Moontower #188


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)

Moontower #187


In the past few weeks about 5-10 people have reached out to ask me for advice in the vein of “my kid is 6 and likes math and what should I put in front of them to foster this”. They are usually looking for specific answers.

I offer a few things my kids have enjoyed (everything can be found on the blog, ie here and here) but I want to be clear — I’m no expert. I’m just like the rest of the parents who have the same goal of watching their kids’ curiosity flourish.

To kill many birds with one stone here’s the gist of my email responses:

I don’t create pressure. Let learning be a source of joy. Insight is its own reward and to train someone to appreciate that when they are young is a life-long gift because they can find stimulation in the pleasures of the mind and the mundane.

Sure, math proficiency has plenty of instrumental value in life, but appreciation and beauty is the bigger gift here (I also suspect this is an antidote to the doping that broader media does to people — if you find beauty in the evergreen you don’t need to constantly be taking drags from the current times and you’re perspective and emotional state will be better off for it. No science behind that — just my hunch).

You are already doing the single largest muscle movement –> literally giving a shit about your kids’ curiosity flourishing. Like seriously that’s 90%. The specific instances of expression — coding, writing, drawing, cooking, composing — or any other forms of creation are secondary. Creating not just consuming is the key because by being able to manipulate the world (I don’t mean manipulate in some evil sense) around you, you reinforce your agency.

When I see fear and extreme tribalism I see people retreating away from agency and frankly accepting some learned helplessness. Your role as a guardian is to shepherd a healthy sense of agency (unhealthy would be to program an overconfident narcissist).

Code and writing are symbol-manipulative domains — some will gravitate to that more than say carpentry or being a physical maker. I’d be open-minded about the specific expression and focus on nurturing the upstream creation and play impulses.

And if you got this far you exemplify an ironic phenomenon — the people who reach out looking for help/guidance/opinion/validation on their approaches are the people who don’t need to (this is not a back-handed way of saying don’t reach out btw, it’s just an observation!)

This young portal in the Moontower codex is an attempt to consolidate some specific learning stuff if interested:

🧠Moontower Brain Plug-In

A Word From Moontower’s Sponsor…

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.

Money Angle

I made this for you.

🔗Investment Blogs I Read


Money Angle For Masochists

Last week’s masochism had 2 parts.

  1. A hands-on walkthru of spotting a hidden option in an ETFThe walkthru builds intuition socratically and since it’s already in question-and-answer form you can use it with minimal modification to scaffold an interview question.

    Again, that link: Financial Hacking: ETF vs Negative Oil Futures

  2. A bit more advanced was the description of how I actually traded it in real life. A fellow professional option trader endorsed the approach and I’m not above shilling that:

I’m flattered to be given credit for explaining something so anyone can understand it. But recognizing why the pricing was the way it was, is not an act of “galaxy brain” genius. It was experience.

This is worth an explanation with a generous helping of personal color.

Back in 2009, I was trading as an independent (I had a backer deal where I put cash up in escrow that represented the most I could possibly lose and in exchange for that and some economy of scale stuff, the backer got 30% of my profits). I had left SIG a year earlier but because of my non-compete couldn’t trade oil-related derivatives.

I could trade natural gas options though. My backer, despite bankrolling about 100 traders, some of them with large businesses employing as many as 20 people, never had anyone trade natty options for them. My pitch emphasized a “steady hands” approach. As a dyed-in-the-wool market maker, I had little use for opinions or fundamental research. I had an arbitrage mindset — I would focus on my advantages of being a grinder. I stood in the pit, trading order flow that came to the floor, I had a partner who handled all the voice brokers upstairs and we had an assistant who made markets on the screens. The 3 sources of info would allow us to stitch a master vol surface or “sheet” that we would push out to all 3 spokes in an ongoing conversation that provided feedback as to when we should update fair values.

[Multiple times per day…”raise summer small calls 2 clicks, multiple brokers bidding and lower Jan meaty puts a point — I’m seeing consumer flow buying calls on winter fence strips, they haven’t printed yet”. The PitBulls experience rhymes with this. See Mock Trading]

Our backer was focused on futures and futures options but I had spent most of my first 6 years as a trader in ETFs — so I convinced them to let me build out the infra to price and trade options on UNG as a 4th spoke to find relative value trades against our core options book.

I was long UNG options vs a short in NG futures options because UNG vol traded at a discount.

Bad timing.

In the summer of 2009, in the wake of what Goldman deemed the “commodity super cycle” while pushing commodities as an asset class, commodity ETFs were under scrutiny for allowing financial speculators to more easily drive up the price of energy, food, and materials. Natural gas prices were in the crosshairs — the UNG fund announced it would cap the number of shares it would issue.

With a shortage of shares, UNG surged to a large premium over NAV (I don’t remember exactly what it was but something like 20% is lodged in my head). A large player had done their homework placing a smart 9-figure bet — they “created” all the remaining shares betting this would happen. I won’t speculate who that was in print but my hunch is not unironic.

I was in a bad spot.

Every time gas futures sold off, UNG basically stayed unchanged — the premium to NAV would just expand. When NG rallied, UNG still barely moved — the premium simply narrowed. Every day I was forced to pay theta on my UNG options while getting chopped to pieces on my short NG options. Meanwhile, the vol discount widened from about 1 point (the threshold where the arb became interesting) to about 20 points! Without a proper “creation” function, UNG was no longer hinged to NG futures.

I lost about $250k of my own money in under 2 weeks…a multiple standard dev p/l event for that time frame (I realize this is a quaint sum in a world where that’s the cost of a kitchen with red-knobbed ranges but even back then I’m like buy me a drink before you do me so dirty).

[My backers, to their credit, were understanding. They never flinched and allowed us to continue trading and building. We expanded into trading options on SLV, BAL, JO and SGG as our footprint in futures options grew.]

