Practice Second Gear Thinking

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

But markets price in common information.

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

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

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

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

“Theory of Mind”

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

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

Second order sensitivities

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

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

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

An exercise in thinking about second-order sensitivities

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

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

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

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

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

What does this depend on?

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

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

But delta of his business to RE prices decomposes further:

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

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

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

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

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

To ponder:

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

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

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

What does a logistics or S-curve function signify?

What phenomena follow a convex function? A concave function?

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


Sell Your Textbooks For Boardgames

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

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

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

These excerpts will save you a click.

What

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

Main findings

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

Murky interpretations

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

Practical upshot (emphasis mine)

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

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

Parenting Is Personal

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

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

Tim quotes from Russ’ eulogy to his father:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Moontower #178

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

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

Tim quotes from Russ’ eulogy to his father:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


Money Angle

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

But markets price in common information.

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

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

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

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

“Theory of Mind”

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

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

Second order sensitivities

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

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

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

An exercise in thinking about second-order sensitivities

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

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

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

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

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

What does this depend on?

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

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

But delta of his business to RE prices decomposes further:

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

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

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

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

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

To ponder:

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

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

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

What does a logistics or S-curve function signify?

What phenomena follow a convex function? A concave function?

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

Money Angle For Masochists

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

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

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

These excerpts will save you a click.

What

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

Main findings

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

Murky interpretations

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

Practical upshot (emphasis mine)

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

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


For an outro enjoy:

Spread’em Tight by

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

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

Stay groovy!

Survey Results: A Little Bit About You

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

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

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

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

Demographics

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

Politics and Education

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

Industry

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

Title

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

Income

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

Investing/Giving

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

Open Ended Questions

Some preamble:

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Amusing Bits

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

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

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

Moontower #177

Friends,

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

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

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

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

Demographics

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

Politics and Education

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

Industry

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

Title

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

Income

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

Investing/Giving

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

 

Open Ended Questions

Some preamble:

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

     

Amusing Bits

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

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

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


Money Angle

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

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

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

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

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

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

Money Angle For Masochists

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

Twitter avatar for @jaym217

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

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

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

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

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

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

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

A Socratic Dissection Of An Option Trade


Last Call

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

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

Moontower Munchies (Wednesdays)

This is a lightweight email.

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

Or

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

 

Happy Lunar New Year rabbits…stay groovy!

The Dizziness of Freedom

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

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

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

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

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

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

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

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

Moontower #176

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

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

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

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

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

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

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

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

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

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


Money Angle

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

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

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

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

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

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

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

    It’s Time to Work (5 min read)

     

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

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

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


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

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

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

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

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

Let’s go.


Money Angle For Masochists

Understanding Implied Forwards (14 min read)
Moontower

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

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

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

A few excerpts in that vein:

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


    The post includes a discussion of my own process.

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

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

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

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


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


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

 


Last Call

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

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

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

Here are my notes from their interview with Peter Bregman:

You are not defined by your earlier choices

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

Behavior change —> Bias to action

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

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

Decision-Making

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

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

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

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

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

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

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

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

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

Here they are with my commentary:

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

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

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

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

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

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

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

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

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

Stay groovy!

Understanding Implied Forwards

These are not trick questions:

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

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

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

If you are comfortable with the math you have the prerequisites required to learn about a useful finance topic — implied forwards!

Implied forwards can help you:

  • find trading opportunities
  • understand arbitrage and its limits

We’ll start in the world of interest rates.

The Murkiness Of Comparing Rates Of Different Maturities

Consider 2 zero-coupon bonds. One that matures in 11 months and one that matures in 12 months. They both mature to $100.

Scenario A: The 11-month bond is trading for $92 and the 12-month bond is trading for $90.

What are the annualized yields of these bonds if we assume continuous compounding?1
Computing the 12-month yield

r = ln($100/$90) = 10.54%
Computing the 11-month yield

r = ln($100/$92) * 12/11 = 9.10%

This is an ascending yield curve. You are compensated with a higher interest rate for tying up your money for a longer period of time.

But it is very steep.

You are picking up 140 extra basis points of interest for just one extra month.

Let’s do another example.

Scenario B: We’ll keep the 12-month bond at $90 but say the 11-month bond is trading for only $91.
Computing the 11-month yield

r = ln($100/$91) * 12/11 = 10.29%

So now the 11-month bond yields 10.29% and the 12-month bond yields 10.54%

You still get paid more for taking extra time risk but maybe it looks more reasonable. It’s kind of hard to reason about 25 bps for an extra month. It’s murky.

