Friends,

Let’s start with this single reply in a thread that caught fire.

I encourage you to scroll the thread — it’s like having a listening device inside a confessional. Every living generation’s gripes being aired out. Enough baggage to weigh down an Airbus A380.

If you have been reading Moontower for at least 2 years you know where some of my sympathies lie:

In Adding My .02 To The WSB Insanity, I offered:

A hypothetical.

Suppose there are 15 courses of actions one can take. 5 are illegal, 5 more are unethical. That leaves 5 acceptable actions. It feels like our collective calculus is moving to a rule of “if it’s legal, why not?”

The ethics ozone layer between what’s legal and what we should do is fully depleted. The air is irrevocably polluted. I’m not pointing fingers solely on daytraders who are openly coordinating behavior in ways that stun anyone who has ever sat through securities compliance training. There is a sense that the game is rigged and while I think the specific targets in these trading examples are misdirected, it certainly feels that way in a broader sense. Especially when we consider the runaway examples of inequality I’ve discussed [see Is Social Harmony The Last Collateral?]

The last tweet in the side chat below is an echo of Adam Singer’s tweet at the start of this post.

Browsing Twitter this week I saw an account announce that people have an imperative to make as much money as they want within the confines of the law.

Look, last week I admit I have a fast cringe reflex. Hustlers are quick to say that instead of abstaining from cringey activity, the key to your dreams is killing the cringe reflex. This is reasonable. And that’s why it’s dangerous — it’s written in the same ink as the grift manuals. It’s the raw material for collapsing the firewall known as ethics that runs along the letter of the law and its spirit. It takes but 1 second of second-order reasoning to understand this does not scale. The proverbial picture replacing 1000 words:

Annoyed by the profit-as-religion tweet, I crafted a thread response (because I’m childish) and the janky Twitter app failed to send it. 4x. There was 2 silver linings to my frustration:

1. I deleted the Twitter app (again)
2. I hopped on a video call with Dave, Tom and Adam — a group of investors who have been thinking deeply about how we climb out of the collective Molochian quicksand.Here’s the recording:

   PolyCrisis, Institutional Decay, and AI in Q2 2023: An Update with Dave Nadig (53 min)

There’s a sense that life is increasingly turning into a tournament. There will always be some group of psychopathic wealthy with self-serving comprehensions of evolution and a strain of ambition who would have been warlords in a different era. Today, most of those outliers express their sociopathy in token-collecting.

But there’s a thick layer of grounded rich people who don’t feel rich enough because they see the minimum acceptable life as becoming increasingly unattainable for younger generations and their perfectly rational individual response is to make even more money so they can self-insure their children’s safety nets. This mindset taken to its extreme closes the self-fulfilling behavior loop promoted by the cringe-merchants.

I guess if prisoner’s dilemmas were a cinch to solve we wouldn’t have needed Nash-level minds wasting cycles on them. But alas, it’s still fun to bang your head on such puzzles.

If you are interested, Dave hosted a panel at a conference with Adam, Tom and several finance minds to discuss these topics. I reached out to tell him how much I enjoyed it. Our ongoing conversations on these subjects is what earned my naive role on the video call in the first place — the Straussian inference here is to listen to the panel talk if you only have time for one.

• Exchange 2023 – The Future of Finance (98 min)

Money Angle

• Flirting With Models: Designing the Cockroach Portfolio (55 min)Corey Hoffstein interviews Jason Buck. I’ve hyped the hell out of these guys before (The Most Underrated Finance Channel On YouTube) because I want you to see why I weaseled my way into being their friends. They are brilliant guys who don’t take themselves too seriously. And their investing approaches are highly resonant with the principles I espouse in Moontower.

  It’s very much why I’m an investor in Jason’s cockroach fund and had Mutiny be the first sponsor of this letter. I knew Jason before he ever launched this fund and was honored to be a general sounding board on his ideas. I can’t believe how well he synthesizes and articulates complex trade-offs so the average investor can understand. The whole episode goes down extra-easy because Jason is the Dos Equis guy.

  Don’t miss this one.

• The Mindful Money Playbook (RadReads)”Reimagine your relationship to money, status and joy”

  I’d like to say I have a hand in this because I’ve been urging Khe to re-factor and package his thoughts about money and life into a book. He thinks and communicates lucidly for laypeople despite a highly professional background (months after we got to know each other I learned that when he was at Blackrock he was on the team that studied the types of strategies I worked in!).

  The book is totally free and built on Notion.

• How To Get Rich (Netflix)Ramit Sethi is one of the personal finance gurus I recommend (there’s a lot of nonsense out there). Yinh and I started watching these 8 30-minute episodes and I’m struck out how good Ramit is at meeting people where they are in terms of dealing with their finances. He is a perfect mix of tough but compassionate and this is not easy when mass media often selects for a more mono-approach to establish a brand. Instead, Ramit builds his message and therefore brand around the concept of “how to build YOUR rich life” which means questioning conventional wisdom and ruthlessly cutting desires which are not truly yours while doubling-down on what you care about.

  I’ve wrote about him 4 years ago and his message is still the same. See He Will Teach You To Be Rich (2 min read)

Money Angle For Masochists

Option amateurs underappreciate the role of funding in pricing derivatives. Professional options traders need to be obsessed with funding costs because they are trading for tiny, often sub-penny, margins.

Here’s a simple example to demonstrate the tyrannical effect of funding on pricing:

What is a 1-year American at-the-forward call option on a non-div paying, 20% implied vol, $100 stock worth?

You need to feed the model an interest rate to get an answer. You look at the yield curve and see a 5% rate (making this up) for 1 year. This yields a forward price of $105 (we can hand-wave simple vs compounded rates for this purpose).

Imagine the bid-ask for this call is 40 cents wide $7.80 – $8.20

If you buy on the bid and sell on the offer you make a .40 profit. Easy-peasy.

Now imagine you buy the bid and hedge the position until expiry. What implied vol did you buy?

The first thing to recognize is that you will be shorting the stock to hedge. Assuming it’s easy to borrow, you are still not going to receive a 5% rate on the cash proceeds. Your prime broker needs to earn its margin. If 5% is the risk-free rate, let’s assume they pay you 4.5% on cash balances. Conversely, the prime broker will at 5.5% (this is known as the “long rate” and it’s the rate you finance long positions at). If you sell the call on the offer you will need to pay that rate to finance the shares you buy.

Uh oh.

If you buy the call you need to use a 4.5% rate in the model to back out an implied vol and if you sell the call you need to use a 5.5% rate in the model. You can see where this is going.

• If you buy the call on the bid you are paying 20.06% implied vol.
• If you sell the call on the offer you are selling 19.95% implied vol.

(Check the math if you want)

You think you’re trading vol but because of the bid-ask spread on your funding rate, you are basically trading the same implied vol even if you buy the bid and sell the ask.

Rho is the sensitivity of the option price for a 1% change in the interest rate. The vega of an option is the sensitivity of its price for a 1-point change in volatility.

The rho of this call option is 46 cents vs a vega of 40 cents.

A 1% difference in funding rate (ie 4.5% vs 5.5%) is an institutional level bid-ask. It can be much worse for retail.

If you are trying to make markets you think you’re trading vol but are you even?

Pricing and carrying longer-dated options is crucially dependent on funding costs and the bid-ask spreads might not even be wide enough to compensate a market maker for their funding spread.

Another way of saying this: the market-maker with such a 1% wide funding rate is making a 20% “choice” market in the vol. If the bid-ask was tighter they would be bidding a higher vol than they were offering!

(Again this assumes they hold and manage the position as opposed to spreading the options off by say buying one call and selling another or having the privileged position of just getting ping-ponged on their posted bid-ask all day)

Friends,

In Wednesday’s Munchies, I pointed you to Venkatesh Rao’s brain-expanding interview on Infinite Loops. One view I’m still marinating on is how finding a sense of meaning is not “a matter of spiritual retreats and going on soul-searching journeys and having shamans take you on ayahuasca retreats and things like that. It’s not about that at all. It’s the first time you come to a hard decision in your career or life, make the hard decision, see how good you are at making tough calls, and then keep doing that and meaning-making will take care of itself.”

To call meaning-making essential is not stepping out on a limb, unless you’re a nihilist.

Rao makes a bolder claim — looking for meaning is “intensely practical.”

