Moontower #185

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 #184


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 #183


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 #182


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 #181


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?

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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 #180


[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.

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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!

Moontower #179

I’ll be brief up top today because both Money Angles are long.

In Wednesday’s Munchies I linked to Notes From Your Move (What Boardgames Teach Us About Life)

I forgot one fun bit Joan Moriarty wrote in the book:

At family gatherings, my father’s relatives used to play [a game] called Fictionary. One player would take a dictionary, open it to a random page, find a word none of the players knew (this might take a couple of tries) and then write down the definition. The other players would each invent a phony definition for the word, write those down, and pass them to the player with the dictionary. Then, one at a time and in a random order, all the definitions, real and fake, would be read aloud. On the second reading, the players would try to guess which was the real definition. They would score one point for guessing correctly, and one point for each other player who was tricked into that their phony definition was the real one.

Party game fans will feel deja vu. This is the game Balderdash.

Joan makes a comment in the book about how sometimes a clever entrepreneur can get people to pay for something that is actually available for free. I love the game Decrypto but it’s also a game that you could play for free. Unlike Balderdash, the game components and art are actually pretty cool. Take my $20 please.

I do have fond memories of playing Balderdash with a group of NYC friends back in the day. My friend Ben had written a couple amazing answers that I kept in my wallet for many years until the ink finally bled off the slips of paper. One twist we added is to keep a spreadsheet where you log who voted for who’s answer every round. We liked seeing if certain people were susceptible to another player’s specific writing style.

I think my friend Lukshmi had me pretty dialed in.

Anyway, go play some games.

Well read about money first, then go play some games…

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Money Angle

Here’s a simple coin flip game. It costs $1 to play.

  • Heads: you get paid an additional $1 (ie 100% return)
  • Tails: you lose $.90

The expectancy of the game is $.05 or 5%.

We compute expectancy:

.5 * $1.00 + .5 * (-$.90)

It’s exactly the same calculation as a weighted average or arithmetic mean. This is a useful computation for many simple one-off decisions. Like should I buy an airline ticket for $1000 or the refundable fare for $1,100?

If there’s a 10% chance I need a refund then the extra $100 saves me $1,100.

10% * $1,100 =$110 which is greater than the $100 surcharge. 9% is my breakeven probability.

It’s tempting to use this logic in investing. Let’s say you expect the stock market to return 7% per year on average for 40 years. Start with $100 and plug in numbers:

$100 * 1.07⁴⁰ = $1497

Yay, you expect to have about 15x your starting capital after 40 years!

Eh. Sort of.

See the word “expect” in math terms and in colloquial terms is a bit different.

If I bet $1 on that coin game I theoretically expect to have $1.05 after 1 trial. In reality, I’m either going to end up with $2 when I double up or $.10 when I lose.

Another example:

I roll a die. If it comes up “1”, I win $600. Otherwise, nothing happens. Theoretically, I expect to win $100:

1/6 * $600 + 5/6 * $0 = $100

But if I asked you what you “expect” to happen if you play this game…you “expect” to win nothing. You only win 1/6 of the time after all.

Back to the investing example.

Investing is not a one-off game. It’s a compounding game where you plow your total capital back into the sausage machine to get that 7%

That’s why we use 1.07⁴⁰.

You are counting on your $100 growing by 1.07 * 1.07 * 1.07…

So that 15x number…that’s mathematical expectancy the same way the dice game is worth $100 or the coin game is worth $1.05 even though those outcomes are never actually experienced.

What you expect to happen in the colloquial sense of the term is the geometric mean. The arithmetic average is a measure of centrality when you sum the results and divide by the number of results. (In our examples you are summing results weighted by their probabilities, but you are still summing). The geometric mean corresponds to the median result of a compounding process. Compounding means “multiplying not summing”. The median is the measure that maps to our colloquial use of “expected” because it’s the 50/50 point of the distribution. That’s the number you plan life around.

The theoretical arithmetic mean result of playing the lotto might be losing 50% of your $2 Powerball ticket (which is another way of saying you are paying 2x what the ticket is mathematically worth). The median result is you lit your cash on fire. You plan your life around the median, especially when it’s far away from the mean. We’ll come back to that.

With investing we are multiplying our results from one year to the next together. The geometric mean is what you actually “expect” in the colloquial sense of the term. The geometric mean is more familiarly known as the CAGR or ‘compound annual growth rate’.

What is the relationship between the arithmetic mean to the geometric mean? This is the same exact question as “what is the relationship of mathematical expectancy and the CAGR?”

It’s an important question since that theoretical arithmetic mean is only expected if we live thousands of lives (actually there are ways to experience the arithmetic mean without relying on reincarnation. This is pleasant news because what good is being rich if you come back a pony.) We want to focus on the CAGR, which is much closer to what we might experience.

It turns out that number is lower.

How much lower? It depends on how volatile the investment is. The formula that relates the arithmetic mean and CAGR:

CAGR = Arithmetic Mean – .5 * σ²


σ = annualized volatility

If an investment earned 7% per year with a standard deviation(ie volatility) of 20% you can estimate the CAGR as follows:

CAGR = .07% – .5 * .20² = .05

In arithmetic expectancy, over 40 years you expect to earn 1.07⁴⁰ = 15. You expect to have 15x’d your money.

But the median outcome, which corresponds to the geometric mean is 1.05⁴⁰ = 7.

7x is much closer to what you “expect” in the colloquial sense of the term. Less than 1/2 the arithmetic expectation!

The formula tells us that the arithmetic and geometric mean (“CAGR”) will diverge by the volatility. And that volatility term is squared…which means the divergence is extremely sensitive to the volatility.

This is a table of CAGRs where you can see the destructive power of volatility:

Why is volatility so impactful on a compounded return?

An easy way to see the impact of high volatility is to imagine making 50% and losing 50%. The order doesn’t matter. You have net lost 25% of your initial capital.

We can compute the geometric mean by weighting each possibility by its frequency in the exponent (in this case the exponents must sum to 2 because that’s the sample space — up and down):

.5¹ x 1.5¹ = .75

Go back to the first game in the post. You invest $1 in a coin game. Heads to make 100%, tails you lose 90%. This game had a positive arithmetic expectancy of 5%.

What is our arithmetic expectancy if you compound (ie re-invest) by playing 2x then the total possibilities are:

HT: 2 x .1 = .2

HH: 2 x 2 = 4

TH: .1 x 2 = .2

TT: .1 x .1 = .01

Since each scenario is equally likely (25% each) the arithmetic expectancy is simply the average = 1.1025

This jives with 1.05² = 1.1025

The average arithmetic return compounds as expected.

