports a temporary synchronization of price returns.

Elm Wealth’s Victor Haghani has done a public good by commuting his pain as LTCM partner to teaching the necessity of sound bet sizing. His famous coin-flipping studies show how econ and finance professionals manage to continuously blow up 60/40 advantages by betting far more than what Kelly prescribes.

It gets better. In Fortune’s Formula, I learned that someone betting the prescribed Kelly fraction of their bankroll (which btw implies they have an edge in the first place) has a 50% chance of experiencing a 50% drawdown and a 1/3 chance of experiencing a 50% drawdown before doubling up. In other words, the Kelly fraction is not even conservative. Many traders and gamblers I know will max their betting at half-Kelly.

[The book points out that halving your Kelly fraction will cut your drawdown risk in half but your return only by a quarter so even though your long-term wealth compounds more slowly, the risk-reward is better. That fact alone tells you that the scaling law is extremely punitive if you overbet at all nevermind overbet at the rate Leo was.]

Why Leo, why?

I’m not attacking Leo. I mean he’s very rich, and a bona fide genius. But if the goal is to learn from what we see, I can’t shy from documenting the mistakes despite the optics of seemingly picking on someone half my age.

[His defenders are quick to point out that he’s still up 80% for the year, but all this does is highlight the thin line between zero and hero. We overfit narratives with a comfort that is comically out of tune with what is warranted by circumstance. If Leo loses an extra 25%, an utter blip given his vol, at 4x leverage his investors are zeroed. He made a great call to liquidate, but the presence of liquidity to do so is never a given. In the final hours of a deeply fragile situation, every routine event, hell a Trump tweet, has butterfly potential. Putting yourself in a situation where there is no margin for error is itself a mistake. Leo’s future will revise and buff down the pointy edges of the story’s path dependence, but honesty demands acknowledging that no matter what he becomes, today he is neither lion nor lamb but liquidation was inevitable. He is a man alternating as we do between grace and folly, with neither ever being our full legacy.]

Let’s proceed.

Structure Mistakes

Matt Levine:

If you are all-in on this thesis, you might be more than all-in on this thesis. You won’t put 100% of your money (and your investors’ money) into the AI boom. You’ll put, like, 300% of your money into the AI boom. You’ll borrow money to lever up your bets on the AI boom. As your AI stocks go up, you’ll borrow more to buy more. Getting a 200% return on your money by buying SK Hynix stock is great, but getting a 1,000% return on your money requires borrowing more money to buy more stock. This is a naturally long-term trade. Aschenbrenner’s famous June 2024 essay series is titled “Situational Awareness: The Decade Ahead.” The point is not, like, “SK Hynix will beat earnings expectations next quarter”; the point is stuff like “by the end of the decade, we are headed to $1T+ individual training clusters, requiring power equivalent to >20% of US electricity production.”

You have a vision of the future and want to make a fortune; you need to match your funding to the duration it will take to see the thesis play out. The use of recourse leverage, subject to daily revaluation, is wholly inconsistent with the horizon.

He must know this.

That’s why companies issue equity. They don’t want to worry about the next loan payment. The duration of the financing and vision are aligned. A business that cannot fund ops from cash flows is depleting capital and will need to issue more equity. In that sense, its leverage is not reevaluated every day its beholden to investor appetites at discrete points when it refinances. Meanwhile, a self-sustaining profit machine is more like permanent capital. If it doesn’t like investor bids, it can create its own liquidity by buying itself back.

There was a failure in appreciating structure. The vehicle you use to express a vision is no less important than the vision itself. Founders Fund is Peter Thiel’s GOAT-level investing vehicle, which uses locked-up capital to invest in private companies. Meanwhile, Clarium, his hedge fund that invested in public markets, lost 90% and closed in the wake of the GFC. That a hyper-opinionated genius could succeed and fail so loudly in seemingly similar tasks should alert you to the nature of edge, its prerequisites, and limitations with respect to how you express it.

Hubris?

The most famous Leopold I knew of before Aschenbrenner was another genius.

Nathan Leopold.

In bullet form:

  • First words at four months and three weeks
  • Studied fifteen languages, claimed five fluently.
  • Graduated in his teens Phi Beta Kappa at Chicago, headed for Harvard Law.
  • A nationally recognized ornithologist at nineteen

Enamored with Nietzsche’s Übermensch (“supermen”) as transcendent individuals with superior intellect, Leopold wrote to his a precocious friend Loeb, that such a man is “exempted from the ordinary laws which govern men.”

They conspired to get away with the perfect murder as proof and tribute to their superiority. They spent 7 months planning the abduction, disposal, and even a ransom demand purely as misdirection.

All this only to be caught by eyeglasses dropped near the body. While the glasses had an ordinary prescription and an ordinary frame, they featured an unusual hinge sold to three customers in Chicago. One was Leopold.

Kelly math would have been trivial to Aschenbrenner by the time he was 10. He probably would have used the word “trivial”.