At the risk of overgeneralizing, a few things stand out:

  1. Market risks (ie prices moving up and down) are the most trivial. It’s the ever-present possibility of rule changes (and the politics that can drive them) that remind you that the last line of defense in risk management are constraints to gross exposures not just nets.The UNG trade is also reminiscent of that trope about how a casino’s risk manager is more likely to lose sleep over an Ocean’s Eleven heist scenario than a string of bad luck at the tables.
  2. Battle scars are great teachers. When USO traded at a premium as CL futures went negative, my reflex was not “that’s stupid” but “there’s more to this”. Even though UNG and USO went premium for different reasons I wouldn’t have figured out the gameplan as fast as I needed if I didn’t have that prior weird (and painful) pattern to match to. This is also an argument for having a team of trusted people to bounce ideas off. You don’t have to touch every stove yourself.

With this fuller context, you can re-visit the “galaxy brain” approach to trading USO options during that Covid dislocation:

🔗Options on USO when oil went negative


From My Actual Life

Is this just a Bay Area thing?

This is a promo to tour your rich neighbors’ homes.

It’s a thing that happens every year to raise money for some great causes so restraint is in order…but also…gag me with your maître d’s handkerchief.

They used to be “kitchen tours” so you could at least pretend you were getting re-model inspiration. But the title now feels like saying the quiet part out loud. I’ll admit — the setup is quite clever. Since the ticket proceeds go to charity, all parties can whitewash the White Lotus psychology off their bodies.

Yinh was just telling me of an interview she listened to where the guest’s goal was to be a “billionaire”. Not to create X or Y or whatever where wealth would be a byproduct, but literally to be a billionaire.

To have your mind preoccupied with attaining an amount of money you could never spend well beyond the point of diminishing returns is a way to spend your attention I suppose. If fetishes are any indication there’s no limit to the breadth of what humans get off on. Fine, you do you. But this desire to be a billionaire, a feat as unlikely as playing in the NBA, does feel like a modern virus.

Sometimes I wonder what it must be like to not have a 90s teen, haterade, shoegaze disposition. It’s quite maladapted for the times we live in. Times where if you don’t aspire to “generational wealth”, the Gary V tribe will tar-and-feather you as a commie.

There’s a certain cringe I feel around such hustle-types that is partially my own un-therapized hangups and partially captured by Venkatesh’s sentiment here (bold is mine):

The phrase “man in the arena” has recently been doing the rounds. It comes from a 1910 Teddy Roosevelt speech, and points to an archetype of a risk-taking doer who is in the fray making the hard decisions, even as self-important spectators keep up ceaseless unhelpful commentary. It is an elevated version of the more familiar solutionist/doerist/builder (builder in Web3) archetype.

In theory, the “man in the arena” has the highest agency in a situation, and is positioned to either reap the biggest reward in case of success, or pay the highest cost in case of failure. At their notional best, men in the arena are warrior-saint-heroes who take on great risks on behalf of humanity, and steal promethean fires from the heavens for the rest of us to enjoy. Even if it means risking eternal torment of the sort Prometheus had to endure. Though the archetype does not address accountability to others, it has strong connotations of virtuous responsibility and conscientiousness. The “man in the arena” believes in noblesse oblige.

In practice, the typical “man in the arena” is usually executing a cunning heads-I-win-tails-you-lose gambit, and isn’t quite the saint the pious startup discourses makes him out to be. But that’s fine. The man in the arena is after all merely human, with very human levels of lust for rewards and aversion to losses.

I’m generally sympathetic to people in the arena, even if I don’t take their self-serving accounts of themselves at face value. I like making Arena Man jokes (by analogy to The Onion’s stock character, Area Man) to poke fun at their self-importance and pious posturing, but in general, I am not ill-disposed towards them. Of course, Arena Men look to privatize gains and socialize losses, and try to come across as martyrs to greater causes whatever the outcome, but then, so do most people in most situations.

When Midjourney-esque AI models extend to video the first prompt I’m giving it:

“Create a celebrity deathmatch where Arena Man fights Area Man with 90s Teen As the ref and Florida man in the stands”

And for love of zeus, if your definition of being a man-in-the-arena invokes the words “self-storage” or “passive income”…you’re telling on yourself.

The 90s Thing

Chris Eberly pointed me to Chuck Klosterman’s The Nineties with the comment:

I’ve had this theory for a while that we are unable to fit in today because the 90s was about slackers, anti brand, Office Space, etc. this book actually covers quite a bit of it with facts both for and against this idea ..

I’ve read many of Chuck’s books (one of the most popular investing posts I’ve ever written references my favorite What If We’re Wrong) so this 90s book is going straight into my veins. I’m sure you’ll hear about it.

Stay groovy


Moontower #186


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.

The inert child who never worked with his hands, who never had the feeling of being useful and capable of effort, who never found by experience that to live means living socially, and that to think and to create means to make use of a harmony of souls; this type of child… will become pessimistic and melancholy and will seek on the surface of vanity the compensation for a lost paradise.

And thus, a lessened man, he will appear at the gates of the university. And to ask for what? To ask for a profession that will render him capable of making his home in a society in which he is a stranger and which is indifferent to him. He will enter into a society to take part in the functioning of a civilization for which he lacks all feeling.

Maria Montessori

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:
    notion image

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

  1. 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


Moontower #185


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.


  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:

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 SympathizerHow 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”]


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.


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 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:

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

Stay groovy ☮️

Moontower #184

GPT Stuff

A college buddy texted me:

The link referenced is totally 🤯. My friend just scratched the surface of what’s possible!


  • How to Use ChatGPT on Google Sheets With GPT for Sheets and Docs

    What Can You Do With GPT-Powered Google Sheets?

