Putting Moloch To Rest

Last week, I talked about Moloch, the evil god of child sacrifice, as a metaphor for unhealthy competition — “race to the bottoms”, prisoner’s dilemmas, and coordination problems generally.

We summon Moloch when competitive pressures require us to optimize for narrow rewards, especially ones that are easily measurable or “legible” while dispensing with the wider range of values that resist measurement.

Putting something of a face to the phenomenon is useful. It’s adaptive to recognize Moloch so we can re-direct our blame from individuals to the system. We are collectively in charge of the system. We need to recognize the high leverage nodes and rules within that system, not only to protect them from tampering, but to make sure they make sense for our communal well-being in the first place.

Our primary levers are incentives. They take many forms. They can be hard like carrots and sticks or soft like status and honor. I think of culture as the sum of these incentives. This is apparent if you tried to decompose subcultures, national identities, or the values of corporations into what makes their members tick. That which makes one rise or fall within the confines of a specific organization or tribe.

I said the comet in Don’t Look Up should have been named Moloch. But I don’t want to leave this topic making you feel I double-clicked on apocalypse.exe. I promised a lifeline, so this week I’ll give you some materials that point us in the right direction.

I’ll start with an interview with poker player Liv Boeree. While the entire conversation she has with host, Alexander Beiner, is provocative infotainment dealing with game theory and culture, she is obsessed with the Moloch metaphor. I love the race-to-the-bottom example she dwells on: Instagram beauty filters and their effect on teenagers (or really everyone) on social media. She herself finds the temptation to use them quite powerful.

Here are more excerpts that caught my attention:

Moloch’s unhealthy optimization embodied by the “Paperclip Maximizer”

A byproduct of [unhealthy competition] is that if you play it out to its logical conclusion, it means that you will turn basically everything in the universe into this one thing. The ultimate instantiation of that is the “Paperclip Maximizer”. This is a thought experiment, I think by Eliezer Yudkowsky of how a superintelligent AI could go wrong. Suppose it’s unbelievably good at getting whatever it wants done, done. But it’s stupid to the extent that it was basically programmed to do this one narrow thing, which in this instance, you wanted to make paperclips. You wanted the AI to make more paperclips better than what you can currently do. It’s a paperclip maker, but because it’s so unbelievably good, it turns everything from the factory it’s in [into paperclips]. It figures out how to pull the constituent parts of atoms, the blood, the hemoglobin in your blood, the iron. It extracts and dismantles until it can tie anything in the universe into paperclips.

How maximizing can “dismantle the universe into a low complexity state

This is analogous a little bit to the heat death of the universe. Because that is actually a very low complexity state. it’s just a homogenous grey soup. The universe started out with very low complexity, a singularity of matter and energy. If we’re talking in terms of Kolmogorov complexity, which is basically, “how many bits of code do you need to describe a thing?” The universe started out pretty simple. Then time started, things started unfolding and suddenly we started seeing hydrogen and then helium and that coalesced into stars, which could have created greater heavier elements. All this beautiful complexity started emerging. Patternicty is like a dance between order and disorder. A bit of hierarchy, but a bit of anarchy. This creates this highly complex, dynamic system that’s very hard to describe. To write the piece of code to describe the universe, you basically have to just create the universe. That’s what a highly complex system is.

But at some point, the stars will die out and so on. All this sort of free energy that is used to create all this complexity will start dissipating. And then it’ll slowly as far as we know, turn into this gray soup, which has low complexity. Entropy will do this over time.

Never thought of this as good vs evil!

This is like what a paperclip maximizer would do. It’s permanently curtailing. There’s no more complexity to rise. The universe has reached this steady state. And that seems like a tragedy of enormous potential because, at least up until now, it seems like the universe is trying to emerge into greater and greater states of complexity. So I hate to boil it down to like good and evil terms, but to me good is that which creates, allows for greater emergence and complexity to appear and thereby utility. Useful information that we can process and make wonderful things with.

And evil is that which does the opposite. It turns things into a low diversity, very basic situation, whether it’s a cloud of hydrogen or as Ginsburg describes [in the Howl poem] Moloch, who is a cloud of “sexless hydrogen”. So it’s like this force of entropy, but it’s slightly different because entropy is actually neutral. Entropy is just like time effectively. Whereas Moloch is the thing that turns everything into this like one modern focus, sacrificing everything in order to win this one thing — hence the child sacrifice.

The role of healthy competition

Competition can also be an enormous force for good. The capitalistic model has risen the world to what it is right now. We would not be living the cushy life with a lot of the luxuries that capitalism has provided.

How technology fits into this

Technology is exponential, making Moloch’s life much easier to destroy the universe. But at the same time, we’re also building technologies that enable cooperation to better coordinate with one another.

 

My takeaway

Moloch is the evil that comes from overly narrow optimization in service of a competition that has lost the script. Coordination problems devolve into sub-optimal equilibria that are difficult to escape from.

If there is a remedy, I suspect it’s a mix of the following (I included readings I really enjoyed for each prong):

  1. Surplus/redundancy/slack in a system to relieve the pressure to slide into counterproductive or sociopathic competitions✎ Studies on Slack (26 min read)by Scott Alexander

    ✎ Greedy Algorithms And The Need For Illegibility (6 min read)
    by Rohit Krishnan

    ✎ Casualties of Perfection (4 min read)

    by Morgan Housel

  2. Cooperation✎ An Ode To Cooperation (7 min read)
    by Matt Hollerbach

    (this lightly quantitative take on cooperation also underpins portfolio theory!)

  3. Appreciating the limits of legibilityMoloch sustains itself from unhealthy competition. What makes a competition unhealthy is when it becomes all-consuming by compressing our values into a narrow band like the paper clip AI. The AI must process structured and unstructured data, but its meta-intelligence needs to make choices directed by goals.I can’t see how “goals” in any holistic sense of the word can be a solved problem. How can we escape the simple trope “Not all that we measure matters, and not everything that matters can be measured”?

    We impose legibility, then recursively use the legibility to make inferences that further cement that what we originally measured was important otherwise we wouldn’t have measured it. There’s a circularity that makes us vulnerable to mutated assumptions. Sometimes, it’s a good idea to climb up into a Moontower with some friends, take a pause from the battle, and use that calm, high vantage point to wonder, “which unsaid assumptions bear more weight than they should? And how did that happen?”

    When you’re feeling open let yourself wander into this essay by Tom Morgan:

    ✎ The Most Interesting Thing I’ve Ever Read (25 min read)

    (If you find the title clickbaity, congrats — you understand Moloch!)

    I mentioned how Moloch is a force that sacrifices values that are hard to measure. Tom’s essay will bridge you into a sea of thinking that deliberates both the power of science and its limitations (at least in its current state) as a means to receive knowledge.

    [also, thanks to Tom for pointing me to a number of sources that I read after the original Moloch post]


A Final Indulgence

I’ll stretch a bit here.

Moloch feeds by forgetting that the objects of our desire are actually proxies for what we need. We feed our egos with sex, money, and status to gain control. We impose legibility to gain control. Is control freedom? Or is control safety (i.e. the freedom from fear)?

Competition feels like it turns unhealthy when it becomes about control. The illusion of control is it promises both freedom and safety. The control doesn’t mutually scale. For there to be a controller, there must be a controlled.

The trade-offs between freedom and safety, individualism and community feel very stark today. If it feels binary, it’s because the prevailing narratives have profited from framing these values in such divisive terms. The tension between these values is natural, but our sensation of the tension might be amplified artificially.

I’m not downplaying the trade-off so much as trying to restore its grey hue. I’m not well-equipped to do so, but I urge you to listen to war journalist and author Sebastian Junger’s interview with Russ Roberts. The stories within are engaging but the nuanced discussion, trading off between freedom and safety, is the payoff. I feel like the word “freedom” is a political football that has been turned into a cartoon and this interview’s depth makes it quite apparent.

Moontower #133

Last week, I talked about Moloch, the evil god of child sacrifice, as a metaphor for unhealthy competition — “race to the bottoms”, prisoner’s dilemmas, and coordination problems generally.

We summon Moloch when competitive pressures require us to optimize for narrow rewards, especially ones that are easily measurable or “legible” while dispensing with the wider range of values that resist measurement.

Putting something of a face to the phenomenon is useful. It’s adaptive to recognize Moloch so we can re-direct our blame from individuals to the system. We are collectively in charge of the system. We need to recognize the high leverage nodes and rules within that system, not only to protect them from tampering, but to make sure they make sense for our communal well-being in the first place.

Our primary levers are incentives. They take many forms. They can be hard like carrots and sticks or soft like status and honor. I think of culture as the sum of these incentives. This is apparent if you tried to decompose subcultures, national identities, or the values of corporations into what makes their members tick. That which makes one rise or fall within the confines of a specific organization or tribe.

I said the comet in Don’t Look Up should have been named Moloch. But I don’t want to leave this topic making you feel I double-clicked on apocalypse.exe. I promised a lifeline, so this week I’ll give you some materials that point us in the right direction.

I’ll start with an interview with poker player Liv Boeree. While the entire conversation she has with host, Alexander Beiner, is provocative infotainment dealing with game theory and culture, she is obsessed with the Moloch metaphor. I love the race-to-the-bottom example she dwells on: Instagram beauty filters and their effect on teenagers (or really everyone) on social media. She herself finds the temptation to use them quite powerful.

Here are more excerpts that caught my attention:

Moloch’s unhealthy optimization embodied by the “Paperclip Maximizer”

A byproduct of [unhealthy competition] is that if you play it out to its logical conclusion, it means that you will turn basically everything in the universe into this one thing. The ultimate instantiation of that is the “Paperclip Maximizer”. This is a thought experiment, I think by Eliezer Yudkowsky of how a superintelligent AI could go wrong. Suppose it’s unbelievably good at getting whatever it wants done, done. But it’s stupid to the extent that it was basically programmed to do this one narrow thing, which in this instance, you wanted to make paperclips. You wanted the AI to make more paperclips better than what you can currently do. It’s a paperclip maker, but because it’s so unbelievably good, it turns everything from the factory it’s in [into paperclips]. It figures out how to pull the constituent parts of atoms, the blood, the hemoglobin in your blood, the iron. It extracts and dismantles until it can tie anything in the universe into paperclips.

How maximizing can “dismantle the universe into a low complexity state

This is analogous a little bit to the heat death of the universe. Because that is actually a very low complexity state. it’s just a homogenous grey soup. The universe started out with very low complexity, a singularity of matter and energy. If we’re talking in terms of Kolmogorov complexity, which is basically, “how many bits of code do you need to describe a thing?” The universe started out pretty simple. Then time started, things started unfolding and suddenly we started seeing hydrogen and then helium and that coalesced into stars, which could have created greater heavier elements. All this beautiful complexity started emerging. Patternicty is like a dance between order and disorder. A bit of hierarchy, but a bit of anarchy. This creates this highly complex, dynamic system that’s very hard to describe. To write the piece of code to describe the universe, you basically have to just create the universe. That’s what a highly complex system is.

But at some point, the stars will die out and so on. All this sort of free energy that is used to create all this complexity will start dissipating. And then it’ll slowly as far as we know, turn into this gray soup, which has low complexity. Entropy will do this over time.

Never thought of this as good vs evil!

