Calibrated Confidence

Author and veteran trader Brent Donnelly’s recent post, #37, in his highly educational, free Substack series 50 Trades In 50 Weeks dissects common traits of successful traders:

Week 37: Common Traits of Top Traders (10 min read)

It’s a terrific read for what it validates, but also for what is surprising (“You can succeed in trading with any level of risk appetite.”) It’s also a great read to see how he constructs a survey to challenge his beliefs.

I want to zoom in on one of the key 5 key traits he identifies: “calibrated confidence”.

When we hosted the StockSlam sessions in October we gave a couple of homeworks before the in-person events. One of the homeworks involved this module:

You will be asked to make 90% confidence intervals on some facts.

90% confidence interval can be understood with an example:

I have not been outside for a few hours, and without looking up the answer, “I’m 90% confident that the temperature outside my window is between 45°F and 60°F, or (45,60).”  If I wanted to be more (like 99%) confident, I would widen the interval, and conversely a tighter interval would coincide with less confidence.

Example questions included:

  • Without looking anything up, what is your 90% confidence interval on the number of bones in the human body?
  • What is your 90% confidence interval on the length (# of letters) of the longest word in English?

Note what you are doing. You are making markets where you think fair value is 90% to be inside your bid/ask spread.

This is highly relevant to trading and handicapping.

If you get 10 out 10 markets “right” then you are more conservative than we asked you to be. In other words, you were too wide. In markets, this means you will never trade. You are bidding $50 for a stock trading $60. You will get no market share.

If you get say 5 out of 10 markets right, then you were too confident. In markets, everyone will trade with you and you will be sadder for it.

Trading is only partially about knowing “fair value”. It’s in your meta-knowledge about fair value that the magic happens. You are always dealing in uncertainty…your feel for the degree of uncertainty is how you recognize opportunity or defend yourself. This is not just market-maker talk. It’s the essence of what Buffet understood when he said “margin of safety”.

Google “Paul Slovic’s horse bettor study” and you will find several posts such as:

How Can Confidence Kill Investment Returns? (4 min read)

They all talk about a 1973 study where experienced horse handicappers are given a few pieces of data of their own choosing. Armed with their preferred data, they are able to make good bets, but critically, they are well-calibrated about their accuracy. Their confidence and accuracy were in agreement.

However, as the bettors are given increasing amounts of data their accuracy falls, but their confidence shoots up. No bueno.

Presumably, they were less experienced in weighing the additional data which turns out to be noise to their handicapping process, but the presence of more info gave them the illusion that they would be better. A disastrous combo.

Improving Our Handicapping Skills

It sounds discouraging to realize that decision-making is not just an exercise in accurate prediction but also judging how wide our error bars should be. But there’s plenty of good news. This is not a skill anyone is born with. It is learned.

[This is why prop trading firms who recruit elite students from top schools screen for teachability which I suspect is randomly allocated across skill. There are elite students or athletes who can remain humble learners despite the advantages of their talents and there are insufferably overconfident talents who have yet to get hit by the Mack truck of peak competition. This latter group is dangerous to themselves and if given enough rope, to their backers too.]

3 suggestions to get better:

  1. Self-diagnose. You can take a fun calibration test to establish some context:

    This thread includes my results as well as many others including several side threads of interpretation and discussion.

  2. Read Superforecasting: The Art and Science of PredictionThis book is a great primer on what it takes to predict but most importantly frames prediction as a skill we can improve at. I took extensive notes which weave my thoughts into some of the key points.
  3. Bet on stuffHow long will it take to finish your school or work assignment?What percent of random sample of people from your contact list knows what date the winter solstice falls on?(My wife and I bet on what facts are “common knowledge” when one of us gets defensive to the other’s attack “how did you not know that?” We’ll poll some people with a text message and bet on the consensus. These “studies” are highly correlated with one of us having “one drink too many”.)

    Calibration is a nice benefit of a betting culture (1 min read).

The Investing Version Of “Nothing Good Happens After Midnight”

This was a brutal week in the investing world. The fraud at FTX was one of the largest overnight destructions of wealth in financial history. It impacts holders of crypto assets, the employees building projects in decentralized finance, equities, and traditional VC firms (Sequoia allegedly wrote down a $200mm investment to zero).

Excerpting from kyla scanlon:

And with FTX and SBF, it’s worse than other times in crypto. It’s so much worse. They posed themselves as these people that were trying to make the world better. There’s a difference between crypto going down because no one believes in it and crypto going down because it’s systematically being rugged…Many innocent people got wrapped into this because they saw Tom Brady or they saw Sam’s face on a telephone pole – and it was supposed to be safe.

In a calibrating industry, it’s easy to find holes to exploit, which is what FTX did perfectly. They saw opportunity, the VCs saw that they saw an opportunity, and people that wanted to be in crypto believed all of them. And of course, it’s like – well why *wouldn’t* you believe them. And that’s the hardest part.

While I agree with everything she says in the post, I want to address what’s unsaid.

There’s way too much obsession with investments as a way to get rich in the first place. It’s misallocated attention. It’s misplaced energy. I feel like the collective benefit of saying this is so diffuse that nobody has the incentive to tell you the truth. Just like Big Food or Big Ag will never commission a study on “intermittent fasting”. No single entity profits from the absence of eating 3 American-sized meals a day.

Same with investing. Who gains from telling people that much of the brain cycles we spend on investing are a waste of time? Maybe advisors with white-glove fees and Vanguard. Vanguard is a quasi-mutual company (investors are owners of the asset manager in a sense). Bogle undercut an industry to tell you what others wouldn’t. There are worse people to be aligned with.

We need a bit of real talk. I’m sorry if you feel like I should have told you sooner (although, I did). At first glance, this talk might sound discouraging. But take a second glance. This should liberate you. This will give you back countless hours of your time that you can use to row towards your goal with strength. Without distraction. And with less reliance on fate.

[This is an edited version of an off-the-cuff thread I wrote when I was too lazy to get out of bed yesterday]

Unless you are already rich, the proposition of earning 6% per year (insert your favorite ERP) with a 20% standard deviation and a fat left tail is not going to lead to the durable wealth you want. At least not on the timeline you want. This is discouraging and fairly obvious if you look at the proposition for what it is (some people might think you earn 10% per year in equities or harbor some other delusions about the proposition. It’s 2022, you’re entitled to “use Your own illusions” — sorry it’s the 30-year anniversary).

But we’re Americans. We are all entitled to do better than average, right? 🤨

So we snuggle up to crypto, privates, self-storage, or whatever makes you feel special. Unfortunately, investing done well, shouldn’t feel comfortable. Truly fat risk premiums feel like caffeine before bed. They make you anxious and insomniac. You should be afraid of feeling warm and righteous. This is the fundamental nature of beating point spreads.

Don’t you think that adjusted for risk (even simply by a street-smart “this sounds too good to be true” instincts) that the propositions of these shiny investments are similar to what you are presented in public markets? That’s actually your best-case scenario, where you avoid stepping on landmines.

Think about it.

There are super rich, savvy people staffing professionals in their family offices with tentacles everywhere bidding on everything. It’s very unlikely to find something special unless it’s your literal full-time job. And even when you do find something compelling in your part-time research, there should be a lower bound to your skepticism that inhibits you from sizing the exposure in a way that would make you rich quickly anyway.

If you put on your ‘equilibrium thinking’ cap you realize that it’s contradictory to think you can get rich quickly, in a prudent way, investing as a part-timer. Someone needs to hold underperformance bags. Unless this is your craft, you should expect to be a baggie if you push. The very conceit that you can find and pull out a meaningful number of diamonds from a coal pile picked over 24/7 by well-capitalized professionals is illogical.

Said simply: If you do not devote your life to the competitive task of investing, you cannot get rich quickly. You might by accident but hope is not a strategy. (Anyone know the money-weighted returns of ARKK or crypto investors? I suspect, despite positive track records in return space, their total dollar p/l is very negative. Sometimes the simplest benchmark is useful — what are your net dollar profits? There are fund managers that have probably made more from fees than their investors have made in p/l.)

And devoting your life to investing is not a guarantee either. It’s a low signal-to-noise endeavor. The best you can often hope for is a “chip and a chair”.

Nothing Good Happens After Midnight

You know exactly what that expression means.

The markets version of this is:

Don’t obsess about investing beyond the point of diminishing returns.

Yes, you should absolutely learn about:

  • compounding
  • saving
  • fees
  • taxes
  • diversification
  • implementing or getting help to construct a portfolio with simple rules

Now stop and go home. It’s that last double-shot Irish-car bomb at last call that causes the morning headache (or coyote morning 😬)

If you want to get rich without being reckless, Naval Ravikant has a valid formula:

  • specific knowledge
  • leverage
  • accountability (own your risks)

[I would actually edit this. My version:

  • do work nobody wants to do because it’s hard or otherwise unattractive
  • leverage
  • scarcity

I’d like to say “accountability” but looking at the new American dream of private gains/socialized losses and all types of bureaucratic capture I need to annoyingly quote Taleb:

Courage cannot be faked; the warrior bore the risk of his deserved glory in the service of his countryman. The ‘primacy of the risk-taker’ has been a feature of nearly all human civilization. When we reward leaders who did not bear commensurate risks we undermine virtue. Society frays as the truly virtuous/courageous bristles as they watch.]

A thought for the time

For the innocents and believers who made careers in crypto and made it their specific knowledge, I’m sad and sorry. I have a closet of FTX swag because I have a friend there and felt terrible watching this week.

I do believe it was a good bet to go into that world (although not to denominate your whole net worth in it… specific knowledge and the numeraire you take its yield in are different) and would have considered it myself. A career in crypto was a reasonable bet because the human capital is fungible with other careers, thus lowering its opportunity cost.

In addition, crypto as a small investment allocation was reasonable. But as an investment, like all investments, sizing is everything.

If you want to go big or go home, it’s best to do so on your skills or personal edge. Not on arms-length allocations to something that is big, accessible by mouse, and widely known about. The risk/reward once it had achieved mass awareness couldn’t be too out of line with other investable assets despite what all the promotors tell you.

And, critically, before you can allow yourself to get excited, remember that any sensible sizing rules neuter the returns to effort. That means you’ll always be disappointed in how much you won when you were right. In chapter 2 of Laws Of Trading Agustin Lebron explains — good trades make you wish you traded bigger, bad trades make you wish you traded less or none.

The very act of trading subscribes you to remorse. In hindsight, you always regret your sizing.

A parting message

Focus on your human capital to get rich. Your human capital > financial capital, it just doesn’t show up on a spreadsheet. In my own life, I don’t even say “investing”. I think of growing assets as “savings plus”. I’m just trying to maximize the chance of meeting my future liabilities.

I’ll rely on myself to get rich (not that anything that vague would motivate me, but you know me by now).

More on these themes from the Moontower Money Wiki:

Portfolio Theory In The Wild: Funding YouTube Creators

The Business Breakdowns podcast interviewed Aaron DeBevoise, found of Spotter.

Link (with transcript):

Spotter is a private company that provides knowledge and capital to YouTube creators including MrBeast.

There were 2 great examples of “portfolio theory in the wild”. I will relate them back to where I’ve covered these ideas before and their implication.

1) Optimize the asset

Aaron describes the funding model:

We’re actually not equity for creators. We don’t have a say in their business. There’s no feeling of obligation outside of continuing to do what they do. Loans are really scary for creators because the whole issue with creators is that their business is actually fairly volatile…our approach was, hey, we’ll purchase or license the back catalog, the catalog — the videos that have already been uploaded all the way through the deal and we know their information. It’s almost like postbox office financing for movies. You already know what the box office is and therefore, you can predict what the future might hold and the creator gets to keep 100% of your future videos’ revenues. So if you have 1,000 videos today, we’ll license all 1,000 — the revenue from that, the revenue stream from those videos, the first bit is you upload after the deal, 100% of the revenue goes to you, and we keep 100% of the past. So it’s really not a loan, it’s not equity. It’s more of a cash-flow acquisition financing.

