My Investing Shame Is Your Gain

For this 150th issue Moontower, I have a confession.

I write this Money Angle section each week but as recently as 6 years ago, I didn’t really care about or understand investing. The delay in learning has cost returns and even shame. I might as well get the most out of that expensive tuition by sharing the story so others can learn from my mistakes.

When I graduated in 2000, the options and still-new ETF trading businesses were a party. The internet bubble led to high volumes and volatility. The volumes were a step-function higher than anything seen before. I’d estimate prop shops made 4-5x the profits they typically expected.

Before the dot-com days, options trading was a cottage industry where a typical trader could earn a low six-figure pay working relatively short hours without having to ingratiate their personalities to either clients or corporate overlords. A roaring stock market and the emergence of electronic trading transformed the landscape. The existing prop shops and sole proprietors had expertise and so-called time-place advantage on the exchange floors. The competition from banks hadn’t arrived because like I said, it used to be a niche industry. Banks were not internalizing flow just yet. In fact, to play catch-up Goldman paid a shocking sum of $6.5B for Spear, Leeds, and Kellogg after acquiring Hull months earlier.

The upshot. Prop shops were hiring like crazy. I snuck into SIG’s largest ever cohort. I started working in August 2000. I was a trader with my own book by October 2001. (Story time: I finished SIG’s class at the end of summer 2001. I took a 1-week vacation visiting my friends in Cupertino before heading back to NY to my assigned pit on the AMEX. During that trip to CA, my mother called waking me up after a 5am bender. 2 planes had crashed into the World Trade Center. She was in Midtown and called because she “just wanted to hear my voice”. I dismissed her as crazy and went back to sleep. Later that morning, when I turned on the news, it was the worst I ever felt in my life. Only to be topped a few minutes later when I tried to call her and couldn’t get through because the phones were overloaded. When I got back to NY the exchanges were still closed and I wouldn’t start trading for a few weeks).

I was 23-years-old, had my own trading account, and making $100k including bonus. It was more money than anyone in my family made. In the next year, I would pay off my student loans but what would I do with my savings next? Growing up, my parents didn’t have extra money to invest. I didn’t learn about compounding and what 100 bps means in the long run.

There was also a perverse combination of influences that kept investing in markets off my radar. First, the bursting of the internet bubble made me feel thankful for not investing in stocks. Second, as a trader we were trained to have no opinions. I thought of option customers as deluded gamblers. Suckers and tourists unless they had inside info. As market-makers, we were always worried about toxic flows. Toxic flow is informed flow. It’s either flow frontrunning a larger incoming flow or straight-up insider trading (I clerked at the post were options on XAL traded. That’s the AMEX Airline Index. Put option action before 9/11 was investigated with attempts to trace profits back to Al Queda. No smoking guns were found). In my model of markets, you either cheated to make money or you were the casino. Otherwise you were just gambling. Pretty dark.

I was starting to accumulate savings with my debts paid off. SIG had 401k matching so it seemed like a no-brainer to put money there. I think I just used a target-date fund. It was a snap decision. Retirement felt really far away so money trapped in a 401k felt fake to me. Later, when I was self-employed I would contribute $50k/year to a SEP IRA and just jam it into stocks. Again, fake money since half of it would have been taxed if I didn’t contribute.

But what would I do with liquid savings if I wasn’t going to invest beyond a 401k? The default was to buy a place to live so I wasn’t “throwing money away on rent” (that’s the wrong framing of rent; learning is unlearning). With this goal in mind, I was focused on saving about $75k for a down payment on an apartment. As a near-term goal it was money I couldn’t afford to lose, so investing didn’t make sense anyway.

In 2005, I bought a coop studio in midtown on 57th between Lexington and 3rd Ave. It was a 450 sq ft fixer that I renovated. (Random: the apartment was above a memorabilia store that had a Guns N’ Roses VMA award presumably from the night Duff and Slash, stumbling drunk, accepted the moon man while slurring their words and cursing on live TV. They were asking $5,000 for it. The most burning missed trade in my career.) Between the apartment and renovations, my savings were now depleted to a healthy reserve. No reason to invest.

2 years later, I score a low seven-figure bonus. So what do I do? I buy a condo in LIC off of plans. Paid the developer’s costs and everything. It was 2007 in NYC. That’s how it was. Toppy.

By the time the place is built and I move in, the GFC is in full swing. I never had great timing. (Not even as a vol trader…that’s why it’s critical to manage risk and size well. Timing is impossible to nail consistently but it’s not as important. Harley Bassman likes to say “sizing is more important than entry level”. Co-sign.)

I was in the midst of taking 6 months off after leaving SIG to start my own trading business with a backer. I’m shopping for an engagement ring, expect to have big wedding expenses in the next year, and embarking on a new venture where I’d have to post cash in escrow with the backer. Plus I’m watching the financial world implode. With all these demands and an apartment that is immediately underwater from its basis, there was no way was I going to stick money in the market.

So here I am, I just turned 30, a trader for 7 years, and I still don’t know a thing about investing.

I won’t drag out the next decade in detail, but I remained apathetic about investing. When we moved to SF in 2012, we started looking for homes. Another imminent purchase, so no point in investing, right? Since I don’t understand investing I figure I’ll just buy a house in cash and at least lock in the after-tax mortgage rate as a return. I know, I know. (Look, writing this is part of the healing.)

We can zoom ahead until about age 36. We just bought our family house in the ‘burbs and have a 1-year-old. This focuses you on the future. While my wife and I enjoy substantial W2 incomes, high taxes and relaxed spending habits make something abundantly clear — the strategy of just outrunning will eventually tire. I’m sitting there without equity in anything except a house.

That’s when I turned to the internet. I started lurking on Twitter. Listening to podcasts. I approached investing with a beginner’s mind. I realized that my trading background actually harmed me but it was because of how I generalized its lessons. It was my own failure. [See: How I Misapplied My Trader Mindset To Investing]

I became swept up in a process of unlearning and reconciling. What about trading applies to investing? The answers are still unfolding for me. When I started this newsletter I was mostly sharing links and concepts I found interesting. Somewhere along the line, I began translating from one domain to the other. The feedback told me that people outside trading could learn from the niche I spent my whole career in if I could peel off the skin to get to the fruit.

The quest to get better at investing goes hand in hand with learning and teaching. Some of the cornerstones from which I approach investing education:

  • Markets, from the perspective of most people, are “efficiently inefficient”. Efficiency is highly seat-dependent. Sitting in the cockpit at my last job, I could see inefficiency. I have no such visibility from my living room. My experience in trading has paradoxically contributed to this view — I’ve spent a lot of time in awe of how something that I thought was clever was actually priced in before I got there. That’s a hint that the relative efficiency of markets is not a paradox.
  • I can appreciate others being incurious about investing (I still consider it a chore…I find finance conceptually fascinating but investing is about a lot more than concepts). So I’m sensitive to people’s preference for simple. Investing is a wicked domain with tremendous luck. One of my favorite statistics comes from my buddy Nick Maggiulli. The dates are cherry-picked but somebody lived them:if you had invested from 1960-1980 and beaten the market by 5% each year, you would have made less money than if you had invested from 1980-2000 and underperformed the market by 5% a year.

    The returns to effort dimish extremely quickly. Charley Ellis describes investing as “a loser’s game” like amateur tennis. You win by not losing. Not making giant errors. Not carrying 18% credit card debt. Not concentrating your wealth in the latest shiny rock.
  • Not everyone grows up knowing about compounding. There’s a lot of financial literacy stuff for kids or teens out there. Much of it is impractical unless the youth is specifically interested in investing. Yet the idea of compounding, not just financially, but in relationships, knowledge, and skills is critical. Finding ways to deliver this message so that it sticks is a worthy challenge.
  • Separate what matters from what doesn’t matter. Investing is a playground for decision-making. You can be doubly helpful if you can help map investing rationale to general thinking. A hunch — the best lessons from investing and portfolio theory are more useful outside investing.

My last confession for today. I didn’t really understand where equity returns came from for most of my adult life. I thought that over time “stocks just go up” without any sense of why. That’s just willful ignorance at some point. I wanna believe I knew where returns came from if you pressed me but I’m not sure. Either way, I’m sympathetic to others who don’t get where returns come from.

A non-zero percentage of people who invest in RE fall in this camp. There’s something about them not being able to see the cashflow that makes them think stocks are fairy dust and not businesses. The whole dividend darling marketing spiel is aimed straight at them even though dividends are tax-inefficient.

[The decision to pay dividends or not has nothing to do with whether a company is a good business. It’s a capital allocation decision. Jake uses a simple picture to show they are mathematically equivalent to buybacks. Stock prices fall by the amount of the dividend. If you have ever exercised a call option early you know this. In fact, when you see the “change in price” column in a data vendor after a distribution, that change is net of the dividend. So if a $50 stock pays a $1 dividend and the next day is trading for $49, the vendor will say the stock is “unchanged”.

Dividends, just like the buybacks, reduce the amount of cash on a company’s balance sheet. In the case of the dividend, the price of the stock falls reducing the company’s market cap by the amount of cash they spent. In the buyback scenario, the price of the stock remains unchanged but the shares outstanding falls. Again, the market cap falls by the amount of cash the company spent.]

It’s totally understandable to have mistaken beliefs about where stock returns come from. All of the charts we look at are price charts. How many charts do you see of earnings or FCF in mainstream financial outlets? It’s not nefarious but it makes you wonder. How can financial content be displayed so that it improves our understanding? How can investing education be incorporated effectively into pre-teen and teen education?

I’m a trader and a lot of investing basics managed to avoid me. It’s understandable. People’s asset allocations are not openly discussed. There’s so much financial information online but it’s hard to know what’s trustworthy especially when you are a beginner. There’s no brand that comes to mind as the obvious choice for financial literacy.

As I continue learning, I’ll keep doing my small part to share and educate. There’s work to be done here.

*Special thanks to Nick and Jake. We had dinner a few weeks ago and the seeds of this post fell out of that conversation. We were also celebrating the early success of Nick’s outstanding book Just Keep Buying. I have read nearly all of Nick’s blog posts and when I came to investing it was formative. Now you can get all the lessons in one tidy place. And there’s a kicker — the book is better than the blog. So even if you read Nick regularly, the book is worth buying. It’s also a perfect book to give someone when they are in high school or college or their early 20s.

If I had this book back then, I never would have written this post.

Damn that thought has major Terminator plot vibes.


When I started learning about investing, this post would have been welcome:

✍️Return: Where Does It Come From? (11 min read)
by @kbracker

This is an evergreen post fundamental to investing education. It explains the components of equity returns.

Kevin Bracker is a retired finance professor.

His YouTube channel is epic. In-depth examples of fundamental, quantitative, and derivative concepts. Check it out.

Moontower #150

Friends,

I had a trip booked this week, but when one of the kids got Covid last week I expected our whole household to go down with it.

Somehow nobody else got it, so…

I’m in Panama.

I wrote this before I left. I hope I’m alive right now.

Let’s just hop into one of the best posts I’ve read in recent memory.

✍️The Arc Of The Practical Creator (16 min read)
by @moretothat

Lawrence Yeo’s work is a trojan horse. Your mind’s guard thinks “oh what a cuddly cartoon, open the gate”. Then boom. You’re staring into a philosophical mirror. The words belong to a cartoon, yet the sentiment is unmistakably yours.

I’ve been enjoying these posts for years but this felt like an opus tying together many themes I read Lawrence for. The object-level matter is a set of directions leading you towards the path you want to walk. It’s a guided tour of the forks you’ll see along the way, their meaning, and a framework for deciding which way to go.

The meta-lesson has to do with agency. The meaning you create by your choices. And a paradoxically liberating insight — the path is endless.

I took notes as a reference. You can find them in my public Notion: Moontower’s Favorite Posts By Others

The most pragmatic bits are captured in the description of the arc. The deepest bits are timeless wisdom. They are reminders that creativity is important because it’s about agency. The word “creativity” is imbued with impractical or whimsical connotations usually relegated to art, music, performance, or writing. This gives the impression that creativity is rare or somehow reserved for the few.

Creativity resides in each of us. You don’t need permission to unlock it. And it’s not just a plaything. You have a duty to your well-being to unlock it. Lawrence, take us out:

Every stage will be challenging, and that’s the point.

Creative endeavors are inspiring because the scope of the problem often feels bigger than your capacity to solve it. But because you find that problem so worthwhile, you’re willing to put in the effort required to provide the best solution possible. Through this process, you become a more capable person, which allows you to address more worthwhile problems in turn. It’s this beautiful cycle that gives you a sense of purpose and meaning in how you spend your time and energy.

So regardless of which stage you’re in, understand that there is no easier or harder. There is just challenge. And the only way to cultivate a healthy relationship with challenge is to develop the patience required to manage it properly.


Money Angle

For this 150th issue Moontower, I have a confession.

I write this Money Angle section each week but as recently as 6 years ago, I didn’t really care about or understand investing. The delay in learning has cost returns and even shame. I might as well get the most out of that expensive tuition by sharing the story so others can learn from my mistakes.

When I graduated in 2000, the options and still-new ETF trading businesses were a party. The internet bubble led to high volumes and volatility. The volumes were a step-function higher than anything seen before. I’d estimate prop shops made 4-5x the profits they typically expected.

Before the dot-com days, options trading was a cottage industry where a typical trader could earn a low six-figure pay working relatively short hours without having to ingratiate their personalities to either clients or corporate overlords. A roaring stock market and the emergence of electronic trading transformed the landscape. The existing prop shops and sole proprietors had expertise and so-called time-place advantage on the exchange floors. The competition from banks hadn’t arrived because like I said, it used to be a niche industry. Banks were not internalizing flow just yet. In fact, to play catch-up Goldman paid a shocking sum of $6.5B for Spear, Leeds, and Kellogg after acquiring Hull months earlier.

The upshot. Prop shops were hiring like crazy. I snuck into SIG’s largest ever cohort. I started working in August 2000. I was a trader with my own book by October 2001. (Story time: I finished SIG’s class at the end of summer 2001. I took a 1-week vacation visiting my friends in Cupertino before heading back to NY to my assigned pit on the AMEX. During that trip to CA, my mother called waking me up after a 5am bender. 2 planes had crashed into the World Trade Center. She was in Midtown and called because she “just wanted to hear my voice”. I dismissed her as crazy and went back to sleep. Later that morning, when I turned on the news, it was the worst I ever felt in my life. Only to be topped a few minutes later when I tried to call her and couldn’t get through because the phones were overloaded. When I got back to NY the exchanges were still closed and I wouldn’t start trading for a few weeks).

I was 23-years-old, had my own trading account, and making $100k including bonus. It was more money than anyone in my family made. In the next year, I would pay off my student loans but what would I do with my savings next? Growing up, my parents didn’t have extra money to invest. I didn’t learn about compounding and what 100 bps means in the long run.

There was also a perverse combination of influences that kept investing in markets off my radar. First, the bursting of the internet bubble made me feel thankful for not investing in stocks. Second, as a trader we were trained to have no opinions. I thought of option customers as deluded gamblers. Suckers and tourists unless they had inside info. As market-makers, we were always worried about toxic flows. Toxic flow is informed flow. It’s either flow frontrunning a larger incoming flow or straight-up insider trading (I clerked at the post were options on XAL traded. That’s the AMEX Airline Index. Put option action before 9/11 was investigated with attempts to trace profits back to Al Queda. No smoking guns were found). In my model of markets, you either cheated to make money or you were the casino. Otherwise you were just gambling. Pretty dark.

I was starting to accumulate savings with my debts paid off. SIG had 401k matching so it seemed like a no-brainer to put money there. I think I just used a target-date fund. It was a snap decision. Retirement felt really far away so money trapped in a 401k felt fake to me. Later, when I was self-employed I would contribute $50k/year to a SEP IRA and just jam it into stocks. Again, fake money since half of it would have been taxed if I didn’t contribute.

But what would I do with liquid savings if I wasn’t going to invest beyond a 401k? The default was to buy a place to live so I wasn’t “throwing money away on rent” (that’s the wrong framing of rent; learning is unlearning). With this goal in mind, I was focused on saving about $75k for a down payment on an apartment. As a near-term goal it was money I couldn’t afford to lose, so investing didn’t make sense anyway.

In 2005, I bought a coop studio in midtown on 57th between Lexington and 3rd Ave. It was a 450 sq ft fixer that I renovated. (Random: the apartment was above a memorabilia store that had a Guns N’ Roses VMA award presumably from the night Duff and Slash, stumbling drunk, accepted the moon man while slurring their words and cursing on live TV. They were asking $5,000 for it. The most burning missed trade in my career.) Between the apartment and renovations, my savings were now depleted to a healthy reserve. No reason to invest.

2 years later, I score a low seven-figure bonus. So what do I do? I buy a condo in LIC off of plans. Paid the developer’s costs and everything. It was 2007 in NYC. That’s how it was. Toppy.

By the time the place is built and I move in, the GFC is in full swing. I never had great timing. (Not even as a vol trader…that’s why it’s critical to manage risk and size well. Timing is impossible to nail consistently but it’s not as important. Harley Bassman likes to say “sizing is more important than entry level”. Co-sign.)

I was in the midst of taking 6 months off after leaving SIG to start my own trading business with a backer. I’m shopping for an engagement ring, expect to have big wedding expenses in the next year, and embarking on a new venture where I’d have to post cash in escrow with the backer. Plus I’m watching the financial world implode. With all these demands and an apartment that is immediately underwater from its basis, there was no way was I going to stick money in the market.

So here I am, I just turned 30, a trader for 7 years, and I still don’t know a thing about investing.

I won’t drag out the next decade in detail, but I remained apathetic about investing. When we moved to SF in 2012, we started looking for homes. Another imminent purchase, so no point in investing, right? Since I don’t understand investing I figure I’ll just buy a house in cash and at least lock in the after-tax mortgage rate as a return. I know, I know. (Look, writing this is part of the healing.)

We can zoom ahead until about age 36. We just bought our family house in the ‘burbs and have a 1-year-old. This focuses you on the future. While my wife and I enjoy substantial W2 incomes, high taxes and relaxed spending habits make something abundantly clear — the strategy of just outrunning will eventually tire. I’m sitting there without equity in anything except a house.

That’s when I turned to the internet. I started lurking on Twitter. Listening to podcasts. I approached investing with a beginner’s mind. I realized that my trading background actually harmed me but it was because of how I generalized its lessons. It was my own failure. [See: How I Misapplied My Trader Mindset To Investing]

I became swept up in a process of unlearning and reconciling. What about trading applies to investing? The answers are still unfolding for me. When I started this newsletter I was mostly sharing links and concepts I found interesting. Somewhere along the line, I began translating from one domain to the other. The feedback told me that people outside trading could learn from the niche I spent my whole career in if I could peel off the skin to get to the fruit.