This is like what a paperclip maximizer would do. It’s permanently curtailing. There’s no more complexity to rise. The universe has reached this steady state. And that seems like a tragedy of enormous potential because, at least up until now, it seems like the universe is trying to emerge into greater and greater states of complexity. So I hate to boil it down to like good and evil terms, but to me good is that which creates, allows for greater emergence and complexity to appear and thereby utility. Useful information that we can process and make wonderful things with.

And evil is that which does the opposite. It turns things into a low diversity, very basic situation, whether it’s a cloud of hydrogen or as Ginsburg describes [in the Howl poem] Moloch, who is a cloud of “sexless hydrogen”. So it’s like this force of entropy, but it’s slightly different because entropy is actually neutral. Entropy is just like time effectively. Whereas Moloch is the thing that turns everything into this like one modern focus, sacrificing everything in order to win this one thing — hence the child sacrifice.

The role of healthy competition

Competition can also be an enormous force for good. The capitalistic model has risen the world to what it is right now. We would not be living the cushy life with a lot of the luxuries that capitalism has provided.

How technology fits into this

Technology is exponential, making Moloch’s life much easier to destroy the universe. But at the same time, we’re also building technologies that enable cooperation to better coordinate with one another.

My takeaway

Moloch is the evil that comes from overly narrow optimization in service of a competition that has lost the script. Coordination problems devolve into sub-optimal equilibria that are difficult to escape from.

If there is a remedy, I suspect it’s a mix of the following (I included readings I really enjoyed for each prong):

  1. Surplus/redundancy/slack in a system to relieve the pressure to slide into counterproductive or sociopathic competitions

    ✎ Studies on Slack (26 min read)

    by Scott Alexander

    ✎ Greedy Algorithms And The Need For Illegibility (6 min read)
    by Rohit Krishnan

    ✎ Casualties of Perfection (4 min read)

    by Morgan Housel

  2. Cooperation

    ✎ An Ode To Cooperation (7 min read)
    by Matt Hollerbach

    (this lightly quantitative take on cooperation also underpins portfolio theory!)

  3. Appreciating the limits of legibility

    Moloch sustains itself from unhealthy competition. What makes a competition unhealthy is when it becomes all-consuming by compressing our values into a narrow band like the paper clip AI. The AI must process structured and unstructured data, but its meta-intelligence needs to make choices directed by goals.

    I can’t see how “goals” in any holistic sense of the word can be a solved problem. How can we escape the simple trope “Not all that we measure matters, and not everything that matters can be measured”?

    We impose legibility, then recursively use the legibility to make inferences that further cement that what we originally measured was important otherwise we wouldn’t have measured it. There’s a circularity that makes us vulnerable to mutated assumptions. Sometimes, it’s a good idea to climb up into a Moontower with some friends, take a pause from the battle, and use that calm, high vantage point to wonder, “which unsaid assumptions bear more weight than they should? And how did that happen?”

    When you’re feeling open let yourself wander into this essay by Tom Morgan:

    ✎ The Most Interesting Thing I’ve Ever Read (25 min read)

    (If you find the title clickbaity, congrats — you understand Moloch!)

    I mentioned how Moloch is a force that sacrifices values that are hard to measure. Tom’s essay will bridge you into a sea of thinking that deliberates both the power of science and its limitations (at least in its current state) as a means to receive knowledge.

    [also, thanks to Tom for pointing me to a number of sources that I read after the original Moloch post]


A Final Indulgence

I’ll stretch a bit here.

Moloch feeds by forgetting that the objects of our desire are actually proxies for what we need. We feed our egos with sex, money, and status to gain control. We impose legibility to gain control. Is control freedom? Or is control safety (i.e. the freedom from fear)?

Competition feels like it turns unhealthy when it becomes about control. The illusion of control is it promises both freedom and safety. The control doesn’t mutually scale. For there to be a controller, there must be a controlled.

The trade-offs between freedom and safety, individualism and community feel very stark today. If it feels binary, it’s because the prevailing narratives have profited from framing these values in such divisive terms. The tension between these values is natural, but our sensation of the tension might be amplified artificially.

I’m not downplaying the trade-off so much as trying to restore its grey hue. I’m not well-equipped to do so, but I urge you to listen to war journalist and author Sebastian Junger’s interview with Russ Roberts. The stories within are engaging but the nuanced discussion, trading off between freedom and safety, is the payoff. I feel like the word “freedom” is a political football that has been turned into a cartoon and this interview’s depth makes it quite apparent.


Money Angle

Moontower reader Jeff sent me a treasure trove of free technical course materials to add to the volatility wiki.

Here’s a thread explaining what you’ll find and where to find it:


Last Call

Last month Disney+ in partnership with National Geographic released the documentary about the Thai boys that were trapped in a cave in June of 2018.

The bravery and ingenuity on display will push your conception of what humans can do when they cooperate.

We watched it with the kids. The gripping footage and editing (same team as Free Solo) honored the miracle that was:

The Rescue

Moontower #132

This is an actual story of an elementary school class election:

One of the kids running for class president gave an impassioned speech about what they would change (Maybe no hall monitors anymore, I have no idea, the detail isn’t important). Then the challenging candidate strides up to the podium and declares that if you elect him, he’ll secure the school a…rollercoaster! In the informal “exit poll”, one of the students was asked why they wanted to vote for the rollercoaster candidate and the student said, “I know it probably won’t happen, but what if it did?! That would be soooo cool”.

Surely the challenger is on their way to a lucrative career in politics.

And we are all worse off for it.

Why does it have to be this way?

For the same reason that the realtor who shouts the highest number gets the listing. The reason is…Moloch. A mythical demon that demands child sacrifice has become a metaphor for how things become terrible.

I’ll turn to Scott Alexander for an explanation:

The implicit question is – if everyone hates the current system, who perpetuates it? And Ginsberg answers: “Moloch”. It’s powerful not because it’s correct – nobody literally thinks an ancient Carthaginian demon causes everything – but because thinking of the system as an agent throws into relief the degree to which the system isn’t an agent.

Moloch is the odorless, selective pressures of evolution responding to incentives. It has no moral attribute. It just is. If you are an armchair game-theorist you see Prisoner’s Dilemmas everywhere you look. If you don’t already see them everywhere, bless your heart.

Personally, I constantly fight the resigned feeling that we cannot save ourselves from taking second-helpings of misery pie. “Moloch” is a catchy term that binds to situations known as “coordination problems”. These problems are too devilish to pin on any single individual (although this doesn’t stop anyone from trying to point fingers).

The sub-optimal equilibrium in a Prisoner’s Dilemma is not a mystery in itself. A Nash equilibrium is actually the result of choosing an action that you would have chosen even if you knew how your counterpart would act. The omnipresent Prisoner’s Dilemma is a narrow instance of what Alexander calls, a multi-polar trap — a situation where the best course of action for an individual makes the group worse off.

I dare you to resist nodding as you read this passage:

All these scenarios [described earlier] are in fact a race to the bottom. Once one agent learns how to become more competitive by sacrificing a common value, all its competitors must also sacrifice that value or be outcompeted and replaced by the less scrupulous. Therefore, the system is likely to end up with everyone once again equally competitive, but the sacrificed value is gone forever. From a god’s-eye-view, the competitors know they will all be worse off if they defect, but from within the system, given insufficient coordination it’s impossible to avoid…in some competition optimizing for X, the opportunity arises to throw some other value under the bus for improved X. Those who take it prosper. Those who don’t take it die out. Eventually, everyone’s relative status is about the same as before, but everyone’s absolute status is worse than before. The process continues until all other values that can be traded off have been – in other words, until human ingenuity cannot possibly figure out a way to make things any worse.

Read the essay. It’s one of Alexander’s best (it’s almost 6 years old now).

I’ll warn you. It’s quicksand (don’t worry, I have a plan to pull you out next Sunday). It articulates what you already sense but struggle to put your finger on.

You can find the essay as well as my commentary on it here:

Notes From Moloch


Under the oppression of Baader-Meinhoff, I could not help but think the comet in Don’t Look Up should have been named Moloch.

[Beware spoilers]

Alexander even wrote a review of the movie pointing out its contradictions and never even mentions Moloch.

He instead focuses on whether the writers were advocating for “trust the science”, “trust the experts”, or “don’t trust experts”, or “don’t trust the government”. The movie is a Rorschach. Choose one of those angles if you want. But if you do that, you need to confront the glaring contradictions of those interpretations. Alexander competently explains them in his review.

Still.

It’s not the angle I would have chosen.

I found that approach to the movie too quibbling. Too object level. Sure, this movie can be politically weaponized by either side to confirm their positions (deep state, climate complacency, Covid response). The other side could wave a contradiction in their face and we’ll just talk past each other, just like we do in real life and in the movie.

The real message of this movie is…Moloch.

The comet prompts system-wide institutional failure. A massive failure to coordinate. This is a movie that showed the end-state of gamesmanship and competition that is so exhausting we accept death as mercy. An overdue rest-in-peace. That final scene at the dinner table is disturbing and poignantly stirring at the same time.

Don’t Look Up skewers a culture that has thoroughly and without self-doubt internalized the strategy “it doesn’t matter what you say, but how you say it”. Marketing, storytelling, branding, signaling, persuasion. There is so much emphasis on our ability to hack each other because attention is what is scarce.

Moloch is not moral one way or the other. There is no redemption. In the film, Jennifer Lawrence remains pure. For that, she gets to live out her days bagging groceries. Leo eats from the serpent’s sweet apple nourishing his ego with the foreign but empty calories of in-crowd flattery.

Guess what?

Their fate did not discriminate.


A personal take on Don’t Look Up:

The movie is a comedy. It’s a satire. While I watched it, it felt like a slightly above average movie, but it has lingered so much in my head, that I’m not giving enough credit to how provocative it was as a piece of art. My favorite performance was Mark Rylance playing the rich tech founder meme. (Coincidentally, the best live performance I may have seen of anything ever was Rylance on Broadway in La Bete. He has a 45-minute soliloquy in iambic pentameter that is physically hilarious and verbally brilliant. He would make a rapper proud.)

If you watch Don’t Look Up, do not turn it off before the credits start rolling. You’ll miss the most satisfying part of the film.


Money Angle

In economics, there is a trade-off between efficiency and equality. Efficiency is concerned with maximizing output, and equity is about how that output is distributed. If I give a resource, for example, an education, to 9-year-old Elon Musk that’s more optimal than handing it to Snooki if I care about efficiency. If I want to be fair, I’d split my education budget between the two of them. This trade-off is fairly self-evident when you point it out.

(I’m imagining an Orange County strip-mall landlord droning on about Reagan’s “trickle-down” economics to a YouTube influencer wearing a Che Guevara tank top at a Hollywood Hills cocktail party.)

If we look at the extreme poles of the equality-efficiency spectrum, we would find archetypes for how our activities should be coordinated. Equality, as the primary goal, leads to top-down communism and authoritarianism. Sorry, there is no benevolent dictator.

Efficiency at-all-costs would be coordinated by free markets. “Free” of course is corruptible (i.e. crony capitalism) and anti-trust is a broadly accepted guardrail to protect us from winner-take-all endgames.

As capitalists, it’s more relevant to think about the Moloch essay in the context of markets. To that end, I just wanted to share some Moloch-meets-markets musings.

On Thoughtful Rules

The logic of markets is they are a coordination mechanism to get to truth or what finance-types call “price discovery”. Price discovery provides signals to guide how we allocate our physical and human capital. It does this through the “profit incentive” pathway. Oil prices rise when people demand to fly and drive. So you should drill for more oil because the price offers you a profit.

