Unpacking The Beauty Of A deBoer Book Review

Freddie deBoer’s review of Ross Douthat’s The Deep Places, a memoir of Douthat’s illness, is impressively balanced and justified (I say justified because the definition of balance has shifted from what I can tell from “reasonable opposition” to “any opposition” as if every view holds equal merit. No doubt a side effect of “democratization” of distribution. Look, just because there are a few ghouls who deny the Holocaust or rationalize slavery doesn’t mean the school library should grant them shelf space).

deBoer’s praise of the book is as profound as the experience he had reading it. Yet his well-founded criticisms are never watered down. It’s hard to imagine a reviewer who found so many problems with the narrative taking the effort to extol, with equal sincerity, its virtue. The review is a lesson in seeing and communicating. The nuance stands in such relief to the binary discourses that at this point have left us haggard at best but more likely numb. Reading this review left me feeling that integrity was a fringe value, because it was jarring to see a sweaty writer say “good game” and actually mean it.

You can read the full review here.

My highlights are below (boldface is mine).

The nature of the internet

  1. In the internet era, likeminded people will find each other, including those that are suffering from ailments the conventional medical system can’t treat or even define. It’s therefore no surprise that since the whole world went online the number of people claiming to suffer from disputed diseases with shifting symptoms and complex etiologies has risen dramatically. All of those people, I have no doubt, are in some kind of pain, and we are compelled by decency and shared humanity to confront that pain. But it’s also true that the internet creates conspiracists, it heightens distrust of institutions, it magnifies paranoia. On the internet, no matter how fanciful your sneaking suspicions might be, no matter how disordered and unhealthy, someone will emerge from the digital fog and whisper to you that all of it is real. From this stems gangstalking, stems QAnon, stems people who think they’re getting sick from 5G. It’s a problem from hell and one I don’t know how to fix.

  2. When one group of people in society feels unheard for so long, in time they form a crusade, and the object of that crusade is the most human of all demands: feel our pain. It is natural to want the world to understand our suffering as something different, something deeper, something special. The cacophony of our political lives stems in no small part from the ceaselessly multiplying number of groups that ask that their suffering be seen as something transcendent and unique. The trouble, of course, is that we’re all suffering, and in fact to suffer is the least special, most ordinary thing any person can do.

Why Douthat is an interesting narrator to this story:

  1. I have also known a fair number of people who claimed to suffer from chronic Lyme, and they have all been… crunchy. The diagnosis and its inherent antagonism to the medical establishment fit very well into a kind of bourgie hippie boomer counterculture. Chronic Lyme advocates insist that all manner of people believe they suffer from the disease, and I have no reason to doubt them. But it’s also the case that there is a decided cultural slant to their community, and I associate it more with the world of acupuncture and reiki than dissident conservatives.

    And yet Douthat proves himself to be the right guide, I think precisely because he’s likely never paid money to have his chakras aligned. He so clearly does not want the answer to be found in the types of medicine that are so often superficially ridiculous, but has been moved to by unrelenting illness, and the consequence is that he is open-minded but never credulous.* 2. Douthat seems to attract more progressive ire, I suppose precisely because he refuses to occupy the stereotype of the snarling right-winger. (I can tell you from long experience that there are many people whose first demand is not left-wing politics or right-wing politics but political comprehensibility, for everyone to dutifully sort into teams.) On balance I can think of few writers who have paid more of a price for being thoughtful than Douthat. His recent book The Decadent Society is an often compelling, occasionally meandering collection of complaints that I can imagine emerging from no other writer.

Why deBoer’s affection for the book does not relieve him from his critical duty

  1. What we have in The Deep Places, I think, is the most compelling and moving version of a bad argument; it provoked my admiration again and again even while I shook my head in concern on every page.

  2. I also take Ross Douthat seriously, and to take an author seriously is to subject their books to real critical evaluation, which means that I can’t simply enjoy the elements I liked and ignore those I didn’t. A less fair reason for my critical sympathy is that I suspect The Deep Places may well become a new bible for the chronic Lyme movement. And if so, like all bibles this one will find its considerable nuance and restraint drained from it as it becomes a holy object to a group of people who, whatever the truth of their medical conditions, are looking for someone to tell them that the world has been uniquely hard on them.

  3. The author is excused for loading the dice. But the book is not.

  4. Skepticism towards a particularly story about the origins of pain is not the same as skepticism towards the pain itself.

  5. Setting aside its unjustifiable placement in scare quotes, the use of the word hypochondriac is notable here because, though I have not counted, the word cannot have appeared in the text more than a handful of times. I don’t believe the term Munchausen appears at all. But these are real, documented, prevalent conditions that have serious negative consequences for our overtaxed healthcare system. I spent the entire book wondering when Douthat would confront those conditions directly and with research, rather than expressed as his fleeting fears about the legitimacy of his own feelings. But it never arrived, and if there is one part of this book that I would name a serious flaw, it’s that.

  6. The chronic Lyme community, as sympathetic as I find them, makes difficult demands of the rest of us, including surrendering empirical rigor in the field where it is most essential… I have tried to separate my skepticism towards the illness from my impressions of the book, but I haven’t been able to. I am left with a long record of pain, a man who has responded to that pain in profoundly human and sympathetic ways, and a mess, a terrible mess of illness and medicine and science and conspiracism, and at its core a tangle of bodies and the people who no longer recognize them. And a book I do not know how to evaluate.

deBoer’s logic at work

  1. But I am compelled to point out that, again and again, Douthat shares something that would seem to point firmly against his working theory of his suffering and yet seems not to notice. He references Pamela Weintraub’s Cure Unknown, another chronic Lyme memoir, and notes that “her family of four were all infected in the same yard, the same woods, the same neighborhood – and yet she, her husband, and their two sons followed completely variable paths toward recovery.” Douthat mentions this uncritically and takes it as evidence for the mysterious nature of Lyme. I, on the other hand, hear such a thing and think that a disease that supposedly springs from the same infection by the same bacterium carried by the same parasite in the same geography and yet results in totally dissonant outcomes for treatment and recovery is not one disease in any conventional sense. At times I wanted to say to some imaginary listener, “Isn’t an illness that can seem to have any symptoms imaginable at any given time a little hard to believe?”

  2. At one point, Douthat recalls that his wife asked a skeptical doctor if Lyme’s prevalence in the region meant it was an unsafe place to raise children. I am trying to summon all of my charity here: this is a little much. It’s hard to entertain the notion that a disease that is serious but treatable, and a potential variant that is incredibly rare if it exists at all, poses such a serious threat to children that it might make the 70,000 square miles that constitute New England an irresponsible place to raise a family. Such questions emerged from a harried and exhausted family that had been brought to its breaking point, and I have no desire to mock the sentiment, at all. But the question also has appeared now in an important work of nonfiction by a prominent and successful writer, and it is my responsibility to point out that it is this type of excess that has done so much to discredit chronic Lyme advocates. I recognize that this aside is meant, in part, to demonstrate the degree to which fear of Lyme had crept into their lives. But Douthat clearly saw it as a sensible question, describing the doctor’s response, “he looked at her as if the question had never even occurred to him.” Well, yes, I imagine he would. Skin cancer kills 15,000 people a year. The incidence of skin cancer is significantly higher in regions with a higher UV index. Yet no one has declared the Southwest an irresponsible place in which to raise children. The doctor was surprised by the question because it was not a sensible one.