    Step-by-step walkthrus in the article on how to do the following GPT functions en masse in a spreadsheet:

    1. Generate Text


    2. Translate Text

    3. Summarize text

    =GPT_SUMMARIZE(C44) will summarize the content of cell C44 into the active cell.

    4. Extract data


OpenAi released GPT-4 this week. Here are some buzzworthy examples:

This thread includes a similar example as well as prompts asking GPT-4 to create videogames, a link about Khan Academy building on the tech to create an assistant for teachers, and more.

I’m far too stupid to pontificate on what any of this means. Every day substacks, articles, papers, interviews, and videos comment on AI, alignment, the meaning of creativity, and the future of jobs from writing to coding. I just see a useful tool to use until the day I’m deleted from the simulation in favor of a paperclip.

Money Angle

In the past few days, I’ve been getting around to the feedback and follow-ups from last week’s StockSlam sessions. Here’s a reaction and my response worth sharing widely.


Just wanted to shoot you a quick note – loved the game last week, thanks for putting it on!

I had a hard time playing the game because I didn’t have intuition for the odds of the game… I’m way more of a Quant- the only thing I could think of was trying to execute the optimal strategy.

To figure out the optimal strategy I’d run a Monte Carlo simulation – play the game 100,000 times (programmatically using python or something) and see the distribution of outcomes as well as figure out some conditional probabilities (like what are the odds of last place winning given current relative location). Getting a sense of this would help price different bets – not a sure thing all the time, but better odds!

Generally, I ended up playing the game buying out-of-the-money “horses” (i.e. last place)… I figured with the mean reversion built into the game combined with behavioral biases to dump losers would be a winning strategy… and I ended up with a positive PnL so maybe I was into something!

I don’t know how you did that for a career for so long… so stressful and I was wound up all night from it, haha…

My reply:

An anecdotal observation — I’ve noticed that quants and accountants actually get a bit paralyzed sometimes and it highlights the fact that crunching the numbers to perfection isn’t the core skill of trading.

It really is handicapping how wrong you could be and then acting with a margin of safety commensurate with the possible reward. Basically, if you wait to have the best info you’ll be too late. So the constraint is “how do I act optimally subject to being fast?” Everyone is in the same boat. That’s a key point. The game would be different if everyone had infinite time to crunch the numbers. Trading is playing the game at hand — and that has a speed component. This is inescapable. It’s also true in reality even if the form varies. Buffet might wait for a fat pitch, but when it comes the bat speed still needs to be fast.

Whatever your game, you ultimately get a feel for it by being able to hold your attention on what matters and tuning out the rest. There’s some visualization…being ready to pounce on an incorrect market that you’ve been studying. In StockSlam, you really get a sense of what consensus is for a color in a certain relative position and then your antennae is up for aberrations. You are gathering and measuring data via listening and memory while in real-life the same functions are performed in code. But they are the same functions. And both are downstream from “what do I need to be paying attention to?” That will vary by the time horizon of your strategy.

[The attendee also mentioned that the penalty for not executing the game’s “broker cards” was too low.

My response:

As far as the penalty we are actually thinking to ditch it anyway and use carrots for doing things on your card rather than punishments. But I hear you on the $5 not mattering much but it remains a useful part of the game by letting us examine if players can find the least expensive way to execute the card. You are effectively benchmarking a trade not to “does this have edge” but “is this better than negative $5”.

This is a critical concept in real life. Broadly, satisficing is often better than making perfect the enemy of the good. Also, there are some strategies that are not profitable if you have to cross a spread but are profitable if the benchmark is “it saved me from crossing a spread” (very relevant for an org that has to make many hedging trades per day). Academic papers are notorious for finding strategies that underappreciate indirect transaction costs. But you may be able to repurpose such strategies to warehouse risks instead of crossing bid-asks to shed them. That’s a lower bar than a strategy that needs to cross a spread. In a world of rebate liquidity this is especially true. The cost/rebate structures for taking/ supplying liquidity is like a 4-point swing in a basketball game.]

Related reading (as an exercise you can think of why these posts are so related to what I described above):

  • If You Make Money Every Day, You’re Not Maximizing (28 min read)
  • The Paradox Of Provable Alpha (1 min read)

Money Angle For Masochists

76ers GM Daryl Morey is one of the pioneers who brought Moneyball-type thinking to basketball during his tenure with the Rockets.

His interview with Patrick on Invest Like The Best is insightful and entertaining. I want to zoom in something Morey says:

You are weighing championship odds. And generally, we look over a three year time horizon with that. You could really pick any time horizon, but three years seems to work best with the data. And we basically do a sharp ratio like you would in investing, which is like here’s how championship odds increase, here’s the variance of that move.

Is it on the efficient frontier of return to risk basically and Shane [Battier], obviously, fit that for us.

None of our information is anywhere as good as the financial models. Actually, our underlying data is more predictive, quite a bit predictive. I talk to a lot of quants on Wall Street, and I tell them our signal to noise ratio using whatever measure you want….And they go like — yes, they go like, whoa, you guys are — that’s incredible. And I’m like, yes, but you remember, we have to be best of 30. You guys just have to beat the S&P by 2% and you are geniuses. So each industry has its own challenges.

We’re like a pure play. It’s the lifeblood of our business, whereas in other businesses, I’d say execution probably matters a lot more. In all aspects, including coaching, a well-executed, slightly suboptimal strategy generally will be the best strategy poorly executed. I mean you know that.

That’s generally true in basketball as well. But I would say in our realm of decision-making, it’s really almost a pure decision-making thing. This draft pick beats that draft pick. This free agent for $5 million beats that free agent for $5 million. It’s more of a pure play.

Sports is actually way simpler than most of the people you talk to, way simpler. Our sport, it changes, but not much. Our data is pretty good. Our competitors aren’t coming out with new products. Our competitive dynamics are known.

They’re hard, but they’re — no, we don’t have the Rumsfeld problem of unknown unknowns, like some start-up in stealth mode that might emerge, like, that’s why academics have done more and more papers about sports.

