Friends,

I’m just writing from the hip today about reading.

Since  my first kid was born my reading has cratered to like 3 books a year. While Zak is a convenient scapegoat, the truth is moving to CA is the true culprit. I no longer had that 45-minute E-train commute from Long Island City to the NYMEX. That trenta-sized ice coffee with a paperback was a luxurious start to the morning before switching into literal arena mode (shout out to the main character of fintwit this week).

Zak is 10 and I’m emerging from the fog. I’m on my 12th book this year, participating in my first ever book club and likely joining another. The Kindle app has also helped — the phone is morphing from a pile of Instagram wedged between slices of group chats into a book sandwich (separate thought, but a great use of LLM tech would be to classify a text message into time-sensitive or not and only send notifications for the former).

This year I’ve read:

I’m currently reading 3 books simultaneously:

• Tomorrow, Tomorrow, Tomorrow

  This is for the book club. I’m really enjoying this novel.

• More Than A Number’s Game: A Brief History of AccountingThe book traverses history by examining a different case study per chapter. I’m early in the book, but so far it’s full of highlights.

  Why am I reading this?

  Broadly speaking — accounting, from GAAP to mental accounting, is a striking topic because in the spirit of “we manaage what we measure”, it is the seat of so much decision-making extending to everything. Hell, business accounting is just a narrow application of measurement at large which properly done should consider counterfactuals, opportunity costs, and at least second derivatives.

  The simplest non-obvious questions are like: Do Uber drivers deduct their car’s depreciation from their hourly wage (I see you Jim)? How many businesses actually suck once you properly adjust for maintenance capex or what Buffett calls “owner’s earnings”?

  And much more complicated questions wrangle with — just how much greener is an electric vehicle than a fossil-fuel vehicle (suspect it has a lot to do with where these vehicles are located so you get the non-sound-byte-friendly answer: “it depends”).

  Another thought: While my interest in Georgism was sparked by normative concerns, the most interesting part of it comes from its accounting — specifically the philosophical basis for distinguishing land and other natural resources from capital. It’s an amazing reminder that the connotations of big words like “capitalism” are loaded with design choices in how we do accounting and none of it is a natural law like gravity. Economic policy is not physics. How we understand it is tightly and invisibly wound around our basic accounting definitions.

  (There is nothing about capitalism which suggests that we should account for the land and sky differently, but we do. Which implies that how we treat land is not resting on the principles of capitalism. Which strongly suggests that painting changes in land accounting as anti-capitalist is a self-interested sleight of hand. The Georgist approach actually strikes me as far more in the spirit of capitalism. I sense plenty of room for thoughtful counterpoints but the average reaction to Georgist principles are just the confessions of people habituated to regurgitating convenient viewpoints. And that’s me trying to be nice.)

  If you care to appreciate what this means, it’s best to observe the building of an economic framework from first principles. Give it a try.

  Go to:

  https://notion.moontowermeta.com/moontower-refactors-lars-doucets-review-of-progress-poverty and rip thru the following sections:

  📒Defining Terms

  👷🏾‍♂️Wages, Capital, and Labor
  🔀The Laws of Distribution

• Life in Half A Second by Matthew Michalewicz

  Matthew is a Moontower reader and sent me a signed copy. It’s self-help kind of book which is a style of book you have to force me to read. I actually don’t relate to a lot of the thinking but I definitely glimpse some bridges to my own. And this is helping me flesh out some thoughts that will make it into Moontower I’m sure. Plus, being able to discuss it with the author is pretty dope. We see eye-to-eye on a lot about life so by exploring the parts I struggle to relate to should stimulate a wider perspective.

Books I’m reading aloud with my kids (as I risk afflicting them with the “read several books at once” disease)

• Journey To The Center of the EarthThis is not an easy read, so it’s a great opportunity to see what they understand and act as translator. I’m playing with this idea of having them read books at their level on their own, but I read harder books with them. I have a little story made up about how this gives them different “powers” because I think creating some magic or mystique about the beauty of reading will give them an inexpensive pleasure and sense of appreciation throughout their lives which also happens to have instrumental value.
• Man For All Markets: Biography of Ed ThorpEd and his life are wildly inspirational. He became wildly successful (wealth, family, friends, health) because he was super-curious, playful, independent-minded, and persistent. Money was a byproduct, not something to optimize for. Nearly all the people I find inspirational fit this mold. Money is great and I definitely want more, but never at the expense of boring myself.

  The unrelatable part of Ed’s story is he is one of the towering geniuses of the 20th century.

• Hitchhiker’s Guide To The GalaxyI’m early into this and been meaning to read it for awhile. So far so good. Literal LOL material.
• A Wrinkle In TimeThis has been a slog to be honest. Not sure we’ll finish it, haven’t touched it all summer.

What books are next

These aren’t in order. I impulsively pick in the moment. Fiction books will come from the book clubs so they are TBD.

• A Theory of Fun for Game Design by Raph Koster
• Alchemy by Rory Sutherland
• World For Sale: Money, Power, and the Traders Who Barter the Earth’s Resources
• Cash Rules by David Hale
• Dreamland: The True Tale of America’s Opiate Epidemic
• Dopamine Nation
• Chaos by Tom O’Neill
• Killers of The Flower Moon
• Guitar Zero (re-read)
• Play Anything: The Pleasure of Limits, the Uses of Boredom, and the Secret of Games

Technical books

• Advanced Portfolio Management: A Quant’s Guide for Fundamental Investors (I believe this is standard-issue at Citadel)In the spirit of holistic accounting, I’m interested in pertinent benchmarking and proper performance attribution. This book should help.
• Systematic Trading by Rob Carver
• Positional Trading by Euan Sinclair
• Active Portfolio Management by Grinold & Kahn
• I’m also reading a highly technical manual on derivatives that is formal while covering practical minutiae from the trenches — many that are rarely or never addressed in the canonical texts. This one is not yet (and may never be) published — written by ex-SIG friend, currently in a senior role at a large MM. I keep urging the author to publish because I selfishly want to cite from it.

Money Angle

Myself and a few members of our local club are going to do a financial and investing literacy series for the member families. We put together a first draft syllabus this week and as things move along I’ll share here. Perhaps we’ll even turn into an online series. I’ve been working on one focused on the investing side but it’s only a WIP because of priorities (moontowermoney.com).

The one we are doing for the club will be highly practical drawing on the experience of a financial advisor, a retired Point 72 PM, and some option trader crank who writes on the internet. (Topics will range from “what is a bond” to bringing in experts to talk about how to pay for college)

As I was poking around notes, I re-read some of Byrne Hobart’s Capital Gains missives which is a series devoted to finance education (although the material isn’t quite 101 — it’s more of a redo of 101 for people who have already gotten a finance education. I hope Byrne doesn’t mind me saying that.)

Here’s one that stood out:

The Capital Asset Pricing Model: Risk, Reward, and Reasons (Capital Gains)

Some excerpts/teases:

The temptation is to think that if risk and reward are correlated—if you can reach for higher returns by selling your investment-grade bonds and replacing them with stocks, or selling your large-cap US stocks and replacing those with wilder emerging market stocks—that all forms of risk-taking are rewarded with higher returns. But this isn’t true: the expected return of a single stock of average volatility is the same as the expected return of the market, but the volatility of one stock, compared to a diversified portfolio, is much higher. And thanks to the relentless math of “volatility drag,” i.e. the observation that you don’t offset a -50% loss until you’ve made a +100% return, the expected overall outcome from this particular form of risk-taking is negative.