Ed Thorp, another genius, was able to connect the dots from John Kelly’s equation to its use in investing, effectively inventing the world’s first quant fund (which incidentally seeded Ken Griffin when Thorp shut down and gave Ken all his documents since he saw Ken knew what to do with it all). But I’m increasingly of the mind that Thorp’s genius also included suppressing his own ego enough to take Kelly seriously. It’s an intersection of classical genius and wisdom which itself needn’t be so rare. It’s neither here nor there, but I think the public recognizes that the type of genius we are getting out of Silicon Valley is far narrower than the Thorpian variety.

[Related: The connection and friendship between Thorp and Buffett, whose approach to investing was vastly different, was one of the audience’s favorite parts of the talk I gave at Arbor].

Back to Shkreli referring to a trader he once worked with:

What amazed me was that he managed roughly $300–400 million of his own capital but almost never used it. Eighty to ninety percent of the portfolio was simply cash. He would make these tiny trades—little nibbles—and over more than 20 years, I don’t think he ever had a down quarter. He generated 20–30% annual returns while barely putting capital at risk.

It was an incredible lesson. Then, of course, the moment I got the opportunity to manage capital myself, I was running eight times leverage. Looking back, it was one of the dumbest things I could have done. You live and you learn.

Apparently, you can’t learn risk management. You can only live it. Allocators take note.

The allocator’s mistake

Speaking of allocators…why do they keep falling for this grand thesis routine?

I mean, what makes us human, right?

We love stories. We need stories. We want to see athletes fly. We want the impossible dream. We love that truth is stranger than fiction, after all, fiction is restrained by its need to make sense.

The optimism required to back the impossible is the same optimism required to attempt the impossible. Leopold’s investors were not teachers’ pensions and bean counters. It was his singularity-pilled entrepreneur brethren.

Even if he zeroed the damage would be contained to those who can afford it, so my view is no harm, no foul.

Just to share a personal thought.

I’m deeply uninterested in whiz kids that are too cool for the mundane. I strayed from this once and was burned by giving money to some hotshot who I have no doubt is a genius. It wasn’t a fraud or blowup. Hell, it’s still operating as a respectable, institutionally-approved fund. It’s just expensive mediocrity. If I wanted that, I could find some value fogies quoting Cicero.

I went against my better judgement.

Where is the repurposed crusty trader who’s been turned upside down a few times but never had a losing year, even if sometimes it’s a T-bill? I don’t need him originating the ideas, but I need him to call you an idiot and ask hard questions because he’s just as dubious of smart kids as he is of the government. When you use all your brilliance to dress a pump-and-dump in new tech and memes, he reminds you the tail you’re selling is tied to a statute of limitations, and anything like that is a non-starter.

Gimme the corny words. A warden of capital. A trustee. A fiduciary. At least they have a chance of not being a grift. I still need to figure out if they’re made of what I want at the point of sale and for monitoring the books. Steady hands. Paranoid. Path-aware. Fat Tony. If it leads with sexy, get me outta here.

I want the C in CAGR because I want to minimize drag.

I want the C in curmudgeon because you’ve heard the line:

There are old pilots and bold pilots, but no old, bold pilots.

We have been in a regime where many of the people who can raise money have built returns and stories in a boom environment, but those environments paper over bad habits, which increases the allocator’s adverse selection risk.

If you’re giving someone money for the long run, you want a battle-tested framework honed by the drudgery of risk monitoring, outtrades, system outages, and the paranoia from the memory of a hardcoded number in a spreadsheet getting you picked off.

Nobody is bigger than the market

A lesson we learn again and again, is that nobody is bigger than the market. Not even the crocs. They survive because they respect it. They’ve seen so much in the course of both providing liquidity and also occasionally taking it to manage risk, that they can have no other relationship to it other than respect.

That means keeping concentration away from leverage. There’s no price worth giving up control of your fate.

There seems to be something deep about risk management that eludes genius alone.

  • Leopold couldn’t have been ignorant of betting math.
  • Leopold should have been able to understand structure.
  • Leopold knew growth would require getting thesis, path, and timing right.

I’m left to conclude that the ancient root of most major errors is at hand. Hubris.

I’m even more confident in this because history tells us that being smart doesn’t inoculate you from hubris and, as the murdering Leopold story suggests, can actively fuel it. But since I have never spent a day being a genius, any more than I jump like Jordan or sing like Sinatra, my sense of limitation leaves me unable to empathize with Leopold’s blind spot.

This is a point of encouragement to everyone.

When you are limited, you seek approaches in light of your limitations, which explains the reality we seek all around us. That the quality of our decisions which determines flourishing has no relationship with excessive intelligence.

Since investing and managing money is a decision overlay that sits on top of research and analysis functions, the manager’s efficacy is rate-limited not by brains but by wisdom.

We should be a bit more obsessed with where wisdom comes from than continue to fall for dazzling minds.

If there’s a bit of poetry in this episode, it’s that Leopold’s only out was a singularity bigger than the market’s boring old constructs like liquidity and collateral. Maybe he could have gotten there. And he still has a chance. His mistake was turning it into a race with the crocs.

If you don’t mix Leverage + Concentration, you never have to get in the water.

hedging is for gardeners

Let’s start with this YouTube/Podcast episode where Erik and I discuss hedging.