But our lived (median) experience is much worse. The median result is .20, a loss of 80%!

We could have seen that by computing the geometric mean:

2¹ x .1¹ = .20

Driving the point home with an extreme example

Consider a super favorable bet.

You roll a die:

  • Any number except a ‘6’: 10x your bet
  • Roll a ‘6’: Lose your entire bet

The arithmetic expectancy is ridiculous.

5/6 x 10 + 1/6 x -1 = 8.167 or ~700% return

But if you keep reinvesting your proceeds in this bet, you will go bust as soon as the 6 comes up. The median experience is a total loss, even though the arithmetic expectancy compounded is wildly positive. If you played this game 20 times in a row you’d [arithmetically] expect to make ~ 700%²⁰.

But you have a 97.4% chance of going broke because you need “not a 6” to come up 20 times in a row = 1 – (5/6)²⁰

That arithmetic expectancy of ~ 700%²⁰ is being driven by the single scenario where the 6 never comes up (that occurs 2.6% of the time). In that case, your p/l is $10²⁰ or between a quintillion and sextillion dollars.

But the geometric mean is 0 because multiplying over the 6 sample spaces:

10⁵ x 0¹ = 0

I chose such extreme examples because nothing illustrates volatility like all-or-nothing bets. The intuition you need to keep is that high volatility means you should expect to lose your money even if the arithmetic expectancy is high.

As soon as you start re-investing (ie compounding) your results are going to be governed by that geometric mean which hates volatility.

For the people who tout lotto ticket investments like crypto or transformative technologies with talks of “asymmetrical upside” or “super positive expectancy” remember even if they might be right, the most likely scenario is they lose all their money on that investment. Even literal lotto tickets can tip into positive expectancy. When that happens how much do you put into it?

Exactly. Not much. Because you know what to expect.

The role of rebalancing and diversification

Investing is not a one-off game. You always re-invest. By re-balancing, you “create” more lives by not concentrating your wealth in a single bucket which swamps the rest of your portfolio as it grows. If you never rebalanced BTC on the way up it would have eventually become nearly 100% of your portfolio and then 2022 happened.

If you don’t ever rebalance you are effectively praying that “not a 6” comes up for the 40 years you are compounding wealth. It’s not as extreme as that because market volatility isn’t as extreme as dice or coins. But the principle holds.

You only get one life so you care about the median. Diversification plus rebalancing gives you the god-perspective of getting to invest a fraction of your wealth into many lives.

Keep in mind — rebalancing is not changing your overall expectancy; it’s changing the distribution of returns by pushing the median return (geometric mean or CAGR) up to your theoretical arithmetic return. This trade-off is not free. If you rebalance you don’t get the 1000x payoff that occurs when a single concentrated position hits 50 heads in a row.

Money Angle For Masochists

Imagine a $100 stock that can either go up or down 25% every year.

It’s 50/50 to be up or down.

Let’s look at the distribution of the stock after 4 years (with the probabilities of each price below it)

Look at the extremes after 4 years:

  • $31.64A -25% CAGR over 4 years = cumulative loss of 68%
  • $244.14A +25% CAGR over 4 years = cumulative gain of 144%

If you sumproduct every terminal probability by terminal price you get $100. And yet, while the stock is fairly valued at $100, after 4 years, you have lost money in 11/16th of scenarios (~69%). The right tail is driving the fair value of $100 while most paths take the stock lower.

This is the mathematical nature of compounding. The most likely outcomes are lower even if the stock is fairly priced.

In the real world, stocks don’t just flip up and down like coins. The probabilities are not 50/50 and there aren’t just 2 buckets they can rest in from one year to the next. The beauty of option surfaces is they allow us to separate the probabilities from the distance of the buckets (and the number of buckets is continuous…there’s no price the stock is not allowed to go to).

Here’s some homework you can do with the above data:

  1. What’s the value of the 4-year $146.68 strike call worth?
  2. What’s the value of the 4-year $75 strike put?
  3. How about the 4-year $125 call?

Bonus Questions

Imagine this stock is an ETF and there’s a 2x levered version (which means it’s 2x as volatile) of it.

  • What strike call on the levered ETF is equivalent to the $146.48 strike on the unlevered ETF? (Hint: It’s further than $46.48 OTM)
  • What’s the value of the call at that strike?
  • If I was a market-maker and I got lifted at fair value on the 2x levered ETF 4-year 200 strike call and I go buy the regular ETF 150 4-year 150 calls to cover my risk how many do I need to buy to be perfectly hedged? (Assume you can buy them for what they’re worth…you have enough information to compute their fair value).

If you got through this then you have a new appreciation for how far certain prices are from a spot price and how it depends on time and volatility!

(Solutions & discussion in the footnotes of Well What Did You Expect)

Starting from basics like the volatility tax, progressing to how path influences the volatility tax (trends are more like a volatility rebate and choppiness is a tax….the ratio of trend to chop will determine the ultimate cost of the volatility), and finally bridging these concepts to Black Scholes this series will take your understanding of compounding and how returns work to a deeper level.

  1. The Volatility Drain
  2. Path: How Compounding Alters Return Distributions
    [Between this post and the bonus questions you can start to see why pricing OTM options on levered ETFs given a liquid options market on the unlevered version is an application of these concepts]
  3. Solving A Compounding Riddle With Black-Scholes

Shout Out To Matt Hollerbach

Despite trading options for nearly 20 years at the time, it wasn’t until 2019 that I thought really hard about compounding. I knew how to manipulate formulas and how it related to options but it wasn’t until I discovered Matt’s work that I started to see it from a new angle. Matt makes it approachable and builds up insights in small steps. His blog inspired mine, especially many of my earlier posts. The entire blog is worth spending time working through. It’s similar to what I’ve said about gambling — it’s a place where you will learn how to think about risk and return far better than what finance texts will teach.

These are all-time great ones:

Trend Following is Hot Air

Investing Games

Solving the Equity Premium Puzzle, and Uncovering a Huge Flaw in Investment Theory

It’s painful to watch the median (or should I say average) “investor” reason about how markets work because without these intuitions (you don’t need to know formulas necessarily) you are innumerate. That’s like being illiterate but for like numbers and stuff. And the deficiency is as obvious as illiteracy is to a literate person.

The good news is we can all get better.

Moontower #178

Economist, author, and host of the Econtalker podcast (running since 2006!), Russ Roberts is one of my favorite public personalities. He is wise in the holistic sense of the word. He brings a wide perspective to every topic and guest, including those he disagrees with.

As he promotes his new book Wild Problems: A Guide to the Decisions That Define Us which addresses the important decisions in our lives for which data is not a helpful guide (like marriage, where to live, etc), the microphone is being turned back on him — he was recently on Tim Ferriss’ show. The episode is great but I want to talk about a topic that comes right at the beginning — parenting.