And there are other forms of unfavorable risk/reward tradeoffs: paying higher fees for exposure to the same asset class, for example, is a straightforward cut to returns with no attendant reduction in risk. In the general risk/reward tradeoff, there are some extreme cases where things don’t work as planned: the longer-term a bond is, the more it’s a bet on interest rates, and the more it’s excess return is compensation for taking interest rate risk. But 30-year bonds don’t get returns quite commensurate with their risk—because when bond portfolio managers want to make a big bet on rates, that’s what they have to bet on.

…

How can we square these observations with the fact that many investors have achieved great success through concentrated bets on a handful of positions? One obvious answer is that some of them are lucky; “lottery ticket” is an accurate pejorative term for assets and strategies whose risk isn’t commensurate with reward, but lottery winners do exist.

However, there’s a subtler answer…

…

There are many mediocre tradeoffs between risk and reward, where you can get the same mix of them in different amounts. And there are some bad tradeoffs available, with incremental-reward-free risk. To get a good tradeoff, you need a good reason to expect it: some justified belief that there’s a particular asset that’s mispriced, and a good meta reason to think that nobody else has considered it. In a competitive market, you need not just a theory about the asset in question, but at least some kind of theory of why your competitors haven’t spotted it. Yes, “I’m a better investor than they are” is a theory—but do any of your competitors pick stocks despite consciously thinking they’re bad at it? Especially in an environment where cheap index funds are available, you should assume that the average market participant is about as self-confident as you are. And one fun implication of this is that the best returns accrue to people who think they’re less skilled than the average stock picker, but skilled enough that they shouldn’t leave the whole process up to Standard & Poors.

Which is not to say that investing by picking a small set of smallish, high-variance companies, watching them like a hawk, and enjoying long-term outperformance with some painful dips is a bad trade. It can be a very rewarding hobby! But the opportunity cost is defined by the average performance of index investing. So stock picking ends up being like many other hobbies: it takes time and effort, and if you’re very good at it and somewhat lucky, you might break even.

Money Angle For Masochists

The new post Short Where She Lands, Long Where She Ain’t was incredibly well-received this week so I’m hopeful it’s doing what I intended — prompting investors to match their trade expressions with what they actually think the future outcomes look like. Sometimes you use a mallet (“just buy the stock”) and sometimes your view demands a scalpel (“if the stock is not higher then it’s much much lower”) and that is the realm of options.

Here’s a re-print of the insights and answers to questions I anticipated:

🔭High-level insights

1. You want the stock to land near your short strike or away from your long strike. Over a large sample of trades, if the stock expires near your long strike more often than the theoretical distribution then you will lose. If it lands there less often than theoretical, you’ll win on average. For short options, the opposite is true. Even though the options in these sims are perfectly priced, there is still noise because we are still drawing a sample.

2. Put-call parity is iron-clad. You are either long options or short options. These sims let you see that whether you delta hedge a call or put the outcome distribution is the same. All that matters is whether you are long or short an option, not the type! [My professional risk software didn’t even display calls vs puts at the high level. It just summed total options per strike. You could drill down to see if your exposure was calls vs puts because it mattered for funding and pin risk reasons.]

3. “Pay me $10k up front and I’ll flip a million-dollar coin with you” That’s options market-making in one line. Remember these sims are perfectly priced options. Now imagine you have a trading business and net a penny of option per trade (this is a very generous assumption — margins are often smaller than this). In the example of the 110-call with 8-steps until expiry you’d be making a penny of edge with a standard deviation of 88 cents! Of course the Sharpe ratio at the trade level isn’t the same as the Sharpe ratio at the strategy level. Because edge scales by N and risk scales by square root(N) you can have a great business if you do LOTS of trades while maintaining that edge. The flip side: if you don’t do lots of trades your results are noise. Welcome to epistemological nihilism.

Q&A

If you are not a delta-hedger, but trading the options outright for direction does this matter?

Sure does. If you buy a call because you’re bullish, your alternative could have easily been to buy the equivalent delta worth of stock. If the stock then goes to your long strike, you lost not only your premium but the foregone return on the shares you would have owned! This reinforces the point that options require you to be right on direction and timing/volatility (time and volatility are intricately linked). Remember, options are priced for specificity. The leverage is amazing if you call the outcome and timing correctly, but like a parlay, you will often lose if you get any part of the bet wrong. Remember the put-call parity insight — no matter what you do, you are trading volatility. Without a view on that, you shouldn’t touch the options. If this doesn’t make sense, you don’t understand options. The house is more than happy to have you delude yourself in the noise I described above.

You are a market-maker and see a giant flurry of call buying in the context of bullish news. You decide the buyers are overpaying — the prices are implying a volatility your process has deemed as “excessive”. Do you hope the call buyers are right?

As a market maker, you try to understand your counterparties. The prices people are paying (which imply a volatility) and strikes they are chasing give you a sense of how much conviction and how far they think the stock can run. If you suspect they are bidding “too much” for these calls you will sell them and you will buy the stock yourself to hedge the calls. What am I rooting for and what am I worried about? Let’s start with my 2 primary fears:

• The stock acts like GME and just explodes higher. No vol that I sell is high enough. It rips thru my short strike, it keeps going, it’s hard to buy, gamma squeeze, you know the drill. That’s the obvious risk.

• The stock gaps down through a trap door. No liquidity. I collect the option premium but I ride my long shares into the grave.

What am I rooting for? The stock continues to go higher, but slowly. The call owners feel the theta breathing down their necks and are anxious to monetize. They got the trade thesis right but…they overpayed for the options. The market makers have them just where they want them. If they are aggressive, they will understand that there is a supply of calls being held by weak (as opposed to diamond) hands and start offering the volatility down themselves, accelerating the losses felt by the option longs. It’s a game of chicken and the first option owner that offers is the tell. They’re going to throw in the towel. As the market maker this is fun. I win on my long shares and I will get to cover my vol shorts hopefully at cheap levels. The way I think about trades where the counterparty is using the options for direction is whether their being correct on direction is stabilizing or destabilizing. In 2021, GME going up further was highly destabilizing. It didn’t make sense. It was “irrational”, “forced squeeze”, etc. A destabilizing move is a liquidity vacuum. Once something doesn’t make sense, there is a phase shift in sentiment from logical thought to the next print is going to be driven by the most desperate account. Death spirals are divergent, not mean-reverting processes.

On the other hand, a stabilizing move is one that occurs in the direction of consensus and makes sense. Think early 2022. Hedge funds had actually degrossed ahead of the sell-off and option skew notoriously underperformed going from expensive to multi-year lows during the sell-off. Fund managers were well positioned for the sell-off. Here’s Financial Times quoting Benn Eifert…

Option manager called the sell-off the most telegraphed:

There are always some people caught unawares, but the central bank pivot from “it’s transitory” to “we’re going to nuke inflation” was petty well-telegraphed, and the impact widely expected.

My discretionary sense of whether a move is stabilizing or destabilizing plays a large role in how I manage an option position for the name. That sense comes from the semi-conscious process of pattern-matching how the market is positioning, how aggressively and what the broader news context is. I’ll add one bit.

