Can Your Manager Solve Betting Games With Known Solutions?

One of the best threads I’ve seen in a while. It’s important because it shows how betting strategies vary based on your goals.

In the basic version, the “Devil’s Card Game” is constrained by the rule that you must bet your entire stack each time.

You can maximize:

  1. expectation
  2. utility (in the real world Kelly sizing is the instance of this when utility follows a log function)
  3. the chance of a particular outcome.

At the end of the thread, we relax the bet sizing rules and allow the player to bet any fraction of the bankroll they’d like. This is a key change.

It leads to a very interesting strategy called backward induction. In markets, the payoffs are not well-defined. But this game features a memory because it is a card game without replacement. Like blackjack. You can count the possibilities.

The thread shows how the backward induction strategy blows every other strategy out of the water.

If we generalize this, you come upon a provocative and possibly jarring insight:

The range of expectations simply based on betting strategies is extremely wide.

That means a good proposition can be ruined by an incompetent bettor. Likewise, a poor proposition can be somewhat salvaged by astute betting.

I leave you with musings.

  1. Is it better to pair a skilled gambler with a solid analyst or the best analyst with a mid-brow portfolio manager?
  2. How confident are you that the people who manage your money would pick the right betting strategy for a game with a known solution?Maybe allocators and portfolio managers should have to take gambling tests. If analytic superiority is a source of edge, the lack of it is not simply an absence of one type of edge. It’s actually damning because it nullifies any other edge over enough trials assuming markets are competitive (last I checked that was their defining feature).

Why I Share Online And The Decision To Leave Trading

Friends,

Soooo…getting back into the groove after vacation has been a failure. Been hard to conjure any productivity. While I was in Hawaii, I left my phone in the room most of the time. Was nice to mostly unplug. But vacation is fantasyland and then you come home. Instead of building on a healthy habit, I gave myself permission to guiltlessly hang out on Twitter as if I earned something. My history of swallowing a pint of ice cream after the rare cardio session is ample warning that in my personal constitution no good deed goes unpunished.

The upshot of all this?

Instead of having some tidy, prepared essay I’m gonna just overshare about life today. If you’re here for nerd stuff feel free to skip ahead to Money Angle, no hard feelings.

Ok. So there was a Twitter thread where a friend and a stranger were talking about me. The stranger was asking the friend why a portfolio manager (don’t mind me as I adjust my imaginary tie) would share insight about trading publicly. The tone, insofar as one can detect tone in text, was “traders shut up and trade, grifters teach”.

It’s not the first time I’ve seen something like that and I usually let it slide. I suspect I normally don’t get too much suspicion directed at me because it would be really hard to fake 21 years of prop trading with a massive sample size of daily trades and then write about risk and options in a way that other verified pros find value in. This is not me defending myself. This is you, beloved readers, especially the professional peers amongst you who are so supportive.

But this particular conversation did spark a reaction in me because it was a friend that was stuck in some isolated thread trying to defend me. So I chimed in to give him a break.

This is how I think about my writing about trading:

If you are a pro options trader reading me, then I’m reinforcing what you already know. Sometimes the articulation gives you a vocabulary that clarifies your thinking. I’m not turning over new rocks, but if I scramble them a bit, you may see something new.

If you are a novice trader/investor, you are learning things that are table stakes for the risk-taking side of the industry. The decision-making principles are not secrets. You can find any number of sources to learn from. People prefer to be communicated to in different ways. I’m just one of those many ways.

I would never write about secrets while I was working. I chose to write about the meta. The website is literally called MoontowerMeta. So if you are not violating any policies, you’re not exposing info that your friends use to make money, and you can still find angles that are helpful to readers then you have value to share. Aspiring writers sitting on trading desks, that’s your cue.

[An aside that is gonna trigger some set of people: I could hand over all my professional dashboards and tools, and it wouldn’t make a difference. You won’t get the same results. Experience, discipline, and creativity are not something you can take from another. And they are foundational to a discretionary strategy. Think about this from a game-theoretic point of view. If I could codify (I tried and couldn’t) what I did, then it would be easy to prove the edge. The strategy would then be automated and be oversubscribed or its owners would never sell it to an investor. The fact that it’s discretionary and cannot be proven except by its eventual outcomes means an investor must always worry that I’m full of shit. But that’s also why there’s some middle ground where I want outside funding and investors are willing to fund it. If a purely automated, systematic strategy is a money-printing machine you’ll never see it. And if you do, its legibility will be its eventual downfall as it gains assets]

Still, a big question remains —why share? The stranger was hinting that I had an ulterior motive. Like maybe I had flamed out and was setting up my next job. There’s some truth to that but not in the way he insinuated. (The last year of my career was my best and it was not even close.)

I decided to tweet a thread on why I share. To do that I needed to back up and explain the decision process behind quitting.

The bizarre result was the thread went totally viral. I also realized the way I wrote it must have made people think I just quit. Tsk, tsk. If they were subbing to Moontower they know that is old news. If you didn’t receive this letter in your email don’t make that mistake:

Subscribe.

Before I quit trading, I framed the decision: I’m 43 yrs old. I can stay, make more $$, racing for 10 more years. Or I can leave now, while I have energy, reasonable health and less ageism against me to work towards something that I’m not in a race to get over.

It will take some time to figure out my next step but since my kids are 5 and 8, it’s a great time to take time. When I start my second professional life, it won’t be a race. It’s something I can do til I drop dead.

I’ve written about my lack of interest in any conventional retirement (I don’t play golf, I like to work and write with my free time as long as it’s on my terms). So a sustainable journey reduces my need for a large nest egg to carry through many non-working years. (I also put little trust in market returns as an arbiter of my financial destiny so I’m conservative about how long I need to work). If you know you can work say 20 years longer than if you raced in a finance career, then a lot of pressure is relieved.

Suddenly leaving isn’t so risky.

2 other points:

1. If I stayed I’d be in the same boat at 53 years old. What do I do with myself? I’d have more money, but also so what. Money is not an issue if you are happy working (and you don’t crave caviar every meal)

2. If I’m wrong, I can always get a finance job. It won’t pay what I used to make because the seniority you have with people you know for a long time is a special sort of trust and goodwill. I had a long leash (in finance speak that probably earns you 2 years of underperformance cushion).

I prefer not to take my mortality for granted and when you are in your 40s it becomes far more real. When you receive a phone call instead of a text out of the blue your pulse quickens a bit. I don’t obsess about $ like I did even 10 years ago and definitely not like 20 years ago. I didn’t grow up with it, but have fought the urge to see it as a security blanket catch-all for every kind of anxiety.

Scarcity mindset is adaptive when you are young and broke, because the scarcity can be quite real. The mindset is protection. Like a 40d put. But as you earn, that put becomes further OTM. You are going to be ok. No need to pay theta in the form of suboptimal decisions because you feel the need to service that put as if it’s 40d when it’s really 1 delta.

Everyone gotta do what they gotta do. But if you are unhappy with your fancy job, that’s on you. There are no excuses for that. It’s understandable to feel otherwise but I do believe you need to work through that. It’s really hard to develop a healthy relationship with $. I’m trying to get better at it all the time. Because I have to. It’s not wise to do a job you don’t want to do to allay irrational fears of being broke.

Twitter is a tool for relationships and to spread proof of work. I did one thing for 21 years. When I try to do something else I’m a major underdog. I’m not going back to school. I don’t enjoy school. My online presence is like a proof of work, so when I try to convince someone to take a chance on me in a new field I can show something that looks like a resume to someone that’s open-minded. If you wonder about my incentives on Twitter, I’m being open about it: relationships, proof of work, & optionality in distribution.

There it is. I tweet and write to “find the others” and to make myself marketable to future collaborators and clients. I don’t know if that makes it any less “ulterior” if it’s not in pursuit of a trading gig (if I was going to stay in trading I already had a ridiculous seat. There are not a lot of places to go unless I was going to be a founder, but I have no interest in that. Trying to be an emerging manager is institutional masochism. Respect to my friends on that journey. I love it for them. Not for me. I know enough to never say never, but my mindset is far away from that and I’m not getting any younger.)

This thread went viral because it struck a nerve with so many people. I’m a size 150 bid on how many DMs, texts, emails, and requests for phone calls I received. Many were just extending support but many wanted to discuss their own crossroads.

If you are curious, the replies to the thread are the less vulnerable versions of private messages.

Some made similar leaps in the past, some are in the midst of such a leap, some just starting to hear the whispers from their inner selves, and some were younger people with enough maturity to already anticipate how they might feel in their 40s. It was weirdly overwhelming to get such a candid glimpse of people’s feelings.

I’m happy to discuss any aspect of all this if any of you feel that’s what you need. I had many conversations before making my final decision. One of my local friends is a serial entrepreneur a decade removed from corporate America. He’s similar in age, with a family, and is particularly thoughtful about aligning who he is with his work. Over the course of several hangouts and long morning hikes I came to understand his framework. And parts of it were foreign in interesting ways. I never considered thinking about the problem the way he does. It unlocked thoughts within me but even now I’m still processing it. It’s a bit painful to think through because you need to be so honest with yourself. If you are not rattled, you’re doing it wrong. But I knew he understood me, just based on the questions he asked. In the next week or two, I’ll discuss the framework as well as what I’m thinking about most these days.

Since it’s Twitter, a number of trolls who must hate-follow me said it was a mid-life crisis as if I was defective. I suppose I am. In many ways, it would be easier to have just stayed in my job. But if there’s a defect I’d rather take over from the autopilot and intentionally try to go to the right destination than accidentally land in the wrong one with no fuel left in the tank.


Resources

In the public domain, the 2 friends I found especially helpful were Paul Millerd and Khe Hy.

Paul’s book, Pathless Path, which came out in January is going to be canon on this topic. My notes and review are here. I’ll even buy you a copy if you want. Paul is kind and brilliant. He’s had so many discussions with others on these topics that chatting with him is like plugging yourself straight into a current of flowing wisdom.

Khe’s path was extremely resonant because he was in the same field (in fact long after he left finance I learned that he was in meetings 20 feet from where I was standing in my office). Khe’s writings make him one of the OGs about thinking about our relationships with ourselves and our careers. He has successfully navigated the long path from corporate America to a business that sustains both his clients’ and family’s needs. For the better part of a decade, his writing has put you in the sidecar. I’ve plugged his work at every opportunity because it’s outstanding and he’s the kind of giving soul you love to see crush it. The next cohort of his $10k Work Bootcamp starts in a few weeks. The testimonials are ridiculous and I’m not surprised. He’s taken everything he’s learned and combined it with easy-to-use technology to turn you into a high-leverage weapon. Give it a look hereIt’s 100% free.

Moontower #145

Friends,

Soooo…getting back into the groove after vacation has been a failure. Been hard to conjure any productivity. While I was in Hawaii, I left my phone in the room most of the time. Was nice to mostly unplug. But vacation is fantasyland and then you come home. Instead of building on a healthy habit, I gave myself permission to guiltlessly hang out on Twitter as if I earned something. My history of swallowing a pint of ice cream after the rare cardio session is ample warning that in my personal constitution no good deed goes unpunished.

The upshot of all this?

Instead of having some tidy, prepared essay I’m gonna just overshare about life today. If you’re here for nerd stuff feel free to skip ahead to Money Angle, no hard feelings.

Ok. So there was a Twitter thread where a friend and a stranger were talking about me. The stranger was asking the friend why a portfolio manager (don’t mind me as I adjust my imaginary tie) would share insight about trading publicly. The tone, insofar as one can detect tone in text, was “traders shut up and trade, grifters teach”.

It’s not the first time I’ve seen something like that and I usually let it slide. I suspect I normally don’t get too much suspicion directed at me because it would be really hard to fake 21 years of prop trading with a massive sample size of daily trades and then write about risk and options in a way that other verified pros find value in. This is not me defending myself. This is you, beloved readers, especially the professional peers amongst you who are so supportive.

But this particular conversation did spark a reaction in me because it was a friend that was stuck in some isolated thread trying to defend me. So I chimed in to give him a break.

This is how I think about my writing about trading:

If you are a pro options trader reading me, then I’m reinforcing what you already know. Sometimes the articulation gives you a vocabulary that clarifies your thinking. I’m not turning over new rocks, but if I scramble them a bit, you may see something new.

If you are a novice trader/investor, you are learning things that are table stakes for the risk-taking side of the industry. The decision-making principles are not secrets. You can find any number of sources to learn from. People prefer to be communicated to in different ways. I’m just one of those many ways.

I would never write about secrets while I was working. I chose to write about the meta. The website is literally called MoontowerMeta. So if you are not violating any policies, you’re not exposing info that your friends use to make money, and you can still find angles that are helpful to readers then you have value to share. Aspiring writers sitting on trading desks, that’s your cue.

[An aside that is gonna trigger some set of people: I could hand over all my professional dashboards and tools, and it wouldn’t make a difference. You won’t get the same results. Experience, discipline, and creativity are not something you can take from another. And they are foundational to a discretionary strategy. Think about this from a game-theoretic point of view. If I could codify (I tried and couldn’t) what I did, then it would be easy to prove the edge. The strategy would then be automated and be oversubscribed or its owners would never sell it to an investor. The fact that it’s discretionary and cannot be proven except by its eventual outcomes means an investor must always worry that I’m full of shit. But that’s also why there’s some middle ground where I want outside funding and investors are willing to fund it. If a purely automated, systematic strategy is a money-printing machine you’ll never see it. And if you do, its legibility will be its eventual downfall as it gains assets]

Still, a big question remains —why share? The stranger was hinting that I had an ulterior motive. Like maybe I had flamed out and was setting up my next job. There’s some truth to that but not in the way he insinuated. (The last year of my career was my best and it was not even close.)

I decided to tweet a thread on why I share. To do that I needed to back up and explain the decision process behind quitting.

The bizarre result was the thread went totally viral. I also realized the way I wrote it must have made people think I just quit. Tsk, tsk. If they were subbing to Moontower they know that is old news. If you didn’t receive this letter in your email don’t make that mistake:

Subscribe.