Think back to the test score question this post opened with. There is another way of looking at this if we use a familiar concept — the weighted average.

The Implied Forward Interest Rate

We can think of the 12-month rate as the average rate over all the intervals. Just like a final grade is an average of the individual tests.

We can decompose the 12-month rate into the average of an 11-month rate plus a month-11 to month-12 forward rate:

“12-month” rate = “11-month” rate + “11 to 12-month” forward rate

Let’s return to scenario A:

12-month rate = 10.54%

11-month rate = 9.1%
Compute the “11 to 12-month” forward rate like a weighted average:

10.54% x 12 = 9.1% x 11 + Forward Rate11-12 x 1

Forward Rate11-12 = 26.37%

We knew that 140 bps was a steep premium for one month but when you explicitly compute the forward you realize just how obnoxious it really is.
How about scenario B:

12-month rate = 10.54%

11-month rate = 10.29%
Compute the “11 to 12-month” forward rate like a weighted average:

10.54% x 12 = 10.29% x 11 + Forward Rate11-12 x 1

Forward Rate11-12 = 13.26%

Arbitraging The Forward Rate (Sort Of)

It’s common to have a dashboard that shows term structures. But the slopes between months can be optically underwhelming with such a view. Seeing that the implied forward rate is 13.26% feels more profound than seeing a 25 bps difference between month 11 and month 12.

You may be thinking, “this forward rate is a cute spreadsheet trick, but it’s not a rate that exists in the market.”

Let’s take a walk through a trade and see if we can find this rate in the wild.

The first step is just to ground ourselves in a basic example before we understand what it means to capture some insane forward rate.

Consider a flat-term structure:

[Note: the forward rate should be 10.54% but because I’m computing YTM on a bond price that only goes to 2 decimal places we are getting an artifact. It’s immaterial for these demonstrations]

Now let’s look back at the steep term structure from scenario A:

With an 11-month rate of 9.10% and a 12-month rate of 10.54% we want to borrow at the shorter-term rate and lend at the longer-term rate. That means selling the nearer bond and buying the longer bond.

When you study asset pricing, one of the early lessons is to step through the cash flows. This is the basis of arbitrage pricing theory (APT), a way of thinking about asset values according to their arbitrage or boundary conditions. As opposed to other pricing models, for example CAPM, someone using APT says the price of an asset is X because if it weren’t there would be free money in the world. By walking through the cash flows, they would then show you the free money2. The fair APT price is the one for which there is no free money.

Stepping Thru The Cash Flows

Let’s see how this works:
Today

  1. We short the 11-month bond at $92
  2. We buy 1.022 12-month bonds for $90. We can buy 1.022 of the cheaper bonds from the proceeds of selling the more expensive $92 bond. The net cash flow or outlay is $0.
  3. Spend the next 11 months surfing.

At the 11-month maturity

We will need $100 to pay the bondholder of the 11-month bond so we sell 12-month bonds.

But for what price?

Well, let’s say the prevailing 1-month interest rate matched the rates we were seeing in the flat term structure world of 10.49%, the rate implied by the 11-12 month forward when we initiated the trade.

In that case, the bonds we own are worth $99.13.

[With one month to maturity we compute the continuous YTM: ln(100/99.13) * 12 = 10.49%]

If we sell 1.009 of our bonds at $99.13 we can raise the $100 to pay back the loan. We are left with .0134 bonds.
At the 12-month maturity

Our stub of .0134 bonds mature and we are left with $1.34.

So what was our net return?

Hmm, lemme think, carry the one, uh — infinite!

We did a zero cash flow trade at the beginning. We didn’t lay out any money and ended with $1.34.

That’s what happens when you effectively shorted a 26.37% forward rate but the one-month rate has rolled down to something normal, in this case about 10.50%

[In real life there is all kind of frictions — you know like, collateral when you short bonds.]

Summary table:

What if somehow, that crazy 26.37% “11-12 month forward rate” didn’t roll down to a reasonable spot rate but actually turned out to be a perfect prediction of what the 1-month rate would be in 11 months?

Let’s skip straight to the summary table.

Note the big difference in this scenario: the bond with 1 month remaining until maturity is only worth $97.83 (corresponding to that 26.33% yield, ignore small rounding). So you need to sell all 1.022 of the bonds to raise $100 to pay back the loan.

Besides frictions, you can see why this is definitely not an arbitrage — if the 1-month rate spiked even higher than 26.33% the price of the bonds would be lower than $97.83. You would have sold all 1.022 of your bonds and still not been able to repay the $100 you owe!