Tim quotes from Russ’ eulogy to his father:

“I sometimes think that my dad really could have been a minor American poet or a more renowned storywriter if he had spent less time with his children and grandchildren. The tradeoff was easy for him…He chose us.

“He had many talents. Being a father was the talent he chose to cultivate.”

“All of us who survive him, his good wife, his children and his grandchildren, are so lucky that we had him for so long.

“So If you want to honor my father’s memory, spend more time with your children. Or your parents. Or those you love. For Dad, quality time demanded quantity time. It’s harder than it seems. So many things, more tangible, more alluring, with more immediate returns, call for our attention and distract us.”

He expands during the conversation with Tim (emphasis mine):

I think parenting, but more than parenting, life requires paying attention. And I would say my dad was one of the least meditative people who was born in 1930. There weren’t that many of them, to be honest. It’s a more recent phenomenon, but my dad had zero — I went on three silent meditation retreats while he was alive. And he found that utterly bewildering. So he was not a meditator, but he understood somehow that principle about paying attention to what’s important. And what was important to him was us, his children and his wife and his family. As I said, he used to complain. He said, “It’s terrible. God gave me such a big soul and so little talent. I have so much to say, and I can’t say it.”

He wanted to be a poet. He wrote lots of poems, many of them pretty good. He liked a few of them. And his joke really was — you read the line, but the joke was, he’d like to be a minor American poet. Didn’t want to be Robert Frost or Edna St. Vincent Millay. He would have been happy to be a quieter person with a couple good poems. And he might have achieved that if he had devoted himself to that craft, but he instead devoted himself to us. One of my favorite things about my dad, when we had our kids and I’d say, “Dad, you want to read a story? You want to read a book to one of my kids?” He was so disdainful of that. The idea of reading a book that someone else had written was so cheating to him. All of his stories were made up. He told us hundreds of stories, my children hundreds of stories that he crafted, that he made up. And he could have been a great children’s writer. He could have been maybe a minor American poet, but he spent most of his time with us, his free time.

These excerpts grabbed my attention because, while beautiful, they are not the only way. The larger question for any parental approach is — Are you doing this for kids? Or for you?

A dad I was speaking to recently had his first child. He had been reading me for a while and presumed that my decision to stay home was calculated as the best thing for my kids.

I stopped him right there to share a bit of wisdom that has stayed with me from another friend and his wife. I’ll share it here as well. A little background first. Both members of this couple are elite talents (mentally and physically — genetic mutants kinda). They ultimately split duties explicitly. Where one pursued career, the other managed the family life. But to get to that point there was tremendous introspection about priorities. There was even an off-the-grid type arrangement on the table. They were thinking intentionally, skeptical of the comfort of canned life scripts. And this is despite the fact that one of them is world-class at their profession. Like Russ’ father, they were willing to table personal ambition if that’s what their hearts decided was necessary. In fact, they were torn because the pull to be present with their children was powerful. These pulls, in a spreadsheet sense, were especially expensive given their opportunity costs.

(On an episode of FoundersI learned that David Ogilvy was blown away by an employee who’d consistently leave the office at 5pm. He wondered how this individual could have such discipline! Ogilvy reveals something people often don’t admit — your martyrdom about work can be the opposite — it’s often selfish. High performers are ambitious. They would rather work than go home. Your family’s holistic needs extend well beyond money. Are the boundaries you draw for them…or you? And what stories do you tell yourself about where you draw them?)

I asked them how they eventually decided to have one parent go all-in on their professional career and they harkened back to their own parents. One of them had a father who was like the dad of the neighborhood. He was an active local sports coach too (he himself an Olympic-level athlete) but he was just that guy that the whole town knew. A super-involved community member, all the kids called him coach. His posture is reminiscent of Russ’ description of his own father.

The other member of the couple had a father who was always working. But here’s the thing — both members of the couple felt the same. A deep sense that their fathers loved them. The fathers were as different as their approaches. The introvert and neighborhood “dad”. But their children all felt open lines of communication to their fathers.

And then it dawned on me. Your approach is not about your kids. It’s about you. You can rationalize any specific life plan as “for your kids” but as long as they feel loved, you’ve done your job. My mother was the work-all-the-time archetype. She had to be. She didn’t finish college, got married too early, and often worked 2 jobs. My sis and I were classic 80s latchkey kids. But my mom has always been a best friend. I could talk to her about anything. I was a very insecure kid, always trying to fit in, and increasingly difficult as I got older. But she is a great listener. She never judged me. And while she always challenged me, it was clear — her love was unconditional. All of this was an open invitation to confide in her1. Even if she was at work all the time, there was always an open ear for me.

Russ’ sentiments are profound personal expressions of love and gratitude. But they are not prescriptive. They are simply “my dad lived like X, and we are thankful”. They are opinions reflecting Russ’ own values. Optimizing for kids to reflect back on you the way Russ reflects on his own dad might not work. You are not Russ’ dad. And your kids might not have Russ’ needs.

My own view is staying home with your kids is about what you want. My mom has openly regret that she wasn’t around more, not for us, but for her. She wished she “enjoyed” us more when we were children. But as kids we relished the freedom. Playing with mom wasn’t important to us. She’s not fun like that. And that’s ok.

Your parenting approach is a personal mold to fit within the contours of your strengths and weaknesses. You can find inspiration in others but not a recipe. Don’t let the pressures to be [insert type of parent] come from anyone else. The internet will gladly serve you as much FOMO as you’ll take.

Every time I see this ad I want to swing copywriters right into the sun. GFY.

Money Angle

A theme I harp on is that investing is biology not physics. It’s a competitive game. You figure something out, the game adjusts. When people say “X happens in Y-year cycles” they are thinking like an astronomer who notes the fixed periodicity by which the Earth orbits the sun. This is physics thinking.

But markets price in common information.

Housing has been an inflation hedge. But if everyone knows that, will they bid it up until it’s not? If someone pays 2x the Zestimate for your house, then is this “investment” still an inflation hedge?

Absolute statements in the world of investing without any consideration of price are a red flag that the speaker doesn’t understand the difference. We know the Celtics are good. But what matters to a bettor is their record against the point spread. The point spread is why investing will never be QED’d.

You can learn more about investing from games and betting than books that have “investing” in the title. The investing books are fine for glossaries and knowing the mechanics of a bond just as the rulebook is imperative to play Scrabble. But the rulebook, like the textbooks, teaches you nothing of how to be good at the game at hand.

In an adaptive game, you need to see the next level. Let’s look at 2 types of second-level.