Before I quit trading, I framed the decision: I’m 43 yrs old. I can stay, make more $$, racing for 10 more years. Or I can leave now, while I have energy, reasonable health and less ageism against me to work towards something that I’m not in a race to get over.

It will take some time to figure out my next step but since my kids are 5 and 8, it’s a great time to take time. When I start my second professional life, it won’t be a race. It’s something I can do til I drop dead.

I’ve written about my lack of interest in any conventional retirement (I don’t play golf, I like to work and write with my free time as long as it’s on my terms). So a sustainable journey reduces my need for a large nest egg to carry through many non-working years. (I also put little trust in market returns as an arbiter of my financial destiny so I’m conservative about how long I need to work). If you know you can work say 20 years longer than if you raced in a finance career, then a lot of pressure is relieved.

Suddenly leaving isn’t so risky.

2 other points:

1. If I stayed I’d be in the same boat at 53 years old. What do I do with myself? I’d have more money, but also so what. Money is not an issue if you are happy working (and you don’t crave caviar every meal)

2. If I’m wrong, I can always get a finance job. It won’t pay what I used to make because the seniority you have with people you know for a long time is a special sort of trust and goodwill. I had a long leash (in finance speak that probably earns you 2 years of underperformance cushion).

I prefer not to take my mortality for granted and when you are in your 40s it becomes far more real. When you receive a phone call instead of a text out of the blue your pulse quickens a bit. I don’t obsess about $ like I did even 10 years ago and definitely not like 20 years ago. I didn’t grow up with it, but have fought the urge to see it as a security blanket catch-all for every kind of anxiety.

Scarcity mindset is adaptive when you are young and broke, because the scarcity can be quite real. The mindset is protection. Like a 40d put. But as you earn, that put becomes further OTM. You are going to be ok. No need to pay theta in the form of suboptimal decisions because you feel the need to service that put as if it’s 40d when it’s really 1 delta.

Everyone gotta do what they gotta do. But if you are unhappy with your fancy job, that’s on you. There are no excuses for that. It’s understandable to feel otherwise but I do believe you need to work through that. It’s really hard to develop a healthy relationship with $. I’m trying to get better at it all the time. Because I have to. It’s not wise to do a job you don’t want to do to allay irrational fears of being broke.

Twitter is a tool for relationships and to spread proof of work. I did one thing for 21 years. When I try to do something else I’m a major underdog. I’m not going back to school. I don’t enjoy school. My online presence is like a proof of work, so when I try to convince someone to take a chance on me in a new field I can show something that looks like a resume to someone that’s open-minded. If you wonder about my incentives on Twitter, I’m being open about it: relationships, proof of work, & optionality in distribution.

There it is. I tweet and write to “find the others” and to make myself marketable to future collaborators and clients. I don’t know if that makes it any less “ulterior” if it’s not in pursuit of a trading gig (if I was going to stay in trading I already had a ridiculous seat. There are not a lot of places to go unless I was going to be a founder, but I have no interest in that. Trying to be an emerging manager is institutional masochism. Respect to my friends on that journey. I love it for them. Not for me. I know enough to never say never, but my mindset is far away from that and I’m not getting any younger.)

This thread went viral because it struck a nerve with so many people. I’m a size 150 bid on how many DMs, texts, emails, and requests for phone calls I received. Many were just extending support but many wanted to discuss their own crossroads.

If you are curious, the replies to the thread are the less vulnerable versions of private messages.

Some made similar leaps in the past, some are in the midst of such a leap, some just starting to hear the whispers from their inner selves, and some were younger people with enough maturity to already anticipate how they might feel in their 40s. It was weirdly overwhelming to get such a candid glimpse of people’s feelings.

I’m happy to discuss any aspect of all this if any of you feel that’s what you need. I had many conversations before making my final decision. One of my local friends is a serial entrepreneur a decade removed from corporate America. He’s similar in age, with a family, and is particularly thoughtful about aligning who he is with his work. Over the course of several hangouts and long morning hikes I came to understand his framework. And parts of it were foreign in interesting ways. I never considered thinking about the problem the way he does. It unlocked thoughts within me but even now I’m still processing it. It’s a bit painful to think through because you need to be so honest with yourself. If you are not rattled, you’re doing it wrong. But I knew he understood me, just based on the questions he asked. In the next week or two, I’ll discuss the framework as well as what I’m thinking about most these days.

Since it’s Twitter, a number of trolls who must hate-follow me said it was a mid-life crisis as if I was defective. I suppose I am. In many ways, it would be easier to have just stayed in my job. But if there’s a defect I’d rather take over from the autopilot and intentionally try to go to the right destination than accidentally land in the wrong one with no fuel left in the tank.


Resources

In the public domain, the 2 friends I found especially helpful were Paul Millerd and Khe Hy.

Paul’s book, Pathless Path, which came out in January is going to be canon on this topic. My notes and review are here. I’ll even buy you a copy if you want. Paul is kind and brilliant. He’s had so many discussions with others on these topics that chatting with him is like plugging yourself straight into a current of flowing wisdom.

Khe’s path was extremely resonant because he was in the same field (in fact long after he left finance I learned that he was in meetings 20 feet from where I was standing in my office). Khe’s writings make him one of the OGs about thinking about our relationships with ourselves and our careers. He has successfully navigated the long path from corporate America to a business that sustains both his clients’ and family’s needs. For the better part of a decade, his writing has put you in the sidecar. I’ve plugged his work at every opportunity because it’s outstanding and he’s the kind of giving soul you love to see crush it. The next cohort of his $10k Work Bootcamp starts in a few weeks. The testimonials are ridiculous and I’m not surprised. He’s taken everything he’s learned and combined it with easy-to-use technology to turn you into a high-leverage weapon. Give it a look hereIt’s 100% free.


Money Angle

One of the best threads I’ve seen in a while. It’s important because it shows how betting strategies vary based on your goals.

In the basic version, the “Devil’s Card Game” is constrained by the rule that you must bet your entire stack each time.

You can maximize:

  1. expectation
  2. utility (in the real world Kelly sizing is the instance of this when utility follows a log function)
  3. the chance of a particular outcome.

At the end of the thread, we relax the bet sizing rules and allow the player to bet any fraction of the bankroll they’d like. This is a key change.

It leads to a very interesting strategy called backward induction. In markets, the payoffs are not well-defined. But this game features a memory because it is a card game without replacement. Like blackjack. You can count the possibilities.

The thread shows how the backward induction strategy blows every other strategy out of the water.

If we generalize this, you come upon a provocative and possibly jarring insight:

The range of expectations simply based on betting strategies is extremely wide.

That means a good proposition can be ruined by an incompetent bettor. Likewise, a poor proposition can be somewhat salvaged by astute betting.

I leave you with musings.

  1. Is it better to pair a skilled gambler with a solid analyst or the best analyst with a mid-brow portfolio manager?
  2. How confident are you that the people who manage your money would pick the right betting strategy for a game with a known solution?

    Maybe allocators and portfolio managers should have to take gambling tests. If analytic superiority is a source of edge, the lack of it is not simply an absence of one type of edge. It’s actually damning because it nullifies any other edge over enough trials assuming markets are competitive (last I checked that was their defining feature).


From My Actual Life

We went to the Kaanapali region of Maui for Spring Break with 4 other families.

We ended up hanging out with 13 total families that we knew, nearly half were totally random encounters. With so many friends around, the kids didn’t notice mom and dad drank their 529s in the form of Mai Tai’s.

Fun bit: this pic was taken from the backyard of a friend’s place that also has quite the poker room. The friend was renting it from a certain celeb who liked to host card nights well attended by professional athletes and…Woody Harrelson.

#goals

(If you need any recommendations let me know. Also, with rental cars so expensive Turo was the way to go for many of us.)

Stay groovy!

Finance Guilt

Finance Guilt

I’ve said several times that finance is really just code. Like software, it’s an abstraction skin pulled over physical features. One can feel a bit disembodied if their formulation of the world for 8-12 hours a day are prices. Prices that collapse all of human enterprise, from the dirt under its fingernails to the sunrises and sunsets between now and some expiration date, into some Excel number format.

Just as software intermediates for less, financial innovation lowers the cost of go-betweens. In finance, the things went-between are people paying to offload risk to people looking to get paid for warehousing risk. In software and finance, skimming a tiny bit of rent on those transactions is lucrative.

How good or bad we can feel about the degree of skimming depends on how much surplus is created versus the higher friction model. The value of information liquidity is fairly obvious so Google enjoyed a positive reputation for at least its first decade in business. Meanwhile, finance feels like a constant barrage of “what did Wells Fargo do now?” or words that rhyme with Fonzi. People outside finance can be excused for having a dim, albeit biased, view of the profession since nobody reports on people doing an honest job.

With that in mind, I leave you with Mitchell’s understandable question:

Here’s my quick response:

Agustin’s response:

I’ll wrap with a footnote from a recent post:

The slicing and dicing of risk is finance’s salutary arrow of progress. Real economic growth is human progress in its battle against entropy. By farming, we can specialize. By pooling risk, we can underwrite giant human endeavors with the risk spread out tolerably. People might not sink the bulk of their net worth into a home if it wasn’t insurable. Financial innovation is matching a hedger with the most efficient holder of the risk. It’s matching risk-takers who need capital, with savers who are willing to earn a risk premium. Finance gets a bad rap for being a large part of the economy, and there are many headlines that enflame that view. I, myself, have a dim view of many financial practices. I have likened asset management to the vitamin industry — it sells noise as signal. But the story of finance broadly goes hand in hand with human progress. It might not be “God’s work” as Goldman’s boss once cringe-blurted, but its most extreme detractors as well as the legions of “I wish I was doing something more meaningful with my life” soldiers are discounting the value of its function which is buried in abstraction. Finance is code, so if software is eating the world, financialization is its dinner date.

Moontower #144

[I’m touching down in Maui this morning with my family for Spring Break. I won’t open the laptop this week so Moontower will be off next Sunday.]


Friends,

It’s been a crazy “Q1” as the suits say (seasonal references that favor fiscal orbits over solar ones still can’t escape the “time is a flat circle” vibe. A semantic loss all around, well-played all of us). In keeping with my Spring Break, I’ll re-post links to the more popular articles I wrote in the past few months in case any new or old readers want to catch up. There won’t be new content in the next 2 weeks.

Drawing Better Outcomes From Fat-Tailed Distributions

✍️There’s Gold In Them Thar Tails: Part 1 (13 min read)

✍️There’s Gold In Them Thar Tails: Part 2 (24 min read)

A meta-comment about the process of writing these. The thinking behind the posts was heavily inspired by Rohit Krishnan’s Spot The Outlier. When I first read his article, I knew it was deeply insightful but I struggled to fully grok it. I saved it in my task dashboard so I would re-visit it occasionally. By keeping it top of mind, I was more primed to “see” it in the wild. There was a back and forth between exposing myself to the post, following his references, and trying to reason about it in the context of what I already knew. This brings me to an encouraging point (I think). Understanding an idea you don’t get fully get is often just a matter of repetition broken up by rests and just enough space in your RAM to give your attention filter a chance to see it around you. It’s a mix of focused and diffuse thinking.

I imagine some readers are thinking “Kris, that post was not hard to understand…you’re supposed to be an options trader?!” I found it hard, what can I say. The journey to comprehend it (at least enough to write a few thousand words on it) is more encouraging than the distress of being dense in the first place. Which is a roundabout way of saying to understand something just keep trying from different angles. Give yourself rest. And trust in repeated exposure. I hope that advice helps next time you try to bang a concept into your skull. Fluid intelligence peaks in your 20s so knowing how to learn requires believing that you can. I’m 100% sure you can.

If you enjoyed this ensemble of concepts (finding outliers, Berkson’s Paradox, correlation breakdown in the extremes), I encourage you to read another treatment that adds to and reinforces the conversation:

✍️ Searching for outliers (22 min read)
by @benskuhn

The post is about better decision-making in fat-tailed distributions. Since they exist in many real-world matters, you should care. The end of the post has good recommendations while the beginning helps you differentiate between thin and fat-tailed distributions.

Some highlights:

  • As the dating example shows, most people have some intuition for this already, but even so, it’s easy to underrate this and not meet enough people. That’s because the difference between, say, a 90th and 99th-percentile relationship is relatively easy to observe: it only requires considering 100 candidates, many of whom you can immediately rule out. What’s harder to observe is the difference between the 99th and 99.9th, or 99.9th and 99.99th percentile, but these are likely to be equally large. Given the stakes involved, it’s probably a bad idea to stop at the 99th percentile of compatibility. This means that sampling from a heavy-tailed distribution can be extremely demotivating, because it requires doing the same thing, and watching it fail, over and over again: going on lots of bad dates, getting pitched by lots of low-quality startups, etc. An important thing to remember in this case is to trust the process and not take individual failures, or even large numbers of failures, as strong evidence that your overall process is bad.
  • Often, you’ll have a choice between spending time on optimizing one sample or drawing a second sample—for instance, editing a blog post you’ve already written vs. writing a second post, or polishing a message on a dating app vs. messaging a second person. Some amount of optimization is worth it, but in my experience, most people are way over-indexed on optimization and under-indexed on drawing more samples.
  • This is similar to how venture capitalists are often willing to invest in the best companies at absurd-seeming valuations. The logic goes that if the company is a “winner,” the most important thing is to have invested at all and the valuation won’t really matter. So it’s not worth it to the VC to try very hard to optimize the valuation at which they invest.

Finally, I can offer an example sitting right under everyone’s nose: choosing which books to read. In How to Read: Lots of Inputs and a Strong Filter, Morgan Housel writes:

The conflict between these two – most books don’t need to be read to the end, but some books can change your life – means you need two things to get a lot out of reading: Lots of inputs and a strong filter…A good reading filter is more art than science. You’ll have to find one that works for you. The bigger point is that the highest odds of finding the right piece of information comes from inundating yourself with information but very quickly being able to say, “that ain’t it.”