So the “borrow short, lend long” trade is effectively a way to short a 1-month forward at 26.33%. It might be a good trade but it’s not free money.

Still, this exercise shows how our measure of the forward is a tradeable level!

[If you went through the much more arduous task of adjusting for all the real-world frictions and costs you would impute a forward rate that better matched what you considered to be a “tradeable price”. The principle is the same, the details will vary. I was not a fixed-income trader and own all the errors readers discover.]

The Implied Forward Implied Volatility

Now you’re warmed up.

Like interest rates, implied volatilities have a term structure. Every pair of expiries has an implied forward volatility. The principle is the same. The math is almost the same.

With interest rates we were able to do the weighted average calculation by multiplying the rates by the number of days or fraction of the year. That’s because there is a linear relationship between time and rates. If you have an un-annualized 6-month rate, you simply double it to find the annualized rate. You can’t do that with volatility.3

The solution is simple. Just square all the implied volatility inputs so they are variances. Variance is proportional to time so you can safely multiply variance by the number of days. Take the square root of your forward variance to turn it back into a forward volatility.

Consider the following hypothetical at-the-money volatilities for BTC:

Expiry1 Expiry 2
Implied Vol 40% 42%
Variance (Vol2) .16 .1764
Time to Expiry (in days) 20 30

Let’s compute the 20-to-30 day implied forward volatility. We follow the same pattern as the weighted test averages and weighted interest rate examples.

The decomposition where DTE = “days to expiry”:

“variance for 30 days” = “variance for 20 days” + “variance from day 20 to 30”

Expiry2 variance * DTEExpiry2 = Expiry1 variance * DTEexpiry1 + Forward variance20-30 * Days20-30

Re-arrange for forward variance:

Fwd Variance20-30 = (Expiry2 variance * DTEExpiry2 – Expiry1 variance * DTEexpiry1) / Days20-30

Fwd Variance20-30 = (.1764 * 30 – .16 * 20) / 10

Fwd Variance20-30 = .2092

Turning variance back into volatility:

√.2092 = 45.7%

If the 20-day option implies 40% vol and the 30-day option implies 42% vol, then it makes sense that the vol between 20 and 30 days must be higher than 42%. The 30-day volatility includes 42% vol for 20 days, so the time contained in the 30-day option that DOES NOT overlap with the 20-day option must be high enough to pull the entire 30-day vol up.

This works in reverse as well. If the 30-day implied volatility were lower than the 20-day vol, then the 20-30 day forward vol would need to be lower than the 30-day volatility.

The Arbitrage Lower Bound of a Calendar Spread

The fact that the second expiry includes the first expiry creates an arbitrage condition (at least in equities). An American-style time spread cannot be worth less than 0. In other words, a 50 strike call with 30 days to expiry cannot be worth less than a 50 strike call with 20 days to expiry.

Here’s a little experiment (use ATM options, it will not work if the options are far OTM and therefore have no vega):

Pull up an options calculator where you make a time spread worth 0.

I punched in a 9-day ATM call at 39.6% vol and a 16-day ATM call at 29.70001% vol. These options are worth the same (for the $50 strike ATM they are both worth $1.24).

Now compute the implied forward vol.

Expiry1 Expiry 2
Implied Vol 39.6% 29.70001%
Variance (Vol2) .157 .088
Time to Expiry (in days) 9 16

You can predict what happens when we weight the variance by days:

Expiry1 = .157 * 9 = 1.411

Expiry2 = .088 * 16 = 1.411

Expiry 2 has the same total variance as Expiry 1 which means there is zero implied variance between day 9 and day 16.

The square root of zero is zero. That’s an implied forward volatility of zero!

A possible interpretation of zero implied forward vol:

The market expects a cash takeover of this stock to close no later than day 9 with 100% probability.

A Simple Tool To Build

With a list of expirations and corresponding ATM volatility, you can construct your own forward implied volatility matrix:

Arbitrage?