  3. Well, Occam’s razor can be a cold thing, and it is far from an infallible guide. But I must invoke it here: can it possibly be the most direct, most parsimonious explanation that a disease runs rampant among some of the most affluent and well-connected people in the country, and yet for reasons that remain inscrutable to me, the medical establishment has conspired to belittle and ignore them? Medical researchers live to discover new diseases and doctors flourish professionally when they treat them. So why the conspiracy? For what purpose? Who profits? Both because of the incentives of malpractice law and the fact that more treatment means more money, our doctors tend to over treat, over diagnose. But the chronic Lyme narrative requires us to believe that doctors refuse to take it seriously, despite such suffering… for what?

deBoer’s undiluted praise

  1. But boy, it’s beautifully rendered. Thus my dilemma, as a reviewer. Despite how harsh the above might sound, I experienced this book as a brave and brilliantly-realized cry of pain and loss, and that’s worth the purchase price itself.

    It’s autumn, as I write this. Like any good stereotypical white dude from New England, fall is my favorite season. Pretentiously I tell myself that it’s because fall is the beginning of an ancient ritual of death and rebirth, because it helps me access the most visceral elements of human life, because it helps me imagine that everything I loved that has died will sometime return, flowering and green. More accurately I love fall because the weather is pleasant and the leaves are pretty and football is the only sport I really follow anymore. But either way, fall is my time of ritual. In fall I read old books by dead writers who were unafraid to sift through the silt of mundane experience to find those things that survive the cruel and steady passage of time. I drink dark beer and let pot roast braise for hours on the stove. I curl up into myself.

    The Deep Places is a book for fall; I wandered today through Prospect Park and saw stubborn leaves at last beginning to change, and I thought about old gods and Christ’s love and chronic Lyme and those families that suffer from it, whatever “it” really is. The book’s manner is as spartan and tangled as the denuded trees that grace its cover. Douthat walks a narrow line, depicting a story that must by its nature invite sympathy without appearing to seek it, and he achieves this beautifully. He writes about pain, famously hard to put into words, with clarity and poise. The book is one of those rare few that tread in mourning without the constant reassurance of a happy ending soon to come. And its palette is somber and rich.

    I am one of those untrustworthy types who looks for craft first in anything I read, and I respect degree of difficulty. Writing about suffering is not easy, putting yourself out there so nakedly to a public that seems crueler by the day is not easy, and wandering through such a tangled story of the heart is not easy. For that reason alone, I commend The Deep Places.*

  1. Writing on suffering:

    But the moral imagination does not have limits. Our capacity for compassion cannot be overtaxed. What’s immensely clear in The Deep Places, and rendered beautifully, is that Ross Douthat has suffered, terribly, and his suffering has seeped out into his family and his home and his work. As so many have, he has been forced to deal with frequently uncaring doctors and a Byzantine and cruel medical system when he was least equipped to deal with them. He has seen people close to him express doubts about his sanity, he has questioned whether he will be well enough to continue his career, he has worried ceaselessly about leaving his family fatherless or, worse, of being a permanent burden on them. All of that deserves not just sympathy but understanding, adult and rigorous and friendly and honest understanding. For that reason, above all else, I’m glad that The Deep Places exists and I’m glad to have read it.

    The late Ram Dass once wrote to grieving parents, “something in you dies when you bear the unbearable, and it is only in that dark night of the soul that you are prepared to see as God sees, and to love as God loves.” I do not know what it’s like to love as God loves. But I do know what it’s like to suffer, and then to suffer more, and at last to feel something die inside me. The note of uplift at the end of The Deep Places, uncertain but real, is a record of Douthat’s willingness to let that something die inside of him too, in order to move on. That’s a thing of beauty, and though it’s difficult that Douthat cannot declare himself healthy at the end, it’s the kind of difficulty that should be faced by any adult. In that, his book triumphs.

A Quick Hop From Note-Taking To Writing Online

I started writing online 3 years ago. I wish I started even earlier but as the sign that used to hang in our boys’ preschool used to read:

The best time to plant a tree is yesterday. The second best time is today.

I won’t rehash the benefits of writing online (I have a list of clipped articles on that if you’re interested) but I’ll share a thought on the topic.

I was recently chatting with an internet friend (or what your meatspace spouse might refer to as an “imaginary friend”) who has an established quant finance career. She’s at a juncture in her career but is finding that the most compelling options are coming from inbound opportunities based on her writing. While she has options coming from her direct experience and CV, they aren’t the most interesting. They are well-trodden, established paths. But writing has inadvertently cast a much wider net than her resume ever could have.

I see my writing the same way. I don’t know what my next endeavor is, but I’m making the bet that having a public body of work might allow future partners/collaborators/employers to take a chance on me even though my official career (“option trader”) has been narrow. Writing is a way to demonstrate range. Perhaps I’d be better off getting an MBA or other degree if I’m trying to pivot, but that’s why I call this a bet. It’s also a real-life example of the post I shared last week Portfolio Theory And The Invisible Option On Hobbies.

It’s never been easier to get started. A few thoughts about getting started from personal experience.

  • I did have one head-start. I am a note-taker.

    I’ve explained my system here.

    Just as storing a guitar in a convenient location (without a case) makes you more likely to pick it up and practice, your note-taking habits reduce the drag coefficient of traveling from “idle thoughts” to “words on a page”. The structures I built in Notion lent themselves to connecting ideas better than my old Evernote + Trello PKM stack. (PKM stands for personal knowledge management amongst the “productivity” cult).

    There’s lots of great software to host your PKM. Ann-Laure’s guide can help you choose.

  • For Notion users

    You are 95% of the way to publishing online. I use WordPress as a CMS (content management system) but I just subscribed to Potion.so which allows you to point your Notion pages to a custom domain that you own. If I were starting over today, I would simply buy a domain and connect it to a service like Potion.so or Super.so for a small monthly fee. If you want a free solution, with a little extra effort you can use Fruition.

    These solutions eliminate the need to learn a new CMS. So you can turn a key and have the Notion environment you are comfortable with be an elegant and flexible CMS. For evergreen content, like much of my writing, the chronology of blogs makes little sense. While you can use “categories” and “tags” the end result isn’t quite right for material that looks more wiki-like.

    Here’s a link to all my Notion pages that are now public. Note how Potion allowed me to use my MoontowerMeta domain be the host.

    This lets you:

If you were on the fence about starting to write online, I hope this was helpful.

Dispersion Trading For The Uninitiated

This blog post is a re-factored version of this Twitter thread

Let’s do dispersion trading for the uninitiated.

What Is Dispersion Trading?