The Moloch Series

You cannot unsee the god of unhealthy competition.

✍️Don’t Look Up, It’s Moloch (10 min read)

Once you feel sufficiently Moloch-pilled you need the serum:

✍️Putting Moloch To Rest (7 min read)

To reinforce the cure (again, repetition folks) see this quirky and enjoyable post:

✍️ Slack (4 min read)
by Zvi Mowshowitz

Zvi’s writing has an almost poetic cadence and sticky phrasing. His blog is a minimalist rabbit hole. He’s in the Magic: The Gathering Hall of Fame and a former market maker so I’m probably biased towards his kind of geekery.

Self-improvement

✍️Lessons From Susquehanna (5 min read)

Todd Simkin’s interview re-hashed a collection of deeply influential ideas regarding learning and communication from my professional career

✍️Being A Pro And Permission To Be Serious (12 min read)

Discipline and earnestness feel quaint in the theater of memes modernity hyper-manufactures. Don’t fall for it.

Hedging

✍️From CAPM To Hedging (16 min read)

Ideas in this post:

  • Variance is a measure of dispersion for a single distribution. Covariance is a measure of dispersion for a joint distribution.
  • Just as we take the square root of variance to normalize it to something useful (standard deviation, or in a finance context — volatility), we normalize covariance into correlation.
  • Intuition for a positive(negative) correlation: if X is N standard deviations above its mean, Y is r * N standard deviations above(below) its mean.
  • Beta is r * the vol ratio of Y to X. In a finance context, it allows it allows us to convert a correlation from a standard deviation comparison to a simple elasticity. If beta = 1.5, then if X is up 2%, I expect Y to be up 3%
  • Correlation is symmetrical. Beta is not.
  • R2 is the variance explained by the independent variable. Risk remaining is the volatility that remains unexplained. It is equal to sqrt(1-R2).
  • There is a surprising amount of risk remaining even if correlations are strong. At a correlation of .86, there is 50% unexplained variance!
  • Don’t compute robotically. Reason > formulas.

✍️If You Make Money Every Day, You’re Not Maximizing (28 min read)

Part stories and part technical discussion of how to think about reducing risk.


Money Angle

Finance Guilt

I’ve said several times that finance is really just code. Like software, it’s an abstraction skin pulled over physical features. One can feel a bit disembodied if their formulation of the world for 8-12 hours a day are prices. Prices that collapse all of human enterprise, from the dirt under its fingernails to the sunrises and sunsets between now and some expiration date, into some Excel number format.

Just as software intermediates for less, financial innovation lowers the cost of go-betweens. In finance, the things went-between are people paying to offload risk to people looking to get paid for warehousing risk. In software and finance, skimming a tiny bit of rent on those transactions is lucrative.

How good or bad we can feel about the degree of skimming depends on how much surplus is created versus the higher friction model. The value of information liquidity is fairly obvious so Google enjoyed a positive reputation for at least its first decade in business. Meanwhile, finance feels like a constant barrage of “what did Wells Fargo do now?” or words that rhyme with Fonzi. People outside finance can be excused for having a dim, albeit biased, view of the profession since nobody reports on people doing an honest job.

With that in mind, I leave you with Mitchell’s understandable question:

Here’s my quick response:

Agustin’s response:

I’ll wrap with a footnote from a recent post:

The slicing and dicing of risk is finance’s salutary arrow of progress. Real economic growth is human progress in its battle against entropy. By farming, we can specialize. By pooling risk, we can underwrite giant human endeavors with the risk spread out tolerably. People might not sink the bulk of their net worth into a home if it wasn’t insurable. Financial innovation is matching a hedger with the most efficient holder of the risk. It’s matching risk-takers who need capital, with savers who are willing to earn a risk premium. Finance gets a bad rap for being a large part of the economy, and there are many headlines that enflame that view. I, myself, have a dim view of many financial practices. I have likened asset management to the vitamin industry — it sells noise as signal. But the story of finance broadly goes hand in hand with human progress. It might not be “God’s work” as Goldman’s boss once cringe-blurted, but its most extreme detractors as well as the legions of “I wish I was doing something more meaningful with my life” soldiers are discounting the value of its function which is buried in abstraction. Finance is code, so if software is eating the world, financialization is its dinner date.


Last Call

December 1984:

✍️The Day Los Angeles’ Bubble Burst (4 min read)

Now:

✍️Is the Housing Market Broken? (4 min read)
by Ben Carlson

See y’all in 2 weeks!

Mahalo

Moontower #143

Friends,

This week I published the longest post I’ve ever written. It’s long because it was liberal with stories. This is the long-winded story I used to introduce the concept of hedging.


If You Make Money Every Day, You’re Not Maximizing

This is an expression I heard early in my trading days. In this post, we will use arithmetic to show what it means in a trading context, specifically the concept of hedging.

I didn’t come to fully appreciate its meaning until about 5 years into my career. Let’s start with a story. It’s not critical to the technical discussion, so if you are a robot feel free to beep boop ahead.

The Belly Of The Trading Beast

Way back in 2004, I spent time on the NYSE as a specialist in about 20 ETFs. A mix of iShares and a relatively new name called FEZ, the Eurostoxx 50 ETF. I remember the spreadsheet and pricing model to estimate a real-time NAV for that thing, especially once Europe was closed, was a beast. I also happened to have an amazing trading assistant that understood the pricing and trading strategy for all the ETFs assigned to our post. By then, I had spent nearly 18 months on the NYSE and wanted to get back into options where I started.

I took a chance.

I let my manager who ran the NYSE floor for SIG know that I thought my assistant should be promoted to trader. Since I was the only ETF post on the NYSE for SIG, I was sort of risking my job. But my assistant was great and hadn’t come up through the formal “get-hired-out-of-college-spend-3-months-in-Bala” bootcamp track. SIG was a bit of a caste system that way. It was possible to crossover from external hire to the hallowed trader track, but it was hard. My assistant deserved a chance and I could at least advocate for the promotion.

This would leave me in purgatory. But only briefly. Managers talk. Another manager heard I was looking for a fresh opportunity from my current manager. He asked me if I want to co-start a new initiative. We were going to the NYMEX to trade futures options. SIG had tried and failed to break into those markets twice previously but could not gain traction. The expectations were low. “Go over there, try not to lose too much money, and see what we can learn. We’ll still pay you what you would have expected on the NYSE”.

This was a lay-up. A low-risk opportunity to start a business and learn a new market. And get back to options trading. We grabbed a couple clerks, took our membership exams, and took inventory of our new surroundings.

This was a different world. Unlike the AMEX, which was a specialist system, the NYMEX was open outcry. Traders here were more aggressive and dare I say a bit more blue-collar (appearances were a bit deceiving to my 26-year-old eyes, there was a wide range of diversity hiding behind those badges and trading smocks. Trading floors are a microcosm of society. So many backstories. Soft-spoken geniuses were shoulder-to-shoulder with MMA fighters, ex-pro athletes, literal gangsters or gunrunners, kids with rich daddies, kids without daddies). We could see how breaking in was going to be a challenge. These markets were still not electronic. Half the pit was still using paper trading sheets. You’d hedge deltas by hand-signaling buys and sells to the giant futures ring where the “point” clerk taking your order was also taking orders from the competitors standing next to you. He’s been having beers with these other guys for years. Gee, I wonder where my order is gonna stand in the queue?

I could see this was going to be about a lot more than option math. This place was 10 years behind the AMEX’s equity option pits. But our timing was fortuitous. The commodity “super-cycle” was still just beginning. Within months, the futures would migrate to Globex leveling the field. Volumes were growing and we adopted a solid option software from a former market-maker in its early years (it was so early I remember helping them correct their founder correct the weighted gamma calculation when I noticed my p/l attribution didn’t line up to my alleged Greeks).

We split the duties. I would build the oil options business and my co-founder who was more senior would tackle natural gas options (the reason I ever got into natural gas was because my non-compete precluded me from trading oil after I left SIG). Futures options have significant differences from equity options. For starters, every month has its own underlyers, breaking many arbitrage relationships in calendar spreads you learn in basic training. The first few months of trading oil options, I took small risks, allowing myself time to translate familiar concepts to this new universe. After 6 months, my business had roughly broken even and my partner was doing well in gas options. More importantly, we were breaking into the markets and getting recognition on trades.

[More on recognition: if a broker offers 500 contracts, and 50 people yell “buy em”, the broker divvies up the contracts as they see fit. Perhaps his bestie gets 100 and the remaining 400 get filled according to some mix of favoritism and fairness. If the “new guy” was fast and loud in a difficult-to-ignore way, there is a measure of group-enforced justice that ensures they will get allocations. As you make friends and build trust by not flaking on trades and take your share of losers, you find honorable mates with clout who advocate for you. Slowly your status builds, recognition improves, and the system mostly self-regulates.]

More comfortable with my new surroundings, I started snooping around. Adjacent to the oil options pit was a quirky little ring for product options — heating oil and gasoline. There was an extremely colorful cast of characters in this quieter corner of the floor. I looked up the volumes for these products and saw they were tiny compared to the oil options but they were correlated (gasoline and heating oil or diesel are of course refined from crude oil. The demand for oil is mostly derivative of the demand for its refined products. Heating oil was also a proxy for jet fuel and bunker oil even though those markets also specifically exist in the OTC markets). If I learned anything from clerking in the BTK index options pit on the Amex, it’s that sleepy pits keep a low profile for a reason.

I decided it was worth a closer look. We brought a younger options trader from the AMEX to take my spot in crude oil options (this person ended up becoming a brother and business partner for my whole career. I repeatedly say people are everything. He’s one of the reasons why). As I helped him get up to speed on the NYMEX, I myself was getting schooled in the product options. This was an opaque market, with strange vol surface behavior, flows, and seasonality. The traders were cagey and clever. When brokers who normally didn’t have business in the product options would catch the occasional gasoline order and have to approach this pit, you could see the look in their eyes. “Please take it easy on me”.

My instincts turned out correct. There was edge in this pit. It was a bit of a Rubik’s cube, complicated by the capital structure of the players. There were several tiny “locals” and a couple of whales who to my utter shock were trading their own money. One of the guys, a cult legend from the floor, would not shy away from 7 figure theta bills. Standing next to these guys every day, absorbing the lessons in their banter, and eventually becoming their friends (one of them was my first backer when I left SIG) was a humbling education that complemented my training and experience, illuminating some ways of thought that would have been harder to access in the monoculture I was in (this is no shade on SIG in any way, they are THE model for how to turn people into traders, but markets offer many lessons and nobody has a monopoly on how to think).

As my understanding and confidence grew, I started to trade bigger. Within 18 months, I was running the second-largest book in the pit, a distant second to the legend, but my quotes carried significant weight in that corner of the business. The oil market was now rocking, with WTI on its way to $100/barrel for the first time, and I was seeing significant dislocations in the vol markets between oil and products. This is where this long-winded story re-connects with the theme of this post.

How much should I hedge? We were stacking significant edge and I wanted to add as much as I could to the position. I noticed that the less capitalized players in the pit were happy to scalp their healthy profits and go home relatively flat. I was more brash back then and felt they were too short-sighted. They’d buy something I thought was worth $1.00 for $.50 and be happy to sell it out for $.70. In my language, that’s making 50 cents on a trade, to lose 30 cents on your next trade. The fact that you locked in 20 cents is irrelevant.

You need to be a pig when there’s edge because trading returns are not uniform. You can spend months breaking even, but when the sun shines you must make as much hay as possible. You don’t sleep. There’s plenty of time for that when things slow down and they inevitably will. New competitors will show up soon enough and the current time will be referred to as “the good ole’ days”. Sure enough, that is the nature of trading. The trades people do today are done for 1/20th the edge we used we used to get. That’s not fully explained by falling costs. That’s progress of human knowledge and returns to scale.

I started actively trading against the pit to take them out of their risk. I was willing to sacrifice edge per trade, to take on more size (I was also playing a different game than the big guy who was more focused on the fundamentals of the gasoline market, so our strategies were not running into one another. In fact, we were able to learn from each other). The other guys in the pit were not meek or dumb. As I said earlier, they were bright. Many simply had different risk tolerances because of how they self-funded and self-insured. My worst case was losing my job, and that wasn’t even on the table. I was transparent and communicative about the trades I was doing. I asked for a quant to double-check what I was seeing.

This period was a visceral experience of what we learned about edge and risk management. It was the first time my emotions were interrupted. I wanted assurance that the way I was thinking about risk and hedging was correct so I could have the fortitude to do what I intellectually thought was the right play.


Money Angle

The rest of the post gets into a proper discussion of hedging:

What Is Hedging?

Investopedia defines a hedge:

A hedge is an investment that is made with the intention of reducing the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting or opposite position in a related security.

The first time I heard about “hedging”, I was seriously confused. Like if you wanted to reduce the risk of your position, why did you have it in the first place.? Couldn’t you just reduce the risk by owning less of whatever was in your portfolio? The answer lies in relativity. Whenever you take a position in a security you are placing a bet. Actually, you’re making an ensemble of bets. If you buy a giant corporation like XOM, you are also making oblique bets on GDP, the price of oil, interest rates, management skill, politics, transportation, the list goes on. Hedging allows you to fine-tune your bets by offsetting some of the exposures you don’t have a view on. If your view was strictly on the price of oil you could trade futures or USO instead. If your view had nothing to do with the price of oil, but something highly idiosyncratic about XOM, you could even short oil against the stock position.