Like the interest rate forward example, there’s no arbitrage in trying to isolate the forward volatility unless you can buy a time spread for zero.4

For most of the past decade, implied volatility term structures have been ascending (or “contango” for readers who once donned a NYMEX or CBOT badge). If you sell a fat-looking time spread you have a couple major “gotchas” to contend with:

  1. Weighting the trade
    If you are short a 1-to-1 time spread you are short both vega, long gamma, paying theta. This is not inherently good or bad. But you need a framework for choosing which risks you want and at what price (that statement is basically the bumper sticker definition of trading imbued simultaneously with truth and banality). If you want to bet on the time spread narrowing, ie the forward vol declining, then you need to ratio the trades. The end of Moontower On Gamma discusses that. Even then, you still have problems with path-dependence because the gamma profile of the spread will change as soon as the underlying moves. The reason people trade variance swaps is that the gamma profile of the structure is constant over a wide range of strikes providing even exposure to the realized volatility. Sure you could implement a time spread with variance swaps, but you get into idiosyncratic issues such as bilateral credit risk and greater slippage.
  2. The bet, like the interest rate bet, comes down to what the longer-dated instrument does outright.You were trying to isolate the forward vol, but as time passes your net vega grows until eventually the front month expires and you are left with a naked vol position in the longer-dated expiry and your gamma flips from highly positive to negative (assuming the strikes were still near the money).

Term structure bets are usually not described as bets on forward volatility bets but more in the context of harvesting a term premium as time passes and implied vols “roll down the term structure”. This is a totally reasonable way to think of it, but using an implied forward vol matrix is another way to measure term premiums.

The Wider Lessons

Process

Forwards vols represent another way to study term structures. Since term structures can shift, slope, and twist you can make bets on the specific movements using outright vega, time spreads, and time butterflies respectively. A tool to measure forward vols is a thermometer in a doctor’s bag. How do we conceptually situate such tools in the greater context of diagnosis and treatment?

Here’s my personal approach. Recognize that there are many ways to skin a cat, this is my own.

  1. I use dashboards with cross-sectional analysis as the top of an “opportunity funnel”. You could use highly liquid instruments to calibrate to a fair pricing of parameters (skew, IV risk premium, term premium, wing pricing, etc) in the world at any one point in time. This is not trivial and why I emphasize that trading is more about measurement than prediction. To compare parameters you need to normalize across asset types.
    To demonstrate just how challenging this is, an interview question I might ask is:

    Price a 12-month option on an ETF that holds a rolling front-month contract on the price of WTI crude oil5

    I wouldn’t need the answer to be bullseye accurate. I’m looking for the person’s understanding of arbitrage-pricing theory which is fundamental to being able to normalize comparisons between financial instruments. The answer to the question requires a practical understanding of replicating portfolios, walking through the time steps of a trade, and computing implied forward vols on assets with multiple underlyers. (Beyond pricing, actually trading such a derivative requires understanding the differences in flows between SEC and CFTC-governed markets and who the bridges between them are.)

  2. The contracts or asset classes that “stick out” become a list of candidates for research. There are 2 broad steps for this research.
    • Do these “mispriced” parameters reveal an opportunity or just a shortcoming in your normalization?
      Sleuthing the answer to that may be as simple as reading something publically available or could require talking to brokers or exchanges to see if there’s something you are missing. If you are satisfied to a degree of certainty commensurate with the edge in the opportunity that you are not missing anything crucial, then you can move to the next stage of investigation.
    • Understanding the flow
      What flow is causing the mispricing? What’s the motivation for the flow? Is it early enough to bet with it? Is it late enough to bet against it? You don’t want to trade the first piece of a large order but you will not get to trade the last piece either (that piece will be either be fed to the people who got hurt trading with the flow too early as a favor from the broker who ran them over — trading is a tit-for-tat iterated game, or internalized by the bank who controls the flow and knows the end is near.)

3. Execute

Suppose you determine that the term structure is too cheap compared to a “fair term structure” as triangulated by an ensemble of cross-sectional measurements. Perhaps, there is a large oil refiner selling gasoline calls to hedge their inventory (like covered calls in the energy world). You can use the forward vol matrix to drill down to the expiry you want to buy. “Ah, the 9-month contract looks like the best value according to the matrix. Let’s pull up a montage and see if it’s really there. Let’s see what the open interest is?…”

As you examine quotes from the screens or brokers, you may discover that the tool is just picking up a stale bid/ask or wide market, and that the cheapest term isn’t really liquid or tradeable. This isn’t a problem with the tool, it’s just a routine data screening pitfall. The point is that tools of this nature can help you optimize your trade expression in the later stage of the funnel.

Meta-understanding

This discussion of forward vols was like month 1 learning at SIG. It’s foundational. It’s also table stakes. Every pro understands it. I’m not giving away trade secrets. I am not some EMH maxi6 but I’ll say I’ve been more impressed than not at how often I’ll explore some opportunity and be discouraged to know that the market has already figured it out. The thing that looks mispriced often just has features that are overlooked by my model. This doesn’t become apparent until you dig further, or until you put on a trade only to get bloodied by something you didn’t account for as a particular path unfolds.