If I have a sizeable short call position, my experience tells me that I should be nervous about the downside. If the market is smart (and it is), it will bid for calls when it understands that the distribution has a more positive skew. The counterbalance to a more positively skewed distribution is that the underlying is more likely to go down in price. And if the options are bid because the market understands the distribution then that is usually how I’m going to get hurt. Owning long deltas on a sharp down move. And here’s the salt in the wound:

When I sold the expensive calls I likely bought some other option to hedge the vega. If the skew shifts to the calls, that means I probably own puts which would have begun to screen cheaply. The problem with this is the down move is expected and stabilizing. which means the implied volatility will fall.

This is diabolical.

The stock is going away from my short calls, towards my long puts and I’m carrying long deltas against both types of options. Pain parade.

I have seen traders blow out in these scenarios. Long vol and getting longer vol as a name collapses on a stabilizing move. And every time that vol compresses on a downtick, this position “decays longer” (vanna for the nerds out there).

If you take anything away from this — your assessment for how vol will react is heavily dependent on how far and fast a move can be before it phase shifts from stabilizing to destabilizing or vice versa.

[Whisper voice] The kinks in the skew are a clue which means the right way to iron them out is with a butterfly not a vertical spread. Unless you haven’t been trading options for years, that will mean nothing to you and it also means you are doing life correctly. Take a bow.

How can I use this knowledge to shape trade expressions?

If you’re bearish, consider buying calls to replace part of your long position. If the market falls and they expire worthless, you are happy.

You can then scoop hard deltas at the lower price.

In other words, you were bearish which is highly correlated with the idea that volatility is going to increase. Remember you want to own options where the stock ain’t going. Think of a very expensive 2021 type market — if the expensive stock keeps going up it’s a surprise. It’s destablizing. So the calls will hold up well.

But if the market does tank, you’ll be happy you switched your long shares (or what I call “hard deltas”) to calls (ie “soft deltas”)

You want your hard deltas pointing in the direction of the most likely scenario and your options pointing in the direction of the destabilizing scenario that probably isn’t going to happen.

This thread harps on this a bit more.

I have a hunch my boss doesn’t really understand options but he trades them a lot. Is there a way to tell?

Does he like to say “I’m selling this strike because it’ll never get there”?

That’s a dead giveaway that he’s trading options without understanding their nature. This misunderstanding leads to decisions that are 180 degrees opposite from their thesis.

Why? conditional probability — a cheap option that hits is nitroglycerine because the cheapness signified that its the seller used “it’ll never get their logic”. Their false confidence in that assertion means they underestimated the scenario when sizing their risk. The move is deeply destabilizing because they are offsides in a big way and need to cover.

A short-circuit in Bayesian reasoning displays itself when put-sellers say “I’ll be happy to buy the stock if it gets there”. They are projecting a state of the world where only this one asset changed in price and everything else stayed the same. Or the investor who sold bond puts assuring us they’d “be happy to buy bonds if they hit a 7% yield.”

Well, what if they only hit a 7% yield when inflation is 9%?

I’ll be repetitive — this boss is the same guy who sells calls because he’s bearish.

Bro, you don’t want to be short options away from where you think the stock is going — you want to use hard deltas to point that way and own that option as insurance to put the trade on with conviction.

☮️Stay groovy!

Friends,

This past Thursday at Back To School Night, I’m sitting in my 5th grader’s classroom chair scribbling a note on his dry-erase desk for him to see in morning. His mother is filling out a parent survey that helps the teacher get up to speed on your kid. It looks like she’s finished when she slides it over to me to answer a question she left blank — “What would you like your child to focus on this year?”

An article I read this summer immediately popped into my mind — The State of Being Stuck by math educator Ben Orlin.

The article begins:

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.

Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

Ben, like me staring at that survey question, didn’t want to waste the opportunity. He wondered…

…before settling on this question:

Here’s what Ben got back:

The essence of Wiles’ answer can be boiled down to just six words: “Accepting the state of being stuck.”

For Wiles, this is more than just a vague moral, an offhand suggestion. It’s the essence of his work. It’s an experience at once excruciating, joyful, and utterly unavoidable. And it’s something desperately misunderstood by the public.

“Accepting the state of being stuck”: that’s the keystone in the archway of mathematics. Without it, we’re left with nothing but a pile of fallen bricks.

Wiles began his answer, like any good mathematician, with a premise everyone can accept: “Many people have been put off mathematics,” he said. “They’ve had some adverse experience.”

It’s hard to argue with that.

“But what you find with children,” he continued, “is that they really enjoy it.”

In my experience, it’s true. Kids love games, puzzles, learning to count, playing with shapes, discovering patterns—in short, they love math.

So how does Wiles account for our alienation from mathematics, our loss of innocence?

“What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck,” Wiles said. “People don’t get used to that. They find it very stressful.”

He used another word, too: “afraid.” “Even people who are very good at mathematics sometimes find this hard to get used to. They feel they’re failing.”

But being stuck, Wiles said, isn’t failure. “It’s part of the process. It’s not something to be frightened of.”

Catch me and my teacher colleagues any afternoon, and—if you can get past the “sine” puns and fraction jokes—you’ll likely find us griping about precisely this phenomenon. Our students lack persistence. Give them a recipe, and they settle into monotonous productivity; give them an open-ended puzzle, and they panic.

Students want the Method, the panacea, the answer key. Accustomed to automaticity, they can’t accept being stuck.

…

“What I fight against most,” said Wiles, naming an unlikely enemy, “is the kind of message put out by—for example—the film Good Will Hunting.”

When it comes to math, Wiles said, people tend to believe “that there is something you’re born with, and either you have it or you don’t. But that’s not really the experience of mathematicians. We all find it difficult. It’s not that we’re any different from someone who struggles with maths problems in third grade…. We’re just prepared to handle that struggle on a much larger scale. We’ve built up resistance to those setbacks.”

If you have walked past a rack of popular non-fiction books in the past decade, you are thinking “not another lecture on grit or growth mindset please”. Ben doesn’t go there. In fact, he’s quick to affirm how we often overplay the “grit “ hand:

Recently, the currency of “grit” has fallen among teachers. It’s not that the idea lacks psychological validity. It’s more the weight of its educational connotations. Grit has become an excuse to romanticize poverty as “character-building.” It has devolved into a vague catch-all at best, and at its paradoxical worst, a reason to write kids off as lost causes.

Orlin proposes a 3rd idea:

Wiles is no educational theorist, of course, but I find that he offers a resonant and compelling third path. For him, perseverance is neither about personality (as with grit) nor belief (as with mindset).

Rather, it’s about emotion.

Fears and anxieties come to us all. You can be a nimble mathematician, a model of grit, and a fervent believer in the human potential for growth—but still, getting stuck on a math problem may leave you deflated and disheartened.

Wiles knows that the mathematician’s battle is emotional as much as intellectual. You need to quiet your fear, harness your joy, and cope effectively with the doubt we all feel when stuck on a problem.

Giles offers some counterintuitive ideas as well:

On the value of forgetfulness

“I think it’s bad to have too good a memory if you want to be a mathematician,” Wiles said. “You need to forget the way you approached [the problem] the previous time.”

It goes like this. You try one strategy on a problem. It fails. You retreat, dispirited. Later, having forgotten your bitter defeat, you try the same strategy again. Perhaps the process repeats. But eventually—again, thanks to your forgetfulness—you commit a slight error, a tiny deviation from the path you’ve tried several times. And suddenly, you succeed.