Options are popular instruments for implementing hedges. But even when used to speculate, this is an instance of hedging bundled with a wager. The beauty of options is how they allow you to make extremely narrow bets about timing, the size of possible moves, and the shape of a distribution. A stock price is a blunt summary of a proposition, collapsing the expected value of changing distributions into a single number. Imagine a typical utility stock that trades for $100. Now imagine a biotech stock that is 90% to be worth 0 and 10% to be worth $1000. Both of these stocks will trade for $100, but the option prices will be vastly different.1

If you have a differentiated opinion about a catalyst, the most efficient way to express it will be through the options. They have the most urgent function to a reaction. If you think a $100 stock can move $10, but the straddle implies $5 you can make 100% on your money in a short window of time. Annualize that! If you have an even finer view — you can handicap the direction, you can score a 5 or 10 bagger allocating the same capital to call options only. Conversely, if you do not have a specific view, then options can be an expensive, low-resolution solution. You pay for specificity just like a parlay. The timing and distance of a stock’s move must collaborate to pay you off.

So options, whether used explicitly for hedging or for speculating actually conform to a more over-arching definition of hedging — hedges are trades that isolate the investor’s risk.

The Hedging Paradox

If your trades have specific views or reasons, hedging is a good idea. Just like home insurance is a good idea. Whether you are conscious of it or not, owning a home is a bundle of bets. Your home’s value depends on interest rates, the local job market, state policy. But also on some pretty specific events. Your house value depends on “not having a flood”. Insurance is a specific hedge for a specific risk. In The Laws Of Trading, author and trader Agustin Lebron states rule #3:

Take the risks you are paid to take. Hedge the others.

He’s reminding you to isolate your bets so they map as closely as possible to your original reason for wanting the exposure.

You should be feeling tense right about now. “Dude, I’m not a robot with a Terminator HUD displaying every risk in my life and how hedged it is?”.

Relax. Even if you were, you couldn’t do anything about it. Even if you had the computational wherewithal to identify every unintended risk, it would be too expensive to mitigate2. Who’s going to underwrite the sun not coming up tomorrow? [Actually, come to think of it, I will. If you want to buy galactic continuity insurance ping me and I’ll send you a BTC address].

We find ourselves torn:

  1. We want to hedge the risks we are not paid to take.
  2. Hedging is a cost

What do we do?

Before getting into this I will mention something a certain, beloved group of wonky readers are thinking: “Kris, just because insurance/hedging on its own is worth less than it’s actuarial value, the diversification can still be accretive at the portfolio level especially if we focus on geometric not arithmetic returns…rebalancing…convexi-…”[trails off as the sound of the podcast in the background drowns out the thought]. Guys (it’s definitely guys), I know. I’m talking net of all that.

As the droplets of caveat settle the room like nerd Febreze, let’s see if we can give this conundrum a shape.

Reconciling The Paradox

This is a cornerstone of trading…

Edge scales linearly, risk scales slower

Continue reading:

✍️If You Make Money Every Day, You’re Not Maximizing(28 min read)


From My Actual Life

A month ago I started tutoring elementary school students in math. These kids are in vulnerable communities that were hit extra hard by the impact of remote learning. They are one or more grades behind standards.

One-on-one instruction is effective but a luxury. The non-profit always needs more volunteers. Without volunteers, this cannot happen.

The organization offers training before you start as well as all the supplies you need. There are opportunities to teach in-person for reading and remote for math.

If you live in CA you can help!

You only need to get your fingerprints done for a background check and be willing to commit 30 minutes a week. You can do more if you like. I do 2 sessions a week with a second-grader and a third-grader. You don’t need to be “good” at math. If you can count backward from 10 to 5, you already know things that these kids need help with. Seriously.

Ping me if you are interested. This will give you time to get your background check and training (training is just a few hours).

The next sessions will be summer and then the return to school in the fall.

If You Make Money Every Day, You’re Not Maximizing

If You Make Money Every Day, You’re Not Maximizing

This is an expression I heard early in my trading days. In this post, we will use arithmetic to show what it means in a trading context, specifically the concept of hedging.

I didn’t come to fully appreciate its meaning until about 5 years into my career. Let’s start with a story. It’s not critical to the technical discussion, so if you are a robot feel free to beep boop ahead.

The Belly Of The Trading Beast

Way back in 2004, I spent time on the NYSE as a specialist in about 20 ETFs. A mix of iShares and a relatively new name called FEZ, the Eurostoxx 50 ETF. I remember the spreadsheet and pricing model to estimate a real-time NAV for that thing, especially once Europe was closed, was a beast. I also happened to have an amazing trading assistant that understood the pricing and trading strategy for all the ETFs assigned to our post. By then, I had spent nearly 18 months on the NYSE and wanted to get back into options where I started.

I took a chance.

I let my manager who ran the NYSE floor for SIG know that I thought my assistant should be promoted to trader. Since I was the only ETF post on the NYSE for SIG, I was sort of risking my job. But my assistant was great and hadn’t come up through the formal “get-hired-out-of-college-spend-3-months-in-Bala” bootcamp track. SIG was a bit of a caste system that way. It was possible to crossover from external hire to the hallowed trader track, but it was hard. My assistant deserved a chance and I could at least advocate for the promotion.

This would leave me in purgatory. But only briefly. Managers talk. Another manager heard I was looking for a fresh opportunity from my current manager. He asked me if I want to co-start a new initiative. We were going to the NYMEX to trade futures options. SIG had tried and failed to break into those markets twice previously but could not gain traction. The expectations were low. “Go over there, try not to lose too much money, and see what we can learn. We’ll still pay you what you would have expected on the NYSE”.

This was a lay-up. A low-risk opportunity to start a business and learn a new market. And get back to options trading. We grabbed a couple clerks, passed our membership exams, and took inventory of our new surroundings.

This was a different world. Unlike the AMEX, which was a specialist system, the NYMEX was open outcry. Traders here were more aggressive and dare I say a bit more blue-collar (appearances were a bit deceiving to my 26-year-old eyes, there was a wide range of diversity hiding behind those badges and trading smocks. Trading floors are a microcosm of society. So many backstories. Soft-spoken geniuses were shoulder-to-shoulder with MMA fighters, ex-pro athletes, literal gangsters or gunrunners, kids with rich daddies, kids without daddies). We could see how breaking in was going to be a challenge. These markets were still not electronic. Half the pit was still using paper trading sheets. You’d hedge deltas by hand-signaling buys and sells to the giant futures ring where the “point” clerk taking your order was also taking orders from the competitors standing next to you. He’s been having beers with these other guys for years. Gee, I wonder where my order is gonna stand in the queue?

I could see this was going to be about a lot more than option math. This place was 10 years behind the AMEX’s equity option pits. But our timing was fortuitous. The commodity “super-cycle” was still just beginning. Within months, the futures would migrate to Globex leveling the field. Volumes were growing and we adopted a solid option software from a former market-maker in its early years (it was so early I remember helping their founder correct the weighted gamma calculation when I noticed my p/l attribution didn’t line up to my alleged Greeks).

We split the duties. I would build the oil options business and my co-founder who was more senior would tackle natural gas options (the reason I ever got into natural gas was because my non-compete precluded me from trading oil after I left SIG). Futures options have significant differences from equity options. For starters, every month has its own underlyers, breaking the arbitrage relationships in calendar spreads you learn in basic training. During the first few months of trading oil options, I took small risks, allowing myself time to translate familiar concepts to this new universe. After 6 months, my business had roughly broken even and my partner was doing well in gas options. More importantly, we were breaking into the markets and getting recognition on trades.

[More on recognition: if a broker offers 500 contracts, and 50 people yell “buy em”, the broker divvies up the contracts as they see fit. Perhaps his bestie gets 100 and the remaining 400 get filled according to some mix of favoritism and fairness. If the “new guy” was fast and loud in a difficult-to-ignore way, there is a measure of group-enforced justice that ensures they will get allocations. As you make friends and build trust by not flaking on trades and taking your share of losers, you find honorable mates with clout who advocate for you. Slowly your status builds, recognition improves, and the system mostly self-regulates.]

More comfortable with my new surroundings, I started snooping around. Adjacent to the oil options pit was a quirky little ring for product options — heating oil and gasoline. There was an extremely colorful cast of characters in this quieter corner of the floor. I looked up the volumes for these products and saw they were tiny compared to the oil options but they were correlated (gasoline and heating oil or diesel are of course refined from crude oil. The demand for oil is mostly derivative of the demand for its refined products. Heating oil was also a proxy for jet fuel and bunker oil even though those markets also specifically exist in the OTC markets). If I learned anything from clerking in the BTK index options pit on the Amex, it’s that sleepy pits keep a low-profile for a reason.

I decided it was worth a closer look. We brought a younger options trader from the AMEX to take my spot in crude oil options (this person ended up becoming a brother and business partner for my whole career. I repeatedly say people are everything. He’s one of the reasons why). As I helped him get up to speed on the NYMEX, I myself was getting schooled in the product options. This was an opaque market, with strange vol surface behavior, flows and seasonality. The traders were cagey and clever. When brokers who normally didn’t have business in the product options would catch the occasional gasoline order and have to approach this pit, you could see the look in their eyes. “Please take it easy on me”.

My instincts turned out correct. There was edge in this pit. It was a bit of a Rubik’s cube, complicated by the capital structure of the players. There were several tiny “locals” and a couple of whales who to my utter shock were trading their own money. One of the guys, a cult legend from the floor, would not shy away from 7 figure theta bills. Standing next to these guys every day, absorbing the lessons in their banter, and eventually becoming their friends (one of them was my first backer when I left SIG) was a humbling education that complemented my training and experience. It illuminated approaches that would have been harder to access in the monoculture I was in (this is no shade on SIG in any way, they are THE model for how to turn people into traders, but markets offer many lessons and nobody has a monopoly on how to think).

As my understanding and confidence grew, I started to trade bigger. Within 18 months, I was running the second-largest book in the pit, a distant second to the legend, but my quotes carried significant weight in that corner of the business. The oil market was now rocking. WTI was on its way to $100/barrel for the first time, and I was seeing significant dislocations in the vol markets between oil and products1. This is where this long-winded story re-connects with the theme of this post.

How much should I hedge? We were stacking significant edge and I wanted to add as much as I could to the position. I noticed that the less capitalized players in the pit were happy to scalp their healthy profits and go home relatively flat. I was more brash back then and felt they were too short-sighted. They’d buy something I thought was worth $1.00 for $.50 and be happy to sell it out for $.70. In my language, that’s making 50 cents on a trade, to lose 30 cents on your next trade. The fact that you locked in 20 cents is irrelevant.

You need to be a pig when there’s edge because trading returns are not uniform. You can spend months breaking even, but when the sun shines you must make as much hay as possible. You don’t sleep. There’s plenty of time for that when things slow down. They always do. New competitors will show up and the current time will be referred to as “the good ole’ days”. Sure enough, that is the nature of trading. The trades people do today are done for 1/20th the edge we used to get.

I started actively trading against the pit to take them out of their risk. I was willing to sacrifice edge per trade, to take on more size (I was also playing a different game than the big guy who was more focused on the fundamentals of the gasoline market, so our strategies were not running into one another. In fact, we were able to learn from each other). The other guys in the pit were hardly meek or dumb. They simply had different risk tolerances because of how they were self-funded and self-insured. My worst case was losing my job, and that wasn’t even on the table. I was transparent and communicative about the trades I was doing. I asked for a quant to double-check what I was seeing.

This period was a visceral experience of what we learned about edge and risk management. It was the first time my emotions were interrupted. I wanted assurance that the way I was thinking about risk and hedging was correct so I could have the fortitude to do what I intellectually thought was the right play.

This post is a discussion of hedging and risk management.

Let’s begin.


What Is Hedging?

Investopedia defines a hedge:

A hedge is an investment that is made with the intention of reducing the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting or opposite position in a related security.

The first time I heard about “hedging”, I was seriously confused. Like if you wanted to reduce the risk of your position, why did you have it in the first place.? Couldn’t you just reduce the risk by owning less of whatever was in your portfolio? The answer lies in relativity. Whenever you take a position in a security you are placing a bet. Actually, you’re making an ensemble of bets. If you buy a giant corporation like XOM, you are also making oblique bets on GDP, the price of oil, interest rates, management skill, politics, transportation, the list goes on. Hedging allows you to fine-tune your bets by offsetting the exposures you don’t have a view on. If your view was strictly on the price of oil you could trade futures or USO instead. If your view had nothing to do with the price of oil, but something highly idiosyncratic about XOM, you could even short oil against the stock position.

Options are popular instruments for implementing hedges. But even when used to speculate, this is an instance of hedging bundled with a wager. The beauty of options is how they allow you to make extremely narrow bets about timing, the size of possible moves, and the shape of a distribution. A stock price is a blunt summary of a proposition, collapsing the expected value of changing distributions into a single number. A boring utility stock might trade for $100. Now imagine a biotech stock that is 90% to be worth 0 and 10% to be worth $1000. Both of these stocks will trade for $100, but the option prices will be vastly different 2.

If you have a differentiated opinion about a catalyst, the most efficient way to express it will be through options. They have the most urgent function to a reaction. If you think a $100 stock can move $10, but the straddle implies $5 you can make 100% on your money in a short window of time. Annualize that! Go a step further. Suppose you have an even finer view — you can handicap the direction. Now you can score a 5 or 10 bagger allocating the same capital to call options only. Conversely, if you do not have a specific view, then options can be an expensive, low-resolution solution. You pay for specificity just like parlay bets. The timing and distance of a stock’s move must collaborate to pay you off.

So options, whether used explicitly for hedging or for speculating actually conform to a more over-arching definition of hedging — hedges are trades that isolate the investor’s risk.

The Hedging Paradox

If your trades have specific views or reasons, hedging is a good idea. Just like home insurance is a good idea. Whether you are conscious of it or not, owning a home is a bundle of bets. Your home’s value depends on interest rates, the local job market, and state policy. It also depends on some pretty specific events. For example, “not having a flood”. Insurance is a specific hedge for a specific risk. In The Laws Of Trading, author and trader Agustin Lebron states rule #3:

Take the risks you are paid to take. Hedge the others.

He’s reminding you to isolate your bets so they map as closely as possible to your original reason for wanting the exposure.