Because if you’re trying to isolate how to make good decisions, sports is really the right area to do that in

This is a great section because it highlights how different domains just have different size error bars. Sports signals are stronger than investment signals. The counterbalance to that fact is when Morey says:

I talk to a lot of quants on Wall Street, and I tell them our signal to noise ratio using whatever measure you want….And they go like — yes, they go like, whoa, you guys are — that’s incredible. And I’m like, yes, but you remember, we have to be best of 30. You guys just have to beat the S&P by 2% and you are geniuses. So each industry has its own challenges.

Umm, beating the SP500 by 2% consistently is rarified air even if that number sounds small. Morey admits that only a handful of teams have the requisite talent to even compete for the title. So your probability of winning the championship is either 0 or likely much better than a professional fund manager beating the SP500 by 2%.

Asset managers win by being good salespeople (a friend called this the Matt Levine model — being a good hedge fund is about gathering assets when you get hot and keeping them when you get cold. It’s a scheme for getting rich that has a lot less to do with returns than the industry will admit. Come to think of it, being a valuable sports franchise probably has more to do with the logo and stadium than actually winning…it’s not that winning and returns don’t matter, it’s the gap between how much they matter and how much we think they matter).

I’m guessing Morey threw the 2% number out there without much thought. He was actually making a deep point that if an adversarial game is technically easier (say checkers vs chess) the competition enjoys the same low-difficulty advantage and you are in the same place of having a low chance of winning. But I was curious…how hard is it to beat the SP500 by 2%?

I’ll admit a question like this is in my friend Nick Maggiulli’s wheelhouse so when he reads this he’ll almost certainly have a more complete answer. But I decided to take a quick stab at it.

I pulled up the fund screener and filtered for US equity large-cap funds with at least a 5-year history benchmarked to the SP500 total return (this is an appropriate benchmark for a large-cap US equity fund.)

My criteria for beating the SP500 without getting lucky was the fund needed an information ratio (IR) of .50 or greater. An information ratio is outperformance normalized by tracking error. Tracking error is the standard deviation of the difference in returns between the fund and the SP500. If a fund outperforms by 2% per year but the tracking error is 10% (ie an IR = .2) that feels like noise vs a fund that outperforms by 2% with only 4% tracking error [I realize I’m using a simple, satisficey method for separating signal from noise, so if you are an allocator who just threw up in their mouth, brush your teeth then email me with an education so I can learn too!].

What did the screen turn up?

  • 45 out of 677 funds had IR of .5 or greater (caveat: the IRs use a 3-year lookback)
  • 8 funds out of 677 had at least .5 IR AND outperformed the SP500 total 3-year returns by 200 bps
  • Only 3 funds outperformed by 200 bps for 5 years (the IR ratio is still a 3- year lookback)

Daryl your point is well-taken but beating the SP500 by 2% with skill is 90s Bulls-level for public fund managers.

From My Actual Life

My music school does a class where you form a band for 5 weeks then perform. It’s a great way to accelerate learning. I’m on guitar duty for the show tonight.

Here’s the setlist:

  1. Can’t Let Go by Robert Plant and Alison Krauss
  2. Far From Any Road by The Handsome Family
  3. Fake Plastic Trees by Radiohead
  4. Plush by STP
  5. Stop Draggin My Heart Around by Stevie Nicks and Tom Petty

Ben and Kathryn handle vocals and the harmonies are why 3 of these songs are duets.

[In the Moontower survey this year many of you fretted (pun intended) about imposter syndrome. Well, in this group, 2 out of the other 4 musicians have albums out and a 3rd busked his way singing and playing guitar through Europe in his youth. Fck it…I’m gonna have fun and definitely not worry about my skills (desperate chuckle)]


Ok, talk to you all in mid-April. Until then stay groovy (and not like these 2 terrors 👇)

Moontower #183


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



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:

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.]

Moontower #182


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.

Similar posts I’ve previously published:

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

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:

These are more teen/adult appropriate:

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?


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
  1. Continue until you roll a ‘2’ (but don’t record the ‘2’)
  1. 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!

Moontower #181


My past self makes me cringe.1

I remember a weekend Yinh and I spent in Big Sur before having kids. We stayed at a resort/hotel place for free in exchange for listening to the timeshare spiel. I’m just pushing back on every point, complaining about the math this poor lady on the bottom-of-the-realtor-totem-pole is conveniently ignoring. Looking back, I’m genuinely sorry to have been acting myself in that moment.

When you feel your blood pressure rising you can channel some grace by just thinking of someone you know who would be smooth in that situation. The aspirational move here is just smile and nod. I had the situation exactly backward — it was me who was embarrassing himself, not her with the canned pitch as pushy and nonsensical as it was.

Luckily I have this moon letter thing as an outlet for my teeth-grinding financial complaints. I’m over the timeshare sales thing (well, actually I just pay for a room and save myself the grief. I admit this feels more like a hair dryer solution 2 than addressing the root of my anger) and onto another — I can’t stand when a life insurance salesperson pretends they are doing god’s work by telling me about their widow client’s big settlement. I’m not against buying insurance — I have car insurance and life insurance. But I’m against motte-and-bailey persuasion techniques. If a widow getting paid is deemed a self-congratulatory act of corporate benevolence then Warren Buffet is the priest of puts, a hokey paragon of virtue, backstopping markets with the heart of a patriot. Ok.

Defending life insurance by focusing on the settlements that get paid out is as silly as branding calls sold as income. And for the same reason — there is no consideration of price. Let’s compare:

Defense of insurance: “Look at the settlement the policyholder received. It has so many zeros in it.”

Rebuttal: That would be true even if the insurance cost twice as much. So the issue isn’t whether there would be a settlement it’s the proposition on the whole.