A lot of people don’t get this. If you look at conversations about meaning-making in the abstract…listening to podcasters and getting radicalized, that level of conversation about the meaning crisis, it seems like a philosophical spiritual problem that should be addressed with religion and philosophy, ideas and so forth. It’s not. It’s really as simple as meaning-making is unlocked when you first learn to take courageous decisions and keep doing that, so it becomes a habit.

Connecting dots…when meaning-making is unlocked what actually changes for you?

You acquire an earned sense of agency as opposed to the illusion of agency that “tragic luck” furnishes. This requires being rugged now and again. Any rugging worth a lesson, means you took a real risk.

And I think yes, that is a learnable, teachable skill, but it’s one that the industrial environment with schooling and the paycheck world is actually anti-optimized for. It’s designed to teach you exactly the opposite of that. It’s designed to take you from an naive starting point and keep you tragically lucky for the rest of your life. And if they fail at it, you’re tossed by the wayside. That’s what the industrial world is set up to do, make you tragically lucky or throw you into the garbage heap.

Rao, coming around the bend with the baton, is arguing that our sense of agency is stunted by an institutionally enforced “narrow band of risk”. When I rummage through my feelings about education I come to a similar conclusion — the purpose of education is to bootstrap a sense of agency.

I’ll let one of my favorite education writers Matt Bateman take the baton for the last leg.

From Vocational Training For The Soul:

In the 20th century, there are two distinct rationales for education: vocational and characterological. Putting aside how well education actually does at getting you a better job or helping you become a better person or citizen, the idea is that the core of schooling should do both.

The most obvious place to look for the economic upside of an education is in the three Rs: writing, reading, and math. There are questions as to whether the specific math that students learn is optimally practical—should it instead emphasize, say, statistics, or personal finance, or maybe even spreadsheets?—literacy and numeracy are deployed throughout the economy and do indeed comprise an unambiguously useful part of education.

Literature, history, and the arts all fall under the heading of soulcraft. Even science, the practical driver of the modern world, is not that useful as you learn it in school. A small minority of students deploy their scientific knowledge in their careers, and those that do get specialized training far beyond what you get in K-12. These things are meant to prepare you for appreciation of or participation in the human project in a non-vocational way.

These divisions are very much alive today, as people struggle to find a coherent view of what our largely dysfunctional education system is supposed to accomplish. Some criticize education for not providing more economic upside, arguing for a more practical education, shorn of classical trappings. Others defend the humanistic value of education and argue that we should spend more time on non-economic upsides. This debate cuts across K-12, higher education, and even early childhood education.

Is there a way to transcend these divisions? Is there a way to get a handle on the vocational value of education that integrates its humanistic elements, rather than downplaying or siloing them?

It is commonplace today for a person to be profoundly alienated from the entire domain of work. This is not a Marxist critique about owning one’s labor, nor an aristocratic pining for a life of leisure. It is an observation that, for many people, work is a source of bitterness, not dignity. A seemingly small subset of people find meaning in work, and the rest fail to “find their passion”—a notion that is likely part of the problem—or simply resent work in a more general way.

While we still speak here and there of the value of a work ethic, the “ethic” part of this is, for us, obscure. We do not naturally see one’s personal relationship to work as a major moral issue. But it is one: the people who manage to find meaning in work are not the lucky few who land the good jobs, but the good who manage to build their souls in a certain way.

Education should offer more general value than the skills acquired on the job or in vocational training—but that general value, the soulcraft aspect of education, is not vocationally inert. It can and should nurture the beliefs and virtues associated with a life of work.

Bateman goes on to explain 4 practical ways to nurture such soulcraft. My favorite animates knowledge by linking it to actual humans. This is important (in my opinion) because without narrative disjointed ideas might as well be trivia.

• The content of education should place more emphasis on the biographies that underlie it. There is no item of knowledge in education that is not the result of the work of some past human.

My second favorite:

• We should allow opportunities for real work where possible. This is especially true of older adolescents, who can get jobs—from the entry-level to technical, depending on the teen’s skills and circumstances. But scaffolded opportunities can be provided for younger adolescents and elementary students to experience the reality, even the economic reality of work.

This week’s sponsor is PitBulls (myself, Tina and Steiner)!

PitBulls is the updated brand of StockSlam.

A large market-making firm is hosting PitBulls Sessions on May 17, 18, and 19 in Chicago. This is our 3rd series of doing these after NYC and SF. Come learn, have fun, and meet people with similar interests.

It’s totally free…and even better our host is always hiring!

• You can learn more and apply here.
• For some videos and context see: Mock Trading

Money Angle

I went on the Market Champions podcast with host Srivatasan Prakash (Spotify link) which was released this evening. Towards the end Sri asked me the old Richard Dennis turtle question (or Randolph and Mortimer framing if you prefer)…are traders born or made?

Look, I’m encouraging people to come to Pitbulls in May to learn how to think about trading and decision-making because I think these are teachable skills. But the proper answer is “it depends”. You can listen to the interview for a fuller take but before asking the question it pays to define terms. “Trader” is a vague term. Portfolio managers fit the spirit of the word better than those titled “execution trader”.

[I remember interviewing at a large AUM stock-picking fund in the mid-2000s for an execution job. I had a friend at the fund who got me the interview. When I was rejected I circled back and asked my mole what the problem was — “they knew you’d be bored.” The job was more formulaic than what I was doing. Meanwhile, I was pissed because the job would have paid about 2x what I was making at SIG which should remind you that beta pays a lot more than arbitrage. Sorry nerds, but on average, you skim more off the top knowing which side of the plate a fork setting belongs than knowing an exchange’s rebate tiers.]

Trading is a broad job description and it’s more of a team sport than commonly portrayed. Yet regardless of what criteria you choose to classify it, the most satisfying version of it is when it’s creative. Delightful puzzle-solving especially under live fire where the stakes aren’t life and death — just money. For some types of people, this is a deeply attractive way to spend your day (although I’d warn you that a lot of time it’s rote and boring — soldiers, firefighters, poker pros — it’s a lot of downtime, folding hands and waiting punctuated by periods of action where instincts and muscle-memory matter more than intellect).

In the interview, I make this point with a unique trading scenario I encountered back in 2020 when oil prices went negative. It involved several relative value dislocations between USO (an ETF that holds oil futures), oil futures, and the options on each.

In general, the model to price the relative value between options on USO vs futures options requires creativity and detailed thinking. But when oil went negative several new dislocations announced themselves — and if you were a paint-by-numbers trader then some of the dislocations were actually a trap. If you think more like a financial hacker, it was an opportunity. But you had to be quick — napkin calculations over intricate models.

If the puzzles of financial hacking interest you read ahead.

Money Angle For Masochists

The Setup

You are a trader specializing in making markets in oil futures and related derivatives. Your tradeable universe includes:

• listed on oil futures
• listed oil options
• an ETF that holds front-month oil futures (like USO)

1. The market closes. You observe the following facts:

   

   The ETF share price closes at $6.00, in line with its NAV.

2. You walk into the office the next day. All of the prices and facts are unchanged. However, you notice: The 0-strike put on the futures is $1.00 bid! You scratch your head. The zero-strike put has a bid?? Understanding that markets don’t present free money so easily, you come to the most likely explanation — oil futures can go negative!

Now the fun begins.

The following questions will slowly help you identify what opportunities might exist. I’ve provided hints that become increasingly strong so if you want to challenge yourself don’t rush for help too soon.

To continue:

Financial Hacking: ETF vs Negative Oil Futures

Note: If you are interviewing a junior or mid-level trader this might inspire some new questions.

From My Actual Life

Something I recently started doing that might be of interest to parents:

I’m reading “Journey to the Center of the Earth” by Jules Verne to my almost 7-year-old.

Written in the 1800s, the writing style is challenging.

So I read a bit, then I “translate” it into a more natural language for him. I’ve explained to him that if he reads the books he’s able to read and I read this book to him (instead of him trying to read it himself, which he was trying to do, but I have zero confidence he’s understanding), the combination will give him “magic.” I try to create some mystique around reading because I want him to think reading gives him special powers. Because that’s a fun thing to think, of course (and we probably should think about more things in such ways because it helps us notice the joy in being alive and stuff).

One of the chapters ended in a particularly suspenseful way. And I tried to explain the concept of suspense to him (to his and his teacher’s credit, he mentioned that when they read in school, they pause to try to predict what will happen next in the story).