The quest to get better at investing goes hand in hand with learning and teaching. Some of the cornerstones from which I approach investing education:

  • Markets, from the perspective of most people, are “efficiently inefficient”. Efficiency is highly seat-dependent. Sitting in the cockpit at my last job, I could see inefficiency. I have no such visibility from my living room. My experience in trading has paradoxically contributed to this view — I’ve spent a lot of time in awe of how something that I thought was clever was actually priced in before I got there. That’s a hint that the relative efficiency of markets is not a paradox.

  • I can appreciate others being incurious about investing (I still consider it a chore…I find finance conceptually fascinating but investing is about a lot more than concepts). So I’m sensitive to people’s preference for simple. Investing is a wicked domain with tremendous luck. One of my favorite statistics comes from my buddy Nick Maggiulli. The dates are cherry-picked but somebody lived them:

    if you had invested from 1960-1980 and beaten the market by 5% each year, you would have made less money than if you had invested from 1980-2000 and underperformed the market by 5% a year.

    The returns to effort dimish extremely quickly. Charley Ellis describes investing as “a loser’s game” like amateur tennis. You win by not losing. Not making giant errors. Not carrying 18% credit card debt. Not concentrating your wealth in the latest shiny rock.

  • Not everyone grows up knowing about compounding. There’s a lot of financial literacy stuff for kids or teens out there. Much of it is impractical unless the youth is specifically interested in investing. Yet the idea of compounding, not just financially, but in relationships, knowledge, and skills is critical. Finding ways to deliver this message so that it sticks is a worthy challenge.
  • Separate what matters from what doesn’t matter. Investing is a playground for decision-making. You can be doubly helpful if you can help map investing rationale to general thinking. A hunch — the best lessons from investing and portfolio theory are more useful outside investing.

My last confession for today. I didn’t really understand where equity returns came from for most of my adult life. I thought that over time “stocks just go up” without any sense of why. That’s just willful ignorance at some point. I wanna believe I knew where returns came from if you pressed me but I’m not sure. Either way, I’m sympathetic to others who don’t get where returns come from.

A non-zero percentage of people who invest in RE fall in this camp. There’s something about them not being able to see the cashflow that makes them think stocks are fairy dust and not businesses. The whole dividend darling marketing spiel is aimed straight at them even though dividends are tax-inefficient.

[The decision to pay dividends or not has nothing to do with whether a company is a good business. It’s a capital allocation decision. Jake uses a simple picture to show they are mathematically equivalent to buybacks. Stock prices fall by the amount of the dividend. If you have ever exercised a call option early you know this. In fact, when you see the “change in price” column in a data vendor after a distribution, that change is net of the dividend. So if a $50 stock pays a $1 dividend and the next day is trading for $49, the vendor will say the stock is “unchanged”.

Dividends, just like the buybacks, reduce the amount of cash on a company’s balance sheet. In the case of the dividend, the price of the stock falls reducing the company’s market cap by the amount of cash they spent. In the buyback scenario, the price of the stock remains unchanged but the shares outstanding falls. Again, the market cap falls by the amount of cash the company spent.]

It’s totally understandable to have mistaken beliefs about where stock returns come from. All of the charts we look at are price charts. How many charts do you see of earnings or FCF in mainstream financial outlets? It’s not nefarious but it makes you wonder. How can financial content be displayed so that it improves our understanding? How can investing education be incorporated effectively into pre-teen and teen education?

I’m a trader and a lot of investing basics managed to avoid me. It’s understandable. People’s asset allocations are not openly discussed. There’s so much financial information online but it’s hard to know what’s trustworthy especially when you are a beginner. There’s no brand that comes to mind as the obvious choice for financial literacy.

As I continue learning, I’ll keep doing my small part to share and educate. There’s work to be done here.

*Special thanks to Nick and Jake. We had dinner a few weeks ago and the seeds of this post fell out of that conversation. We were also celebrating the early success of Nick’s outstanding book Just Keep Buying. I have read nearly all of Nick’s blog posts and when I came to investing it was formative. Now you can get all the lessons in one tidy place. And there’s a kicker — the book is better than the blog. So even if you read Nick regularly, the book is worth buying. It’s also a perfect book to give someone when they are in high school or college or their early 20s.

If I had this book back then, I never would have written this post.

Damn that thought has major Terminator plot vibes.


When I started learning about investing, this post would have been welcome:

✍️Return: Where Does It Come From? (11 min read)
by @kbracker

This is an evergreen post fundamental to investing education. It explains the components of equity returns.

Kevin Bracker is a retired finance professor.

His YouTube channel is epic. In-depth examples of fundamental, quantitative, and derivative concepts. Check it out.

Stay groovy!

Greeks Are Everywhere

The option greeks everyone starts with are delta and gamma. Delta is the sensitivity of the option price with respect to changes in the underlying. Gamma is the change in that delta with respect to changes in the underlying.

If you have a call option that is 25% out-of-the-money (OTM) and the stock doubles in value, you would observe the option graduating from a low delta (when the option is 25% OTM a 1% change in the stock isn’t going to affect the option much) to having a delta near 100%. Then it moves dollar for dollar with the stock.

If the option’s delta changed from approximately 0 to 100% then gamma is self-evident. The option delta (not just the option price) changed as the stock rallied. Sometimes we can even compute a delta without the help of an option model by reasoning about it from the definition of “delta”. Consider this example from Lessons From The .50 Delta Option where we establish that delta is best thought of as a hedge ratio 1:

Stock is trading for $1. It’s a biotech and tomorrow there is a ruling:

  • 90% of the time the stock goes to zero
  • 10% of the time the stock goes to $10

First take note, the stock is correctly priced at $1 based on expected value (.90 x $0 + .10 x $10). So here are my questions.

What is the $5 call worth?

  • Back to expected value:90% of the time the call expires worthless.10% of the time the call is worth $5

.9 x $0 + .10 x $5 = $.50

The call is worth $.50

Now, what is the delta of the $5 call?

$5 strike call =$.50

Delta = (change in option price) / (change in stock price)

  • In the down case, the call goes from $.50 to zero as the stock goes from $1 to zero.Delta = $.50 / $1.00 = .50
  • In the up case, the call goes from $.50 to $5 while the stock goes from $1 to $10Delta = $4.50 / $9.00 = .50

The call has a .50 delta

Using The Delta As a Hedge Ratio

Let’s suppose you sell the $5 call to a punter for $.50 and to hedge you buy 50 shares of stock. Each option contract corresponds to a 100 share deliverable.

  • Down scenario P/L:Short Call P/L = $.50 x 100 = $50Long Stock P/L = -$1.00 x 50 = -$50

    Total P/L = $0

  • Up scenario P/L:Short Call P/L = -$4.50 x 100 = -$450Long Stock P/L = $9.00 x 50 = $450

    Total P/L = $0

Eureka, it works! If you hedge your option position on a .50 delta your p/l in both cases is zero.

But if you recall, the probability of the $5 call finishing in the money was just 10%. It’s worth restating. In this binary example, the 400% OTM call has a 50% delta despite only having a 10% chance of finishing in the money.

The Concept of Delta Is Not Limited To Options

Futures

Futures have deltas too. If the SPX cash index increases by 1%, the SP500 futures go up 1%. They have a delta of 100%.

But let’s look closer.

The fair value of a future is given by:

Future = Seʳᵗ

where:

S = stock price

r = interest rate

t = time to expiry in years

This formula comes straight from arbitrage pricing theory. If the cash index is trading for $100 and 1-year interest rates are 5% then the future must trade for $105.13

100e^(5% * 1) = $105.13

What if it traded for $103?

  • Then you buy the future, short the cash index at $100
  • Earn $5.13 interest on the $100 you collect when you short the stocks in the index.
  • For simplicity imagine the index doesn’t move all year. It doesn’t matter if it did move since your market risk is hedged — you are short the index in the cash market and long the index via futures.
  • At expiration, your short stock position washes with the expiring future which will have decayed to par with the index or $100.
  • [Warning: don’t trade this at home. I’m handwaving details. Operationally, the pricing is more intricate but conceptually it works just like this.]
  • P/L computation:You lost $3 on your futures position (bought for $103 and sold at $100).
    You broke even on the cash index (shorted and bought for $100)
    You earned $5.13 in interest

    Net P/L: $2.13 of riskless profit!

You can walk through the example of selling an overpriced future and buying the cash index. The point is to recognize that the future must be priced as Seʳᵗ to ensure no arbitrage. That’s the definition of fair value.

You may have noticed that a future must have several greeks. Let’s list them:

  • Theta: the future decays as time passes. If it was a 1-day future it would only incorporate a single day’s interest in its fair value. In our example, the future was $103 and decayed to $100 over the course of the year as the index was unchanged. The daily theta is exactly worth 1 day’s interest.
  • Rho: The future’s fair value changes with interest rates. If the rate was 6% the future would be worth $106.18. So the future has $1.05 of sensitivity per 100 bps change in rates.
  • Delta: Yes the future even has a delta with respect to the underlying! Imagine the index doubled from $100 to $200. The new future fair value assuming 5% interest rates would be $210.25.Invoking “rise over run” from middle school:delta = change in future / change in index
    delta = (210.25 – 105.13)/ (200 – 100)
    delta = 105%

    That holds for small moves too. If the index increases by 1%, the future increases by 1.05%

  • Gamma: 0. There is no gamma. The delta doesn’t change as the stock moves.

Levered ETFs

Levered and inverse ETFs have both delta and gamma! My latest post dives into how we compute them.

✍️The Gamma Of Levered ETFs (8 min read)

This is an evergreen reference that includes:

  • the mechanics of levered ETFs
  • a simple and elegant expression for their gamma
  • an explanation of the asymmetry between long and short ETFs
  • insight into why shorting is especially difficult
  • the application of gamma to real-world trading strategies
  • a warning about levered ETFs
  • an appendix that shows how to use deltas to combine related instruments

And here’s some extra fun since I mentioned the challenge of short positions:

Bonds

Bonds have delta and gamma. They are called “duration” and “convexity”. The duration is the sensitivity to the bond price with respect to interest rates. Borrowing from my older post Where Does Convexity Come From?:

Consider the present value of a note with the following terms:

Face value: $1000
Coupon: 5%
Schedule: Semi-Annual
Maturity: 10 years

Suppose you buy the bond when prevailing interest rates are 5%. If interest rates go to 0, you will make a 68% return. If interest rates blow out to 10% you will only lose 32%.

It turns out then as interest rates fall, you actually make money at an increasing rate. As rates rise, you lose money at a decreasing rate. So again, your delta with respect to interest rate changes. In bond world, the equivalent of delta is duration. It’s the answer to the question “how much does my bond change in value for a 1% change in rates?”

So where does the curvature in bond payoff come from? The fact that the bond duration changes as interest rates change. This is reminiscent of how the option call delta changed as the stock price rallied.

The red line shows the bond duration when yields are 10%. But as interest rates fall we can see the bond duration increases, making the bonds even more sensitive to rates decline. The payoff curvature is a product of your position becoming increasingly sensitive to rates. Again, contrast with stocks where your position sensitivity to the price stays constant.

Corporations

Companies have all kinds of greeks. A company at the seed stage is pure optionality. Its value is pure extrinsic premium to its assets (or book value). In fact, you can think of any corporation as the premium of the zero strike call.

[See a fuller discussion of the Merton model on Lily’s Substack which is a must-follow. We talk about similar stuff but she’s a genius and I’m just old.]

Oil drillers are an easy example. If a driller can pull oil out of the ground at a cost of $50 a barrel but oil is trading for $25 it has the option to not drill. The company has theta in the form of cash burn but it still has value because oil could shoot higher than $50 one day. The oil company’s profits will be highly levered to the oil price. With oil bouncing around $20-$30 the stock has a small delta, if oil is $75, the stock will have a high delta. This implies the presence of gamma since the delta is changing.

Games

One of the reasons I like boardgames is they are filled with greeks. There are underlying economic or mathematical sensitivities that are obscured by a theme. Chess has a thin veneer of a war theme stretched over its abstraction. Other games like Settlers of Catan or Bohnanza (a trading game hiding under a bean farming theme) have more pronounced stories but as with any game, when you sit down you are trying to reduce the game to its hidden abstractions and mechanics.

The objective is to use the least resources (whether those are turns/actions, physical resources, money, etc) to maximize the value of your decisions. Mapping those values to a strategy to satisfy the win conditions is similar to investing or building a successful business as an entrepreneur. You allocate constrained resources to generate the highest return, best-risk adjusted return, smallest loss…whatever your objective is.

Games have mine a variety of mechanics (awesome list here) just as there are many types of business models. Both game mechanics and business models ebb and flow in popularity. With games, it’s often just chasing the fashion of a recent hit that has captivated the nerds. With businesses, the popularity of models will oscillate (or be born) in the context of new technology or legal environments.

In both business and games, you are constructing mental accounting frameworks to understand how a dollar or point flows through the system. On the surface, Monopoly is about real estate, but un-skinned it’s a dice game with expected values that derive from probabilities of landing on certain spaces times the payoffs associated with the spaces. The highest value properties in this accounting system are the orange properties (ie Tennessee Ave) and red properties (ie Kentucky). Why? Because the jail space is a sink in an “attractor landscape” while the rents are high enough to kneecap opponents. Throw in cards like “advance to nearest utility”, “advance to St. Charles Place”, and “Illinois Ave” and the chance to land on those spaces over the course of a game more than offsets the Boardwalk haymaker even with the Boardwalk card in the deck.

In deck-building games like Dominion, you are reducing the problem to “create a high-velocity deck of synergistic combos”. Until you recognize this, the opponent who burns their single coin cards looks like a kamikaze pilot. But as the game progresses, the compounding effects of the short, efficient deck creates runaway value. You will give up before the game is over, eager to start again with X-ray vision to see through the theme and into the underlying greeks.

[If the link between games and business raises an antenna, you have to listen to Reid Hoffman explain it to Tyler Cowen!]

Wrapping Up

Option greeks are just an instance of a wider concept — sensitivity to one variable as we hold the rest constant. Being tuned to estimating greeks in business and life is a useful lens for comprehending “how does this work?”. Armed with that knowledge, you can create dashboards that measure the KPIs in whatever you care about, reason about multi-order effects, and serve the ultimate purpose — make better decisions.

Thoughts For New Grads

Over the past few years, I’ve shared a lot of writing about careers and career transitions. Sometimes you know where you want to go and it’s just a matter of putting one foot in front of the other. For others, they sense what they are doing is not the right fit.

This doubt is especially unsettling at the start of a career. It’s easier to pivot when you are younger and opportunity costs are low. Oftentimes it’s just a matter of fighting through the initial discomfort.

I wanted to quit my trading career my first day into it.

I was 22 years old, hapless in my attempts to understand the language of bids and offers ricocheting from the smelly mouths I was standing next to on the Amex trading floor. “Everyone has to start somewhere” is true but hardly consolation when you feel useless. Fetching traders’ lunch was the only time I felt useful. Useful but stupid. I’m in Cafe World on the corner of Trinity and Rector staring at a diagram of where on the plate my boss wanted his Singapore mei fun noodles while lamenting the wisdom of taking on college debt for this privilege.

Fortunately, the initial learning curve for trading isn’t too steep if you are immersed on an exchange floor. I didn’t have to waste much time figuring out if this was a mistake, because it only took a little persistence to get to a place where I could be useful. I became proficient in Excel in less than 2 months. I stopped “offering for” and “bidding at” in less time than that. I could see that my development was in line with my cohort. These clues were helpful because I’ve always felt some suspicion about grit.

I thought grit was overrated.

It wasn’t a buzzword back then, but I always had a feeling that Venkat Rao put into words when he said “hard equals wrong” in Calculus of Grit.

There’s a bit I want to highlight:

School’s failure to reveal most people’s strengths sets their lives on a needlessly masochistic journey.

Venkat explains:

Why? Think of it this way. The disciplinary world very coarsely measured your aptitudes and strengths once in your lifetime, pointed you in a roughly right direction and said “Go!” The external environment had been turned into a giant obstacle course designed around a coarse global mapping of everybody’s strengths.

So there was no distinction between the map of the external world you were navigating and the map of your internal strengths. The two had been arranged to synchronize. If you navigated through a map of external achievement, landmarks, and honors, you’d automatically be navigating safely through the landscape of your internal strengths.

But when you cannot trust that you’ve been pointed in the right direction in a landscape designed around your strengths, you cannot afford to navigate based on a one-time coarse mapping of your own strengths at age 18.

If you run into an obstacle, it is far more likely that it represents a weakness rather than a meaningful real-world challenge to be overcome, as a learning experience.

Don’t try to go over or through. It makes far more sense to go around. Hack and work around. Don’t persevere out of a foolhardy superhuman sense of valor.

It can be difficult to tell when you should persevere vs cut your losses. I offer some thought and links in On GritTo be clear, I think grit is important. But if anything it’s probably more overrated than ever since an airport book was published on it.

In the years since I read that post, I came across an essay that I think is a perfect companion to the grit discussion. The subtext, at least in how I read it, is to orient your heading so it’s downhill. No matter how you read it, it’s a terrific essay. Since it’s commencement season, send it to a recent grad.

✍️How Will You Measure Your Life? (16 min read)
by Clayton M. Christensen

Here are excerpts I like to return to.

On how Clayton responds to advice-seekers…

When people ask what I think they should do, I rarely answer their question directly. Instead, I run the question aloud through one of my models. I’ll describe how the process in the model worked its way through an industry quite different from their own. And then, more often than not, they’ll say, “OK, I get it.” And they’ll answer their own question more insightfully than I could have.

On remembering why you do something at all…

Over the years I’ve watched the fates of my HBS classmates from 1979 unfold; I’ve seen more and more of them come to reunions unhappy, divorced, and alienated from their children. I can guarantee you that not a single one of them graduated with the deliberate strategy of getting divorced and raising children who would become estranged from them. And yet a shocking number of them implemented that strategy. The reason? They didn’t keep the purpose of their lives front and center as they decided how to spend their time, talents, and energy.

Had I instead spent that hour each day learning the latest techniques for mastering the problems of autocorrelation in regression analysis, I would have badly misspent my life. I apply the tools of econometrics a few times a year, but I apply my knowledge of the purpose of my life every day. It’s the single most useful thing I’ve ever learned. I promise my students that if they take the time to figure out their life purpose, they’ll look back on it as the most important thing they discovered at HBS. If they don’t figure it out, they will just sail off without a rudder and get buffeted in the very rough seas of life.

Not everything that matters is good at giving you prompt feedback. If you fail to appreciate this, you chase what’s easily legible at the cost of things that are hard to measure.

Allocation choices can make your life turn out to be very different from what you intended. Sometimes that’s good: Opportunities that you never planned for emerge. But if you misinvest your resources, the outcome can be bad. As I think about my former classmates who inadvertently invested for lives of hollow unhappiness, I can’t help believing that their troubles relate right back to a short-term perspective.