📺Delta Hedging Cost Benefit Analysis | The Options Trench

  • What hedging is: reducing or isolating risks you do not want, to maximize exposure to ones you intend to get paid on
  • The difference between direct hedges and correlated, indirect hedges with basis risk.
  • Why every hedge has a cost, including premiums, bid-ask spreads, commissions, slippage, and opportunity cost.
  • Why you will almost always have “ragrets”: if the hedge works, you wish you hedged more; if it does not, you regret paying for it.
  • How protective puts, put spreads, collars, and covered calls change risk and cost.
  • The tradeoff between cheaper short-dated protection and more expensive long-dated protection.
  • How rising stock prices can make an old put hedge less effective by increasing your unprotected “deductible.”
  • Two ways to manage hedges: rebalance on a fixed schedule or act when risk crosses a predetermined band.
  • How hedges can preserve capital and buying power during market stress, when the best opportunities may appear.
  • An introduction to delta hedging, active delta management, gamma scalping, and how these concepts apply to options strategies.

I noticed this tweet a few weeks ago and it reminded me an example of my training days back in my AMEX days with SIG.

You had full discretion to delta hedge against the option orders you’d do. But as you learn in the podcast, hedging is a cost. You don’t want to hedge if the risk is tolerable. “Hedging is for gardeners.”

SIG had a big balance sheet and very tolerant of letting deltas ride so the bias to hedge was to hedge only if you thought the option order was “smart”. For example, if a cust has a pattern of selling puts right before the stock price rips higher, you want to hedge aggressively when you buy the puts. In fact, you might want to “overhedge.” Instead of buying the amount of shares prescribed by the delta you hedge “1-to-1” or “1 up” meaning you buy 100 deltas worth, effectively turning the put into synthetic calls.

Fast forward to 2026:

This is conceptually similar to our point above about how rising stock prices can make an old put hedge less effective by increasing your unprotected “deductible.” You need to roll the position if your exposure strays sufficiently far from the one you intend to have on. In this case, jbulltard who wants to be short puts wants to be shorter more substantial puts than the 60 strike so he “rolled up” either to re-strike his delta or vol position (or both).

In training, we discussed a scenario which the tweet reminded me of, but in the opposite direction. The question posed by an instructor was:

Imagine a customer coming in to roll his or her put down. They will need to sell a put spread as they close the higher strike and buy the lower one. If you are a market-maker providing liquidity to the seller by buying the put spread to hedge, you buy the stock.

Hold it right there.

If this customer is taking a profit by selling the higher strike put and opening a long position in the lower strike, they are actually still bearish. This customer that has been correct is not covering their short. Technically, they are less short than they were before rolling, but the roll is to get more option firepower in the next leg down. Think of the intent.

As a market-maker, you don’t want to hedge when you buy this put spread. The customer has given you the position you want. You’re short deltas, betting on the same side as the smart customer!

The option flow service above seems like it correctly identified that the trade was a put spread, but it presented the trade as someone buying the put spread. Technically, someone did buy it since there’s a buyer and seller on every trade, but the presumption when you say someone bought the spread is that a customer or “paper” bought the spread, not the market-maker.

become an option mixologist

To piggyback off David Epstein’s explanation of chunking, I’ve discussed the technique several times in my writing in the context of options. I use the chess player’s word for it (although I’m not a chess player): dissection.

These articles give concrete examples:

The second one links to a video where you can follow along on an example.

At first, you consciously look for groups or patterns that compress a theme, but with practice this becomes automatic. You can’t help but see the pattern.

Like the sports examples, an experienced trader will be able to pull the trigger faster than slavish processing would allow. The shortcuts become part of their wiring. You could see this in an open outcry trading pit or even amongst the best mock trading students back in the old floor days. That ability to say “sold” or “buy’em” faster than a large group of competitive traders because you saw the arb line up is happening at a subconcious pattern level. You make the trade and working out the particulars of the “why” while the instructor is still in the act of halting the the class to ask why you made the trade. I don’t know how it works but my pop science guess is that your synapses which have been strenghtened along specific pathways are a step ahead of your explicit reasoning.

Dissection is a deliberate form of “chunking”. But if we zoom out a ring from the specifics of option structures to the parameters they express, there are only 3 we generally care about: volatility (or variance), skew, kurtosis. In stats terms, these map to the 2nd, 3rd, and 4th statistical moments of the distribution.

There’s a vanna-vega-volga model sometimes referred to as “the cost of gammas” framework which actually formalizes this idea by mapping the parameters to their costs.

Volatility is represented by the cost of the straddle.

Skew is represented by the cost of a risk reversal.

Kurtosis is represented by the cost of a strangle.

These map to pertinent Greeks as well:

straddle → gamma

RR → vanna

strangle → volga

You pay IV premiums for all of these convexities. Vol risk premia for the straddle, you pay skew premiums for the ability to be long spot-vol correlation in the direction for which IV tends to rise as the market moves (so in SPY you pay a premium for the puts but in oil today you pay a premium for the calls), and finally, for volga, or “vol gamma” you pay an IV premium for wingy options.