So with the idea of suspense established, I just asked him to come up with suspenseful sentences. I’ve never asked him to do that, and he didn’t reply with anything substantive, but that’s okay, whatever… (I did give him an example: “The boy thought he locked the door, but then he saw the knob turn,” and my son goes, “that would freak me out,” and since this was just before bed, I felt a bit guilty..oops)

Just sharing for other parents’ benefit, I think we all want to find ways to show the joy of reading and wanted to start showing him “techniques,” a word I asked Alexa to define for him. So he can identify the author’s “weapons” and so maybe one day he can use them when he writes.

Stay groovy

☮️

Friends,

There’s this thing called “content brain” that you get when you write online.

Thomas Bevan explains:

You develop content-brain as each day you spend you peak creative energy feeding the algorithm the bite sized chunks of easily digestible nonsense that it craves.

You degenerate from essays and paragraphs down to fortune cookies and quotations.

[Kris: the mechanism conjures the still-fresh-on-my-mind reading of Amusing Ourselves To Death]

Rather than actually writing you merely write about writing. You become a commentator rather than a practitioner.

I’m as guilty as anyone. And if you want to give me lashes, I’ll even provide the whip — see my old post The Literary Version Of A Chart Crime.

Despite the justifiable negative characterization, “content brain” is also a filter. Its most refined expression in financial writing is story-mining history to explain some evergreen concept in a memorable way. At the same time there’s a dangling sense that you can see the string suspending the magician’s levitation act. The more skillful the writer the less visible the string.

While I was in Vietnam I had to suppress many urges to intellectualize the experience for the purpose of talking about it here. And then several people told me they look forward to me writing about it.

Well, I’m going to disappoint them.

Why?

1. I actively didn’t want to be in my head. I told myself I didn’t want to “find the insights” in the experience. I just x’d out the FindInsight.exe window that auto-boots when I do something novel. Partly in the name of being present but mostly because I don’t have the chops to give Vietnam and its people the words they deserve.
2. I read Viet Thanh Nguyen’s The Sympathizer (Khe texted me to recommend it when he noticed I was in Saigon). You are better off reading 1 sentence from Nguyen than a blog article from me.

So to that end:

• My thoughts on the book
• My favorite quotes from the book
• Deeper themes
  • Paradox
  • Purity (anti-paradox?) and meaning
  • The theme of “representation”
• Other topics of note
  • Vietnamese (and immigrant) culture
  • Sex quotes
  • Impression of Americans (this is full of banger observations!)

For the theatrically inclined:

Here’s the trailer for the 2024 release of a series of the show on HBO MAX. Robert Downey is one of the stars. I’ll take the liberty of making one connection here — in The Sympathizer there’s a theme of “representation” and the book’s protagonist is cast in a dilemma of how to influence a film made about the Vietnam War, an unsubtle reference to Apocalypse Now, and its choice of actors for Vietnamese roles.

In the tongue-in-cheek film Tropic Thunder, Downey’s character does the blackface thing in the name of method-acting but the movie is in on the self-skewering joke. In the series adaptation of The Sympathizer, Downey does the Eddie-Murphy-plays-lots-of-chacters-thing.

I willfully decided this is not an accident. I’m giving Downey massive props for commitment to a highly meta display of satire that breaks the container from a single film and lands an impressively drawn-out professional wink.

A Little Help

I could use some help for someone dear.

Do you know of any FP&A recruiters or jobs? I know a fantastic person looking. She has 20+ years experience.

(Bay Area based or remote preferred)

Money Angle

I managed to read 4 books during my trip — the Postman book, The Sympathizer, How To Lie With Statistics — and one finance book.

And it’s f’n awesome:

Financial Hacking by Philip Maymin.

I wish I wrote this book. The approach is deeply familiar and resonant — build intuition by tinkering. Since my formal math education pretty much stopped in 12th grade, I had to build intuition for derivatives instead of relying on formulas and proofs.

• The book is a fun read. The tone is conversational — Maymin is talking directly to you. The book is casual. Loaded with quotes from pop culture (esp the Simpsons) on nearly every page.

• The question-and-answer tempo is engaging and highly reminiscent of workflow on a trading desk. A recurring trope is “your boss just said X, how do you respond assuming you don’t have time to come up with a formal presentation”

• While the references to Mathematica might feel dated, the logic is easily transported to Python or your tools of choice.

• I would make this book mandatory reading for someone who has completed a basic finance rotation and has a few months of live trading under their belt. It’s also a great refresher for seasoned traders — especially if you are preparing for an interview.

• You’ll get the most out of this book if you engage with the questions actively. In fact, I’d use this book as a source of interview questions for mid-career traders.

• A practical argument for the “financial hacking” approach:
  • build intuition so that we can quickly gain deep understanding of even brand new products, faster than the competition. To that end, we don’t look to find delicate new pricing formulas, but rather rigorous and useful ways of looking at the problem… If you think of the timeline involved in new products, those who implement well-established pricing formulas are several years late to the party. Those who completely derive what will eventually become well-established pricing formulas are probably about a year late. The purpose of this book is to make you ready to be the first one to trade, when the new product just comes out, and its mispricing is likely at a maximum, or at the very least at its most volatile. It is in times like those that a prepared, flexible financial hacker and trader can pick attractive spots.
• Once you have read the book, you may agree with my contention that this is the single most important statement in the treatise:
  • These kinds of practical issues are ignored in standard textbook discussions of riskless profit opportunities but they are precisely the issues that financial hackers worry about most. And you will almost surely never experience anything with this level of certainty at any time in your career [referencing a trade where you are given the outcome]. There will always be doubts about your model, your inputs, and your forecast. According to standard theoretical concepts of arbitrage, none of those questions matters. According to real-world practical experience, you can’t even begin to trade until you have answered all of them.

Money Angle For Masochists

Ok nerds, I made it easy to drill down into the topics. Obviously, buy the book if this is useful.

It’s hard to pick one of these to explore here, but I’m going to go with the warrant one for 3 reasons:

1. If you are unfamiliar with warrants (I never traded them myself) you’ll acquire basic background knowledge.
2. The “devious” part of the puzzle is a great test of your arbitrage-goggles.(Totally self-serving comment but I did get the right answer to this puzzle as well as most of the questions in the book — when you don’t spend your days in the mines anymore you worry about how rusty you are getting so the check-up is nice.)
3. I weaponized the logic of the puzzle’s solution — it’s implicitly a proof that “selling calls is not income”!

I’ll get you started here.

The setup:

Warrants are just call options issued by the company itself (as opposed to a call option written in a listed market by an arbitrary counterparty).

Imagine 2 identical stocks. One with a call option outstanding and the other with a warrant outstanding. These respective derivative contracts have the same exact terms (expiration date, expiration style, etc) and the stocks themselves have the same attributes but are distinct entities. This is not a trick — you can accept the assumptions — the terms of the contracts and the behavior of the 2 different stocks is identical.

Question 1: What is worth more — the call option on Stock A or the warrant on Stock B?

Then the more “devious” version”

Question 2: What if a single company has both a warrant and call option (again identical terms) outstanding…which is worth more?

You can find the answers to the questions as well as my case for how this proves that “selling calls for income” is a nonsense statement. [In that explanation, you will also have more mental foundations shaken when you start to consider the ramifications of “implied delta”]

🔗 https://notion.moontowermeta.com/the-warrant-puzzle

I’ll mention one more thing that doesn’t have to do with the book. Again, this concept of “selling calls for income”. If you overwrite calls each month on a stock you own you are doing something very similar to just selling a portion of your position every month. If you own 100 shares of X, and you sell a .20 delta call, you theoretically liquidate 20% of your position. It may not feel like that because usually the calls expire worthless but look at 2 approaches:

Strategy #1: You sell 20% of your holdings a month instead of selling calls

Your position shrinks by 20% each month. In 10 months your position is .80¹⁰ or 10% of what you started with. Zeno’s paradox aside, in about a year you are out of your position.

Strategy #2: You overwrite .20 delta calls every month

Most months you keep the call premium, approximately 1 in 5 months, your entire position gets called away.

The relative performance of the 2 strategies is going to depend on the volatility and path of the stock!

[This is a significant insight to noodle on by the way]

It’s tempting to think “well if I get assigned on those .20d calls less than 1-in-5 times then I’m selling the calls for more than they are worth”.

Sorry. That’s not the full test.

Just think of the scenario where you sell 20% of the holding instead of selling the call option — then the stock drops to zero. You will never have been assigned on your call but that call-overwriting strategy will have much worse results than the “sell a portion of your holdings” strategy. And what did the performance disparity depend on? The volatility.