When people who have a high need for achievement—and that includes all Harvard Business School graduates—have an extra half hour of time or an extra ounce of energy, they’ll unconsciously allocate it to activities that yield the most tangible accomplishments. And our careers provide the most concrete evidence that we’re moving forward. You ship a product, finish a design, complete a presentation, close a sale, teach a class, publish a paper, get paid, get promoted. In contrast, investing time and energy in your relationship with your spouse and children typically doesn’t offer that same immediate sense of achievement.

Kids misbehave every day. It’s really not until 20 years down the road that you can put your hands on your hips and say, “I raised a good son or a good daughter.” You can neglect your relationship with your spouse, and on a day-to-day basis, it doesn’t seem as if things are deteriorating. People who are driven to excel have this unconscious propensity to underinvest in their families and overinvest in their careers—even though intimate and loving relationships with their families are the most powerful and enduring source of happiness.

If you want your kids to have strong self-esteem and confidence that they can solve hard problems, those qualities won’t magically materialize in high school. You have to design them into your family’s culture—and you have to think about this very early on. Like employees, children build self-esteem by doing things that are hard and learning what works.

Give me an example…

The lesson I learned from this is that it’s easier to hold to your principles 100% of the time than it is to hold to them 98% of the time. If you give in to “just this once,” based on a marginal cost analysis, as some of my former classmates have done, you’ll regret where you end up. You’ve got to define for yourself what you stand for and draw the line in a safe place.

Be careful how you strive…

Once you’ve finished at Harvard Business School or any other top academic institution, the vast majority of people you’ll interact with on a day-to-day basis may not be smarter than you. And if your attitude is that only smarter people have something to teach you, your learning opportunities will be very limited. But if you have a humble eagerness to learn something from everybody, your learning opportunities will be unlimited. [Me: This is a powerful prescription to make yourself more teachable]: Generally, you can be humble only if you feel really good about yourself—and you want to help those around you feel really good about themselves, too.

His final recommendation…

Don’t worry about the level of individual prominence you have achieved; worry about the individuals you have helped become better people. This is my final recommendation: Think about the metric by which your life will be judged, and make a resolution to live every day so that in the end, your life will be judged a success.

This echoes the wisdom of another late visionary, Michael Crichton:

“If you want to be happy, forget yourself. Forget all of it—how you look, how you feel, how your career is going. Just drop the whole subject of you. People dedicated to something other than themselves are the happiest people in the world.”

It’s a lot of brilliance in a couple of paragraphs:

✍️Happiness (3 min read)
by Michael Crichton

Moontower #149

Friends,

Last week I took an uncharacteristic adventure into macro which turned out to be my most popular post ever. Not to be all “Thom Yorke hates Creep” since you can only be that sickeningly self-important if you are actually in Radiohead, but come on. I give you what I got every week and all you really want to know is what happens to inflation when the moon is in Taurus.

Seriously, 400 new subs signed up for Moontower after that post which is 10x my normal weekly adds. There are over 4000 subs now which is up 1k in 6 weeks after getting 3000 in 3 years. On one hand, thank you. On the other, be aware that my commercial instincts are trash. As such I will not feed the ducks and you will still find me meandering into macro often. Annoyingly, my most 2nd most popular post ever was also frickin’ macroMarkets Will Permanently Reset Higher (My Sacrifice to the Delta Gods)

Here’s the best 5 seconds of your day.

Moving on.

Over the past few years, I’ve shared a lot of writing about careers and career transitions. Sometimes you know where you want to go and it’s just a matter of putting one foot in front of the other. For others, they sense what they are doing is not the right fit.

This doubt is especially unsettling at the start of a career. It’s easier to pivot when you are younger and opportunity costs are low. Oftentimes it’s just a matter of fighting through the initial discomfort.

I wanted to quit my trading career my first day into it.

I was 22 years old, hapless in my attempts to understand the language of bids and offers ricocheting from the smelly mouths I was standing next to on the Amex trading floor. “Everyone has to start somewhere” is true but hardly consolation when you feel useless. Fetching traders’ lunch was the only time I felt useful. Useful but stupid. I’m in Cafe World on the corner of Trinity and Rector staring at a diagram of where on the plate my boss wanted his Singapore mei fun noodles while lamenting the wisdom of taking on college debt for this privilege.

Fortunately, the initial learning curve for trading isn’t too steep if you are immersed on an exchange floor. I didn’t have to waste much time figuring out if this was a mistake, because it only took a little persistence to get to a place where I could be useful. I became proficient in Excel in less than 2 months. I stopped “offering for” and “bidding at” in less time than that. I could see that my development was in line with my cohort. These clues were helpful because I’ve always felt some suspicion about grit.

I thought grit was overrated.

It wasn’t a buzzword back then, but I always had a feeling that Venkat Rao put into words when he said “hard equals wrong” in Calculus of Grit.

There’s a bit I want to highlight:

School’s failure to reveal most people’s strengths sets their lives on a needlessly masochistic journey.

Venkat explains:

Why? Think of it this way. The disciplinary world very coarsely measured your aptitudes and strengths once in your lifetime, pointed you in a roughly right direction and said “Go!” The external environment had been turned into a giant obstacle course designed around a coarse global mapping of everybody’s strengths.

So there was no distinction between the map of the external world you were navigating and the map of your internal strengths. The two had been arranged to synchronize. If you navigated through a map of external achievement, landmarks, and honors, you’d automatically be navigating safely through the landscape of your internal strengths.

But when you cannot trust that you’ve been pointed in the right direction in a landscape designed around your strengths, you cannot afford to navigate based on a one-time coarse mapping of your own strengths at age 18.

If you run into an obstacle, it is far more likely that it represents a weakness rather than a meaningful real-world challenge to be overcome, as a learning experience.

Don’t try to go over or through. It makes far more sense to go around. Hack and work around. Don’t persevere out of a foolhardy superhuman sense of valor.

It can be difficult to tell when you should persevere vs cut your losses. I offer some thought and links in On GritTo be clear, I think grit is important. But if anything it’s probably more overrated than ever since an airport book was published on it.

In the years since I read that post, I came across an essay that I think is a perfect companion to the grit discussion. The subtext, at least in how I read it, is to orient your heading so it’s downhill. No matter how you read it, it’s a terrific essay. Since it’s commencement season, send it to a recent grad.

✍️How Will You Measure Your Life? (16 min read)
by Clayton M. Christensen

Here are excerpts I like to return to.

On how Clayton responds to advice-seekers…

When people ask what I think they should do, I rarely answer their question directly. Instead, I run the question aloud through one of my models. I’ll describe how the process in the model worked its way through an industry quite different from their own. And then, more often than not, they’ll say, “OK, I get it.” And they’ll answer their own question more insightfully than I could have.

On remembering why you do something at all…

Over the years I’ve watched the fates of my HBS classmates from 1979 unfold; I’ve seen more and more of them come to reunions unhappy, divorced, and alienated from their children. I can guarantee you that not a single one of them graduated with the deliberate strategy of getting divorced and raising children who would become estranged from them. And yet a shocking number of them implemented that strategy. The reason? They didn’t keep the purpose of their lives front and center as they decided how to spend their time, talents, and energy.

Had I instead spent that hour each day learning the latest techniques for mastering the problems of autocorrelation in regression analysis, I would have badly misspent my life. I apply the tools of econometrics a few times a year, but I apply my knowledge of the purpose of my life every day. It’s the single most useful thing I’ve ever learned. I promise my students that if they take the time to figure out their life purpose, they’ll look back on it as the most important thing they discovered at HBS. If they don’t figure it out, they will just sail off without a rudder and get buffeted in the very rough seas of life.

Not everything that matters is good at giving you prompt feedback. If you fail to appreciate this, you chase what’s easily legible at the cost of things that are hard to measure.

Allocation choices can make your life turn out to be very different from what you intended. Sometimes that’s good: Opportunities that you never planned for emerge. But if you misinvest your resources, the outcome can be bad. As I think about my former classmates who inadvertently invested for lives of hollow unhappiness, I can’t help believing that their troubles relate right back to a short-term perspective.

When people who have a high need for achievement—and that includes all Harvard Business School graduates—have an extra half hour of time or an extra ounce of energy, they’ll unconsciously allocate it to activities that yield the most tangible accomplishments. And our careers provide the most concrete evidence that we’re moving forward. You ship a product, finish a design, complete a presentation, close a sale, teach a class, publish a paper, get paid, get promoted. In contrast, investing time and energy in your relationship with your spouse and children typically doesn’t offer that same immediate sense of achievement.

Kids misbehave every day. It’s really not until 20 years down the road that you can put your hands on your hips and say, “I raised a good son or a good daughter.” You can neglect your relationship with your spouse, and on a day-to-day basis, it doesn’t seem as if things are deteriorating. People who are driven to excel have this unconscious propensity to underinvest in their families and overinvest in their careers—even though intimate and loving relationships with their families are the most powerful and enduring source of happiness.

If you want your kids to have strong self-esteem and confidence that they can solve hard problems, those qualities won’t magically materialize in high school. You have to design them into your family’s culture—and you have to think about this very early on. Like employees, children build self-esteem by doing things that are hard and learning what works.

Give me an example…

The lesson I learned from this is that it’s easier to hold to your principles 100% of the time than it is to hold to them 98% of the time. If you give in to “just this once,” based on a marginal cost analysis, as some of my former classmates have done, you’ll regret where you end up. You’ve got to define for yourself what you stand for and draw the line in a safe place.

Be careful how you strive…

Once you’ve finished at Harvard Business School or any other top academic institution, the vast majority of people you’ll interact with on a day-to-day basis may not be smarter than you. And if your attitude is that only smarter people have something to teach you, your learning opportunities will be very limited. But if you have a humble eagerness to learn something from everybody, your learning opportunities will be unlimited. [Me: This is a powerful prescription to make yourself more teachable]: Generally, you can be humble only if you feel really good about yourself—and you want to help those around you feel really good about themselves, too.

His final recommendation…

Don’t worry about the level of individual prominence you have achieved; worry about the individuals you have helped become better people. This is my final recommendation: Think about the metric by which your life will be judged, and make a resolution to live every day so that in the end, your life will be judged a success.

This echoes the wisdom of another late visionary, Michael Crichton:

“If you want to be happy, forget yourself. Forget all of it—how you look, how you feel, how your career is going. Just drop the whole subject of you. People dedicated to something other than themselves are the happiest people in the world.”

It’s a lot of brilliance in a couple of paragraphs:

✍️Happiness (3 min read)
by Michael Crichton


Money Angle

Greeks Are Everywhere

The option greeks everyone starts with are delta and gamma. Delta is the sensitivity of the option price with respect to changes in the underlying. Gamma is the change in that delta with respect to changes in the underlying.

If you have a call option that is 25% out-of-the-money (OTM) and the stock doubles in value, you would observe the option graduating from a low delta (when the option is 25% OTM a 1% change in the stock isn’t going to affect the option much) to having a delta near 100%. Then it moves dollar for dollar with the stock.

If the option’s delta changed from approximately 0 to 100% then gamma is self-evident. The option delta (not just the option price) changed as the stock rallied. Sometimes we can even compute a delta without the help of an option model by reasoning about it from the definition of “delta”. Consider this example from Lessons From The .50 Delta Option where we establish that delta is best thought of as a hedge ratio 1:

Stock is trading for $1. It’s a biotech and tomorrow there is a ruling:

  • 90% of the time the stock goes to zero
  • 10% of the time the stock goes to $10

First take note, the stock is correctly priced at $1 based on expected value (.90 x $0 + .10 x $10). So here are my questions.

What is the $5 call worth?

  • Back to expected value:90% of the time the call expires worthless.

    10% of the time the call is worth $5

.9 x $0 + .10 x $5 = $.50

The call is worth $.50

Now, what is the delta of the $5 call?

$5 strike call =$.50

Delta = (change in option price) / (change in stock price)

  • In the down case, the call goes from $.50 to zero as the stock goes from $1 to zero.Delta = $.50 / $1.00 = .50
  • In the up case, the call goes from $.50 to $5 while the stock goes from $1 to $10Delta = $4.50 / $9.00 = .50

The call has a .50 delta

Using The Delta As a Hedge Ratio

Let’s suppose you sell the $5 call to a punter for $.50 and to hedge you buy 50 shares of stock. Each option contract corresponds to a 100 share deliverable.

  • Down scenario P/L:Short Call P/L = $.50 x 100 = $50

    Long Stock P/L = -$1.00 x 50 = -$50

    Total P/L = $0

  • Up scenario P/L:Short Call P/L = -$4.50 x 100 = -$450

    Long Stock P/L = $9.00 x 50 = $450

    Total P/L = $0

Eureka, it works! If you hedge your option position on a .50 delta your p/l in both cases is zero.

But if you recall, the probability of the $5 call finishing in the money was just 10%. It’s worth restating. In this binary example, the 400% OTM call has a 50% delta despite only having a 10% chance of finishing in the money.

The Concept of Delta Is Not Limited To Options

Futures

Futures have deltas too. If the SPX cash index increases by 1%, the SP500 futures go up 1%. They have a delta of 100%.

But let’s look closer.

The fair value of a future is given by:

Future = Seʳᵗ

where:

S = stock price

r = interest rate

t = time to expiry in years

This formula comes straight from arbitrage pricing theory. If the cash index is trading for $100 and 1-year interest rates are 5% then the future must trade for $105.13

100e^(5% * 1) = $105.13

What if it traded for $103?

  • Then you buy the future, short the cash index at $100
  • Earn $5.13 interest on the $100 you collect when you short the stocks in the index.
  • For simplicity imagine the index doesn’t move all year. It doesn’t matter if it did move since your market risk is hedged — you are short the index in the cash market and long the index via futures.
  • At expiration, your short stock position washes with the expiring future which will have decayed to par with the index or $100.
  • [Warning: don’t trade this at home. I’m handwaving details. Operationally, the pricing is more intricate but conceptually it works just like this.]
  • P/L computation:You lost $3 on your futures position (bought for $103 and sold at $100).
    You broke even on the cash index (shorted and bought for $100)
    You earned $5.13 in interest

    Net P/L: $2.13 of riskless profit!

You can walk through the example of selling an overpriced future and buying the cash index. The point is to recognize that the future must be priced as Seʳᵗ to ensure no arbitrage. That’s the definition of fair value.

You may have noticed that a future must have several greeks. Let’s list them:

  • Theta: the future decays as time passes. If it was a 1-day future it would only incorporate a single day’s interest in its fair value. In our example, the future was $103 and decayed to $100 over the course of the year as the index was unchanged. The daily theta is exactly worth 1 day’s interest.
  • Rho: The future’s fair value changes with interest rates. If the rate was 6% the future would be worth $106.18. So the future has $1.05 of sensitivity per 100 bps change in rates.
  • Delta: Yes the future even has a delta with respect to the underlying! Imagine the index doubled from $100 to $200. The new future fair value assuming 5% interest rates would be $210.25.Invoking “rise over run” from middle school:

    delta = change in future / change in index
    delta = (210.25 – 105.13)/ (200 – 100)
    delta = 105%

    That holds for small moves too. If the index increases by 1%, the future increases by 1.05%

  • Gamma: 0. There is no gamma. The delta doesn’t change as the stock moves.

Levered ETFs

Levered and inverse ETFs have both delta and gamma! My latest post dives into how we compute them.

✍️The Gamma Of Levered ETFs (8 min read)

This is an evergreen reference that includes:

  • the mechanics of levered ETFs
  • a simple and elegant expression for their gamma
  • an explanation of the asymmetry between long and short ETFs
  • insight into why shorting is especially difficult
  • the application of gamma to real-world trading strategies
  • a warning about levered ETFs
  • an appendix that shows how to use deltas to combine related instruments

And here’s some extra fun since I mentioned the challenge of short positions:

Bonds

Bonds have delta and gamma. They are called “duration” and “convexity”. The duration is the sensitivity to the bond price with respect to interest rates. Borrowing from my older post Where Does Convexity Come From?:

Consider the present value of a note with the following terms:

Face value: $1000
Coupon: 5%
Schedule: Semi-Annual
Maturity: 10 years

Suppose you buy the bond when prevailing interest rates are 5%. If interest rates go to 0, you will make a 68% return. If interest rates blow out to 10% you will only lose 32%.

It turns out then as interest rates fall, you actually make money at an increasing rate. As rates rise, you lose money at a decreasing rate. So again, your delta with respect to interest rate changes. In bond world, the equivalent of delta is duration. It’s the answer to the question “how much does my bond change in value for a 1% change in rates?”

So where does the curvature in bond payoff come from? The fact that the bond duration changes as interest rates change. This is reminiscent of how the option call delta changed as the stock price rallied.

The red line shows the bond duration when yields are 10%. But as interest rates fall we can see the bond duration increases, making the bonds even more sensitive to rates decline. The payoff curvature is a product of your position becoming increasingly sensitive to rates. Again, contrast with stocks where your position sensitivity to the price stays constant.

Corporations

Companies have all kinds of greeks. A company at the seed stage is pure optionality. Its value is pure extrinsic premium to its assets (or book value). In fact, you can think of any corporation as the premium of the zero strike call.

[See a fuller discussion of the Merton model on Lily’s Substack which is a must-follow. We talk about similar stuff but she’s a genius and I’m just old.]

Oil drillers are an easy example. If a driller can pull oil out of the ground at a cost of $50 a barrel but oil is trading for $25 it has the option to not drill. The company has theta in the form of cash burn but it still has value because oil could shoot higher than $50 one day. The oil company’s profits will be highly levered to the oil price. With oil bouncing around $20-$30 the stock has a small delta, if oil is $75, the stock will have a high delta. This implies the presence of gamma since the delta is changing.

Games

One of the reasons I like boardgames is they are filled with greeks. There are underlying economic or mathematical sensitivities that are obscured by a theme. Chess has a thin veneer of a war theme stretched over its abstraction. Other games like Settlers of Catan or Bohnanza (a trading game hiding under a bean farming theme) have more pronounced stories but as with any game, when you sit down you are trying to reduce the game to its hidden abstractions and mechanics.

The objective is to use the least resources (whether those are turns/actions, physical resources, money, etc) to maximize the value of your decisions. Mapping those values to a strategy to satisfy the win conditions is similar to investing or building a successful business as an entrepreneur. You allocate constrained resources to generate the highest return, best-risk adjusted return, smallest loss…whatever your objective is.

Games have mine a variety of mechanics (awesome list here) just as there are many types of business models. Both game mechanics and business models ebb and flow in popularity. With games, it’s often just chasing the fashion of a recent hit that has captivated the nerds. With businesses, the popularity of models will oscillate (or be born) in the context of new technology or legal environments.