To a beginner, the zoo of option structures is overwhelming. Seriously look at this page, the screenshot is only part of what I could capture:

It doesn’t even cover them all. There’s still jelly rolls, Christmas trees, rev/cons, diagonals, strips, “stupids”. I’m not kidding on that last one (it’s buying or selling a package of options in the same maturity but different strikes, so buying both the 700 and 650 puts as opposed to spreading them).

But if you understand that there are only 3 parameters we care about, then all of this collapses into a few themes. There’s a million different types of cocktails, but according to the mixologists at Death & Co there’s just key elements to the drink:

  1. alcohol (base)
  2. sugar (sweetener)
  3. acid (brightener)

If you prefer the cooking analogy, it’s salt, fat, acid, heat.

All recipes, whether in options, cuisine, music (there are thousands of chords but you can collapse to major/minor modified by dominant, sus, and add9) can be reduced to a few themes.

How does this help?

I’ll give you an example from our Discord this week.

Someone asked:

Anyone got any ideas for screening for good call spreads or put spreads to buy systematically in a potentially semi-automated way using moontower. A lot of the guidance I’ve read is ‘if you have a directional view’… well umm, I’m a ding dong with no directional ideas want something algorithmic.

I’m also a ding-dong, I just happen to understand that the price of option structures derives from the cost of our 3 friends: volatility, skew, and kurtosis.

This was my response:

What makes a vertical or debit spread generally cheap?

Low IV and high skew at the strike you are selling. So relatively cheap ATM/.25d call spread will have low IV and high call skew.

A relatively cheap OTM call spread could come from the IV being relatively low and the .25d call skew being low if that’s the long leg of the spread.

So here are a few suggestions…

  1. Sort for low IV percentile and high call skew for ATM to .25d call spreads or
  2. Sort for low IV percentile and low call skew if you want to buy an OTM call spread, meaning your buy leg is say .25d
  3. Use our Trade Ideas tab to look at names that score well on “Buy Vol” and then also sort by call skew in the table below!

You can also talk to the agent about building a prompt for this and then make it an Automation.

Our Trade Ideas algo scores names based on how they stack up to various preset trade themes (ie “buy vol”, “sell vol”, “long calendar”) according to their parameters and what signatures we look for. You simply add the column for 25d call skew which tells you the percentile, and using the logic from my answer, find names where the parameters present attractive spreads.

You had to understand that the price of the option structures map to these 3 themes in the first place and suddenly the zoo of possible option trades is massively reduced in dimensionality. It’s the progression from option bartender at your college party to option mixologist where you understand that all drinks are just a few flavors.

And just to address the Automations thing, we have a new feature in our tool. An example of one of mine where the agent emails me on a schedule when a name with a strong “Buy Vol” score’s strike vols are down and vice versa:

How I Teach Middle Schoolers To Build Stock Portfolios

If you construct a portfolio from 2 stocks and one is $100 and the other is $10, buying a share of each means the first will dominate your portfolio’s risk, assuming they have the same volatility.

If you have $100,000 to invest, you can balance the risk by equal-weighting the holdings: $50k into each stock. You buy 500 shares of A and 5,000 shares of B.

But what if they aren’t the same volatility?

Equal-weighting means the most volatile stocks determine performance. If your $100,000 is split equally between the 2 stocks and A moves 10% per day while B moves 1% per day, you aren’t diversified. Stock A will mostly determine your returns.

We can achieve more balance via equal-risk-weighting, which adjusts how many dollars go into each stock based on its volatility.

Weight each stock by 1/vol:

  • Stock A gets 1/10
  • Stock B gets 1/1.

Divide by the total (1/10 + 1 = 1.1) and you get about 9% in A and 91% in B. Stock A is 10x as risky, so it gets about 1/10th the dollars.

On $100,000 that’s roughly $9k of A and $91k of B, corresponding to

  • 91 shares of A
  • 9,100 shares of B

Compared to the equal-dollar portfolio, the equal-risk portfolio requires you’d sell about 409 shares of A and buy about 4,100 shares of B, moving roughly 41% of your total portfolio value from the jumpy stock to the calm one.

No masochism for the kids but in case you’re interested…

Equal risk weighting is the starting point for so-called risk parity weighting. The difference is that instead of only considering the volatility a holding adds to the portfolio, the correlation is considered. A stock highly correlated with the rest of your portfolio contributes a lot of risk, while an anti-correlated one does a better job diversifying and reducing total portfolio risk. The effect can be so strong that even a highly volatile but anti-correlated stock can reduce total risk.

Computing a correlation-aware risk contribution requires a full covariance matrix and an optimizer — i.e., a guess-and-test calculator — to find the portfolio weights, since there’s no closed-form solution. If the kids can grok equal vol-weighting I feel like I’ve done my job, and they can discover risk parity on their own if they’re so inclined.)

Your own Portfolio HQ Spreadsheet

This workbook is designed to organize and monitor your first portfolio.

⏬ Download

The sheet is view-only. Select “duplicate” from the file menu to get your own copy.