The problem is that the system can work too well.

The profit incentive is powerful because money is fungible with everything that’s promised to satisfy any human desire. Money, of course, is incapable of that, but very few people believe they have “enough”. We expect businesses and individuals to claw for profits and, obediently, they do.

This is fine and good. But it still requires some top-down design. Why?

Because when our horns are locked in competition for that oh so sweet profit, Moloch demands we push ourselves right up to the line. The person who wins that last dollar must dispense with every other value so long as it doesn’t violate the law. Norms are not even effective restraints at the pinnacle of competition where you are likely to find sociopaths.

To keep Moloch from running wild we need the lines we draw to accommodate the fact that once we yell “go” everyone will look for every possible edge. Our lines must account for externalities. That’s what anti-pollution laws are. Our accounting laws serve similar functions. A carbon credit is an accounting term that “internalizes” an externality. It forces the emitter to own what they’ve done. They need to put it into their profit calculus.

On Flexibility

Of course, even well-considered laws will be gamed. But I couldn’t help notice that the marketplace seems to be telling us that the laws are behind the times.

Consider examples coming from different directions:

  1. Matt Levine’s “everything is securities fraud” thesis suggests that any practice that damages shareholder value, even if it’s legal can be used retroactively as the basis for a lawsuit. This forces management to consider their externalities even if stodgy laws and accounting rules cannot keep up with a rapidly changing world.
  2. From the other side, ESG, at least in its idealized form, is pushing to internalize the externalities by pushing our wider discarded values back onto balance sheets as more explicit liabilities. Instead of using judges, they want to use accounting laws and influence investing norms.
  3. Then you have crypto’s techno-libertarianism. If you love the idea of smart contracts’ black-and-whiteness, you should prefer the ESG reform to the whim of human judgments after-the-fact. If smart contract purists are more comfortable choosing the letter over the spirit of the law, they must be dead-set on demanding bright lines for every issue. (Sounds great if you hate nuance. Like religious fundamentalists. Or toddlers.)

    Smart contracts are a brilliant idea. Just not for every decision context.

On Liquidity

Price discovery increases with liquidity. This is mostly uncontroversial (if there were no VCs reading this I would have ditched the word “mostly” but I do love Moontower readers, so an olive branch is in order). And if price discovery and liquidity are good, is more always better?

The amount of brainpower and resources devoted to capturing that last penny of arbitrage in markets is formidable. What is the true cost of that price being “discovered”? I don’t even know where to start with that one (Jessica, in her characteristic snark, wonders a similar question on Twitter).

Let’s consider a more tractable question from Byrne Hobart. As he thought about the proposed repeal of 1031 exchanges, he wrote (bold is mine):

The defense of 1031 exchanges is that they encourage growth, because they keep people spending money on new property developments instead of cashing out and enjoying their gains. Which embeds two assumptions:

  1. It’s generally better to tax consumption than investment, and
  2. Real estate investment is a particularly worthy kind of investment to avoid taxing.

Assumption #1 sounds true, but is circumstantial. Assumption #2, though, is hard to defend. Real estate speculation does produce jobs, but it also produces macroeconomic volatility and sometimes threatens the financial system. From a macroprudential perspective, where the goal is to reduce the odds of financial crises, it might make more sense to have 1031 exchanges for everything but real estate: sell your company, and you can roll the money into starting a new one; sell a mall or skyscraper, and you get taxed. But it’s always fiendishly hard to predict the long-term incentives created by a change in the tax code. Any tax on realizing gains, for example, is implicitly a subsidy on borrowing against appreciated assets instead of realizing those gains. If that’s true, the net effect of eliminating 1031 exchanges would be that real estate portfolios would turn over less often. If we assume that people vary in their ability to make good real estate investments, this would mean that the best such investors wouldn’t make as many discrete investing decisions, which would make prices a bit less efficient. Which might be a reasonable tradeoff: making real estate investing a less tax-optimal choice could be a fair trade in exchange for making real estate prices less reflective of their value. But it’s still a tradeoff, not a straightforward benefit. Quirks in the tax code become load-bearing over time; even if they didn’t make economic sense when they were made, the structure of the economy only makes sense in light of the tax incentives that economic actors have already responded to. If you assume that people are reasonably good at reacting to incentives—or, more plausibly, that over time the people who are good at doing this end up controlling more assets—then any change in those incentives has complicated and unpredictable results.

The trade-off is one of price discovery vs the goals of tax-policy. Would we sacrifice liquidity and price discovery for another shared value even if it’s less legible?

This is right back to the heart of the matter. Efficiency we can measure vs equality we can measure. Are we even able to measure these values in a broad context where the multitude of considerations does not give way to the grinding demands of narrow optimization?

Conclusion

I can’t answer these musings. They are just the Money Angle exhaust of reading that damn essay.

The only things I’m reasonably sure of is:

  1. Communism is hell. Look I had to throw Satan a bone with all this attention I’m showering on another demon.
  2. Capitalism’s efficiency-equality tensions remind us that it is a compromise that must be tended with care because the invisible hand is connected to Moloch’s arm.

Last Call

Any longtime reader knows how big a fan I am of Khe Hy. He’s transparent, kind, and very smart.

While you still have that New Year’s bolt of energy and inspiration check out his totally free upcoming summit.

Your Roadmap for an Epic 2022 (Link)

Ready to hit your goals and accelerate your career? Start strong into 2022 with this free 3-day training for the RadReads community.

Khe’s material and delivery is a cut above. And I’m pretty skeptical of productivity porn. If you have energy swirling around inside you but struggling to convert it from potential to kinetic energy, take a look. It’s riskless.

Separately, if you’re thinking about entrepreneurship, read his recent story:

Why I’m Giving Up On Solopreneurship (Link)

Don’t Look Up, It’s Moloch

This is an actual story of an elementary school class election:

One of the kids running for class president gave an impassioned speech about what they would change (Maybe no hall monitors anymore, I have no idea, the detail isn’t important). Then the challenging candidate strides up to the podium and declares that if you elect him, he’ll secure the school a…rollercoaster! In the informal “exit poll”, one of the students was asked why they wanted to vote for the rollercoaster candidate and the student said, “I know it probably won’t happen, but what if it did?! That would be soooo cool”.

Surely the challenger is on their way to a lucrative career in politics.

And we are all worse off for it.

Why does it have to be this way?

For the same reason that the realtor who shouts the highest number gets the listing. The reason is…Moloch. A mythical demon that demands child sacrifice has become a metaphor for how things become terrible.

I’ll turn to Scott Alexander for an explanation:

The implicit question is – if everyone hates the current system, who perpetuates it? And Ginsberg answers: “Moloch”. It’s powerful not because it’s correct – nobody literally thinks an ancient Carthaginian demon causes everything – but because thinking of the system as an agent throws into relief the degree to which the system isn’t an agent.

Moloch is the odorless, selective pressures of evolution responding to incentives. It has no moral attribute. It just is. If you are an armchair game-theorist you see Prisoner’s Dilemmas everywhere you look. If you don’t already see them everywhere, bless your heart.

Personally, I constantly fight the resigned feeling that we cannot save ourselves from taking second-helpings of misery pie. “Moloch” is a catchy term that binds to situations known as “coordination problems”. These problems are too devilish to pin on any single individual (although this doesn’t stop anyone from trying to point fingers).

The sub-optimal equilibrium in a Prisoner’s Dilemma is not a mystery in itself. A Nash equilibrium is actually the result of choosing an action that you would have chosen even if you knew how your counterpart would act. The omnipresent Prisoner’s Dilemma is a narrow instance of what Alexander calls, a multi-polar trap — a situation where the best course of action for an individual makes the group worse off.

I dare you to resist nodding as you read this passage:

All these scenarios [described earlier] are in fact a race to the bottom. Once one agent learns how to become more competitive by sacrificing a common value, all its competitors must also sacrifice that value or be outcompeted and replaced by the less scrupulous. Therefore, the system is likely to end up with everyone once again equally competitive, but the sacrificed value is gone forever. From a god’s-eye-view, the competitors know they will all be worse off if they defect, but from within the system, given insufficient coordination it’s impossible to avoid…in some competition optimizing for X, the opportunity arises to throw some other value under the bus for improved X. Those who take it prosper. Those who don’t take it die out. Eventually, everyone’s relative status is about the same as before, but everyone’s absolute status is worse than before. The process continues until all other values that can be traded off have been – in other words, until human ingenuity cannot possibly figure out a way to make things any worse.

Read the essay. It’s one of Alexander’s best (it’s almost 6 years old now).

I’ll warn you. It’s quicksand (don’t worry, I have a plan to pull you out next Sunday). It articulates what you already sense but struggle to put your finger on.

You can find the essay as well as my commentary on it here:

Notes From Moloch


Under the oppression of Baader-Meinhoff, I could not help but think the comet in Don’t Look Up should have been named Moloch.

[Beware spoilers]

Alexander even wrote a review of the movie pointing out its contradictions and never even mentions Moloch.

He instead focuses on whether the writers were advocating for “trust the science”, “trust the experts”, or “don’t trust experts”, or “don’t trust the government”. The movie is a Rorschach. Choose one of those angles if you want. But if you do that, you need to confront the glaring contradictions of those interpretations. Alexander competently explains them in his review.

Still.

It’s not the angle I would have chosen.

I found that approach to the movie too quibbling. Too object level. Sure, this movie can be politically weaponized by either side to confirm their positions (deep state, climate complacency, Covid response). The other side could wave a contradiction in their face and we’ll just talk past each other, just like we do in real life and in the movie.

The real message of this movie is…Moloch.

The comet prompts system-wide institutional failure. A massive failure to coordinate. This is a movie that showed the end-state of gamesmanship and competition that is so exhausting we accept death as mercy. An overdue rest-in-peace. That final scene at the dinner table is disturbing and poignantly stirring at the same time.

Don’t Look Up skewers a culture that has thoroughly and without self-doubt internalized the strategy “it doesn’t matter what you say, but how you say it”. Marketing, storytelling, branding, signaling, persuasion. There is so much emphasis on our ability to hack each other because attention is what is scarce.

Moloch is not moral one way or the other. There is no redemption. In the film, Jennifer Lawrence remains pure. For that, she gets to live out her days bagging groceries. Leo eats from the serpent’s sweet apple nourishing his ego with the foreign but empty calories of in-crowd flattery.

Guess what?

Their fate did not discriminate.


A personal take on Don’t Look Up:

The movie is a comedy. It’s a satire. While I watched it, it felt like a slightly above average movie, but it has lingered so much in my head, that I’m not giving enough credit to how provocative it was as a piece of art. My favorite performance was Mark Rylance playing the rich tech founder meme. (Coincidentally, the best live performance I may have seen of anything ever was Rylance on Broadway in La Bete. He has a 45-minute soliloquy in iambic pentameter that is physically hilarious and verbally brilliant. He would make a rapper proud.)

If you watch Don’t Look Up, do not turn it off before the credits start rolling. You’ll miss the most satisfying part of the film.


Money Angle

In economics, there is a trade-off between efficiency and equality. Efficiency is concerned with maximizing output, and equity is about how that output is distributed. If I give a resource, for example, an education, to 9-year-old Elon Musk that’s more optimal than handing it to Snooki if I care about efficiency. If I want to be fair, I’d split my education budget between the two of them. This trade-off is fairly self-evident when you point it out.