Wiles has a nifty analogy for this: it’s like a chance mutation in a strand of DNA that yields surprising evolutionary success.

“If you remember all the false, failed attempts before,” said Wiles, “you wouldn’t try. But because I have a slightly bad memory, I’ll try essentially the same thing again, and then I’ll realize I was just missing this one little thing.”

Wiles’ forgetfulness is a shield against discouragement. It neutralizes the emotions that would push him away from productive work.

Coming back to the parent survey…how did I reply?

I want Zak to build the muscle of persisting through drawn-out problems.

This skill is more valuable in a holistic, psychological sense than just being a technique. It’s hard to feel truly empowered unless you become familiar with the pattern of feeling stuck and the emotional reward of chipping your way out of it. If you find success too quickly, you’ll fear that you can’t repeat it. You’ll feel like an imposter. You’ll be imbalanced — with a bias towards protection, not growth. Coddling your ego or hating on others when you should be prepping for your next climb from a new valley.

Money Angle

I had a little financial adventure this week that’ll I’ll try to connect to some broader concepts in the Masochism section.

My wife’s sister’s family lives next door. We removed part of the fence so we have our own little commune with 3 generations living together. It has been the largest life upgrade I can think of.

The catch: it’s temporary — both families are renting.

We aren’t actively looking for a house to buy, but we asked our friend whose also the realtor who sold our house for us to just keep an eye out for “situations that could accommodate both our families”.

We got a call this week. She has a client selling a house that hasn’t been on the market for 50 years. An old 3/2 near the elementary school on half an acre. Oh yeah, and they are also selling the completely undeveloped flat half-acre lot behind them (there’s an easement making this back parcel a “flag lot”).

By offering the lots separately they are able to draw a wider buyer pool. But also makes the deal hairy. If you just want the front lot, you will be reserved in your bidding because you know at some point there’s going to be a house built in your backyard. Who wants to live next right next to a construction project for 2 years?

But this is also tricky for the person who buys just the vacant parcel. The 3 adjacent neighbors and the family who buys the lot with the house are going to NIMBY the permit and building process. Not to mention, that you need to pull utilities to the vacant lot (estimated to be about $150k).

The ideal buyer would want to lift both lots presumably with a plan to live in the old house while they build a new house. But that is a tiny buyer pool — population us.

We bid on both as a package. Because of the complications described earlier, the parcels aren’t selling immediately. We made a cash bid below the sum of where the legs are bid with the sense that the sellers know if they fill a single leg, it will be harder to fill the other and we were the clean option.

We would find out the next day if our bid was accepted.

I’ll bring you into the discussion of risk we had that night as we waited.

We believe our bid had a margin of safety of about 25% below fair value based on comps (comps for the vacant lot are higher variance and indirect — basically backing out land value from the price of teardowns and near teardowns). Building is a hairy proposition around here so even though you shouldn’t expect a builder’s margin, there is some margin which I describe as the market’s “Here’s a carrot, I dare you to upend your life to navigate the labyrinth of CA construction”.

We didn’t expect to get win the bid. Even though the bids for the individual lots were shakier because of the total dynamic, we were still bidding well below them. But what if we did?

I’d actually be concerned. Since the fair value of the lot with the house was easily-comped, getting hit would tell me the vacant lot had a landmine if it isn’t purchased by say, a direct neighbor (where we assume the individual lot bids came from). What if the direct neighbor was bidding for the lot because they just wanted more space (or a pool/tennis court, etc)? If we got hit perhaps it’s because the utilities are way more expensive to pull (I have a friend that owns a bunch of SFH’s in town and told me a story of how the water utility wanted $750k to feed a hillside parcel).

In short, if you bid below the sum of the legs and you get filled, you need to update your prior of what fair value is. We had a few knowledgeable friends including a local builder lined up to walk the property with us in the event that we get our bid hit. I was planning to be down at the permit office learning what I could this coming week, ready to ask the utilities about “worst case scenario quotes”, and primed to talk to insurance companies (Allstate and State Farm who make up the bulk of CA property insurers have stopped underwriting new policies in the state as of this summer— this is a whole other topic that gives me black swan vibes — well grey swan if I can see it guess). In short, we fired out a bid knowing we could back out risklessly. If we got filled it would be a highly restrained win until we investigated the risks more closely.

As expected our offer bid was not accepted.

Money Angle For Masochists

The meta-risks above exist wherever deals are made.

Adverse selection

There is a lot of money floating around the Bay Area, a shortage of supply, and multi-generational relationships that we are not insiders of(we’ve been here close to a decade only). Given our relationship with the broker and the hair on this deal, we felt some of that was mitigated but probably not all. After all, our limited knowledge of the neighbors is a soft underbelly in our reasoning.

The catchy name for this concept is the “market for lemons”. Its strongest form contends that all used cars are overpriced according to the logic here. As a matter of practice, I suggest using that heuristic as the default but seek to disprove it because there is always the possibility of an inefficiency in your specific situation. It would be worthwhile to consider what conditions would make your situation more or less likely to lend itself to adverse selection.

Whenever you compete for a deal you must understand where you stand in the pecking order, who else has seen the deal, and what their passing on it might be saying.

Winner’s Curse

Fair value is not what you think conditional on getting filled. In Ben Orlin’s book Math Games With Bad Drawings, he discusses the value of playing auction games:

Because everything has a price, and auction winners often overshoot it.

We live in a world on auction. Photographs have been auctioned for $5 million, watches for $25 million, cars for $50 million, and (thanks to the advent of non-fungible tokens) jpegs for $69 million. Google auctions off ads on search terms, the US government auctions off bands of the electromagnetic spectrum, and in 2017, a painting of Jesus crossing his fingers fetched $450 million at auction. Before we dub this the worst-ever use of half a billion dollars, remember two things: (1) The human race spent $528 million on tickets to The Boss Baby, and (2) it’s a notorious truth about auctions that the winner often overpays.

Why does this winner’s curse exist? After all, under the right conditions, we’re pretty sharp at estimation. Case in point: In the early history of statistics, 787 people at a county fair attempted to guess the weight of an ox. These were not oxen experts. They were not master weight guessers. They were ordinary, fair going folks. Yet somehow their average guess (1,207 pounds) came within 1% of the truth (1,198 pounds). Impressive stuff. Did you catch the key word, though? Average. Individual guesses landed all over the map, some wildly high, some absurdly low. It took aggregating the data into a single numerical average to reveal the wisdom of the crowd.

Now, when you bid at an auction — specifically, on an item desired for its exchange value not for sentimental or personal reasons — you are in effect estimating its value. So is every other bidder. Thus, the true value ought to fall pretty close to the average bid. Here’s the thing: Average bids don’t win. Items go to the highest bidder, at a price of $1 more than whatever the second highest bidder was willing to pay. The second-highest bidder probably overbid, just as the second-highest guesser probably overestimated the ox’s weight.

To be sure, not all winners are cursed. In many cases, your bid isn’t an estimate of an unknown value but a declaration of the item’s personal value to you. In that light, the winner is simply the one who values the item most highly. No curse there.

But other occasions come much closer to Caveat Emptor: The item has a single true value which no one knows precisely and everyone is trying to estimate.

I like an example from Recipe For Overpaying: investor Chris Schindler explains why high volatility assets exhibit lower forward returns: a large dispersion of opinion leads to overpaying. He points to private markets where you cannot short a company. The most optimistic opinion of a company’s prospects will set the price.