I know it’s hard to believe — but calls are puts and puts are calls and this demonstration didn’t rely on the put-call parity formula to make the point. Mayim gives an intuitive proof of p-c parity as well.

Generalizing

Stocks that pay dividends are the equivalent of strategy #1 (although on a much smaller scale since dividends are closer to 2% than 20%). If the stock didn’t pay a dividend you can create your own by just selling a portion of your holdings. The same logic holds for selling calls.

That there is a whole asset management sales-machine that revolves around call-selling and dividend-paying stocks obscures the reality that the economics are pretty similar (taxes are a central difference). That a company making $10 in earnings might retain/reinvest it instead of paying it is an overrated distinction.

[After all, once a company pays a dividend, the stocks drops by the amount of the dividend since its assets fall by the cash amount. This is literally why you exercise in-the-money call options early — the stock is going to drop and you need to own the shares to receive the dividend that compensates the call holder for share decline.

Mayim even uses this point in a separate context — to show that even spot prices are forwards! This is a more important point for arbitrage traders than investors — a handful of readers might recall a nefarious strategy of picking off stock specialists by requesting a different settlement date than the standard T+3 ahead of a special dividend. This strategy ended up in court. I’ve always thought those extreme couponers who read fine print as a form of offense would enjoy high-finance shenanigans. I see such cleverness as Moloch embodied — when you actively hunt for the limit of where the spirit of a law gives way to the letter you take the free-rider problem and make it a feature for personal gain. Congratulations on your yacht, I guess.]

From My Actual Life

I initialized a social media escape pod: I’m moontower.bsky.social on Bluesky. I don’t have invite codes sorry. I’m not active there (yet).

Twitter might be frustrating but there’s plenty of community there. In fact, without me asking, just by conveying a story, I received over $500 in donations which Yinh and I matched for a neighborly cause.

The aftermath:

https://twitter.com/KrisAbdelmessih/status/1646898185254871040?s=20

(Twitter disabled embeds in Substack. “Take my ball and go home energy” is always a sign of strength. Right?]

Stay groovy ☮️

Friends,

Wednesday’s Moontower Munchies, Mondegreen Minds, was a celebration of computational thinking. I shared a quote by Montessori instructor Matt Bateman in reference to math:

It matters for your soul. Math is the realm of precision, exactitude, quantity, measurement, and logic. If that’s the realm you’ve populated with secondhand incantations, that will invariably transfer to areas of life in which those things are cognate. (Which is every area.) The exactitude of the mind, the quality of judgment of the mind, and the independence of the mind are interrelated.

He quotes Maria Montessori herself:

When you say “There goes a man of vague mentality. He is clever but indefinite,” you’re hinting at a mind with plenty of ideas, but lacking in the clarity which comes from order period of another you might say, “He has a mind like a map. His judgments will be sound” in our work, therefore, we have given a name to this part of the mind, which is built up with exactitude, and we call it “the mathematical mind.”

Bateman asks:

Is your mind made of routines that are alien incantations that you mysteriously “work”? Or is it understood, made up of independently cognized algorithms, which you can mull and interrelate, and in which you have earned confidence?

The reason I write anything on any particular day is usually opaque to me. Most of my alien incantations come from the mind-cleansing bombardment of a hot shower whose snippets I can sometimes reassemble into a cohesive message. I don’t ask why any particular topic occurs to me but this week my urge to promote computational thinking had a few sparks.

I’ll mention 2 here and another in Money Angle.

• This was StockSlam week.Steiner had a vacation in the Bay Area so we used the opportunity to host the pit trading simulation in SF and Walnut Creek. I love doing these sessions to meet people, play games, foster in-person connections, and help participants viscerally feel the concepts I write about.

  The world of finance, trading, and betting is an amazing laboratory to improve your thinking and decision-making. Being forced to put a price on a belief sharpens fuzzy thinking.

• A meeting with a local friendWhere I live in CA nobody talks shop (this is probably not true on the peninsula or showbiz land). Here folks people are obsessed with skiing (Tahoe this and Tahoe that and best season ever, yadda yadda) and mountain biking. I’m no adrenaline junkie and my Egyptian blood hates the snow.

  So I was surprised a) that a friend was actually in town and b) that they wanted to talk shop (kinda). This person invests in pre-IPO companies today but spent the past 20 years in software sales and the 90s as a software engineer. They reached out because they wanted to learn more about options. Not because they wanted to devote themselves to trading, but because they thought dabbling in options would help them be more methodical in their thinking.

  A few points they mentioned:

  • They felt that their computational thinking muscle had atrophied since their engineering days, especially with a life in sales. While they had developed strong pattern recognition and business acumen, they felt gaps in how they synthesized those inputs into decisions.
  • The founder of their fund seems to think in terms of options but uses a different language to describe scenarios. This reinforced my friend’s sense that this was a place they should improve.
  • They wanted to take a more hands-on role in helping their kids (who incidentally take chess lessons at my house) think rigorously and thought directing their own attention in that direction would help.

My responses:

1. The grass isn’t greener. I was jealous of their experience.Those pattern-recognition inferences are inputs and can only be gathered by decades of reps. The reasoning part can be taught much faster. If you spent just a year in a trading/arbitrage environment you’d have a useful lens to carry with you for life. Acquiring a practical mental catalog of business models takes much longer. I believe I can take my brain and stick it in someone else (provided they had some minimum aptitude, desire, and work ethic). I can’t acquire the equivalent fraction of what they know in the same amount of time.

   [Obvious alert: this is why you try to assemble complementary teams. In Gauntlet, you want the long-range Archer, the healing Wizard potions, the Barbarian to deliver damage, and the Valkryie’s armor for protection.]

2. We all get rusty.Despite years of trading and writing, when I read Agustin Lebron’s Laws Of Trading (my notes) I realized how lazy my own thinking had gotten. It put me right back in the culture and mind habits of prop firms in a way that reminded me that weeds of lossy heuristics were growing in my mental garden.
3. I promised to send a list of posts to get the gears turningAs I sat down that afternoon to compile the list, I figured I should make it available to anyone who felt the same.

With that enjoy a new portal:

🧠Moontower Brain Plug-In

📖Learn

• 🧮General Numeracy and Decision-Making
• 💰Personal Investing Topics
• 📐Advanced Financial Reasoning

🏋🏾Practice

• ✏️Exercises and Word Problems
• 🚸Games and Word Problems For Kids

Money Angle

In a recent interview with Tim Ferriss, VC Bill Gurley admits:

If there was a scale of financial sophistication between one and 10, and you would say a really smart person in New York is an 8.5, the average Silicon Valley person on financial literacy is a two.

And it’s funny because they make fun of Wall Street, but it’s just out of ignorance, they don’t know anything.

Bill said it, not me (the transcript is worth reading for the full context but I’m not twisting him… those words are the spirit). I don’t know enough to have an opinion on this but I do find it surprising. Financial literacy starts at home and VCs don’t strike me as a cohort that rose from the gutter so either I’m wrong about the source of financial literacy or maybe poor kids play lacrosse after all.

Either way, the workings of money are abstractions like code. It touches almost every decision since it prices time (interest rates function as an exchange rate between time and money). It’s a basic life skill in an increasingly abstract, financialized world. Teaching our kids about it is basic hygiene.

Last night, we had our regular family dinner with my wife’s sister’s fam (4 adults, 4 kids — grades 1, 4, 5 and 7 plus another 4th grader who was spending the night). We usually go around the table asking each person about something they were grateful for that week or what’s something they tried at and failed (I know, I know it’s a bit cliche. These prompts do lead to provocative discussions and serve to put kids and adults on the same level).

But this time we did something different.

Yinh wanted to use the Silicon Valley Bank run as a learning moment. She started by explaining how banks invest deposits in longer-dated loans to earn a yield. To nudge the kids towards understanding the risk, she said the bank invests in loans that only pay back once a year. While not mechanically true, the point was to have them recognize the liquidity mismatch between the long-dated loan and the deposits that can be withdrawn anytime.

I taught them how rising interest rates cause the value of the loans to fall. But I also dispensed with mechanical accuracy in favor of intuition. I told Zak he plays the role of the bank. He loans me $100 and I promise to repay him $110 in one year. But then, immediately, mom asks to borrow that $100 from me but she’ll pay me back $120 in a year.