(I’m imagining an Orange County strip-mall landlord droning on about Reagan’s “trickle-down” economics to a YouTube influencer wearing a Che Guevara tank top at a Hollywood Hills cocktail party.)

If we look at the extreme poles of the equality-efficiency spectrum, we would find archetypes for how our activities should be coordinated. Equality, as the primary goal, leads to top-down communism and authoritarianism. Sorry, there is no benevolent dictator.

Efficiency at-all-costs would be coordinated by free markets. “Free” of course is corruptible (i.e. crony capitalism) and anti-trust is a broadly accepted guardrail to protect us from winner-take-all endgames.

As capitalists, it’s more relevant to think about the Moloch essay in the context of markets. To that end, I just wanted to share some Moloch-meets-markets musings.

On Thoughtful Rules

The logic of markets is they are a coordination mechanism to get to truth or what finance-types call “price discovery”. Price discovery provides signals to guide how we allocate our physical and human capital. It does this through the “profit incentive” pathway. Oil prices rise when people demand to fly and drive. So you should drill for more oil because the price offers you a profit.

The problem is that the system can work too well.

The profit incentive is powerful because money is fungible with everything that’s promised to satisfy any human desire. Money, of course, is incapable of that, but very few people believe they have “enough”. We expect businesses and individuals to claw for profits and, obediently, they do.

This is fine and good. But it still requires some top-down design. Why?

Because when our horns are locked in competition for that oh so sweet profit, Moloch demands we push ourselves right up to the line. The person who wins that last dollar must dispense with every other value so long as it doesn’t violate the law. Norms are not even effective restraints at the pinnacle of competition where you are likely to find sociopaths.

To keep Moloch from running wild we need the lines we draw to accommodate the fact that once we yell “go” everyone will look for every possible edge. Our lines must account for externalities. That’s what anti-pollution laws are. Our accounting laws serve similar functions. A carbon credit is an accounting term that “internalizes” an externality. It forces the emitter to own what they’ve done. They need to put it into their profit calculus.

On Flexibility

Of course, even well-considered laws will be gamed. But I couldn’t help notice that the marketplace seems to be telling us that the laws are behind the times.

Consider examples coming from different directions:

  1. Matt Levine’s “everything is securities fraud” thesis suggests that any practice that damages shareholder value, even if it’s legal can be used retroactively as the basis for a lawsuit. This forces management to consider their externalities even if stodgy laws and accounting rules cannot keep up with a rapidly changing world.
  2. From the other side, ESG, at least in its idealized form, is pushing to internalize the externalities by pushing our wider discarded values back onto balance sheets as more explicit liabilities. Instead of using judges, they want to use accounting laws and influence investing norms.
  3. Then you have crypto’s techno-libertarianism. If you love the idea of smart contracts’ black-and-whiteness, you should prefer the ESG reform to the whim of human judgments after-the-fact. If smart contract purists are more comfortable choosing the letter over the spirit of the law, they must be dead-set on demanding bright lines for every issue. (Sounds great if you hate nuance. Like religious fundamentalists. Or toddlers.)

    Smart contracts are a brilliant idea. Just not for every decision context.

On Liquidity

Price discovery increases with liquidity. This is mostly uncontroversial (if there were no VCs reading this I would have ditched the word “mostly” but I do love Moontower readers, so an olive branch is in order). And if price discovery and liquidity are good, is more always better?

The amount of brainpower and resources devoted to capturing that last penny of arbitrage in markets is formidable. What is the true cost of that price being “discovered”? I don’t even know where to start with that one (Jessica, in her characteristic snark, wonders a similar question on Twitter).

Let’s consider a more tractable question from Byrne Hobart. As he thought about the proposed repeal of 1031 exchanges, he wrote (bold is mine):

The defense of 1031 exchanges is that they encourage growth, because they keep people spending money on new property developments instead of cashing out and enjoying their gains. Which embeds two assumptions:

  1. It’s generally better to tax consumption than investment, and
  2. Real estate investment is a particularly worthy kind of investment to avoid taxing.

Assumption #1 sounds true, but is circumstantial. Assumption #2, though, is hard to defend. Real estate speculation does produce jobs, but it also produces macroeconomic volatility and sometimes threatens the financial system. From a macroprudential perspective, where the goal is to reduce the odds of financial crises, it might make more sense to have 1031 exchanges for everything but real estate: sell your company, and you can roll the money into starting a new one; sell a mall or skyscraper, and you get taxed. But it’s always fiendishly hard to predict the long-term incentives created by a change in the tax code. Any tax on realizing gains, for example, is implicitly a subsidy on borrowing against appreciated assets instead of realizing those gains. If that’s true, the net effect of eliminating 1031 exchanges would be that real estate portfolios would turn over less often. If we assume that people vary in their ability to make good real estate investments, this would mean that the best such investors wouldn’t make as many discrete investing decisions, which would make prices a bit less efficient. Which might be a reasonable tradeoff: making real estate investing a less tax-optimal choice could be a fair trade in exchange for making real estate prices less reflective of their value. But it’s still a tradeoff, not a straightforward benefit. Quirks in the tax code become load-bearing over time; even if they didn’t make economic sense when they were made, the structure of the economy only makes sense in light of the tax incentives that economic actors have already responded to. If you assume that people are reasonably good at reacting to incentives—or, more plausibly, that over time the people who are good at doing this end up controlling more assets—then any change in those incentives has complicated and unpredictable results.

The trade-off is one of price discovery vs the goals of tax-policy. Would we sacrifice liquidity and price discovery for another shared value even if it’s less legible?

This is right back to the heart of the matter. Efficiency we can measure vs equality we can measure. Are we even able to measure these values in a broad context where the multitude of considerations does not give way to the grinding demands of narrow optimization?

Conclusion

I can’t answer these musings. They are just the Money Angle exhaust of reading that damn essay.

The only things I’m reasonably sure of is:

  1. Communism is hell. Look I had to throw Satan a bone with all this attention I’m showering on another demon.
  2. Capitalism’s efficiency-equality tensions remind us that it is a compromise that must be tended with care because the invisible hand is connected to Moloch’s arm.

Notes From Moloch

Select excerpts from Slatestarcodex’s:

Meditations on Moloch (Link)

The premise:

The implicit question is – if everyone hates the current system, who perpetuates it? And Ginsberg answers: “Moloch”. It’s powerful not because it’s correct – nobody literally thinks an ancient Carthaginian demon causes everything – but because thinking of the system as an agent throws into relief the degree to which the system isn’t an agent.


Categories and examples of “multi-polar traps”

Situations where the best course of action for an individual makes the group worse off.

I sorted them as follows:

  1. Prisoner’s Dilemma
    • Dollar auctions (think of “pay to bid” auctions)
    • Tragedy of the commons problems (ie overfishing)

  2. Race to the bottom
    • Malthusian Traps (intense competitive pressures that penalize attempts at “slack”)
    • Capitalism (an instance of the evolutionary mechanism underlying Malthusian traps)
    • Two-income traps (From within the system, absent a government literally willing to ban second jobs, everyone who doesn’t get one will be left behind.)
    • Agriculture (Maybe hunting-gathering was more enjoyable, higher life expectancy, and more conducive to human flourishing – but in a state of sufficiently intense competition ag wins)
    • Arms races
    • Education signaling
    • Science and pseudo-science research
    • Gov’t corruption
    • Politics (Congressmen tactics to get elected)

All these scenarios are in fact a race to the bottom. Once one agent learns how to become more competitive by sacrificing a common value, all its competitors must also sacrifice that value or be outcompeted and replaced by the less scrupulous. Therefore, the system is likely to end up with everyone once again equally competitive, but the sacrificed value is gone forever. From a god’s-eye-view, the competitors know they will all be worse off if they defect, but from within the system, given insufficient coordination it’s impossible to avoid.

…in some competition optimizing for X, the opportunity arises to throw some other value under the bus for improved X. Those who take it prosper. Those who don’t take it die out. Eventually, everyone’s relative status is about the same as before, but everyone’s absolute status is worse than before. The process continues until all other values that can be traded off have been – in other words, until human ingenuity cannot possibly figure out a way to make things any worse.

My own local example:

The public school system shifted the start date of the scholastic year up from late August to early August to gain an artifical advantage in year-end standardized test scores by giving the students more time to prepare. Eventually, all schools will adopt this to maintain competitiveness and we’ll sacrifice the value of summer vacations in August when people commonly take off work and camps are not in session.

Select Excerpts

On incentives and initial conditons…

Any human with above room temperature IQ can design a utopia. The reason our current system isn’t a utopia is that it wasn’t designed by humans. Just as you can look at an arid terrain and determine what shape a river will one day take by assuming water will obey gravity, so you can look at a civilization and determine what shape its institutions will one day take by assuming people will obey incentives. But that means that just as the shapes of rivers are not designed for beauty or navigation, but rather an artifact of randomly determined terrain, so institutions will not be designed for prosperity or justice, but rather an artifact of randomly determined initial conditions.

We just analogized the flow of incentives to the flow of a river. The downhill trajectory is appropriate: the traps happen when you find an opportunity to trade off a useful value for greater competitiveness. Once everyone has it, the greater competitiveness brings you no joy – but the value is lost forever. Therefore, each step of the Poor Coordination Polka makes your life worse.

Capitalism

Capitalism is a lossy accounting system in that it can elevate priorities without precision. Not unlike napalm. Its a victim of its own success in the sense that any critique of it galvanizes its defense with soothing rationalizations both by the rich and by those to whom it has unknowingly imprisoned. Look, capitalism is good. It doesn’t need religious arguments in its favor to affirm that. Those arguments discredit its supporters which is a collective self-own. It’s possible to discuss its merits and flaws in the same room.

With that said, here’s a nuanced point from the essay…

I know that “capitalists sometimes do bad things” isn’t exactly an original talking point. But I do want to stress how it’s not equivalent to “capitalists are greedy”. I mean, sometimes they are greedy. But other times they’re just in a sufficiently intense competition where anyone who doesn’t do it will be outcompeted and replaced by people who do. Business practices are set by Moloch, no one else has any choice in the matter. (from my very little knowledge of Marx, he understands this very very well and people who summarize him as “capitalists are greedy” are doing him a disservice)

Politics

Politics is similarly skewed…

As well understood as the capitalist example is, I think it is less well appreciated that democracy has the same problems. Yes, in theory it’s optimizing for voter happiness which correlates with good policymaking. But as soon as there’s the slightest disconnect between good policymaking and electability, good policymaking has to get thrown under the bus. For example, ever-increasing prison terms are unfair to inmates and unfair to the society that has to pay for them. Politicans are unwilling to do anything about them because they don’t want to look “soft on crime”, and if a single inmate whom they helped release ever does anything bad (and statistically one of them will have to) it will be all over the airwaves as “Convict released by Congressman’s policies kills family of five, how can the Congressman even sleep at night let alone claim he deserves reelection?”. So even if decreasing prison populations would be good policy – and it is – it will be very difficult to implement.

The libertarian-authoritarian axis on the Political Compass is a tradeoff between discoordination and tyranny. You can have everything perfectly coordinated by someone with a god’s-eye-view – but then you risk Stalin. And you can be totally free of all central authority – but then you’re stuck in every stupid multipolar trap Moloch can devise. The libertarians make a convincing argument for the one side, and the monarchists for the other, but I expect that like most tradeoffs we just have to hold our noses and admit it’s a really hard problem.