You should be feeling tense right about now. “Dude, I’m not a robot with a Terminator HUD displaying every risk in my life and how hedged it is?”.

Relax. Even if you were, you couldn’t do anything about it. Even if you had the computational wherewithal to identify every unintended risk, it would be too expensive to mitigate3. Who’s going to underwrite the sun not coming up tomorrow? [Actually, come to think of it, I will. If you want to buy galactic continuity insurance ping me and I’ll send you a BTC address].

We find ourselves torn:

  1. We want to hedge the risks we are not paid to take.
  2. Hedging is a cost

What do we do?

Before getting into this I will mention something a certain, beloved group of wonky readers are thinking: “Kris, just because insurance/hedging on its own is worth less than its actuarial value, the diversification can still be accretive at the portfolio level especially if we focus on geometric not arithmetic returns…rebalancing…convexi-…”[trails off as the sound of the podcast in the background drowns out the thought]. Guys (it’s definitely guys), I know. I’m talking net of all that.

As the droplets of caveat settle the room like nerd Febreze, let’s see if we can give this conundrum a shape.

Reconciling The Paradox

This is a cornerstone of trading:

Edge scales linearly, risk scales slower

[As a pedological matter, I’m being a bit brusque. Bear with me. The principle and its demonstration are powerful, even if the details fork in practice.]

Let’s start with coin flips:

[A] You flip a coin 10 times, you expect 5 heads with a standard deviation of 1.584.

[B] You flip 100 coins you expect 50 heads with a standard deviation of 5.

Your expectancy scaled with N. 10x more flips, 10x more expected heads.

But your standard deviation (ie volatility) only grew by √10 or 3.16x.

The volatility or risk only scaled by a factor of √N while expectancy grew by N.

This is the basis of one of my most fundamental posts, Understanding Edge. Casinos and market-makers alike “took a simple idea and took it seriously”. Taking this seriously means recognizing that edges are incredibly valuable. If you find an edge, you want to make sure to get as many chances to harvest it as possible. This has 2 requirements:

  1. You need to be able to access it.
  2. You need to survive so you can show up to collect it.

The first requirement requires spotting an opportunity or class of opportunities, investing in its access, and warehousing the resultant risk. The second requirement is about managing the risk. That includes hedging and all its associated costs.

The paradox is less mystifying as the problem takes shape.

We need to take risk to make money, but we need to reduce risk to survive long enough to get to a large enough number of bets on a sliver of edge to accumulate meaningful profits. Hedging is a drawbridge from today until your capital can absorb more variance.

The Interaction of Trading Costs, Hedging, and Risk/Reward

Hedging reduces variance, in turn improving the risk/reward of a strategy. This comes at a substantial cost. Every options trader has lamented how large of line-item this cost has been over the years. Still, as the cost of survival, it is non-negotiable. We are going to hedge. So let’s pull apart the various interactions to gain intuition for the various trade-offs. Armed with the intuition, you can then fit the specifics of your own strategies into a risk management framework that aligns your objectives with the nature of your markets.

Let’s introduce a simple numerical demonstration to anchor the discussion. Hedging is a big topic subject to many details. Fortunately, we can gesture at a complex array of considerations with a toy model.

The Initial Proposition

Imagine a contract that has an expected value of $1.00 with a volatility (i.e. standard deviation) of $.80. You can buy this contract for $.96 yielding $.04 of theoretical edge.

Your bankroll is $100.

[A quick observation so more advanced readers don’t have this lingering as we proceed:

The demonstration is going to bet a fixed amount, even as the profits accumulate. At first glance, this might feel foreign. In investing we typically think of bet size as a fraction of bankroll. In fact, a setup like this lends itself to Kelly sizing5. However, in trading businesses, the risk budget is often set at the beginning of the year based on the capital available at that time. As profits pile up, contributing to available capital, risk limits and bet sizes may expand. But such changes are more discrete than continuous so if we imagine our demonstration is occurring within a single discrete interval, perhaps 6 months or 1 year, this is a reasonable approach. It also keeps this particular discussion a bit simpler without sacrificing intuition.]

The following table summarizes the metrics for various trial sizes.

What you should notice:

  • Expected value grows linearly with trial size
  • The standard deviation of p/l grows slower (√N)
  • Sharpe ratio (expectancy/standard deviation) is a measure of risk-reward. Its progression summarizes the first 2 bullets…as trials increase the risk/reward improves

Introducing Hedges

Let’s show the impact of adding a hedge to reduce risk. Let’s presume:

  • The hedge costs $.01.

    This represents 25% of your $.04 of edge per contract. Options traders and market makers like to transform all metrics into a per/contract basis. That $.01 could be made up of direct transaction costs and slippage.

    [In reality, there is a mix of drudgery, assumptions, and data analysis to get a firm handle on these normalizations. A word to the uninitiated, most of trading is not sexy stuff, but tons of little micro-decisions and iterations to create an accounting system that describes the economic reality of what is happening in the weeds. Drunkenmiller and Buffet’s splashy bets get the headlines, but the magic is in the mundane.]

  • The hedge cuts the volatility in half.

Right off the bat, you should expect the sharpe ratio to improve — you sacrificed 25% of your edge to cut 50% of the risk.

The revised table:

Notice:

  • Sharpe ratio is 50% higher across the board
  • You make less money.

Let’s do one more demonstration. The “more expensive hedge scenario”. Presume:

  • The hedge costs $.02

    This now eats up 50% of your edge.

  • The hedge reduces the volatility 50%, just as the cheaper hedge did.

Summary:

Notice:

  • The sharpe ratio is exactly the same as the initial strategy. Both your net edge and volatility dropped by 50%, affecting the numerator and denominator equally. 

  • Again the hedge cost scales linearly with edge, so you have the same risk-reward as the unhedged strategy you just make less money.

If hedging doesn’t improve the sharpe ratio because it’s too expensive, you have found a limit. Another way it could have been expensive is if the cost of the hedge stayed fixed at $.01 but the hedge only chopped 25% of the volatility. Again, your sharpe would be unchanged from the unhedged scenario but you just make less money.

We can summarize all the results in this chart.

The Bridge

As you book profits, your capital increases. This leaves you with at least these choices:

  1. Hedge less since your growing capital is absorbing the same risk
  2. Increase bet size
  3. Increase concurrent trials

I will address #1 here, and the remaining choices in the ensuing discussion.

Say you want to hedge less. This is always a temptation. As we’ve seen, you will make money faster if you avoid hedging costs. How do we think about the trade-off between the cost of hedging and risk/reward?

We can actually target a desired risk/reward and let the target dictate if we should hedge based on the expected trial size.

Sharpe ratio is a function of trial size:

where:

E = edge
σ = volatility
N = trials

If we target a sharpe ratio of 1.0 we can re-arrange the equation to solve for how large our trial size needs to be to achieve the target.

If our capital and preferences allow us to tolerate a sharpe of 1 and we believe we can get at least 400 trials, then we should not hedge.

Suppose we don’t expect 400 chances to do our core trade, but the hedge that costs $.01 is available. What is the minimum number of trades we can do if we can only tolerate a sharpe as low as 1?

Using the same math as above (1/.075)2 = 178

The summary table:

If our minimum risk tolerance is a 1.5 sharpe, we need more trials:

If your minimum risk tolerance is 1.5 sharpe, and you only expect to do 2 trades per business day or about 500 trades per year, then you should hedge. If you can do twice as many trades per day, it’s acceptable to not hedge.

These toy demonstrations show:

  • If you have positive expectancy, you should be trading
  • The cost of a hedge scales linearly with edge, but volatility does not
  • If the cost of a hedge is less than its proportional risk-reduction you have a choice whether to hedge or not
  • The higher your risk tolerance the less you should hedge
  • The decision to dial back the hedging depends on your risk tolerance (as proxied by a measure of risk/reward) vs your expected sample size

Variables We Haven’t Considered

The demonstrations were simple but provides a mental template to contextualize cost/benefit analysis of risk mitigation in your own strategies. We kept it basic by only focusing on 3 variables:

  • edge
  • volatility
  • risk tolerance as proxied by sharpe ratio

Let’s touch on additional variables that influence hedging decisions.

Bankroll 

If your bankroll or capital is substantial compared to your bet size (perhaps you are betting far below Kelly or half-Kelly prescribed sizes) then it does not make sense to hedge. Hedges are negative expectancy trades that reduce risk.

We can drive this home with a sports betting example from the current March Madness tournament:

If you placed a $10 bet on St. Peters, by getting to the Sweet 16 you have already made 100x. You could lock it in by hedging all or part of it by betting against them, but the bookie vig would eat a slice of the profit. More relevant, the $1000 of equity might be meaningless compared to your assets. There’s no reason to hedge, you can sweat the risk. But what if you had bet $100 on St. Pete’s? $10,000 might quicken the ole’ pulse. Or what if you somehow happened upon a sports edge (just humor me) and thought you could put that $10k to work somewhere else instead of banking on an epic Cinderella story? If St. Pete’s odds for the remainder of the tourney are fair, then you will sacrifice expectancy by hedging or closing the trade. If you are rich, you probably just let it ride and avoid any further transaction costs.

If you are trading relatively small, your problem is that you are not taking enough risk. The reason professionals don’t take more risk when they should is not because they are shy. It’s because of the next 2 variables.

Capacity Per Trade

Many lucrative edges are niche opportunities that are difficult to access for at least 2 reasons.

  • Adverse selection

    There might only be a small amount of liquidity at dislocated prices (this is a common oversight of backtests) because of competition for edge. 

    Let’s return to the contract from the toy example. Its fair value is $1.00. Now imagine that there are related securities that getting bid up and market for our toy contract is:

 bid  ask
.95 – 1.05

10 “up” (ie there are 10 contracts on the offer and 10 contracts bid for)

Based on what’s trading “away”, you think this contract is now worth $1.10.

Let’s game this out.

You quickly determine that the .95-1.05 market is simply a market-maker’s bid-ask spread. Market-makers tend to be large firms with tentacles in every related market to the ones they quote. It’s highly unlikely that the $1.05 offer is “real”. In other words, if you tried to lift it, you would only get a small amount of size.

What’s going on?

The market-maker might be leaving a stale quote to maximize expectancy. If a real sell order were to come in and offer at $1.00, the market maker might lift the size and book $.10 of edge to the updated theoretical value. 

Of course, there’s a chance they might get lifted on their $1.05 stale offer but they might honor only a couple contracts. This is a simple expectancy problem. If 500 lots come in offered at $1.00, and they lift it, they make $5,000 profit ($.10 x 500 x option multiplier of 100). If you lift the $1.05 offer and they sell you 10 contracts, they suffer a measly $50 loss. 

So if they believe there’s a 1% chance or greater of a 500 lot naively coming in and offering at mid-market then they are correct in posting the stale quote.

What do you do?

You were smart enough to recognize the game being played. You used second-order thinking to realize the quote was purposefully stale. In a sense, you are now in cahoots with the market maker. You are both waiting for the berry to drop. The problem is your electronic “eye” will be slower than the market-maker to snipe the berry when it comes in. Still, even if you have a 10% chance of winning the race, it still makes sense to leave the quote stale, rather than turn the offer. If you do manage to get at least a partial fill on the snipe, there’s no reason to hedge. You made plenty of edge, traded relatively small size, and most importantly know your counterparty was not informed!

As a rule, liquidity is poor when trades are juiciest. The adverse selection of your fills is most common in fast-moving markets if you do not have a broad, fast view of the flows. This is why a trader’s first questions are “Do I think I’m the first to have seen this order? Did someone with a better perch to see all the flow already pass on this trade?”

In many markets, if you are not the first you might as well be last. You are being arbed because there’s a better relative trade somewhere out there that you are not seeing.

[Side note: many people think a bookie or market-maker’s job is to balance flow. That can be true for deeply liquid instruments. But for many securities out there, one side of the market is dumb and one side is real. Markets are often leaned. Tables are set when certain flows are anticipated. If a giant periodic buy order gets filled at mid-market or even near the bid, look at the history of the quote for the preceding days. Market-making is not an exercise in posting “correct” markets. It’s a for-profit enterprise.]

  • Liquidity

    The bigger you attempt to trade at edgy prices, the more information you leak into the market. You are outsizing the available liquidity by allowing competitors to reverse engineer your thinking. If a large trade happens and immediately looks profitable to bystanders, they will study the signature of how you executed it. The market learns and copies. The edge decays until you’re flipping million dollar coins for even money as a loss leader to get a look at juicier flow from brokers. 

    As edge in particular trades dwindles, the need to hedge increases. The hedges themselves can get crowded or at least turn into a race.

Leverage

If a hedge, net of costs, improves the risk/reward of your position, you may entertain the use of leverage. This is especially tempting for high sharpes trades that have low absolute rates of return or edge. Market-making firms embody this approach. As registered broker-dealers they are afforded gracious leverage. Their businesses are ultimately capacity constrained and the edges are small but numerous. The leverage combined with sophisticated diversification (hedging!) creates a suitable if not impressive return on capital.

The danger with leverage is that it increases sensitivity to path and “risk of ruin”. In our toy model, we assumed a Gaussian distribution. Risk of ruin can be hard to estimate when distributions have unknowable amounts of skew or fatness in their tails. Leverage erodes your margin of error.

General Hedging Discussion

As long as hedging, again net of costs, improves your risk/reward there is substantial room for creative implementation. We can touch on a few practical examples.

Point of sale hedging vs hedging bands

In the course of market-making, the primary risk is adverse selection. Am I being picked off? If you suspect the counterparty is “delta smart” (whenever they buy calls the stock immediately rips higher), you want to hedge immediately. This is a race condition with any other market makers who might have sold the calls and the bots that react to the calls being printed on the exchange. That is known as a point-of-sale hedge is an immediate response to a suspected “wired” order.

If you instead sold calls to a random, uninformed buyer you will likely not hedge. Instead, the delta risk gets thrown on the pile of deltas (ie directional stock exposures) the firm has accumulated. Perhaps it offsets existing delta risk or adds to it. Either way, there is no urgency to hedge that particular deal.