How should Zak feel? Well, sad. He’s going to get $110 in one year but since his mom is willing to pay $20 for a loan he could have lent her only $90 and still known he’s going to get back $110 in a year. Of course, this isn’t accurate interest rate math, but save that for a 7th grader. For a 4th grader, this delivers the point intuitively. [And for adults who think buying individual bonds instead of a bond fund somehow is less risky because they know how much nominal money they’ll get back, think through Zak’s position here — he is still getting $110 back but he’s definitely sad even though the counterfactual universe where he invests in a bond fund that gets marked down to $90 is optically worse.]

I was fortunate that my mother taught me about money. I can still remember my brain hurting when she explained a mortgage to me. It took a while to get my head around it. Remembering that keeps me patient — I’m grateful she persisted until it got through my dense skull. She didn’t push, she just repeated herself calmly every time I was frustrated “how does this work again?”. It sinks in eventually. If anything, the exposure will prime them to learn faster when they do encounter it down the line when the stakes are higher in school or real life.

[If you think my difficulty in understanding a mortgage was stupid, I got a better one for you. When I was about 12 or 13 an older kid told me a prostitute is “someone that gets paid to have sex with you”.

Sit down for this.

My mental model for “someone gets paid to X with or at you” was…a hitman.

I now believed that there was a person whose career was to have someone pay them to have sex with a 3rd party. Until then I had the impression that sex was a desirable activity but then hearing it connoted as something that is delivered as revenge or assault made me wonder if sex might actually be a gross punishment.

Dazed and confused is a fitting description of my existence so I’ve got that going for me and this blog.]

Money Angle For Masochists

We played StockSlam after dinner. The kids (well not the 1st grader) and adults were all into it.

There are 8 colors or shares that take a random walk over 10 rounds. The shares of the color that climb the highest are worth $100 at expiration. The rest of the shares are worthless. So you are trading a derivative contract (a future) not the share prices directly.

Purple is in the lead:

The rules are simple. You are mock trading in an open outcry environment. You start with 4 shares of each color and cash. It’s a free-for-all where you can trade with anyone at any price. You can bid, offer, or make 2-sided markets. It’s exactly what we did when we trained although simpler since we aren’t using options (although depending on the audience we will also trade options as side bets…”what’s your offer on the blue 150 call?”— if you get lifted, you can buy blue shares to delta hedge and isolate the vol).

The game is a deeply layered experience. You can just play for fun. It’s wildly energetic — we make sure everyone gets involved and there are gentle ways to do that, different personalities manifest in so many ways…some sling from the hip, some are shy or don’t want to open their mouths until they think they know the value of everything but then it all changes and you realize that approach won’t work.

But what attracted me to the game, beyond the fun, was how it bursts with trading lessons. Based on the audience we modulate the experience up and down. We give homework leading up to the event and bridge the rationale of the questions to insights embedded in the game. We connect real-life investing and trading concepts to the game (and honestly we don’t even get to them in these 2+ hour events…everyone wants to play not listen to lecture).

The single most powerful lesson though is one I harp on all the time — trading is about measurement not prediction. In the game, prediction is not even possible. The walk is random. But skill expresses itself strongly! Your ears pipe in pricing data so you can triangulate fair value and find aberrations. The visceral feel of playing skillfully is well-matched to the feeling of trading effectively in real life. When I pull you aside and ask why you did X or Y, a good answer will take the same form of sound trading rationale — “well, I bid 17 for green because red which is in the same position just traded 20 and I know Sam bought a bunch of green last round for 12 and is looking to flip a quick profit”. Your transacting like crazy but you can kind of tell without stopping to count if you are making or losing money when you get into the flow.

Getting In The Trading Headspace

Let’s pose some questions and entertain some scenarios.

At the start of the game, all the colors start at 100. I might start by just throwing out a 14 bid for red or a 9 offer in yellow just to see or a 16 offer in green, etc to get a read of the thought processes when the game is a blank slate.

Let’s look at a scene futherer along:

Suppose the following montage represents the situation in the pit:

Purple: 28-32

Green: 20-24

Blue: 20 bid

Gray: 10 bid

Jane yells “Pink/orange 1×3…even bid for the pink. I’ll buy pink, sell 3 orange for even”

What do you do?

If you sell the 1×3 you will get long 3 orange and short 1 pink. You can then turn around and lift the 1 green at 24 while hitting the 10 bid in the gray 3x.

What’s your net position:

+3 orange

-1 pink

+ 1 green

-3 gray

Chunking the risk:

• You’re long 3 orange and short 3 grays (they are worth about the same, as they are 96 and 95 respectively in the race).
• You are long 1 green and short 1 pink (again worth similar amounts based on their race position)

The risk on these positions is basically a wash…but you collected $6!

[You sold 3 grays at $10 each and bought 1 green for $24. The pink/orange 1×3 traded premium neutral]

If you keep doing positive expectancy trades and manage to not get too unbalanced in your positions you will have a high Sharpe and be profitable by expiration. If you just try to load up on the color you think will win, that’s a zero expectancy strategy that’s high risk/high reward and will have a garbage Sharpe over many games.

As we play the game I might come over and nudge you:

• “Hey, do you think the gray bid had any room? If you can squeeze an 11 bid out of them then you would have collected $9 instead of $6.”
• “What if the gray bid was thin and you could only sell 2 on the 10 bid? Do you see how liquidity and gauging the size on the bid/offer is important? You are now ‘hung’ on 2 grays that you couldn’t offload. Is the trade still worth doing if you have to hit a 9 bid on the remaining 2 lot for an average price of 9.33?”
• “The green bid was only 20, you could have bid 22 and maybe the 24 offer would have stepped down and offered 23s or better yet just hit your mid-market bid.”
• “Blue is 20 bid…maybe those oranges and grays were kinda cheap relatively and the good side of the trade was just buying the orange 3x via the first ratio trade but not locking it in by selling the grays. Don’t do a trade good by $5 and then do a trade bad by $2 to lock it in if you don’t have to…you have to maximize when you have the best of it because you may find yourself needing to give up edge sometimes to manage risk”.
• “With the green offered at 24, maybe you can dangle a 22 offer in the blue…if you get lifted turn around and take the greens. You’ll have legged the spread for 2…maybe you try to offer out the pink/blue spread at 7 fishing for a 5 bid. Paste those and your net position is long green/short pink for a $3 credit!”

This is trading.

Replace colors with option strikes/maturities and all the many combinations of vertical spreads, synthetics, straddles, and underlying… churn all day, and let the chips fall where they may.[see Mock Trading Options With Market Makers]

If you trade enough with a positive edge the expiration results are just noise — you win some, you lose some. The p/l over time converges to your edge.

Knowing the arbitrage relationships in options is the same as knowing that the field of colors can’t be worth less than or more than $100. Today we measure fair value from liquid consensus using machines — in the game we gather consensus by listening. In the pit, it’s loud and busy and orders are flying around everywhere. You learn to focus attention on what matters. And that changes depending on the context. The same is true in modern trading.

Today we enter trades with code or mouse clicks not vocal cords but the concepts are the same. That’s why prop firms still use mock trading to train. The arena is a Socratic forum that opens up conversations about practical scenarios. It’s like having a poker coach press you on “Why did you call that bet? What did you think they were holding? With what odds? If you think they just caught a 2 pair with that Jack of clubs on the river, do you think they really would have called the big bet on the turn with a low pair and no draw?”

Mock trading in the presence of an experienced trader is an opportunity to debug your thinking.

This was Friday night:

And then Saturday night with the family:

Purple at 30

cc @moreproteinbars pic.twitter.com/GBm9JqQ8wL

— Kris (@KrisAbdelmessih) March 12, 2023

rea events ranged from 10 to 25 people. I’m still in awe of a 6th grader who could just see the Matrix. The kid was fast and a total shark, preying on people that were still getting their bearings. After the game, he had opinions about shifting some of the probabilities in the algo and adding skew. I asked his mom if he was coding or using Excel and she said “no, not yet”.

”Umm, give him to me”. With some tools for expression he’ll be off to the races!

Otherwise, with respect to the game, I will share more as appropriate. We did have a videographer at all the sessions so at some point there will be more to see. In the meantime, if you are interested in having us do a team-building or educational seminar at your office, conference, or school hit me up and we’ll figure something out. By the way, the game shown above is just one of several games we actually trade on. The attendees will remember their favorite “bunny” I’m sure.]

Friends,

I used an air fryer this week. My family was proud of me.