Imagine selling an index straddle and buying each of the components’ straddles in proportion to the index weights. In practice, liquidity makes this impossible. Instead one settles for a “dirty dispersion” position. The trade is “short correlation”. It wants the average correlation between the stocks in the basket to be as low as possible.

Why Is Dispersion Trading A Correlation Bet?

Consider a 2 stock index:You own the straddles on the stocks and you are short the index straddle.
 
Case 1: Low correlation
  • The 2 stocks rip in opposite directions.
  • The index is unchanged. 
That’s a homerun! You win on every leg. You win on the call leg of one stock’s straddle, the put leg of the other stock’s straddle and the index doesn’t go anywhere allowing you to collect on the full short premium.
 
Now let’s move to the opposite scenario. 
 
Case 2: High correlation
 
  • The stocks move exactly together in a big way.

  • You win on your stock straddles but you will lose more on your index short.

Why?

The index is cheaper than the sum of the legs in straddle space. To understand why, we will need some simple math. 

An Intuitive Equation

Correlation represents the spread between an index’s vol and the vol of the components. 

There are 3 terms:
  • Index variance
  • Avg stock variance
  • Avg cross corr of each stock to every other stock
The equation:
 
Index variance = avg stock variance x avg cross correlation
 
We can re-arrange the equation to see the correlation as the ratio of index variance to stock variance:
 
Avg corr = index variance / avg stock variance
 
Notice that unless the correlations are 1, index var < stock var!
 
So if the index variance is trading for 50% of the variance of the avg weighted stock vols then the implied cross correlation is .50

Be careful, you need to take square roots to move from var space to vol space which is how prices are more commonly interpreted. In other words, you must square the ratio of index vol to stock vol you get the implied corr.
 
Example: If the index vol is 20% and the avg weighted stock vol is 30% then:
 
implied correlation = (.2/.3)^2

Implied correlation = .44

 

The Shape Of Correlation Risk

If stock vols are constant, and index vols increase, implied correlation must be increasing.
 
Likewise, if correlation surges the spread of index vol to stock vols must be narrowing (at corr = 1 they would converge.)

 

Here’s index vol relation to corr for a fixed stock vol of 30%

 
Trade Structures Are Tricky

If you structure a trade vega neutral or premium neutral you will be short correlation convexity.

  • As corr increases: you get shorter vol as the index short will grows faster than the stock vol longs.
  • As corr falls: vice versa. You get longer vol as it falls!
Dispersion trades are not just short correlation (notice this is the same risk premia as any risk-on position), but concave:
 
Your position size has negative gamma with respect to changes in correlation.
 
Dispersion is tricky. There is a lot of room for creativity in how you structure these trades. A few considerations:
 
  • You may choose to overweight stock long vega to flatten the curvature, but now you increase exposure to owning options.
  • What do you want your local gamma/theta profile to be? How do you want your “shocked” portfolio to look (matrix approach would ask “what’s my p/l with spot down 10% and correlation doubling?”)
  • How much basis or synthetic basket risk you want to take with names you include or not since this is a “dirty” trade in the first place?

 

The Correlation Surface

If you put the 3D options glasses on, you’ll notice that correlation has its own surface!

  • Upside implied correlations are cheaper than downside correlations.
  • Implied correlation has a term structure as well.

Implied correlation surfaces vary across sectors as well. Energy, biotech, bank etfs. The sector indices have implied correlations between basket components.

Then consider FX vol markets. They care about the rate vols of the individual fiat legs and, you guessed it, the correlation. 

How about a US investor trading options on a foreign index of an exporter nation. Like Japan. There’s an implied correlation between the yen and the equity index itself. Google the term quanto if you want to explore that idea. 

Broader Risk Lessons

The risk for any portfolio of long/short trades (either delta one or volatility) is as correlations increase your gross positions become exposed. You can’t hide behind “nets” when corrs explode higher. This is especially dangerous because most “hedged” portfolios are levered. 

Imagine a beta neutral trade where you are long 2 units of “alpha stock” and short 1 unit of index (assume they are the same vol, but “alpha” stock is .50 corr).

  • When correlations increase towards 100%, you are no longer neutral but long equiv of 1 unit of index into a falling market, increasing correlation mkt.

    Relative value books tend to blow up as corrs increase since corrs are used to weight positions.

  • A portfolio that wins as correlation increases (which is itself correlated with equity risk premia) should cost carry! 

    This is, in fact what we find. Implied correlation trades at a premium to realized correlation (and correlation swaps which have linear risks). You pay a premium to hold a long implied correlation position. Those selling correlation via dispersion trades are capturing a risk premia or source of carry correlated with conventional risk premia.

    Index options “should” be overpriced because it’s a systematic risk premium. The dispersion traders are the ones who bet when the overpricing is “excessive”. I wouldn’t advise trying that at home though. 

Parting Thoughts

How do implied correlations correlate to systematic risk premia? How do they compare to realized corrs?These types of questions are the start of seeing the world as one big spiderweb of risk premia and cross correlations.

Armed with this understanding, go build the dashboard to find the cheapest hedges, the most efficient basis, or the most levered shot at correlation regimes shifting. In other words, you don’t have to have a view on whether assets are cheap or not. You can look for situations where implied correlations are [over]confident in particular regimes persisting.  

Moontower #121

The Monty Hall Problem was popular on Twitter this week. It’s worth taking a look at it because the Bayesian logic behind the solution is pertinent to reasoning about uncertainty in general.

Let’s start by turning to Wikipedia:

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let’s Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker’s letter quoted in Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine in 1990:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

I’ll give you space to think about it.

So what happened?

Vos Savant’s response was that the contestant should switch to the other door.

She was right.

Man, if only the “You mad, bro?” was a thing back then. If that answer makes you mad, don’t worry, you are in good company:

Many readers of vos Savant’s column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling vos Savant wrong. Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy. Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant’s predicted result.

I’m a dude, and even I got the “mansplain” vibe from the bold-faced section. Wikipedia continues:

The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true.

So I chimed in on Twitter with my favorite way to understand why you should switch:

You can find a fuller discussion of the problem and its variants by Professor Jeffrey Rosenthal here.

Rosenthal considers my explanation “shaky” because it fails in some of the variants.

The reason it works in this version is that the host is a “trusted actor”. He is 100% to open an empty door. If he opened a door at random, then your reflex that switching shouldn’t matter would be correct.

Problems like this are Bayesian and can be approached using what Rosenthal calls the “proportionality principle”.

The Proportionality Principle: If various alternatives are equally likely, and then some event is observed, the updated probabilities for the alternatives are proportional to the probabilities that the observed event would have occurred under those alternatives.

That’s a mouthful. Let me start with an example I made up, then map the proportionality principle’s definition, line by line, to the solution. [don’t crucify me for the made-up shooting percentages]

Paul George and Kawhi Leonard are equally likely to have the ball on the last play of the game down by 2. You discover the Clippers won. Paul George is a 50% 3-pt shooter and Kawhi is a 25% 3-pt shooter.