This reminds me of a story I heard from my wife about an elementary school class election. One kid gave an impassioned speech about what they would change (no hall monitors anymore? I have no idea what kids see as the real issues in that otherwise simulcrum of no reality I know of called “school”). Anyway, the challenging candidate rolls up to the podium and declares that if you elect him, he’ll secure the school a…rollercoaster! In the exit poll one of the students was asked why they voted for the rollercoaster candidate and the student said, “I know it probably won’t happen, but what if it did?! That would be soooo cool”.

I suspect the challenger is on their way to a lucrative career in politics.

And we are all worse off for it.

How conservative and liberal views of societal evolution dictate thir imperatives

Societies, like animals, evolve. The ones that survive spawn memetic descendants – for example, the success of Britan allowed it to spin off Canada, Australia, the US, et cetera. Thus, we expect societies that exist to be somewhat optimized for stability and prosperity. I think this is one of the strongest conservative arguments. Just as a random change to a letter in the human genome will probably be deleterious rather than beneficial since humans are a complicated fine-tuned system whose genome has been pre-optimized for survival – so most changes to our cultural DNA will disrupt some institution that evolved to help Anglo-American (or whatever) society outcompete its real and hypothetical rivals.

The liberal counterargument to that is that evolution is a blind idiot alien god that optimizes for stupid things and has no concern with human value. Thus, the fact that some species of wasps paralyze caterpillars, lay their eggs inside of it, and have its young devour the still-living paralyzed caterpillar from the inside doesn’t set off evolution’s moral sensor, because evolution doesn’t have a moral sensor because evolution doesn’t care. Suppose that in fact patriarchy is adaptive to societies because it allows women to spend all their time bearing children who can then engage in productive economic activity and fight wars. The social evolutionary processes that cause societies to adopt patriarchy still have exactly as little concern for its moral effects on women as the biological evolutionary processes that cause wasps to lay their eggs in caterpillars. Evolution doesn’t care. But we do care. There’s a tradeoff between Gnon-compliance – saying “Okay, the strongest possible society is a patriarchal one, we should implement patriarchy” and our human values – like women who want to do something other than bear children.

Too far to one side of the tradeoff, and we have unstable impoverished societies that die out for going against natural law. Too far to the other side, and we have lean mean fighting machines that are murderous and miserable. Think your local anarchist commune versus Sparta.

An optimistic angle. Or maybe not.

Franklin continues: “The project of civilization [is] for man to graduate from the metaphorical savage, subject to the law of the jungle, to the civilized gardener who, while theoretically still subject to the law of the jungle, is so dominant as to limit the usefulness of that model. This need not be done globally; we may only be able to carve out a small walled garden for ourselves, but make no mistake, even if only locally, the project of civilization is to capture Gnon. “

I maybe agree with Warg here more than I have ever agreed with anyone else about anything. He says something really important and he says it beautifully and there are so many words of praise I want to say for this post and for the thought processes behind it. But what I am actually going to say is…

Gotcha! You die anyway!

My Concluding Thoughts

  • First a general thought:

    This essay is infotainment. It’s a work of art, it’s provocative, and one I expect to return to because it is stirring. Its sense-making Slatestar at his best. It’s dreary by default. But I see a glimmer of liberation peeking from behind its nimbus:

    If you accept its hopelessness and kneel to Moloch, you might fare better. But it’s delaying the inevitable. Instead, you can rebel. It might be quiet. And maybe nobody will care. But a large part of your reality is your own internal narration of it. There are truths that inhabit the physical world. Beyond that, things veer pretty quickly towards “it’s all made up”. This is liberation. How you feel about how you play matters. You might as well play your way since it doesn’t matter anyway.

    But this is not even the useful part.

    The real gift is once you witness how others deal with this non-mattering, you have found a magic compass. It points you to the family you choose. It gives you back control of your attention. And while we’re here, that’s probably the most useful choice we have.

  • A (pollyannish?) thought:

    This essay highlights how capitalism and competition narrow our values. ESG seeks to broaden our values. There is some irony in that one of the arguments in favor of ESG is that if we internalized our externalities, through what amounts to a broader system of accounting, that it would also maximize a Chicago-school capitalists brand of utility.

    Perhaps this is true. Companies that are more virtuous might be better for “shareholder value” in the long run. But part of me finds that reasoning patronizing. Like hiding the dog’s pill in peanut butter. 

    The ESGer is conceding a point they shouldn’t have to. Instead of trying to fit a wider set of values into an existing legible accounting system we could realize that the system is a needless sacrifice to legibility.

    (I don’t need a lecture on the grifty aspects of ESG. Every movement that gains traction brings its share of mops and sociopaths.)

  • Finally:

    You should read the essay. It’s a classic from a good writer. If you need another breadcrumb, one of the questions Slatestar poses:

    Why do things not degenerate more and more until we are back at subsistence level?

    I can think of three bad reasons – excess resources, physical limitations, and utility maximization – plus one good reason – coordination.

    You’ll need to read it to explore the answers.

Unibrow

I’m going to take you into the holidays with a quick personal story.

I was driving Zak, my 3rd grader, to basketball practice.

Zak: Dad, I learned something today.

Me: What’s that bud?

Zak: I learned I had a unibrow today. XXX told me.

Me: (heart sinks as the vapor of childhood innocence wafts out the car window) Was XX mean about it?

Zak: No. (Nonchantly. Almost surprised I would ask.)

Me: How did it make you feel?

Zak: (a pause that felt like forever to me but was probably only 2 seconds) It feels cool. I have a unibrow and I’m double-jointed so it’s hard for other people to be like me.

Mic drop for mom and dad. You can go to college now, there’s nothing left for us to do kid.

Seriously, this was the opposite of me at his age. I remember feeling bad for blue-eyed kids because they were different. My desire was just to fit in and not get made fun of for eating pita bread.

I don’t actually believe we have anything to do with this kid’s understated confidence. He’s sensitive and sweet. Full of joy. I have another son and know the difference. I know many of you have children that seem like they’re from different planets and can relate to how mysterious these creatures under your same roof are.

I learn a lot from watching Zak. His dominant characteristic is “happy wherever he is”. I seriously try to channel him when I’m anxious. The exchange we had in the car was a proud moment in the face of the tension all parents face — trying to balance prepping these small humans for reality and preserving their innocence.

Still, this is not really a parenting win.

Sometimes it’s just them. And you can learn from them if you take them seriously. It’s a strange privilege to admire your kid. I’m proud of him but that’s a weak description because “being proud” of a gift that comes from nowhere is not the right feeling.

I’m just grateful.

Happy Holidays!

Moontower #131

Friends,

First, a quick mention that Moontower is taking the next 2 weeks off and returning on January 9th. We can all use a bit less stimulation at the end of the year. Play some boardgames, go to sleep late, binge some shows, gain a few pounds. Laugh so hard bourbon eggnog comes out your nose. Shower your loved ones with attention. You’re not missing anything, including Moontower.


Money Angle

Two personal finance ideas to wrap the year:

  1. When the calendar rolls to 2022, I’m re-loading another slug of 7.12% I-bonds. I explained them in I-Bonds For You (2 min read)
  2. I’m buying my car lease out. If your lease period is ending, compare its residual with the used market price. Your leases are options that are way in-the-money. You should buy your leases out if they are expiring. Do not just give the car back. I’m hearing that dealers are offering to pay lessees to get the cars back. You have maximum negotiating power right now.

From My Actual Life

I’m going to take you into the holidays with a quick personal story.

I was driving Zak, my 3rd grader, to basketball practice.

Zak: Dad, I learned something today.

Me: What’s that bud?

Zak: I learned I had a unibrow today. XXX told me.

Me: (heart sinks as the vapor of childhood innocence wafts out the car window) Was XX mean about it?

Zak: No. (Nonchantly. Almost surprised I would ask.)

Me: How did it make you feel?

Zak: (a pause that felt like forever to me but was probably only 2 seconds) It feels cool. I have a unibrow and I’m double-jointed so it’s hard for other people to be like me.

Mic drop for mom and dad. You can go to college now, there’s nothing left for us to do kid.

Seriously, this was the opposite of me at his age. I remember feeling bad for blue-eyed kids because they were different. My desire was just to fit in and not get made fun of for eating pita bread.

I don’t actually believe we have anything to do with this kid’s understated confidence. He’s sensitive and sweet. Full of joy. I have another son and know the difference. I know many of you have children that seem like they’re from different planets and can relate to how mysterious these creatures under your same roof are.

I learn a lot from watching Zak. His dominant characteristic is “happy wherever he is”. I seriously try to channel him when I’m anxious. The exchange we had in the car was a proud moment in the face of the tension all parents face — trying to balance prepping these small humans for reality and preserving their innocence.

Still, this is not really a parenting win.

Sometimes it’s just them. And you can learn from them if you take them seriously. It’s a strange privilege to admire your kid. I’m proud of him but that’s a weak description because “being proud” of a gift that comes from nowhere is not the right feeling.

I’m just grateful.

Happy Holidays!


Wrapping 2021

Moontower Gratitude

I started writing online nearly 3 years ago. I started by curating stuff I enjoyed and adding commentary to it before finding my own voice. Of the stuff I write my favorite thing is the challenge of breaking down concepts into something a HSer can handle, if not younger. I also enjoy organizing notes or resources into references. This little online writing experiment has told me I’m probably supposed to be a teacher and librarian. While I’m not likely to find my way into a school setting, I will carry these clues into whatever comes next for me commercially. Without having the feedback and encouragement of an audience like you I would have less options as I think about the next step.

So thank you.

(In case curious, subs grew from 1,100 to 2,700 in 2021)

Encouragement

And if you are even thinking about writing online then you should be writing online. The easiest way to start is to curate stuff from one sphere of your life (say Twitter) and bring it to another (ie your meatspace friends). The raw material is free and there’s value in it for an offline audience who checks their email. It’s the most basic arbitrage. Think it over during some of that holiday downtime.

A Request

While you are mixing it up with your loved ones this season see if there is one person who you think would enjoy or benefit from Moontower. If you are enjoying Moontower you are giving both them and me a small gift by spreading the word.

Just say, “you should check out this letter named after that scene in Dazed and Confused where some stoners contemplated how many people in Austin were having sex at this very moment. I’ll text you the link



Writing Recap

This is the self-promotional section meant to quicksand recent subs into the rest of my work muahahahaha.

Top Moontower Posts of 2021

  1. Why Investing Feels Like Astrology (19 min read)
  2. Using The TSLA Price Endgame To Understand Options (12 min read)
  3. How Options Confuse Directional Traders (8 min read)
  4. The “R” Word (13 min read)
  5. Structuring Directional Option Trades (8 min read)
  6. Understanding Edge (10 min read)
  7. How I Misapplied My Trader Mindset To Investing (14 min read)
  8. Talking To The Diamond Hands (22 min read)
  9. Understanding Vega Risk (6 min read)
  10. A Former Market Maker’s Perception Of PFOF (9 min read)

Math Posts

  1. Solving A Compounding Riddle With Black-Scholes (13 min read)
  2. I Felt Bad For Picking My 3rd Grader Off (8 min read)
  3. Jensen’s Inequality As An Intuition Tool (10 min read)
  4. The Monty Hall Problem Is More Than A Game (4 min read)
  5. Berkson’s Paradox (5 min read)

Other Projects

  • Moontower Volatility Wiki (Link)

    This is a reference for anyone interested in options, from beginners to seasoned pros to academics. The material is mostly crowdsourced but I vet it to maintain some minimum bar of usefulness.