Defense of covered calls: “The premium you collect is extra income, and if the calls go in-the-money you’ll be happy anyway”

Rebuttal: This would be true if I sold the calls for 1/2 the price that I actually sold them for.

In other words, both of these defenses are empty words because they skirt the defining point:

It’s not the merit of the idea — it’s the price.

The wrong price will ruin any proposition. Ideas without prices are worthless. “It’s a good idea to brush your teeth.” But if brushing your teeth took 8 hours a day, you’re better off pulling them all and getting implants.

“It’s a good idea to get insurance” has the invisible qualifier “assuming the price is reasonable”. From there we can debate “reasonable” and we should. But I assure you the percentage of time spent in a life insurance consultation that’s devoted to decomposing its cost is not commensurate to how important it is in the decision.

Money Angle

Let’s harp on this “merit cannot exist independent of price” idea. We’ll return to insurance for a moment.

The griftiness of insurance sales as a function of complexity is an inverted U curve. Term insurance is not complex, it’s highly competitive and low margin. Private placements, which I’ve written about, are sold to very wealthy people who likely have a CFO-type managing their money. It’s the midwit crowd from all ends of the income spectrum that express their snowflake exceptionalism in exactly the wrong place and end up paying for their agents’ kids’ private school tuition.

Many insurance products are complex and seriously difficult to understand — every now and then I’ll take a hard look at one and just think, “they expect the average person to comprehend what’s actually going on inside this black box?!” And of course, the answer is “no”. That’s actually the point.

Here’s a tip — run away if you can’t understand the insurance product better than the salesperson. This is not as high a bar as you think. Salespeople are experts at sales not financial engineering. If they weren’t selling annuities they’d be selling cars or homes. (It’s a blanket statement so there are exceptions — but you know who will agree with me the most? Nerdy advisors who don’t have perfect teeth. This is the old Taleb bit “surgeons shouldn’t look like surgeons”.)

When I look at insurance products, especially structured products, I look for the options embedded in them. The costs for these options is opaque. Many of them have analogs in the listed options markets, but ultimately the ones buried in insurance policies resemble illiquid flex options with long-dated maturities and substantial padding added to their prices. If you wanted to be rigorous about valuing an insurance policy you’d need to know everything from the value of these hidden options to how much credit risk to discount the various issuer’s policies by. Apples-to-apples comparisons are impossible. This de-commoditizes the products giving unscrupulous salepeople ample room to practice their dark art.

An aside about options thinking

I know someone who negotiates and prices leases for commercial office space. They work on huge leases with clients like FAANG. One of the things they mentioned was how they would try to embed provisions in leases which were basically hard-to-price options. The person also spent a couple years with an options market-making group and is generally very quantitative — I would use the person for math help regularly.

I also know of a few wildly successful option traders who did quite well in personal RE investing by structuring options with potential sellers (one of these stories was focused on an ex-colleague of mine which was discussed in a certain big city’s media post-GFC).

And one more related bit — an option manager I know is friends with a fund manager who deals exclusively in the pre-IPO share market. This is a class of funds that provide liquidity to late-stage VC portfolio company employees. The manager was able to help the fund manager by showing them how a particular option embedded in their structures was deeply mispriced.

A final aside on the usefulness of option thinking…in Option Theory As A Pillar Of Decision-Making, I include this:

Getting to The Price

A current example of the need to assess a proposition by understanding its price comes from the boom in covered-call ETFs. Jason Zweig of the WSJ recently published:

Why Investors Are Piling Into Funds That Promise Not to Beat the Stock Market (paywalled)

After great returns last year, covered-call funds are all the rage among income-oriented investors. But their high yields aren’t a free lunch.

The article covers the explosion in AUM in covered-call funds like the JPMorgan Equity Premium Income ETF (JEPI) or Global X Nasdaq 100 Covered Call ETF (QYLD).

These ETFs manage roughly $20B and $6B aum respectively.

We’ll talk about QYLD because its holdings are published while JEPI is a discretionary, actively managed ETF. (But I still want to know who gets to hungry-hungry hippo those option orders!).

QYLD sells covered calls on the Nasdaq 100. That means it sells a call option while owning the underlying index. If you buy 100 shares of QQQ and sell a call option you could do the same thing. That’s not an argument against this product though. Ease is a valid use case for a product.

More background: it sells the 1-month at-the-money call as opposed to out-of-the-money calls which is what people generally think of with covered-call strategies (when I was just a boy they called these “buy-writes” but I haven’t heard that term since Arrested Development was on the air).

I’ve addressed “selling options for income” as euphemistic, sales-led framing. I’m not necessarily opposed to selling options but when you brand it as “income” you are blatantly misrepresenting reality. You are pretending the option premium is income when the bulk of it is just the fair discounted weighted average of a set of possible futures. My bone with the marketing pitch is that there’s no discussion of price. Again, whether this is a good strategy depends on price and the price isn’t static. (I feel like like I’ve force-fed you like foie gras on this topic. If I have to hear about this “strategy” from one more medical professional I hope I better be sedated on an operating table so I can finally drown it out)

When the marketers show me the level of implied correlations they are selling in the calls then we can have a good-faith conversation. Or how about when they tell me who the buyer for those calls is? Because I can assure you there’s no natural buyer — the boys and girls buying those calls are only doing so because they are too cheap. They didn’t wake up in the morning and think “I’m not going to look at prices, I just think owning call options that go to zero is a reasonable way to invest my money.” You know what traders are thinking when they see the marketers pitch: “Thank you for stocking the pond, we’ll be waiting”.

And they will be waiting. Market-makers are lions in the bush who know the dinner’s migration patterns. Unlike lions, they need to be discreet. You can’t just pounce and scare everyone off. You don’t want to make a scene. So they pre-position.

The market-makers’ pre-positioning serves a dual purpose.