The bar is that low. I mean look what happened that time Yinh and my MIL weren’t around:

I’m also not handy. This utter lack of domestic skills means the very sight of a Conestoga wagon gives me chills. It might as well be the trailer for Hereditary. (I also don’t watch scary movies…but I am an avid reader of their Wikipedias.)

So now that we have this family commune thing going on with my in-laws next door, I feel extra pressure to pull my weight. I really only have 2 things going for me:

1. I enjoy making cocktails. The others enjoy drinking them. (Lately, I’ve been making mai-tais but instead of white rum, I’m using blanco tequila.)
2. I have the patience of a cadaver. (I’m also a space cadet that will not have his boarding pass out after waiting on a long line to get to the agent — I don’t know if this is the downside to my hard-to-rile disposition but I’ve definitely annoyed my share of people in life and the worst part is this same quality makes their annoyance roll off me too easily.)

The benefit of patience is that if I try to teach something and the person can’t get it — it’s always my fault in my mind. There has to be a way. So I get the privilege of trying to help the kids with their schoolwork and can usually do it in a way that doesn’t make them snap at me when they are frustrated. Not always but I am conscious of not taking them to a place where they shut down. As any parent knows, kids put up walls and they are often only permeable to a 3rd party. (I’m not a fan of tough love unless the kid is making careless errors. Give kids credit and space and recognize that sleep helps minds consolidate. You can drill a piano scale without a sense of progress only to find that it’s easier in the morning. Patience allows breaks to do their unconscious work, but you need to trust it. Persistence and rest are a powerful combo but don’t mix well with immediacy.)

I love that moment when a kid (or anyone really) discovers they can do or understand something that felt too big. The feeling of empowerment unlocks far more than the particular lesson’s objective.

With all that said, I create lessons to challenge them. You can meet them wherever they’re at by breaking problems into smaller bites and inserting them at the point where they feel most comfortable.

I published these math word problems with guidance for how to teach your child or student.

• Teach A Kid Binary and Other Non-base-10 Number Systems
• The Dave and Busters Lesson
• The Cost of Heating The Pool (includes spreadsheet)
• Electric Vehicle vs Gas-Powered Breakeven (includes spreadsheet)

Similar posts I’ve previously published:

• A Socratic Money Lesson For 2nd Graders
• Fun Ways To Teach Your Kids Encryption

This one started as a kid lesson but turned into something about portfolio risk:

• I Felt Bad For Picking My 3rd Grader Off

I have several lessons in the queue. After doing them with my kids and their cousins I’ll write ‘em up and share.

In the meantime, there are more posts indexed here:

• Moontower General & Childhood Education

These are more teen/adult appropriate:

• Numeracy & Decision-Making

Go slow and give people credit. Many people never had someone help them see they are capable.

Now if I would just direct this advice to myself in an apron…

Money Angle

Today I’ll share a personal investing story. It’s in the thinking-out-loud category. I can see the spots where someone could say “that’s stupid” (don’t let that deter you from pointing them out). And that’s why I want to share it — this is the messy process of making a decision. It’s imprecise. It has more “vibes” than I’m supposed to admit. But at the end of the day, there’s an irreducible amount of “putting your finger in the air” with most investing decisions.

The Housing Trade

At the start of 2022, I felt housing might be screwed. Home prices and inflation were red-hot and the risk of the Fed’s hand being forced to raise interest rates was beginning to materialize. Mortgage payments were extra sensitive to bond duration math if rates were to start lifting from such a low base. This would slow housing demand. On the supply side, there were still materials and labor supply shortages. Superficially this is bullish housing but that was already in the price. Looking ahead, this combination felt (notice the vibes…I’m not looking any data up. It’s pure staring out the window) like it could destroy demand. The idea of demand destruction reverberates from my oil trading past. OPEC doesn’t optimize for the maximum price the way you might expect from a cartel. They can be quick to supply the market because they don’t want to kill their customers. Sure a high price means the inventory in the ground is worth more but the business of producing oil, the business that enjoys a multiple, is burnt toast.

The most vulnerable part of the stack felt like the homebuilders because, like an oil refiner, they sit in between the raw materials and the finished goods. They would be squeezed on both sides. Cancellations + high costs.

I pulled up a chart in March of 2022 (this is what it looks like through this weekend of course).

Since the beginning of the year, in less than 90 days, XHB underperformed SPY by nearly 20%.

The market was well ahead of me. Dammit. It appears there’s nothing to do. In the liquid market at least.

I had 2 ideas that could be applied to stale markets.

1. Decline to invest in the next batch of Austin flips. We had been bankrolling a friend’s short-term flips in Austin since the pandemic. We were just receiving our return from the most recent one and while we’d normally just re-invest, we took a break.
2. Sell the house we bought in Texas the prior summer. We had a renter in place and we still hadn’t owned the house for a year (meh, short-term gains). We asked our realtor what he thinks the house could fetch and he indicated the market was still hot. He thought we could get 35-40% more than we paid the prior July (which is really nuts since the house had already appreciated since the pandemic and our purchase price was a 12% overbid to the listing price). The realtor’s number sounded optimistic but looking at comps I thought there was maybe a 15-20% chance of catching his number and in most other cases get some kind of quick profit. But I wasn’t really pricing it off profit. I was worried about risk. The cap rate would be terrible if rates went up even 1% and since we were committed to CA we didn’t want the property anymore anyway. The liquid markets were a sell signal. The illiquid market was lagging.

A family with small kids and another on the way was renting the house so our ability to move quickly was a bit hampered with respect to showing but we did get the house on the market by April. We immediately caught a bid above our ridiculous asking price! 2 days later, the stock market dove. Yinh and I were convinced they would back out.

We were right. A day later we got the call. They’re out. Apparently, their financial advisor told them to cancel. I feigned annoyance while secretly thinking “smart advisor”.

Skipping ahead, we cut the price and caught one single bid. But we needed to agree to a long closing period. We’d wake up every day “please no whammy”.

It finally closed in October. We made a touch over 20% before commission which felt so lucky. By now it was also a long-term capital gain.

But what do we do with the cash?

Rebalance.

You sell the thing up 20%, what’s on sale to buy?

We would reallocate the cash to stocks on a relatively vol-neutral basis (if we sold $1 of house, maybe buy about $.50 of stocks if we think stocks are twice as volatile as residential RE).

But there was another risk on my mind.

Being renters ourselves we were effectively “short” or underweight housing after selling the property. From a liability-matching investing lens, this was unsettling. Conveniently, the homebuilders were now down about 40% compared to SPY — the thing I wanted to short a few months earlier I now wanted to buy because it filled a risk hole AND was pricing in pain. So we put 1/4 of the proceeds from the house sale into IWM and 1/4 into XHB.

(I just cut half the position a couple weeks ago as we reduced our net equity exposure and rolled into T-bills. I keep our equity exposure in a band and I chose to sell XHB based on its outperformance.)

Things I believe

1. Markets are smart. Liquid markets adjust quickly.
2. My life’s work is not figuring out what prices are right, so my allocations are driven by desired exposures or non-exposures to risk. That’s the best I can do given how much time I am willing to spend thinking about things I have no control over.
3. Within that framework, my choice of diversified exposure is relative value voodoo and vibes. But you know what…even in my professional trading that was true. In that case, my life’s work was to measure option prices at much closer resolutions than anything I’m doing here, but pulling the trigger felt pretty much the same. What’s the liquid market telling me about about fair value and what do I do with that info? Any individual trade is noise, but if I’m disciplined about risk then no decision carries the risk of the whole portfolio and the framework is left to converge to its logic over time — capture a risk premium without mortally wounding yourself along the way.
4. Luck will betray you one day so enjoy it when she smiles upon you. We felt like we caught the last bid in America on that house. If we listed the house a few months earlier (which we might have except for the complications with the tenant — no fault of anyone was just a matter of details) we would have been extra lucky, but we would have gotten a worse price on our stock buys.And if we don’t make the sale? Pain parade. We miss the profits, don’t get to rebalance, and I curse myself for getting into an illiquid asset. I hate illiquidity already. As I get more experience, I want to rule out illiquidity more and more. Ruling-in needs to be for a justifiably unique exposure. The option to rebalance has a value — whether you choose to ignore it or not is up to you. See How Much Extra Return Should You Demand For Illiquidity?