In both business and games, you are constructing mental accounting frameworks to understand how a dollar or point flows through the system. On the surface, Monopoly is about real estate, but un-skinned it’s a dice game with expected values that derive from probabilities of landing on certain spaces times the payoffs associated with the spaces. The highest value properties in this accounting system are the orange properties (ie Tennessee Ave) and red properties (ie Kentucky). Why? Because the jail space is a sink in an “attractor landscape” while the rents are high enough to kneecap opponents. Throw in cards like “advance to nearest utility”, “advance to St. Charles Place”, and “Illinois Ave” and the chance to land on those spaces over the course of a game more than offsets the Boardwalk haymaker even with the Boardwalk card in the deck.

In deck-building games like Dominion, you are reducing the problem to “create a high-velocity deck of synergistic combos”. Until you recognize this, the opponent who burns their single coin cards looks like a kamikaze pilot. But as the game progresses, the compounding effects of the short, efficient deck creates runaway value. You will give up before the game is over, eager to start again with X-ray vision to see through the theme and into the underlying greeks.

[If the link between games and business raises an antenna, you have to listen to Reid Hoffman explain it to Tyler Cowen!]

Wrapping Up

Option greeks are just an instance of a wider concept — sensitivity to one variable as we hold the rest constant. Being tuned to estimating greeks in business and life is a useful lens for comprehending “how does this work?”. Armed with that knowledge, you can create dashboards that measure the KPIs in whatever you care about, reason about multi-order effects, and serve the ultimate purpose — make better decisions.


Last Call

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

This is a re-post from one of my favorite all-time interviews.

C. Thi Nguyen received his Ph.D. in philosophy from the University of California, Los Angeles. He is currently associate professor of Philosophy at the University of Utah. He has written public philosophy for venues such as Aeon and The New York Times, and is an editor of the aesthetics blog Aesthetics for Birds. He was the recipient of the 2020 Article Prize from the American Philosophical Association. His recent book is Games: Agency as Art.

But here’s the most fun part:

Nguyen’s Board Games: so many recommendations

I’ve played several of these. The list and descriptions are glorious.

 

Stay groovy!


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The Gamma Of Levered ETFs

Levered ETFs use derivatives to amplify the return of an underlying index. Here’s a list of 2x levered ETFs. For example, QLD gives you 2x the return of QQQ (Nasdaq 100). Levered ETFs use derivatives to get the levered exposure. In this post, we will compute the delta and gamma of levered ETFs and what that means for investors and traders.

Levered ETF Delta

In options, delta is the sensitivity of the option premium to a change in the underlying stock. If you own a 50% delta call and the stock price goes up by $1, you make $.50. If the stock went down $1, you lost $.50. Delta, generally speaking, is a rate of change of p/l with respect to how some asset moves. I like to say it’s the slope of your p/l based on how the reference asset changes.

For levered ETFs, the delta is simply the leverage factor. If you buy QLD, the 2x version of QQQ, you get 2x the return of QQQ. So if QQQ is up 1%, you earn 2%. If QQQ is down 1%, you lose 2%. If you invest $1,000 in QLD your p/l acts as if you had invested $2,000.

$100 worth of QLD is the equivalent exposure of $200 of QQQ.

Your dollar delta is $200 with respect to QQQ. If QQQ goes up 1%, you make 1% * $200 QQQ deltas = $2

The extra exposure cuts both ways. On down days, you will lose 2x what the underlying QQQ index returns.

The takeaway is that your position or delta is 2x the underlying exposure.

Dollar delta of levered ETF = Exposure x Leverage Factor

In this case, QLD dollar delta is $200 ($100 x 2).

Note that QLD is a derivative with a QQQ underlyer.

Levered ETF Gamma

QLD is a derivative because it “derives” its value from QQQ. $100 exposure to QLD represents a $200 exposure to QQQ. In practice, the ETF’s manager offers this levered exposure by engaging in a swap with a bank that guarantees the ETF’s assets will return the underlying index times the leverage factor. For the bank to offer such a swap, it must be able to manufacture that return in its own portfolio. So in the case of QLD, the bank simply buys 2x notional the NAV of QLD so that its delta or slope of p/l matches the ETFs promise.

So if the ETF has a NAV of $1B, the bank must maintain exposure of $2B QQQ deltas. That way, if QQQ goes up 10%, the bank makes $200mm which it contributes to the ETF’s assets so the new NAV would be $1.2B.

Notice what happened:

  • QQQ rallied 10% (the reference index)
  • QLD rallies 20% (the levered ETF’s NAV goes from$1B –> $1.2B)
  • The bank’s initial QQQ delta of $2B has increased to $2.2B.

Uh oh.

To continue delivering 2x returns, the bank’s delta needs to be 2x the ETF’s assets or $2.4B, but it’s only $2.2B! The bank must buy $200M worth of QQQ deltas (either via QQQs, Nasdaq futures, or the basket of stocks).

If we recall from options, gamma is the change in delta due to a change in stock price. The bank’s delta went from 2 (ie $2B/$1B) to 1.833 ($2.2B/$1.2B). So it got shorter deltas, in a rising market –> negative gamma!

The bank must dynamically rebalance its delta each day to maintain a delta of 2x the ETF’s assets. And the adjustment means it must buy deltas at the close of an up day in the market or sell deltas at the close of a down day. Levered ETFs, therefore, amplify price moves. The larger the daily move, the larger the rebalancing trades need to be!

I’ve covered this before in Levered ETF/ETN tool, where I give you this spreadsheet to compute the rebalancing trades:

From Brute Force To Symbols

There was confusion on Twitter about how levered ETFs worked recently and professor @quantian stepped up:

Junior PM interview question: An X-times leveraged fund tracks an underlying asset S. After time T, S have moved to ST = (1+dS)S0. The initial delta is of course X. What is the portfolio gamma, defined as (dDelta)/(dS), as a function of X?

Despite correctly understanding how levered and inverse ETFs work I struggled to answer this question with a general solution (ie convert the computations we brute-forced above into math symbols). It turns out the solution is a short expression and worth deriving to find an elegant insight.

@quantian responded to my difficulty with the derivation.

I’ll walk you through that slowly.
Mapping variables to @quantian’s question:
  • NAV =1

You are investing in a levered ETF that starts with a NAV of 1

  • X = The leverage factor

The bank needs to have a delta of X to deliver the levered exposure. For a 2x ETF, the bank’s initial delta will be 2 * NAV = 2

  • S = the underlying reference index

The dynamic:

  • When S moves, the bank’s delta will no longer be exactly X times the NAV. Its delta changed as S changed. That’s the definition of gamma.
  • When S moves, the bank needs to rebalance (buy or sell) units of S to maintain the desired delta of X. The rebalancing amount is therefore the change in delta or gamma.

Let’s find the general formula for the gamma (ie change in delta) in terms of X. Remember X is the leverage factor and therefore the bank’s desired delta.

The general formula for the gamma as a function of the change in the underlying index is, therefore:
X (X – 1)
where X = leverage factor
Intuition

There are 2 key insights when we look at this elegant expression:

  1. The gamma, or imbalance in delta due to the move, is proportional to the square of the leverage factor. The more levered the ETF, the larger the delta adjustment required. If there was no leverage (like SPY to the SPX index), the gamma is 0 because 0 (0-1) = 0

  2. The asymmetry of inverse ETFs — they require larger rebalances for the same size move! Imagine a simple inverse ETF with no leverage.

-1 (-1 – 1) = 2

A simple inverse ETF, has the same gamma as a double long ETF.

Consider how a double short ETF has a gamma of 6!:

-2 (-2 -1) = 6 

When I admit that I had only figured out the rebalancing quantities by working out the mechanics by brute force in Excel, @quantian had a neat observation:

I originally found this by doing the brute force Excel approach! Then I plotted it and was like “hm, that’s just a parabola, I bet I could simplify this”

X2– X shows us that the gamma of an inverse ETF is equivalent to the gamma of its counterpart long of one degree higher. For example, a triple-short ETF has the same gamma as a 4x long. Or a simple inverse ETF has the gamma of a double long. The fact that a 1x inverse ETF has gamma at all is a clue to the difficulty of running a short book…when you win, your position size shrinks and the effect is compounded by the fact that your position is shrinking even faster relative to your growing AUM as your shorts profit!

I’ve explained this asymmetry before in The difficulty with shorting and inverse positions as well as the asymmetry of redemptions:

  • As the reference asset rallies, position size gets bigger and AUM drops due to losses. As reference asset falls, position size shrinks while AUM increase due to profits.
  • Redemptions can stabilize rebalance requirements in declines and exacerbate rebalance quantities in rallies as redemptions reduce shares outstanding and in turn AUM while in both cases triggering the fund’s need to buy the reference asset which again is stabilizing after declines but not after rallies. In other words, profit-taking is stabilizing while puking is de-stabilizing.

Rebalancing In Real Life

The amount of the rebalance from our derivation is:

X(1 + X ΔS) – X (1+ ΔS)

where:

X = leverage factor

ΔS = percent change in underlying index

Another way to write that is:

X (X-1) (ΔS)

In our example, 2 * (2-1) * 10% = $.2 or an imbalance of 20% of the original NAV!

In practice, the size of the rebalance trade is of practical use. If an index is up or down a lot as you approach the end of a trading day then you can expect flows that exacerbate the move as levered ETFs must buy on up days and sell on down days to rebalance. It doesn’t matter if the ETF is long or inverse, the imbalance is always destabilizing in that it trades in the same direction as the move. The size of flows depends on how much AUM levered ETFs are holding but they can possibly be mitigated by profit-taking redemptions.

During the GFC, levered financial ETFs had large rebalance trades amidst all the volatility in bank stocks. Estimating, frontrunning, and trading against the rebalance to close was a popular game for traders who understood this dynamic. Years later levered mining ETFs saw similar behavior as precious metals came in focus in the aftermath of GFC stimulus. Levered energy ETFs, both in oil and natural gas, have ebbed and flowed in popularity. When they are in vogue, you can try to estimate the closing buy/sell imbalances that accompany highly volatile days.

Warning Label

Levered ETFs are trading tools that are not suitable for investing. They do a good job of matching the levered return of an underlying index intraday. The sum of all the negative gamma trading is expensive as the mechanical re-balancing gets front-run and “arbed” by traders. This creates significant drag on the levered ETF’s assets. In fact, if the borrowing costs to short levered ETFs were not punitive, a popular strategy would be to short both the long and short versions of the same ETF, allowing the neutral arbitrageur to harvest both the expense ratios and negative gamma costs from tracking the index!

ETFs such as USO or VXX which hold futures are famous for bleeding over time. That blood comes from periods when the underlying futures term structure is in contango and the corresponding negative “roll” returns (Campbell has a timeless paper decomposing spot and roll returns titled Deconstructing Futures Returns: The Role of Roll Yield). This is a separate issue from the negative gamma effect of levered or inverse ETFs.

Some ETFs combine all the misery into one simple ticker. SCO is a 2x-levered, inverse ETF referencing oil futures. These do not belong in buy-and-hold portfolios. Meth heads only please.

[The amount of variance drag that comes from levered ETFs depends on the path which makes the options especially tricky. I don’t explain how to price options on levered ETFs but this post is a clue to complication — Path: How Compounding Alters Return Distributions]

Key Takeaways

  • Levered ETFs are derivatives. Their delta changes as the underlying index moves. This change in delta is the definition of gamma. 

  • Levered and inverse ETFs have “negative gamma” in that they must always rebalance in a destabilizing manner — in the direction of the underlying move.
  • The required rebalance in terms of the fund’s NAV is:

X (X-1) (ΔS)

  • The size of the rebalance is proportional to the square of the leverage factor. The higher the leverage factor the larger the rebalance. For a given leverage factor, inverse ETFs have larger gammas. 

  • The drag that comes from levered ETFs means they will fail to track the desired exposure on long horizons. They are better suited to trading or short-term risk management.

Appendix: Using Delta To Summarize Exposures

We can see that delta is not limited to options, but is a useful way to denote exposures in derivatives generally. It allows you to sum deltas that reference the same underlying to compute a net exposure to that underlying.

Consider a portfolio:

  • Short 2000 shares of QQQ
  • Long 1000 shares of QLD
  • Long 50 1 month 53% delta calls

By transforming exposures into deltas then collapsing them into a single number we can answer the question, “what’s my p/l if QQQ goes up 1%?”

We want to know the slope of our portfolio vis a vis QQQ.

A few observations:

  • I computed net returns for the portfolio based on the gross (absolute value of exposures)
  • The option exposure is just the premium, but what we really care about is the delta coming from the options. Even though the total premium is <$37k, the largest delta is coming from the options position.

3-Card Macro

Here’s a rarity for this letter. Let’s play macroeconomics.

I don’t usually write about “macro” because it feels like astrology. You can look at any bit of data (the “current thing” as they say on the internet is inflation) and see it molded to be the cause or result of whatever axe a speaker is trying to grind. People who just learned what inflation was on Tuesday have incorporated it into their pre-existing worldview so seamlessly that by Friday their updated narrative is more coherent than ever.

Macro is the raw material for story-telling. For marketing. It’s a political battering ram for both sides. But macro is a ball of yarn. The discourse that’s consumable is reduced so much to aid absorption that the logic, by necessity, ends up sounding unassailable. It must. The logic is solving for convenience. Not understanding.

So I don’t write about it because I don’t think it’s especially useful. It’s more likely to give you brainworms by beefing up your priors. It will calcify hunches into commandments when the evidence only merits “things to learn more about”.

“Buy Potatoes”

While I don’t write about macro, I’m hardly immune to the animal urge to read about it and pretend I understand how the world works. My mind’s sentry just keeps me from taking it too seriously. [I suspect the sentry has saved me many times and cost me many times and I can’t tell if it’s worth the free rent it gets in my head. The question is moot, since I can’t evict it anyway. It’s like SF up in there.]

My first macro boner happened (was searching for the right verb here and “happens” is the most fitting action word to apply to boners) while reading Michael Lewis’ Liar’s Poker when I was 21. When Michael was a junior salesperson on the Salomon trading desk, he was taken under the wing of a senior trader named Alexander:

The second pattern to Alexander’s thought was that in the event of a major dislocation, such as a stock market crash, a natural disaster, the breakdown of OPEC’s production agreements, he would look away from the initial focus of investor interest and seek secondary and tertiary effects.

Remember Chernobyl? When news broke that the Soviet nuclear reactor had exploded, Alexander called. Only minutes before, confir mation of the disaster had blipped across our Quotron machines, yet Alexander had already bought the equivalent of two supertankers of crude oil. The focus of investor attention was on the New York Stock Exchange, he said. In particular it was on any company involved in nuclear power. The stocks of those companies were plummeting. Never mind that, he said. He had just purchased, on behalf of his clients, oil futures. Instantly in his mind less supply of nuclear power equaled more demand for oil, and he was right. His investors made a large killing. Mine made a small killing. Minutes after I had persuaded a few clients to buy some oil, Alexander called back.

“Buy potatoes,” he said. “Gotta hop.” Then he hung up. Of course. A cloud of fallout would threaten European food and water supplies, including the potato crop, placing a premium on uncon taminated American substitutes. Perhaps a few folks other than potato farmers think of the price of potatoes in America minutes after the explosion of a nuclear reactor in Russian, but I have never met them.

But Chernobyl and oil are a comparatively straightforward example. There was a game we played called What if? All sorts of complications can be introduced into What if? Imagine, for example, you are an institutional investor managing several billion dollars. What if there is a massive earthquake in Tokyo? Tokyo is reduced to rubble. Investors in Japan panic. They are selling yen and trying to get their money out of the Japanese stock market. What do you do?

Well, along the lines of pattern number one, what Alexander would do is put money into Japan on the assumption that since everyone was trying to get out, there must be some bargains. He would buy precisely those securities in Japan that appeared the least desirable to others. First, the stocks of Japanese insurance companies. The world would probably assume that ordinary insurance companies had a great deal of exposure…

If you are 21 years old today, how can you not hear “buy potatoes” and not think of trading as Settlers of Catan? Trading is the ultimate boardgame. It’s just that now, an algo sweeps all the call offers on Brent futures before Alexander finishes reading the headline. [Actually, the market-makers’ streaming call offers have a “panic” setting that gets triggered if they get hit on more than couple related strikes at a time and pull their co-located quotes before they get picked off by the news-reading algo. So prices can gap to something closer to fair value on very little trading volume. The graveyard of backtesting signals that don’t appreciate this would occupy every blade of grass on the planet if it were a physical place].

The blessing and curse of our frontal lobes is a desire to understand how the complex world works. Macro brings the romance of chess to investing. It lures mandate-dodging pros and tourists alike with scalable p/l if you can:

a) make accurate predictions

and

b) identify mispriced lines with respect to those predictions.

In reality, it’s more like 3-card Monte where you have no chance of guessing where the card is and if you get lucky the reward is the false confidence to wager more next time. [I highly recommend the Wikipedia for 3-card Monte. The analogy of “marks” and “shills” to the finance marketing machine writes itself].

My personal relationship with macro is as follows:

  1. I’ve got some mental model of how things work
  2. Stuff happens — none of it was predicted by that model
  3. Backfit new models to explain the strange stuff
  4. Repeat

Seriously, the meme never stops giving.

With that, in this week’s Money Angle, I’m going to go full-Tobias [narrator: you never go full Tobias] and share some macro takes I found resonant in explaining the past several decades.


Money Angle

Since this is macro story-telling I’d consider this entertainment. I’m just picking a story that feels right. These are the re-factored views of Lyn Alden and Cem Karsan.

In Lyn’s March newsletter, we start by rewinding the clock.

  1. The globalized labor arbitrage begins
    Starting in the early 1980s, China began to open its economy to the rest of the world. And then starting in the early 1990s, the Soviet Union collapsed and its various former states also began to open their economies to the world. This combination brought a massive amount of untapped labor into global markets within a rather short period of time, which allowed corporations to geographically arbitrage their operations (a.k.a. offshore a big chunk of their labor force and various facilities) to take advantage of this. This was disadvantageous to laborers and tradespeople in developed markets, and advantageous to executives and shareholders, particularly in the US where we shifted towards massive trade deficits in the 1990s. But it did also help hundreds of millions of people rise out of abject poverty in these developing countries, and created hundreds of millions of new global consumers for those global brands as their wealth grew. China experienced a massive increase in the average standing of living, and so did many former Soviet states.

  2. Bean counters then optimized on the back of this arbitrageAll sorts of management approaches regarding “lean manufacturing” and “just in time delivery” became popular among corporations and MBA programs during this era. Some of these had their roots in the early 20th-century manufacturing revolution (via Ford, Toyota, and others), but they were basically rediscovered, expounded upon, and brought to a new level in the 1980s, 1990s, and 2000s across the entire manufacturing sector.