Host Ali Hamed correctly compares it to the music royalty business where investors buy the cashflow an artists’ back catalog. Aaron zeros in on the key differences (emphasis mine):

That’s a great, great comparison. I mean, it’s the first one that always comes out as the music royalty financing business is very similar to this. But there are some really specific differences. So in music, 20 years ago, a lot of the financings that were happening were discounts on future potential cash flows, but those cash flows were fairly determined. It was literally like where are you going to get distributed on radio or on other platforms, but it wasn’t that you were going to go optimize those music assets too much. So it was — we should expect you to make $1 million, we’ll pay $800,000 today. And then the multiple started to expand because the opportunity to optimize those assets, the music royalties, distributing on Spotify and other platforms became so much bigger that, that’s why the multiples grew plus competition. It’s fundamentally different and the optimization of YouTube assets is really around advertising. In our current business, we don’t really buy distribution rights to other platforms. We really focus on the YouTube opportunity, which makes it a really clean deal. So our focus is ad optimization. We can get more dollars out of an individual video than an auction would be delivering. At some point, as we get better at that ad optimization, can pay creators a premium to what they would otherwise make.

The second thing that’s really different, and I think is the most important difference is the motivation behind why people sell royalties to music versus what someone can do on YouTube. So typically, the music royalty licensing business or acquisition business is an exit strategy for most musicians. It’s not really, hey, I’m going to sell $0.5 million worth of my royalty so I can market my next album with a lot more money. You see Sting selling his past catalog for $300 million, and he’s not going to make six more albums out of that. Whereas in YouTube, the ability for that creator to immediately deploy that capital and grow their business is really amazing. And so that’s why we see exponential growth in creators that we’re giving money to. They’re taking the money. And yes, they might buy a house or something. But most of the time, they’re investing in themselves because the growth opportunity is there. So we’ve actually seen deals where we’ll do a deal that’s — the first deal is $4 million where the next deal might be four times the size of that in, like, span of eight months.

Aaron explains how they “optimize the asset”:

The auction itself, like I said, has millions of advertisers. The way that they buy is really based on audience. They think, hey, I have a product that fits males 18 to 34, who like gaming. And then they buy that way. That’s really effective to buy at scale for advertisers, but it doesn’t actually specifically pick out content that is either suitable or aligned with the brand’s initiatives. So he can’t go out and say, hey, I’m going to buy MrBeast because I love what he stands for and his audience has much higher engagement. And therefore, I think I can get more effective click-through rates. What we do is we’re able to say, hey, actually, I know you might be landing on MrBeast, right? Or you might be landing on some other channel, but you don’t know that you are. And we, because we own those assets can actually say, we will guarantee that you land on these assets. And the reason we’ve actually invested in these assets is because they have high level of engagement and high levels of engagement leads to predictable behavior.

It’s not that we went out and just said, here are bunch of underpriced assets that we can now sell at a higher rate. You use a bunch of valuable assets that you’re not realizing that they’re valuable as an advertiser until we tell you. And once you do that, when you put your ads on our content, it’s actually a way more effective ad buy, meaning that in the auction, you probably have to serve two or three ads for every one ad you serve on the content that has high engagement. There was this opportunity to optimize for the advertiser, and therefore, they should be willing to pay you more for those ad units.

Their ability to do this rests on a data advantage which acts as a moat:

First and foremost, it’s a data-driven business. We have 10 years of historical data around all sorts of data points around viewership and monetization that helps us be able to predict the future pretty well. And that has proven to be very challenging to do just if you wanted to start today, it would be really hard. And even we’ve gotten way better at it as we financed more content. So actually financing more content has allowed us to get more accurate, and pay higher prices. So the better you get, the more you can afford to pay because the more accurate you’re going to be and continuing to build that moat where we’re seeing second deals and third deals. The reason we can get those second and third deals to much higher prices is not only because the creator has done a better job or has become more popular. It was because we’ve learned that catalog over time. And so when we look at another video on top of a catalog that we already own, we have a way higher confidence in our role in the performance of those assets.

2) This is a portfolio business


Any one channel can have a downturn and other channels have an upturn…It is a portfolio play. So the more you deploy on YouTube, the safer you are, which allows us to be more aggressive in our pricing with creators because we can assume that we’ll deploy $1 billion. And that’s obviously safer thousands of channels than doing any kind of single event, right? Single-picture financing on movies is one of the riskiest things you can do… And this is why creators going to banks by themselves is really hard. An individual creator can literally have a terrible 12 months and then become a hit again. Never going to be a business where banks can individually loan out capital to creators based on their YouTube revenue streams.

Relating This Back To Portfolio Theory

By figuring out how to “optimize the asset” and diversify properties that on their own highly volatile, Spotter becomes the most efficient bidder for the financing deals. since they are able to earn the highest returns on the assets both from playing offense (optimizing the asset) and defense (diversification), they are better suited to own the risk and therefore capture the return. And since they can be the highest bidder, they get first look at upcoming deals.

The idea of “optimizing an asset” is similar to a familiar theme in the rise of large tech companies. In recent decades has been their ability to deploy capital safely because of the insights afforded from virtuous data loops. In A Former Market Maker’s Perception of PFOF, I describe the dynamic in the context of market makers paying for order flow:

These [prop] shops came of age at the same time as the giant tech firms. This is a hint of how much they have in common. The difference is the size of the relative opportunities, but the tactics are similiar.

It started with skill and luck. The early big bets on talent and technology meant they were bringing guns to a knife fight. SIG wasn’t know as the “evil empire” on the Amex just because of the black jackets we wore. They understood the risk-reward was completely outsized to what it should be 25 years ago. They were amongst the first to tighten markets to steal market share. They accepted slightly worse risk-reward per trade but for way more absolute dollars. They then used the cash to scale more broadly. This allowed them to “get a look on everything”. Which means you can price and hedge even tighter. Which means you can re-invest at a yet faster rate…The parallels to big tech write themselves. A few firms who bet big on the right markets start printing cash. This kicks off the flywheel:

Provide better product –> increase market share –> harvest proprietary data. Circle back to start.

The lead over your competitors compounds. Competitors die off. They call you a monopoly.

In Making Uncommon Knowledge Common, Kevin Kwok describes a unifying theme behind the success of 3 companies Rich Barton founded (Zillow, Glassdoor, and Expedia!):

The Rich Barton Playbook for winning markets through Data Content Loops…In order to grow their demand high enough to become a beneficial flywheel, Barton’s companies use a Data Content Loop to bootstrap their demand and create unique content and index an industry online (homes for Zillow, hotels and flights for Expedia, companies for Glassdoor). These Data Content Loops help the companies reach the scale where other loops like SEO, brand, and network effects can kick in. Barton’s companies then use this content to own search for their market. This gives them a durable and strong source of free user acquisition, which enables them to own demand…The Data Content Loops of Barton’s companies let them be the authoritative public source on a subject at scale and low cost. The ultimate purpose of the “Data Content Loops + SEO” strategy of Barton’s companies is to own the demand side of an industry…Barton’s companies take industries that are low frequency and use their Data Content Loops and SEO to acquire users for free and engage them more frequently…Owning demand ultimately becomes its own compounding loop since becoming a trusted brand builds its own network effects.

The upshot of all of this: competitors who don’t have the same information or capabilities, will think Spotter is overpaying.

This same dynamic shows up in trading. Your default response to a strange-looking price shouldn’t be “that’s dumb”, it’s “what am I missing?”

Recall this section from You Don’t See The Whole Picture:

When You Don’t Understand The Price You Don’t Understand The Picture

Price is set by the buyer best equipped to underwrite the risk.

A market-maker example:

If X is willing to pay me a high looking price for a stock or option, what’s the probability they are selling something else to someone else such that they are happy to pay me the “high” price? 

Let’s say a call overwriter sees a modest surge in implied vol and is happy to collect some extra premium. Except he’s selling calls to a Citadel market-maker who’s happy to pay the “high” price because her desk is selling index vol. In fact, they are selling index implied correlation at 110%. You might be happy selling the calls for 2% when they are usually worth 1%, but if the person buying them from you knows they are worth 3% at the time you sold them then make no mistake, you are playing a losing game.

However, if your professional edge is in deeply understanding the stock you are selling calls on, then you might be the one capturing the edge in the expensive calls. You are capturing it ultimately from the fact that index volatility is ripping higher and market makers are simply capturing the margin between the weighted option prices of the single stock in proportion to the index volatility. So you, the informed single stock manager, is making edge against the index volatility buyer who set off the chain of events.

The decomposition of the edge between you and the market maker is unclear. But the lesson is you must know where you stand in the pecking order.

An option relative value trade example:

 If volatility surges in A but not in B and they are tightly correlated let’s look at how 2 different market participants might react.


The naive investor is not monitoring the universe of names. They do not think cross-sectionally. They see a surge in A and decide to sell it. It may or may not work out. It’s a risky trade with commensurate reward potential.


The sophisticated trader recognizes they can sell A and buy B whose option prices are still stale (perhaps there has been a systematic seller in B who has been price insensitive. Maybe from the same class of investor our friend “naive” came from. They don’t look at the market broadly and realize the thing they are selling is starting to “stick out” as cheap to all the sharps).

Here’s the key: the sophisticated trader will do the same trade as the naive one but by hedging the vol with B, they can do the whole package bigger than if they simply sold A naked.

The sophisticated traders are the ones who see lots of flow. They “know where everything is”. While in this example, sophisticated and naive both sold A there will be times when sophisticated is lifting naive’s offer. Sophisticated has sorted the entire market and is optimizing buys and sells cross-sectionally.

Are you the fish at the table?

Flow traders and market makers are always wondering if their counterparty is legging a portfolio that they’d like to leg themselves if they saw the whole picture…Mathematical expectancy, like a house’s edge, is priced by its most efficient holder. If prices are always being set by the party who most efficiently underwrites/hedges/prices the risk and you know you are not one of those parties then you should wonder…am I being arbed?


Spotter digs a moat between itself and its competitors by:

  1. narrowly focusing on one channel — YouTube
  2. this allows it to optimize the assets within that investing landscape
  3. which allows it to build the most efficient portfolio; and therefore bid the highest

This series of actions gives Spotter “first look” at the deals in the space further reinforcing the loop, allows it to deploy capital faster, and ultimately have a small advantage compound until it creates a meaningful gap between itself and the competition.

Further reading

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

It talks about how, now more than ever, activities you may do for fun might turn into opportunities.

An Example Of Using Probability To Build An Intuition For Correlation

The power of negative correlations is powerful when you see how rebalancing increases your expected compounded return. This isn’t intuitive to a typical, especially retail investor.

I’ve tried to make it easier to understand:

One of my favorite finance educators recently wrote an absolute must-read thread on this topic.

He creates a model with 2 simplifying features:

  • There are only 2 stocks
  • They are rebalanced to equal weight

You can use the intuition from this exercise to guide your portfolio thinking more broadly. It’s beautifully done and you should work through it carefully not just for the intuition but the practical knowledge of how to compute an expected return in a compounding context. However, there is a part I struggled with that I want to zoom in on because I’ve never before seen it presented as @10kdiver does it:

He converts probability to an estimate of correlation!

This is really cool. But because I struggled and the learnings of the thread are both important I dual purpose to writing this post.