Getting filled in an auction should make you update fair value. In Laws of Trading, Agustin Lebron gives an example from the market-making context. He starts by echoing what we know about the winner’s curse — any bidding strategy requires the bidder to estimate the item’s fair value conditional on having won the auction. This requires estimating how many bidders and how wide their uncertainty is regarding the item. But the problem is that some bidders are better informed than others. So if you are relatively uninformed and win the auction you are sad. [This topic came to life constantly to anyone who came to the StockSlam sessions — Steiner generously joked that if you traded with the Kris bot, you track down the info that shows how you just got arbed.]

But Agustin then gives an example of how to Bayesian update:

You may interpret a market maker’s width as an expression of confidence and using that to update your fair value by weighting their mid-price by the confidence.

If I’m 54.10-54.30 and you are 53.50-53.90 then I’m 2x as confident. So my new fair value is 2/3 x 54.2 +1/3 x 53.70 = 54.03

My Bayesian analysis of being filled on a limit order vs market order

Imagine a 1 penny-wide bid/ask.

If you bid for a stock with a limit order your minimum loss is 1/2 the bid-ask spread. Frequently you have just lost half a cent as you only get filled when fair value ticks down by a penny (assuming the market maker needs 1/2 cent edge to trade). But if you are bidding, and super bearish news hits the tape (or god forbid your posting limit orders just before the FOMC or DOE announce economic or oil inventory), your buy might be bad by a dollar before you can read the headline.

If you lift an offer with an aggressive limit (don’t use market order which a computer translates at “fill me at any price” which is something no human has ever meant), then your maximum and most likely loss scenario is 1/2 the bid-ask spread.

Do you see the logical asymmetry conditional on being filled?

Know what you’re leaning on

When you are a market-maker and you get filled it’s because your bids and offers are conditional on other bids and offers in the market. My bid in XLE might be pegged to the market’s bid for OIH. This is known as “leaning on an order”. My model has some value for the spread and if I get filled, I’m presumably able to leg the spread at a price I’m happy with. If I didn’t think I could leg the spread, I’d adjust my bid for XLE.

In real life, I might bid for a house but there’s still some conditional peg in place. If the stock market suddenly dove on a surprise 75 bps rate hike, I’d pull my house bid. It’s stale. The world and my assessment of the house’s value has changed. The period that defines staleness differs depending on whether you deal in real estate or HFT but the concept persists.

[This actually happened to us when we were in contract to sell our TX property last year. I had to act pissed when the realtor said the buyer’s financial advisor suggested they pull the bid when the stock market nosedived in the spring, but secretly, I thought “good advisor”. He was very right. We ended up selling the house nearly 10% cheaper].

The key is to always keep the reasoning for the price you bid or offered fresh. If you lose sight of why the price you are bidding makes sense, then your decision is no longer linked to an auditable chain of logic where you can go out and test the assumption (ie for example if you tried selling some OIH you might find the bid isn’t real or unusually thin and therefore your XLE bid might be “propping up the market” and the OIH bid is just leaning on you — it just has a different assessment of the spread value between the 2 stocks). Once you lose the chain of logic, you’ve lost the grip on the kite. Your bids will just float capriciously in the winds of emotion, narrative, and behavioral biases.

I’ll leave it there.

☮️Stay groovy!

Friends,

Some recent convos had sex with lingering thoughts from a podcast on a bed of a blank page this morning and today’s Moontower is the weird baby that popped out.

I recently listened to my first episode of Dan Carlin’s Hardcore History — a tour of the transatlantic slave trade entitled: Human Resources. Dan’s story-telling and research shine in this nearly 6-hour episode. He deserves all the accolades he gets. The style, quality and nuance of his work are well-advertised, I’m just late to the party. He immediately jumped into my ring of favorite creators.

I’m also a fan of the Founder’s podcast. Because I found an interview with its host David Senra to be as compelling if not more than the books he highlights (a high bar), I decided to hunt down interviews with Carlin. The first one I clicked on with Lex Friedman did not disappoint.

• 3+ hour interview (Lex Friedman on YouTube)

Here are 4 excerpts that stood out to me, but the whole interview is good.

https://moontowermeta.com/a-few-excerpts-from-dan-carlin-on-lex-friedman/

I’ll post one of the excerpts here because I like Carlin’s approach — he answers the question probabilistically (and his gambling mindset in general to handicapping answers is prevalent in the way he reasons) but explains the framework he is adopting to approach the question.

[Meta observation: Answers to questions often fall out trivially from the model you choose to approach it, so it’s a reminder that your choice of model in the first place is critical — any ensuing logic will unconsciously inherit its assumptions. The work of overriding assumptions to adjust for differences between the reference model and the question at hand is where devilish details lie. But when encountering an argument, it’s a good idea to question the choice of model before quibbling over details.]

On to the excerpt:

Lex asks how we will “destroy ourselves”. Carlin gives a framework for handicapping what calamity will undo us.

Lex: If you were to wager on the method in which human civilization collapses, rendering the result unrecognizable as progress, what would be your prediction? Nuclear weapons? A societal breakdown through traditional war? Engineered pandemics, nanotechnology, artificial intelligence, or something we haven’t anticipated? Do you perceive a way humans might self-destruct or might we endure indefinitely?

Dan’s response (emphasis mine):

My perspective is primarily influenced by our ability to unite and focus collectively. This informs my estimates of the likelihood of one outcome versus another.

Consider the ’62 Cuban missile crisis. We faced the potential of nuclear war head-on. That, in my view, is a hopeful moment. It was one of the few instances in our history where nuclear war seemed almost certain. Now, I’m no ardent Kennedy admirer, despite growing up during a time when he was almost revered, especially among Democrats. However, I believe John F. Kennedy, acting alone, likely made decisions that spared the lives of over a hundred million people, countering those around him who preferred the path leading to disaster.

Reviewing that now, a betting person would have predicted otherwise. This rarity underpins our discussions about the world’s end. The power to prevent catastrophe was in the hands of a single individual, rather than a collective.

I trust people at an individual level, but when we unite, we often resemble a herd, degrading to the lowest common denominator. This situation allowed the high ethical principles of one human to dictate the course of events.

When we must act collectively, I become more pessimistic. Consider our treatment of the planet. Our discussions predominantly center around climate change, which I believe is too narrow a focus. I become frustrated when we debate whether it’s occurring and if humans are responsible. Just consider the trash. Disregard climate for a moment; we’re harming the planet simply through neglect. Making the necessary changes to rectify this would necessitate collective sacrifice, requiring a significant consensus. If we need around eighty-five percent agreement worldwide, the task becomes daunting. It’s no longer about one person like John F. Kennedy making a single decisive move. Therefore, from a betting perspective, this seems the most likely scenario for our downfall as it demands a massive collective action.

Current systems may not even be in place to manage this. We would need the cooperation of intergovernmental bodies, now largely discredited, and the national interests of individual countries would need to be overridden. The myriad elements that need to align in a short span of time, where we don’t have centuries to devise solutions, make this scenario the most probable simply because the measures we would need to undertake to avoid it appear the least likely.”

[a later thread that rounds out his thinking on this]

“Returning to our primitive instincts, we are conditioned to address immediate and overwhelming threats. I hold a considerable amount of faith in humanity’s response to imminent danger. If we were facing a cataclysmic event such as a planet-threatening explosion, I believe humanity could muster the necessary strength, empower the right individuals, and make the required sacrifices. However, it’s environmental pollution and climate change that pose a different challenge.