What’s the probability Paul George took the shot?

So the long way of doing this is to map the paths to victory.

I took the liberty:

What does this tell us?

  1. The Clippers win 3/8 of the time (1/8 + 1/4). This makes sense since 37.5% is the average of their shooting percentages and they each have a 50% probability of getting the ball.
  2. The state of “having won” is 37.5% of the whole set of possibilities. Paul George making the winning shot happens 25% of the time. But since the whole of our restricted “having won” condition is 37.5% we can see that 25% / 37.5% = 2/3

    So Paul George took the shot 2/3 of the time. Going into that last play we expect he wins us the game 1/4 of the time (50% chance of getting the ball x 50% chance of making the shot) but once we “condition” the question on “The Clippers won”, the probability that he took the shot jumps to 2/3!

The proportionality principle allows us to make a shortcut. Follow me step-by- step through the definition laid out above.

  1. If various alternatives are equally likely, [check. Each player is 50% to get the ball]
  2. and then some event is observed, [the event was the Clippers winning]
  3. the updated probabilities for the alternatives are proportional to the probabilities that the observed event would have occurred under those alternatives. [for the Clippers to win one of these players needed to make the shot. Since Paul George is 2x as likely to make the shot (50% shooting % vs 25%), then he is a 2-1 favorite to have taken the shot. 2-1 is the same as 2 out of 3, therefore Paul George was 2/3 to have taken the shot. In case you didn’t notice, the way to convert odds to probabilities is to take a number in the “x to y odds” form and divide it by x+y. So 2-1 odds is the same as 2/(2+1) or 2/3. Just don’t forget which side of that expression is the “favorite” or “underdog”. This is similar how you convert gambling money lines to implied probabilities. All odds are implied probabilities because once you convert them into a fraction they are always less than 1.]

Real-life applications

If you like this kind of probability math, you can look into Bayes Theorem, which is about how we update our “priors”, ie our probability estimates at the get-go, once we get new information (sometimes called “conditioning”, because, well we impose new conditions).

If you don’t like this type of math, perhaps you feel like it’s not relevant. I assure you it is. Just imagine a disease has occurs 1 in 100,000 people but the test for it has a 5% false-positive rate. If you test 100,000 people for it, 5,000 of them will test positive in error yet only 1 person in the population actually has the disease. You’ve got 4,999 doomscrolling WebMD when their odds of actually having the sickness (after the positive test!) are on par with getting struck with lightning at some point in their life.

If this still sounds abstract, then you are my hero for somehow avoiding innumerate covid headlines.

Money Angle

  • I wrote a new post this week.

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

    The post uses lessons from portfolio theory to show:

    The value of an asset viewed in isolation is actually a floor.

    There is an option value above the equity value. In fact, you can think of the equity value as the 0 strike of that extra optionality.

    The post is a qualitative discussion of what drives that option’s value. While portfolio theory reveals this invisible option, the lesson has an even wider appeal.

    It tells us that hobbies, especially uncommon ones, can have large optionality values and in the current networked world those weird things you do for leisure could be more rewarding than you considered before you started doing them (of course, you don’t need to care about that, but just in case you were curious, it’s there if you look).

  • Seeing yourself on camera and hearing your own voice is always unsettling. But I realized the plumbing of voice trading in the options market, including the signal chain from negotiation to an option hitting the tape, is not widely understood even amongst professionals.

    So the Pirates, Jason and Corey were extremely generous to give me a spot to explain it. It’s pretty “inside baseball” and it won’t make you any money but it has a “day in the life of a trader” feel to it.

    I demand you subscribe to the channel. The Pirates content is smart, fun, and interesting. They even do videos explaining their thinking behind the channel and how to grow on YouTube which they are trying to do.

Last Call

You ever see something and wonder how you could never have seen that until now? This is one of those pictures.

Like, I’m not surprised a tree-swinger is toned, but it’s kinda strange that I’m just seeing this for the first time. I mean, I already knew kangaroos take ‘roids.

The Monty Hall Problem Is More Than A Game

The Monty Hall Problem was popular on Twitter this week. It’s worth taking a look at it because the Bayesian logic behind the solution is pertinent to reasoning about uncertainty in general.

Let’s start by turning to Wikipedia:

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let’s Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker’s letter quoted in Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine in 1990:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

I’ll give you space to think about it.

So what happened?

Vos Savant’s response was that the contestant should switch to the other door.

She was right.

Man, if only the “You mad, bro?” was a thing back then. If that answer makes you mad, don’t worry, you are in good company:

Many readers of vos Savant’s column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling vos Savant wrong. Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy. Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant’s predicted result.

I’m a dude, and even I got the “mansplain” vibe from the bold-faced section. Wikipedia continues:

The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true.

So I chimed in on Twitter with my favorite way to understand why you should switch:

You can find a fuller discussion of the problem and its variants by Professor Jeffrey Rosenthal here.

Rosenthal considers my explanation “shaky” because it fails in some of the variants.

The reason it works in this version is that the host is a “trusted actor”. He is 100% to open an empty door. If he opened a door at random, then your reflex that switching shouldn’t matter would be correct.

Problems like this are Bayesian and can be approached using what Rosenthal calls the “proportionality principle”.

The Proportionality Principle: If various alternatives are equally likely, and then some event is observed, the updated probabilities for the alternatives are proportional to the probabilities that the observed event would have occurred under those alternatives.

That’s a mouthful.

Let me start with an example I made up, then map the proportionality principle’s definition, line by line, to the solution. [don’t crucify me for the made-up shooting percentages]

Paul George and Kawhi Leonard are equally likely to have the ball on the last play of the game down by 2. You discover the Clippers won. Paul George is a 50% 3-pt shooter and Kawhi is a 25% 3-pt shooter.

What’s the probability Paul George took the shot?

So the long way of doing this is to map the paths to victory.

I took the liberty:

What does this tell us?

  1. The Clippers win 3/8 of the time (1/8 + 1/4). This makes sense since 37.5% is the average of their shooting percentages and they each have a 50% probability of getting the ball.
  2. The state of “having won” is 37.5% of the whole set of possibilities. Paul George making the winning shot happens 25% of the time. But since the whole of our restricted “having won” condition is 37.5% we can see that 25% / 37.5% = 2/3

    So Paul George took the shot 2/3 of the time. Going into that last play we expect he wins us the game 1/4 of the time (50% chance of getting the ball x 50% chance of making the shot) but once we “condition” the question on “The Clippers won”, the probability that he took the shot jumps to 2/3!

The proportionality principle allows us to make a shortcut. Follow me step-by- step through the definition laid out above.