A note on taxes

We will pay LT gains taxes of about 30% between Fed and CA. Why not 1031 exchange? Well, I thought real estate prices would be too sticky (ie they won’t come down enough) before our 6-month window to close on a new property. I expected wide bid-asks as sellers locked into low fixed rates try to wait out market weakness. I didn’t want to sell something up 20% to buy something down 5 or 10% when I could buy something down 40% (which is more standard deviations — again, think in vol-adjusted terms. This is also why buying high growth wasn’t attractive even if they were down more than housing…they are higher vol plus the skew in their distributions means volatility is understating the risks — that’s a post for another time).

More generally, let’s examine the math of 1031 tax savings. Imagine the house I sold went from $800k to $1mm. My tax liability is about 30% of 200k or $60k. But the brokerage cost of what I buy on the backend is pretty close to that (5% of $1mm when I eventually sell the 1031 property). It’s true that the cost is deferred but the cost is also inflation indexed since it’s a percent of the home value. You are not saving nearly as much as you think because you are forced into a high transaction cost asset and the cost is a percentage of the entire asset value, not just the profit.

[Note 1: If you don’t have to pay that fat state tax and your LT gains rate is closer to 20% than this argument is even stronger.]

[Note 2: This argument is much less compelling if you plan to never sell and get stepped-up basis for your heirs. But you get stepped-up basis on stocks when you die too. But anyway, I’m not in the never-sell camp because the tax tail isn’t going to wag my risk dog. There’s always a price that warrants saying “sold” to. If a HODLer wins they get concentrated. That might be ok for your human capital but that’s not a strategy for a random number generator. And from my unenlightened seat, the market’s job is to set prices for great assets so that they are effectively random. If you disagree, you should invest for a living. I heard you can get rich doing that. Actually, you have a better chance of getting rich by convincing people you could do that.]

Money Angle For Masochists

New Post:

🔗The Snake Eyes Option

The Snake Eyes game is something my 1st grader plays at school. The rules are simple:

1. Roll a pair of dice and record the sum

2. Continue until you roll a ‘2’ (but don’t record the ‘2’)

3. Your score is the sum of all your rolls

Example 1

Your rolls are as follows: [9, 4, 12, 2]

Your score is 9 + 4 + 12 = 25

Example 2

Your rolls: [2]

Your score is zero.

The rules are simple. Let’s have some fun now.

What’s the 300-strike call worth?

In this homework assignment, we build gradually towards the pricing of an option in a game scenario.

• It can be used as an interview question for a junior trader position or really any position that requires computational thinking
• It requires nothing more than basic probability including conditional probability (although you do not need Bayes Thereom, just logic. You will need to do a lot of reasoning the same way you need to turn any involved word problem into math statements)

Extra Credit: Validate your answer via simulation. I included my Python code.

From My Actual Life

In class, kids are assigned a number based on last name alphabetically. “Abdelmessih” is usually a shoe-in for #1 unless there’s an Aaron floating around.

My older boy said he was #2.

Curious I looked up the class roster and saw an Egyptian last name was ahead of him. We exclaim, “Zak you have another Egyptian in your class!”

He cocks his head, “Who’s the other one?”

We are failures.

Stay groovy!

Friends,

[Turns down the volume on The Cult blasting in the background]

I’ll tell you what gets me jealous.

Being head-down obsessed with something. The feeling of being indistractable (F you Grammarly, that’s a word now). I don’t mean artificially like you just installed the Freedom app or enabled “focus mode” on your phone. I mean, you don’t even care to click on any Substack unless its title included your social security number. You got a lead foot with zero drag coefficient.

I’m jealous of this because I know what that feels like, but also because the grass is always greener. As unromantic reality is when you are in that mode, the obligations to yourself and others lapse to varying degrees. You’re waiting for a drink at the bar and your reflection in the Tom Dixon pendant peers back at you “Is that a double chin?” Or it can arrive with more drama. A calendar invite for a “Mid Life Crisis”.

We mostly find ourselves balancing between devotion and discovery. Exploit vs explore. I suspect it’s better to average these poles over time rather than try to sit in the middle at all times. Switching between the modes seems like a happier and more effective way to embrace the current setting, especially if you remember that the mode is temporary.

I left the day-to-day grind 2 years ago. Instead of spending savings on a home reno or car with suicide doors, I’m consuming a leisurely period of discovery. Like a reno, this is a consumption/investment hybrid. I’m dabbling in several projects with faith in my instincts that a worthy object of devotion will present itself. Not because things just happen, but because you do things, that lead to private information and that combined with other information hints at a jungle path you are both eager to and adapted for cutting and sweating through. It’s a highly active process. It’s not sitting back and reading (although I do want to do that too NBA2k23 and writing seem to be as still as I can sit).

This week an old friend who got laid off reached out to talk. He was giving himself a few months of explore mode but was a bit wary of its potential to be overly heady or abstract. Points for knowing oneself. I can relate. I threw the following suggestions as a sort of anchor to utility that I find helpful and he appreciated them so much he said it would be useful to others. I actually think of them as solutions to a generic rut, but to some, being thrown into discovery mode can feel like a rut.

1. Exercise every day. Even if it’s just a 45-minute walk.
2. Meet 2 new people in person every month. Coffee, hike, whatever. I got this idea from my wife who has a casual pro-bono coaching practice and this is the single biggest action item that unlocks overwhelming responses from the people who actually follow through.
3. This is a personal and recent one I’ve been telling people — listen to the Founders podcast. It’s a free EpiPen shot in your ass.For the reflexive ankle-biter, I recognize there’s a midwit objection to this show — “oh it’s all survivorship bias”. This is an obvious observation and completely besides the point. The show is not a recipe. It’s an inspiration for obsessives and people in discovery mode who appreciate obsession mode. The show is repetitive. That’s one of its strongest features. My own writing is intentionally repetitive. There are only a small number of ideas that matter (this is a recursive point since one of those ideas is power law).

   Communication is like rotating a shape to fit in a puzzle — angle the words in just the right way to complete the picture. Except everyone has a different puzzle and needs to see the pieces from their own special angle (this is also why objecting to things that have been done before is silly unless we for some reason are optimizing for novelty not understanding). The Founders’ stories enthusiastically harp on the few qualities that are necessary but insufficient conditions for success. The rest of any extreme outcome is luck anyway.

In addition to these suggestions, here’s a troubleshooting technique:

Track how you spend your time. Results are a lagging indicator of work — so if you are disappointed in your outcomes you should at least rule out the possibility that you are lying to yourself about your effort. Your poor results could be due to bad luck, bad timing, working on the wrong things, or honestly many factors. But the one factor you have clear control over is your effort. It’s just too easy to lie to ourselves about that. Fortunately, keeping track of time spent is just as easy.

Whatever mode you are in, embrace it. It won’t last forever and that’s why you can enjoy it without guilt.

Today’s letter is brought to you by the team at Ezra:

Ezra is on a mission to detect cancer early for everyone in the world.

In this week’s Moontower edition, the team at Ezra invites you to understand your risk of cancer for free using the Ezra Cancer Risk Calculator. In just 5 minutes and two dozen questions, you can learn what types of cancer you’re potentially at risk for.

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Should you decide to skip the quiz and sign up for an Ezra Full Body MRI scan, use the code MOONTOWER150 at checkout for $150 off your scan.

Visit ezra.com to learn more.

A personal note about Moontower’s sponsor Ezra

Last October, during the StockSlam Sessions in NYC I met the founder of Ezra, Emi Gal. We meet for a couple hours every week on Zoom thanks to a trading-related project we are collaborating on and in the process have become real-life friends (the internet FTW yet again — no internet, no Twitter, no writing online, no StockSlam critical mass, no meeting other members of your flock scattered around the world).

Emi offered to let Ezra scan Yinh and I for free. I was hesitant. I’m a hypochondriac and know if you start poking around you’re always bound to find something (knowing Bayes Theorem should be a hypochondriac’s best friend, but combatting neuroticism with logic is about as effective as denying the existence of love because it eludes “proof”. But I digress)

Emi was extremely understanding and in fact, related strongly to my feeling. But his framing swayed me. The scan is peace of mind either way. It scores every finding on a spectrum of concern from a non-event to go to the ER asap. It notes anomalies to keep track of and you can opt out of certain bits of info like you can on a genetic test. You might not want to know about things you can’t do anything about.