  1. The meta-lesson

    This is the easy one:

    When I read the post, it was easy to nod along thinking “yep, that makes sense…ok, ok, got it”. Except for that, I don’t “got it”. I couldn’t reconstruct the logic on my own on a blank sheet of paper which means I didn’t learn it. Paradoxically, this demonstrates how good @10diver’s explanation was. Extrapolate this paradox to many things you think you learned by reading and you will have internalized a useful life lesson — get your hands dirty to actually learn.

  2. Diving into the probability math I struggled with.

    Let’s do it…

Zooming In: The Probability Basis For Correlation


Example computation for CAGR (also seen in tweet #4):

CAGR_A = =((1+A_up_size)^(A_prob_up*hold_period)*(1+A_down_size)^(A_prob_down*hold_period))^(1/hold_period)-1

Define the probability space

We are focusing on tweets 6-10 in particular. The summary matrix:

Understanding the boxes:

Start with the logic: “what would the probability space look like if they were perfectly correlated?”

  • Top left box = X (This corresponds to both up)

They would go up together 80% of the time if they were perfectly correlated. We generalize “probability of stocks up together as X”

  • Top right box = .8-X (This corresponds to B up, A down)

Since stock B goes up 80% of the time we know its probability of going down is .8-X

  • Bottom left box = .8 – X  (This corresponds to A up, B down)

Since stock A goes up 80% of the time we know its probability of going down is .8-X

  • Bottom right box = X – .6 (This corresponds to both down)

With one box left it’s easy, we know all the boxes must sum to 100% probability.

100% – [X + 80% -X + 80% – X] = X – .6

We called the probability of moving up together X. We set the matrix up using the simple case of the stocks being perfectly correlated (ie moving up together 80% of the time). But they don’t need to be perfectly correlated. So now we can find the range of X, a joint probability, that is internally consistent with each stock’s individual probability of going up.

What is the probability range of X ie “how often the stocks move together”?

Upper bound

X is defined as “how often they move up together”. Another way to think of this:  the upper bound of the joint probability is the lower bound of how often either stock goes up.

Let’s change the numbers and pretend stock A goes up 50% of the time and stock B goes up 80% of the time. Then 50% is the upper bound of how often they can both up together. (Stock A is the limiting reagent here, it can’t move up more than 50% of the time). So the minimum of their “up” probabilities represents an upper bound on X.

Back to the original example, the upper bound of how often these stocks move together is 80% because the minimum of either stock’s individual probability of going up is 80%. Mathematically this is

.8 – X > 0 so:

Upper bound of X = 80%

Lower bound

Proceeding with the logic that no box can be negative, the bottom right box cannot be less than 60%. This represents the least co-movement possible given the stocks’ probabilities.

Lower bound of X = 60%

Think of it this way, if there were 10 trials each stock could have 2 down years. If they were maximally correlated the stocks would share the same down 2 down years. If they were minimally correlated they would never go down at the same time. The probability of both stocks going down simultaneously would be zero, but since the 4 down years would be spread out over 10 years, the pair of stocks would only go up simultaneously 60% of the time.


The probability of the stocks moving together, X, is bounded as:

60% < X < 80%

X is not a correlation. X is a probability. The fact that the stocks can co-move from 60-80% of the time maps to a correlation.

A Key Insight

A zero correlation means 2 variables are independent! If they are independent, the joint probability is a simple product of their individual probabilities.

That’s why the 0 correlation point corresponds to 64%:

X = .8 x .8 = 64%

Loosely Mapping Probability to Correlation

If you’re feeling spry, you can use the probability space and covariance math to compute the actual correlation. But, we can estimate the rough shape of the correlation using zero correlation (statistical independence corresponding to X = 64%, the joint probability of both stocks going up together) as the fulcrum.

Look back at tweet #10 to see the extremes:

At the lowest correlation, corresponding to a co-movement of 60% frequency:

  • The correlation is slightly negative. It’s below the 64% independence point.
  • The stocks NEVER go down together.
  • The stocks move in opposite directions 40% of the time
  • When the stocks do move together, it’s up.
  • The stocks have a negative correlation despite being up together 60% of the time.

At the highest correlation point, corresponding to 80% frequency of co-movement:

  • The stocks go up 80% of the time together
  • They go down 20% of the time together
  • They never move in opposite directions.
  • The magnitude of the max positive correlation is greater than the magnitude of the maximum negative correlation since the independence point is near the lower end of the range.

Rebalancing Benefits Improve As Correlations Fall

The thread heats up again in tweet #17 by identifying the possible values of the portfolio rebalanced to 50/50 at the end of a year.

In tweet #18, those states are weighted by the probabilities to generate expected values of the portfolio, which can finally be used to compute the CAGR of the portfolio if rebalanced annually.

The lower the value of X (the joint probability of the stocks moving up together), the lower the correlation.

The lower the correlation, the higher the expected value of a rebalanced portfolio.

The remainder of the thread speaks for itself:

  • When X = 60% (ie, strongly negative correlation), we have:
    • Without re-balancing: $1 –> $5.94
    • With re-balancing: $1 –> $17.85 (>3x as much!), over the same 25 years.
    • Thus, negative correlations + re-balancing can be a powerful combination.

  • If we do this well, our portfolio can end up getting us a HIGHER return than any single stock in it! We just saw an example with 2 stocks. Each got us only ~7.39%. But a 50/50 re-balanced portfolio of them got us ~12.22%. When I first saw this, I couldn’t believe it!

    [Moontower note: in practice, portfolios usually have many names and a variety of weighting schemes. While the intuition is similar the math is more complex and you are now looking at a matrix of pairwise correlations, assets with varying volatilities and therefore different weights in the portfolio]

  • This is the ESSENCE of diversification. We minimize correlations, so our portfolio nearly always has both risen and fallen stocks. We “cash in” on this gap via re-balancing — ie, we periodically sell over-valued stocks and put the money into under-valued ones.

  • Negative correlations aren’t strictly necessary. We could use stocks with zero — or even positive — correlation. But the MORE heavily correlated our stocks, the LESS “bang for the buck” we get from re-balancing.

Wrapping Up

The idea that low or negative correlations improve with falling correlations is common knowledge in professional circles. Still, the intuition is elusive. The sheer size of the effect on total CAGR is shocking.

Until @10kdriver’s thread, I hadn’t seen a mapping from probability which is intuitive to correlation which is fuzzy (recall that when the 2 stocks had a negative correlation they still went up together 60% of the time!)

When I read the thread, I found myself nodding along but I needed to walk through it to fully appreciate the math. That’s a useful lesson on its own.

If you found this post helpful, I use another of @10kdiver’s threads to show how we can solve a compounding probability problem using option theory:

Solving A Compounding Riddle With Black-Scholes (13 min read)

Trading Is A Team Sport

In Liar’s Poker, author Michael Lewis recounts his days of being a junior salesperson on the Salomon trading desk in the 1980s. He was impressed by a senior trader, Alexander, who took Lewis under his wing.

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, confirmation 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…

I read this as a college student, not much younger than Lewis himself when he lived this story. Fancying myself more clever than I actually am, I put myself in Alexander’s shoes. I did well in school without working too hard, so the allure of making money by being quick and clever without working too hard seemed like an obvious next step for a corner-cutter like me. With the benefit of experience, when I think about Liar’s Poker and this passage I’m more struck but what I missed:

  1. Alexander was a discretionary trader whose mind compiled logic quickly in an era when he didn’t have to compete with machines that do that particular task faster than a human. No shade to him of course. Ironically, the book talks far more about the math whizzes and PhD’s that Solomon was a pioneer in recruiting to Wall Street to price a brand-new asset class — mortgage-backed securities. Since borrowers have the option to pre-pay their mortgages when rates fall, mortgages and their derivatives required deeper analysis then putting your finger in the air. Smart was not enough. You had to have a demonstrated ability to do quantitative research. I was enamored by Alexander who represented the past, instead of noticing that the nerds were the future.
  2. Despite referencing Alexander’s tutelage, Lewis made it seem that Alexander’s guidance wasn’t exactly expected. Alexander just took a liking to Lewis. The mentorship was benevolence. There was no sense that developing juniors was a priority. These were desks of lone-wolf mercenaries, not long-term-oriented businesses focused on succession. The defining trading/investing film of the recent generation was another Lewis story — The Big Short. In his dramatization of the big winners who bet against the “real-estate always goes up” crowd, the most memorable was Michael Burry. Burry is portrayed as an eccentric, autistic contrarian who would have scored 100 on the disagreeable scale of the Big Five Personality test. A quintessential lone wolf, whose sole outlet was a drum kit next to his trading station.

The first point is mostly appreciated by now in the trading community. The top prop shops aren’t offering $400,000 pay packages to recent grads for their well-roundedness. They are looking for math/coding wizards with substantial academic or side-projects on their resumes. For all the talk of being a fox in a world of hedgehogs, the biggest financial head-starts are offered to the pointiest candidates. I would have no chance of getting hired in such a world out of college today. (My timing was lucky I guess but it’s worth remembering how pissed I was early in my career that there were plenty of rich people who barely knew how to use a mouse. Time, as they say, is a flat circle)

The second point about lone-wolfs is worthy of a deeper discussion. The trope of folks like Druckenmiller and Soros ripping yards of futures based on their spidey sense (or aching back) is not useful. They are outlier geniuses with pattern-matching skills that underpin the same fluid intuition you find in the world’s best athletes. The game slows down so they can find the open man a millisecond ahead of the defender.  For everyone else, successful trading is a team sport where the whole is greater than its parts.

The Importance of a Team In Trading

The Value Of Multiple Perspectives

Like a portfolio of uncorrelated bets, a combination of complementary team members can yield results that don’t resemble any one of the individuals. This isn’t always good. If you’re running a relay you still want everyone to be similar in a particular way — namely, fast.

When it comes to cognition and decision-making, having variant perceptions, relationships and skills are highly desirable if all the members can be similar in one way — a shared goal. In the Good Judgment Project, Professor Phil Tetlock and his fellow researchers were looking for what conditions and qualities lead to better forecasts, an activity of obvious importance to investors and traders. 

They discovered that teams performed better than their best individuals.

The results were clear-cut each year. Teams of ordinary forecasters beat the wisdom of the crowd by about 10%. Prediction markets beat ordinary teams by about 20%. And superteams beat prediction markets by 15% to 30%.

Looking behind the numbers, Tetlock identifies a few themes:

  • Emergence

    Teams are more than the sum of their parts. This cuts both ways…even actively open-minded individuals could surrender to “groupthink”.

  • Diversity trumps ability

This provocative claim highlights how the aggregation of different perspectives can improve judgment. The key to diversity was, unsurprisingly, cognitive diversity.

The revealing result: When they constructed the superteams they optimized for ability and those teams happened to be highly diverse because the superforecasters themselves were highly diverse. They did not optimize for diversity first, but it turned out the most diverse teams were the most effective.

  • The asymmetry of the extremizing algorithm

    The “extremizing algorithm” is a technique where you boost a 70% prediction closer to the extreme, perhaps bumping it to 85%. It’s a technique that is employed when the forecasters have diverse perspectives because it leads to better-calibrated forecasts.

    You do the opposite (push the forecast probability closer to 50%) to combat “groupthink” if the team is comprised of people who think the same or possess similar knowledge. The use of the extremizing algo allowed teams of regular forecasters to actually perform better than some superteams!

    [My own observation: this is the same logic by which correlated observations “shrink” the sample size, an idea familiar to data analysts.]