  1. If various alternatives are equally likely, [check. Each player is 50% to get the ball]
  2. and then some event is observed, [the event was the Clippers winning]
  3. the updated probabilities for the alternatives are proportional to the probabilities that the observed event would have occurred under those alternatives. [for the Clippers to win one of these players needed to make the shot. Since Paul George is 2x as likely to make the shot (50% shooting % vs 25%), then he is a 2-1 favorite to have taken the shot. 2-1 is the same as 2 out of 3, therefore Paul George was 2/3 to have taken the shot. In case you didn’t notice, the way to convert odds to probabilities is to take a number in the “x to y odds” form and divide it by x+y. So 2-1 odds is the same as 2/(2+1) or 2/3. Just don’t forget which side of that expression is the “favorite” or “underdog”. This is similar how you convert gambling money lines to implied probabilities. All odds are implied probabilities because once you convert them into a fraction they are always less than 1.]

Real-life applications

If you like this kind of probability math, you can look into Bayes Theorem, which is about how we update our “priors”, ie our probability estimates at the get-go, once we get new information (sometimes called “conditioning”, because, well we impose new conditions).

If you don’t like this type of math, perhaps you feel like it’s not relevant. I assure you it is. Just imagine a disease has occurs 1 in 100,000 people but the test for it has a 5% false-positive rate. If you test 100,000 people for it, 5,000 of them will test positive in error yet only 1 person in the population actually has the disease. You’ve got 4,999 doomscrolling WebMD when their odds of actually having the sickness (after the positive test!) are on par with getting struck with lightning at some point in their life.

If this still sounds abstract, then you are my hero for somehow avoiding innumerate covid headlines.

A Cleaner Dashboard: Z-Scores Instead Of Price Changes

Most investors or traders’ dashboards includes a watchlist with the field “percentage price change”. Perhaps you have several fields for this. Daily, weekly, monthly.

Here’s a useful way to filter out the noise and get a nicer view of the market action:

Re-scale all the moves in terms of standard deviations

My preference, although it relies on having options data, is to use implied volatility which is the market’s consensus for what the standard deviation is.

Here’s the formulas:

  • Daily = % change on day * 16/IV from yesterday’s ATM straddle
  • Weekly = % change on week * 7.2 / IV week ago
  • Monthly =% change on month * 3.5 / IV month ago

Implied vols are annualized numbers so the factors (16, 7.2, and 3.5) re-scale the vols for the measurement period.

These are just Z-scores!

Observations

  • If the absolute value of any of these numbers exceeds 1, the asset moved more than 1 implied standard deviation.
  • You can put all the assets on the x-axis of a barchart to see them visually. If you want, you can even subtract 1 from each value to see the excess move above one standard deviation. Or you set your filter at any other level.
  • This is not a tool to find opportunities or anything fancy, it’s literally just a cleaner way to visualize price moves and ignore noise.

I was too lazy to make one for stocks or futures, but the output will look like this (instead of MPG imagine it was “price change”):

If you want to use straddle prices which represent mean absolute deviation or MAD then divide the formulas further by .8.

The reason you use .8 is explained in my post Straddles, Volatility, and Win Rates.

What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold

We’re going to go on a little ride to talk about trade prospecting. We’ll use the natural gas futures and options market to demonstrate how to think about markets and what’s required to actually identify opportunities.
The nat gas market is all the rage these days as we head into the winter of 2021/22.

Let’s start with some background.

The Widowmaker

Enter the famous March/April futures spread in the natural gas market. This was the football famously tossed between John Arnold’s Centaurus and Brian Hunter’s Amaranth. You can get a good recount of the story here as recounted by the excellent @HideNotSlide.

The reason it’s a “widowmaker” is the spread can get nasty. The March future, henceforth known by its future code (H), represents the price of gas by the end of winter when supply has been withdrawn from storage.  April (J) is the price of gas in the much milder “shoulder” month. H futures expire in Feb but are called “March” because they are named by when the gas must be delivered. Same with J. They expire in March, but delivered in April. The H/J spread references the spread or difference between the 2 prices.

If you “buy” the spread, you are buying H and selling J.

  • If the price of the spread is positive, the market is backwardated. H is trading premium to J.
  • If the spread is negative, H<J (ie contango)
On 10/6/2021 the spread settled at +$1.44 because:
  • H future = $5.437
  • J future = $3.997

Introducing Options Into The Mix

There are vanilla options that trade on each month.
So there are options that reference the March future and they expire a day before the future (so in February).
  • H settled $5.437 so the ATM straddle would be approximately the $5.45 strike. Strikes in nat gas are a nickel apart.
  • For April futures the ATM strike is the $4.00 line. You can see the J straddle (ATM C + P) settled around $1.14
Image

Commodities Are Not Like Equities

Every option expiry in equities references the same underlying — the common stock price. If you trade Sep, Oct, Nov, or Dec SPY options they all reference the same underlying price.
The December 100 call cannot be worth less than the November 100 call because of simple arbitrage conditions. Your December options also capture the volatility that occurs in November (in fact if you wanted to bet on the volatility just in December, you would structure a time spread that bought December vol and sold November vol, to strip out all the time before November expiration. The structure of that trade is beyond the scope of this post.)
This doesn’t work in commodities because each month has a different underlyer.
Recall H =$5.437 and J = $3.997
  • The H $5 call is almost .44 ITM
  • The J $5 call is a full dollar OTM

Despite J options having a month longer until expiry, the J $5 call trades waaaay under the H $5 call.

It gets better.

Even if H and J were trading the same price, the H $5 call can trade over the J $5 call. This is where newcomers to commodities from equities find their muscle memory misfires.

The H implied volatility can go so far north of the J vol that it can swamp the 1 month time difference.

As described earlier, in an equity, March and April options would reference the same underlyer so owning April vol exposes you to the March vol.

Not true in NG.

Severing the arbitrage link between spreads

Backwardation
H is trading above J. The spread is backwardated. But H and J are not fungible. They are deliverable at different times. If you need H gas, you need H gas. It’s cold today. You cannot wait for J gas to be delivered. You won’t need it then.
This is generally true in commodities.
There is no arb to a backwardated market.
Contango
A contango market can be bounded by the cost of storage. Be careful though. The steep contangos of oil in Spring 2020 and around the GFC are lessons in “limits to arbitrage”. The cost of storage is effectively infinite if you run out of storage. So contango represents the market “bidding for storage”. You can’t just build new storage overnight. The other major input into contango spreads is the funding cost of holding a commodity either via opportunity cost or interest rates. THE GFC was a credit crunch. Funding was squeezed. That cuts right to the heart of “cost of carry” that contango represents.

So we now understand that H and J can become unhinged from each other. That’s why the spread is a widowmaker. It can be pushed around until convergence happens near the expiry of the near month. That’s when reality’s vote gets counted.

More Complexity: Options On Those Crazy Spreads

You can also trade options directly on the H/J futures spread. Since H/J is considered a calendar spread, the options are cleverly named:
Calendar spread options.
The cool kids refer to them as “CSOs”.
Let’s talk CSOs.
We established that the H/J future spread is $1.44
  • You can buy a call option on that spread. You can buy (or sell) an OTM call, like the H/J $10 call.
  • You can buy an ITM call like the H/J $1 call. That option is 44 cents ITM.
  • You can buy a put on the spread. If you buy the H/J 0 put (pronounced “zero put”), that option is currently OTM. It goes ITM if H collapses relative to J and the spread goes negative (ie contango).
These exist in WTI oil as well. Imagine a fairly typical market regime where oil is in contango. The CL1-CL2 spread might trade -.40. That means the front month is .40 under the second month. CSOs trade on these negative spreads as well! If someone buys the -$1.00 put they are betting the market gets even more steeply contango.
I’ll pause for a moment.