In practice, firms use hedging bands to manage directional risk. In a similar process to our toy demonstration, market-makers decide how much directional risk they are willing to carry as a function of capital and volatility. This allows them to hedge less, incurring less costs along the way, and allowing their capital to absorb randomness. Just like the rich bettor, who lets the St. Peter’s bet ride.

In The Risk-Reversal Premium, Euan Sinclair alludes to band-based hedging:

While this example shows the clear existence of a premium in the delta-hedged risk-reversal, this implementation is far from what traders would do in practice (Sinclair, 2013). Common industry practice is to let the delta of a position fluctuate within a certain band and only re-hedge when those bands are crossed. In our case, whenever the net delta of the options either drops below 20 or above 40, the portfolio is rebalanced by closing the position and re-establishing with the options that are now closest to 15-delta in the same expiration.

Part art, part science

Hedging is a minefield of regret. It’s costly, but the wisdom of offloading risks you are not paid for and conforming to a pre-determined risk profile is a time-tested idea. Here’s a dump of concerns that come to mind:

  • If you hedge long gamma, but let short gamma ride you are letting losers grow and cutting winners short. Be consistent. If your delta tolerance is X and you hedge twice a day, you can cut all deltas in excess of X at the same 2 times every day. This will remove discretion from the decision. (I had one friend who used to hedge to flat every time he went to the bathroom. As long as he was regular this seemed reasonable to me.)

  • Low net/high gross exposures are a sign of a hedged book. There are significant correlation risks under that hood. It’s not necessarily a red flag, but when paired with leverage, this should make you nervous. 

  • Are you hedging your daily, weekly, or monthly p/l? Measures of local risk like Greeks and spot/vol correlation are less trustworthy for longer timeframes. Spot/vol correlation (ie vol beta) is not invariant to price level, move size, and move speed. Longer time frames provide larger windows for these variables to change.  If oil vol beta is -1 (ie if oil rallies 1%, ATM vol vols 1%) do I really believe that the price going from 50 to 100 cuts the vol in half?

  • There are massive benefits to scale for large traders who hedge. The more flow they interact with the more opportunity to favor anti-correlated or offsetting deltas because it saves them slippage on both sides. They turn everything they trade into a pooled delta or several pools of delta (so any tech name will be re-computed as an NDX exposure, while small-caps will be grouped as Russell exposures). This is efficient because they can accept the noise within the baskets and simply hedge each of the net SPX, NDX, IWM to flat once they reach specified thresholds.

    The second-order effect of this is subtle and recursively makes markets more efficient. The best trading firms have the scale to bid closest to the clearing price for diversifiable risk6. This in turn, allows them to grab even more market share widening their advantage over the competition. If this sounds like big tech7, you are connecting the dots. 

Wrapping Up

The other market-makers in the product options pit were not wrong to hedge or close their trades as quickly as they did. They just had different constraints. Since they were trading their own capital, they tightly managed the p/l variance.

At the same time, if you were well-capitalized and recognized the amount of edge raining down in the market at the time, the ideal play was to take down as much risk as you could and find a hedge with perhaps more basis risk (and therefore less cost because the more highly correlated hedges were bid for) or simply allow the firm’s balance sheet to absorb it.

Since I was being paid as a function of my own p/l there was not perfect alignment of incentives between me and my employer (who would have been perfectly fine with me not hedging). If I made a great bet and lost, it would have been the right play but I personally didn’t want to tolerate not getting paid.

Hedging is a cost. You need to weigh that with the benefit and that artful equation is a function of:

  • risk tolerance at every level of stakeholder — trader, manager, investor
  • capital
  • edge
  • volatility
  • liquidity
  • adverse selection

Maximizing is uncomfortable. Almost unnatural. It calls for you to tolerate larger swings, but it allows the theoretical edge to pile up faster. This post offers guardrails for dissecting a highly creative problem.

But if you consistently make money, ask yourself how much you might be leaving on the table. If you are making great trades somewhere, are you locking it in with bad trades? If you can’t tell what the good side is that’s ok.

But if you know the story of your edge, there’s a good chance you can do better.


Momentum Psychology

His tweet brought my attention to @cobie and his masterful description of psychology.

I also appreciated Josh Brown’s take on the sell-off in so-called growth or momentum names. Here’s an excerpt from Jan 31’s It’s not over yet.

I’m less interested in the real-time action. Focus the evergreen psychology instead:

Where do bounces come from in a midst of a correction?

Sometimes it’s just that stocks have fallen too far for sellers to want to keep selling. This isn’t bullish. In fact, this type of bounce can suck people back in by creating the appearance that the worst is over. Growth stocks in particular. Because belief dies hard and enthusiasm for cutting edge technologies fades slowly, not suddenly. Which mean the give-up process is long and drawn out – even after a stock is cut in half sometimes the worst is still yet to come. The slow bleed after is often worse than the initial shocking drop that preceded it.

Over at Verdad Capital, Dan Rasmussen revisits their “Bubble 500” list of overpriced growth stocks, originally created in the Summer of 2020. It’s filled with money-losing companies working in exciting areas of technology such as electric vehicles and gene editing therapy and so on. Needless to say, this list of bubble stocks has gotten absolutely destroyed year-to-date, after having run straight up in Verdad’s face through the middle of 2021.  Dan explains two very important things in his update this week: The first is that sell-offs for growth stocks differ from sell-offs for value stocks in one very important way:

This breakdown is significant, especially for growth stocks. Remember, growth stocks trend, and value stocks mean revert. The psychology is simple. People hear about a hot stock that’s gone up 3x, they buy some, it goes up 2x, they buy more: the whole attraction of buying a hot growth stock is the historic return trajectory. Value stocks are the opposite: you do well buying them when they’re down…

This idea is counterintuitive – that some stocks actually become worse buys as they are falling to lower prices, but the explanation is psychological, not financial. Stocks trading at excessive valuations require a fan base to sustain their share prices. That fan base is often a bandwagon-jumping melange of traders and investors who are attracted to recent gains. Yes, they’ll latch onto the fundamental story, but the fact that the stock has been and currently is going up is the main thing. When the stock breaks, so too does the fandom. And when the fan base moves on to greener pastures or runs out of money, a new fan base will not form for this stock with its chart in decline. Broken growth stocks become orphans. There is no natural place for them to find a home.

Momentum is a divergent strategy while “value” is a mean-reverting strategy. Several years ago the research team at OSAM published edifying papers on how these approaches work. I wrote a summary here:

✍️ Notes on OSAM’s Factors from Scratch (6 min read)

Value works by fading overreaction. Momentum is attributed to underreaction. In a name trending higher, the sellers are discounting the substance of new information too aggressively. In dork world, we call this anchoring. If you pay attention to “anomalies” you may recognize the concept of post-earnings drift as an acute example of anchoring. Wikipedia even has an entry for it.

Fear or FOMO in markets cuts both ways. On the way down, we fear a loss of wealth. On the way up we fear social embarrassment — we aren’t keeping up with our neighbors. We are caught between self-preservation and shame. I wonder if being part of the herd is any consolation on the way down while everyone loses. Or is this just another miserable psychological asymmetry inseparable from speculation?

Anyway, I don’t have much to add. Investing requires you to be honest about your desires, constraints, and emotional tolerance. If you can get honest with yourself, you can initiate a plan that you can stick to. You want to avoid ad-hoc decisions with the bulk of your savings (I’m not gonna poo poo on gambling with 1 or 2% of your wealth, especially if it suppresses wider risk-seeking behavior. Agustin Lebron’s Laws of Trading has a provocative section about “risk set points” that operate like weight set points. If your life becomes too dull in one way you spice it up in another and vice versa. Maybe Alex Honnold’s portfolio is all in bonds 🤷🏽).

Oh and just a quick observation that you can ponder in the context of those flashy, earningless momentum stocks. If you start at $1 and double 6x you get to $64. If the stock drops 50%, you’ve only erased 1 halving.

Be careful knife catching.

Moontower #142

First, a giant thank you for reading this letter. This is Moontower’s 3-year anniversary. This week the 3,000th subscriber joined. Thank you to the 45 people or so who agreed to read that very first issue.

Writing online allowed me to unlock myself in ways that I couldn’t without your support. So truly, thank you.


Ok friends, let’s proceed.

This week, I published the sequel to There’s Gold in Them Thar Tails.

It begins with a recap of part 1:

  1. We saw that an explosion of choice whether it’s a job or college applicants, songs to listen to, athletes to recruit has made selection increasingly difficult.
  2. A natural response is to narrow the field by filtering more narrowly. We can do this by making selection criteria stricter or deploying smarter algorithms and recommendation engines.
  3. This leads to increased reliance on legible measurements for filtering.
  4. Goodhart’s law expects that the measures themselves will become the target, increasing the pressure on candidates to optimize for narrow targets that are imperfect proxies or predictors of what the measure was filtering for.
  5. Anytime we filter, we face a trade-off between signal (“My criteria is finding great candidates”) and diversity. This is also known as the bias-variance trade-off.
  6. Diversity is an essential input to progress. Nature’s underlying algorithm of evolution penalizes in-breeding.
  7. In addition to a loss of diversity, signal decays as you get closer to the extremes. This is known as tail divergence. The signal can even flip (ie Berkson’s Paradox).
  8. The point where the signal noise overwhelms the variance in the candidates is an efficient cutoff. Beyond that threshold, selectors should think more creatively than “just raise the bar”.

Part 1 ends with a discussion of strategies for selectors and selectees.

Part 2 extends the discussion with what tail divergence says about life and investing.

✍️There’s Gold In Them Thar Tails: Part 2 (24 min read)

It’s a long post including footnotes, but there is a large section about options trading that will only appeal to masochists.

The post roadmap:

  1. We begin with the challenge of scaling our moral intuitions up to an age where our ethics must be explicitly coded. AI and automation require making species-level questions less rhetorical.
  2. The prescription is humility. The simple math of regression shows this as correlations break down or invert in the extremes. The CAPM to Hedging post was actually a diversion that ended up being a stand-alone post as I was writing the tiny math section in Part 2.
  3. From there we move into trading and investing strategies to exploit our misunderstanding of extremes. 2 words: respect path. We start with a story of a famous investor/governor who stubbornly didn’t respect path.
  4. We then talk about familiar path-respecting approaches to investing: care with leverage, appreciating “rebalance timing luck” (hugs to@choffstein) and finally thinking about path vs terminal value.
  5. This opens the door to a discussion of trade expressions and the need to map them tightly to our isolated trade premises. I use options to demonstrate 3 path-aware approaches: static, dynamic, combined.
  6. The combined approach is touched on briefly. It’s technical but not complicated and lends itself more to a video (maybe one day). It’s also an example of why it’s useful to understand option structures and the basic arbitrage relationships.
  7. Then we move to general investing styles that respect path: venture and “gorilla” investing. They both know what they don’t know about extreme outcomes and construct strategies that are robust to that reality.I’m not an expert in those approaches but was drawn to their common link of manufacturing convexity. Convexity is not volatility or leverage. It’s the slope of your p/l steepening in the direction of the market because your position size changes.

    When your signals are weak as they are for extreme outcomes, you want to preserve convexity into the unknown. If you can do that, you can funnel wider. This can be higher yielding than tuning your signals harder.

  8. Review and concluding remarks — Happy prospecting!

Money Angle

Speaking of Corey Hoffstein:

His tweet brought my attention to @cobie and his masterful description of psychology.

I also appreciated Josh Brown’s take on the sell-off in so-called growth or momentum names. Here’s an excerpt from Jan 31’s It’s not over yet.

I’m less interested in the real-time action. Focus the evergreen psychology instead:

Where do bounces come from in a midst of a correction?

Sometimes it’s just that stocks have fallen too far for sellers to want to keep selling. This isn’t bullish. In fact, this type of bounce can suck people back in by creating the appearance that the worst is over. Growth stocks in particular. Because belief dies hard and enthusiasm for cutting edge technologies fades slowly, not suddenly. Which mean the give-up process is long and drawn out – even after a stock is cut in half sometimes the worst is still yet to come. The slow bleed after is often worse than the initial shocking drop that preceded it.

Over at Verdad Capital, Dan Rasmussen revisits their “Bubble 500” list of overpriced growth stocks, originally created in the Summer of 2020. It’s filled with money-losing companies working in exciting areas of technology such as electric vehicles and gene editing therapy and so on. Needless to say, this list of bubble stocks has gotten absolutely destroyed year-to-date, after having run straight up in Verdad’s face through the middle of 2021.  Dan explains two very important things in his update this week: The first is that sell-offs for growth stocks differ from sell-offs for value stocks in one very important way:

This breakdown is significant, especially for growth stocks. Remember, growth stocks trend, and value stocks mean revert. The psychology is simple. People hear about a hot stock that’s gone up 3x, they buy some, it goes up 2x, they buy more: the whole attraction of buying a hot growth stock is the historic return trajectory. Value stocks are the opposite: you do well buying them when they’re down…

This idea is counterintuitive – that some stocks actually become worse buys as they are falling to lower prices, but the explanation is psychological, not financial. Stocks trading at excessive valuations require a fan base to sustain their share prices. That fan base is often a bandwagon-jumping melange of traders and investors who are attracted to recent gains. Yes, they’ll latch onto the fundamental story, but the fact that the stock has been and currently is going up is the main thing. When the stock breaks, so too does the fandom. And when the fan base moves on to greener pastures or runs out of money, a new fan base will not form for this stock with its chart in decline. Broken growth stocks become orphans. There is no natural place for them to find a home.

Momentum is a divergent strategy while “value” is a mean-reverting strategy. Several years ago the research team at OSAM published edifying papers on how these approaches work. I wrote a summary here:

✍️ Notes on OSAM’s Factors from Scratch (6 min read)

Value works by fading overreaction. Momentum is attributed to underreaction. In a name trending higher, the sellers are discounting the substance of new information too aggressively. In dork world, we call this anchoring. If you pay attention to “anomalies” you may recognize the concept of post-earnings drift as an acute example of anchoring. Wikipedia even has an entry for it.