  1. It spreads the market impact over a longer window of liquidity. This is actually pro-social — it’s “markets properly working”. The telegraphed order is not as scary even though it’s a large size because the end of it is known and there’s no adverse selection risk. It’s what’s known as a “dumb” or uninformed order. It’s not reasonable to expect zero market impact because unless there’s someone who wants to buy all these options, the pool of greeks need to be absorbed by a get-paid-to-warehouse-risk-in-exhange-for-profit entity. The market is just an auction for that clearing price and the greeks dropped on the market will be recycled in adjacent markets emanating from the original disturbance. (I.e. the market makers will buy vega from you and sell it in some other correlated market where the entire proposition presents an attractive relative value play — it’s just a big web. Market-makers are the silk between the nodes.)
  2. You want the option seller to get filled near the offer so they feel good about the fill. That’s what it means to “not leave a scene”. So now that you are short vol 3 days ahead of the anticipated arrival of the order, knowing that the current vol level incorporates the impact of your own selling, you are ready to buy the new supply “in line”. Remember this is not frontrunning. It’s a probabilistic bet. The market-makers have no fiduciary duty to the fund (as opposed to actual frontrunning where the broker trades ahead of an order they control). Market-makers want the brokers to “feel” like they got a good fill. There are no fingerprints. A TCA that looks at execution price vs arrival price is already benchmarked to a mid-market price that has been faded to absorb the flow.

What does this mean for the cost of something like QYLD?

A napkin math approach


  • At the current AUM, they sell about 5,000 NDX at-the-money call options (equivalent to 200,000 QQQ options) every month.
  • Implied volatility is about 25% so the fund collects 2.89% of the index level 3 in premium monthly. (Can you see how ridiculous it is to call this income? Would you call it income regardless of how little premium it collected? What if the option was in-the-money and they collected the same amount of premium? Conflating premium with income is a timeshare tactic except it’s pushed by corporations who know better not Jane “it’s this job or dogfood for dinner” Doe.
  • The ATM call is pure extrinsic value.

The question is how much vol slippage can we expect on that order. I asked around and a full vol point seems like a reasonable estimate. Because of the “setting the table” pre-positioning effect it’s hard to get a perfect answer. So we’ll use 1 vol point and you can adjust the final analysis by changing it.

If there is 1 full vol click of slippage and the option you sell is pure extrinsic, than you are losing:

1 vol point / 25 vol points x 2.89% of AUM x 12 months in annual slippage.

That’s 139 bps in annual slippage. That needs to added to the 60 bp expense ratio for the fund.

So you are paying 1.99% per year for a beta-like exposure created with vanilla products. And the alleged income is not income. It’s a correctly priced option premium in one of the most liquid equity index markets in the world.

Even if I grant you a 10% VRP (variance-risk-premium is an idea that options are bid beyond their fair value for any number of reasons like convexity-preference, hedging demand, or the possibility that markets allocate prices according to efficient portfolios and single assets being mispriced might not be from a portfolio point-of-view) that means the alleged income is 10% of what the marketers claim.

This whole trend in covered-call ETFs feels more like an innovation for getting paid for commoditized exposures in a fee-compressed landscape than an innovation that actually improves investing outcomes.

An (Overly) Candid Opinion

I’m not some socialist arguing against giving people an abundance of choice. I just want to remind you that no smart-sounding idea gets a free pass without consideration of its cost. And my own wholly personal opinion is you are paying a lot for convenience here. Plus the more AUM these things get the worse the slippage.

A saying I repeat too much: Asset management is the vitamin industry. It sells placebos. It sells noise as signal.

The proliferation of option products seems like something devised by products people not alpha people, a complaint I’d charge against most of the asset management world (which probably means I’m being too harsh but also I’m not criticizing any single firm — I don’t even know anything about these large fund companies because they were not part of my career genealogy. To me, they were always just the names of customers). Another reason I should be softer on all this is that, in aggregate, active management is critical. But there’s a paradox of thrift thing where we should (and this is dark) encourage it for others but not subscribe ourselves.

If you are truly obsessed and love investing then you can figure out your own way and maybe I’m just a faint admonishing voice in the background that you mostly ignore (I do hope I help you think better around the edges at least). But for the casual investor whose targeted by pitches and thinks they are missing out, you are given permission to live FOMO-free. There’s nothing to see except a midwit trap.

[And definitely don’t look at these. Gag me.

Actually, any TSLA options mm wants to gag me for raining on their parade. That should tell you something.]

Money Angle For Masochists

A few weeks ago I published A Socratic Dissection Of An Option Trade.

The post is part homework problems and part discussion. I see more posts like this in the future. This week I have another “homework” post:

New Post: Practice Pricing Options By Hand 📝

This assignment will help you do basic reasoning about option prices. It requires no more than elementary arithmetic and the concept of expected value.

There are 6 questions in total and the answers/discussions are included in the link.

It starts with:

A stock is fairly priced at $100. In one year, it will either be $50 or $125. What are the probabilities that make the stock fairly priced?

Step-by-step you will complete the following table.

By the end, you novices will have a fresh perspective on what delta means. Experienced readers will be reminded that your faith in model deltas relies on the distribution. Fitting skews, and by extension deltas, when the distribution is lumpy (think nat gas, earnings, FDA rulings, Fed Funds) is like trying to catch fireflies with chopsticks — you set your sheets based on the straddle printing and then the 28d put trades 10 ticks over your sheets and you’re sitting there “is vol higher or is the skew blowing out?” and then the longer-dated calls trade super cheap and your just “wtf is going on?”


From My Actual Life

I’ll just inject cuteness from my personal life since I feel like this was a cranky issue.

Moontower #180


I’m going to brag.

We pulled it off. That dream where your siblings or friends live in the same cul-de-sac and the kids just go back and forth to their cousins’ house. Built-in babysitting for impromptu date nights or even a night away.

My wife’s sister and her family moved into the house behind us 2 months ago. We cut a gap in the fence between the properties and my brother-in-law strung lights across the path (we get coyotes so the kids get extra-nervous traversing at night…we keep a box of small animal bones we find in the yard which reminds me I need to order one of these).

We are 2 families of 4 plus grandma who lives in an ADU at our house. The kids are 6, 9, 11, 13. The 3 younger ones walk to school together every day. The oldest is the only girl and despite her interests maturing quickly, the kids are thick as thieves. Any pair of them gets along great.

The arrangement comes with some costs. We all rent so there’s always the sword of displacement hanging over our heads. And renting in general doesn’t sit well with everyone (although I love it and it would take something really special to make me want to own again— I have zero interest in spending mindshare on my house). But the trade-off is worth it.

Just this week, we had 2 large family dinners next door plus a big Super Bowl party. The kids’ friends were around a lot, staying over for dinner, playing basketball in the driveways. There were 2 cousin sleepovers and on one night when Yinh had to catch up on work late into the evening, I just stayed up chatting with my in-laws until midnight (thanks for that you guys— we had some tragic news in our community this week, and it was helpful to have people to talk to IRL).

My brother-in-law has a home gym in a shipping container that’s on the property. I can pop over for a workout midday. He and our other friend/neighbor train together 3 mornings a week. And the meal plan situation should make you hate me. Grandma and my bro love to cook and will prepare dinner for everyone.

It has felt like a lucky plot twist. We sold our house over 2 years ago and explored moving to a lower-cost-of-living state. But like a couple that takes a break and realizes that the grass is not greener, we came back with a renewed commitment to where we live. Everywhere has warts. The only one that bothers us here is the cost of living. So we sat down and thought about our priorities hard. “Emotionally” moving (I mean we were serious — we bought a house in Texas and scratched the trade a year later after changing our minds) and coming back is an expensive but effective way to examine your priorities. But the price of information about ourselves has been an absolute bargain.

Leaning into our lives here and not wondering about “what could be” elsewhere, is incredibly liberating. It gave our in-laws the confidence to take the giant step of moving from the city to live near us. As adults neither my brother nor sister here has lived anywhere except SF — they still can’t believe it gets to the 30s at night out in the ‘burbs. It made investing time and money in our social club a no-brainer (I’ll eventually do an update about that — we are nearly 70 members now…the roster of events promoting togetherness and personal growth is taking shape and it’s a project I’m excited about and proud to be a part of. It also takes a village and I could see potentially writing a guide or blueprint for how to make this happen in other communities, but for now, we are still very much learning as it comes along).

Enough gloating.

I’m gonna do that thing where I take the concentrated dose of blue meth satisfaction and cut it so everyone can get a taste. I’ll generalize the lesson. Because that demonstrates the point: Community underpins all of this. It’s social bonds. It’s a reminder that the original social media was not just a performance for onlookers disguised as a conversation. It was touch. It was sharing. It was cooking for each other and helping each other’s kids out. But mostly, when you get to the heart of it – it’s being seriously invested in one another. If my in-laws are not well, I’m not well. Lives are meant to be interlocked. It’s a vulnerability for sure.

But is winning by yourself actually winning?

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.

Uses the latest research

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The Ezra calculator accounts for multiple lifestyle factors such as age, family history, etc..

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Your information is fully confidential and won’t be shared with anyone.

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Exclusive deal for Moontower readers: 

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Money Angle

There are a couple of ideas that tug on me with a force I haven’t felt before my experience in the last 2 years.

Regarding my career

It’s become more of a priority to sustain a living in a way that feels deeply tied to others. There are a lot of ways to make money, but finding a way that doesn’t feel alienating, finding a way that feels like I’m lifting others is harder to pull off. To be clear, any constraint limits your options. Expectancy-wise I’m paying for this preference the same way a remote worker might be taking a pay cut compared to the counterfactual. But this is only a concern if I measure expectancy only in dollars. That’s falling into a trap of letting legible accounting dictate all of what matters. You know what’s more baller — giving your soul a bank account and finding a way to stack it. That means more energy for everyone else around you.

Look, if you have the luxury of reading a Substack at your desk, then simply making money is easy. You just have to be good at something. By definition, mediocrity is everywhere. It’s a low bar for ambition. Making enough money on your terms takes either top 1% talent or being good at something plus courage. If you stop at just being above average at something, some overlord will always stand ready to make you part of their portfolio. But you’ll just be another asset to be rebalanced on their schedule.

You don’t become irreplaceable until you display how you are different (I’m obviously talking about the differences that are helpful while remaining aware that many strengths are weaknesses in other contexts). You cannot do this from a place of fear. You can’t maximize opportunities if you can’t afford to say no. So it stands to reason that you don’t want to build your life in a way that makes you unable to say no. That’s the real trap of conformity. Conformity isn’t clothing. It’s not even what you say necessarily. It’s relegating your agency for comfort to someone with a different mix of values because you were too lazy to identify your own. And the irony is they probably did the same.

[It’s out of scope for this post, but this idea is deeply intertwined with learning which I believe is really about agency and freedom from conformity. And I don’t mean that in some truther way which is just conformity sold as alternative. Like what “grunge” became. And I say this as someone with all the albums.]

Spending Money Strategically

I mentioned that emotionally moving was expensive. It’s expensive to transact real estate and travel. But the costs were worth the information. That’s a concept that exists in poker or even trading. For example, you can “fish” mid-market by dangling a one-lot to see where the bots live (and to defend yourself against such tactics, in a dark pool for example, you can define a minimum trade size).

In The Art and Science Of Spending Money, Morgan Housel offers a menu of ways to spend money that you may not have considered. #10 explains why:

Not knowing what kind of spending will make you happy because you haven’t tried enough new and strange forms of spending.