Right now, you playing with an example in your mind. Something like: “so if I buy the -$.25 call, I’m rooting for…ahh, CL1 to narrow against CL2 or even trade premium into backwardation”

Don’t be hard on yourself. This is supposed to hurt. It hurts everyone’s head when they learn it. It’s just a language. The more you do it, the easier it gets and with enough reps you won’t remember what it was like to not be able to understand it natively.

Real-life example

These prices are from 10/6/2021 settlement.
H settled $5.437
The H 15 strike call settled $.42
H/J spread = $1.44
H/J $10 CSO call = $.38
Let’s play market maker.
You make some markets around these values:
  • Suppose you get lifted on the CSO call at $.40 (2 cents of edge or 20 ticks. 1/10 cent is min tick size)
  • Meanwhile the other mm on your desk gets her bid hit on the vanilla H 15 call at $.40 (also 2 cents of edge)

Your desk has legged getting long the H 15 call, and short the H/J 10 call for net zero premium. If we zoomed ahead to expiration what are some p/l scenarios?

  • H expires at $5 and J is trading $4 on the day H expires or “rolls off”. Therefore H/J = $1
    • Both calls expire worthless. P/L = 0
  • H expires $15 and J is trading $4 so H/J is $11.
    • Ouch. Your long call expired worthless and your short H/J $10 call expired at $1.00. You just lost a full $1.00 or 1,000 ticks. That’s a pretty wild scenario. H went from $5.43 to $15 and J…didn’t even move?!

How about another scenario.

  • H goes to $16 and J to $7. So H/J expires at $9.
    •  The $10 CSO call you are short expires OTM and the vanilla H 15 call earned you $1.00. Now you made 1000 ticks.

It quickly becomes clear that vol surfaces for these products are untamed. Option models assume bell-curvish type distributions. They are not well-suited for this task. You really have to reason about these like a puzzle in price space. I won’t really dive into how to manage a book like this because it’s very far out of scope for a post but it’s critical to remember that pricing is just one consideration. Mark-to-market, path, margin play a huge role.

Sucker Bets

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

Why? Because it has to balance 2 opposing forces.

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

Let me show you what’s going on with the CSOs:

Image

The CSO options tell us that the H/J spread has roughly 3% chance of settling near $2, a 2% chance of ending near $3 and a 0%  chance of settling anywhere higher than that.
And yet the futures spread is trading $1.44 today! And the options fully expect that to collapse.
What is going on?
Look at history. Even in cold winters, the spread almost always settles….at zero! When H expires, it is basically going to be at the same price as J.
Now, I know nothing of gas fundamentals. And none of this is advice. And I’m not currently up on the market, but I am explaining how these prices look so crazy (as in whoa look at all this opportunity) but it’s actually fair.
The market does something brilliant.
It appreciates path while never giving you great odds on making money on the terminal value of the options.

The Wider Lesson

So how do you make money without a differentiated view on fundamentals in such a market?

There are 2 ways and they double as general lessons.

  1. Play bookie

    You have a team that trades flow. You are trading the screens and voice, you’re getting hit on March calls over here, you’re getting lifted on March puts over there, you’re buying CSO puts on that phone, your clerk is hedging futures spreads on the screens. Unfortunately, this is not really a trade. This is a business. It needs software, expertise, relationships. Sorry not widely helpful.

  2. Radiate outwards

    The other way to make money is prospecting elsewhere, with the knowledge that the gas market is smart. It’s the fair market. It’s not the market where you get the edge, it’s the one that tells you what’s fair or expected. So you prospect for other markets or assets that have moved in response to what happened in the gas market, but did so in a naive way. A way that doesn’t appreciate how much reversion the gas market has priced in. Can you find another asset that’s related, but whose participants are using standard assumptions or surfaces? Use the fair market’s intelligence to inform trades in a dumber or less liquid or stale market.

Trading As a Concept

Many people think that trading is about having a view. Trading is really about measuring the odds of certain outcomes based on market prices. Markets imply or try to tell us something about the future. The job is to find markets that say something contrary about the future and take both bets. Arbitrage is an extreme example of this. If one person thinks the USA basketball is 90% to win the gold and another thinks the field is 15% to win the gold you can bet against them both and get paid $105 while knowing you’ll only owe $100. Trading identifying similar examples but of course in reality they are hard to find, more difficult, and require creativity and proper access.To see the present clearly you must be agnostic. You look for contrary propositions. Trading is not about having strong opinions. It’s not thematic. You don’t have some grand view of what the future looks like or the implications of some emerging technology or change in regulations. You just want to find prices that disagree.
Why would you slug it out in smart markets? Use them to find trades in markets that radiate away from them that are not incorporating parameters from the smart market fully. If you can’t get away from fair markets, you are going to need to be absolutely elite.
Battling it out in SPY reminds me of this cartoon:

The solutions in markets are rarely going to be where it’s easy to see because that’s where everyone will be looking.

Happy prospecting.


If you found CSOs interesting recognize there are physical assets that are just like options on a spread.

  • Oil refineries =Heat/Gas crack options
  • Power plants =  Spark spread options
  • Oil storage facility = WTI CSO puts
  • Soybean mill that crushes soy into meal/bean oil

If you had a cap ex program to build one of these assets how would you value it? You’d need to model volatility for the spread between its inputs and outputs!

The owners of these assets understand this. They are the ones selling CSOs! It’s the closest hedge to their business.


I got the data for this post from the CME website’s nat gas settlements page.
The dropdowns on the right of the page should keep you busy.
Image

Portfolio Theory And The Invisible Option On Hobbies

In summer of 2020, I published a short post (4 min read) that I believe holds several deeply important investing meta-lessons. It’s called You Don’t See The Whole Picture.

Using the dad voice I use on my sons when I think they are sandbaggin’, I’ll say: you should really read it.

I’ll wait.


Ok, just so we are on the same page, I’ll spell out its lessons:

  1. The impact of correlations is not intuitive. The investment universe is mind-blowingly vast so the returns to concentration along with the narratives will grab the headlines. But boring risk management is the “blocking and tackling” of winning the long game.

    Prescription:  Take portfolio construction seriously. Because it’s not intuitive, grokking it can give you an edge1.

  2. Smart investors understand correlations and portfolio theory. In their battle to construct the most efficient risk-adjusted portfolios, they arb away the reward for idiosyncratic risk.

    Prescription: Diversify so you are only left the irreducible systematic risks that you do get paid for2.

  3. The correct reflex for a price that doesn’t make sense is not “that’s stupid”, but “what am I missing?”

    Prescription: Mind your dashboard3. Are the tools you look at capable of showing you the correct picture? A dissonant price means your model of how things work is incomplete. 