In this video, I show you how to use the sheet and talk about the Investment “lab” we did this week.

investing orbits

Here’s a summer reading book rec for investors:

My wife and I are both reading this. It’s laugh-out-loud funny. Gary is an excellent writer. The novel is written from the point of view of an elite school’s endowment CIO. It presents as a series of meetings with prospective managers, deals with politics within the endowment but also with the external culture of the investing world. If you are in finance, Gary’s sharp eye will delight you til no end.

I’m less than halfway through it and already I can’t recommend it enough. It was recommended to me by an allocator (thanks Tom!) and I saw in a recent Byrne Hobart letter that one of Byrne’s friends physically accosted him for not having read this book yet.

You can see Matt Levine’s endorsement in the screenshot. I wouldn’t have articulated what Matt wrote, but once he said it, I noticed that’s the exact feeling I get reading it.

The CIO’s banter, verbal chess, and inner monologue reveal a fox-like savvy honed by years of battle with both the market and the managers who make convincing cases for how they’ve mastered them. It gave me a tremendous appreciation for the difficulty of the job. If you are not a professional investor and have confused the most generous market run in anyone’s living memory for your own brilliance, then considering the CIO’s constraints will update your context for the pro version.

I found this recently reinforced by Jeremy Giffon in this terrific interview on ILTB.

Patrick: You have this funny view that the whole myth of how difficult it is to beat the market, however you want to define the market, is wrong. I’m curious for you to expound on that. That seems to have become, post-Jack Bogle, one of the deeply held truths of the market is that it’s extraordinarily difficult to beat the market, so you shouldn’t even try. You should just opt out of the battle. I think you have a very different view on this.

JeremyBuffett and Munger were my main teachers on investing. Buffett says that he wants his estate outside of Berkshire to be put in the S&P. That’s his advice to the general public. People take that to say that Buffett’s saying you can’t beat the market. I don’t think that’s what he’s saying. I think he’s saying for the average person, you shouldn’t try and beat the market. Implicit in that statement is leaving out any sort of active investor. Maybe the anecdotal side would be Buffett saying you should put all your money into the S&P. That’s the most rational thing you should do. On the other side is the sort of empirical argument, which is, look, most professionals don’t even beat the market after fees. This is this one-two punch of — the godfather of investing says, don’t try. Seemingly the smartest people with the best incentives in the world can’t do it.

And then the other thing is, for a professional manager — and this is sort of the paradox with the Buffett thing — it is really hard to beat the market because you have all these other factors that the average person doesn’t have. And this is the Peter Lynch argument — and increasingly I think Peter Lynch was a genius about this — which is that, yeah, when you’re a professional manager, by and large, you have all these mandates, you’re running a business, you have customers that you need to keep happy. It’s more difficult for the professional money manager to beat the market than the average amateur.


This is from Mandy Xu at the CBOE this week:

The outperformance of small-caps is a sign that the equity rally – which has long been dominated by the mega-cap Tech names – is starting to broaden out. In fact, over the past month, Tech has been the worst performing sector (-10%) while YTD laggards such as Healthcare and Financials have been the best performing (+12% and +8%, respectively). The calm at the index level (SPX Index -1.7% over the past month) belies these large rotations underneath the surface. This is why single stock volatility has been so elevated, even as the VIX® Index has fallen. The spread between the two, as measured by the VIXEQSM-VIX Index spread, widened to an all-time high of 31% last week.

If the single stock volatility is high relative to the index volatility, that’s another way to say the realized correlation between the stocks is very low. The index is dampening volatility because it’s acting well-diversified. A so-called stock-pickers market.

There’s so much violence under the surface. A momentum rotor whirring to give different categories an unpredictable spotlight before abruptly re-targeting.

I’m going to think aloud here a bit.

On the one hand, the momentum rotor feels like a market technicals concept. It’s the signature of flows and liquidity reaction functions. The intent of the orders that generate these flows might have a fundamental thesis behind them. In an investing mind. The trading world is indifferent to the ultimate intent but seeks to collect a service fee by spreading the acute dollar pressure in one part of the investing crust to another part of the surface.

From this perspective, the marginal price is set by an active investor. Perhaps the cumulative orders of levered pods.

At the same time, we hear of the “passive” bid. The Trump accounts and their monogamy to the SP500 (for the moment anyway) being yet one more increment to the bid.

If passive is the marginal price setter, I’d actually expect correlations to be structurally increasing. Not only do they seem to be structurally falling, they are conspicuously dormant at today’s historical lows.

I’m not sure the best way to reconcile these arguments. Is it an artifact of observation at a short time scale (rotor flows) vs a longer time scale (a slice of S in the GDP identity is pro-rata routed to the SP500 as long as the economy grows)? It’s reminiscent of the Earth’s dual rotation, where the planet spins on its own axis while orbiting the sun. The momentum rotor is called a “day” and the steady levitation of valuation comes from the passage of the “years”.

Regardless of the reconciliation of orbits or lack thereof, I am fractured by an ongoing dissonance:

I don’t discuss any of this in the Investment Beginnings Course!

It’s easy to anticipate a commoner’s consolation. “Kris, you are right to be teaching the textbook basics; we want the kids to learn investing, not gambling.” But it does feel quaint and too convenient to not address the marginal price setter. Buffett does so in a particularly striking way based on Graham’s allegory:

He said that you should imagine market quotations as coming from a remarkably accommodating fellow named Mr. Market who is your partner in a private business. Without fail, Mr. Market appears daily and names a price at which he will either buy your interest or sell you his.