  • A Summary Of Jesse Livermore’s Upside Down Markets (Link)

    Upside Down Markets is a book-length paper by the pseudonymous @Jesse_Livermore. It’s one of the most educational economic pieces I’ve read and it’s extremely relevant to today’s environment. I urge you to read the paper. Still I cleaned up my notes and shared them which are in a reference-friendly outline form.

  • Moontower Home (Link)

    Most of my effort is focused on evergreen content rather than commentary on what’s going on in real-time. A chronological blog is a poor way to organize this type of writing. Wikis and indexes make more sense. I started using Potion.so this year to centralize Notion as my CMS.

    This home-on-the-web branches to everything I’ve done.

Moontower #130

You may have heard that “filter bubbles” are a source of tension. People are silo’d in their little worlds and don’t know or understand the views of others who think differently. If that’s the correct diagnosis for what is happening around us, then exposure and education are the prescriptions.

I’m skeptical.

I recently listened to an interview with philosopher C. Thi Nguyen, author of Games: Agency As Art on physics Sean Carroll’s Mindscape podcast. It was one of those interviews I listened to twice and wrote notes on.

You can check out the conversation and see my notes:

Notes From C.Thi Nguyen Interview About Games and Society (14 min read)

Feel free to skip to the parts you are interested in. The lessons feel like they confirm my skepticism. It ties back to how our minds feel when we play games and, provocatively, some really basic human needs.

I won’t say too much because it’s worth at least skimming the takeaways, but I’ll share a single thought I have crystallized in the past few months:

What ideologies lack in rightness, they make up for in tidiness and convenience.

Of course, if you internalize Nguyen’s views, you can also see why my thought is deeply ironic.

Give it a listen.

Money Angle

This week I published:

Solving A Compounding Riddle With Black-Scholes (14 min read)

It’s a bit longer than a usual post as I try to balance ELI5 with dragging things out too much.

I’ll do a quick overview here.

It starts with:

If you have read about “volatility tax” or geometric returns, you can quickly dismiss choice #4 in the poll (click the tweet to see the choices). Over 2k people (30%) of respondents picked the one that requires doing no work.

There are still 3 answers to choose from. Since N was only 10 years it was easy enough to pen and paper the binomial tree. But before you even do that there’s another insight you could have.

Just like any 3,5,7 or odd-game series, there must be a winner…so if Stock B has more up years than bad years it will probably outperform A. The odds of that are 50/50.

But…this question is about year 10. An even year. That means Stock B could experience 5 up years and 5 down years. The “volatility tax” will punish that scenario (“volatility tax” in a nutshell: .90*1.10*$100 = $99)

So in a 10-year horizon, B loses to A if B has:

0 ups, 10 downs
1u,9d
2u,8d
3u,7d
4u,6d

and crucially… 5u, 5d

We can draw Pascal’s Triangle to see the coefficient for the middle term: 5u, 5d

[The coefficient is the number of ways an outcome can occur or =combin(10,5) in Excel]

252/1024 = 24.6%

24.6% of the time the volatility tax causes A > B.

The remaining paths represent 75.4% of the paths and those have a clear winner that is evenly split between A>B and B>A.

75.4% / 2 = 37.7%

So volatile stock B only outperforms stock A 37.7% of the time!

Part of the reason the post is long is that I explain much of this stuff slowly and contextualize it with a discussion of geometric returns. This is just basic stuff, so far.

The better part follows.

It starts with a problem in my process, even though it’s the right answer…

My logic doesn’t scale as N grows.

Here’s why:

Image

What can we do now?

The annual compounding, binomial framework lent itself to simple binomial-formula-chugging or tree-building. But if we switch to a continuous compounding framework we can use option math!

Put Your Options Hats On

The first thing I did is just approximate the volatility of Stock B with a round number…20%. (you make 30% or lose 10% each year. 20% vol is good enough for this context)

The original question using 20% vol:

What’s the probability that stock B with its 10% annual return and 20% volatility outperforms stock A with its 10% annual return and zero volatility in 10 years?

Now let’s rephrase the original question as an option’s question:

What is the probability that a 10-year call option on stock B with a strike price of $271.83 expires in-the-money?

[*$271.83 is the bogey set by stock A derived from continuously compounding $100 at 10% per year for 10 years (ie Seʳᵗ)]

Often when people hear “probability of expiring ITM” they think, “that’s delta”. Not quite. The post has some refresher on why.

Don’t worry, Black-Scholes still has the answer to our question. Here’s why:

Image

So what happens when we compute N(d2) or “probability of expiring ITM” for Stock B at a strike of $271.83.

Boom.

37.6%

Respectably close to the answer we got from the binomial brute force.

This makes sense because the compounding effect on the payoff distribution is almost identical and Black-Scholes’ underlying distribution is the assumption of continuously compounded (ie log) returns.

This summary pic is the coup-de-gras but I explain how I built it (again the post is intentionally tedious, so if you are experienced, feel free to skim/skip)

Image

Finally, I toss in some intuition for why skew is often counterintuitive:

Image

And then I circle back to props to @10kdiver because I’m a fan of the effort he puts into explaining. He’s got beaucoup skills, so it gives me something to aspire to as far as trying to communicate concepts better.

Please check his threads here: https://10kdiver.com/twitter-threads/

Perth Tolle’s Interview On Yinh’s Growth From Failure Podcast

Fintwitters and folks in asset management likely already know Perth Tolle, founder of Life & Liberty Indexes and creator of the Freedom ETF, which tracks the freedom-weighted emerging markets index.

One of the neat things about Yinh’s podcast is she tends to find people with interesting stories who are relatively unknown, many of them having never been interviewed before. Perth, on the other hand, is well-known in the finance world. She has been interviewed in many places and is a regular on CNBC.

And yet, she still had this to say which I will leave as its own teaser:

Listen to the interview here:

https://www.growthfromfailure.com/podcast/perth-tolle

In this episode:
– Perth’s first exposure to censorship
– Moving from China to the US
– Delaying law school to move to Hong Kong
– How she became interested in finance and investments
– Creating the Freedom ETF
– Her “Grand Design”

To learn more about Perth, the Freedom ETF or Life and Liberty Indexes, you can visit:


Job Opportunities

TradFi

[Re-posting. This led to some amazing inbound last week. I hear some people charge for this kinda thing.]

An awesome team (I can’t overstate awesome here) is looking for a junior full-stack developer. You will learn from seasoned quant PM and be part of building a HF from the ground up.

Requirements:

  • Ability to work on full-stack including DevOps
  • Python, JS/React, SQL, Redis

Good to have:

  • C# and experience with distributed systems

This group is very groovy, if you’re hungry and eager to learn and build, it will be an amazing opportunity.

Hit them up here: omk.jrdev@gmail.com

Crypto

My friend Charlie Graham is a successful tech entrepreneur and world-class puzzle creator and solver. After our sons’ basketball game yesterday he mentioned that he’s trying to find a senior Elixir developer for his latest venture, Hawku.

Hawku is a well-funded startup that is:

building a marketplace that is focused on the specific needs of gaming and utility NFTs. Our vision is to provide prospective buyers with the real-time data they need to research, buy and sell utility-based assets.

Hawku already has a platform that provides the key information players need to research, buy and sell horse NFTs for the popular Zed.run game platform.  In the four months since it launched, Hawku has already reached 3M monthly page views and has built an avid following.

This is a list of the open positions: https://jobs.hawku.com/

This is the post for the senior/lead Elixir dev.


Have a groovy week!

Kris

Solving A Compounding Riddle With Black-Scholes

A few weeks ago I was getting on an airplane armed with a paper and pen, ready to solve the problem in the tweet below. And while I think you will enjoy the approach, the real payoff is going to follow shortly after — I’ll show you how to not only solve it with option theory but expand your understanding of the volatility surface. This is going to be fun. Thinking caps on. Let’s go.

The Question That Launched This Post

From that tweet, you can see the distribution of answers has no real consensus. So don’t let others’ choices affect you. Try to solve the problem yourself. I’ll re-state some focusing details:

  • Stock A compounds at 10% per year with no volatility
  • Stock B has the same annual expectancy as A but has volatility. Its annual return is binomial — either up 30% or down 10%.
  • After 10 years, what’s the chance volatile stock B is higher than A?

You’ll get the most out of this post if you try to solve the problem. Give it a shot. Take note of your gut reactions before you start working through it. In the next section, I will share my gut reaction and solution.

My Approach To The Problem

Gut Reaction

So the first thing I noticed is that this is a “compounding” problem. It’s multiplicative. We are going to be letting our wealth ride and incurring a percent return. We are applying a rate of return to some corpus of wealth that is growing or shrinking. I’m being heavy-handed in identifying that because it stands in contrast to a situation where you earn a return, take profits off the table, and bet again. Or situations, where you bet a fixed amount in a game as opposed to a fraction of your bankroll. This particular poll question is a compounding question, akin to re-investing dividends not spending them. This is the typical context investors reason about when doing “return” math. Your mind should switch into “compounding” mode when you identify these multiplicative situations.

So if this is a compounding problem, and the arithmetic returns for both investments are 10% I immediately know that volatile stock “B” is likely to be lower than stock “A” after 10 years. This is because of the “volatility tax” or what I’ve called the volatility drain. Still, that only conclusively rules out choice #4. Since we could rule that without doing any work and over 2,000 respondents selected it, I know there’s a good reason to write this post!

Showing My Work

Here’s how I reasoned through the problem step-by-step.

Stock A’s Path (10% compounded annually)

Stock B’s Path (up 30% or down 10%)

The fancy term for this is “binomial tree” but it’s an easy concept visually. Let’s start simple and just draw the path for the first 2 years. Up nodes are created by multiplying the stock price by 1.3, down modes are created by multiplying by .90.

Inferences

Year 1: 2 cumulative outcomes. Volatile stock B is 50/50 to outperform
Year 2: There are 3 cumulative outcomes. Stock B only outperforms in one of them.

Let’s pause here because while we are mapping the outcome space, we need to recognize that not every one of these outcomes has equal probability.

2 points to keep in mind:

  • In a binomial tree, the number of possibilities is 2ᴺ where N is the number of years. This makes sense since each node in the tree has 2 possible outcomes, the tree grows by 2ᴺ.
  • However, the number of outcomes is N + 1. So in Year 1, there are 2 possible outcomes. In year 2, 3 possible outcomes.

Probability is the number of ways an outcome can occur divided by the total number of possibilities.

Visually:


So by year 2 (N=2), there are 3 outcomes (N+1) and 4 cumulative paths (2ᴺ)

We are moving slowly, but we are getting somewhere.

In year 1, the volatile investment has a 50% chance of winning. The frequency of win paths and lose paths are equal. But what happens in an even year?

There is an odd number of outcomes, with the middle outcome representing the number of winning years and the number of losing years being exactly the same. If the frequency of the wins and losses is the same the volatility tax dominates. If you start with $100 and make 10% then lose 10% the following year, your cumulative result is a loss.