These three ideas point to a subtle implication which extends beyond investing but is [to me at least] most legible from the lens of portfolio and options theory:

The value of an asset viewed in isolation is actually a floor.

DCF As The Zero Strike

Let’s stay in the business world for now.

A company’s value can be much higher than a DCF-based valuation if it improves the portfolio of its most efficient holder. In that post, the SUN shareholder’s portfolio is the highest and best use of RAIN shares. I’d expect the SUN shareholder to set the marginal price of RAIN.

Meanwhile non-holders of SUN are looking at RAIN in a vacuum and concluding it’s an overpriced coin flip not an investment. It’s gotta be a bubble, right?

They just don’t see what SUN shareholders see. It’s like when a market maker gets their bid hit on a slug of super cheap XYZ vol, only to find out that some hedge fund bought a convert or ASR at a much lower implied XYZ vol. Just like the person selling RAIN shares to SUN holder, the market maker is getting arbed by someone who sees a fuller picture.

So when we value a business, say using DCF (“discounted cash flow” he said as he dismounted a dinosaur), that’s the floor price. Even if there were no other potential investors that could be a strategic buyer for our business, we know it’s worth its DCF4.

So there is optionality struck at the DCF value!

The option represents the gap between the DCF and the price a strategic investor would pay.

Understanding The Option

The value of a traditional call option depends on several easily observable inputs: the strike, distance from the strike, interest rates, and time to expiry. The input we cannot observe is the volatility of the underlying asset during the the life of the option.

If you have heard of the “greeks” they are just measures of sensitivity of the price of an option with respect to one of these inputs5.

So the big question: what does this option to be acquired by a more efficent portfolio or strategic investor depend on?

Connectivity and divergence

I don’t have any formal or quantitative explanations but the reasons feel intuitive.

Connectivity

If “DCF in isolation” is our lower bound, the option struck from that point starts to accrue value as the number of entities in the world grow. A seesaw is worthless until a second kid shows up. More interconnections means more possible portfolio combinations. And the value of the option is maximized by the portfolio that can find the best combination on the frontier of risk/reward. 

Embedded in connectivity is how networked information is. You could have a world with many companies, but if they don’t know about each other. That information bottleneck would impair the value of the option even if there were theoretically many combinations.

Divergence

This goes back to how counter-correlations lower the risk of portfolios. If your business looks like every other, than there is no room for you to marginally improve the portfolio of a suitor. They already would have acquired one of the businesses you resemble. The premium to your DCF value is a function of your divergence or scarcity.

To recap so far:

  • Straightforward valuation methods like DCF set a floor on a company’s value. 

  • There is additional optionality value that comes from the fact that the idiosyncracies of a business may offset risks of other businesses in an investor’s portfolio. The investor can afford to pay a premium to DCF for this diversification and come out ahead6

  • The value of that extra optionality depends on how many possible combinations exist (ie how networked the world is) and how divergent the company’s risks or opportunties are. While any attempt to compute “greeks” for these sensitivites is above my paygrade (this is a blog post and my pay is zero) they feel like useful concepts to consider. I’d also recommend, in the spirit of option greeks, to consider them in an “all else equal” manner7.

Beyond Investing

A business is just an instance of the wider category “generating”. Businesses generate solutions. A car is a  solution.

Every activity from playing sport or writing a song or cooking is generating. Some of these activities are useful to others. But the value can also be isolated. If you decide to hike across the country, it generates intrinsic value for you. Before you did it, you considered the value and decided on its own it was a worthwhile endeavor.

But as connectivity increased, the idea that you could blog about a hike (perhaps even funding it) expanded the value of this otherwise narrow but concentrated endeavor. The hiker always owned a call option on the rewards of this endeavor, but the internet gave that option value.

A graphic designer. An orater. A mind that excels at games. All of these concentrated endeavors are generating functions. But the leverage embedded in connectivity maximizes their value. A nerd with a niche interest in cryptography suddenly finds their hobby of significant complementary value to the finance establishment.

In an age of side-hustles, doing something for its own sake can seem wasteful. Or some people might feel “I don’t want to do X unless I’m going to get really good at it”. I feel that way sometimes too. For a certain type of person, it’s an encouraging reminder, that as the world continues forming synapses, those “selfish” hours spent doing something “weird” might have a lot more value than what you think they do today. I suspect the value of these options can only be seen in hindsight8.  But take heart.

At worst, they are their own reward and any upside, no matter how remote, is yours too.




Teach A Math Idea To Internalize It

My 8-year-old Zak is going to be taking the OLSAT soon. It’s a 64-question test that looks an awful lot like an IQ test. The test (or one of its brethren like the CoGat) is administered to all 3rd graders in CA. If you score in the top 2 or 3% you can be eligible for your local ‘gifted and talented’ program. 20% of the questions are considered “very challenging” and that’s where the separation on the high end happens.

I gave Zak a practice test just to familiarize him with it. He’s never taken a test with a time limit before and never filled out Scantron bubbles. Do not underestimate how confusing those sheets are to kids. It took a while for him to register how it worked because he only saw choices A,B,C,D for each of the 64 questions.

Daddy, the answer to question 1 is ‘cat’ not A,B,C, or D

I know, Zak, it’s just that…you know what bud, how about just circle the right answer on the question for now.

Hopefully, some practice breaks the seal so he isn’t scared when he sits for his first test ever. I think a small amount of prep is helpful even though I get the sense that caring about tests is not in style around here. Call me old-fashioned. I’m not bringing out a whip, but having the option to go to the program seems worth putting in a token effort if you think your kid has a shot.

Anyway, he took one test. Poking around a bit, I think his raw score would land him in the 90th percentile. Not good enough but it was his first shot and if he doesn’t improve much, that’s also totally fine too. Plenty of people are content just flipping burgers (I’m kidding, calm down. Also, get your own kid to stuff your insecurities into). One thing did stand out. He got all the math questions (about 1/3 of the test) correct.

Hmm.

It made me think of how I was a decent math student growing up.

I'm Something of a Scientist Myself | Know Your Meme

Not good enough to compete with peers who did math team in HS, but enough to get through Calc BC. Regretfully, I never took another math class after that. I optimized my college courses for A’s not learning. Short-sighted.

I really felt the pain of that decision when I got hired to trade options and was surrounded by a cohort in which 50% of the trainees had an 800 math SAT. (There were 3 people in our office of about 60 that had an SAT verbal > math. I was one of them.) That inferiority exists even to this day. Until Google Translate can decode academic papers, those things are for lining birdcages.

However…

Every now and then, I’ll come across a math topic that seems useful for making estimates about practical things, so I’ll learn it.

And then I’m reminded I have no math gifts because that learning process is uphill in molasses. When I was young I did lots of practice problems (how else are you supposed to become a doctor and please mom) which got me proficient. Today, it’s a similar process. I just power through it.

But there is a difference in how I power through it.