“Theory of Mind”

Wikipedia defines “theory of mind” as the “capacity to understand other people by ascribing mental states to them.”

In poker, when you bet, you know your cards and some sense of how they might rank at the table. But the key piece of information, is “when I make a bet, what hand do my opponents think I have?” Without considering such second-order knowledge how do you weigh the information you receive when they call your bet? You must inhabit your opponent’s mind. It’s the same skill you need to interpret market prices (see Staring Out The Window). What expectations and beliefs are in the price? This is second-order thinking.

Second order sensitivities

Besides second-order thinking, we must identify second-order effects. In the options world, the “greeks” are sensitivities. Delta is the option’s sensitivity to the underlying. Gamma is a second-order sensitivity that describes how an option’s delta changes with respect to the underlying.

But this topic is everywhere. If a company sells more widgets it makes more profit. But second-order effects mean attracting more competition or saturating a market. Every satisfied customer is one less customer that needs satisfying. So if I build a model of profitability based on units sold, when does the function inflect? When does opportunity fade into unsold inventory?

[A fun way to think about second-order sensitivities is playing “engine builder” boardgames like Dominion or Wingspan where synergies between your cards lower the marginal costs of later actions2. In essence, the cards have gamma based on how you stack them. Every time I use a card it might increase my odds of winning by X. That’s the delta or “benefit per use”. But the delta itself increases with synergy, so as the game progresses, you get more delta or benefit/use ratio, from the same card]

An exercise in thinking about second-order sensitivities

Commercial real estate investor Bill Lenehan on Invest Like The Best:

Here in Marin County, where values have gone up substantially and having a small house in Montana, where that market has similarly boomed post-COVID is that it is unquestionable that these property values are not sustainable…As someone who’s trying to build a business, which includes recruiting people, training them, compensating them, et cetera, doing that in this housing market is substantially more challenging. Well, I guess it feels good that the house is worth more than you paid for it. Net-net, I would welcome a decline in housing to a more normalized level.

Bill is looking at second-order effects. What would it look like if we translated bits of this quote to “greeks”?

Bill’s personal net worth sounds like it had an uptick because he owns a home in Marin. But he knows it would go up even more if it didn’t go up by residential home appreciation. That’s because he knows he has a larger delta to his business than his home.

Define delta as a change in Bill’s net worth with respect to real estate prices

What does this depend on?

For our narrow example, we will limit this to 2 sources of his net worth.

  • The weight of his home as % of net worth
  • The (delta of his business to RE prices) x (his ownership of the business)

But delta of his business to RE prices decomposes further:

  1. There’s the value of his company’s real estate
  2. The expected growth of the business which depends on operating margins amortized into a current valuation.

Bill recognizes that the growth of the business is the largest driver of his net worth and the rise in value of his Marin home represents a slowdown on this larger (albeit nebulous) factor.

First-order thinking is delta. “What happens to my income if I work more hours?” That’s a simple line with a slope of “pay per hour”. Suppose the extra work means you need to employ a babysitter. The slope is just “net pay per hour after paying the sitter”. But if the sitter is a student who can only work an additional 5 hours per week, then the delta or net pay per hour changes because you need to find a higher-priced sitter at some threshold of hours. That’s gamma – the change in your delta. What if there are no other sitters? Then you hit a wall. Your payoff function is abruptly halted. Or what if it inflects because now you need more massages because work makes your body hurt? These are all second-order effects on your delta (slope = net pay per hour) with respect to an increase in hours.

Mathematically, deltas are the slopes of lines. The cause-effect relationship of anything important is rarely so simple. It is convenience that compels us to describe how things work by pointing to lines. The deltas themselves change reminding you that linear thinking is just a snapshot in time. In fact, that’s all a calculus derivative is — zooming in so close to a function that its slope at that point describes a line.

When you listen to explanations, try to fill in the gaps of logic that the speaker understands but are unsaid. You are making the “greeks” or sensitivities explicit. Then you are only one step away from asking “what other greeks are at play?” and what is the “shape of their functions?”

To ponder:

What does a “too much of a good thing” function look like?

How about a hormesis (ie “a little of bad” thing) function?

What does a discontinuous phase transition(ie “gas > liquid> solid”) look like?

What does a logistics or S-curve function signify?

What phenomena follow a convex function? A concave function?

What’s a “winner-take-all” function look like?

Money Angle For Masochists

My bias is traders should study gambling, not investors and definitely not macroeconomics. I feel trading requires self-awareness and unique mix of humility and confidence. Humility demands questioning how you know what you think you know. But this is also a description of a cat chasing its epistemological tail. This needs to be balanced with the confidence to make a decision before you are comfortable, otherwise, you will be too late.

This brings me to Aaron Brown’s article in Bloomberg (paywalled):

Want to Succeed on Wall Street? Learn Poker, Not Economics

These excerpts will save you a click.


The Federal Reserve Bank of New York in conjunction with researchers at the University of Southern California and University College London for a paper titled Strategic Sophistication and Trading Profits: An Experiment with Professional Traders. The authors recruited 56 professional traders, plus an equal-size sample of students for controls, and evaluated their performance in a computer-simulated trading game. They then tested their subjects on a wide range of specific skills to see which skills were correlated to trading success.

Main findings

  • Among students, the only useful predictor of trading success was general intelligence.
  • Among professional traders, though, neither intelligence nor other personality traits and cognitive skills mattered much. Success did not depend on any fundamental insight about value. What mattered was strategic sophistication in the sense of taking an analysis of other people’s behavior to high levels. This calls to mind the folk wisdom found in poker, which is that “beginners think about their cards. With a little experience, they start thinking of the other guy’s cards. Poker begins when you think about what the other guy thinks about your cards.” The Fed paper suggests that professional traders are playing poker, while the students are playing games like chess, backgammon, or blackjack that depend on intelligence rather than guessing what other people are thinking.
  • The paper’s finding goes well beyond the claim that strategy is valuable for trading. It suggests that other things such as intelligence, risk strategies, personality traits or knowledge of fundamental value do not matter — or at least are evenly distributed among traders that they can’t be used to predict success.

Murky interpretations

  • The Fed paper did not find any advantage to years of education or experience or other indicators of trading. Who should you believe? The Turtle experiment and Wall Street folk wisdom have one great advantage, in that they are based on real people trading large amounts of money in real financial markets. Unfortunately, that makes controlled experimentation prohibitively expensive. Formal studies and other academic work conducted under laboratory conditions make the results much more scientific but at the cost of being one layer removed from reality.
  • If you are not a trader but want to be one, either for your own account or for an institution, the study suggests you should play poker rather than attending class and take game theory courses over economics…but
  • Conventional wisdom says you should develop your comparative advantages, whatever they are, and study successful traders. If your interest is to understand the economic function of trading, the study suggests it is a game that rewards aggregating information from others’ bids and offers and using that information to provide liquidity. Conventional wisdom suggests trading is a broader skill that combines fundamental and technical information to produce an equilibrium, with many different types of traders performing different functions.