Even though the business that the two of you own may have economic characteristics that are stable, Mr. Market’s quotations will be anything but. For, sad to say, the poor fellow has incurable emotional problems. At times he feels euphoric and can see only the favorable factors affecting the business. When in that mood, he names a very high buy-sell price because he fears that you will snap up his interest and rob him of imminent gains. At other times he is depressed and can see nothing but trouble ahead for both the business and the world. On these occasions he will name a very low price, since he is terrified that you will unload your interest on him…

Mr. Market has another endearing characteristic: He doesn’t mind being ignored. If his quotation is uninteresting to you today, he will be back with a new one tomorrow. Transactions are strictly at your option. Under these conditions, the more manic-depressive his behavior, the better for you.

Mr. Market is there to serve you, not to guide you.

Yet, I have my humble reservations about Buffet’s view. It’s not that I think it’s wrong, it’s that it leaves you in a quandary about a critical aspect of decision-making. How do you weigh information when forming an opinion?! A strict reading of Buffet is that Mr. Market is emotional and irrational. But traders are taught to respect bids and offers. They are made with real money in proportion to conviction. It’s exactly why we say betting is a tax on bullshit. The essence of trading decisions is how you form priors and then Bayesian update. You can’t ignore bids and offers if you think they contain information (and you certainly would care about if the bids and offers are forced or “uneconomic”).

[The maximalist Buffet view is that “short-term”, an admittedly poorly defined descriptor, price behavior contains no information. I’m not actually opposed to this possibility under some conditions but it’s obviously not universally true. The price signals from shortages and surpluses in the physical world matter. It’s the entire basis of capitalism. Insofar as share prices are an inference on the supply and demand of the physical world, we should not ignore their deltas. But the amplification embedded in the math of capitalizing those inferences into a multiple leaves a lot of room for accepting and refuting its justifications.]

Circling back to what I teach the kids in the future or possible course edits might be to discuss macro simply in terms of Kalecki-Levy type accounting identities. They aren’t predictive but they are explanatory. Every liability is someone else’s asset. So if the G deficit spends, the private sector savings mechanically increase (I need to review the framework, to be accurate in teaching it, but you get the gist). Some of that S will be siphoned into stocks, creating structural demand to be weighed against the arrival of issuance (ie supply).

From that foundation, one can see the movement of the index of all corporate shares as one orbit, and the micro discernment of relative value underneath being the subject of traditional valuation canon, while the trading/gambling science informing the physical “equations” that govern the sector rotor.

I stuck with physics in adherence to the orbital analogy but we all know investing is biology.

But I’ll wrap with a quote from my article about why it feels like astrology (this remains the most widely read post in moontower history):

In a recent interview on Corey Hoffstein’s Flirting With Models, volatility manager Cem Karsan explains:

In the very long term, all that matters is cash flows. At some point you’re gonna have a liquidity crisis and when the liquidity is not available, companies have to create their own liquidity and that’s where fundamentals matter…they matter, to the extent that they are necessary for purchasing their own stock or buying other companies.

I’ve used this analogy before, it’s kind of hokey, but I can’t think of a better one. If you’re on an airplane, 30,000 feet off the ground, that 30,000 feet off the ground is the valuation gap. Valuations are really high, but those engines are firing. Are you worried up in that plane about the valuations or are you worried about the speed and trajectory of where you’re going, based on the engines, based on the flows? The flows are what matter for where you’re going.

But when all of a sudden those engines go off, how far off the ground you are is all that matters. And so, [valuation] is more of a risk management tool, and ultimately it really matters when you have a liquidity crisis. It also matters if rates were to go back to 8, 9, 10%. Something crazy again, where nobody can borrow money, and there is no liquidity. Cash flows are all that matters again and we have a world where fundamentals are all that matters. So I want to be clear. It’s not that fundamentals don’t matter at all, it’s that they don’t matter in a world of massive liquidity.

I’m not naive enough to envision a unifying theory of investing, but teaching the class does motivate an impulse to do better than the textbook in tying things together in a way that is not just correct-ish but useful and relevant. And respectful to preteens and teens’ intellects, for whom education is increasingly patronizing.

Delta-hedged risk reversals

We recently added multi-leg support to our Attribution Visualizer, our tool for allowing you to track an option contract’s p/l assuming you hedged the delta daily. The tool breaks out the p/l according to gamma + theta (which sum to realized p/l) and to implied vol (vega p/l).

With multi-leg support, you can now entertain yourself with countless questions. Like “how would a masochistic skew trade work out if I trade a risk reversal and hedge daily?”

I ran a few risk reversals through the attribution tool.

USO: Buy call/sell put after the Iran war started

Date: March 13

Expiry: June 18, 2026 (~ 3 months)

Spot: $119.92

Risk reversal: 140c / 100p (equidistant strikes ~ each 17% OTM)

Initial hedge: Short 73 shares per risk reversal (the RR had .73 delta)

The war had already flipped the skew hard toward upside strikes. The $140 call traded 94% vol against the $100 put’s 83% IV. It cost $5.83 in option premium.