Instead of practice problems, I watch YouTube until I can write the ELI5 version for others. Everyone has heard that if you want to test your knowledge, teach it to others. In that case, it’s a win-win. We all learn.

So that’s what I did this week. I wrote an ELI5 version of a concept called Jensen’s Inequality.

  • Jensen’s Inequality As An Intuition Tool (10 min read)

    You will learn:

    • Why I found Jensen’s Inequality interesting
    • The conditions and statement of the inequality
    • An example that affects us all
    • Spotting Jensen’s in the wild

    If you struggle to understand it after reading it tell me. I am challenging myself to see if I can relay not just the concept but the significance of it with minimal effort on behalf of the reader. If I can get to the point where I’m “putting in the effort so you don’t have to” then I’ll feel like I’m being useful here.

    If you think you got it, test yourself the way I did. Construct an example. (That’s what I did with the “traffic on the way to Sizzler” example.)

  • If you grok Jensen’s Inequality and want to relate it to portfolio construction Corey is your guy. Before I learned of this concept his tweets would have made no sense to me, but now I at least kinda get it.

Moontower #120

My 8-year-old Zak is going to be taking the OLSAT soon. It’s a 64-question test that looks an awful lot like an IQ test. The test (or one of its brethren like the CoGat) is administered to all 3rd graders in CA. If you score in the top 2 or 3% you can be eligible for your local ‘gifted and talented’ program. 20% of the questions are considered “very challenging” and that’s where the separation on the high end happens.

I gave Zak a practice test just to familiarize him with it. He’s never taken a test with a time limit before and never filled out Scantron bubbles. Do not underestimate how confusing those sheets are to kids. It took a while for him to register how it worked because he only saw choices A,B,C,D for each of the 64 questions.

Daddy, the answer to question 1 is ‘cat’ not A,B,C, or D

I know, Zak, it’s just that…you know what bud, how about just circle the right answer on the question for now.

Hopefully, some practice breaks the seal so he isn’t scared when he sits for his first test ever. I think a small amount of prep is helpful even though I get the sense that caring about tests is not in style around here. Call me old-fashioned. I’m not bringing out a whip, but having the option to go to the program seems worth putting in a token effort if you think your kid has a shot.

Anyway, he took one test. Poking around a bit, I think his raw score would land him in the 90th percentile. Not good enough but it was his first shot and if he doesn’t improve much, that’s also totally fine too. Plenty of people are content just flipping burgers (I’m kidding, calm down. Also, get your own kid to stuff your insecurities into). One thing did stand out. He got all the math questions (about 1/3 of the test) correct.

Hmm.

It made me think of how I was a decent math student growing up.

I'm Something of a Scientist Myself | Know Your Meme

Not good enough to compete with peers who did math team in HS, but enough to get through Calc BC. Regretfully, I never took another math class after that. I optimized my college courses for A’s not learning. Short-sighted.

I really felt the pain of that decision when I got hired to trade options and was surrounded by a cohort in which 50% of the trainees had an 800 math SAT. (There were 3 people in our office of about 60 that had an SAT verbal > math. I was one of them.) That inferiority exists even to this day. Until Google Translate can decode academic papers, those things are for lining birdcages.

However…

Every now and then, I’ll come across a math topic that seems useful for making estimates about practical things, so I’ll learn it.

And then I’m reminded I have no math gifts because that learning process is uphill in molasses. When I was young I did lots of practice problems (how else are you supposed to become a doctor and please mom) which got me proficient. Today, it’s a similar process. I just power through it.

But there is a difference in how I power through it.

Instead of practice problems, I watch YouTube until I can write the ELI5 version for others. Everyone has heard that if you want to test your knowledge, teach it to others. In that case, it’s a win-win. We all learn.

So that’s what I did this week. I wrote an ELI5 version of a concept called Jensen’s Inequality.

  • Jensen’s Inequality As An Intuition Tool (10 min read)

    You will learn:

    • Why I found Jensen’s Inequality interesting
    • The conditions and statement of the inequality
    • An example that affects us all
    • Spotting Jensen’s in the wild

    If you struggle to understand it after reading it tell me. I am challenging myself to see if I can relay not just the concept but the significance of it with minimal effort on behalf of the reader. If I can get to the point where I’m “putting in the effort so you don’t have to” then I’ll feel like I’m being useful here.

    If you think you got it, test yourself the way I did. Construct an example. (That’s what I did with the “traffic on the way to Sizzler” example.)

  • If you grok Jensen’s Inequality and want to relate it to portfolio construction Corey is your guy. Before I learned of this concept his tweets would have made no sense to me, but now I at least kinda get it.

Money Angle

My buddy Jake sent me this post:

Active vs. Passive Investing and the “Suckers at the Poker Table” Fallacy.

It’s an 8-minute read worthy of your time because it demonstrates several useful realities about markets.

  • Reconciling a paradox: The idea that smart active managers can profit from the distortion of passive flows but if everyone is passive then there are no longer active suckers to exploit.

    The author does a neat demonstration decomposing market returns into money-weighted returns (active) and dollar-cost-averaging (passive) to disentangle beta from alpha.

  • Markets are not a zero-sum game, even if the battle for “alpha” is.

    The size of the profits pie is not fixed…The “suckers at the poker table” paradigm goes astray because there isn’t some exogenous fixed size of the investment pie investors are fighting over. The returns are endogenous: They are in part determined by how smart the investors are, how well the capital in the economy is allocated, and by everything else that impacts economic and market outcomes.

    …Smart money going into appropriately priced investment opportunities grows the whole pie. Dumb money going to bad businesses shrinks the pie. Once it’s not a strictly zero-sum game, you don’t need “suckers at the poker table” to outperform.

  • The demonstration shows how there is no such thing as truly passive. And if I may add, that means benchmarking your investing, which is constrained by your personal asset/liability picture (ie sometimes you get a bonus or extra cash to add to the market and sometimes you need to pull money out to send a kid to college) to some index is not a great comparison.

    If you’re planning to invest for an objective other than buying and holding forever, you have to make decisions about when and how much to invest and when and how much to withdraw. On a sufficiently long timeline, the probability of being a completely passive investor goes to zero.

    Eventually, you have to make an active investment decision, and at that point, the shrewd investors are lying in wait. Everyone eventually has to pay Charon to cross the river Styx.

In addition to these points, there’s a brief aside about the Grossman-Stiglitz Paradox which is a rabbit hole of its own. I’d buy stock in that paradox as something you will continue to hear more about.

Finally, while the author finds the zero-sumness of poker to be a poor analogy for investing, he links to a post about how poker has useful lessons for risk management called Getting Schooled In Risk (12 min read).

From My Actual Life

I got married 12 years ago on October 2nd. The wedding was in Cabo which means everyone sweat right through their clothes. The pictures of the reception look like the finish line of a marathon.

When I was at my mom’s house this summer, I found a treat in the magazine stand. It was the personalized US Weekly Yinh made for the guests. I’m unapologetically biased, but this is the greatest document ever made.