    Moontower readers will recognize the MBA mindset of selling options. Engineers build beyond spec, or “overengineer”. Biologists know our redundant kidney is an insurance policy.

    We constantly trade slack for efficiency as Moloch whistles by. The balance between efficiency and slack (or efficiency and fairness for that matter) is hard to find. So we can count on overshooting until the “gotchas” show themselves.

    Of course, this was somewhat of an illusion. Companies basically traded away resilience in favor of efficiency, while pretending that there was minimal downside, and yet this type of approach only works under a benign global environment. Outside of the Middle East and a few localized regions around the world, the 1980s through the 2010s was generally a period of limited war as far as supply chains were concerned, with significant global openness and cooperation. Extremely efficient and highly complex supply chains, with limited redundancy or inventory, could thrive in this stars-aligned macro environment. Any company not playing that game would be less efficient in this environment, and thus would be out-competed.

  3. As we enter a new regime, comparisons to recent history are breakingGoing forward, any back-tests about inflation or disinflation that only go back twenty or thirty years are practically useless. This whole 1980s-through-2010s disinflationary period (with one substantial cyclical inflationary burst in the 2000s) was during a backdrop of structurally falling interest rates and increasing globalization, with the sacrifice of resiliency for more efficiency. The world is now looking at the need to duplicate many parts of the supply chain, find and develop potentially redundant sources of commodities, hold higher inventories of everything, and in general boost resilience at the cost of efficiency.

  4. The 1940s as the reference pointI’ve been making a macroeconomic comparison between the 2020s and the 1940s for nearly two years now, and the similarities unfortunately continue to stack up. For the most part, I was referring to monetary and fiscal policy and the long-term debt cycle for that comparison, with charts like this that my readers are quite familiar with by now.

    This unusually wide gap between inflation and interest rates is one of the key reasons I regularly compare the 2020s to the 1940s (rather than primarily the 1970s, despite some other similarities there), and I have been making that comparison for nearly two years before the gap became as wide as it is now.

    Since debt was so high in the 1940s (unlike the 1970s where it was low), and the inflation was driven by fiscal spending and commodity shortages in the 1940s (rather than a demographic boom and commodity shortages as in the 1970s), the Fed held interest rates low even as inflation ran hot in the 1940s (unlike the 1970s where they raised rates to double-digit levels).

  5. Will Russia’s latest adventure hasten the broader movement to diversify away from USD reserves?Diversification of global reserves and payment channels into a more multi-polar reserve currency world, with a renewed emphasis on neutral reserve assets. Much like how COVID-19 accelerated the practice of remote work, I think Russia’s war with Ukraine and the associated sanction response by the West will accelerate that diversification of global reserves and payment channels…In a world where official reserves can be frozen, some degree of reserve diversification would be rational for most countries to consider, and as investors, we should probably expect this to occur over time. This is especially true for countries that are not strongly aligned with the United States and western Europe.

  6. The conundrum facing US policymakers

    Unfortunately for the Fed, the US economic growth rate is already decelerating, and basically the only way to reduce supply-driven inflation with monetary policy is to reduce demand for goods, which is recessionary.

    Credit markets are already weakening, the Treasury market is becoming rather volatile and illiquid, and the Fed has ended quantitative easing. The Fed is likely to continue monetary tightening until financial markets get truly messy, at which point they may reverse course to the dovish side yet again.

    Stagflationary economic conditions are inherently hard for central banks to deal with; stagflation is somewhat outside of their expected models. In fact, the Fed might end up being forced to tighten liquidity with one hand and loosen liquidity with the other hand.

    This is another reason why countries may shift towards gold and other commodities for a portion of their official reserves. Not only can fiat reserves (bonds and deposits) be frozen by foreign countries that issue those liabilities, they also keep getting devalued with interest rates that are far below the prevailing inflation rate because debt levels are too high to raise rates above the inflation level.

We now shift to Cem Karsan. In an interview with Hari Krishnan, Cem discusses how policy in the aftermath of the GFC is misunderstood. This is important because policy is changing, and if you failed to interpret the effect of policy in the last decade, you may be caught flat-footed as the policy changes.

I don’t want to be subtle about the potential problem.

Popular investment strategies have been fit to recent decades. Roboadvisors, 60/40, “model portfolios” and target-date funds are now the default. Once you tell an advisor your age and risk tolerance they strap you into an off-the-shelf glide path and go looking for their next client. And it’s hard to fault them. They have no edge in the alpha game. 60/40 and similar approaches are low-cost, commoditized solutions that allow an advisor to (correctly) not spend time stock-picking. With fee compression in advisory, FAs can defend their net profits by outsourcing the investing portion of the job while focusing on planning and sales. To further cement their incentives, the prisoner’s dilemma of advisory means they can’t stray too far from popular asset allocation prescriptions because the advisors are the one short tracking error volatility.

Lyn believes the macro world is changing sharply. Cem has been beating this drum for the past year at least. Let’s see what he says.

  1. Monetary policy came to dominate because it’s relatively free from political stand-offsMy mental model of macro involves essentially monitoring the Fed (ie monetary policy) and then fiscal policy. We’ve essentially had one of those two major pipes sealed shut for 42 years. Our founding fathers in the US created a system that was purposely made to not change laws quickly or easily. That was fine until the economy became more dynamic and quicker. Congress decided they couldn’t act quickly enough to economic crises. So they created the Federal Reserve but they wanted to control its mandate, to not give it broad latitude. So they created a clear mandate of price stability and maximum employment, and only gave them one tool, — monetary policy. Essentially, there’s only been one game in town because the only way things would ever get past from a fiscal perspective is in a crisis. The monetary solution was faster, so monetary policy has been the only game in town for 42 years.

  2. The nature of loose monetary policy is to encourage investmentMonetary policy is free-market economics, right? It is empowering nature to go about and, and create kind of optimal outcomes. From a growth perspective, that is GDP-maximizing. We have created a technological revolution, almost unintentionally, but by being monetary policy supply-side dominant. We’ve created the Ubers and Amazons and Tesla’s of the world, companies that never would have existed in previous periods because they wouldn’t have had the cash flow to survive. But infinite cash flow ultimately led to longer duration bets. And this is why growth has outperformed value because cash flows haven’t mattered when money is free. If there’s no need to make money, the need is to capture market share and get bigger, to ultimately make money in the long run. You send money to corporations, corporations make more money. Ultimately, that leads to more globalization. If you send money to corporations, what is the corporation’s mandate, by definition, they have to maximize profitability, maximizing profitability means lowering costs of their goods, right and capturing more market share. So that’s the power of competition.

    [This echoes Lyn’s discussion of globalization]

    Remember Moloch’s main trick for fanning unhealthy competition, is to reduce our values to narrow optimizations. When an institution is highly specialized its incentives become perverse from a society-level purview.

    Let’s see why.

  3. Monetary policy didn’t appear to have side effects because the Fed’s narrow mandate failed to consider wider signs of economic vitalityIf you look at incentives, you’ll see the results. The incentives have been to these two simple ideas of price stability and maximum employment. Greenspan realized that the economy had somewhat changed. And that more monetary policy wasn’t causing inflation. It took the natural rate of unemployment down from 6% to 4%. And kept doing more monetary policy, which led to the tech bubble. Without having to worry about inflation their mandate was basically maximum employment. If that’s the case, right? Why wouldn’t you just do more, it’s a free lunch, right. And so the world has had a free lunch now, for 40 years, interest rates have gone lower and lower. Maximum employment has been more and more sticky at the lower end.

    But there was a catch. And it wasn’t the Fed’s job to address it. (In fact, you could argue that thru the “wealth effect” the catch was intended.)

  4. It’s not really the Fed’s fault. The problem is they didn’t have a mandate for inequality, or a lot of other issues.The Fed is permitted to neglect growing gaps in equality. These gaps finally caught up to us during Covid, but this time the government responded. We ran a giant fiscal deficit with PPE loans, extended unemployment benefits, direct transfer payments, rent moratoriums, and general forgiveness. Support for these measures was broad enough to get them passed.

    But perhaps the most important result was the recognition that inequality itself is stark. The keyboard class just hummed along on Zoom, often getting paid more, while having less opportunities to spend. They built up massive savings which if I didn’t know better seems to be conspicuously spent on house overbids and jerking the ladder up with renewed and unprecedented force.

    Let’s turn to Cem’s framing of inequality and why it’s a value we cannot ignore.

    Ultimately this goes back to Socrates. Do you give the best violin players the best violins? Or do you give the worst violin players the best violins? At the end of the day, we’ve given the best violin players the best violins. And Socrates would argue that that’s what you should do, because it creates infinitely beautiful music. But there are a bunch of violin players that don’t get to make music anymore. So we start talking about inequality about 10 years ago, and it’s really built up in five years, and COVID accelerated that trend. Again, all of a sudden, COVID happens. We get that populist kind of reaction, which had been building, what created Donald Trump and created Bernie Sanders. This is not a political statement. The world has become more populist, because of this inequality that’s essentially been created by monetary policy for two generations. And so now the fiscal response is where we are.

    This policy shift is noteworthy for investors. Especially if you have mistaken beliefs about how loose monetary policy affects supply and demand. In the aftermath of the GFC, with the monetary spigot open, the consensus was it would lead to broad inflation.

    Cem offers a counterintuitive explanation that fits what we actually witnessed since the GFC.

  5. The important difference between fiscal and monetary policy — fiscal is inflationary. Monetary, counterintuitively is not.This whole thing is important in terms of the pipes and how everything works. That fiscal policy piece that’s been sealed shut for 40 years now has $12 trillion in fiscal policy. $12 trillion in Fiscal policy is an order of magnitude in real terms bigger than the New Deal. It is about the same size as the new deal when adjusted for the size of the economy. The New Deal filled a hole over a decade, which was called the Great Depression. This is not the Great Depression. We spent about one and a half trillion of that $12 trillion, there’s about $10 trillion still in the pipe to come, and we’re about to reopen.

    So it is not a surprise that we are having inflation. Fiscal policy has a velocity of one, it goes directly into people’s pockets, sometimes even more with things like infrastructure spending. Monetary policy has a velocity of almost zero, it goes directly to “Planet Palo Alto”. And Palo Alto creates new technologies. They’re sophisticated, futuristic people. They provide new self-driving cars and things getting delivered to your doorstep. They create supply. That’s the thing that people don’t understand — monetary policy actually increases supply, it does not increase demand. And so it is deflationary.

  6. The role of the Fed todayWhen the Fed was created, the economy was very different. It was dependent on labor. The trickle-down effects of a laborer getting paid more was enough to counteract those inflationary supply effects. That is no longer the case. So ultimately, the Fed has a mandate, which is completely unreasonable — to control price stability. With supply-side economics, the only way that they can control this ultimately is to pull back. And slow capital markets decrease via the wealth effect. Ultimately, there’s a significant lag, so they are not in a position to ultimately control inflation without bringing down markets.

Cem is saying that raising rates is a blunt tool. It’s a monetary solution to a fundamentally non-monetary problem because it only works on one side of the ledger. Demand. Rate hikes can only reasonably expect to slow the economy by decreasing demand. It doesn’t address the main problem which is a lack of supply to absorb the demand. In fact, it aggravates it. If you believe inflation is a purely monetary phenomenon this is a belated prompt to unlearn that.

How I relate this to MMT

MMT discourse gets lambasted because it appears irresponsibly profligate. Consider the Investopedia definition of modern monetary theory:

Modern Monetary Theory (MMT) is a heterodox macroeconomic framework that says monetarily sovereign countries like the U.S., U.K., Japan, and Canada, which spend, tax, and borrow in a fiat currency that they fully control, are not operationally constrained by revenues when it comes to federal government spending.

Critics of MMT read that as “these crazy MMTers think you can print as much money as you want and spend it”.

This is a strawman. MMT supporters think it’s not useful to think a government is like a household that has to pay its debt back. This isn’t because they are irresponsible. It’s because they recognize that any discussion of whether a certain amount of debt is reasonable, depends on what it is backed by. Debt is neither good nor bad. Its merit depends on what is productive assets back it.

So an MMTer believes you can run a deficit (so government expenditures do not need to be matched with revenues) as long as the expenditures lead to investments in productive capacity. In other words, is the spending creating projects and jobs that will generate a real return? This is hardly unfamiliar logic. When students enroll in medical school, their loans are collateralized by the expectation of increased earnings power that comes with getting “M.D.” after your name. Constraining their current ability to spend by their current earnings would be a horrible loss of economic efficiency.

MMT is deeply focused on inflation

In the MMT world, inflation is a serious topic because a highly inflationary environment is evidence that the spending was not wise. Inflation is a test.

I direct you to my notes on Jesse Livermore’s Upside Down Markets paper on the mechanics of inflation:

Jesse, in a nod to Adam Smith’s invisible hand, calls the inflation the”invisible fist”. The requirement to return principal and interest to a lender constrains the expansion of credit and therefore spending power. Unproductive spending will lead to the destruction of financial wealth. If I borrowed money for a lemonade stand but then spent it on a vacation, my deficit spending will have created new financial wealth for the system, but it won’t have created any new real wealth. I won’t receive future cash flows to repay the loan.

The first place where the invisible fist will destroy financial wealth will be on my personal balance sheet. I originally accounted for the business as a new financial asset that offset the new liability that I had taken on. If that new financial asset never comes into existence, or if it turns out to be worthless, then it’s going to get written off. I’m going to end up with a new liability and nothing else—a negative cumulative hit to my net worth. The next place where the invisible fist will destroy financial wealth will be on the lender’s balance sheet. The loan will get defaulted on. In a full default, the lender will suffer a hit to his financial wealth equivalent in size to the financial wealth that I added to the balance sheets of the people that I bought the vacations from. The lender will experience an associated decrease in his spending power, compensating for the increase in spending power that my unproductive vacation expenditures will have conferred onto those people. In the end, the total financial wealth and spending power in the system will be conserved. The invisible fist will not allow them to enjoy sustained increases, since the real wealth in the system—its capacity to fulfill spending—did not increase. In this way, the invisible fist will prevent an inflationary outcome in which the supply of financial wealth overwhelms the supply of real wealth.

One of the leading MMT theorists, Stephanie Kelton, explains that, if anything, the MMT crowd takes inflation more seriously than mainstream economics. This makes sense if inflation, not the size of the deficit, is the true cause for concern.

In We Need to Think Harder About Inflation, she writes:

It’s the typically cavalier way of thinking about inflation that has come to dominate mainstream economics. Keeping a lid on inflation is the central bank’s job, not something Congress, the White House, or anyone else really needs to waste time thinking about. If inflation accelerates above some desired target, the Fed will knock it back down by tightening monetary policy. Easy peasy. (Unless, of course, the Fed “falls behind the curve,” allowing “inflation expectations to become unanchored” and other mumbo-jumbo.)

All you really need is an “independent” central bank that is deemed “credible” by market participants, and you can sit back and relax. There’s a one-size-fits-all way to deal with any inflation problem. To dial inflation down, simply dial up the overnight interest rate. You might throw in some “forward guidance” to help shape “inflation expectations” but that’s really still about managing inflation via adjustments in the short-term interest rate…

It’s this sort of cavalier attitude and reverence for monetary policy that troubles me. We’re supposed to accept—as a matter of faith—that the central bank can always handle any inflation problem because mainstream economics says so?

The “invisible fist” today

So have we plowed too much money into unproductive projects? Have we overpaid for the projects and startups? The market tries to sort the question out every day.

In keeping any sense of proportion we should recognize that crypto is a tiny portion of the overall economy. But as a metaphor, it poses an interesting question. Have we dumped too much money into cat gifs, figuratively speaking? Are a few becoming insanely rich while society holds the bag?

I’m partial to Michael Pettis’ idea of the bezzle. In Minsky Moments in Venture CapitalAbraham Thomas explains how bezzle conditions emergeThe key insight is that high prices create a positive feedback loop because prices themselves tell you something about risk. High prices signify safety. This is a paradox because a high price is also an asymmetric risk to reward. The paradox tends to resolve itself abruptly:

One way to understand Minsky cycles is that they’re driven by the gap between ‘measured risk’ and ‘true risk’.

When you lend money, the ‘true risk’ you take is that the borrower defaults3. But you can’t know this directly; instead you measure it by proxy, using credit spreads. Credit spreads reflect default probabilities, but they also reflect investor demand for credit products. A subprime credit trading at a tight spread doesn’t necessarily imply that subprime loans have become less risky (though that could be true); the tight spread may also be driven by demand for subprime loans. Measured risk has deviated from true risk.

Similarly, when you invest in a startup, the ‘true risk’ that you take is that the startup fails. But you can’t know this directly; instead you measure it by proxy, using markups. Markups reflect inverse failure probabilities (the higher and faster the markup, the more successful the company, and hence the less likely it is to fail — at least, so one hopes). But markups also reflect investor demand for startup equity. Once again, measured risk has deviated from true risk.

During Minsky booms, measured risks decline. During Minsky busts, measured risks increase. The flip from boom to bust occurs when the market realizes that true risks haven’t gone away.

Squaring all of this with my own priors

We started with Lyn and Cem’s analysis of how we got to today. If the world de-globalizes many of the deflationary headwinds that convolved with loose monetary policy will reverse. The new regime would be inflationary. How inflationary is anyone’s guess. Is the floor for the foreseeable future 2%, 4%, higher?

If bubbles pop and bezzles recede, would that make inflation worse as we discover that spending was wasted and economic supply did not grow where it needed to (ahem housing and energy)?

Or will deflation come roaring back as drawdowns push wealth effects in reverse and higher borrowing costs on huge loan balances crowd out future growth?

My prior is torn between:

a) inflation will fall in a way that surprises people. Low inflation is actually the default because wealth inequality acts as what I call an “inflation heat sink”. Here’s my explanation using the boardgame Monopoly:

Unfortunately, if you think inflation is going to fall the trade is probably not to buy treasuries since real rates are already quite negative. The related insight is more concerning. Bonds can keep falling as inflation falls and nothing would be glaringly mispriced. Ouch, 60/40.

and

b) Stimulative fiscal policy is inflationary in the short-run (and in the long-run if the spending is unproductive) and while fiscal policy is highly political, neither party is afraid to run big deficits at this point anymore.

If inflation accelerates (or at least fails to abate) it’s not clear what investments it would be good for. People like to promote real estate as an inflation hedge. Given the low affordability already built into prices, outpacing real rates is hardly a given. Maybe that’s where you lose the least? What inflation expectations are already embedded in commodity prices? How to invest for inflation from current prices is a hard problem.

Unwinding imbalances

I tend to believe Lyn and Cem’s story about how the forces that brought us to today are unwinding. If we have spent the past 40 years building a giant imbalance between capital and labor this reversal is ultimately a good thing. But it’s not going to make capital happy. If you have been an outsize winner for the past decade, you’re probably going to moan about it when the imbalance narrows (hey it’s understandable that we respond to marginal changes to our situation, but it’s not reasonable to miss the big picture that prior wins have been out of proportion to contribution). What was given to you easily by the Fed’s support of high duration bets, can be taken away. Don’t expect sympathy.