This may sound so negative that you may wonder why I even bother writing about this on the internet. Most people are so far out of their depth, is this even useful? My answer is a confident “yes” if you can learn the right lesson from it:

There is no silver bullet. Successful trading is the sum of doing many small things correctly including reasoning. Understanding arbitrage-pricing principles is a prerequisite for establishing what is baked into any price. Only from that vantage point can one then reason about why something might be priced in a way that doesn’t make sense and whether that’s an opportunity or a trap7. By slowly transforming your mind to one that compares any trade idea with its arbitrage-free boundary conditions or replicating portfolio/strategy, you develop an evergreen lens to ever-changing markets.

You may only gain or handle one small insight from these posts. But don’t be discouraged. Understanding is like antivenom. It takes a lot of cost and effort to produce a small amount8. If you enjoy this process despite its difficulty then it’s a craft you can pursue for intellectual rewards and profit.

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


Examples Of Comparing Interest Rates With Different Compounding Intervals

Simple Interest

If you pay someone $90 today and they promise to give you $100 in 12 months, you are making a loan. This is the same idea as buying a bond. To back out the simple interest rate denoted (ie assuming no compounding) we solve for r:

90 * (1+r) = 100

r = 100/90 – 1

r = 11.11%

Annualizing

If the loan was only for 6 months, then we’d annualize the interest rate by multiplying by 2 (12 months / 6 months) for a rate of 22.22%

Compound Interest

Let’s return to the 12-month loan and say that the rate is compounded semi-annually. Then the computation is:

90 * (1+r/2)² = 100

r /2 = (100/90).5 – 1

r = 10.82%

If you compound more frequently than annually, it makes sense that the implied interest rate is lower. Consider the path of the principal + accrued interest:

Compounding semi-annually means interest gets credited at the 6-month mark. So the rate for the next 6 months is being applied to the higher accrued value amount which means the implied rate to end up at $100 (the same way the simple interest case ends up $100) must be lower than the simple interest case.

Continuous Interest

We can compound interest more frequently. Quarterly, monthly, daily. Since the number we are backing out, namely the implied rate, is being applied to a growing basket of principal + accrued interest at each checkpoint (I think of the compounding interval as a checkpoint where the accrued interest is rolled into the remaining loan balance), the implied rate to end up at $100 must be smaller. If we take this logic to the extreme and keep cutting the time interval into smaller increments we eventually hit the limit of Δt → 0. The derivatives world models everything in continuous time finance so interest rates get the same treatment.

Mechanically, the math is no harder.

To compute the continuously compounded interest rate we still just solve for r:

90 * ert = 100

t is a fraction of a year. So for the 12-month case:

90 * er*1 = 100

er = 100/90

r ln(e) = ln(100/90)

r = 10.54%

As expected, this is a lower implied rate than the 11.11% simple rate and the 10.82% semi-annual rate. Again, because we are compounding continuously.

Annualizing remains easy. If $90 grows to $100 in just 6 months, we compute the continuously compounded rate as follow:

90 * er*1/2 = 100

er*1/2 = 100/90

r *1/2 = ln(100/90)

r = 21.07%

This can be contrasted with the 22.22% 6-month loan using simple interest we computed earlier.

Application To Real Life

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

APYs disclosed on financial products make yields comparable. But now you understand how APYs convert different rate schedules into a single measure.

Interview with Bill Burnett & Dave Evans on Designing Your Life

From the Peter Bregman podcast:

Are you living your best life? You can’t think your way to the future – you have to design your way. I’m joined today by Bill Burnett and Dave Evans, authors of Designing Your Life: How to Build a Well-Lived, Joyful Life. Discover the five mindsets, how to make decisions in the face of uncertainty, and what to do if you have a “gravity problem.”

YouTube link

This was a ton of great insight packed into 30 minutes. The following are my notes of what I want to retain not a summary. This was dense, you should watch it yourself.


You are not defined by your earlier choices

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

Behavior change —> Bias to action

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

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

Decision-Making

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

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

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

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

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

For example, you say: ”I’d like to do it I’d like to be a gardener or do something in the garden but I’ve decided the only solution is moving to the Berkshires. Since we can’t move to the Berkshires, I can’t have a garden, therefore I can’t be happy”

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

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

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

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

Here they are with my commentary:

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

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

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

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

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

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

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

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