At expiration, the stock expired at $114.87

So how did it work out to buy the premium IV?

moontower.ai
moontower.ai

Not good. The cumulative delta-hedged p/l was a loss of over $4.50 as you lost to both realized vol and vega. At the initiation of the trade, paying the premium vol meant you were flattish gamma but paying theta.

You were also long vega because, despite the options being equidistant, at a generally elevated vol level the lognormality of the underlying distribution and its associated positive skew pumps up the delta of calls. In fact, the 140 call was ~.47 while the 100 put, which is closer in dollar space, was only .27d. The higher call delta says the 140 strike is much “closer in vol space”. That’s why the equidistant risk reversal cost so much premium to buy the call. You are buying at OTM that has a delta that we usually associate with near ATM options!

Let’s adjust the strikes so that our call and put are both ~.25d

To equalize deltas against the $100 put you have to buy…drum roll please…

The $190 call! 58% OTM for 101% IV. Now you collect a $2.17 credit to own the call and short the 100 put. Your initial Greeks mostly vanish.

The trade still loses, but it fares much better as the loss is only $1.29.

It’s tempting to conclude paying a premium vol doesn’t work. But if you bought the much cheaper call and shorted the put on a hedged riskie in SPY before the war started, then you got smoked if you chose April 30th expiry (SPY bottomed the last day of Q1), recovered once the market started rallying, only to lose again as the market…continued rallying! SPY riskie:

moonotwer.ai

I’ve said it repeatedly over the years in different ways, but riskies are the whips and leather of the option world. If you bought the call on the SPY Feb 720/650 risk reversal on the first trading day of the year and hedged daily until expiration, you actually would have lost $.25 despite the following:

  • the trade collected about $2.75 in premium at the outset
  • the stock’s closing prices stayed inside the range of $675-$700
  • the call you bought was 10.2% IV and the put you sold was 16.8% IV
moontower.ai

In Financial Hacking, Philip Maymin invents an optimistic junior trading assistant who sits down his bosses at the bank to explain that he has found an infinite money machine. Selling the high IVs in SPY puts and buying the cheap IV in SPY calls. Maymin asks the reader to figure out why this logic doesn’t work.

Our tool provides the day-by-day audit which feeds the charts. Armed with that, Claude does an admirable job of not only answering Maymin’s prompt to the reader but also pinpointing exactly which days carry the biggest weight in the answer.

VIX and buy signals

Here’s Victor Haghani:

A high VIX1 is widely considered to be one of the cleaner buy signals out there. A recent piece in The Financial Times made the case directly: when the VIX climbs above 30, forward returns have been well above average, positive most of the time, with double-digit six-month gains.

The Financial Times case is “buy the f’n dip” logic with a VIX gate. It’s exactly the type of thing that a layreader numbly nods at when the SPX is sitting near an all-time high. The Financial Times’ case is lazy from the perspective of both investors and active traders. For the investor, it’s just survivorship bias. Knowing what we know now every pullback has just presented a bargain. The market literally “going on sale” like it’s Prime day. VIX spikes over 30 just coincide with the sales.

The question you care about is one that an active trader hearing that statement would think to hypothesis test. Given that buying any time before an all-time-high has been worked out well, how do I distinguish between relatively better or worse buys?

Back to Victor:

What that leaves out is risk. Buying the spike means taking on a lot more of it, and the strategies that did the opposite, trimming exposure when fear ran high, held up better. So the popular signal may have it backwards.

Raw returns aren’t the right thing to optimize. You care about compounded returns since investing is a repeated game. Compounded returns are risk-adjusted returns because a geometric growth process penalizes volatility.

Elm Wealth tests FT’s claim not on raw return but Sharpe Ratio, or how much return you’re getting per unit of risk taken, as the variable to maximize if we care about risk-adjusted returns.

When Fear Spikes, Should You Buy? Elm Wealth | 5 min read

What they found when they ran the numbers on S&P 500 and VIX data from 1990–2026, they found:

  • A plain static stock/T-bill portfolio: Sharpe ratio of 0.50
  • A strategy that buys more when VIX > 30% (the popular advice): 0.47 which is slightly worse than the null case
  • A strategy that reduces exposure when VIX is high (inverse sizing): 0.54
  • A simple momentum strategy (cut exposure when the market is falling, which is typically when VIX is elevated): 0.59 — the best performer

It’s always bears repeating how risk scales:

When volatility doubles, the risk of holding stocks is actually four times as large (because variance, not standard deviation, is what matters to risk).

To merely hold your position when VIX doubles, expected returns would need to quadruple. To justify doubling down, they’d need to increase eightfold, which the authors deem practically implausible.

This post led to some smart quants chiming in on X.

Here’s @ptuomov:

VIX AND EQUITY WEIGHT

The correct time to take more equity risk is when VIX has been high for six months but has been trending down. The correct time to take less equity risk is when VIX has been low for six months but has been trending up.

The target equity weight is then proportional to the target equity risk divided by VIX. Therefore, at most times, low VIX corresponds to high equity weight and high VIX to low equity weight.