The most direct way to correct the imbalance would be to heavily tax high earners and the rich but it’s not politically viable. But there’s a backdoor. The combination of fiscal stimulus, especially if done in a progressive way, will bolster the economy while we raise interest rates. The net effect will offset labor’s pain in an economic slowdown. But it will still be inflationary since we are supporting demand (by giving $$ to those who actually spend it) while constraining supply (by raising hurdle rates on capital expenditures). To a rich person invested in growth and expensive real estate, this will feel like stagflation as labor’s slice of the pie increases relatively while demand for the rich person’s assets slows (opposite of how loose monetary conditions created inflation for homes and stocks but not labor and importable goods). It would be a shadow progressive tax using inflation to take back financial wealth while creating conditions for lower-wage earners to keep up with the price of goods and services.

No matter how the economic picture unfolds, the theme that feels alive under the surface is imbalance. It doesn’t matter that the average American lives better than a 16th-century king. We relentlessly compare and that’s never going to stop. The imbalance matters. We have accumulated massive amounts of debt. If the debt isn’t truly backed by the collective wealth of the individuals who make up the economy, eventually a catalyst will shatter the illusion that we can continue rolling it over.

Mechanically, that debt is of course backed by the sum of our assets. But when push comes to shove, how is it apportioned? What is the fair attribution? Do our anti-trust laws and tax policy divide the risk and rewards fairly (whatever that means from an equitable and efficiency perspective)? It’s not as easy as saying “the market gets this right”. The rules are political. Power is not accorded solely due to merit (whatever that means). So sure, the debt is backed by our assets, but good luck calling the loans back in.

I recently re-watched Ray Dalio’s How The Economic Machine Works. I assigned it to some young teens who are trying to learn about the economy. The video shows how the macroeconomy is built up from everyday transactions. A loan (ie credit) is one such transaction. The credit cycle is endemic to the economy itself. Dalio overlays the short-term credit cycle (small squiggles) on the long-run cycle.

(credit: the hatchfund.com)

The end of long-term debt cycles are times of massive upheaval. Historically this has meant violence, currency devaluations, and victors dividing the spoils regardless of who was previously listed as a creditor.

Dalio, uses a highly understated word for this adjustment. Deleveraging. The default process (whether outright or via inflation) is redistributive. Politics determines the winners and losers. It’s always been give and take. But we need to keep talking.

If we cannot find a way to cooperate, the problem of imbalance and feelings of injustice don’t just disappear.

Redistribution finds a way.


Addendum

I realize MMT is a polarizing topic. I have a cursory understanding of it, so feel free to correct me: I think the core insight that a government doesn’t need to run like a household is correct mechanically. The problem is how the debt is allocated to the citizens in the form of taxes and transfer payments. So from a policy point of view, I don’t know if MMT frameworks lead to effective practical policy. Effective is always a matter of debate and depends on your constituency’s perspective. In that sense, MMT is no different than any other framework that claims to have good reasons for how it grows and splits the pie.

The great personal dividend of MMT is how it popularized the sectoral balances approach to understanding the economy. Similar to Dalio’s video, it views the economy as a collection of small transactions. Since every buy is someone else’s sell, we can use a giant T account of credits and debits to understand the economy from basic accounting. Those credits and debits flow through the household, government, corporate and “foreign sectors”. Economists associated with this approach include Godley, Pettis, Kalecki, and Levy.

To demonstrate the power of this lens, I encourage you to read Jesse Livermore’s Upside Down Markets paper. It completely reshaped my understanding of macro into something that I believe is closer to reality. Whenever I hear a macro argument, I at least try to place it within the sectoral balances framework to see if it is at least self-consistent. The advantage of basic accounting identities is they are identities. They are tautologically true and that’s a useful razor for an initially evaluating an argument.

Jesse’s paper is a beast. Many people won’t read a 40k word paper. I encourage everyone to read this one. While it’s a dense exploration of timely macroeconomics ideas, Jesse’s rare ability to tackle the complexity in an approachable, step-by-step progression is an amazing opportunity to learn.

Having said that, I realize many people still won’t read the paper. So I decided to try my hand at creating this explainer. I completely re-factored it to turn it into a personal reference. You can use it too:

✍️Moontower Guide To Jesse Livermore’s Upside Down Markets (link)

Moontower #148

Here’s a rarity for this letter. Let’s play macroeconomics.

I don’t usually write about “macro” because it feels like astrology. You can look at any bit of data (the “current thing” as they say on the internet is inflation) and see it molded to be the cause or result of whatever axe a speaker is trying to grind. People who just learned what inflation was on Tuesday have incorporated it into their pre-existing worldview so seamlessly that by Friday their updated narrative is more coherent than ever.

Macro is the raw material for story-telling. For marketing. It’s a political battering ram for both sides. But macro is a ball of yarn. The discourse that’s consumable is reduced so much to aid absorption that the logic, by necessity, ends up sounding unassailable. It must. The logic is solving for convenience. Not understanding.

So I don’t write about it because I don’t think it’s especially useful. It’s more likely to give you brainworms by beefing up your priors. It will calcify hunches into commandments when the evidence only merits “things to learn more about”.

“Buy Potatoes”

While I don’t write about macro, I’m hardly immune to the animal urge to read about it and pretend I understand how the world works. My mind’s sentry just keeps me from taking it too seriously. [I suspect the sentry has saved me many times and cost me many times and I can’t tell if it’s worth the free rent it gets in my head. The question is moot, since I can’t evict it anyway. It’s like SF up in there.]

My first macro boner happened (was searching for the right verb here and “happens” is the most fitting action word to apply to boners) while reading Michael Lewis’ Liar’s Poker when I was 21. When Michael was a junior salesperson on the Salomon trading desk, he was taken under the wing of a senior trader named Alexander:

The second pattern to Alexander’s thought was that in the event of a major dislocation, such as a stock market crash, a natural disaster, the breakdown of OPEC’s production agreements, he would look away from the initial focus of investor interest and seek secondary and tertiary effects.

Remember Chernobyl? When news broke that the Soviet nuclear reactor had exploded, Alexander called. Only minutes before, confir mation of the disaster had blipped across our Quotron machines, yet Alexander had already bought the equivalent of two supertankers of crude oil. The focus of investor attention was on the New York Stock Exchange, he said. In particular it was on any company involved in nuclear power. The stocks of those companies were plummeting. Never mind that, he said. He had just purchased, on behalf of his clients, oil futures. Instantly in his mind less supply of nuclear power equaled more demand for oil, and he was right. His investors made a large killing. Mine made a small killing. Minutes after I had persuaded a few clients to buy some oil, Alexander called back.

“Buy potatoes,” he said. “Gotta hop.” Then he hung up. Of course. A cloud of fallout would threaten European food and water supplies, including the potato crop, placing a premium on uncon taminated American substitutes. Perhaps a few folks other than potato farmers think of the price of potatoes in America minutes after the explosion of a nuclear reactor in Russian, but I have never met them.

But Chernobyl and oil are a comparatively straightforward example. There was a game we played called What if? All sorts of complications can be introduced into What if? Imagine, for example, you are an institutional investor managing several billion dollars. What if there is a massive earthquake in Tokyo? Tokyo is reduced to rubble. Investors in Japan panic. They are selling yen and trying to get their money out of the Japanese stock market. What do you do?

Well, along the lines of pattern number one, what Alexander would do is put money into Japan on the assumption that since everyone was trying to get out, there must be some bargains. He would buy precisely those securities in Japan that appeared the least desirable to others. First, the stocks of Japanese insurance companies. The world would probably assume that ordinary insurance companies had a great deal of exposure…

If you are 21 years old today, how can you not hear “buy potatoes” and not think of trading as Settlers of Catan? Trading is the ultimate boardgame. It’s just that now, an algo sweeps all the call offers on Brent futures before Alexander finishes reading the headline. [Actually, the market-makers’ streaming call offers have a “panic” setting that gets triggered if they get hit on more than couple related strikes at a time and pull their co-located quotes before they get picked off by the news-reading algo. So prices can gap to something closer to fair value on very little trading volume. The graveyard of backtesting signals that don’t appreciate this would occupy every blade of grass on the planet if it were a physical place].

The blessing and curse of our frontal lobes is a desire to understand how the complex world works. Macro brings the romance of chess to investing. It lures mandate-dodging pros and tourists alike with scalable p/l if you can:

a) make accurate predictions

and

b) identify mispriced lines with respect to those predictions.

In reality, it’s more like 3-card Monte where you have no chance of guessing where the card is and if you get lucky the reward is the false confidence to wager more next time. [I highly recommend the Wikipedia for 3-card Monte. The analogy of “marks” and “shills” to the finance marketing machine writes itself].

My personal relationship with macro is as follows:

  1. I’ve got some mental model of how things work
  2. Stuff happens — none of it was predicted by that model
  3. Backfit new models to explain the strange stuff
  4. Repeat

Seriously, the meme never stops giving.

With that, in this week’s Money Angle, I’m going to go full-Tobias [narrator: you never go full Tobias] and share some macro takes I found resonant in explaining the past several decades.


Money Angle

Since this is macro story-telling I’d consider this entertainment. I’m just picking a story that feels right. These are the re-factored views of Lyn Alden and Cem Karsan.

In Lyn’s March newsletter, we start by rewinding the clock.

  1. The globalized labor arbitrage begins


    Starting in the early 1980s, China began to open its economy to the rest of the world. And then starting in the early 1990s, the Soviet Union collapsed and its various former states also began to open their economies to the world. This combination brought a massive amount of untapped labor into global markets within a rather short period of time, which allowed corporations to geographically arbitrage their operations (a.k.a. offshore a big chunk of their labor force and various facilities) to take advantage of this. This was disadvantageous to laborers and tradespeople in developed markets, and advantageous to executives and shareholders, particularly in the US where we shifted towards massive trade deficits in the 1990s. But it did also help hundreds of millions of people rise out of abject poverty in these developing countries, and created hundreds of millions of new global consumers for those global brands as their wealth grew. China experienced a massive increase in the average standing of living, and so did many former Soviet states.

  2. Bean counters then optimized on the back of this arbitrage

    All sorts of management approaches regarding “lean manufacturing” and “just in time delivery” became popular among corporations and MBA programs during this era. Some of these had their roots in the early 20th-century manufacturing revolution (via Ford, Toyota, and others), but they were basically rediscovered, expounded upon, and brought to a new level in the 1980s, 1990s, and 2000s across the entire manufacturing sector.

    Moontower readers will recognize the MBA mindset of selling options. Engineers build beyond spec, or “overengineer”. Biologists know our redundant kidney is an insurance policy.

    We constantly trade slack for efficiency as Moloch whistles by. The balance between efficiency and slack (or efficiency and fairness for that matter) is hard to find. So we can count on overshooting until the “gotchas” show themselves.

    Of course, this was somewhat of an illusion. Companies basically traded away resilience in favor of efficiency, while pretending that there was minimal downside, and yet this type of approach only works under a benign global environment. Outside of the Middle East and a few localized regions around the world, the 1980s through the 2010s was generally a period of limited war as far as supply chains were concerned, with significant global openness and cooperation. Extremely efficient and highly complex supply chains, with limited redundancy or inventory, could thrive in this stars-aligned macro environment. Any company not playing that game would be less efficient in this environment, and thus would be out-competed.

  3. As we enter a new regime, comparisons to recent history are breaking

    Going forward, any back-tests about inflation or disinflation that only go back twenty or thirty years are practically useless. This whole 1980s-through-2010s disinflationary period (with one substantial cyclical inflationary burst in the 2000s) was during a backdrop of structurally falling interest rates and increasing globalization, with the sacrifice of resiliency for more efficiency. The world is now looking at the need to duplicate many parts of the supply chain, find and develop potentially redundant sources of commodities, hold higher inventories of everything, and in general boost resilience at the cost of efficiency.

  4. The 1940s as the reference point

    I’ve been making a macroeconomic comparison between the 2020s and the 1940s for nearly two years now, and the similarities unfortunately continue to stack up. For the most part, I was referring to monetary and fiscal policy and the long-term debt cycle for that comparison, with charts like this that my readers are quite familiar with by now.

    This unusually wide gap between inflation and interest rates is one of the key reasons I regularly compare the 2020s to the 1940s (rather than primarily the 1970s, despite some other similarities there), and I have been making that comparison for nearly two years before the gap became as wide as it is now.

    Since debt was so high in the 1940s (unlike the 1970s where it was low), and the inflation was driven by fiscal spending and commodity shortages in the 1940s (rather than a demographic boom and commodity shortages as in the 1970s), the Fed held interest rates low even as inflation ran hot in the 1940s (unlike the 1970s where they raised rates to double-digit levels).

  5. Will Russia’s latest adventure hasten the broader movement to diversify away from USD reserves?

    Diversification of global reserves and payment channels into a more multi-polar reserve currency world, with a renewed emphasis on neutral reserve assets. Much like how COVID-19 accelerated the practice of remote work, I think Russia’s war with Ukraine and the associated sanction response by the West will accelerate that diversification of global reserves and payment channels…In a world where official reserves can be frozen, some degree of reserve diversification would be rational for most countries to consider, and as investors, we should probably expect this to occur over time. This is especially true for countries that are not strongly aligned with the United States and western Europe.

  6. The conundrum facing US policymakers

    Unfortunately for the Fed, the US economic growth rate is already decelerating, and basically the only way to reduce supply-driven inflation with monetary policy is to reduce demand for goods, which is recessionary.

    Credit markets are already weakening, the Treasury market is becoming rather volatile and illiquid, and the Fed has ended quantitative easing. The Fed is likely to continue monetary tightening until financial markets get truly messy, at which point they may reverse course to the dovish side yet again.

    Stagflationary economic conditions are inherently hard for central banks to deal with; stagflation is somewhat outside of their expected models. In fact, the Fed might end up being forced to tighten liquidity with one hand and loosen liquidity with the other hand.

    This is another reason why countries may shift towards gold and other commodities for a portion of their official reserves. Not only can fiat reserves (bonds and deposits) be frozen by foreign countries that issue those liabilities, they also keep getting devalued with interest rates that are far below the prevailing inflation rate because debt levels are too high to raise rates above the inflation level.

We now shift to Cem Karsan. In an interview with Hari Krishnan, Cem discusses how policy in the aftermath of the GFC is misunderstood. This is important because policy is changing, and if you failed to interpret the effect of policy in the last decade, you may be caught flat-footed as the policy changes.

I don’t want to be subtle about the potential problem.

Popular investment strategies have been fit to recent decades. Roboadvisors, 60/40, “model portfolios” and target-date funds are now the default. Once you tell an advisor your age and risk tolerance they strap you into an off-the-shelf glide path and go looking for their next client. And it’s hard to fault them. They have no edge in the alpha game. 60/40 and similar approaches are low-cost, commoditized solutions that allow an advisor to (correctly) not spend time stock-picking. With fee compression in advisory, FAs can defend their net profits by outsourcing the investing portion of the job while focusing on planning and sales. To further cement their incentives, the prisoner’s dilemma of advisory means they can’t stray too far from popular asset allocation prescriptions because the advisors are the one short tracking error volatility.

Lyn believes the macro world is changing sharply. Cem has been beating this drum for the past year at least. Let’s see what he says.

  1. Monetary policy came to dominate because it’s relatively free from political stand-offs

    My mental model of macro involves essentially monitoring the Fed (ie monetary policy) and then fiscal policy. We’ve essentially had one of those two major pipes sealed shut for 42 years. Our founding fathers in the US created a system that was purposely made to not change laws quickly or easily. That was fine until the economy became more dynamic and quicker. Congress decided they couldn’t act quickly enough to economic crises. So they created the Federal Reserve but they wanted to control its mandate, to not give it broad latitude. So they created a clear mandate of price stability and maximum employment, and only gave them one tool, — monetary policy. Essentially, there’s only been one game in town because the only way things would ever get past from a fiscal perspective is in a crisis. The monetary solution was faster, so monetary policy has been the only game in town for 42 years.

  2. The nature of loose monetary policy is to encourage investment

    Monetary policy is free-market economics, right? It is empowering nature to go about and, and create kind of optimal outcomes. From a growth perspective, that is GDP-maximizing. We have created a technological revolution, almost unintentionally, but by being monetary policy supply-side dominant. We’ve created the Ubers and Amazons and Tesla’s of the world, companies that never would have existed in previous periods because they wouldn’t have had the cash flow to survive. But infinite cash flow ultimately led to longer duration bets. And this is why growth has outperformed value because cash flows haven’t mattered when money is free. If there’s no need to make money, the need is to capture market share and get bigger, to ultimately make money in the long run. You send money to corporations, corporations make more money. Ultimately, that leads to more globalization. If you send money to corporations, what is the corporation’s mandate, by definition, they have to maximize profitability, maximizing profitability means lowering costs of their goods, right and capturing more market share. So that’s the power of competition.

    [This echoes Lyn’s discussion of globalization]

    Remember Moloch’s main trick for fanning unhealthy competition, is to reduce our values to narrow optimizations. When an institution is highly specialized its incentives become perverse from a society-level purview.

    Let’s see why.

  3. Monetary policy didn’t appear to have side effects because the Fed’s narrow mandate failed to consider wider signs of economic vitality

    If you look at incentives, you’ll see the results. The incentives have been to these two simple ideas of price stability and maximum employment. Greenspan realized that the economy had somewhat changed. And that more monetary policy wasn’t causing inflation. It took the natural rate of unemployment down from 6% to 4%. And kept doing more monetary policy, which led to the tech bubble. Without having to worry about inflation their mandate was basically maximum employment. If that’s the case, right? Why wouldn’t you just do more, it’s a free lunch, right. And so the world has had a free lunch now, for 40 years, interest rates have gone lower and lower. Maximum employment has been more and more sticky at the lower end.

    But there was a catch. And it wasn’t the Fed’s job to address it. (In fact, you could argue that thru the “wealth effect” the catch was intended.)

  4. It’s not really the Fed’s fault. The problem is they didn’t have a mandate for inequality, or a lot of other issues.

    The Fed is permitted to neglect growing gaps in equality. These gaps finally caught up to us during Covid, but this time the government responded. We ran a giant fiscal deficit with PPE loans, extended unemployment benefits, direct transfer payments, rent moratoriums, and general forgiveness. Support for these measures was broad enough to get them passed.

    But perhaps the most important result was the recognition that inequality itself is stark. The keyboard class just hummed along on Zoom, often getting paid more, while having less opportunities to spend. They built up massive savings which if I didn’t know better seems to be conspicuously spent on house overbids and jerking the ladder up with renewed and unprecedented force.