What makes these threats particularly insidious is their slow development. They defy our innate fight or flight mechanisms and contradict our ability to confront immediate dangers. Addressing these problems requires a level of foresight. While some individuals can handle this, the majority are more concerned, understandably so, about immediate threats rather than those looming for the next generation.

Could we engage in a nuclear war? Absolutely. However, there’s sufficient inertia against this due to people’s instinctive understanding. If I, as India, decide to launch an attack against China, it’s clear that we will have 50 million casualties tomorrow. If we suggest that the entire planet’s population could be extinguished in three generations if we don’t act now, the evolutionary trajectory of our species might hinder our response.”

The remaining excerpts cover:

• An example of how propaganda can scramble your beliefs in a way that creates collective distortions that are hard to see
• The problem with dictators or strongmen even if they are wise and benevolent
• Will the US tear itself apart in a second civil war?

[Note: I used GPT-4 to clean up sections of this transcript: https://www.happyscribe.com/public/lex-fridman-podcast-artificial-intelligence-ai/136-dan-carlin-hardcore-history]

Money Angle

Here’s a stream of consciousness reflecting on a few recent private convos jambalayed with some of Dan Carlin’s thoughts.

I was hanging out with a good buddy (and former biz partner) and talking shop a bit about the options biz. I’ve heard about how implied correlation is “trading in the 0th percentile” but that selling it continues to be profitable in 2023 because it’s “realizing” even less than implied (to be clear he runs a big strategy and we don’t discuss what he does so there is no suggestion that he is also doing this. He merely confirmed that implied corr was historically low). This reminded me of the misery that was 2017, where the best trade would have been to just lay into single-digit SPX vol because realized vol was so low you’d wonder if the stock market even opened anymore. The opening bell rings and you immediately ask “What’s for lunch?”.

While we were walking around Ghirardelli Square, my boy made a throwaway comment that my mind hasn’t emptied from the trash.

The hard leg is always where the money is.

I thought about how, in 2021, the dumbest possible idea — buying a dog coin — was the best trade at one point and shorting it was too at a different point. But both were hard at the ripest times to do it and easiest when they were riskiest.

I thought about the double lot property I looked at this week with a realtor friend (the same one who sold both my house and my biz partner’s — if you are in the East Bay I’d be happy to intro. Good realtors are like good mechanics — gold amongst pyrite). There’s no math that makes the price of the homes make sense. Property in a specific location has little substitute and just trades like art. As my realtor properly diagnoses — “Kris, you’re like my lawyer father, you see the risk. But the people who win these auctions only see their family on a Christmas card”. This was not a knock on those people. As my friend Jared likes to say, their bank accounts have a phone number in them — I’ve seen enough behavior here to know that while folks aren’t Miami-flashy, a Ferrari is a rounding error sum of money in a home negotiation, not a decision. If you move from the Bay Area or NYC your bid would be obnoxious to the locals too.

It feels to me that everything is a momentum trade — selling dispersion at low levels, buying homes at 0 after-expense cap rates, having no top on what you’d pay for Harvard, hell, it’s an imperfect measure but even stock market earnings yield is less than t-bills.

It’s all momentum until some grand event makes it abundantly clear that the world has changed. Then you get the situation currently embodied in the no-bid CRE markets of say SF and Chicago.

Liquidity is utterly discontinuous in such a world. Value will become increasingly resistant to traditional measurement because there is so much wealth in search of a return you can reason that any opportunity where the math makes in a textbook spreadsheet, the value is sitting on a landmine, already passed on by the infinitely patient family offices of moguls who are not forced to chase LP-friendly payoff diagrams.

I chatted this week with another good friend who finds and stacks strategies at a well-known pod shop. He talked about a trend he had seen in motion much earlier — the accelerating difficulty in finding talent/alpha. He’s impressed at the speed at which the market for alpha is getting efficient but this is what you’d expect when pods are eating the investment world. Millenium manages $50B that is laser-focused on uncorrelated skill (grapevine tells me they increased how many pods that trade dispersion in recent years — cue the “markets are biology not physics” analogy — which means the marginal bid for single stock vol has increased. This actually means the environment for covered call selling might be unusually nice. This doesn’t contradict my broad admonitions about call-selling. It actually makes my point — that you should be discerning about the practice and not think of it as passive income or free money but understand what circumstances make the strategy more or less ripe.)

All of this makes me wonder about the distribution of investment outcomes in aggregate. Suppose the underlying economy is steady. Does the median return increase at the expense of the left tail (keeping the expectancy the same)? In a world where capital is more easily deployed and more concentrated, what happens to the shape of returns?

Look at the deal the Saudis have offered Mbappé or their pot-splashing with LIV golf. It all feels related. Financialization, private-equityization, Softbankization. Increasing rewards for capturing attention (see athletes or Cathie Wood). The internalization of rage bait as a social media strategy. Twitter X is rapidly being consumed by engagement tactics (dystopian thought: this trains people to be numb as they will eventually adopt defenses against engagement until we lose the ability to know what we should pay attention to). The harder profit is to find the greater the temptation to cut another forest down. We are great at identifying growth. Less great at understanding its costs. Wouldn’t be a bad tagline for America if taglines were honest.

(In Dan Carlin’s slavery pod I felt that the moral concerns didn’t gain steam until the cost of enslaving Africans became more apparent. You know that expression “narrative follows price”? Maybe we don’t moralize until a loathsome but profitable practice reaches its blood-from-a-stone phase and the cost of moralizing is lower. If you try on that perceptive for a day you’ll either want to claw your eyes out or you’ve already sold humanity to zero.]

All of this echoes Dan Carlin’s suspicion that our undoing will be collective action problems. If you believe that the logic of efficient markets (a collective action coordination mechanism that differs from democracy) is playing itself out in a rules landscape that has significant divergences from the political question of “what is good for broad-based flourishing”? You could imagine capitalism resting on many different types of rule frameworks. But you’d also expect the ruling framework, the one called a “free market”, to be shaped by its victors (corporations are people too, right?).

To Carlin again — propaganda can scramble your beliefs in a way that creates collective distortions that are hard to see

[Carlin is a war historian and while he admits to his bias towards individualistic ideals “I’m famously one of those people who buys into the ideas of traditional Americanism”, his characteristic nuance is well-displayed in his deep skepticism of the “military-industrial complex” and how its inclination towards self-preservation as an institution often exerts undue influence in when America looks at its menu of choices]

“Many people living today seem to think that patriotism requires a belief in a strong military and all the features we have in the present. However, this is a departure from traditional Americanism, which viewed such elements with suspicion during the first hundred years of the republic. They saw them as foes to the very values that Americans celebrated. The question arises, how could freedom, liberty, and individualistic expression thrive with an overarching military always engaged in warfare?

The founders of this country examined examples such as Europe and concluded that standing militaries or armies were the enemy of liberty. Today, we have a standing army deeply woven into our society. If one could go back in time and converse with John Quincy Adams, an early president of the United States, and reveal our current situation, he would likely find it terrible and dreadful.

Somewhere in our history, Americans seemed to have strayed from their path and forgotten their founding principles. We have successfully combined the modern military-industrial complex with the traditional benefits of the American system and ideology, so much so that they have become entangled in our thought process. Just one hundred and fifty years ago, they were seen as polar opposites and a threat to each other. When discussions arise about the love of the nation, I harbor suspicion towards such sentiments.