Tetlock’s discoveries demonstrate the superiority of teams. The group’s diverse thinkers simulated a consensus-finding mechanism akin to how markets generate “best guesses”. In Superforecasting, Tetlock explains:

Bits of useful and useless information are distributed throughout a crowd. The useful information all points to a reasonably accurate consensus while the useless information sometimes overshoots and sometime undershoots but critically…cancels out. 1

How A Team Reduces Bias In Practice

Corporations are cooperative environments with shared values, operating in adversarial ecosystems. They want to make better decisions. They should try to hire diverse candidates that, like the relay are all “fast” in whatever that means in context. If an employee’s responsibility and impact on the business is in proportion to their decision-making ability, then we’d expect an internal “wisdom of crowds” mechanism to select for merit.

This is where anyone that’s actually worked in a large organization starts laughing. Politics, nepotism, and countless other biases are sand in the gears of meritocracy. This isn’t news. But let’s accept that a full-figured version of meritocracy, where inclusion is understood to be a long-term advantage, is the goal. We can invent a story about a prop firm trading its own money as a place that has strong incentives to pursue this full-figured meritocracy.

Trading firms have a special reverence for the wisdom of markets. Their internal obsession with separating skill from luck gives them a fighting chance of allocating the best decision-makers to the highest-leverage seats in the org chart. Trading firms would like to hire for diversity to incant its potential to spark internal crowd wisdom.

But there’s a problem.

Depending on where they set the minimum threshold for “fast” in their relay, they will struggle to hire, cost-effectively, enough candidates that are both sufficiently “pointy” and diverse (this is a chicken-and-egg problem circumscribed by today’s culture war…again beyond this post).

Recognizing the perils of bias, how can a firm inoculate itself?

The short answer is: “with great difficulty”.

In Notes From Todd Simkin On The Knowledge Project, Shane Parrish points out a grating paradox in cognitive science — knowing our biases doesn’t seem to help us overcome them.

SIG’s Todd Simkin concurs:

It is definitely true that it is sort of descriptive of the past. A lot of these heuristics and biases are things that we can see when we after we’ve already identified that a mistake has been made. And we say, Okay, well, why was the mistake made? Say, oh, because I was anchored, or because of the way the question was framed, or whatever it might be, we have a really hard time seeing it in ourselves.

But we know the cure for this. I wrote:

This is a topic the brilliant Ced Chin has studied in depth. Ced told me that the literature suggests the only way cognitive bias inoculation works is via group reinforcement. I told him that was exactly the cultural DNA when I was at SIG which makes me believe there is a lot of value in being aware of bias. Anytime you replayed your decision process, it was a cultural norm to point out where in the process you were prone to bias.

Todd shares SIG’s prescription to Ced’s diagnosis:

We have a really easy time seeing when someone else is making that type of stupid mistake. A big part of our approach to education is to teach people to talk through their decisions, and to end to talk about why they’re doing what they’re doing with their peers, the other people on their team. If we can do that real-time, that’s great. Often in trading, you don’t have that opportunity, because things are just too immediate. But certainly, anytime things have changed. If you’re doing things differently, it’s a really good time to turn to the traders around you. And the quantitative researchers around you and the assistant traders and your team and say, Hmm, it looks like all the sudden Gamestop is a whole lot more volatile than it was a week ago. Here’s how I’m positioning for this trading. What do you guys think? And have someone say, oh, it seems like you’re really anchored to last week’s volatility. If things have changed that much, you need to move much more quickly than you’re moving right now. So you don’t realize that you’re anchored, that’s the whole nature of being anchored, is that you don’t recognize the outsized importance that the anchor has on your decision, but somebody else who’s a little bit more distant from it can. So if we’re good at encouraging communication, then we’re going to be really good at getting other people to help improve your decision process.

In a sentence, what you need is frequent communication, in a culture that makes it safe to disagree, where the shared value is “truth”.

Todd nails it:

I know that you are fond of pointing out that you are the sum of the five people that you spend the most time with. So if the people that you’re spending the most time with are your co-workers who are thinking about trading the same way you are, then maybe you’re going to combine the same types of errors, it’s certainly better than then trying to act on your own. But even better is if you have a culture that rewards truth-finding, as opposed to rewarding action. If nobody feels personally attacked, because of somebody else pointing out their error, but instead feels like we together have now done more to get closer to, to some truth to the better way to act or the you know, the more accurate, fair value of this asset that we’re trading, then everybody feels like it’s a win. And they will therefore encourage the involvement of the people around them.

Building The Team

At this point, you realize:

  1. Trading is highly competitive
  2. The competition demands elite decision-making skills
  3. You can make much better decisions if you assemble the right kind of team
  4. With a team in place, the key is communication

Agustin Lebron’s Advice

One of my favorite voices in the prop game is trader and author of Laws Of Trading is Agustin Lebron.

I’ve extracted his insights from a great thread he appropriately titled Alpha Leak of the Week. It echoes the earlier wisdom:

If you don’t have a small heterogeneous group of people to talk about trading with, stop what you’re doing and build one. Here’s how:

  1. Your public twitter presence (reading/following/posting) is not a substitute. Nor is a discord channel with 100 people. You can’t be truly honest and vulnerable to a hundred people, and it’s hard to interactively teach/learn with them.

  2. What you need is tight trusted interaction with a small group of people. 3 is probably too small, 8 is probably too big. h/t @etdebruin for teaching me the value of such a group.

    [David Senra on the Founders Podcast mentions A. Paul Hare’s classic Creativity in Small Groups showed that groups of 4 to 7 are more effective problem solvers because they are more democratic, egalitarian, inclusive, and mutualistic. Bezos echoed this when he said teams should be able to be fed by “2 pizzas”.]

  3. The group should be heterogeneous. 4 clones of yourself isn’t going to help. Of course, you can go too far in heterogeneity and that’s bad because if you can’t agree on foundations then no communication can happen.

  4. The trick to this is that every member of such a group needs to be highly valuable and complementary to the group bc the group needs to be small. So you have a chicken and egg problem. You’re green, so seasoned traders don’t want you. You need to join a group to grow and not be green anymore. This is where you need to be creative. What can you barter? How can you be useful? This is no different than being a clerk or assistant trader. The clerk needs to be useful to the trader they report to. You need to trade something for that learning. Asking for mentors doesn’t work. Deserve one.

  5. Develop norms for how your group operates. Cadences for conversations, conventions on meta-language (i.e. how to signal levels of confidence in ideas, how to ask usefully questions, etc). The goal is to create a safe collective mind where everyone can learn and develop.

    I’ll add a point to this. SIG’s internal language around expectancy, especially “how many cents of edge are in a trade” had a wider purpose of dispensing with any wishy-washy reasoning. There was room for confidence intervals or error bars around estimates but ultimately people’s guesses needed to be pinned down. At the end of the day, you are not arguing with the market. You are making a concrete bid or offer price. There are no points for sophistry. Just results and the process that led to them.


If I were trying to be a prop trader from my pajamas, I’d form a Discord channel of sharp, open-minded, truth-seeking, teachable teammates before I even opened a brokerage account.

This group should:

  • provide inspiration and ideas
  • give you synthetically more reps by sharing experiences so you don’t have to touch every hot stove.
  • expand your circle of competence with orthogonal skills/relationships

I’ve written about how Twitter reminds me of the trading pits, but Agustin is right. You have to form a tighter-knit group for it to have accountability and effectiveness. Twitter can help you source willing members.

Remember, when Shane Parrish asks what the most important variables are for being a better decision-maker, he expects Todd might say “probabilistic thinking”.

But Todd did not hesitate with his answer:

Talk more is number one, that beats probabilistic thinking. That beats sort of anything else. Truth-finding is being able to bring in other people in the decision process in a constructive way. So finding good ways to communicate, to improve the input from others. Thinking probabilistically I think is definitely a very, very important piece of trying to diagnose what works by trying to think of where where things fall apart, where people fail. The other place that people fail is falling in love with their decision process and not being open to being wrong. So an openness to feedback to finding disconfirming information to actively seeking out disconfirming information, which is really uncomfortable. But that I think is the other piece that is super important for being a good trader.

Learning Is Behavioral Change: A Presentation By Alix Pasquet

Frederik Gieschen hosted a presentation by hedge fund manager Alix Pasquet.

The presentation is titled:

Learning for Analysts and Future Portfolio Managers (YouTube)

This presentation is overflowing with ideas and insights. I took notes. They are not intended to be comprehensive, but rather a filter of what stood out to me. If the topics sound interesting definitely check out the video yourself, there’s a lot of detail I’m leaving out.

Alix mentions that the presentation was inspired by Bill Gurley’s talk:

Runnin’ Down a Dream: How to Succeed and Thrive in a Career You Love (YouTube)


About Alix

  • Runs a “behavioral hedge fund” Prime Macaya that seeks to exploit uneconomic group behavior
  • Alix came from the game world specifically poker and backgammon

Key Takeaways From The Presentation

The presentation was focused on learning in the context of rising from an analyst to portfolio manager. Many of the lessons felt more universal which is what interested me. 

  • In the investment business, we are paid to learn
  • Learning is behavioral change. If your behavior hasn’t changed you haven’t learned.
    • Jim O’Shaughnessy quote emphasizes application: “Don’t look for the meaning, look for the uses”
  • Create the conditions to learn as opposed to relying on willpower.
    • There’s an emphasis on community for feedback, collaboration, filtering, and as a forcing function (ie instead of practicing public-speaking alone, join Toastmasters. I found this resonant because being forced to play guitar on stage or gives your practice more intent)

Structure of the Presentation

The first hour is focused on:

  • Problems in learning
  • Mindsets required for learning

The second hour focuses on:

  • Conditions, procedures and actions steps.

    These include specific discussions about:
    • being a good mentee
    • personal knowledge management
    • the idea of a personal lab where you can practice your learning
    • support structures
    • the role of physical exercise
    • inspectional reading
    • studying frauds and deception to “know your enemy”
    • exploiting group behavior

What Caught My Eye

Ideas That Resonated

  • Alix believes “learning is a team sport” which echoes my belief that “trading is a team sport” 

  • Problems as well as smart people and goals are useful filters for narrowing what to learn

  • The investing job needs to be about more than the money because you will compete with passionate, competitive people determined to learn and get better.

    “Many that have brain power should literally be doctors and nuclear physicists but they’re out there chasing stocks. I love what I do but I have no notion that I’m helping out the world here. We’re having fun with what we do and hopefully, we’ll make some money. One day we can help the world but this is not a business where you’re adding value to the world and if you have the intelligence and you don’t love this business go do something else.”

  • Overfitting lessons

    “Analysts don’t understand that they need to tailor their style structure processes and resources according to their own personalities and temperament. They try to replicate what others have done not realizing that these people have totally different personalities and have gone through totally different environments.

    No lesson is better than the wrong lesson. The key suggestion I would make is to involve others. Get feedback from others that will keep you intellectually honest because in the hedge fund business we have a tendency of doing this thing called “revisionist history” which frankly exists to protect our confidence but sadly it doesn’t improve our investment performance.”

    Me: Unwarranted confidence from “resulting” undermines one of the most key inputs to sound betting — calibration. Consider the Paul Slovic horse handicappers study that found  the accuracy of handicapperss’ predictions did not improve from the original 5 variables they desired as they were given more variables. Their confidence went up although their accuracy did not! The handicappers with only 5 variables were well-calibrated. They were close to 2x better than chance at predicting the winner (20% vs 10%) and they estimated their confidence as such. When they were given more variables their accuracy remained 20% but confidence grew to 30%!
  • Investing feedback is long and deceptive unlike games

    • “Futsal principle”

      “Futsal is soccer at the fraction of the size of a football team pitch. The number of players is smaller. You would think that it increases the number of strategic interactions by double but actually, it increases the number of interactions by eight to sometimes 16 times. And what that does is you’re learning at a very, very fast clip.