    Let’s turn to Cem’s framing of inequality and why it’s a value we cannot ignore.

    Ultimately this goes back to Socrates. Do you give the best violin players the best violins? Or do you give the worst violin players the best violins? At the end of the day, we’ve given the best violin players the best violins. And Socrates would argue that that’s what you should do, because it creates infinitely beautiful music. But there are a bunch of violin players that don’t get to make music anymore. So we start talking about inequality about 10 years ago, and it’s really built up in five years, and COVID accelerated that trend. Again, all of a sudden, COVID happens. We get that populist kind of reaction, which had been building, what created Donald Trump and created Bernie Sanders. This is not a political statement. The world has become more populist, because of this inequality that’s essentially been created by monetary policy for two generations. And so now the fiscal response is where we are.

    This policy shift is noteworthy for investors. Especially if you have mistaken beliefs about how loose monetary policy affects supply and demand. In the aftermath of the GFC, with the monetary spigot open, the consensus was it would lead to broad inflation.

    Cem offers a counterintuitive explanation that fits what we actually witnessed since the GFC.

  5. The important difference between fiscal and monetary policy — fiscal is inflationary. Monetary, counterintuitively is not.

    This whole thing is important in terms of the pipes and how everything works. That fiscal policy piece that’s been sealed shut for 40 years now has $12 trillion in fiscal policy. $12 trillion in Fiscal policy is an order of magnitude in real terms bigger than the New Deal. It is about the same size as the new deal when adjusted for the size of the economy. The New Deal filled a hole over a decade, which was called the Great Depression. This is not the Great Depression. We spent about one and a half trillion of that $12 trillion, there’s about $10 trillion still in the pipe to come, and we’re about to reopen.

    So it is not a surprise that we are having inflation. Fiscal policy has a velocity of one, it goes directly into people’s pockets, sometimes even more with things like infrastructure spending. Monetary policy has a velocity of almost zero, it goes directly to “Planet Palo Alto”. And Palo Alto creates new technologies. They’re sophisticated, futuristic people. They provide new self-driving cars and things getting delivered to your doorstep. They create supply. That’s the thing that people don’t understand — monetary policy actually increases supply, it does not increase demand. And so it is deflationary.

  6. The role of the Fed today

    When the Fed was created, the economy was very different. It was dependent on labor. The trickle-down effects of a laborer getting paid more was enough to counteract those inflationary supply effects. That is no longer the case. So ultimately, the Fed has a mandate, which is completely unreasonable — to control price stability. With supply-side economics, the only way that they can control this ultimately is to pull back. And slow capital markets decrease via the wealth effect. Ultimately, there’s a significant lag, so they are not in a position to ultimately control inflation without bringing down markets.

Cem is saying that raising rates is a blunt tool. It’s a monetary solution to a fundamentally non-monetary problem because it only works on one side of the ledger. Demand. Rate hikes can only reasonably expect to slow the economy by decreasing demand. It doesn’t address the main problem which is a lack of supply to absorb the demand. In fact, it aggravates it. If you believe inflation is a purely monetary phenomenon this is a belated prompt to unlearn that.

How I relate this to MMT

MMT discourse gets lambasted because it appears irresponsibly profligate. Consider the Investopedia definition of modern monetary theory:

Modern Monetary Theory (MMT) is a heterodox macroeconomic framework that says monetarily sovereign countries like the U.S., U.K., Japan, and Canada, which spend, tax, and borrow in a fiat currency that they fully control, are not operationally constrained by revenues when it comes to federal government spending.

Critics of MMT read that as “these crazy MMTers think you can print as much money as you want and spend it”.

This is a strawman. MMT supporters think it’s not useful to think a government is like a household that has to pay its debt back. This isn’t because they are irresponsible. It’s because they recognize that any discussion of whether a certain amount of debt is reasonable, depends on what it is backed by. Debt is neither good nor bad. Its merit depends on what is productive assets back it.

So an MMTer believes you can run a deficit (so government expenditures do not need to be matched with revenues) as long as the expenditures lead to investments in productive capacity. In other words, is the spending creating projects and jobs that will generate a real return? This is hardly unfamiliar logic. When students enroll in medical school, their loans are collateralized by the expectation of increased earnings power that comes with getting “M.D.” after your name. Constraining their current ability to spend by their current earnings would be a horrible loss of economic efficiency.

MMT is deeply focused on inflation

In the MMT world, inflation is a serious topic because a highly inflationary environment is evidence that the spending was not wise. Inflation is a test.

I direct you to my notes on Jesse Livermore’s Upside Down Markets paper on the mechanics of inflation:

Jesse, in a nod to Adam Smith’s invisible hand, calls the inflation the”invisible fist”. The requirement to return principal and interest to a lender constrains the expansion of credit and therefore spending power. Unproductive spending will lead to the destruction of financial wealth. If I borrowed money for a lemonade stand but then spent it on a vacation, my deficit spending will have created new financial wealth for the system, but it won’t have created any new real wealth. I won’t receive future cash flows to repay the loan.

The first place where the invisible fist will destroy financial wealth will be on my personal balance sheet. I originally accounted for the business as a new financial asset that offset the new liability that I had taken on. If that new financial asset never comes into existence, or if it turns out to be worthless, then it’s going to get written off. I’m going to end up with a new liability and nothing else—a negative cumulative hit to my net worth. The next place where the invisible fist will destroy financial wealth will be on the lender’s balance sheet. The loan will get defaulted on. In a full default, the lender will suffer a hit to his financial wealth equivalent in size to the financial wealth that I added to the balance sheets of the people that I bought the vacations from. The lender will experience an associated decrease in his spending power, compensating for the increase in spending power that my unproductive vacation expenditures will have conferred onto those people. In the end, the total financial wealth and spending power in the system will be conserved. The invisible fist will not allow them to enjoy sustained increases, since the real wealth in the system—its capacity to fulfill spending—did not increase. In this way, the invisible fist will prevent an inflationary outcome in which the supply of financial wealth overwhelms the supply of real wealth.

One of the leading MMT theorists, Stephanie Kelton, explains that, if anything, the MMT crowd takes inflation more seriously than mainstream economics. This makes sense if inflation, not the size of the deficit, is the true cause for concern.

In We Need to Think Harder About Inflation, she writes:

It’s the typically cavalier way of thinking about inflation that has come to dominate mainstream economics. Keeping a lid on inflation is the central bank’s job, not something Congress, the White House, or anyone else really needs to waste time thinking about. If inflation accelerates above some desired target, the Fed will knock it back down by tightening monetary policy. Easy peasy. (Unless, of course, the Fed “falls behind the curve,” allowing “inflation expectations to become unanchored” and other mumbo-jumbo.)

All you really need is an “independent” central bank that is deemed “credible” by market participants, and you can sit back and relax. There’s a one-size-fits-all way to deal with any inflation problem. To dial inflation down, simply dial up the overnight interest rate. You might throw in some “forward guidance” to help shape “inflation expectations” but that’s really still about managing inflation via adjustments in the short-term interest rate…

It’s this sort of cavalier attitude and reverence for monetary policy that troubles me. We’re supposed to accept—as a matter of faith—that the central bank can always handle any inflation problem because mainstream economics says so?

The “invisible fist” today

So have we plowed too much money into unproductive projects? Have we overpaid for the projects and startups? The market tries to sort the question out every day.

In keeping any sense of proportion we should recognize that crypto is a tiny portion of the overall economy. But as a metaphor, it poses an interesting question. Have we dumped too much money into cat gifs, figuratively speaking? Are a few becoming insanely rich while society holds the bag?

I’m partial to Michael Pettis’ idea of the bezzle. In Minsky Moments in Venture CapitalAbraham Thomas explains how bezzle conditions emergeThe key insight is that high prices create a positive feedback loop because prices themselves tell you something about risk. High prices signify safety. This is a paradox because a high price is also an asymmetric risk to reward. The paradox tends to resolve itself abruptly:

One way to understand Minsky cycles is that they’re driven by the gap between ‘measured risk’ and ‘true risk’.

When you lend money, the ‘true risk’ you take is that the borrower defaults3. But you can’t know this directly; instead you measure it by proxy, using credit spreads. Credit spreads reflect default probabilities, but they also reflect investor demand for credit products. A subprime credit trading at a tight spread doesn’t necessarily imply that subprime loans have become less risky (though that could be true); the tight spread may also be driven by demand for subprime loans. Measured risk has deviated from true risk.

Similarly, when you invest in a startup, the ‘true risk’ that you take is that the startup fails. But you can’t know this directly; instead you measure it by proxy, using markups. Markups reflect inverse failure probabilities (the higher and faster the markup, the more successful the company, and hence the less likely it is to fail — at least, so one hopes). But markups also reflect investor demand for startup equity. Once again, measured risk has deviated from true risk.

During Minsky booms, measured risks decline. During Minsky busts, measured risks increase. The flip from boom to bust occurs when the market realizes that true risks haven’t gone away.

Squaring all of this with my own priors

We started with Lyn and Cem’s analysis of how we got to today. If the world de-globalizes many of the deflationary headwinds that convolved with loose monetary policy will reverse. The new regime would be inflationary. How inflationary is anyone’s guess. Is the floor for the foreseeable future 2%, 4%, higher?

If bubbles pop and bezzles recede, would that make inflation worse as we discover that spending was wasted and economic supply did not grow where it needed to (ahem housing and energy)?

Or will deflation come roaring back as drawdowns push wealth effects in reverse and higher borrowing costs on huge loan balances crowd out future growth?

My prior is torn between:

a) inflation will fall in a way that surprises people. Low inflation is actually the default because wealth inequality acts as what I call an “inflation heat sink”. Here’s my explanation using the boardgame Monopoly:

Unfortunately, if you think inflation is going to fall the trade is probably not to buy treasuries since real rates are already quite negative. The related insight is more concerning. Bonds can keep falling as inflation falls and nothing would be glaringly mispriced. Ouch, 60/40.

and

b) Stimulative fiscal policy is inflationary in the short-run (and in the long-run if the spending is unproductive) and while fiscal policy is highly political, neither party is afraid to run big deficits at this point anymore.

If inflation accelerates (or at least fails to abate) it’s not clear what investments it would be good for. People like to promote real estate as an inflation hedge. Given the low affordability already built into prices, outpacing real rates is hardly a given. Maybe that’s where you lose the least? What inflation expectations are already embedded in commodity prices? How to invest for inflation from current prices is a hard problem.

Unwinding imbalances

I tend to believe Lyn and Cem’s story about how the forces that brought us to today are unwinding. If we have spent the past 40 years building a giant imbalance between capital and labor this reversal is ultimately a good thing. But it’s not going to make capital happy. If you have been an outsize winner for the past decade, you’re probably going to moan about it when the imbalance narrows (hey it’s understandable that we respond to marginal changes to our situation, but it’s not reasonable to miss the big picture that prior wins have been out of proportion to contribution). What was given to you easily by the Fed’s support of high duration bets, can be taken away. Don’t expect sympathy.

The most direct way to correct the imbalance would be to heavily tax high earners and the rich but it’s not politically viable. But there’s a backdoor. The combination of fiscal stimulus, especially if done in a progressive way, will bolster the economy while we raise interest rates. The net effect will offset labor’s pain in an economic slowdown. But it will still be inflationary since we are supporting demand (by giving $$ to those who actually spend it) while constraining supply (by raising hurdle rates on capital expenditures). To a rich person invested in growth and expensive real estate, this will feel like stagflation as labor’s slice of the pie increases relatively while demand for the rich person’s assets slows (opposite of how loose monetary conditions created inflation for homes and stocks but not labor and importable goods). It would be a shadow progressive tax using inflation to take back financial wealth while creating conditions for lower-wage earners to keep up with the price of goods and services.

No matter how the economic picture unfolds, the theme that feels alive under the surface is imbalance. It doesn’t matter that the average American lives better than a 16th-century king. We relentlessly compare and that’s never going to stop. The imbalance matters. We have accumulated massive amounts of debt. If the debt isn’t truly backed by the collective wealth of the individuals who make up the economy, eventually a catalyst will shatter the illusion that we can continue rolling it over.

Mechanically, that debt is of course backed by the sum of our assets. But when push comes to shove, how is it apportioned? What is the fair attribution? Do our anti-trust laws and tax policy divide the risk and rewards fairly (whatever that means from an equitable and efficiency perspective)? It’s not as easy as saying “the market gets this right”. The rules are political. Power is not accorded solely due to merit (whatever that means). So sure, the debt is backed by our assets, but good luck calling the loans back in.

I recently re-watched Ray Dalio’s How The Economic Machine Works. I assigned it to some young teens who are trying to learn about the economy. The video shows how the macroeconomy is built up from everyday transactions. A loan (ie credit) is one such transaction. The credit cycle is endemic to the economy itself. Dalio overlays the short-term credit cycle (small squiggles) on the long-run cycle.

(credit: the hatchfund.com)

The end of long-term debt cycles are times of massive upheaval. Historically this has meant violence, currency devaluations, and victors dividing the spoils regardless of who was previously listed as a creditor.

Dalio, uses a highly understated word for this adjustment. Deleveraging. The default process (whether outright or via inflation) is redistributive. Politics determines the winners and losers. It’s always been give and take. But we need to keep talking.

If we cannot find a way to cooperate, the problem of imbalance and feelings of injustice don’t just disappear.

Redistribution finds a way.


Addendum

I realize MMT is a polarizing topic. I have a cursory understanding of it, so feel free to correct me: I think the core insight that a government doesn’t need to run like a household is correct mechanically. The problem is how the debt is allocated to the citizens in the form of taxes and transfer payments. So from a policy point of view, I don’t know if MMT frameworks lead to effective practical policy. Effective is always a matter of debate and depends on your constituency’s perspective. In that sense, MMT is no different than any other framework that claims to have good reasons for how it grows and splits the pie.

The great personal dividend of MMT is how it popularized the sectoral balances approach to understanding the economy. Similar to Dalio’s video, it views the economy as a collection of small transactions. Since every buy is someone else’s sell, we can use a giant T account of credits and debits to understand the economy from basic accounting. Those credits and debits flow through the household, government, corporate and “foreign sectors”. Economists associated with this approach include Godley, Pettis, Kalecki, and Levy.

To demonstrate the power of this lens, I encourage you to read Jesse Livermore’s Upside Down Markets paper. It completely reshaped my understanding of macro into something that I believe is closer to reality. Whenever I hear a macro argument, I at least try to place it within the sectoral balances framework to see if it is at least self-consistent. The advantage of basic accounting identities is they are identities. They are tautologically true and that’s a useful razor for an initially evaluating an argument.

Jesse’s paper is a beast. Many people won’t read a 40k word paper. I encourage everyone to read this one. While it’s a dense exploration of timely macroeconomics ideas, Jesse’s rare ability to tackle the complexity in an approachable, step-by-step progression is an amazing opportunity to learn.

Having said that, I realize many people still won’t read the paper. So I decided to try my hand at creating this explainer. I completely re-factored it to turn it into a personal reference. You can use it too:

✍️Moontower Guide To Jesse Livermore’s Upside Down Markets (link)


Be groovy to the mom’s out there!

-K

Moontower #147

I exhausted my writing energy in this week’s Money Angle, so today you get a grab bag.

🏫Schoolhouse.world (check it out)

This is the latest initiative by Sal Khan (definitely a hero). It’s a peer-to-peer live tutoring service focused on HS math and test prep. If we know anything about KhanAcademy then we can expect this is just the beginning.

Schoolhouse.world is a platform for free, peer-to-peer tutoring–where anyone, anywhere can receive live help, build their skills, and pay it forward by becoming a tutor themselves.

I happened to be browsing the list of donors to KhanAcademy and was heartened to see how bipartisan it was. Their mission transcends our differences.

Elon’s Giant Package (12 min read)
by @ranjanxroy

Some background before reading Ranjan’s post.

Earlier this week Matt Levine wrote:

Twitter is a strange company; it has enormous influence on politics and culture but is not great at making money. It has a lot of power as a venue of public discussion, and there is a lot of debate among Twitter’s employees and users, and among politicians and regulators, about how it should use that power. Elon Musk certainly cares about this stuff, and has explicitly said that he wants to buy Twitter not for economic reasons but for “free speech.”

The narrative is “free speech”, but I’m personally a bit skeptical because my impulse is buying Twitter seems more coherent as Elon:

1) secures distribution. It’s like marketing capex that also happens to have vanity value.

And it makes sense for things that have vanity value to be uneconomic. Indulge me:

2) wants cover to diversify from TSLA shares. If Twitter is run like a “clown car that crashed into a goldmine” then presumably it has potential upside independent of vanity.

Ranjan’s mini-grand theory on what Elon’s up to with Twitter was resonant with my prior. After reading that, consider something I’ve mentioned before. Portfolio theory asserts that things which don’t make sense in isolation can be brilliant when paired with the right strategy or synergistic buyer. Especially today. It’s spelled out further in:

Portfolio Theory And The Invisible Option On Hobbies (7 min read)

Twitter is more useful to Elon than anyone else on Earth. Whether it’s useful enough to him to justify the price is another matter, but it’s not shocking that he’d be the most justifiable high bid for it.

Let’s end with some housing talk. I think comparisons to 2007 are off base. Lending standards are tighter and people are flush with cash right now. It’s not to say I’m bullish exactly, but I think the downside in nominal terms is fairly contained. I suspect RE will be dead money in real terms for a while but then again, everything might be. It could be the tallest midget for the foreseeable future. I’m also the ass who sold his house in late 2020 so maybe discount everything I just said by 200%.

Read Calculated Risk instead:

Don’t Compare the Current Housing Boom to the Bubble and Bust (4 min read)
by Bill McBride


Money Angle

In the past few years, I’ve written several posts about option greeks.

If you are familiar with them, you know my goal is to explain things like you are 5 years old (well more like 12…my kids don’t know how an option works yet). I struggle to read technical finance papers because I’m, like a human being and stuff. I assume others feel that way about option greeks.

My latest post occured to me as I was falling asleep Tuesday night, so I spent Wednesday in a fever of writing that reminded me why I don’t write technical posts all the time. Even a concept I feel very comfortable with took about 10 hours to write about.

Check it out:

Moontower On Gamma (15 min read)

Gamma is a concept that maps perfectly to acceleration in physics which is an intuitive and familiar concept we encounter in daily life. We can use that analogy to see why p/l is the same idea as “distance traveled”. From there, it’s delightful to see why option profits have a squared term.

If you want the krisnotes with less of the math:

Just a reminder, I maintain the Moontower Volatility Wiki with the help of the online nerd community. It’s a collection of resources for quant finance with a focus on options. I curate what goes into it, but it’s a community effort ultimately:

👽Moontower Volatility Wiki


Last Call

I’ve been following and chatting with Adam Butler and his teammates Rodrigo Gordillo and Mike Philbrick from ReSolve Asset Management for a while. They are a super-smart, thoughtful group of guys that I learn from. They asked me to come on their show which could have been very intimidating (these guys talk to people with way more things figured out than I ever will), but they made me feel comfortable enough to just riff.