I am wary of government and strive hard not to fall prey to manipulation. I perceive a substantial part of what they do as manipulation and propaganda. Therefore, I believe a healthy skepticism of the nation-state aligns perfectly with traditional Americanism.”

I’ll leave you with a thought — let’s do an analogy substitution.

What if the version of capitalism we endure today is the military-industrial complex and Georgism is actually more aligned with the meritocratic principles this country is supposedly based on?

Money Angle For Masochists

My biz partner friend is way more of a math guy than me. If you want to be a trader you’ll get more mileage studying gambling than investing. Although I’ve done some study of gambling, it’s nothing compared to my friend’s info diet. He’s been a giant sports analytics nerd for the past 20 years (one day I might share a story of his meeting with an NFL team owner. I get stressed thinking about it, so can’t imagine how my buddy feels).

I asked him for some book recs in the vein of Scorecasting written by AQR quant Tobias Moskowitz (you may remember me recommending his children’s novel Rookie Bookie).

The list:

• Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong
• The Book: Playing the Percentages in Baseball
• Seminal: Bill James
• Win Shares
• Basketball on Paper: Rules and Tools for Performance Analysis
• The Expected Goals Philosophy: A Game-Changing Way of Analysing Football
• The Hidden Game of Football: A Revolutionary Approach to the Game and Its Statistics

Finally, my internet friend Andrew is an independent trader who came out of the sports gambling world. I’ve spoken to him several times. Very smart, you should follow him and check out the sports modeling books he’s written:

• Andrew Mack

From My Actual Life

We had a pair of 15-year-old Japanese exchange students stay with us this past week. Our kids have new older brothers — this crew loved each other. Play is a universal language.

Stay groovy ☮️

Friends,

I’m still in summer travel mode but I stole some time to write homework-type post related to options. I talk about it below.

Otherwise, here are some links:

1) If you wanna follow me on Meta’s Twitter clone that they released this week:

https://www.threads.net/@moontower_kris

2) With all the travel, I’ve had a chance to hang out with lots of family and friends who are not the terminally online types (sounds healthy). ChatGPT came up in a lot of convos and I thought sharing these links more broadly, especially for people that are not immersed in the discourse, might be useful.

• 10 Ways You Can Use ChatGPT to Learn Better (Scott H Young)Scott is one of my favorite writers on all things learning. This was a good post for separating what ChatGPT is good and for. The term “word calculator” has stuck with me.
• GPT Best Practices (Open AI)This interactive document from the creators of ChatGPT gives sugeestion and provides an in-line sandbox for you to practice yourself.

Money Angle

Continuing with the GPT resources:

ChatGPT for Finance: Promise and Peril (Dave Nadig)

Again, I’m just cherry-picking resources from writers and thinkers I trust. Dave put together a really nice guide here, and it assumes no knowledge so even if you tinker a bit some of the background he provides really helps fill in the gaps.

It opens:

Over the past month or so, my inbox and DMs have been flooded with questions about AI, in no small part due to my interview with Professor Stuart Russell at Berkeley and our recent webinar with ROBO Global’s Zeno Mercer and Resolve Asset Management’s Adam Butler. One crystal-clear pattern has emerged. Everyone wants real-world, specific examples of how AI can and can’t enter into an advisor’s, investor’s, or creator’s workflow.

I aim to please. Today, I will peel back the curtain and give concrete examples of how to use ChatGPT effectively to accelerate investment research and content creation. Meanwhile, I’ll also dispel some of the hyperbole around what ChatGPT can and can’t do.

Money Angle For Masochists

This is today’s meat. It’s a long post that includes exercises for the reader. I built it in a modular way so even if you didn’t want to go full brain damage there are useful sections that can stand alone from the whole.

What We Can Learn From Vertical Spreads (Moontower)

Intro

First, a self-indulgent remark…

I enjoy helping people learn about options. Not for instrumental reasons like the “world needs more options traders”. But in an appreciative sense — option theory is a rich toolbox for decision-making in investing and life in general. The word “decision” implies an option.

Notwithstanding, the typical person learning about options is thinking instrumentally — “how do I use these things to make money?” Of course, there’s no blog post or even book-sized answer to this question. As any craft goes, there’s basic vocabulary and principles, but these are necessary but insufficient conditions for success. You need years of trial and error to achieve competence.

Since trading/investing is a low signal-to-noise endeavor your epistemology requires strict discipline — the flip side of narrow bid-ask spreads and low-cost trading means your lack of edge can be masked for a long time. You know a loan shark is a bad deal, so you only visit Sleepy Sal as a last resort. But one broken kneecap and your LTV goes to zero. Brutal but honest. Everyone understands the deal.

Meanwhile, Robinhood administers the morphine of hidden fees to lengthen the duration of its most valuable asset — your overconfidence. Robinhood calls itself Robinhood without a hint of irony. They ate the whole wheel of cheese. I’m not even mad, I’m impressed.

Good news

At risk of pollyanna-posting, I’ll propose just getting smarter. If you have read this far you are totally capable of learning. Unsurprisingly, options discourse either tends to one of 2 poles:

• Physics-esque math geekdom Jargon-heavy complexity certainly has a place in finance but is best ignored as a small ecological niche.

• The “option premiums are to be sold for passive income” grift I’ve covered why this frame is nonsense ad nauseum here, here, here, and indirectly in almost all my writing.

There is a needle to be thread between these framings.

With no more than HS or even middle school math, you have enough tools to tinker and build intuition alongside your live experimentation. This homework is an example of what I’m talking about.

The purpose of this exercise

I get approached for help with options by retail traders frequently. On the one hand, it puts me in an uneasy situation — I’m not really a fan of people using their precious human capital on a machine that conspires to make you think it’s worth trying when base rates say otherwise. On the other hand, who the hell am I to discourage grown-ups who have read the disclaimers and proceed anyway. On balance, it’s a good thing that card-counting books are on the shelves even if most people who fancy themselves Ed Thorp are delusional about what it takes.

So it goes….my sympathies point to being helpful even if the occasional learner impales themselves. They probably would have anyway and there are more people that will be saved by either re-allocating their attention when they realize this is a grind or shed the misunderstandings that keep them plateaued.

All of this really cuts to the heart of Moontower’s approach to unlocking others: part Zen and The Art Of Options Trading, part shedding misunderstandings.

I can’t give you answers, but I can help rule out wrong answers. In that spirit, this exercise, despite its simplicity, will stimulate growth-inducing reflection.

The origin of this exercise

A reader approached me about a strategy they were exploring. It was familiar because it belonged to the class of strategies I’d describe as “harvesting”. Sell some variation of optionality (cash-secured puts, covered calls, iron condors, strangles, etc), earn steady profits.

This reader is selling downside butterflies on the SP500.

When someone has researched a strategy, they are mentally invested in confirming that it works. So right off the bat, I was heartened by the reader’s honest approach — “Kris, tell me what’s wrong with my strategy?”

It’s a fair question. But it’s not quite the right question.

1. I haven’t done the work so I’m not in the best position to say whether the strategy is good or bad but more importantly…

2. The “teach a man to fish” Socratic lesson is to demonstrate the implicit misunderstandings of the reader’s approach. That will lead them to higher-resolution questions that will scaffold their ability to answer the original question.