Practical upshot (emphasis mine)

If you like poker more than class and game theory more than economics, it’s good news. You may lose in trading competitions with fellow students, but you have a bright future on Wall Street. On the other hand, if you’re counting on traders to assess fundamental economic value, the study is bad news. It suggests they’re focused on outsmarting each other, not on investigating reality.

Whatever you think about the study and possible implications, it’s always good to see a careful, controlled, rigorous analysis in an area where opinions tend to be much stronger than the foundations for those opinions.

For an outro enjoy:

Spread’em Tight by

This is a nice post about option market-maker thinking. My own description of the job:

Pay me $10k up front and I’ll flip a $1mm coin with you

Stay groovy!

Moontower #177


Let’s review December’s Moontower reader survey. For context, this letter went out to ~ 9k recipients and has an open rate of 50%. 180 readers responded, or about 4% of the typical number of readers who open the letter.

[The actual views of the letter are 2x that number routinely and for a popular issue I’ve seen as high as 5x that number as it gets passed around by men who stare at computer screens all day. More on that ahead.]

My guess, based on how the responses rolled in, is that it mostly represents subscribers as opposed to people who clicked on the Twitter link. 180 responses was about 2/3 of what I was hoping for, but based on Zoho’s survey math it’s not a terrible sample — 95% confidence, 7% margin of error — which feels like a decent enough resolution. The bigger question, as is the case with any survey, is whether the sample was representative. My gut says yes because I wasn’t too surprised by the results.

We’ll start with numbers before getting to the provocative part — the answers to the open-ended questions. The anonymity brought out honest, vulnerable answers.


  • 2/3 in US
  • 20% non-white (Indian and Asian most common minority)
  • 70% b/t 25 and 45 yrs old
  • 45% have children (90% of parents have kids college-aged or younger)
  • 95% male (Male heavy, not surprising but 19 to 1?! Can’t say this didn’t rattle me)

Politics and Education

  • 85% moderate to progressive political leaning
  • More than 1/3 have a graduate degree
    • 1/3 of the grad degrees are a terminal degree (MD, PhD, JD)


  • >50% in finance
    • 50% of these are in asset management front offices (risk/trading)
    • 14% of these are advisors or allocators
  • 25% software


  • 40% director/founder/c-suite
  • 12% entry level


  • 50% > $250k annual household income
  • 11% > $750k annual household income (concentrated in asset management/front office/securities brokerage)
    • 50% of this cohort >$2mm annual household income


  • 50% self-report as “accredited investors”
  • Only 15% have more than 40% of wealth in home equity
  • 50% could estimate the annual volatility of their portfolio (this percentage is also true for the people with > $750k income)
  • 50% of respondents give more than 1% of income to charity;
    • Of the people who give more than 1%, 30% give more than 5%


Open Ended Questions

Some preamble:

  • Thanks for the honesty
  • I took liberties in the name of summarization by assigning most of the responses into general categories but I’m no doctor.
  • Percentages won’t add to 100% b/c some responses included multiple answers and some responses went uncategorized
  1. What personal shortcoming/insecurity comes to mind? (116 responses)
  • Half of the reported shortcomings revolve around some version of low confidence or fear.
  • A quarter of the responses are matters of self-control whether it’s ADD, listlessness, a lack of discipline, or indecisiveness. An answer I didn’t see that could fit either next to or envelop many of these —”lack of meaning”. It can be hard to motivate unless the reason seems urgent or at least worthwhile. Kind of like the dizziness of freedom I mentioned last week.
  • The remaining balance of insecurities are directly framed as difficulties in handling our own perceptions of others or being competitive (ie vanity/status games). The low confidence categories also have an interpersonal aspect but they are not framed directly in that way. They seem to have more of a component of self-esteem. It’s all interrelated but I tried to find a distinction. Basically “Am I frustrated with others or myself?”
  • Imposter syndrome is one of those fears that we hear a lot about. Like many fears, it’s adaptive to a point. One of my heroes (we are going to get to that word later), Sal Khan, has a brilliant framing of it you can borrow:

    [That blurb is from my notes from one of the best interviews I listened to recently: Sal Khan On The Finding Mastery Podcast]

    The idea of healthy imposter syndrome is best captured in Bardo during the hallucinogenic bathroom scene when the protagonist’s father advises: “Take a swig of success, swish it around and spit it out, otherwise it will poison you.”

  1. If you had no money concerns and purchased all the things you wanted and checked off every place on your travel bucket list (like imagine you won the lotto and several years have elapsed since), what would you do with your time?
    (150 responses)

    Other than the 5 people who want to specifically design houses, this was not shocking. Sadly, but also not shocking, only 3% answered, “what I’m doing now”.

    The only thing I’ll say here is if you say you want to garden when you retire, and you don’t garden now, you are fooling yourself. Your actions reflect priority. Sure there are some things which money is a prerequisite for, but I’m just a seller of the idea that your current self arrives at some mental projection of your future self where you will do the things you think you like. Look at the first question — half of the responses are fear. Look at the demographics. Most of you are less than 45 years old and by the standards of geography and history — rich. (I get that nobody ever feels rich — hedonic treadmill, the banana republic parody we seem to live in, egg prices. But the material reality is, as Jack Raines points out, that you have already won.)

    If this is the wrong language to speak to you, consider the outside view. What do half of the rich boomers you see do as they travel around the world on cruise ships or finally get the value out of those timeshares they’ve been roosting on? They complain about money and inflation instead of all these amazing aspirations they had about what they’d do when they had money or time.

    Or they spend their time in doctors’ offices. I’m not saying this to be mean. (I have aging parents and these are not personally easy times…but they do cultivate perspective). I’m saying this to merge this question and the one before it with a blunt solution at least a few of you might need — start living right now. Every week I hear of a friend of a friend dropping dead. That’s something that you hear more of in your 40s. It’s counterintuitive…but I hope that it kills your fear.

    3. What’s stopping you from being more like your hero? (83 responses)

    I will start by admitting that this question is poorly posed. The word “hero” conjures worship, cults, Aquaman. There were only 83 real responses because “I’m an adult — I don’t have heros”. Fair enough. Yinh had the same reaction and I projected my own connotation of that word on everyone else.

    We have all heard the expression “don’t meet your heros”…those on a pedestal can only fall down. But I’m not talking about a person I want to wholesale exchange my life with or even be handed their superpower.