Fear or FOMO in markets cuts both ways. On the way down, we fear a loss of wealth. On the way up we fear social embarrassment — we aren’t keeping up with our neighbors. We are caught between self-preservation and shame. I wonder if being part of the herd is any consolation on the way down while everyone loses. Or is this just another miserable psychological asymmetry inseparable from speculation?

Anyway, I don’t have much to add. Investing requires you to be honest about your desires, constraints, and emotional tolerance. If you can get honest with yourself, you can initiate a plan that you can stick to. You want to avoid ad-hoc decisions with the bulk of your savings (I’m not gonna poo poo on gambling with 1 or 2% of your wealth, especially if it suppresses wider risk-seeking behavior. Agustin Lebron’s Laws of Trading has a provocative section about “risk set points” that operate like weight set points. If your life becomes too dull in one way you spice it up in another and vice versa. Maybe Alex Honnold’s portfolio is all in bonds 🤷🏽).

Oh and just a quick observation that you can ponder in the context of those flashy, earningless momentum stocks. If you start at $1 and double 6x you get to $64. If the stock drops 50%, you’ve only erased 1 halving.

Be careful knife catching.


From My Actual Life

I wrote this 1 year ago but I’m reprinting it with updated ages. I flew into NYC on St. Patrick’s day this week, 6 years after this story. I spent yesterday at my nephew’s birthday in NJ.

St. Patrick’s Day now reminds me of a story that is now 6 years old…

March 17, 2016. I flew into NYC for a 36-hour business trip. I was hopping around the city meeting with bank derivative sales desks. Routine relationship maintenance. I planned poorly. I was late to every meeting since you can’t cross 5th Ave during the St Patty’s parade.

Anyway, that evening I was at dinner as a client. When I went to the restroom I checked my phone. My family chat was blowing up.

My sister just had a baby.

I hadn’t told my east coast fam I was in NYC because it was just a quick trip. But right then, I called my mom in NJ and stunned her with the knowledge that I was an hour away in NYC.

When I returned to the table, I excused myself from dinner, hopped on a bus to my childhood house in Hazlet, borrowed my mom’s car and drove down to Jersey Shore Medical Center.

It was close to midnight.

When I walked into the hospital room I’ll never forget my sister’s look of ‘what are you doing here?’

I got to meet my new nephew, spent an hour chatting with my sis and her husband, and made it back to NYC with enough time to grab my bags and get back to JFK.

Since then, St Patrick’s Day has meant much more than day drinking.

Happy 6th birthday to my nephew!

There’s Gold In Them Thar Tails: Part 2

This is Part 2 of a discussion of how sourcing talent or outcomes in the tails or extremes of a distribution call for our selection criteria to embrace more variance than searches in the heart of a distribution. To catch up please read There’s Gold In Them Thar Tails: Part 1.

If you can’t be bothered here’s the gist:

  1. We saw that an explosion of choice whether it’s a job or college applicants, songs to listen to, athletes to recruit has made selection increasingly difficult.
  2. A natural response is to narrow the field by filtering more narrowly. We can do this by making selection criteria stricter or deploying smarter algorithms and recommendation engines.
  3. This leads to increased reliance on legible measurements for filtering.
  4. Goodhart’s law expects that the measures themselves will become the target, increasing the pressure on candidates to optimize for narrow targets that are imperfect proxies or predictors of what the measure was filtering for.
  5. Anytime we filter, we face a trade-off between signal (“My criteria is finding great candidates”) and diversity. This is also known as the bias-variance trade-off.
  6. Diversity is an essential input to progress. Nature’s underlying algorithm of evolution penalizes in-breeding.
  7. In addition to a loss of diversity, signal decays as you get closer to the extremes. This is known as tail divergence. The signal can even flip (ie Berkson’s Paradox).
  8. The point where the signal noise overwhelms the variance in the candidates is an efficient cutoff. Beyond that threshold, selectors should think more creatively than “just raise the bar”.

At the end of part 1, there were strategies for both the selector and the selectees to increase diversity to improve outcomes in the extremes.

If narrower filters are less effective in the tails (ie more noise, weaker correlations between criteria and match quality), we should be intentional about the randomness we introduce to the process. A 1500 SAT is a noisy predictor of “largest alumni donor 20 years from now”. Instead, accept the 1350 SAT from the homeschooled kid in Argentina. Experiment with criteria and let chance retroactively hint at divergent indicators that you would never have thought to test. One of the benefits of such an experiment is that if you are methodical about how you introduce chance you can study the results for a hidden edge. If nobody else has internalized this thinking because they think it’s too risky (it’s not…the signal of the tighter filter had already degraded), then you have an opportunity to leap ahead of your competitors who underestimate the optionality in trying many recipes and keeping the ones that taste good. You tolerate some mayonnaise liver sandwiches before you discover pb&j.

In part 2, we reflect on what tail divergence says about life and investing.


Where Instincts Fail

Tail divergence is the simple observation that attributes that correlate with certain outcomes lose their predictive ability as we get into the extremes. If you are 6’7, you’re better at basketball than most of the population. But you couldn’t step foot on the hardwood with the lowly Rocket’s 12th man. Taken further, Berkson’s Paradox shows that it’s possible for the correlation to flip. LessWrong thinks the flippening may be causal because of too much of a good thing:

Maybe being taller at basketball is good up to a point, but being really tall leads to greater costs in terms of things like agility… Maybe a high IQ is good for earning money, but a stratospherically high IQ has an increased risk of productivity-reducing mental illness. Or something along those lines.

The safest generalization to absorb:

When speculating about the tails of a distribution your intuition is less reliable. 

If you can pinpoint causality, that’s a bonus. Simply realizing your guesses about extremes is random is an advantage. It splits your brain wide open to get your imagination oxygen. 

Behavioral psychology recognizes the usefulness of heuristics to make judgements while highlighting how “biases” such as framing can short-circuit our “System 1” machinery. Intuition is a useful guide when we have deep experience in a domain, but we should seek external data (base rates) or guidance when we stray from the mundane.

If our intellectual adventures take us from “mediocrastian” to “extremistan” then data is not necessarily a helpful tour guide. It can even be harmful if it encourages a false sense of security or a load-bearing assumption that turns out to be hollow 1

A recent example of intuition failing in an extreme scenario still stings. When Covid first started spreading in the US, asset prices and city rents dove lower. Financial markets stabilized and began recovering when the government commit to replacing lost demand with an unprecedented fiscal package for an unprecedented event. My suburban house shot up 15% in value as locked-down city dwellers wanted more space. Seeing the divergence between home price and rentals, I quickly diagnosed the home price bump as a premium needed to absorb a sudden, but transitory urban exodus until we could get a vaccine. While it wasn’t the main consideration for selling the “trade setup” was not lost on me. My intuition in this extreme scenario couldn’t have fathomed that the price would shoot 20% more (and still going, ughh) through where I sold as the lockdowns lifted. My trading intuition degrades less gracefully than I’d like to admit as the orbits get further from financial options. 

Moral Intuition

As technology and science fiction converge, it would be dangerous to lazily extrapolate how we handle routine computer-enabled behavior to edge cases. If you have ever played dark forms of “would you rather?” then you are already familiar with the so-called trolley problem:


credit: abpradio.com

The Conversation explains the so-called trolley problem in the context of self-driving cars:

The car approaches a traffic light, but suddenly the brakes fail and the computer has to make a split-second decision. It can swerve into a nearby pole and kill the passenger, or keep going and kill the pedestrian ahead.

This is spiky terrain. What is the value of a life? This is not a novel dilemma. In Tails Explained, I show how courts use probabilities of accidental (ie rare) deaths to estimate tort damages. What is novel is the scale of these considerations once robots take the wheel. The giant fields of AI safety and ethics are proof that scaling up tort law is not going to cut it. We are forced to explicitly study realms that ancient moralities only needed to consider rhetorically. 

In Spot The Outlier,  Rohit writes:

the systems we’d developed to intuit our way through our lives have difficulty with contrived examples of various trolley problems, but that’s mainly because our intuitions work in the 80% of cases where the world is similar to what we’ve seen before, and if the thought experiment is wildly different (e.g., Nozick’s pleasure machine) our intuitions are no longer a reliable guide.

In The Tails Coming Apart As A Metaphor For Life, Slatestarcodex says:

This is why I feel like figuring out a morality that can survive transhuman scenarios is harder than just finding the Real Moral System That We Actually Use. There’s a potentially impossible conceptual problem here, of figuring out what to do with the fact that any moral rule followed to infinity will diverge from large parts of what we mean by morality.

A wave of exponential automation threatens to capsize our moral rafts. Slatestar invokes one of my favorite paragraphs2 of all-time to make his point. 

When Lovecraft wrote that “we live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far”, I interpret him as talking about the region from Balboa Park to West Oakland on the map above [This is a metaphor for moral territory he builds in the full post].

Go outside of it and your concepts break down and you don’t know what to do.

The full opening paragraph of Call Of Chtulu deserves your eyes:

The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age.

Slatestar edits Lovecraft:

The most merciful thing in the world is how so far we have managed to stay in the area where the human mind can correlate its contents.

This is not an optimistic outlook for our ability to reconcile our based local morality with a species-level perspective. Reasoning about extremes is more futile than we’d like to think. As we  search for outliers, we need humility. 

Even The Math Prescribes Humility

Let’s translate tail divergence to math terms. We discussed how SAT has predictive power of GPA. The issue is that this power loses efficacy as we get to the top-tier of GPAs, just as being tall starts to tell us less about the best basketball players once we are dealing with the sample that has made it to the NBA. 

This loss of signal manifests as a correlation breakdown over some range of the X or explanatory variable. This is the result of the error terms or variance in a regression increasing or decreasing over some range. The fancy word for this is “heteroscedasticity”. 

See this made-up example from 365DataScience:

The variance of the errors visibly changes as we move from small values of X to large values. 

It starts close to the regression line and goes further away. This would imply that, for smaller values of the independent and dependent variables, we would have a better prediction than for bigger values. And as you might have guessed, we really don’t like this uncertainty.

Ordinary least squares (ie OLS) regression is a common technique for computing a correlation. However, equal variance (homoscedasticity) is one of the 5 assumptions embedded in OLS. Tail divergence is evidence that the data set violates this assumption, so we shouldn’t be surprised when the filters we used in the meat of the distributions lose efficacy in the extremes. 

If you broke the regression into 2 separate lines, one for the low to middle range of SAT scores and one for the top decile of SAT scores we could compute different correlations to GPA. If the tails diverge, we would see a lower correlation for the higher range. Correlations even as high as 80% have discouraging amounts of explanatory power. 

For the derivation, see From CAPM To Hedging.

We shouldn’t be surprised when the most successful person from your 8th grade class, wasn’t a candidate for the “most likely to succeed” ribbon. The qualities that informed that vote leave a lot of “risk remaining” when trying to predict the top performers in the wide-open game of life. 

Since the nature of extremes are untamed, we need humility. This is true, but abstract. What does “humility” mean practically? It means making decisions that are robust to the lack of determinism in the tails. In fact, we can construct approaches that actively seek to harness the variance in the tails. 

The world of trading and investing is a perfect sandbox to explore such approaches.

Take Advantage of Poor Tail Intuition In Investing

I know the heading is ironic. 

Let’s see if we can use “option-like” approaches to use the divergence or uncertainty in the tails to our advantage. 

Respect Path

Rohit summarized the argument succinctly:

If measurement is too strict, we lose out on variance. 
If we lose out on variance, we miss out on what actually impacts outcomes.

Tails are unpredictable by the same models that might be well-suited for routine scenarios. In fact, rare outcomes can be stubbornly resistant to description by any models in a complex system. The robust response to this situation is not to lean into our models but to relax the filters in favor of diversity, which increases our chance of capturing an outcome nobody has foreseen, because, by definition, nobody’s model could have predicted (and therefore bid it up) in the first place. 

How do you do that?

2 words: Respect. Path. 

Recall from part 1, that David Epstein’s research-based suggestion:

One practice we’ve often come back to: not forcing selection earlier than necessary. People develop at different speeds, so keep the participation funnel wide, with as many access points as possible, for as long as possible. I think that’s a pretty good principle in general, not just for sports.

What does this mean in a trading context?

This is easy to explain by its opposite. Let’s rewind a decade. Jon Corzine managed to blow up MF Global by focusing on the belief that European bonds (remember the Greek bond crisis?) would pay out in the end and placing that bet with extreme leverage. While the bonds eventually paid out, the margin calls buried MF Global. This is a common story. I chose it because it exemplifies how a lack of humility is the murder weapon. 

The moment you employ leverage, you are worshiping at the altar of path. Corzine refused to make the appropriate sacrifices to the gods. He focused on the terminal value of the bonds. A focus so myopic, Corzine still stubbornly clings to the idea that he was right. [I once went to dinner with an option trader who worked closely with Corzine. He described him as both smart and unfazed in his path-blindness. I’d like to take issue with “smart” but he’s the one giving a fortune away, so I’ll just shut up.] 

He might be rich, but if you were a stakeholder or client in MF Global, he’s a villain. Let’s not be like Jon Corzine. 

Ways To Respect Path

Treat leverage with respect

The most common forms of financial leverage we employ are mortgages. The primary path risk here is needing to re-locate suddenly and potentially needing to sell at a bad time. If there are many potential forks on your horizon, the liquidity in renting can be worth it3.

 

“Rebalance timing luck”

This is a term coined by Corey Hoffstein in his paper The Dumb (Timing) Luck of Smart Beta. First of all, this topic is central to any analysis of performance. You can have 10 different trend-following strategies with the same approximate rules but if they vary in their execution by a single day, the impact of luck can be tyrannical. Imagine one strategy was long oil the day it went negative, another strategy got out of the position one day earlier. Is the difference in performance predictive? It’s a bedeviling issue for allocators trying to parse historical returns. 