But why does it finding something give you peace of mind? Because you found it early. That’s the point. Early detection is the best weapon we have against cancer (1 in 8 Ezra clients discover potential cancer). As someone that’s turning 45 this summer and less-than-enthused at my first colonoscopy, this is a top-of-mind topic.

I had been approached by various companies about sponsoring this letter. Last year I had Mutiny Fund as a sponsor. They are friends of mine and I’m invested in their fund so I was stoked to have them. With Ezra, I actually asked Emi if they would sponsor Moontower.

I’m neurotic. I’ve written a bit about my personal health-hacking history. I don’t have great health genes (and this is a deeper convo but my awareness of my mortality played a non-insignificant role in my decision to leave a career that I wasn’t enjoying anymore). My sanity requires I don’t just chase down every weird feeling I get in my body, especially since getting older just means you get more weird feelings by default.

Ezra offers a low-effort, high-value peace-of-mind intervention that I want you to be aware of.

Money Angle

This is from a new post: Geometric vs Arithmetic Mean In The Wild (6 min read)

In this post, we review our lessons from last week’s Well What Did You ‘Expect’?

• “Expectation” as a weighted arithmetic mean
• When to use geometric mean (hint: in investing contexts)
• The relationship between the 2 means

Now we move on to witnessing how the math theory fits actual SP500 history.

This Is Not Just Theoretical

I grabbed SP500 total returns by year going from 1926-2023. Here’s what you find:

Simple arithmetic mean of the list: 12.01%

Standard deviation of returns: 19.8%

These are actual sample stats.

What did an investor experience?

If you start with $100 and let it compound over those 97 years, you end up with $1,151,937. 

What’s the CAGR?

CAGR = ($1,151,937 / $100)^(1/97) – 1 

CAGR = 10.12%

These are the actual historical results. An average annual return of 12.01% translated to an investor’s lived experience of compounding their wealth at 10.12% per year. 

Comparing the sample to theory

If you knew in advance that the stock market would increase 12.01% per year and you used the CAGR formula with our sample arithmetic mean return and standard deviation, what compound annual growth rate would you predict?

CAGR = Arithmetic Mean – .5 * σ²

CAGR = 12.01% – .5 * 19.8%²

CAGR = 10.06%

An average arithmetic return of 12.01% at 19.8% vol predicted a CAGR of 10.06% vs an actual result of 10.12%

Not too shabby. 

I used the same parameters to run a simulation where every year you draw a return from a normal distribution with mean 12% and standard deviation of 19.8% and compounded for 97 years.  

I ran it 10,000 times. (Github code — it works but you’ll go blind)

Theoretical expectations

CAGR = median return = mean return – .5 * σ²

CAGR = .12 – .5 * .198² = 10.04% 

Median terminal wealth = 100 * (1+ CAGR)^ (N years)

Median terminal wealth = $100 * (1+ .104)^ (97) = $1,072,333

Arithmetic mean wealth = 100 * (1+ mean return)^ (N years)

Arithmetic mean wealth = $100 * (1+ .12)^ (97) = $5,944,950

The sample results from 10,000 sims

The median sample CAGR: 10.19%

The median sample terminal wealth = $1,2255,90

The mean terminal wealth: $5,952,373

Summary Table

The most salient observation:

The median terminal wealth, the result of compounding, is much less than what simple returns suggest. When you are presented with an opportunity to invest in something with an IRR or expected return of X, your actual return if you keep re-investing will be lower than if you take the simple average of the annual returns.

If the investment is highly volatile…it will be much lower. 

The distribution of terminal wealth

The nice thing about simulating this process 10,000x is we can see the wealth distribution not just the mean and median outcomes.

Remember the assumptions:

• Drawing a random sample from a normal distribution with a mean of 12% and standard deviation of 19.8%
• Assume we fully re-invest our returns for 97 years

And our results:

• The median sample CAGR: 10.19%
• The median sample terminal wealth = $1,2255,90
• The mean terminal wealth: $5,952,373

This was the percentile distribution of terminal wealth:

The mean wealth outcome is 5x the median wealth outcome due to a 2% gap between the arithmetic and geometric returns. The geometric return compounded corresponds exactly to the median terminal wealth which is why we use CAGR, a measure that includes the punishing effect of volatility. 

In terms of mathematical expectation, if you lived 10,000 lives, on average your terminal wealth would be nearly $6mm but in the one life you live, the odds of that happening are less than 20%.

The chart was calculated from this table:

Note that, also 20% of the time, your $100 compounded for 97 years turns into $257,498 or a CAGR of 8.4%. A result that is 1/5 of the median and 1/20 of the mean. Ouch. 

So when someone says the stock market returns 10% per year because they looked at the average return in the past, realize that after adjusting for volatility and the fact that you will be re-investing your proceeds (a multiplicative process), you should expect something closer to 8% per year. 

And one last thing…you should be able to see how rates of return, when compounded for long periods of time, lead to dramatic differences in wealth. Taxes and fees are percentages of returns or invested assets. Make sure you are spending them on things you can’t get for free (like beta).

A Question I Wonder About

(This might venture into masochism for casual Money Angle readers)

If you draw a return a simple return at random from a normal (ie bell curve) distribution and compound it over time, the resultant wealth distribution will be lognormally distributed with the center of mass corresponding to the CAGR return.

We saw that theory, simulation and reality all agreed. 

Or did they?

The simulation and theory were mechanically tied. I drew a random return from N [μ=12%, σ = 19.8%] and compounded it. But reality also agreed.

It may have been a coincidence. Let me explain. 

Stock market returns are not normally distributed. They are well-understood to differ from normal because they have a heavy fat-left tail and negative skew.

1. The fat-left tail describes the tendency for returns to exhibit extreme (ie multi-standard deviation) moves more frequently than the volatility would suggest.
2. Negative skew means that large moves are biased toward the downside.

These scary qualities are counterbalanced by the fact that the stock market goes up more often than it goes down. In the 97-year history I used to compute the stats, positive years outnumbered negative years 71-26 or nearly 3-1. 

The average returns, whichever average you care to look at, is the result of this tug-of-war between scary qualities and a bias toward heads. With the distribution not being a normal bell curve it feels suspicious that the relationship between CAGR and arithmetic mean returns conformed so closely to theory.

I have some intuitions about negative skew (that’s a long overdue post sitting in my drafts that I need to get to) that tell me that in the presence of lots of negative skew, volatility understates risk in a way that would artificially and optically narrow the gap between CAGR and mean return. By extension, I would expect that the measured CAGR of the last 97 years would have been lower relative to the theory’s prediction. 

But we did not see that.

I have 2 ideas why the CAGR was held up as expected, despite non-normal features that should penalize CAGR relative to mean return. 

1. Path

In Path: How Compounding Alters Return Distributions, we saw that trending markets actually reduce the volatility tax that causes CAGRs to lag arithmetic returns. It’s the “choppy” market that goes up and down by the same percent that leaves you worse off for letting your capital compound instead of rebalancing back to your original position size. The volatility tax or “variance drain” occurs when the chop happens more than trends (holding volatility constant of course). But since the stock market has gone up nearly 3x as often as it went down perhaps this trend compounding “bonus” offset the punitive negative skew effect on CAGR. 

2. What negative skew?

Using annual point-to-point returns, I’m not seeing negative skew. 

I’ve exhausted my bandwidth for this topic so I’ll leave it to the hive. Hit me up with your guesses. 

Money Angle For Masochists

For those who want to take the concept of compounding to the limit (of Δt→0 that is, muahahaha), see another new post:

Understanding Log Returns (2 min read)

This post will help you understand the concept of normalizing distance in option theory. Strike prices are in absolute dollars and transforming them into percent moneyness is still not exactly the right way to compare distances. In practice, you use delta or standard deviation, but even underneath those rulers is the concept of a log return.

In this short post, I dwell on log returns because it’s often taught quickly leaving that foggy “I think I get it” feeling in a student.

Again, I’m being explicit in my use of repetition and a slightly different angle to see if it works for you.

One last thing…

Back in October Tina Lindstrom, Mike Steiner, and I hosted 3 nights of what we called the StockSlam Sessions in NYC.

We are bringing the event to the Bay Area March 8, 9, and 10th.

It’s totally free. If you like learning about games, math, trading, decison-making, and like shouting and thinking quick, you will love it!

It’s a total privilege to be a sherpa for these sessions. No egos allowed. No experience required.

Based on my experience and the feedback from NYC, the social aspect and chance to meet new friends was truly unique and uplifting.

Apply here!

Stay groovy!