    A hero is someone who embodies a personal aspiration. It’s someone who I keep in mind as a model for behavior. A teacher with a loving but firm demeanor. A parent that stays calm when the children turn the living room into a winter wonderland out of tiny cut-up styrofoam (this happened in December. I wish I kept a picture but I was too busy overreacting with the giant a-hole daddy voice).

    Visualizing heroes is how I hack our preloaded “mimic others” bloatware for good use. Where did your own aspirations come from? You’re not Buffalo Bill trying to wear their skin. You’re trying to channel inspiration. “How might X approach this? How would X react to this situation?” You can have a stable of heroes for different situations. They can be celebrities, people you know, or even fictional.

    Ultimately, I blame myself for the poor wording. I could have used “role model” or just “someone you admire”. Semantics aside, I hope the visualization hack, should you try it, is useful.

    And one last thing…look at those responses — from “welp” to “selfish” to “low priority”, those of you who responded did so with deep self-awareness. Y’all are clearly familiar with the Kipling quote:

    If you don’t get what you want, you either didn’t really want it, or you tried to negotiate over the price

    [In our house there’s no such thing as “I didn’t have enough time”…it’s always “I didn’t prioritize it”. Be responsible or get help. There are definitely victims in the world — but we are not them]


Amusing Bits

  • 2/3 of you can drive stick (I actually never tried)
  • 40% played a sport in college (nearly 20% of the NCAA athletes were basketball players)Book recs that showed up more than once:

And to wrap this up, you should know that 45% of you have seen Dazed & Confused and the rest of you buried a dagger in my heart.

It’s paywalled, but Freddie deBoer did an awesome ranking of Linklater films. D&C is #2. Its spiritual sequel, Everybody Wants Some!!, was #3.

Money Angle

Byrne Hobart is one of these alien finance writers like Matt Levine who I just marvel at. Geniuses that dazzle with both quality and quantity. One of the differences is Byrne presumes a bit more financial knowledge from his audience. I was stoked to see he launched a second letter, Capital Gains, that breaks down one financial concept a week. It’s more basic than his regular writing making it a great resource to forward to learners as a reference or simply see a new way of communicating something you already know. Even for you, Byrne will make you see in a fresh way.

For example, this bit at the end of his recent Capital Gains post:

  • Money Manager Fees: Who Gets Paid How? (6 min read)Understanding why different types of funds charge different fees

    The thing for investors to watch out for is not the total fee load, but to look at what they’re paying for compared to what they’re getting. A multi-strategy fund can plausibly be undercharging if the pass-through fees and performance fees eat half the gross return, if what’s left is an uncorrelated return that beats other alternatives. And a mutual fund can be overcharging when it asks for 50 basis points a year if it claims to be offering stock-selection alpha but is really delivering market-tracking beta at a high markup.

    And this applies to individuals, too: you can decompose your own compensation into the beta-like returns from what line of work you’re in, what your educational background is, and your location. But it’s hard to get upside trading one kind of beta for another; for example, if you move somewhere for a high-paying job, you’ll make more, but a lot of that extra income compensates for a higher cost of living.

    Alpha is whatever value you add on top of what’s expected based on superficial and commoditized traits. Selling beta at a markup can be a very good living, but delivering alpha is more lucrative and ultimately more satisfying.

Money Angle For Masochists

On August 5th 2022, this tweet appeared on my timeline:

Twitter avatar for @jaym217

J @jaym217
CVNA Leaps are priced for perfection. K=50 Straddle can potentially be sold for ~50$ if you can hedge upside blowout risk

The tweet asserts that the LEAPs are expensive or “priced for perfection”. The next part of the sentence is shaky if you take it literally — “if you can hedge the upside blowout risk”. You “can” sell the straddle for about $50 whether or not you can hedge the upside, but the author is prudently demonstrating where the risk resides. I give a total hall pass to the writing as my own tweets are often thrown together while standing in line at Trader Joe’s.

Allow me to re-word the tweet without worrying about character limits and without feeling rushed.

“Optically, the CVNA LEAP straddle is expensive because it’s trading for the same premium as the strike price. I can’t get burned on the downside so my only concern is the unbounded upside of the call option I’m short, so if I can truncate the potential loss there, this straddle is a good candidate to sell”

The original poster exhibits a solid understanding of options. But…markets are hard. They don’t leave free or near-free money laying around. It turns out, with 5 months of hindsight, this is a good case study in the limits of optically attractive trades.

By dissecting what has happened we can learn about how to think of options “dynamically”.

I’m going to try a rhetorical approach to this lesson to make it more interactive. If you want to continue strap in:

A Socratic Dissection Of An Option Trade

Last Call

This is the last “Last Call”. Your feedback indicated the main body, Money Angle, and my personal life were your favorite parts.

I suspect curated links are still useful because I appreciate them in letters I sub to but I decided to just send a 2nd email every week. Here’s the description from my re-written About page:

Moontower Munchies (Wednesdays)

This is a lightweight email.

It could be a few links I found interesting. I focus on productivity, self-hacking, modernity, finance, learning tools, and sometimes philosophy or culture.


It could be one link to a piece of content with my notes. I’m a compulsive note-taker and often scribble my own comments into them connecting ideas to something else in my grey(ing) matter.


Happy Lunar New Year rabbits…stay groovy!

Moontower #176

I meant to put together a summary and discussion of December’s Moontower survey. There are many interesting topics, especially in response to the open-ended questions that you answered so thoughtfully and vulnerably. Alas, I spent a lot of time writing the Money Angle For Masochists section so the survey summary is delayed until next Sunday.

Instead, I’ll point you to an interview that keeps lingering for me.

In 2021, Tim Ferriss interviewed George Mumford. Mumford has been a mindfulness coach to MJ, Kobe, and countless other elite performers. Mumford’s personal story is as inspiring as any. And if your life has been touched by the darkness of addiction it will be extra relatable.

There was a particular excerpt that resonated that I included in the Meaning Section of my Affirmations and North Star page. It reminded me of the proverbial donkey placed equidistant between 2 troughs of food who starves to death.

On the “dizziness of freedom” (all emphasis mine):

Freedom is not free. The dizziness of freedom is because you’re on a road less traveled, you’re on shaky ground. The ground you’re on is moving to the degree that — I’m going back to 1846, Søren Kierkegaard, and he said that one side of the coin is freedom or potential. The other side is anxiety or uncertainty. So he called it the “alarming possibility of being able.” So when you grow, when you change a behavior or a habit, you have to experience anxietyYou have to experience uncertainty. You have to experience discomfort.