$100 x 1.1 x .9 = $99

Order doesn’t matter.

$100 x .9 x 1.1 = $99

In odd years, like year 3, there is a clear winner because the number of wins and losses cannot be the same. Just like a 3-game series.

Solving for year 10

If we extend this logic, it’s clear that year 10 is going to have a big volatility tax embedded in it because of the term that includes stock B having 5 up years and 5 loss years.

N = 10
Outcomes (N+1) = 11 (ie 10 up years, 9 up years, 8 up years…0 up years)
# of paths (2ᴺ) = 1024

We know that 10, 9, 8,7,6 “ups” result in B > A.
We know that 4, 3, 2,1, 0 “ups” result in B < A

The odds of those outcomes are symmetrical. So the question is how often does 5 wins, 5 losses happen? That’s the outcome in which stock A wins because the volatility tax effect is so dominant.

The number of ways to have 5 wins in 10 years is a combination formula for “10 choose 5”:

₁₀C₅ or in Excel =combin(10,5) = 252

So there are 252 out of 1024 total paths in which there are 5 wins and 5 losses. 24.6%

24.6% of the time the volatility tax causes A > B. The remaining paths represent 75.4% of the paths and those have a clear winner that is evenly split between A>B and B>A.

75.4% / 2 = 37.7%

So volatile stock B only outperforms stock A 37.7% of the time despite having the same arithmetic expectancy!

This will surprise nobody who recognized that the geometric mean corresponds to the median of a compounding process. The geometric mean of this investment is not 10% per year but 8.17%. Think of how you compute a CAGR by taking the terminal wealth and raising it to the 1/N power. So if you returned $2 after 10 years on a $1 investment your CAGR is 2^(1/10) – 1 = 7.18%. To compute a geometric mean for stock B we invert the math: .9^(1/2) * 1.3^(1/2) -1  = 8.17%. (we’ll come back to this after a few pictures)

The Full Visual

A fun thing to recognize with binomial trees is that the coefficients (ie the number of ways a path can be made that we denoted with the “combination” formula) can be created easily with Pascal’s Triangle. Simply sum the 2 coefficients directly from the line above it.

Coefficients of the binomial expansion (# of ways to form the path)

 

Probabilities (# of ways to form each path divided by total paths)

Corresponding Price Paths

Above we computed the geometric mean to be 8.17%. If we compounded $100 at 8.17% for 10 years we end up with $219 which is the median result that corresponds to 5 up years and 5 down years! 

The Problem With This Solution

I solved the 10-year problem by recognizing that, in even years, the volatility tax would cause volatile stock B to lose when the up years and down years occurred equally. (Note that while an equal number of heads and tails is the most likely outcome, it’s still not likely. There’s a 24.6% chance that it happens in 10 trials).

But there’s an issue. 

My intuition doesn’t scale for large N. Consider 100 years. Even in the case where B is up 51 times and down 49 times the volatility tax will still cause the cumulative return of B < A. We can use guess-and-test to see how many winning years B needs to have to overcome the tax for N = 100.

N = 100

If we put $1 into A, it grows at 1.1^100 = $13,871

If we put $1 into B and it has 54 winning years and 46 losing years, it will return 1.3^54 * .9^46 = $11,171. It underperforms A.

If we put $1 into B and it has 55 winning years and 45 losing years, it will return 1.3^55 * .9^45 = $16,136. It outperforms A.

So B needs to have 55 “ups”/45 “downs” or about 20% more winning years to overcome the volatility tax. It’s not as simple as it needs to win more times than stock A, like we found for shorter horizons.

We need a better way. 

The General Solution Comes From Continuous Compounding: The Gateway To Option Theory

In the question above, we compounded the arithmetic return of 10% annually to get our expectancy for the stocks.

Both stocks’ expected value after 10 years is 100 * 1.1^10 = $259.37.

Be careful. You don’t want the whole idea of the geometric mean to trip you up. The compounding of volatility does NOT change the expectancy. It changes the distribution of outcomes. This is crucial.

The expectancy is the same, the distribution differs.

If we keep cutting the compounding periods from 1 year to 1 week to 1 minute…we approach continuous compounding. That’s what logreturns are. Continuously compounded returns.

Here’s the key:

Returns conform to a lognormal distribution. You cannot lose more than 100% but you have unlimited upside because of the continuous compounding. Compared to a bell-curve the lognormal distribution is positively skewed. The counterbalance of the positive skew is that the geometric mean or center of mass of the distribution is necessarily lower than the arithmetic expectancy. How much lower? It depends on the volatility because the volatility tax1 pulls the geometric mean down from the arithmetic mean or expectancy. The higher the volatility, the more positively skewed the lognormal or compounded distribution is. The more volatile the asset is in a positively skewed distribution the larger the right tail grows since the left tail is bounded by zero. The counterbalance to the positive skew is that the most likely outcome is the geometric mean.

I’ll pause here for a moment to just hammer home the idea of positive skew:

If stock B doubled 20% of the time and lost 12.5% the remaining 80% of the time its average return would be exactly the same as stock A after 1 year (20% * $200 + 80% * $87.5 = $110). The arithmetic mean is the same. But the most common lived result is that you lose. The more we crank the volatility higher, the more it looks like a lotto ticket with a low probability outcome driving the average return.

Look at the terminal prices for stock B:

The arithmetic mean is the same as A, $259.

The geometric or mean or most likely outcome is only $219 (again corresponding to the 8.17% geometric return)

The magnitude of that long right tail ($1,379 is > 1200% total return, while the left tail is a cumulative loss of 65%) is driving that 10% arithmetic return.

Compounding is pulling the typical outcome down as a function of volatility but it’s not changing the overall expectancy.

A Pause To Gather Ourselves

  • We now understand that compounded returns are positively skewed.
  • We now understand that logreturns are just compounded returns taken continuously as opposed to annually.
  • This continuous, logreturn world is the basis of option math. 

Black-Scholes

The lognormal distribution underpins the Black-Scholes model used for pricing options.

The mean of a lognormal distribution is the geometric mean. By now we understand that the geometric mean is always lower than the arithmetic mean. So in compounded world we understand that most likely outcome is lower than the arithmetic mean. 

Geometric mean  = arithmetic mean – .5 * volatility²

The question we worked on is not continuous compounding but if it were, the geometric mean = 10% – .5 * (.20)² = 8%. Just knowing this was enough to know that most likely B would not outperform A even though they have the same average expectancy.

Let’s revisit the original question, but now we will assume continuous compounding instead of annual compounding. The beauty of this is we can now use Black Scholes to solve it!

Re-framing The Poll As An Options Question

We now switch compounding frequency from annual to continuous so we are officially in Black-Scholes lognormal world. 

Expected return (arithmetic mean)

  • Annual compounding: $100 * (1.1)¹⁰ = $259.37
  • Continuous compounding (B-S world): 100*e^(.10 * 10) = $271.83

Median return (geometric mean)

  • Annual compounding: $100 x 1.0817¹⁰ = $219.24
  • Continuous compounding (B-S world): $100 * e^(.10 – .5 * .2²) = $222.55
    • remember Geometric mean  = arithmetic mean – .5 * volatility²
    • geometric mean < arithmetic mean of course

The original question:

What’s the probability that stock B with its 10% annual return and 20% volatility outperforms stock A with its 10% annual return and no volatility in 10 years?

Asking the question in options language:

What is the probability that a 10-year call option on stock B with a strike price of $271.83 expires in-the-money?

If you have heard that “delta” is the probability of “expiring in-the-money” then you think we are done. We have all the variables we need to use a Black-Scholes calculator which will spit out a delta. The problem is delta is only approximately the probability of expiring in-the-money. In cases with lots of time to expiry, like this one where the horizon is 10 years, they diverge dramatically. 2

We will need to extract the probability from the Black Scholes equation. Rest assured, we already have all the variables. 

Computing The Probability That Stock “B” Expires Above Stock “A”

If we simplify Black-Scholes to a bumper sticker, it is the probability-discounted stock price beyond a fixed strike price. Under the hood of the equation, there must be some notion of a random variable’s probability distribution. In fact, it’s comfortingly simple. The crux of the computation is just calculating z-scores.

I think of a z-score as the “X” coordinate on a graph where the “Y” coordinate is a probability on a distribution. Refresher pic3:

Conceptually, a z-score is a distance from a distribution’s mean normalized by its standard deviation. In Black-Scholes world, z-scores are a specified logreturn’s distance from the geometric mean normalized by the stock’s volatility. Same idea as the Gaussian z-scores you have seen before.

Conveniently, logreturns are themselves normally distributed allowing us to use the good ol’ NORM.DIST Excel function to turn those z-scores into probabilities and deltas. 

In Black Scholes,

  • delta is N(d1)
  • probability of expiring in-the-money is N(d2)
  • d1 and d2 are z-scores

Here are my calcs4:

Boom.

The probability of stock B finishing above stock A (ie the strike or forward price of an a $100 stock continuously compounded at 10% for 10 years) is…

37.6%!

This is respectably close to the 37.7% we computed using Pascal’s Triangle. The difference is we used the continuous compounding (lognormal) distribution of returns instead of calculating the return outcomes discretely. 

The Lognormal Distribution Is A Lesson In How Compounding Influences Returns

I ran all the same inputs through Black Scholes for strikes up to $750.

  • This lets us compute all the straddles and butterflies in Black-Scholes universe (ie what market-makers back in the day called “flat sheets”. That means no additional skew parameters were fit to the model or the model was not fit to the market).
  • The flys lets us draw the distribution of prices.

A snippet of the table:

I highlighted a few cells of note:

  • The 220 strike has a 50% chance of expiring ITM. That makes sense, it’s the geometric mean or arithmetic median.
  • The 270 strike is known as At-The-Forward because it corresponds to the forward price of $271.83 derived from continuously compounding $100 at 10% per year for 10 years (ie Seʳᵗ). If 10% were a risk-free rate this would be treated like the 10 year ATM price in practice. Notice it has a 63% delta. This suprises people new to options but for veterans this is expected (assuming you are running a model without spot-vol correlation).
  • You have to go to the $330 strike to find the 50% delta option! If you need to review why see Lessons From The .50 Delta Option.

This below summary picture adds one more lesson:

The cheapest straddle (and therefore most expensive butterfly) occurs at the modal return, about $150. If the stock increased from $100 to $150, you’re CAGR would be 4.1%. This is the single most likely event despite the fact that it’s below the median AND has a point probability of only 1.7%

Speaking of Skew

Vanilla Black-Scholes option theory is a handy framework for understanding the otherwise unintuitive hand of compounding. The lognormal distribution is the distribution that corresponds to continuously compounded returns. However, it is important to recognize that nobody actually believes this distribution describes any individual investment. A biotech stock might be bimodally distributed, contingent on an FDA approval. If you price SPX index options with positively skewed model like this you will not last long. 

A positively skewed distribution says “on average I’ll make X because sometimes I’ll make multiples of X but most of the time, my lived experience is I’ll make less than X”.

In reality, the market imputes negative skew on the SPX options market. This shifts the peak to the right, shortens the right tail, and fattens the left tail. That implied skew says “on average I make X, I often make more than X, because occasionally I get annihilated”. 