Part I: Setup

1. The scenario that underpins the exercise and assumptions are given
2. I hold the reader’s hand as they build a binomial tree.
3. The reader prices options on the tree. No option models. Just arithmetic.

Interlude: Discussion About Spreads and Specifically Option Spreads

A word on spread trading in general

Every trade is based on a model of how the world works, even if that model is as basic as “stocks go up on sunny days in Chicago”. Models by definition are simplified representations of how things work.

When we spread trade (buying one instrument and selling a related instrument) we cancel out some amount of model-risk. If our stock valuation model is based on interest rates, when we buy and sell related stocks we are sterilizing the assumptions of model by letting them offset. Of course, not every stock is equally sensitive to interest rates or whatever parameters our model takes, but the principle of offsetting remains substantial.

In the work you did above, you priced options in an actuarial manner based on an easily computable distribution. In the real world, model such as Black Scholes allow us to price options with continuous distributions and with a set of assumptions about how prices evolve. Everyone knows the assumptions break down in real life but the model’s value is not in its accuracy in absolute terms but as a measure or ruler.

If you have a broken scale, it will not represent your weight accurately but it will still be useful for comparing your weight to mine. How we calibrate a function depends on the use case. Similarly, my guitar can be tuned to itself so that it can reproduce a song pleasantly. But as soon as I start playing with others we need to make sure the group is in tune.

💡A word on spread trading in options

An early lesson for options traders is the value of spreads in risk management. I can offset option risks such as exposure to delta, vega, gamma and so on by taking an opposing position in a similar option.

Vertical spreads, where you buy and sell options of different strikes in the same maturity, are terrific examples of this. They allow us to sterilize the impact of bad assumptions in the model itself by reducing the risk to simply distribution. Distributional risks are benign, like over/under bets. The max loss is known and we are insulated from risks like bad interest rate or volatility assumptions.

The closer the strikes are to each other the more the risks offset. As they get further apart the risks increase. We become more vulnerable to discontinuities in our assumptions. Imagine a $100 stock. If I told you that Carl Icahn would make a cash takeover bid of $120 IF the stock dropped below $95 (suppose he knew the board would be far likelier to accept in that scenario) then a naively continuous model would not realize that the 117 strike and 123 strike don’t have a regular relationship to one another. The distribution is not smooth between these points.

The less 2 instruments (or strikes) are related the less insulation you get from model assumptions you get from hedging.

Generally speaking, when we trade narrow vertical spreads or butterflies (which are spreads of spreads — even more insulation) we can say our position is “model-free”. Your risks are more proportional to distributional probability than magnitude which is a more benign circumstance.

Part II: Understanding Vertical Spreads and Butterflies

Quick Refresher on Vertical Spreads

1. We price call spreads
2. We price put spreads from the call spreads (as opposed to pricing puts first!)
   This is derived from something call an option “box” — these are usually understood in the context of an alternative to t-bills.

   

   But they are also the key to understanding put-call parity between vertical spreads!
   

   The value of a put spread must be equal to:
   

   The difference between the strikes – the value of the call spread

   
   To see why, consider the following structures:

   • Long the 100 call, short the 100 put No matter what happens at expiration, you will be buying the stock for $100.
     • If the stock expires above $100, you will exercise the call
     • If the stock expires below $100, you will be assigned on the put
       

       This position acts exactly like a long stock position and in fact is often referred to as “synthetic stock” or “combo”.
       

       Let’s consider the opposite position on another strike.

   • Short the 105 call, long the 105 put This is short synthetic stock. No matter what happens, at expiry you will be short the stock at $105. You are short the 105 “combo”.
     

     Ok, combining these ideas:

     • Long the 100 combo
     • Short the 105 combo

   

   Net result: At expiry, you will buy the stock for $100 and sell it at $105.

   This structure is known as a “box”

   Of course, if you expect to make $5 profit on expiration, in a world where there is no free money, you can expect this structure to cost you the present value of $5 today.

   I can see you wondering “Kris, what the heck does this have to do with put spreads?”

   Look at the picture again.

   

   A box can be decomposed into:

   Long the 100/105 call spread

   +

   Long the 105/10 put spread

   
   The sum of these structures must equal the value of the box which equals the distance between the strikes!

   
   Re-arranging: Box – Call Spread = Put Spread
   

   In our example, the 100/105 call spread is worth $1.85.

   
   Box – Call Spread = Put Spread

   
   $5 – $1.85 = $3.15 = 105/100 put spread

   
   You can use this identity to price all the put spreads simply from knowing the call spreads!
   

3. We dive into the pricing of butterflies and appreciate them for what they really are: a spread of spreads!

Part III: Reasoning About Strategies and Extraplolating To Decision-Making In General

This tutorial was a response to a reader who wanted to know if their butterfly selling strategy was sound.

We built a simple binomial stock model to underpin pricing for calls, puts and vertical spreads. Ideally, this exercise, should have helped the reader to isolate what types of questions they to consider to hone in on their ultimate question:

“Does selling butterflies make sense?”

If those questions remain hard to infer then hopefully the subsequent Socratic discussion will help. The flow of the questions should be helpful to anyone engaged in a repeated strategy.

1. Through a series of exercises, we study the risk and reward of vertical spreads and butterflies
2. We conclude with inferences and discussion. I’ll re-print 2 sections of that here.

Why you should resist the seduction of high hit rate strategies

If a strategy has a high hit rate, it is operating on a highly skewed trade. Your high hit ratio tells you nothing about whether this strategy is profitable in the economic sense of the word. It takes a very long time/large sample to learn anything about how well you calibrated on low probability events. If something you believe to be a 1% probability is actually a 2% probability you are wrong by 100%. That will be reflected in the payoff space — something that you are accepting 50-1 odds for should demand 100-1 odds. If you insist on conflating positive expectancy with hit rates you could save yourself the headache and just run a martingale strategy in a casino. You’ll have negative edge but you’ll probably win and at least you’ll get some free drinks and a hotel room. I’m not arguing that you have negative expectancy on your skewed strategy, but the burden of proof is on you to prove otherwise and the point is that the more skewed the payoff of the strategy is the worse the epistemological foundation for your conclusions. Which means you can never really push. And if you know today, that you are building a strategy you can’t push too hard, then the question is it worth pursuing in the first place (it’s a bit meta but it feels like another tree with conditional probabilities at the nodes).

Addressing the original reader

The reader who reached said something I’ve heard in various forms:

”I’m selling downside because the market drifts upwards”

By having this exercise mimic this idea by biasing the coin probability to the upside and then pricing the spreads we can see that the market is already assigning a lower probability to the downside.

In real-life, implied skew makes the put spreads worth less; this exercise kluges that. So when you sell those put spreads using “markets go up” logic you are doing the same thing as someone bets on the Nuggets because they’ll probably win — brah, it’s already in the price. Your job is to find why the price is wrong.

From My Actual Life

On my 35th birthday, Yinh and I rolled into the hospital in SF to induce the birth of our first kid. He was stubborn and didn’t want to share a birthday — he came the next day.

This coming week we will celebrate Zak’s 10th birthday. I’ll save the sappiness for the letter I will give him. But as I reflect on the caboose end of the years where his mother and I are the center of his world, the tension of preserving his joy and innocence while preparing him for the future feels like it’s about to go up a notch.

Still, if it wasn’t confusing that would be its own source of worry.

Stay groovy!

☮️

P.S.

I’ll be in LA Thursday with my boy Khe.

Come hang out