You get comfortable with being uncomfortable. Before you have freedom, you don’t have to think. You don’t have to reflect. You don’t have to take a risk. You don’t have to be vulnerable. Now you’ll be in freedom and you’re going through a different door. You’re trying something else. Then the dizziness is you do this thing, you can do that thing.

So you start understanding there’s no meaning in the universe other than what you give it, that when you do one thing you lose something else. If I have five choices and I make one, I lose four. So now I’m in here, now I’m worrying about, did I make the right choice? The uncertainty is a military term they use, VUCA, V-U-C-A. From moment to moment, things are volatile, uncertain, complex, and ambiguous. So you have to embrace uncertainty, ambiguity. That’s part of life. This is what life is about. It’s about saying “yes and”. Yes, it’s frustrating. It’s unpleasant, and it’s okay. This is it. When I grow, this is what comes with it. If I achieve my goals, you look at the positive, but there’s a negative.

The other side is you’re in a rowboat with people. You change, they’ve got to change. They’ve got to move. They don’t want to move. Or they got you in a box and now you’re out of the box. So now they’ve got to see who you are. They’re going to keep you in a box and get mad at you. So for whatever reason, it always comes down to discomfort, being uncomfortable. The nervous system is wired this way. If it’s pleasant, we approach. If it’s unpleasant, we avoid. And if it’s neither, we’re indifferent, we space out, because the nervous system does so.

When you impute meaning onto something, and say, “It’s going to be great. Even though it’s uncomfortable, I know on the other side, this is the only way out.” Once I commit to that and I have the experience of going through it and then coming to another level of grace, of ease, of peace, then I continue to do that. That’s what I talk about — the superpower trust. You need trust, but when you can verify it through insight, through information, through experience, now it goes from confidence to conviction, and then now, you get on a beneficial cycle where things keep getting better— the rich get richer, because you know that if you learn and you achieve, it’s going to generate enthusiasm and you’re going to want to learn more. You’re going to want to commit to it, because you know that — this is what the elite performers do. They see those things as challenges. “Oh, this is great. This is an opportunity for me to express myself.” So that mindset is the growth mindset, but it’s also pursuing excellence.

Money Angle

One bit of feedback I got from the survey was that Money Angle can sometimes fly over readers’ heads. I can own a share of the blame for my writing style. But also some topics are really unnecessary for the average investor or reader and by discussing them in the same section I often discuss basic topics can overwhelm someone who can’t tell what’s relevant to their current or future learning tree and what’s not.

I moved all the brain damage to the new Money Angle For Masochists section.

Today’s regular Money Angle section is a couple of links:

  • How Much Growth Can You Expect? (6 min read)
    Nick Maggiulli

    Nick is a master of making investing topics scrutable for the average person. Last year he published his first book Just Keep Buying which I recommend and buy for people. It tackles personal financial questions intelligently without overcomplicating the nature of investing.

    In this blog post, he presents realistic numbers for what investing is actually capable of in the long-term (which is much less than the financial media would like you to believe).

    If happiness is the gap between reality and expectations the post will help you calibrate to decrease your chance of disappointment. Another of his posts, his first of 2023, is in my opinion, a natural (though unintended) sequel to this calibration:

    It’s Time to Work (5 min read)


  • Examples Of Comparing Interest Rates With Different Compounding Intervals (2 min read)

    I wrote this quick post as scaffolding for the post you’ll find below in Money Angle For Masochists to build up to the idea of continuously compounded interest. If you already understand how to compute yields and various compounding intervals then you can skip this one. If you don’t then be aware of 1 of its real-life uses:

    Note in all these cases, $90 is growing to $100. We are just seeing that the implied rate depends on the compounding assumption. In real life, when you see “compounded daily” or “compounded monthly” and so on, you are now equipped with the tools to compare rates on an apples-to-apples basis. If a rate is lower but compounds more frequently than another rate the relative value between both loans is ambiguous. 

Before we continue to the masochism, let’s try a math problem:

Suppose you have an 85 average on the first 4 tests of the semester. There’s one test left. All tests have an equal value in your final score. You need a 90 average for an A in the class.

What do you need on the last test to get an A in the class?

What is the maximum score you can get for the semester?

If you are comfortable with this math then you have all the quantitative knowledge to understand the next topic. I suspect the post might still be challenging despite the math being grade school level. If you find it difficult, I’d like to know where you start to get lost. I think it’s a good topic and would like to make it accessible for anyone who was interested.

Let’s go.

Money Angle For Masochists

Understanding Implied Forwards (14 min read)

Learn about implied forwards starting with interest rates and then moving into implied volatility. Implied forwards will help you:

  1. find trading opportunities
  2. understand arbitrage and its limits

While the post works through the dry mechanics there are wider lessons that can be applied to general pricing and reasoning that should have a larger audience than just option degenerates and the people who read footnotes (this post has many).

A few excerpts in that vein:

  • When you study asset pricing, one of the early lessons is to step through the cash flows. This is the basis of arbitrage pricing theory (APT), a way of thinking about asset values according to their arbitrage or boundary conditions. As opposed to other pricing models, ie CAPM, someone using APT says the price of an asset is X because if it weren’t there would be free money in the world. By walking through the cash flows, they would then show you the free money. The fair APT price is the one for which there is no free money.
  • Process
    Forwards vols represent another way to study term structures. Since term structures can shift, slope, and twist you can make bets on the specific movement using outright vega, time spreads, and time butterflies respectively. A tool to measure forward vols is a thermometer in a doctor’s bag. How do we conceptually situate such tools in the greater context of diagnosis and treatment?

    The post includes a discussion of my own process.

  • Meta-understanding
    This discussion of forward vols was like month 1 learning at SIG. It’s foundational. It’s also table stakes. Every pro understands it. I’m not giving away trade secrets. I am not some EMH maxi but I’ll say I’ve been more impressed than not at how often I’ll explore some opportunity and be discouraged to know that the market has already figured it out. The thing that looks mispriced often just has features that are overlooked by my model. This doesn’t become apparent until you dig further, or until you put on a trade only to get bloodied by something you didn’t account for as a particular path unfolds.

    This may sound so negative that you are wondering why I even bother writing about this on the internet. Most people are so far out of their depth, is this even useful?

    My answer is a confident “yes” if you can learn the right lesson from it:

    There is no silver bullet. Successful trading is the sum of doing many small things correctly including reasoning. Understanding arbitrage-pricing principles is a prerequisite for establishing what is baked into any price. Only from that vantage point can one then reason about why something might be priced in a way that doesn’t make sense and whether that’s an opportunity or a trapBy slowly transforming your mind to one that compares any trade idea with its arbitrage-free boundary conditions or replicating portfolio/strategy, you develop an evergreen lens to ever-changing markets.