This is a very low-resolution statement because each word represents many variable choices when you get into research:

Define “high”, define “trending”, “six months” was probably just a placeholder term

The degrees of freedom on the choice notwithstanding, the idea makes sense:

You are using the signals from the derivatives market, a place where leverage attracts early movers and smart money, to give a leading indicator on “the market environment is changing from the status quo” and collective anchoring biases make the wider market underreact. The way to profit from the seeds of this new information is to follow the trend.

There’s that line what the wise man does in the beginning, the fool does in the end.

The quant view is trying to find the signal of moving from the end of one cycle to the beginning of another. Trend following in a sense has a long option flavor. The premium is all the false starts and the payoff is when you finally catch a trend.

Meanwhile, buying the dip is a short option strategy in that it is betting on mean reversion as opposed to further divergence. Buying stock when VIX spikes is a mean reversion trade. But when you examine that as a strategy from the vantage point of all-time highs, it takes for granted that the mean is a good thing.

When you read a claim about a course of action, it’s good mental hygiene to first triage it as: is this directionally long or short vol?

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

AI Traders

Any moontower.ai subscriber can prompt our trained agent. Even if you aren’t a sub you can give it a try for free. Our team plans have included an API but we just launched an MCP allowing users to connect their own AI’s to our API endpoints.

This gives users maximum flexibility. We are tuning our agent on a regular basis, but if you prefer your own tool stack and AI you have that choice now.

We use evals for automatically RLHF’ing Moontower Agent and I also have a manual process where I give the agent and the MCP (using Claude Code) the same prompt, and then judge them myself. Very old-fashioned. I’ll share more about what we’re learning from this in the future, but in the meantime, here’s a relevant article from the market-making firm Optiver:

Where AI Trading Models Work and Where They Still Fall Short (4 min read)

Optiver’s Applied AI team did a different kind of eval. They gave several leading large language models the same assessments they give human interns and junior traders.

The results indicate where LLMs excel…

  • grasping trading theory
  • calculating fair value
  • recognizing risk

…and where they still stumble:

  • multi-step reasoning
  • updating beliefs on the fly
  • maximizing expected value under pressure

Even before AI was dominating the conversation, traders have always been obsessed with learning from data. A common example is in transaction analysis. Looking at the trades you did filtered by counterparty, venue, method (ie voice/electronic) as you suss out where you are most likely to be adversely selected. This is a hard problem even with structured data. For example, it might be straightforward to filter by how you do against live option orders (as opposed to delta neutral packages), but there are so many possible permutations. Should I consider how the quote was framed before the order came in? Do I treat a resting order differently than if I’m hit or lifted? Does time of day matter?

But now consider the scope of the unstructured data problem. The counterfactual. The order a broker showed me, I passed on and proceeded to trade without my participation. You’d need to record every phone call (actually this is already done for compliance reasons. In fact, when I interned at a bank in 1995 one of my tasks was to change the giant reel of tape!). But you’d need to link the audio of what the order was to the print when it hit the tape. Or track the fact that it never even traded. It’s like tracking the p/l of a non-trade that could have been. With transcription so cheap, this is feasible now, but it wasn’t when I was thinking about it. You could have traders note when they passed on a trade, but this would be so tedious that it was always a non-starter on a high-volume market-making desk.

My guess is that some trading shops might be doing things like this now (if not, you’re welcome for the idea). But this Optiver article made me wonder when trading rooms will be mic’d up. Jarvis listening to all the conversations, meetings, and debates to cheaply turn unstructured data to structured data.

Your voice, its quiver, your cadence, your pauses, your keystrokes, your glances, your heart rate. Insofar as humans will still be trading, it’s hard to imagine the data obsession that’s already penetrated the MLB not make its way to desk talent.

You’ll know singularity is close when the employee handbook stipulates bathroom breaks as the only acceptable cause to remove your electrodes. Buy stock in Gillette. Every man on a W2 will need to shave their chest for a clean connection.


Related

Elm Wealth let AI compete with humans in their popular Crystal Ball Challenge. You can give it a try yourself:

https://crystal-ball.elmwealth.com/

Elm’s founder Victor Haghani:

A couple of weeks ago we let you loose on our Crystal Ball Challenge: tomorrow’s headlines, $1 million to trade in stocks and bonds, and four AI models to beat. Humans showed up in force, logging thousands of plays and adding over 1,500 entries on the leaderboard.

Here is how the AI models are doing against human players so far:

– Claude: winning 65% of the time
– ChatGPT: 50%, a coin flip
– ️ Grok: 43%
– Gemini: 40%

Both the Wall Street Journal and The Economist covered the experiment this month, and both keyed on the same finding: the AIs are great at reading market-moving news, but they struggle to size their bets appropriately. Knowing what to trade turns out to be the easy part. Knowing how much is what trips them up.

If you have not played yet, three of the four AIs are losing more than half their matchups. Pick your fight. If you have played but not lately, your spot on the leaderboard might no longer safe.

 

And finally, just before I scheduled this to send out I came across Dwarkesh’s:

Subtitle: “Labs are throwing away the most valuable data”.

🗒️transcript