Evolution is the most powerful force in the world, capable of transforming single-cell organisms into modern humans.

But evolution has no idea what it’s doing. There’s no guide, no manual, no rulebook. It’s not even necessarily good at selecting traits that work.

Its power is that it “tries” trillions upon trillions of different mutations and is ruthless about killing off the ones that don’t work. What’s left – the winners – stick around.

There’s a theory in evolutionary biology called Fisher’s Fundamental Theorem of Natural Selection. It’s the idea that variance equals strength, because the more diverse a population is the more chances it has to come up with new traits that can be selected for. No one can know what traits will be useful; that’s not how evolution works. But if you create a lot of traits, the useful one – whatever it is – will be in there somewhere.

There’s an important analogy here about spending money.

A lot of people have no idea what kind of spending will make them happy. What should you buy? Where should you travel? How much should you save? There is no single answer to these questions because everyone’s different. People default to what society tells them – whatever is most expensive will bring the most joy.

But that’s not how it works. You have to try spending money on tons of different oddball things before you find what works for you. For some people it’s travel; others can’t stand being away from home. For others it’s nice restaurants; others don’t get the hype and prefer cheap pizza. I know people who think spending money on first-class plane tickets is a borderline scam. Others would not dare sit behind row four. To each their own.

The more different kinds of spending you test out, the closer you’ll likely get to a system that works for you. The trials don’t have to be big: a $10 new food here, a $75 treat there, slightly nice shoes, etc.

Here’s Ramit Sethi again: “Frugality, quite simply, is about choosing the things you love enough to spend extravagantly on—and then cutting costs mercilessly on the things you don’t love.”

There is no guide on what will make you happy – you have to try a million different things and figure out what fits your personality.

Recently, I’ve seen a wild example of this.

My wife has a close friend that was in the rat race grind. After joining Yinh on the board of OrFA, the friend has been regularly visiting the orphanage in Vietnam. She’s a tall blond, as American as apple pie. A stranger in a strange land in the Vietnamese countryside. But she found herself deeply moved by not only the children but the local culture and all its people. She has dramatically re-arranged her entire life to prioritize her involvement and presence in Vietnam. Witnessing the impact on an otherwise familiar, professional life that started with a donation and some curiosity has been a powerful frame shake. (My family, 13 of us in total, are going to Vietnam for a few weeks this year and have already planned a soccer match between all the kids at the orphanage. If my kids moan about what’s for dinner after that trip, they’re getting lit the f up).

This is a reminder. You can just do things. You can’t introspect your way to knowing what you want. It’s too much projection of your current self into a different reality. It doesn’t recognize that the feedback changes you.

Spending money in a new way is just another method to try on different versions of yourself. To explore personal frontiers on the not-so-crazy lark that there are deeply rewarding modes to explore the world that you are completely ignoring. Your fixation on the crowded paths your surroundings have directed you towards might frustrating, not because of any personal failings, but because those paths are overbid (look no further than the college admission Hunger Games).

If you can’t be happy unless you get that house or that wedding or that title, it’s not because they are your destiny — it’s because you haven’t taken your imagination off-leash.


Money Angle For Masochists

New post:

Using Log Returns And Volatility To Normalize Strike Distances (8 min read)

We start with a review:

Consider a $100 stock. In a simple return world, $150 and $50 are each 50% away. They are equidistant. But in compounded return world they are not. $150 is closer. This blog post will progress from an understanding of natural logs to normalizing the distance of asset strikes.

We extend the review to a math lesson. If you have ever struggled with natural logarithms and e, this is your lucky day.

You probably remember hearing about the constant e and the natural log from math class. You also repressed it. Because it was taught poorly.

You might already know how to annualize compounded returns. You will learn how to annualize log returns by understanding how to decompose e into 2 components: rate and time.

Thus far we have learned to standardize distance or growth rates using continuous compounding. An unfancy reason why this is useful is you don’t need to footnote every compounding example with an interval. A total return and compounded return vary with the interval. Log returns dispense with the need to quibble about intervals.

At this point, we have normalized returns for continuous compounding.

Now we can go to the next step and standardize returns based on an asset’s volatility. This is how we find the moneyness of strikes. This is the beginning of proper comparisons and benchmarking. This is the essence of measurement, which is what I emphasize is most of the job-to-be-done in trading. It’s kind of like how data science is mostly cleaning data. The analysis is often the easy part.

By the end of the post, you will have done nothing but a little logic and simple algebra to understand this picture:

The post concludes:

What’s the point of all this?

For anyone within sneezing distance of a derivatives desk, these are rudiments. These computations are the meaning behind the Black Scholes’s z-scores (d1 and d2) and probabilities. These standardizations are critical for comparing vol surfaces. If you can’t contextualize how far a price is you cannot make meaningful comparisons between option volatilities and therefore prices.

If you only trade linear instruments because you are a well-adjusted human then hopefully you still found this lesson helpful. Seeing math from different angles is like filling in the grout in the tiles of your mental processing. You can measure the distance (or accumulated growth, positive or negative) in log space to account for compounding. You can standardize comparisons by using the asset’s vol as a measuring stick. And after all that, if you still don’t enjoy this, you can feel better about your life choices to do work that doesn’t rely on it.

If you do rely on understanding this stuff, hopefully you got e.00995-1 better today.

Stay groovy!

Moontower #179


[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.

Uses the latest research

The Ezra Cancer Risk Calculator is based on the Harvard Cancer Risk Index developed by the Harvard Center for Cancer Prevention

Considers your lifestyle

The Ezra calculator accounts for multiple lifestyle factors such as age, family history, etc..

Fully confidential

Your information is fully confidential and won’t be shared with anyone.

You can complete the 5-minute quiz by clicking here.

Exclusive deal for Moontower readers: 

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 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. 

  1. 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 LindstromMike 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!