      And one of the patterns that we’ve seen is great investors often have gone through a futsal period in their careers. So Dan Loeb, for example, in the early 90s, he worked at Jeffries right at the moment when the Resolution Trust Corporation was selling off the problem assets of the savings and loan debacle at discounted prices in a two year period. He saw a deal every few days. And that increased the number of reps that he saw. But also, he had great customers, he had a young David Einhorn and a young David Tepper as customers. And the exposure and the reps were amazing.”
  • Like Alix, I found Mauboussin to be the bridge between trading and investing

    Measure what is incorporated in the “outside view” then work backward:

    • “PIE”: price implied expectation

    • Options implied expectation

    • Narrative/sentiment analysis
  • Imitate, Assimilate, Innovate

    Mediocre investors and business builders try to innovate first, often fail, and fall back on  imitation so they can eat. Originality starts with imitating first.

    Me: resonant just based on what I’ve read about writers. We learn to play covers before we create ourselves.
  • Importance of Mentors

    • “If you’re early on in your career and they give you a choice between a great mentor or higher pay, take the mentor every time. It’s not even close. And don’t even think about leaving that mentor until your learning curve peaks. There’s just nothing to me so invaluable in my business, but in many businesses, as great mentors. And a lot of kids are just too short-sighted in terms of going for the short-term money instead of preparing themselves for the longer term.”—Stanley Druckenmiller

      Me: reminds me of the greatest advice I received coming out of college: No matter who you work for you will be rich. The question is who do you want to work with? She knew that I knew that I would learn more at Susq and when you are 22 years old that’s what you optimize for. That’s the best way to invest in yourself. That’s when your human capital dwarfs the value of your financial capital. We are all living longer. Even at 30 I’d give the same advice. It’s a long road.
  • Community as leverage

    • Community (peers and mentors) can often have access to the context you need for an idea that might otherwise be a dead end
    • Ability to crowdsource if you have an audience (usually content is a key to having an audience in the first place so content is also a form of leverage)
    • Importance of network diversity. Belong to multiple networks which can be sorted by geography, interests, age etc

Notable Ideas

  • “Analysts do not understand that there’s a difference between analytical thinking and portfolio management thinking”

    • Bill Miller: “The difference between analytical thinking and pm thinking is you give an analyst a problem and they deconstruct it and figure out what makes a problem tick but you give a problem to a pm and his first question is how do i make money from this?”

      Me: portfolio construction and betting literature is required for analysts to be PMs.

  • Behavioral bias research is more focused on individuals, but markets are more concerned with group behavior. So there’s a “fallacy of composition. If you take 10 people that are prone to cognitive biases, their group behavior may actually be quite rational.”

    Me: a key focus should be on the wisdom and madness of crowds.

  • Learning from your own successes but others’ failures

    Surgeons learn more from their own successes than from their own failures but they learn more from the failures of others than they do from the successes of others. This was over 6500 procedures. Also my neighbor is a doctor and I spoke to him about this study and he actually made a very important comment that surgeons that had made a fatal mistake over the operating table were more likely to leave surgery because their confidence was shaken whereas a successful surgeon that had seen a surgeon have make a fatal mistake can learn better from that. It’s important to retain this as a mindset of learning from your own successes and the failures of others. Don’t get me wrong you can still learn from the successes of others but temper it. Filter it correctly. You don’t want to overindex to the successes you see in others especially since you don’t have all the context, but it might be easier to learn from somebody else’s mistake. Especially since your own mistakes get you very emotionally involved.

  • They study market participants at 4 levels to see if they are “creating opportunities they can exploit”:

    1. what are their skills?
    2. psychology?
    3. positioning?
    4. institutional quirks?
  • Data hierarchy: data —> information —> understanding —wisdom.

    • Your goals are a filter for how you travel from data to information.
    • Procedures are how you move from information to understanding.
    • The meta experience of “testing it again with your network, teaching it to somebody else, and the ability to create things gets you to wisdom”
  • Derek Sivers: “The standard pace is for chumps”

There’s no reason why it needs to take 10,000 hours. You can do it in much much less period of time if you can test it and get immediate feedback in a low-cost way than it is to be thinking about it for a long time and cramming your brain with more information.


  • “Brute intelligence can be a handicap if it leads you to believe you have figured it all out…need to have soft intangibles like integrity, grit, adaptability, flexibility, humility”.

    Me: While traders are screened for these intangibles, especially teachability/intellectual humility, another way to think of this is the importance of teams. There is a role for one-dimensional Russian super geniuses in these organizations — well captured by this quote: “The analyst’s job is to be creative everything else I can outsource to India”

  • “There’s actually no good book on portfolio management which is incredible to me. Not only that, somebody mentioned on a podcast that there’s no analytical team that analyzes what are the best portfolio management techniques”

    Me: pod/prop/and some quant shops no?

  • Alix belief that strong investors should be strong writers and that there’s a connection between these skills.

    Me: I don’t think this is true for traders. So then I wonder if Alix is overstating the case (even after allowing for exceptions) OR is trading and investing sufficiently different that my experience is not relevant. 

    Trading Vs Investing

Notable Book Recs

The entire presentation is actually organized around a reading list by topic so there are so many thoughtful book recs. That alone is worth watching for. The rationale for 2 particular book recs stood out to me:

  • The Age of The Unthinkable

    • This book “doubled the effectiveness of my judgement” and demonstrates how the world is changing rapidly and the importance of learning.

    • He gives the example: “Market structure has changed. Markets are totally different post-2008. The pipes of liquidity have changed. Prior to ‘08 we had market makers, we had prop desks. They were more prevalent. Index funds were smaller, hedge funds were smaller. Now we have no prop desks, quant funds are massive, index funds are massive, hedge funds are massive… As market participants, we’re inclined to study the past, but past markets may not be appropriate to study here because we’ve never seen a bear market with our current market structure.”

Me: this is resonant and reminds me of:

  • The Path of Least Resistance

    • Demonstrates how “structure drives behavior” and the importance of settings and environment.. consider this simple story:

      • Take two people. A very intelligent person and a total moron. You drop both in the Russian tundra in the middle of winter. The intelligent person gets a shack that can’t really handle the environment well and doesn’t have that much food. You put the moron in a shack that can handle the environment well and has enough food. Unless the intelligent person goes over there and forcibly takes it from the moron, he’s gonna die.

      • It’s about creating structures that you can fall back upon, that make you more resilient [as opposed to] being internally resilient or having inner grit. There are people that we think have this level of motivation level of grit and level of determination that’s incredible, but what we don’t see are the support structures that they’ve created in the background or exploited or frankly they were lucky.

      • An example of resilience would be to have ample living costs saved so you can think clearly as you take risk or not upgrading your lifestyle in line with your success so you can continue to take chances. In studying failure, one of the invisible patterns, or as Alix calls it “the silent killer” is investment managers raising their personal overhead:
        • It’s a “monkey on their shoulder that they have to view every single thing through and it impacts their judgment and risk-taking ability. We call it the ‘silent killer’ because we’ve seen it kill a bunch of hedge funds but the manager never talks about it as the reason they couldn’t take risks anymore.”

Staring Out The Window

I threw a $500,000 purchase price and a 7% 30-year fixed rate into a mortgage calculator. That’s a payment of $3,327.

Earlier this year, if you secured a mortgage at 3%, you could have bought a home for $790,000 and had the same payment.

Since housing hasn’t dropped 36% this year homes have gotten much more expensive to own. Considering you can buy 1-year t-bills yielding 4% that are state-tax free and nominally risk-free, the investment case for RE is looking pretty poor unless rents skyrocket or real estate craters to bring cap ratios back up.

If the higher rate environment leads to a recession and lay-offs then I’m doubtful that rent increases are going to be the primary normalization pathway. It feels like employment trends will be a clue to how quickly housing will re-price lower (it’s already started of course). The yield curve is inverted, so the bond market is suggesting that the rate hikes in the near term will slow inflation and the economy.

This is all just simple observation. Like looking out the window. And as one does, when they sit at a window, one muses. And muse I shall.

Musing #1: Bid-Ask Widening

A year ago the people that paid ridiculous prices for RE were market orders. “Fill me at any price”. Many of them were immediately in the money (ie they probably could have turned around and sold a month later for more. Maybe not net of transaction costs but you get the idea). This isn’t shocking. When optimism turns to euphoria, the rate of change of the returns themselves can explode into a parabolic curve. Of course, such curves are unsustainable. The smug moment of being in the money is short-lived in the same way that a fund that buys a ton of stock going into the close usually gets a favorable mark on their daily p/l. Their sloppy buys drove the price higher in a short period of time. The real sellers didn’t have time to react before the close. But as soon as they check the comps overnight, you can be sure the supply is coming tomorrow morning.

I think of it like water going down a drain…once most of the water is through the drain the remaining liquid swirls quickly around the drain before you hear that sucking sound. Whoosh. The last bid is filled. With maximum punnage — the liquidity is gone.

In the meantime, many other buyers were priced out. You can think of them as limit bids. It’s an imperfect analogy but it will suffice. As things go south now, some of those bidders might be anchored to their original bids which were “cheaper” than where the home traded. However, if they get filled on the way down, they actually have more negative edge even though they got this theoretical house for a cheaper price than the original buyer. You could belabor this with a stylized model but understanding this concept is a big step towards understanding trading.

Anyway, the old limit bids are probably the new ask and the real bid/ask spread is wide. Prospective buyers are adjusting their bids much lower to keep the monthly payment constant or at least manageable, but sellers who likely have cheap financing from the prior low rate regime do not have to cross the spread. If current prices are 5% off their highs but the new mortgage math means homes they should be 20% lower (similar to the stock market) the current listing prices are the “asks” of a wide market.

Buyers lifting those offers are giving up edge for convenience/immediacy. That’s the usual reason people willfully give up edge for anything. Sellers hitting bids either need to (relocation, getting laid off, divorce, or any other life thing that shuffles liquidity needs) or they think rents aren’t going to increase as part of the normalization process.

Musing #2: Price Can Ruin Any Investment Idea

Always promotional, the real estate industry in an effort to pump bids, always finds an angle. They look at CPI and rates increasing, and peddle “RE is an inflation hedge”.

I mean, sure. But price matters.

By that logic, RE was also an inflation hedge 6 months ago, so are real estate prices supposed to be higher today given the elevated inflation of the past 6 months?

A few weeks ago Tom Morgan published Eight Investing Gems, which was a list of underappreciated, evergreen concepts sourced from investment professionals. I was flattered to be asked and my response fit well here:

Markets are biology, not physics, and that’s important because every good idea can be ruined by price. For example, real estate with a mortgage might be a good inflation hedge, but if history has taught everyone that lesson then it will be less true going forward. In other words, the price today already incorporates that (imagine paying 3x for your current home… how’s that going to work out as an inflation hedge?)

Prices are what matter. Not blanket, lazy sentences like “RE is an inflation hedge”. You’re not trading sentences.

[It’s also not clear that RE is an inflation hedge during periods of inflation]

Musing #3: Bullwhips Everywhere All The Time


The bullwhip effect refers to a scenario in which small changes in demand at the retail end of the supply chain become amplified when moving up the supply chain from the retail end to the manufacturing end.

With Covid closings followed by re-opening, this effect has received lots of attention. It’s not new. The famous beer game lets you play as a retailer, distributor, manufacturer, or wholesaler to make ordering decisions that balance your inventory against your customer’s demand. Orders are a proxy for demand, but the lag times in delivery lead to over and underreaction in ordering decisions.