    You may only gain or handle one small insight from these posts. But don’t be discouraged. Understanding is like antivenom. It takes a lot of cost and effort to produce a small amountIf you enjoy this process despite its difficulty then it’s a craft you can pursue for intellectual rewards and profit.

    If profit is your only motivation, at least you know what you’re up against.


Last Call

Interview with Bill Burnett & Dave Evans on Designing Your Life (5 min read)

Bill and Dave are at the Stanford Design School, a place that massively influenced another of my favorite online people — boardgame design teacher and middle school educator — Kathleen Mercury.

These guys apply design principles to life and decision-making (and show when not to!). It’s been almost a decade since they published their book and did the TED circuit but the material is timeless.

Here are my notes from their interview with Peter Bregman:

You are not defined by your earlier choices

  • Don’t let “dysfunctional beliefs” or sunk costs trap you (ie I studied X in college so I must practice X)
  • Humans are curiosity-driven. Life may have beaten it out of us but it just needs re-awakening.

Behavior change —> Bias to action

You can’t think your way out of a rut. To solve problems you must take action. They call experiments “life design prototypes”.

  • The answers you seek are out there in the world not in your head.
  • Expand your circle. Those in your bubble often have the same problems or thought patterns — there’s no new data there.
  • “Finite is your friend” —> lower the mental burden of novel experiments by saying you will only do the new thing 6 times, or spend 5 minutes a day doing X


Large focus on awareness of the nature of the decision and the power of re-framing. Problem-solving requires applying the frame that best aligns with your need. Before you can do this, it’s critical to understand your current framing of a problem.

  • Life-design thinking with experimentation won’t help with certain types of decisions. For example, should you buy disability insurance? You can learn everything there is to know about your risks, the costs of insurance, the suppliers of insurance and so on but it’s a decision that you must make one way or another and accept the inherent ambiguity. Acceptance is the answer.

This leads to the single most common re-frame they use:

There is no single answer to your life. There is no single best “you”. There are many possible great satisfying lives that you can have and you never actually know about the ones you didn’t get a chance to try so we’re all getting partial credit on essay questions, not right wrong on true/false on all the big issues of life. Once you accept that this is the nature of being a human being you can say “how’s it going today?” and the answer is “it’s going reasonably well. And that’s fabulous because this is as good as it gets.”

  • Borrowing from decision researchers like Dan Gilbert they mention tactics like “burning bridges” by making certain decisions irrevocable. [Me: This makes a lot of sense to me bc FOMO is an energy suck. I tend to satisfice on everything that doesn’t hold major meaning to me — if I’m like 70% sure that product X will tick my boxes I just buy it and move on. I don’t care enough about my TV to spend a week in analysis/paralysis about how deep the blacks are. But if I were a cinephile I might.]
  • “Anchor problems”: These occur when you become inflexibly anchored to a single solution to a problem.For example, you say: ”I’d like to do it I’d like to be a gardener or do something in the garden but I’ve decided the only solution is moving to the Berkshires. Since we can’t move to the Berkshires, I can’t have a garden, therefore I can’t be happy”

    What you’ve done is you’ve baked the solution into the problem. The solution has been defined as the problem.

    Instead, you might notice there are community gardens in the Upper West Side of Manhattan or you could start by putting a container on the porch. There are a million different ways you can do it but people take a solution, pretend it’s the problem and then say “Oh gosh since I can’t have the thing I want, I can’t solve this problem.” They’ve mistaken a solution for a problem and now they’ve anchored on it and can’t move forward. Once we explain it to them it’s almost laughable. They go, “Oh yea I could reframe this and there are hundreds of ways to be a gardener in Manhattan. Maybe “gardener” is also an anchor problem because the reality is maybe it’s about spending time outdoors in Central Park or maybe it’s about growing something”

  • “Gravity problems”: These are unactionable problems. They are still issues but if a problem cannot be acted on it’s not so much a problem as it is a circumstance. Like gravity. As soon as you realize your problem is a gravity problem, that it’s not actionable the way it’s currently framed, you can unfixate from it. You might hate knowing you will never get rich being a poet, but can you live and write poetry? Of course.

A few lines that were dropped in passing that are actually quite poignant.

Here they are with my commentary:

I’d rather get a B on time then an A too late

Dave’s framing for how to think about optimization. Forgive yourself for being human. Any sensible approach to prioritization means you can’t turn every weakness into a strength. Again, the theme of acceptance. Or not letting perfect be the enemy of the good. I tutor 2nd graders that are far behind their grade level. Am I the best person to do this? Is this the best use of my time? Does this scale? No all counts. But it’s something that needs to be done and they still need people. If the only people who tutor are the “optimal” people to do so then what do you think is going to happen if we are already short tutors?

Some people obsess over peak performance and optimizing and so on. That’s fine. It’s a big world. In most things, I’m more concerned with the area under the curve than its peak.

Meaning comes from engagement, what you spend your time on.

I believe that there is no Meaning with a capital “M”. We create our own meaning and since I put more stock in actions than words, I think what you spend your time on is the best reflection of where you draw your meaning. This is often oblique. Maybe you spend all your time making money on something you don’t necessarily care about. This strikes me as a difficult way to live but it may reflect your value of providing for your family. There’s always a question of balance…the time spent providing is a cost to you and them as well and deciding where the diminishing returns to being at work vs being present are personal and downstream from not just our values and desires but insecurities and ego.

Figuring it out is kind of helpful but actually behaving differently is hugely helpful

Dave dropped that line in the context of therapy (he was explaining that this work is not therapy and ofc there are problems for which you should seek therapy). It reminded me of a story Slatestarcodex told about a psychiatric patient his clinic was helping. The patient was crippled by OCD. Every time she left the house she needed to go home because she thought she left the hair dryer on. The doctors racked their brains trying to get to the origin of the problem until someone suggested a highly effective but, seemingly unsatisfying solution — she could just bring the blow dryer with her:

Approximately half the psychiatrists at my hospital thought this was absolutely scandalous, and This Is Not How One Treats Obsessive Compulsive Disorder, and what if it got out to the broader psychiatric community that instead of giving all of these high-tech medications and sophisticated therapies we were just telling people to put their hair dryers on the front seat of their car? But I think the guy deserved a medal. Here’s someone who was totally untreatable by the normal methods, with a debilitating condition, and a drop-dead simple intervention that nobody else had thought of gave her her life back. If one day I open up my own psychiatric practice, I am half-seriously considering using a picture of a hair dryer as the logo, just to let everyone know where I stand on this issue.

That’s enough for this week. Go Big Blue…it’s been 7 years since they made the NFL playoffs.

Stay groovy!