I sound like a meatball. You can take the kid outta Jersey but, well let’s just say I prefer to hide behind print for a reason. It’s mostly stories with some risk managment ideas sprinkled in.

ReSolve Riffs on Exploring Life Under The (Option) Surface (YouTube)

If you prefer audio only (you don’t have to watch me gesture like a crackhead) here’s the Spotify link.

Moontower on Gamma

The first option greek people learn after delta is gamma. Recall that delta represents how much an option’s price changes with respect to share price. That makes it a convenient hedge ratio. It tells you the share equivalent position of your option position. So if an option has a .50 delta, its price changes by $.50 for a $1.00 change in the stock price. Calls have positive deltas and puts have negative deltas (ie puts go down in value as the stock price increases). If you are long a .50 delta call option and want to be hedged, you must be short 50 shares of the stock (options refer to 100 shares of underlying stock). For small moves in the stock, your call and share position p/l’s will offset because you are “delta neutral”.

This is true for small moves only. “Small” is a bit wishy-washy because small depends on volatility and this post is staying away from that much complexity. Instead, we want to focus on how your delta changes as the stock moves. This is vital because if our option delta changes then your equivalent share position changes. If your position size changes, then that same $1 move in the stock leads means your p/l changes are not constant for every $1 change. If I’m long 50 shares of a stock, I make the same amount of money for each $1 change. But if I’m long 50 shares equivalent by owning a .50 delta option, then as the stock increases my delta increases as the option becomes more in-the-money. That means the next $1 change in the stock, produces $60 of p/l instead of just $50. We know that deep in-the-money options have a 1.00 delta meaning they act just like the stock (imagine a 10 strike call expiring tomorrow when the stock is trading for $40. The option price and stock price will move perfectly in lockstep. The option has 100% sensitivity to the change).

A call option can go from .50 delta to 1.00 delta. Gamma is the change in delta for the change in stock. Suppose you own a .50 delta call and the stock goes up by $1. The call is solidly in-the-money and perhaps its new delta is .60. That change in delta from .50 to .60 for a $1 move is known as gamma. In this case, we say the option has .10 gamma per $1. So if the stock goes up $1, the delta goes up by .10.

While this is mechanically straightforward, some of the lingo around gamma is confusing. People spout phrases like “a squared term”, “curvature”, “convexity”. I’ve written about what convexity is and isn’t because I’ve seen it trip up people who should know better. See Where Does Convexity Come From?. In this post, we will demystify the relationship of these words to “gamma”. In the process, you will deeply improve your understanding of options’ non-linear nature.

How the post is laid out:

Explanations

  • Acceleration
  • The squared aspect of gamma
  • Dollar gamma

Applications

  • Constant gamma
  • Strikeless products
  • How gamma scales with price and volatility
  • Gamma weighting relative value trades

Explanations

Acceleration

You already understand “curvature”. I’ll prove it to you.

You wake up tomorrow morning and see a bizarre invention in your driveway. An automobile with an unrivaled top speed.  You take it on an abandoned road to test it out. Weirdly, it accelerates slowly for a racecar. Conveniently for me, it makes the charts I’m about to show you easy to read.

You are traveling at 60 mph.

Imagine 2 scenarios:

  1. You maintain that constant speed.
  2. You accelerate such that after 1 minute you are now traveling at 80 mph. Assume your acceleration is smooth. That means over the 60 seconds it takes to reach 80 mph, your speed increases equally every second. So after 3 seconds, you are traveling 61 mph, at 6 seconds you are moving 62 mph. Eventually at 60 seconds, you are traveling 80 mph.

Graphically:

In the acceleration case, what was your average speed or velocity during that minute?

Since the acceleration was smooth, the answer is 70 mph.

How far did you travel in each case?

Constant velocity:

Accelerate at 20mph per minute:

If the acceleration is smooth, we can take the average velocity over the duration and multiply it by the duration to compute the distance traveled.

Let’s now continue accelerating this supercar by a marginal 20mph rate for the next 15 minutes and see how far we travel. Compare this to a vehicle that maintains 60 mph for the whole trip. The table uses the same logic — the average speed for the last minute assumes a constant acceleration rate.

Let’s zoom in on the cumulative distance traveled at each minute:

We found it! Curvature.

Curvature is the adjustment to the linear estimate of distance traveled that we would have presumed if we assumed our initial speed was constant. Let’s map this analogy to options.

  • Time –> stock price

    How much time has elapsed from T₀ maps to “how far has the stock moved from our entry?”

  • Velocity –> delta

    Delta is the instantaneous slope of the p/l with respect to stock price, just as velocity is the instantaneous speed of the car.

  • Acceleration –> gamma

    Acceleration is the change in our velocity just as gamma is the change in delta.

  • Cumulative distance traveled –> cumulative p/l

    Distance = velocity x time. Since the velocity changes, multiply the average velocity by time. In this case, we can double-check our answer by looking at the table. We traveled 52.5 miles in 15 minutes or 210 mph on average. That corresponds to our speed at the midpoint of the journey — minute 8 out of 15.
    P/l = average position size x change in stock price. Just as our speed was changing, our position size was changing!

Delta is the slope of your p/l. That’s how I think about position sizes. Convexity is non-linear p/l that results from your position size varying. Gamma mechanically alters your position size as the stock moves around.

The calculus that people associate with options is simply the continuous expression of these same ideas. We just worked through them step-wise, minute by minute taking discrete averages for discrete periods.

Intuition For the Squared Aspect Of Gamma

Delta is familiar to everyone because it exists in all linear instruments. A stock is a linear instrument. If you own 100 shares and it goes up $1, you make $100. If it goes up $10, you make $1,000. The position size is weighted by 1.00 delta (in fact bank desks that trade ETFs and stocks without options are known as “Delta 1 desks”).  Since you just multiply by 1, the position size is the delta. If you’re long 1,000 shares of BP, I say “you’re long 1,000 BP deltas”. This allows you to combine share positions and option positions with a common language. If any of the deltas come from options that’s critical information since we know gamma will change the delta as the stock moves.

If your 1,000 BP deltas come from:

500 shares of stock

+

10 .50 delta calls

that’s important to know. Still, for a quick summary of your position you often just want to know your net delta just to have an idea of what your p/l will be for small moves.

If you have options, that delta will not predict your p/l accurately for larger moves. We saw that acceleration curved the total distance traveled. The longer you travel the larger the “curvature adjustment” from a linear extrapolation of the initial speed. Likewise, the gamma from options will curve your p/l from your initial net delta, and that curvature grows the further the stock moves.

If you have 1,000 BP deltas all coming from shares, estimating p/l for a $2 rally is easy — you expect to make $2,000.

What if your 1,000 BP deltas all come from options? We need to estimate a non-linear p/l because we have gamma.

Let’s take an example from the OIC calculator.

The stock is $28.35

This is the 28.5 strike call with 23 days to expiry. It’s basically at-the-money.

It has a .50 delta and .12 of gamma. Let’s accept the call value of $1.28 as fair value.

Here’s the setup:

Initial position = 20 call options.

What are your “greeks”?

    • Delta  =  1,000

      .50 x 20 contracts x 100 share multiplier

    • Gamma =  240

      .12 x 20 contracts x 100 share multiplier

(the other greeks are not in focus for this post)

The greeks describe your exposures. If you simply owned 1,000 shares of BP you know the slope of your p/l per $1 move…it’s $1,000. That slope won’t change.

But what about this option exposure? What happens if the stock increases by $1, what is your new delta and what is your p/l?

After $1 rally:

    • New delta = 1,240 deltas

      .62 x 20 contracts x 100 share multiplier

      Remember that gamma is the change in delta per $1 move. That tells us if the stock goes up $1, this call will increase .12 deltas, taking it from a .50 delta call to a .62 delta call.

That’s fun. As the stock went up, your share equivalent position went from 1,000 to 1,240.

Can you see how to compute your p/l by analogizing from the accelerating car example?

[It’s worth trying on your own before continuing]

Computing P/L When You Have Gamma 

Your initial delta is 1,000. Your terminal delta is 1,240.

(It’s ok to assume gamma is smooth over this move just as we said the acceleration was smooth for the car.)

Your average delta over the move = 1,120

1,120 x $1 = $1,120

You earned an extra $120 vs a basic share position for the same $1 move. That $120 of extra profit is curvature from a simple extrapolation of delta p/l. Since that curvature is due to gamma it’s best to decompose the p/l into a delta portion and a gamma portion.

  • The delta portion is the linear estimate of p/l = initial delta of 1,000 x $1 = $1,000
  • The gamma portion of the p/l is the same computation as the acceleration example:

Your gamma represents the change in delta over the whole move. That’s 240 deltas of change per $1. So on average, your delta was higher by 120 over the move. So we scale the gamma by the move size and divide by 2. That represents our average change in delta which we multiply by the move size to compute a “gamma p/l”.

where:

Γ = position weighted gamma = gamma per contract  x  qty of contracts  x  100 multiplier

△S = change in stock price

We can re-write this to make the non-linearity obvious — gamma p/l is proportional to the square of the stock move!

Generalizing Gamma: Dollar Gamma

In investing, we normally don’t speak about our delta or equivalent share position. If I own 1,000 shares of a $500 stock that is very different than 1,000 shares of a $20 stock. Instead, we speak about dollar notional. Those would be $500,000 vs $20,000 respectively. Dollar notional or gross exposures are common ways to denote position size. Option and derivative traders do the same thing. Instead of just referring to their delta or share equivalent position, they refer to their “dollar delta”. It’s identical to dollar notional, but preserves the “delta” vocabulary.

It is natural to compute a “delta 1%” which describes our p/l per 1% move in the underlying.

For the BP example:

  • Initial dollar delta = delta x stock price = 1,000 x $28.35 = $28,350 dollar deltas
  • Δ1% = $28,350/100 = $283.50

    You earn $283.50 for every 1% BP goes up.

Gamma has analogous concepts. Thus far we have defined gamma in the way option models define it — change in delta per $1 move. We want to generalize gamma calculations to also deal in percentages. Let’s derive dollar gamma continuing with the BP example.

  1. Gamma 1%

    Gamma per $1 = 240

    Of course, a $1 move in BP is over 3.5% ($1/$28.35). To scale this to “gamma per 1%” we multiply the gamma by 28.35/100 which is intuitive.

    Gamma 1% = 240 * .2835 = 68.04

    So for a 1% increase in BP, your delta gets longer by 68.04 shares.

  2. Dollar gamma

    Converting gamma 1% to dollar gamma is simple. Just multiply by the share price.

    By substituting for gamma 1% from the above step, we arrive at the classic dollar gamma formula:

Let’s use BP numbers.

$Gamma = 240 * 28.35² / 100 = $1,929

The interpretation:

A 1% rally in BP, leads to an increase of 1,929 notional dollars of BP due to gamma. 

Instead of speaking of how much our delta (equivalent share position) changes, you can multiply dollar gamma by percent changes to compute changes in our dollar delta.

Generalizing Gamma P/L For Percent Changes

In this section, we will estimate gamma p/l for percent changes instead of $1 changes. Let’s look at 2 ways.

The Accelerating Car Method

The logic flows as follows (again, using the BP example):

  • If a 1% rally leads to an increase of $1,929 of BP exposure then, assuming gamma is smooth, a 3.5% rally (or $1) will lead to an increase of $6,751 of BP length because 3.5%/1% * $1,929
  • Therefore the average length over the move is $3,375 (ie .5 * $6,751) due to gamma
  • $3,375 * 3.5% = $118 (This is very close to the $120 estimate we computed with the original gamma p/l formula. This makes sense since we followed the same logci…multiply the average position size due to gamma times the move size.)

The Algebraic Method

We can adapt the original gamma p/l formula for percent changes.

We start with a simple identity. To turn a price change into a percent we simply divide by the stock price. If a $50 stock increased $1 it increased 2%

If we substitute the percent change in the stock for the change in the stock we must balance the identity by multiplying by :

We can double-check that this works with our BP example. Recall that the initial stock price is $28.35:

This also checks out with the gamma p/l we computed earlier.

Applications

Constant Gamma 

In all the explanations, we assume gamma is smooth or constant over a range of prices. This is not true in practice. Option gammas peak near the ATM strike. Gamma falls to zero as the option goes deep ITM or deep OTM. When you manage an option book, you can sum your positive or negative gammas across all your inventory to arrive at a cumulative gamma. The gamma of your net position falls as you move away from your longs and can flip negative as you approach shorts. This means gamma p/l estimates are rarely correct, because gamma calculations themselves are instantaneous. As soon as the stock moves, time passes, or vols change your gamma is growing or shrinking.

This is one of the most underappreciated aspects vol trading for novices. Vanilla options despite being called vanilla are diabolical because of path dependence. If you buy a straddle for 24% vol and vol realizes 30% there’s no guarantee you make money. If the stock makes large moves with a lot of time to expiration or when the straddle is not ATM then those moves will get multiplied by relatively low amounts of dollar gamma. If the underlying grinds to a halt as you approach expiration, especially if it’s near your long strikes, you will erode quickly with little hope of scalping your deltas.

Skew and the correlation of realized vol with spot introduce distributional effects to vol trading and may give clues to the nature of path dependence. As a trader gains more experience, they move from thinking simply in terms of comparing implied to realized vol, but trying to understand what the flows tell us about the path and distribution. The wisdom that emerges after years of trading a dynamically hedged book is that the bulk of your position-based p/l (as opposed to trading or market-making) will come from a simple observation: were you short options where the stock expired and long where it didn’t?

That’s why “it’ll never get there” is not a reason to sell options. If you hold deltas against positions, you often want to own the options where the stock ain’t going and vice versa. This starts to really sink in around year 10 of options trading.

Strikeless Products

The path-dependant nature of vanilla options makes speculating on realized vol frustrating. Variance swaps are the most popular form of “strikeless” derivatives that have emerged to give investors a way to bet on realized vols without worrying about path dependence. Conceptually, they are straightforward. If you buy a 1-year variance swap implying 22% vol, then any day that the realized vol exceeds 22% you accrue profits and vice versa(sort of1). The details are not important for our purpose, but we can use what we learned about gamma to appreciate their construction.

A derivative market cannot typically thrive if there is no replicating portfolio of vanilla products that the manufacturer of the derivative can acquire to hedge its risk. So if variance swaps exist, it must mean there is a replicating portfolio that gives a user a pure exposure to realized vol. The key insight is that the product must maintain a fairly constant gamma over a wide range of strikes to deliver that exposure. Let’s look at the dollar gamma formula once again.

We can see that gamma is proportional to the square of the stock price. While the gamma of an option depends on volatility and time to expiration, the higher the strike price the higher the “peak gamma”. Variance swaps weight a strip of options across a wide range of strikes in an attempt to maintain a smooth exposure to realized variance. Because higher strike options have a larger “peak” gamma, a common way to replicate the variance swap is to overweight lower strikes to compensate for their smaller peak gammas. The following demonstrates the smoothness of the gamma profile under different weighting schemes.

Examples of weightings:

Constant = The replicating strip holds the same number of 50 strike and 100 strike options

1/K = The replicating strip holds 2x as many 50 strike options vs 100 strike

1/K² = The replicating stripe holds 4x as many 50 strike options vs 100 strike

Note that the common 1/K² weighting means variance swap pricing is highly sensitive to skew since the hedger’s portfolio weights downside puts so heavily. This is also why the strike of variance swaps can be much higher than the ATM vol of the same term. It reflects the cost of having constant gamma even as the market sells off. That is expensive because it requires owning beefy, sought-after low delta puts.

How Gamma Scales With Price, Volatility, and Time

Having an intuition for how gamma scales is useful when projecting how your portfolio will behave as market conditions or parameters change. A great way to get a feel for this is to tinker with an option calculator.  To demonstrate the effects of time, vol, and price, we hold 2 of the 3 constant and vary the 3rd.

Assume the strike is ATM for each example.

Here are a few rules of thumb for how price, vol, and time affect gamma.

  • If one ATM price is 1/2 the other, the lower price will also have 1/2 the dollar gamma. Linear effect as the higher gamma per option is offset by the dollar gamma’s extra weight to higher-priced stocks.
  • If one ATM volatility is 1/2 the other, the dollar gamma is inversely proportional to the ratio of the vols (ie 1/vol ratio).
  • If an option has 1/2 as much time until expiration, it will have √ratio of more gamma.

Stated differently:

  • Spot prices have linearly proportional differences in gamma. The lower price has less dollar gamma.
  • Volatility has inverse proportionality in gamma. The higher vol has less dollar gamma.
  • Time is inversely proportional to gamma with a square root scaling. More time means less dollar gamma.

Gamma-weighting Relative Value Trades

As you weight relative value trades these heuristics are handy (it’s also the type of things interview test your intuition for).

Some considerations that pop out if you choose to run a gamma-neutral book?

  • Time spreads are tricky. You need to overweight the deferred months and since vega is positively proportional to root time, you will have large net vega exposures if you try to trade term structure gamma-neutral.
  • Stocks with different vols. You need to overweight the higher vol stocks to be vega-neutral, but their higher volatility comes with higher theta. Your gamma-neutral position will have an unbalanced theta profile. This will be the case for inter-asset vol spreads but also intra-asset. Think of risk reversals that have large vol differences between the strikes.
  • Overweighting lower-priced stocks to maintain gamma neutrality does not tend to create large imbalances because spot prices are positively proportional to other greeks (higher spot –> higher vega, higher dollar gamma, higher theta all else equal).

Weighting trades can be a difficult topic. How you weight trades really depends on what convergence you are betting on. If you believe vols move as a fixed spread against each other then you can vega-weight trades. If you believe vols move relative to each other (ie fixed ratio — all vols double together) then you’d prefer theta weighting.

I’ve summarized some of Colin Bennett’s discussion on weighting here. The context is dispersion, but the intuitions hold.

Finally, this is an example of a top-of-funnel tool to spot interesting surfaces. The notations on it tie in nicely with the topic of weightings. The data is ancient and besides the point.

Wrapping Up

Gamma is the first higher-order greek people are exposed to. Like most of my posts, I try to approach it intuitively. I have always felt velocity and acceleration are the easiest bridges to understanding p/l curvature. While the first half of the post is intended for a broad audience, the second half is likely to advanced for novices and too rudimentary for veterans. If it helps novices who are trying to break into the professional world, I’ll consider that a win. I should add that in Finding Vol Convexity I apply the concept of convexity to implied volatility. You can think of that as the “gamma of vega”. In other words, how does an option’s vega change as volatility changes?

I realize I wrote that post which is more advanced than this one in the wrong order. Shrug.