Bullwhips feel like an apt analogy for the over and under reactions that happen in our largest markets:

  1. The underbuilding of homes since the GFC. Builders’ PTSD and higher lending standards for the past decade have contributed to a housing shortage. In the past, I might have associated building velocity with the credit cycle, but the excess of the mid-aughts seemed to have chastened builders despite the loose monetary conditions of the 2010s.
  2. Energy prices, in the wake of shale’s “growth at all costs”, busted in the mid-2010s. They surged back recently as the reality that fossil fuel transition will take longer than expected has collided with underinvestment in production. Drillers were scolded both from their investors (overproduction) and would-be investors (ESG).

[Just FYI, def not advice:

I sold my energy overweights in the Spring and recently started dollar-cost-averaging back in as I add investment exposure in this pullback. Overall, still overweight cash which I’ve been moving directly into T-bills. I’m in the midst of trying to do a rebalance from RE to equities but need one leg to close first so I don’t get middled. I hate illiquidity. In case curious, my prior energy exposure was XLE in an IRA, but I’m re-entering via deferred WTI futures. Instead of a div yield, you get a theoretical roll return. I am not an especially active trader/investor so I figure I’ll share stuff like this when I’m actually doing something. Again, I’m more weighted in cash than most sane people and don’t consider myself a good investor — I mostly try to avoid disaster. I just want to have my assets match my future liabilities — if I want to get rich, I’ll try a higher signal route of relying on myself not random number generators.]

  • Musing #4: Too Many Assholes Playing A “Loser’s Game”

Read this essay:

Too Many Assholes (7 min read)
by Jared Dillian

Jared is an author. He’s published a couple books, one was fiction. He was an index trader for about a decade before becoming a full-time writer amongst many endeavors. Jared is an exceptional financial writer. I read his professional letter regularly for most of the past decade.

This particular essay starts out:

This will be the only financial essay I write, I promise.

His substack is about culture and life not investing. So when he paused to write a single finance post in this collection, I paid attention. It felt very familiar. It has the same feel as his paid daily writing.

I want to offer a perspective on his writing. When people ask him for a free sample of the paid letter he doesn’t give them out. It’s for the same reason I give when people ask me if they should sub to his letter. The individual letters are not useful if you are looking for a great stock tip or definitive proof that the letter will make you money. So if you ask for a single letter, you miss the point. He’s capturing the broad strokes and he’s repetitive. And this is valuable in its gestalt.

I’ll re-hash my Twitter thread on Jared’s post:

This essay could have been called “play the cards not the man” but Jared is a snappier writer so he cut to the heart. It sounds like a folksy kind of essay but it’s deep. If you can internalize his essay you risk making small mistakes, you’ll almost definitely get the timing wrong, but there will be no catastrophes. Since survival is the goal in what Charley Ellis called the “loser’s game” this essay is an irreverent treatise in financial self-preservation.

Jared brings up contrarianism which by definition is required fo outsized returns. But at the turns in markets, the contrarian instinct is defensive. Yes, it can be expensive mid-trend but I’m not advocating for perma-contrarianism anyway. Sometimes contrarianism is common sense when LPs in private funds are climbing over each other to pay 20x revenue for profitless companies.

Options trading provides a well-balanced education in contrarianism. You spend a lot of time fading “point spreads that went too far” so you learn to deal with the discomfort of positions that are against the crowd. And of course, you do need to manage risk around that carefully (position limits are key because once a price enters la-la land there’s no restraint on it go to la-la-la land). At some point, you are selling because you are approaching “there’s nobody left to buy” territory and that is the exact point in time when it’s hardest to do that.

Playing the hindsight game, in the Spring I sold my energy stocks (a touch early but again it was a small mistake) despite being bullish. The thinking: Everything about oil looks bullish but everyone else sees that too. It’s insane to be bearish. But then you have to switch into the mind of a seller…there is no opening seller. So the price must contain a massive premium in it to attract any sell flows.

And that is enough to pull the trigger to sell for me. Yes, I could be wrong, but the risk/reward said “sell”. No fundamentals. Pure psychology.

[This isn’t any kind of victory lap. I’m losing money because I’m basically a long only investor and my current life is not a trading seat where I have the advantage of being in the mix.]

The question to focus on is “What psychology is in the price?” The price includes all the spreadsheets already. It’s the sum of the emotions and the nerds.

Jared focuses on sentiment. It’s not too useful when the game is played near the 50-yard line. In that zone, I’m perfectly fine to outsource to passive collection of market risk premium. With stocks, you know the proposition — earn 5% over the risk-free rate, give or take 15%, and experience a double-digit peak-to-trough drawdown every other year, and something like a 50% drawdown once a decade. Fat tails. That’s the deal. Over the long-run you’ll make money, but sizing that proposition is a personal matter.

The psychology matters more at the turns. The edges of the field. Marching through the redzone, from the 20-yard line to the goaline, can feel dramatic in compounding space. The 5-yard line to the goaline — this is the blow off top in Doge or the Volkswagon short squeeze in 2008…where the bulk of a total return can come from a short time. This is when things are obviously unstable. Sticking around to find out which down is gonna be the pick-6 is baggie roulette.

You don’t need to be some market genius when things feel crazy. Just realize that the only way the price can make sense is if someone crazier came along. Unless you have a very special edge in that game (I suspect at these critical turns the internal mechanics of liquidity are understood by a handful of insiders/clearing firms/exchanges, perhaps it’s a short squeeze, that connect the trading world to the credit/banking world. If that’s the case, you, sitting at home in your pajamas, are playing no-limit hold’em with a worse than random hand against people who know their cards.)

If you don’t have a hero instinct and just try to get the broader picture roughly right you can avoid the giant mistakes. That’s 95% of the battle. 2021 was stupid euphoria. That was obvious even in real-time. Sure you could have been early to that realization and looked foolish for a while but zoom your perspective out and ask yourself:

“Am I feeling fomo or fear?”

That will tell you what everyone else feels and that tells you what’s in the price. You know what that’s called: empathy. You are putting yourself in the minds of others and therefore the price. It sounds like soyboi shit. But that shit is full is wisdom if you can channel it.

Celibacy Vs Condoms: The Answer To Whether You Should Trade Options

The point of dashboards is to help you make better decisions. Decisions that accord with your objectives.

I’m underwhelmed by the standard of dashboards in the investing world. They are not designed to help you make better decisions. They are designed to make you stick a quarter in a slot machine. The focus is on returns not risks. Returns are less predictable than risk and risk itself doesn’t exactly lay down quietly on the operating table for examination. Jason Zweig called attention to Robinhood’s brazen options GUI near the height of call option yolo’ing:

Robinhood’s emails and other communications were prompting me to trade options, another risky strategy I’d signed up to try. I didn’t trade any, largely because the way Robinhood displays options prices confused me. Other brokers show your potential gain and loss equally prominently. When you look into buying a call option on Robinhood, however, the app shows you a measure called “To break even,” with no indication of potential loss.

Interested in selling the same option? Now Robinhood will show you something called “Chance of profit,” again with no measure of possible loss. But if there is (say) a 65% chance of profit if you sell an option, then there must be a 65% chance of loss if you buy it. By instead highlighting “To break even,” Robinhood draws your attention to how little a stock has to rise for you to begin making money by buying an option—even though you could lose as much as 100% of your investment if the stock goes up less than you anticipated (or goes down).

“Chance of profit,” meanwhile, focuses you on the high likelihood of earning at least a small amount when you sell a call option. If the underlying stock goes up more than you expected, though, that could cost you far more in forgone upside than you earned selling the option. Other major brokers, including ETrade, Fidelity Investments and Charles Schwab, don’t pull this sort of switcheroo. They use the same format whether you want to buy an option or sell it—and they don’t use the term “Chance of Profit.”

“How a brokerage firm displays risk and reward shouldn’t hinge upon whether you’re buying or selling an option,” says Roy Haya, head of options strategies at Fort Point Capital Partners LLC, a San Francisco-based investment firm. “Changing the optics like this could encourage activity on both sides of the same trade, and that seems like a suspect way to entice inexperienced options traders.”

“Each [options-quote] display,” says a Robinhood spokeswoman, “seeks to elevate the information that we have found to be most relevant to a seller or a buyer, who have asymmetric opportunities and risks—certainly not to encourage any particular investment strategy.”

Robinhood’s business relies on churn because active trading in options ensures your customers will either blow up or bleed out. Options trading is high margin for the brokerage. A mirror of what it looks like for the client.

Consider this:

1% slippage in a $50 stock means losing 50 cents on your fill.  Now think of options. If you pay 51 cents for an option worth 50 cents you are incinerating 2% in expectancy. And that’s without fees. The absolute smallness of the numbers is insidious. Optically tight bid-ask spreads lure you into trading more. If the markets were really wide and you had to pay $1.00 for that option worth $.50 you’re almost guaranteed to lose. It’s like borrowing money from the mob. You’d know it’s a bad deal. But when the market is tight, your negative edge is obscured just like it is in blackjack. You actually get to win fairly frequently. And that is the hook. You don’t realize you are playing a losing game.

The danger of options is not unlike the danger of risky sex. It’s exciting. If you sell options irresponsibly your win frequency is still high. It feels niiiice. But if you get burned, the outcomes range from an uncomfortable coyote morning all the way to, well, ending up on whatever the Jerry Springer show of today is disavowing your baby, I mean, account. (I was a 90s teen and my references are frozen in the original Jurassic Park amber).

If you buy options irresponsibly, it’s only a matter of time before you end up with a disease. Hep-B. B for “broke”.

Think Before You Even Get Aroused

When it comes to options, I’m a prude. I preach celibacy. I don’t do it in my personal account (my only account these days). No blanket advice is perfect. But I think it errs in the right direction. There are more people who think they should trade options but shouldn’t than there are people who aren’t trading options who should. I can never keep type I and type II errors straight. Even with this “on-the-nose-for-this-post” graphic:

Taking the other side of your trades is such a consistently good business, I’m picturing every customer opening an options account as Tobias:

From my perspective, I just eased into options as a job. It was simply a subset of trading which is what I more broadly signed up for. I wasn’t inherently interested in options, but as I started learning about them I was as vulnerable to the same nerd snipe that many readers of this blog find themselves mired. I just had the advantage of being on the house side.  So if my plea for celibacy has any hope of working I should at least offer a sound rationale that is more than “you’ll go to [financial] hell”. You need to understand the purpose of options in the first place.

Why Anyone Would Trade An Option?

Let’s address reasons to trade an option.

Directional speculation on the underlying

This is a common and intuitive use of options. You’re bullish so you buy some calls. You’re bearish and sell calls or buy puts. Pretty straightforward. The dominant rationale here is using the options for their “delta” and inherent non-recourse leverage. If this is you then my paternal reminder:

This is really a fundamental trade more so than a trade born of some opinion of the option’s price. In other words, 90% of the work is actually upstream of the options trade. That last 10% involves choosing the exact expiry and strike but if you have an explicit forecast for the stock, a forecast that is presumably fueling the burning desire to go through 2FA into your brokerage account, possibly fill out an “Intent To Trade” compliance form, and then the commitment to follow the thing you bought (and follow it you will — you didn’t trade an option because you’re “in it for the long haul”), then the actual option selection is rather trivial. The best bang for your buck easily falls out from a well-fleshed-out forecast.

If the options part is hard, then it’s inheriting the wishy-washy nature of your upstream fundamental analysis.


Buying an option can act like an insurance policy. Puts can protect a long position, calls can protect a short position. As opposed to a stop order which is exposed to gaps, an option is a “hard” stop. You always maintain the right to exercise at the strike price. This hard optionality is presumably baked into the price because it’s valuable (one of my conjectures is that various flavors of option selling strategies that have rules for covering options when they start hemorrhaging are, at their core, attempting to arbitrage this hard-to-pin-down concept. This starts to rhyme with “vol trading” which we’ll get to because, when you get to the nucleus of the logic, these strategies are premised on the idea that the replication is cheaper than the hard option.)

In any case, when hedging, most people buy options. Like speculation, 90% of the work is done upstream of the option’s decision. The rationale for whether you should hedge versus simply use less leverage or run smaller position sizes is complicated. If your core position is X then is that better or worse than a bigger hedged position? That’s a hard question. Consider the logic I’m recycling from Finance As A Laboratory For Decision-Making:

People understand that even though insurance has negative expectancy it can still improve a portfolio that is focused on compounded returns. It makes no sense to look at the line-item of insurance divorced from the optionality it gives you in the rest of your portfolio.

(I could pull lots of links on this idea, but let’s be brief).

This concept is fractal. Let’s zoom in on the smallest portfolio — a spread. You don’t necessarily care about the p/l of any individual leg of a spread trade but the performance of the spread overall.

Before we consider a spread, let’s just look at the single position. Suppose you buy something for $4 when it’s worth $5 but then sell it for $4.50. You made both a:

  • +$1 expected value trade
  • $.50 EV trade.

If you knew it was worth $5 you negated half a good trade with a bad trade.

In real life, you often might like the price of a spread but it’s hard to tell which leg is the “good side”. That’s one of the reasons you trade the spread. Once you do the spread you don’t care about the individual p/ls.

Another reason you may do a spread is that you might like a trade (ie maybe vol is cheap in X) but can do it bigger if you spread it. This is one of those questions that comes up a lot on real trading desks. Do I like the outright, or do I like the trade better paired against something else (and assuming I can do the trade bigger if I spread it)? Do I like being long z units of X exposure, or do I prefer 5z units of (X-Y)? The answer depends on understanding the distribution of the outright vs the spread and the relative price of each within those distributions.

Again, the decision of whether to mitigate the risk requires more brain damage than actually picking the hedge. You can learn more about the logic of hedging in If You Make Money Every Day, You’re Not Maximizing.

If you are rigorous and clear in your decision to hedge, then once again, most of the work is upstream from the options trade.

Some kinky thing called “vol trading”

“Volatility trading” is another reason to trade options. This is a niche reason because it’s actually the inversion of the first 2 reasons. Those reasons originate from very natural impulses — to speculate or cut risk. Vol trading is the business of supplying liquidity to all those normie investors. It’s a strategy that starts with the idea that the options themselves carry their own reason to be traded — they are mispriced. I use the word strategy as if it’s a form of risk premium like “value stocks”, and maybe that argument can be made, but I think it’s more adaptive to understand it as a subset of trading in general. It’s not an investment strategy, it’s a business (see Trading Vs Investing). 

The semantic distinction between investing strategy and business is useful. You wouldn’t open a restaurant as a side hustle or hobby. Despite the ease of “larping as a vol trader” by picking up some language and opening an IB account, you are not vol trading as an investment strategy. Vol trading is a low-margin business, that requires institutional cost structure and infrastructure. The breadth of diversification and sheer transaction quantity demands economies of scale. Core strategies such as dispersion require those economic synergies making it more efficient as an overlay instead of a clinically administered stand-alone strategy. Knock yourself out with An Example “Options Relative Value Trading Framework”.

For the retail masochists

If you insist you want to “vol trade” from home these interviews are the best guides. I warned you.

Both interviews include Darrin Johnson who is the closest I’ve seen to a person grinding options day-in, day-out who came from a pure retail background. The second interview includes Noel smith, SIG alum, who now backs traders and has seen a gamut of independent traders. I think that episode stands out as the best reality check. It debunks lots of misinformation and frames the entire endeavor of trading brilliantly in the context of “this is a business”. There’s also this one line that reminds us that this is not a good career choice for those who prefer a bit more determinism in their vocation:

You do your best and at some point, you put your finger in the air and if you don’t think that everyone does that at some level you don’t understand how the business works. Everybody has to make some kind of a judgment because if you are only looking at the data you have the same data everybody else has and you have a totally in-consensus opinion. You have to make some judgments.

For the aspiring professional masochists

The 99th percentile vol PM probably makes similar money to the 90th percentile investing PM. The competition to be a top vol trader is likely higher simply because its puzzle-like similarities attract nerds with very specific forms of aptitude. But even worse from a “these are the people you’ll be competing with” point of view is that the specific intellectual nature of the job means it’s fun for them.  The net result when combined with the relative smallness of the market (vol trading is to investing as “math rock” is to music) — more competition per unit of pay. If you want to just make money, almost any other avenue is better if you are in any way ambivalent about the work.1

Addressing covered calls and cash-secured put selling

I claim there are 3 reasons to trade options.

  1. Speculation
  2. Hedging
  3. “Vol trade”

The most popular form of retail option trading doesn’t seem to fit in one of these buckets: covered call selling (and its close cousin cash-secured put selling). What gives?

It actually does fit. It’s hedging.

I know that’s not the intent but if you sell a call against a long position, you are hedging.

Repeated game thinking is a useful lens here and one of the most important mental models you should derive from the world of trading. Here’s the logic: if you sell a 25 delta call against your long, your underlying position gets called away 25% of the time2. In fact, any software that aggregates risk would show your net exposure to the stock dropping to 75% after you sold the call option. Whether you sell 25% of your stock outright or sell a call option that theoretically gets assigned every 4th time you make the trade, your net exposure is the same in the long-run. The option expression changes the shape and timing of the exposure, but it is the same exposure. Any large sample will prove it out.

Now there’s the argument that maybe you get called away less than 25% of the time and therefore that 25 delta call is overpriced. If you want to make that argument, fine. Just own it. You are now making a vol bet.

“Selling calls for income” is in the marketing euphemism hall of fame right next to “re-education camp” and “adult entertainment”. It’s a motte-and-bailey argument where the motte is “cash flow is income”. That’s only superficially similar to the credit you receive for the option. The problem is the bailey — you can’t then conclude that the credit is income. It’s not income. It’s the probability-weighted expectation of the stock being above its strike before expiration.

A stock price itself is the discounted sum of future paths. You simply sold a set of those paths, that appears to be income if the stock does not expire above the strike. If there was an accounting ledger the credit is the option premium, but the debit would be the risk. The risk part is conveniently swept under the rug by assurances that “you’ll be happy if the stock gets there”.

If I benchmark to the counterfactual world where I sold 25% of the stock, then the scenarios where the stock goes up by a lot OR goes down, then the call selling strategy was expensive. Do you see course/book promotor’s sleight of hand?

I don’t want to belabor this anymore. I’ve covered it multiple times:

I’m at the point of invoking Brandolini’s Law and moving on.

Wear a Condom

If you preach celibacy while ostriching any discussion of condoms, you are laying irresponsible odds against pubescent urges. When it comes to options, many of you are insatiably horny. If you insist on using options, take the following concepts to heart:


You are paying for specificity via options because they are priced with a particular vol to a specified expiry. The offsetting benefit is you are highly levered to being right.

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

The beauty of options is how they allow you to make extremely narrow bets about timing, the size of possible moves, and the shape of a distribution. A stock price is a blunt summary of a proposition, collapsing the expected value of changing distributions into a single number. A boring utility stock might trade for $100. Now imagine a biotech stock that is 90% to be worth 0 and 10% to be worth $1000. Both of these stocks will trade for $100, but the option prices will be vastly different.If you have a differentiated opinion about a catalyst, the most efficient way to express it will be through options. They have the most urgent function to a reaction. If you think a $100 stock can move $10, but the straddle implies $5 you can make 100% on your money in a short window of time. Annualize that!Go a step further. Suppose you have an even finer view — you can handicap the direction. Now you can score a 5 or 10 bagger allocating the same capital to call options only. Conversely, if you do not have a specific view, then options can be an expensive, low-resolution solution. You pay for specificity just like parlay bets. The timing and distance of a stock’s move must collaborate to pay you off.

Since you pay for specificity, you need a well-formed understanding of your edge. If you’re going to trade options directionally I would want to see the specificity in your fundamental analysis that suggests these particular options are the right options to buy or sell.

It’s so easy to lose on timing or changes in vol even if you get the direction right. See:

Destination vs Path

In a previous Money Angle, I pose the following:

If you have a view about the expected return of an asset in 5 years should you care about the path? Depends who you ask. Anyone marked-to-market (HFs, market-makers, futures traders) will say yes especially if they are managing money for others. PE, RE, and bond investors are more likely to say no…I’m biased by my path-or-die experience in trading. Mark-to-market is the goddess of tomorrow, you can’t afford to piss her off.

Options offer you the chance to isolate bets on either path or terminal value if you want.

A few examples:

  • Market prices are clever.  In What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s GoldI show how market prices are clever. They can balance the wagers of path vs terminal value investors simultaneously! The calendar spread options are priced so that the path of the gas price is highly respected, even if there’s strong consensus about the terminal value of the spread (ie the March-April futures spread which is a pure bet on in winter gas being in short supply).

    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.

  • In options land, many investors like to buy 1×2 ratio spreads because the payoffs look amazing for low-probability events. For example, if a stock is $100 and you can buy the $115 call and sell 2 of the $120 calls for zero premium, you think to yourself:

    a) “If the stock does nothing or goes down I break even”b) “If the stock goes to $120, I make $5” (or $1 if the stock goes to $116)

    c) “I don’t start losing money until the stock goes over $125. That’s 25% away! This is risk-free return”

    Nah dog. That’s first-time-at-the-rodeo thinking.

    The reason the 1×2 is so cheap is the call skew on the $120 strike is pumped up because someone has been buying them like crazy. That’s where the bodies are hidden. The question you need to ask yourself is “conditional on the stock going to $120 did it get there fast and sloppy, or slow and grindy.” If it goes there in a fast way, the market-maker community will be short beaucoup gamma and be scrambling to buy the $120 calls back. You sold some teenies and went to Santorini and are now getting a margin call on the beach because the 120s you’re short are blowing the f out.

    The path-aware trader is plotting how to be long the scenario where your vacation abruptly ends.

  • If path is so important, how can you manage to it?

a) Avoid excessive leverage
b) Pre-determine when you will cut losses (beware this can be a big topic with lots of room for disaster)
c) If you insist on betting on terminal value, do it in fixed premium ways where your max loss is bounded. Now you don’t have to worry about mark-to-market risk.

In There’s Gold In Them Thar Tails: Part 2, I cover the topic of path, how to exploit investors’ lack of appreciation for it, and how Jon Corzine became a symbol for path-blindness.


You probably shouldn’t trade options. But I get it. Everyone gets a little curious.

I hope this post offered some protection.

An Example “Options Relative Value Trading Framework”

Why does vol trading exist?

  • Exists because suppliers and demanders of vol vary along term structure and geography. This can create structural distortions.
  • If you are in the gears, you can understand the players and the rhythm of markets.
  • Total scalability is very limited compared to outright ownership of risky assets. Scalability is in proportion to the total amount of insurance written on the risk assets which is in turn constrained by the credit in the entire system as rationed by the banking system (and manifest through prime brokerage, exchanges, and bilateral credit) since optionality is inherently levered.

Core Competencies

Identifying edge

The Science

Objective: Measure and nowcast what optionality is cheap and expensive globally

    1. Harvest and clean historical and current data (Interest rates, divs, current vols, historical data)
    2. Extract implied parameters: Vol, skew, kurtosis, correlations.
    3. Benchmark fair

The Art

Objective: Portfolio Construction

Trade expressions:

    • relative term structure
    • relative skew
    • relative implied forwards
    • carry (correlation, relative cheapness) vs distribution (percentile analysis)

Risk Management

There is alpha in buying cheap and selling expensive. But in exchange for alpha there is path, self-fulfilling behavior, and adverse selection. The antidote is risk framework designed in anticipation of adverse movements (you don’t want to be full size or worse puking/cutting risk when the trades have their best setups…and the best set-ups happen exactly when others are offsides).

Principles of risk management:

  • The business works so the number 1 rule of the business is: Stay in business. Never jeopardize tomorrow for any perceived edge.
  • The risk framework prioritizes survival and does not contain risk based on historical p/l but constrains position size by shocks. Often pain in a name is a reason to look to enter the trade.
  • Hard risk limits: How much you can lose is determined by position size and aggressive portfolio shocks.
    • Shock examples:
      • bankruptcy for single stock
      • implied parameter shocks
      • extreme time spread shocks for commodities
    • Protocol for position reduction or exclusion
    • Path-awareness: Shocks are not only for p/l tolerance but to estimate what happens to your margin requirement as market risks grow.

Sourcing liquidity

  • Relationships with banks and brokers including electronic connectivity
  • Technology stack to handle effective trade life cycle from execution to clearing, to risk and p/l reporting, to accounting and compliance

Performance attribution

  • TCA of electronic and voice trades
  • Actionable insights based on updated lessons

Horizontal scaling

  • The abstracted framework of doing many positive EV trades and managing the pooled risks is flexible and underpins all alpha trading. Its application inches out from core competency to adjacent classes of securities.
  • Requires new normalizations, data, market structures, understanding new distributions, player landscape

Bet Sizing Is Not Intuitive

Humans are not good bettors.

It takes effort both in study and practice to become more proficient. But like anything hard, most people won’t persevere. Devoting some cycles to improve will arm you with a rare arrow in your quiver as you go through life.

Skilled betting demands 2 pivotal actions:

  1. Identifying attractive propositions

    This can be coded as “positive expected value” or “good risk/reward”. There is no strategy that turns a bad proposition into an attractive one on its own merit (as opposed to something like buying insurance which is a bad deal in isolation but can make sense holistically). For example, there is no roulette betting strategy that magically turns its negative EV trials into a positive EV session.

  2. Effective bet sizing

    Once you are faced with an attractive proposition, how much do you bet? While this is also a big topic we can make a simple assertion — bad bet sizing is enough to ruin a great proposition. This is a deeper point than it appears. By sizing a bet poorly, you can fumble away a certain win. You cannot afford to get bet sizing dramatically wrong.

Of these 2 points, the second one is less appreciated. Bet sizing is not very intuitive.

To show that, we will examine a surprising study.

The Haghani-Dewey Biased Coin Study

In October 2016, Richard Dewey and Victor Haghani (of LTCM infamy) published a study titled:

Observed Betting Patterns on a Biased Coin (Editorial from the Journal of Portfolio Management)

The study is a dazzling illustration of how poor our intuition is for proper bet sizing. The link goes into depth about the study. I will provide a condensed version by weaving my own thoughts with excerpts from the editorial.

The setup

  • 61 individuals start with $25 each. They can play a computer game where they can bet any proportion of their bankroll on a coin. They can choose heads or tails. They are told the coin has a 60% chance of landing heads. The bet pays even money (i.e. if you bet $1, you either win or lose $1). They get 30 minutes to play.
  • The sample was largely composed of college-age students in economics and finance and young professionals at financial firms. We had 14 analyst and associate-level employees of two leading asset management firms.

Your opportunity to play

Before continuing with a description of what an optimal strategy might look like, we ask you to take a few moments to consider what you would do if given the opportunity to play this game. Once you read on, you’ll be afflicted with the curse of knowledge, making it difficult for you to appreciate the perspective of our subjects encountering this game for the first time.

If you want to be more hands-on, play the game here.

Devising A Strategy

  1. The first thing to notice is betting on heads is positive expected value (EV). If X is your wager:

    EV = 60% (x) – 40% (x) = 20% (x)

    You expect to earn 20% per coin flip. 

  2. The next observation is the betting strategy that maximizes your total expected value is to bet 100% of your bankroll on every flip. 

  3. But then you should notice that this also maximizes your chance of going broke. On any single flip, you have a 40% of losing your stake and being unable to continue this favorable game. 

  4. What if you bet 50% of your bankroll on every flip?

    On average you will lose 97% of your wealth (as opposed to nearly 100% chance if you had bet your full bankroll). 97% sounds like a lot! How does that work?

    If you bet 50% of your bankroll on 100 flips you expect 60 heads and 40 tails. 

    If you make 50% on 60 flips, and lose 50% on 40 flips your expected p/l:

1.560 x .5040 = .033

You will be left with 3% of your starting cash! This is because heads followed by tails, or vice versa, results in a 25% loss of your bankroll (1.5 * 0.5 = 0.75).

This is a significant insight on its own. Cutting your bet size dramatically from 100% per toss to 50% per toss left you in a similar position — losing all or nearly all your money.

Optimal Strategy

There’s no need for build-up. There’s a decent chance any reader of this blog has heard of the Kelly Criterion which uses the probabilities and payoffs of various outcomes to compute an “optimal” bet size. In this case, the computation is straightforward — the optimal bet size as a fraction of the bankroll is 20%, matching the edge you get on the bet.

Since the payoff is even money the Kelly formula reduces to 2p -1 where p = probability of winning.

2 x 60% – 1 = 20%

The clever formula developed by Bell Labs researcher John Kelly:

provides an optimal betting strategy for maximizing the rate of growth of wealth in games with favorable odds, a tool that would appear a good fit for this problem. Dr. Kelly’s paper built upon work first done by Daniel Bernoulli, who resolved the St. Petersburg Paradox— a lottery with an infinite expected payout—by introducing a utility function that the lottery player seeks to maximize. Bernoulli’s work catalyzed the development of utility theory and laid the groundwork for many aspects of modern finance and behavioral economics. 

The emphasis refers to the assumption that a gambler has a log utility of wealth function. In English, this means the more money you have the less a marginal dollar is worth to you. Mathematically it also means that the magnitude of pain from losing $1 is greater than magnitude of joy from gaining $1. This matches empirical findings for most people. They are “loss-averse”.

How did the subjects fare in this game?

The paper is blunt:

Our subjects did not do very well. Suboptimal betting came in all shapes and sizes: overbetting, underbetting, erratic betting, and betting on tails were just some of the ways a majority of players squandered their chance to take home $250 for 30 minutes play.

Let’s take a look, shall we?

Bad results and strange behavior

Only 21% of participants reached the maximum payout of $250, well below the 95% that should have reached it given a simple constant percentage betting strategy of anywhere from 10% to 20%

  • 1/3 of the participants finished will less money than the $25 they started with. (28% went bust entirely!)
  • 67% of the participants bet on tails at some point. The authors forgive this somewhat conceding that players might be curious if the tails really are worse, but 48% bet on tails more than 5 times! Many of these bets on tails occurred after streaks of heads suggesting a vulnerability to gambler’s fallacy.
  • Betting patterns and debriefings also found prominent use of martingale strategies (doubling down after a loss).
  • 30% of participants bet their entire bankroll on one flip, raising their risk of ruin from nearly 0% to 40% in a lucrative game!

Just how lucrative is this game?

Having a trading background, I have an intuitive understanding that this is a very profitable game. If you sling option contracts that can have a $2 range over the course of their life and collect a measly penny of edge, you have razor-thin margins. The business requires trading hundreds of thousands of contracts a week to let the law of averages assure you of profits.

A game with a 20% edge is an astounding proposition.

Not only did most of our subjects play poorly, they also failed to appreciate the value of the opportunity to play the game. If we had offered the game with no cap [and] assume that a player with agile fingers can put down a bet every 6 seconds, 300 bets would be allowed in the 30 minutes of play. The expected gain of each flip, betting the Kelly fraction, is 4% [Kris clarification: 20% of bankroll times 20% edge].

The expected value of 300 flips is $25 * (1 + 0.04)300 = $3,220,637!

In fact, they ran simulations for constant bet fractions of 10%, 15%, and 20% (half Kelly, 3/4 Kelly, full Kelly) and found a 95% probability that the subjects would reach the $250 cap!

Instead, just over 20% of the subjects reached the max payout.

Editorialized Observations

  • Considering how lucrative this game was, the performance of the participants is damning. That nearly one-third risked the entire bankroll is anathema to traders who understand that the #1 rule of trading (assuming you have a positive expectancy business) is survival.

  • Only 5 out of the 61 finance-educated participants were familiar with Kelly betting. And 2 out of the 5 didn’t consider using it. A game like this is the context it’s tailor-made for!
  • The authors note that the syllabi of MIT, Columbia, Chicago, Stanford, and Wharton MBA programs do not make any reference to betting or Kelly topics in their intro finance, trading, or asset-pricing courses. 

  • Post-experiment interviews revealed that betting “a constant proportion of wealth” seemed to be a surprisingly unintuitive strategy to participants. 

Given that many of our subjects received formal training in finance, we were surprised that the Kelly criterion was virtually unknown among our subjects, nor were they able to bring other tools (e.g., utility theory) to the problem that would also have led them to a heuristic of constant-proportion betting. 

These results raise important questions. If a high fraction of quantitatively sophisticated, financially trained individuals have so much difficulty in playing a simple game with a biased coin, what should we expect when it comes to the more complex and long-term task of investing one’s savings? Given the propensity of our subjects to bet on tails (with 48% betting on tails on more than five flips), is it any surprise that people will pay for patently useless advice? What do the results suggest about the prospects for reducing wealth inequality or ensuring the stability of our financial system? Our research suggests that there is a significant gap in the education of young finance and economics students when it comes to the practical application of the
concepts of utility and risk-taking.

Our research will be worth many multiples of the $5,574 winnings we paid out to our 61 subjects if it helps encourage educators to fill this void, either through direct instruction or through trial-and-error exercises like our game. As Ed Thorp remarked to us upon reviewing this experiment, “It ought to become part of the basic education of anyone interested in finance or gambling.”

I will add my own concern. It’s not just individual investors we should worry about. Their agents in the form of financial advisors or fund managers, even if they can identify attractive proposition, may undo their efforts by poorly sizing opportunities by either:

  1.  falling far short of maximizing

    Since great opportunities are rare, failing to optimize can be more harmful than our intuition suggests…making $50k in a game you should make $3mm is one of the worst financial errors one could make.

  2. overbetting an edge

    There isn’t a price I’d play $100mm Russian Roulette for

Getting these things correct requires proper training. In Can Your Manager Solve Betting Games With Known Solutions?, I wonder if the average professional manager can solve problems with straightforward solutions. Nevermind the complexity of assessing risk/reward and proper sizing in investing, a domain that epitomizes chaotic, adversarial dynamics.

Nassim Taleb was at least partly referring to the importance of investment sizing when he remarked, “If you gave an investor the next day’s news 24 hours in advance, he would go bust in less than a year.”

Furthermore, effective sizing is not just about analytics but discipline. It takes a team culture of truth-seeking and emotional checks to override the biases that we know about. Just knowing about them isn’t enough. The discouraged authors found:

…that without a Kelly-like framework to rely upon, our subjects exhibited a menu of widely documented behavioral biases such as illusion of control, anchoring, overbetting, sunk-cost bias, and gambler’s fallacy.


Take bet sizing seriously. A bad sizing strategy squanders opportunity. With a little effort, you can get better at maximizing the opportunities you find, rather than needing to keep finding new ones that you risk fumbling.

You need to identify good props and size them well. Both abilities are imperative. It seems most people don’t realize just how critical sizing is.

Now you do.