If timing is not part of your alpha, then leaving it to chance can swamp the edge you worked so hard to find, capture, and market to investors. This is a recipe for disappointment for either the manager (who gets unlucky) or the investor who chose the fund from a crop of competitors based on noise. 

Respecting path means smoothing the effect of rebalance timing luck. This is commonly done by dividing a single strategy into multiple strategies differing only by their rebalance schedule. The ensemble will average the luck across executions, hopefully adhering the results closer to its intended expression. 

Path vs terminal value thinking

Corzine had a terminal value opinion (“if I hold these bonds to maturity I’ll get paid”). Still, any trade that is marked-to-market must still weather path. Leverage makes the trade acutely fragile with respect to path. Even if his bet was a good one at the time, the expression was negligent because it did not properly reflect his constraints. 

It’s critical that the expression of a bet clings closely to its thesis. If you want to bet on the final outcome of a trade, you need to insulate the expression from path. Similarly, you can bet on path while being indifferent to the final outcome. For example, a momentum investor may devise a rule-based strategy to levitate with an inflating bubble but exit before holding the bag. These participants bet on path not terminal value. The past few years have glorified such a game of hot potato. 

Whether this game of hot potato is really a game of Russian roullete depends on the expression. Many momentum strategies use stops or trailing stops to escape a trade where the trend has petered out or reversed. This expression mimics a long option position. They are creating unbounded upside and limiting their downside. This expression is banking on a dangerous assumption: liquidity. They are constructing a “soft” option presumably because they think it’s cheaper than purchasing a financial or what I call a “hard” or contractual option.

Let’s ignore realized volatility which is a first order determinant of whether the option is cheaper. The biggest problem is gap risk. Soft-option constructions assume continuity. But we know technology breaks, markets close, stocks get halted, countries invade each other, exchanges cancel trades. Pricing gap risk is impossible. That’s why derivative traders say the only hedge for an option is a similar option. Trading strategies are said to be robust to model risk if they contain offsetting exposures to the same model. If you’re short a call option on TSLA the only real hedge  is to be long a different TSLA call. Reliance on the mathematical model cancels out. 

Zooming in on options (feel free to skip and jump down to Investing for Path)

Some market participants focus on terminal value or the “long run” while others are focused on path. The price of options are consensus mechanisms that balance both views. I discussed this in What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold:

The nat gas market is very smart. The options are priced in such a way that the path is highly respected. The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear.

Why? Because it has to balance 2 opposing forces.

        1. It’s not clear how high the price can go in a true squeeze or shortage
        2. The MOST likely scenario is the price collapses back to $3 or $4.
Let me repeat how gnarly this is.
 
The price has an unbounded upside, but it will most likely end up in the $3-$4 range.
 
Try to think of a strategy to trade that.
 
Good luck.
        • Wanna trade verticals? You will find they all point right back to the $3 to $4 range.
        • Upside butterflies which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper) are zeros.
The market places very little probability density at high prices but this is very jarring to people who see the jacked call premiums.
 
That’s not an opportunity. It’s a sucker bet.

Investors with different time horizons often trade with each other. It’s even possible they have the same long-term views but Investor A thinks X is overbought in the near-term and sells to Investor B who just wants to buy-and-hold. Investor A is hoping to buy X back cheaper. They are trying to time the market and generate trading P/L, expecting to find a more attractive entry to X later. Perhaps A is a trader more than an investor. A is obsessively conscious of near-term opportunity costs or hurdle rates. As an options trader, I am generally more focused on path than terminal value. 

Let’s see how trade expression varies with your lens of terminal value vs path. 

Static Expressions

A static trade expression means you put your trade on and leave it alone until some pre-defined catalyst. For options this is typically expiration. The reason you might do this is you are aware that you cannot predict the path but do not want to be shaken out of the position because you like the odds the market is offering on the terminal value of a proposition. To use natural gas, suppose the gas futures surge to $6 amidst a polar vortex but you think there is a 25% chance the price falls to $4.50 by expiration.

Suppose you can buy a vertical spread that pays 4-1 on that proposition. The bet is positive expectancy so you decide to take it. This is a discrete bet. The worst-case scenario is losing your premium. You can size the trade by feel (I’m willing to risk 1% to make 4%) or some version of Kelly sizing. Instead of trading towards a target amount of risk (whether that’s delta, vega, etc) you budget a fixed dollar amount towards it and let it ride. I refer to this type of bet as “risk-budgeting”.

When “risk-budgeting” a trade you specify a fixed bet size and you do not use leverage or pseudo-leverage (for example taking a short option position which demands margin). The point is to set-it-and-forget-it. 

These types of trades were a small minority of my allocations, but they are the easiest to manage. By design, you are not getting cute with the expression, because you expect the path to your possible outcome to be hairy. This is a self-aware strategy for respecting path.

Dynamic Expressions

Most of my trades were actively managed.  Running a large options portfolio means lots of churn as you whack-a-mole opportunities. You find more attractive positions to warehouse than what’s currently on the books, or perhaps you are adding to get to a more full-size position.

The key is most of the focus is on path not terminal value. Sometimes I’m buying vol because I have a view on volatility, but often I’m buying vol if I think there are going to be more vol buyers. The first kind of buying is a hybrid of path and terminal value thinking, but the second type of vol buying has a momentum mindset. My view on realized vol takes a backseat to my view on flows if I think the option demand will exceed supply at current levels of implied volatility. 

Other dynamic trade expressions:

    1. Implied sentiment

      Another path-aware expression is to bet on the expectations embedded in prices. I might load up on oil calls not because I think oil is going to $200, but because I think the awareness that such a price is possible can emerge due to some catalyst (“saber-rattling”). I’m thinking in terms of path not terminal value when my thesis is “sentiment can go from apathy to fear”. I’m betting on a change in the Overton Window. The change in sentiment can increase call option implied vols and even the futures. But the option trade expression is a purer play than the futures.

      [The number of ways an oil future can rise is greater than the number of drivers to push oil call skew higher, so the call options isolate the thesis better by being directly levered to it. Agustin Lebron’s 3rd Law Of Trading: Only take the risks you are paid to take.]

    2. Owning the wing

      Tail options are on average “expensive” in actuarial terms. But there are several reasons why I do not short them. 

      1. “Average” is hiding a lot of detail. The excess premium in those options can be proportionally small to what those options can be worth conditional on stressed states of the world. Buying them when they are relatively cheap to their own elevated premiums can be worthwhile, especially if those options put you in the driver’s seat when the world starts melting down. If you are the only one with bullets in a warzone, there’s a good chance you have them because the terminal-value-Jon-Corzine crowd underestimated path. Then you can sell the options “closing” at truly outlandish prices. I want the tails because I don’t want to be running a trading business with a prime broker’s trapdoor beneath me. 

      2. I’m not smart enough to know when to sell tail options opening. I buy them when they are relatively cheap (which usually still means expensive to Corzine brains) and I sell them closing when they go nuclear. Like when you throw some insane offer out there and it gets taken. As a rule you don’t want to sell wings to someone who spent more than a few moments thinking about it or used a spreadsheet or model or calculator or star chart. You sell them to people who are forced to buy them. When Goldman blows their customer out they don’t haggle. 

        In practice, ratio put spreads look attractive to terminal value people who like to “buy the one and sell the two” because their breakeven is so “far” out-of-the-money and they get to win on medium drawdowns. I often like to sell the 1 and buy the 2 because conditional on the 1×2 “getting there”, the 2 are going to be untouchable. 

        [The buyer of the one in a 1×2 is happiest in the grinding trend scenario where strike vols underperform the skew.]

      3. In The “No Easy Trade” Principle I explain how implied market parameters do not vary as widely as realized parameters because markets are discounting machines4.

        Markets bet on mean reversion. Vols often underreact when they are rising (or falling) as the regime changes. These turns can be great path trades. They are momentum opportunities to lift or hit slower participants who are anchored to the prior regime. These opportunities are very profitable since you are not only putting the bet on the right way, but you are able to get liquidity from stale actors. (The trouble with many opportunities is getting liquidity — if you know something is going up but everyone else does too, your signal is valid but insufficiently differentiated. Turning every measly 5 lot offer into a new bid makes the market more efficient without extracting a reward for it. In fact, if you do that, you don’t understand expectancy or the principle of maximization. Your job isn’t to correct incorrect markets. It’s to make money. The overlap is imperfect.) The challenge is you somehow need to not be anchored yourself 5.

      4. Humility is recognizing that the craziest event has yet to happen. Market shocks are a feature. They look different every time because we prepare for the last war. The instruments that measure our vitals become the targets themselves. Tail options provide volatility convexity, or exposure to “vol of vol”. You don’t need to know the nature of the next shock to know that you will have wanted vol convexity. See Finding Vol Convexity. 

Combining Expressions

I’ll mention this for completeness but it’s a topic I should probably do a video for. It’s not complicated but it’s a bit technical for a post like this. When running an options book, it’s possible to treat some of the positions dynamically and some of them statically. In practice, I “remove” line items that have well-defined risks from of my position at the most recent mark-to-market value so that I do not incorporate their Greeks into my book. I don’t hedge it with the rest of the pile.

For example, if I notice an out-of-the-money put spread on my books, instead of dynamically managing a position that was short a tail, I’d put the spread in another account and sell the corresponding delta hedge associated with it. Going forward it would not generate any Greeks in my main risk view so there’s no need to hedge (remember hedging is a cost). The risk is sequestered to the premium. Let’s say it’s $75,000 worth of put spreads. The expectancy of the spread is presumably zero, so it’s like having a simple over/under bet on the books. If expiration goes my way I get to make a multiple of that, but I know the worst (and most likely) case is losing $75k which given the size of the book is noise. If my capital swamps the risk, there’s no point in hedging it especially since it’s short a tail that’s sensitive to vol of vol.

 

Investing for path

VCs

Venture capital is a strategy that is robust to path. The fact that the portfolio marks are fairy dust helps, but in this context is not important. Why is venture a strategy that exploits divergence in the tails?

Because from its construction, it admits it doesn’t know much. If you believe you are sampling from start-ups that have a power-law distribution (admittedly a big “if”), then the correct strategy is indeed to “spray and pray”6.

Byrne Hobart piggybacks Jerry Neumann in his explanation:

One of my favorite blog posts on venture returns is Jerry Neumann’s power laws in venture. His key point is that if venture returns follow a power-law distribution, average returns rise indefinitely as you get a bigger sample set. There is no well-defined mean! If you measure adult height, you quickly converge on 5’9” for American men and 5’4” for American women. You will find outliers, but they’re equally common at both ends of the distribution. But if you measure startup investing returns, you’ll keep getting tripped up: flop, failure, failure, flop, Google, fad, fraud, freaky scandal, Facebook…

Does this imply that the ideal strategy for venture is to invest in as many companies as possible? If you’re sampling from a power-law distribution, that’s what you should do. 

Lux Capital partner Josh Wolfe’s approach epitomizes the spirit of searching for gold in the tails. On Invest Like The Best, he explained his investing beliefs:

  • Confident that curiosity, following leads, and relentlessness will lead you to the next idea.
  • Confident you won’t know when or how you happen upon the idea.
  • Confident that the idea lies in the edges of companies that are doing innovative things, often from first principles or science, and very few people are looking there.

These principles propagate from a commitment to benefitting from optionality and positive convexity of non-linear relationships. 

The key line follows:

When analyzing how they found deals it only made linear, narrative sense after the fact.

This is reinforced in On Contrarianism, where I quote Wolfe as well as Marc Andreesen and trader Agustin Lebron on why the best investments start out controversial. The gist is that an idea must be so radical and far-fetched that it doesn’t get bid up while also being possible. The intersection of great ideas after-the-fact that sound dumb before-the-fact is nearly invisible. Most ideas people think are dumb, are indeed, dumb. Venture understands this and systematically wraps a sound process around a low hit rate. 

“Gorilla” Investing

Gorilla investing is another strategy designed to look like a long option. The gist of it is to invest an equal amount in a list of candidates that are competing for a giant market. As the winners start pulling away, you shed the losers and reallocate the proceeds back into the winners. 

Since it rebalances away from losers into winners, it explicitly bets against mean reversion. It’s a divergent strategy that growth investors employ in winner-take-all sectors7.

The strategy requires extensive judgment, but I highlight it as another example of an investing algorithm with roots in epistemic humility. If you want to learn more about this strategy see the notes for Gorilla Game or pick up the book. 

Conclusion

Like venture or Rohit’s advice on recruiting, gorilla investing casts a wide net from a sufficiently narrowed field and lets attrition decide where to allocate more. In Where Does Convexity Come From? I explain that that the essence of convexity is a non-linear p/l resulting from a change in your position size in the same direction as the return of your position. Your exposure to a winning trade grows the more it wins. 

Byrne writes:

Since venture success is defined by dealflow, i.e. by whether or not you have a chance to invest in the hottest companies, the main function of the Series A investment is to get a chance to invest in Series B and Series C and so on. Arguably, the better the fund, the more of its real value today consists of pro-rata rights rather than the investments themselves.

That’s a general case of positive convexity: the better the situation, the higher your exposure.

This is the essence of capturing the upside when our signals struggle to parse winners from an exclusive field. If we cannot predict what will happen in the tails, the next best thing is the ability to increase our exposure to momentum when it’s going our way. This begins with humility and funneling wider than our instincts suggest. From that point, we let actual performance provide us with incremental information on what works and what doesn’t.

Contrast this with a model that takes itself more seriously than tail correlations warrant. The model is filtering prematurely. We don’t look for tomorrow’s star athletes amongst the best 8-year-olds because we know puberty is a reshuffling machine.  

Keep in mind:

  • Correlations break down or invert in the extreme
  • Make your selections robust to path or possibly taking advantage of it. 
  • Systematize finding gold in diversity. There’s a decent chance others won’t be looking there. 

Happy prospecting!