It often puzzles beginning traders that adding “put skew” to a market, which feels like a “negative” sentiment, raises the value of call spreads. But that actually makes sense. A call spread is a simple over/under bet that reduces to the odds of some outcome happening. If the spot price is unchanged, and the puts become more expensive because the left tail is getting fatter, then it means the asset must be more likely to appreciate to counterbalance those 2 conditions. So of course the call spreads must be worth more. 

 

Final Wrap

Compounding is a topic that gives beginners and even experienced professionals difficulty. By presenting the solution to the question from a discrete binomial angle and a continuous Black-Scholes angle, I hope it soldified or even furthered your appreciation for how compounding works. 

My stretch goal was to advance your understanding of option theory. While it overlaps with many of my other option theory posts, if it led to even any small additional insight, I figure it’s worth it. I enjoyed sensing that the question could be solved using options and then proving it out. 

I want to thank @10kdiver for the work he puts out consistently and the conversation we had over Twitter DM regarding his question. If you are trying to learn basic and intermediate level financial numeracy his collection of threads is unparalled. Work I aspire to. Check them out here: https://10kdiver.com/twitter-threads/

Remember, my first solution (Pascal’s Triangle) only worked for relatively small N. It was not a general solution. The Black-Scholes solution is a general one but required changing “compounded annually” to “compounded continuously”. 10kdiver provided the general solution, using logs (so also moving into continuous compounding) but did not require discussion of option theory. 

I’ll leave you with that:

Additional Reading 

  • Path: How Compounding Alters Return Distributions (Link)

This post shows how return distributions built from compounding depend on the ratio of trend vs chop.

  • The difficulty with shorting and inverse positions (Link)

    The reason shorting and inverse positions are problematic is intimately tied to compounding math.

 




Moontower #129

I accidentally “picked off” my 3rd grader.

[If you don’t know what “picked off” means see Money Angle below.]

The story will improve your numerical intuition and illuminate a lesson that is central to both investing and engineering problems.

The Proposition

My 3rd-grader came home with a packet of math worksheets from school. Two of the sheets, a total of 10 questions, were incomplete. He said the teacher didn’t require those sheets to be done.

What a bummer.

I thought they were the best questions from the whole packet. I asked him to solve the total of 10 questions but decided to make my request a little spicier. I offered him the following bet:

If you get them all correct, I will give you $5. Otherwise, you owe me $5.

He thought for a moment, then accepted. Before he went off to work on them, I started to wonder if my impulsive proposition was fair.

Is It A Fair Bet?

After eyeballing the questions, I estimated he had a 90% chance of getting any question correct. Another way to say that, is I expect he gets 1 wrong on average. Right off the bat,  I think I’m going to win. It’s not a fair bet.

This led me to compute a couple numbers.

  1. If my estimate of 90% hit rate per question is correct, what’s the chance he gets them all correct?

    .90¹⁰ = 35%

    That means he’s almost a 2-1 underdog

  2. What would his hit rate need to be per question to make the bet fair?

    First we need to convert what a fair bet means in math language. This is straightforward. Since it’s an even $5 bet then the fair proposition would not be, on average, he gets 1 wrong, but that he gets all the questions correct 50% of the time.

    x¹⁰ = 50%

    x = .50^(1/10)

    x = 93.3%

    So if he had a 93.3% chance of getting any single question correct, then he has a 50% chance of winning the bet.

Flipping The Odds In His Favor

I’m not trying to take candy from a 3rd grader, I just wanted to make him more eager to do the questions. So, I tweaked the bet after he returned with the answers. Each of the 2 worksheets had 5 questions each. I decided to batch the bet as follows:

If he gets all the questions correct, he wins.

If he gets all the questions in one batch correct but not the other, it’s a push.

If he gets less than 100% on each batch then he loses the bet. 

How did this tweak alter the proposition?

In the first bet, if he got anything wrong, he lost. With these rules, he only loses if he gets, at least, one wrong in each batch.

We need to analyze all the possible outcomes that can occur with 2 batches.

First, we must ask:

What is the probability he gets all the questions right within a batch of 5 questions?

Assume he has a 90% hit rate again.

.95⁵= 59%

So for either batch, he has a 59% chance of getting a perfect score and a 41% chance of getting at least one wrong (ie a non-perfect score).

Now we must consider all the possible outcomes of the proposition and their probabilities.

  1. Perfect score in both batches

    59% x 59% = 34.8%

  2. Perfect score in one batch but not the other

    59% x 41% = 24.2%

  3. At least one wrong in both batches

    41% x 41% = 16.8%

If we sum them all up we get 75.8%.

Wait, these don’t add to 100%, what gives??

We need to weigh these outcomes by the number of ways they can happen.

The possibilities with their probabilities are as follows:

  • Win, Win = 34.8%
  • Win, Lose = 24.2%
  • Lose, Win = 24.2%
  • Lose, Lose = 16.8%

Collapsing the individual possibilities into the proposition’s probabilities we get:

  • Win: 34.8%
  • Push: 48.4% (24.2% + 24.2%)
  • Lose: 16.8%

These probabilities sum to 100% and tell us:

  1. The most likely scenario of the bet is a push, no money exchanged
  2. Otherwise, he wins the bet 2x more often than he loses the bet

This is a powerful result. Remember, his hit rate on any individual question was still 90%. By batching, we changed the proposition into a bad bet for him, into a good bet because he gets to diversify or quarantine the risk of a wrong answer.

Even More Diversification

With 2 batches we saw the range of possibilities conforms to the binomial distribution for n = 2:

p² + 2p(1-p) + (1-p)²

where p = probability of perfect score on a batch

In English, the coefficients: 1 way to win both + 2 ways to push + 1 way to lose both

What if we split the proposition into 5 batches of 2 questions each?

These are the bet scenarios:

  1. Win =  5 pairs of questions correct
  2. Lose = at least one wrong in each of the 5 pairs to lose the bet
  3. Push = and any other combination (i.e. 3 perfect batches + 2 imperfect batches)

How do the batch outcomes roll up to the 3 bet scenarios (win, lose, push)?

  1. We must count how many ways there are to generate each of the scenarios.
  2. We must probability-weight each way.

The summary table shows the work.

[Note the coefficients correspond to the coefficients for the binomial expansion (x+y)⁵ which is also the row of Pascal’s Triangle for N = 5]

The net result of quarantining the questions into 5 groups of 2:

35% chance he wins the bet

65% chance he pushes on the bet

Nearly 0% chance he loses on the bet!

If you took this quarantining logic further and treated each question as its own batch then the new phrasing of the bet would be:

If he gets every question correct, he wins

If he gets every question incorrect, he loses

Any other scenario is a push

The corresponding probabilities:

Win = .9¹⁰ = 35%

Lose = .1¹⁰ = E⁻¹⁰ or 0%

So the benefits of separating the bets were mostly achieved above when we batched into groups 5 pairs of questions.

Conclusion

The first bet required my son to get a string of questions correct. Even though I estimated he had a 90% chance of getting any question correct, by making the net outcome dependent on each chain link, the odds of his success became highly contingent on the length of the chain.

With a chain length of 10, the bet was unfair to him. By changing the bet to be the result of success on smaller chains (the batches) I changed the distribution of outcomes. It did not increase his chance of winning, but it reduced his chance of losing by creating offsetting scenarios or “pushes”. In other words, the smaller chains reduced his overall risk without sacrificing his odds of winning. It was a free lunch for him.

When you create long chains of dependency (ahem, positive correlations), an impurity in any link threatens your entire proposition. In these examples, we are dealing with binary outcomes. This is a trivial analysis. With investing, the distributions of the bets are not easily known.  It is well-known, however, that diversifying or not putting all your eggs in one basket is a free lunch. Still, if the investments are highly correlated, you may be fooling yourself and depending on a long chain.

Imagine if the 10 questions my son had were the type of word problem where the answer to each question is the input to the next. That’s a portfolio of highly correlated assets. If you are “yield-farming” crypto stablecoins you have probably thought about this problem. Spreading the risk across many coins can offset many idiosyncratic risks to the protocols. But is there a translucent, hard-to-see chain of correlation tying them all together that only reveals itself when the whole background goes black? That’s systemic risk. Ultimately, the only hedge to such a risk is position sizing at the aggregate level where you sum the gross positions. This is why stress-testing a portfolio to that standard is a quant’s “last level of defense”.

Jarvis, what happens to my portfolio when all correlations go to one?

[If you are in the investing world you will see parallels to this lesson in the ergodicity1problem.]


Money Angle

In trading, “picking someone off” means trading against a counterparty who would flake on the price they offered you if they knew what you know.

If I lift an offer on a TSLA March call option because I’m bullish, the market-maker on the other side of my trade doesn’t care. They would still sell me the call even if I texted them my rationale. But if I had the divine knowledge that Elon was going to tweet in the next 10 seconds that earnings would be reported in March not February, then I would be knowingly “picking off” the market-maker. As an options trader, you need to defend against pick-offs. You also want alerts if someone else is making a price that is not incorporating material, public info. For example, if an OPEC meeting date was moved there might be a tiny window when you could disguise a calendar spread as a routine roll when really you are trying to pick off the other side before they get the memo.

[In reality, when such news happens, market-makers will “sweep” all the resting customer orders with price limits below or above the option’s new fair value. It’s very difficult to pick off another professional who is consuming a real-time news feed.]

A few categories of pick-offs:

  • Pickoff trades related to changes in dates.

    If earnings are moved from early Feb to early March, then the “earnings volatility” needs to come out of the Feb expiry since you are no longer exposed to it, and the March options which now contain that volatility must appreciate relatively.

  • Pickoffs related to change in carry

    If a stock announces a change in its dividend that will affect the carry embedded in the options. If a dividend is slashed, the calls go up relative to the puts. Market makers need to be on top of how corporate actions affect the inputs into their pricing models.

  • Pickoffs related to changes in baskets

    If an ETF’s constituents change that affects vol of the underlying basket. If an ETF restricts creations, this can lead to the options and ETF becoming mispriced (one day I’ll tell the story of how this personally cost me 6 figures).

Pickoffs In Real Life

The tradition of trading floors is full of insane prop betting stories (NYMEX vets have so many to choose from but my personal favorite was watching one guy successfully pound 20 Coors Lites in an hour in one of the upstairs offices).

But picking people off can be as easy as making bets with folks who are arithmetically challenged. Most people are. You only need to look up polls by @10kdiver to see that even professional investors, a subset of the population who should be able to compute a return, struggle numerically.

I am overstating the case a bit.

  1. I don’t know how many of those respondents to those polls are professional investors. I’d also admit there are times I’m impatient and just take a guess just to see the results. This is probably common behavior.
  2. When confronted with a bet, people’s defenses go up. They are wary of strangers bearing gifts and will assume there’s a catch.

[Today’s Moontower was a re-factored version of this post: I Felt Bad For Picking My 3rd Grader Off]


Job Opportunity

An awesome team (I can’t overstate awesome here) is looking for a full-stack junior developer. You will learn from seasoned quant PM and be part of building a HF from the ground up.

Requirements:

  • Ability to work on full-stack including DevOps
  • Python, JS/React, SQL, Redis

Good to have:

  • C# and experience with distributed systems

This group is very groovy, if you’re hungry and eager to learn and build, it will be an amazing opportunity.

Hit them up here: omk.jrdev@gmail.com


Last Call

Musical Encore

I’m always crowdsourcing music recs. I’ve compiled many of them at Moontower Music. The end-of-year Spotify Wrap is an excuse to compile your favorites.

Humor me: