Dispersion Trading For The Uninitiated

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

Let’s do dispersion trading for the uninitiated.

What Is Dispersion Trading?

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

Why Is Dispersion Trading A Correlation Bet?

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

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

Why?

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

An Intuitive Equation

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

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

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

Implied correlation = .44

 

The Shape Of Correlation Risk

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

 

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

 
Trade Structures Are Tricky

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

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

 

The Correlation Surface

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

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

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

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

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

Broader Risk Lessons

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

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

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

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

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

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

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

Parting Thoughts

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

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

A Cleaner Dashboard: Z-Scores Instead Of Price Changes

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

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

Re-scale all the moves in terms of standard deviations

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

Here’s the formulas:

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

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

These are just Z-scores!

Observations

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

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

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

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

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

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

Let’s start with some background.

The Widowmaker

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

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

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

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

Introducing Options Into The Mix

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

Commodities Are Not Like Equities

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

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

It gets better.

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

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

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

Not true in NG.

Severing the arbitrage link between spreads

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

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

More Complexity: Options On Those Crazy Spreads

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

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

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

Real-life example

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

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

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

How about another scenario.

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

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

Sucker Bets

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

Why? Because it has to balance 2 opposing forces.

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

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

Image

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

The Wider Lesson

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

There are 2 ways and they double as general lessons.

  1. Play bookie

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

  2. Radiate outwards

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

Trading As a Concept

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

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

Happy prospecting.


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

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

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

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


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

Portfolio Theory And The Invisible Option On Hobbies

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

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

I’ll wait.


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

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

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

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

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

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

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

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

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

DCF As The Zero Strike

Let’s stay in the business world for now.

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

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

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

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

So there is optionality struck at the DCF value!

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

Understanding The Option

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

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

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

Connectivity and divergence

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

Connectivity

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

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

Divergence

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

To recap so far:

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

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

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

Beyond Investing

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

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

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

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

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

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




Teach A Math Idea To Internalize It

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

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

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

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

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

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

Hmm.

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

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

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

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

However…

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

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

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

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

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

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

    You will learn:

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

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

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

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

Jensen’s Inequality As An Intuition Tool

I came across a tool from mathematics called Jensen’s Inequality. I’m going to explain the rule, provide intuitive examples, then end by pointing you to real-world applications.

A warning to math whizzes — I don’t have formal math training so this post is divorced from pedagogical context. Yes, there will be numerical examples. But the real goal is for readers to recognize when the domain they are reasoning about is subject to the surprising predictions of Jensen’s Inequality. For most of us, the value of this tool is how it nudges our intuition to better predictions, not in the direct application of a formula.

Here’s where we’re going:

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

Why I Found Jensen’s Inequality Interesting

Blindness To Exponents

Exponential phenomena confuse our brains. It has become tiresome to point out that we do not have natural intuition for growth and decay rates. Even finance folk who are apt to appreciate the idea of compounding  seem to not recognize it when the investing skin is pulled off it.

Covid is a timely example. A virus’ R0 (“R naught”) indicates how transmissable it is. Remember “Covid is the flu”. Say the flu has an R0 of 2. So for each person that contracts the flu, they infect 2 more people. Now let’s suppose Covid has an R0 of 3. Here’s how the 2 viruses would spread 1.

R0 is a more complicated function than I’m stylizing here (it should be obvious that behavior, like masks, change it. And if a virus was super effective at replicating itself, well it would find new hosts harder to come by). My point is that even smart people will not hear the “This Is Not A Linear Phenomena” song unless their station is tuned to it. The failure to recognize non-linear domains is serious, because it leads to wildy wrong predictions. And life is prediction. We implicitly predict that the sun will rise tomorrow.

Jensen’s Inequality guides our predictions by forcing us to deliberately consider how the average input maps to the average output. When the function that maps the input to the output is non-linear, Jensen’s Inequality tells us in which direction our predictions will be biased. Stated another way: Jensen’s Inequality informs us when an average occurance is a poor predictor of the average result.

Before we get to any equations, let’s predict the outcome of a simple game.

Dice Payoff

Imagine a game, you stake $1, then roll 2 dice. Whatever the roll returns times your stake amount is how much money you make. That’s the payoff function.

So if you roll a five you receive $5.

Question 1: On average, how much do you expect to get paid?

This is a straightforward expected value problem. You get paid the weighted average of all the outcomes or on average $7.

The average value that you roll will correspond to the average value of the payoff function. If that sounds obvious, that’s the point. So far, so good.

Question 2: If you staked $100, what would you predict the average payoff from playing the game?

A quick way to estimate that would be to ask yourself, “what do we expect to roll on average?” then multiply that by the staked amount. In this case, we roll a 7 on average, and since the staked amount is $100 then on average when we play this game we expect to be paid out $700.

That prediction is correct. We can brute force the expected value of the payoffs.

At this point, things are feeling pretty obvious and redundant, but let me remind you what we did to just answer Question 2. We used a shortcut. We took the expected value of the roll, which was an input, to estimate the expected value of the payoff function or the output. The shortcut worked because the payoff function was linear. We are just scaling the expected input by the staked amount since the function is simply (dice roll x staked amount). This kind of payoff function exists all around us. When you buy a stock, your p/l function is just change in stock price x share quantity. The “staked amount” in our example performs the same scaling role as share quantity.

You can feel the twist coming.

Question 3: Same game but we change the payoff function to (staked amount) x (dice roll)2. What’s the average payoff?

First, what does our shortcut predict? Let’s say we bet $1 again. Since the average value we roll is a 7, then we expect the average payoff to be $72 x $1. So we expect the average payoff of this game to be $49.

As you may have guessed from the unsubtle narrative arc, $49 is the wrong answer. Our shortcut doesn’t work. Brute force method:

It turns out the expected value or average result from the squared game is $54.83, a higher value than what we would predict if we took the average value of the input and simply applied the squared function to it.

It’s intuitive to take the average value of an input, apply a function to it and call that the “expected value of the function”. It turns out that if the function we run the input through is exponential, our estimate will be wrong. So in service of becoming better at making estimates on the fly, we should get better at thinking about what kind of function we are running an input through and if our prediction is likely to be biased higher or lower than the actual expected value of the payoff function.

With that long intro we can now turn to Jensen’s Inequality and its practical applications.

A Look At Jensen’s Inequality

I’ll start with stating the inequality the way I learned it2:

E[f(x)] ≥ f(E[x])

…if f(x) is convex

Let’s try saying this in words several ways, assuming f(x) is convex (a term I will address in a bit):

  • The expected value of a function is greater than or equal to the function applied to the expected value of the input.

  • The average value of a function is greater than or equal to the function applied to the average input.

  • Returning to dice…the [weighted] average of all the squares is greater than the square of the average roll.

In practice this means, you cannot estimate the average value of the function based on the average value of the input IF the function is exponential.

Convex

Let’s address the term “convex”. You know what it is visually.

Mathematically, a convex function:

  • has a first derivative that is greater than 0, meaning that the function has a positive slope everywhere.
  • has a second derivate that is also greater than 0, meaning as X increases the slope itself increases. The steepness of the chart is increasing.

If we go back to the dice example and consider the convex payoff function, we can see the average value of the payoff function of $54.76 is greater than the payoff ($49) at the average roll. In other words, the convex function ensured that:

average value of all payoffs > the payoff of the average roll

Concave

For concave functions, like y = sqrt(x), we have a positive slope, but the slope is decreasing as x increases. The second derivative is negative. Let’s look at a concave case for the dice game by making the payoff function = sqrt(roll).

Notice that the average value of the payoff, if you stake $1, is $2.60. But if you tried to predict the expected payoff by using the shortcut of taking the square root of the average roll you’d predict $2.65 which is the sqrt(7).

Wait a minute. The prediction this time overshot the true expected value of the function?!

That’s correct. If you multiply one side of an inequality by -1 you flip the sign…a convex function can be flipped to concave by flipping the sign as well. So a concave function flips the sign of Jensen’s Inequality, making the overshoot the expected result.

Visualizing the concave payoff:

Let’s practice with a highly stylized example I made up, but relates to something we all intuitively feel.

An Intuitive Example That Affects Us All: Traffic!

We are celebrating a big W, so it’s time to take the kids to Sizzler. We’re going to drive. Sizzler is 10 minutes away + some extra time depending on how many cars are on the road. Let’s keep things very simple and assume the number of cars that can be on the road is 10, 20, 30, 40, or 50 and with equal probability. None of these quantities is enough to slow the flow of traffic to a halt, but the impact of the extra cars is not linear.

We’ll create a function called “time to destination” denominated in seconds and make it a function of “cars on the road”:

f(cars on the road) = x2 + 600 

Let’s play “How long will it take to get to Sizzler?”

Before you discovered this post, you likely would have said 25 minutes. Why? Since we can have 10, 20, 30, 40, or 50 cars all with equal probability, then on average we expect to see 30 cars on the road.

302 + 600 = 1500 seconds or 25 minutes.

But because we know about Jensens’s Inequality we:

  1. recognize the traffic output function is convex
  2. realize that the expected value of the traffic function will be greater than sticking the average number of cars in the road into the traffic function

Enlightened, we instead estimate that on average it will take longer than 25 minutes to pounce on that glorious salad bar with the popcorn shrimp.

How much longer? Brute force tells us 28.3 minutes!

Spotting Jensen’s Inequality In The Wild

Here’s a few common applications that abide Jensen’s Inequality

  • Geometric mean ≤ arithmetic mean

    I’ll need to point you to an actual math person. See his beautiful derivation on YouTube. It’s easy to follow along and quite clever. The key to this inequality is recognizing that the geometric mean, which takes the nth root, is concave just like the sqrt(x) function.

    It’s worth noting that the LN(x) function is also concave so when you are in price space we know that the LN(average price) > the average of the LN(prices). Same idea as the geometric means, concavity flips the sign of Jensens.

  • Call options

    Here’s a generic chart3.

A call option is convex payoff function with respect to the stock price. Its first derivative with respect to the price of a stock is delta which is always positive. In other words, as the stock price goes up, all else equal, the call option always goes up (the slope or delta of a way OTM option is 0 so it’s possible for the call to not change in value, but that’s the lower bound). The second derivative with respect to stock price is gamma and it also is always at least worth 0. That means that as a stock price increases the delta or slope itself increases (or hits the zero lower bound). 

In options land, stock prices are assumed to be lognormally distributed. This is a reasonable distribution since a stock is bounded by zero and stretches to infinity. The expected value of a stock is the current stock price (in a no arbitrage framework)4.

Now let’s go back to Jensen’s Inequality:

E[f(x)] ≥ f(E[x])

…if f(x) is convex

Substituting words:

The expected or average value of a call for all possible prices of the stock (of course weighted by their probabilities) will be greater than the value of the call based on the stock being at it’s expected price (which is just the current price in Black Scholes).

In other words, the average value of a call will be higher than the value of a call in the average scenario.

It is easier to see with a binary stock (as opposed to a lognormally distributed stock). Suppose a binary stock is $10. That’s its expected value. Suppose now that the expected value is driven by the fact that it’s 90% to be worth 0 and 10% to be worth $100. The 50 strike call is worthless in the average scenario (since $10 is the weighted avg of the scenarios…again that’s what a stock price is by definition).

 But the weighted average of its value over both scenarios is $5 (90% x 0 + 10% x (100-50))

Again, the average value of a call will be higher than the value of a call in the average scenario.

So next time somebody uses the logic that they don’t buy options because most options expire worthless you can remind them that the typical outcome is not what drives the value of options. Instead, you should care about the average value of the option over all scenarios.

By the way, nothing I said here is revelatory. It’s not like any serious person thinks OTM options are worthless in the first place and just prices options based on the stock’s expected value. 

  • Technology

    Here’s a qualitative one. Suppose teacher skill follows a bell curve. Skill is the independent variable. Our X. Our payoff function is going to be how many people the teacher can effectively educate. A great teacher will impact a higher percentage of the students they actually come into contact with because they are more effective. If we had to predict the payoff, we might be tempted to apply a function to the average teacher. This would be like taking the 7 we rolled and running it through some payoff function.

    But if we consider the average value of the teacher payoff function for all level of teachers we will find that prior estimate to be wildy too low. Sal Khan comes to mind. He literally broke the function despite being just a good or even great teacher but very much on the bell curve. 

    The point is that technology leads to a huge range of possible payoff functions semingly extending to billions. Estimates of output based on the average input will fail to appreciate the convexity of some of the payoff functions in a hyper-connected world network. 

    This might not map perfectly to Jensen’s Inequality but it was a thought I had as I turned these concepts over in my mind.

Takeways

Be careful when trying to make estimates of how a function or process will payoff based upon the average input. If the function has exponential dynamics, Jensen’s Inequality tells us that the weighted average value of the function will not coincide with average input you feed it.

If the function is convex, the average input will underestimate the average output. If the function is concave, it will overestimate the average output.


A Reader Explains The Psychological Grind Of Trading

This is an email I received from a long-time friend and successful founder of an options trading business (he is bankrolled by a prop shop). He’s chopped a lot of wood, so I changed some details to keep insiders from figuring out who he is. He was very forthcoming and approved this of course.

My understanding is that loss aversion is the idea/phenomenon of different reactions to “losing” versus “winning” despite the same (or even a worse) net actual outcome.  I believe there are several studies of this in a controlled/lab setting, but I didn’t go back to review, as I just needed to get this sent!

The loss aversion reference from our call, referred to annual p/l, as I recall. Below, are a few examples (with more or less real world inputs from my past few years).  

-In scenario #1, we are having a rough year, losing after-expenses around mid-year. Then, we catch one big winner and a strong q4, including 3mm in the last week of the year during the xmas crash.  We finish the year +4mm net.  Overall, that’s a mediocre year to historical avg.  But, given the alternative– an ugly losing year with no bonus, and possible clawbacks going forward, I’m thrilled to realize 750k or so from that slice of my comp (my specific team performance).  That was basically 2018…

-In scenario #2 we are having a home run year, +20mm in the account in March. Then the Cboe closes for 6 weeks while we have our biggest position in 10 years of XXX trading.  The position bleeds, we have no outs, no volume…  then the XXX makes several gaps from [low number to high number], and right back to [low number], on no liquidity.  We negatively scalp (10mm).  XXX p/l is now gone, and the product is dead, and Cboe remains closed.  Meanwhile, Softbank happens in tech, and we are short a lot of tech vega in YYYY, etc.  We lose another 5mm there.  So we go from +20mm to +2mm in 3 months (expenses never slow down).  We spend the 2nd half of the year grinding back some $$, and finish around +7mm.  I get paid a lot more than in scenario #1, but I have horrible PTSD, I don’t sleep for months, I lament (daily..) what could have been if I had booked a 30mm p/l year, and it’s misery all around.  (My XXX trader even had a nervous breakdown and had to take a leave from work.)  This is obviously 2020.   Despite the much better outcome, it’s a much “worse” year in terms of performance/comp.  but it’s all in my head.  Overall, I was paid more, which in trader land, should always be better.  Right?  Right?!

I think these longer term (annual comp) examples illustrate the concept of loss aversion quite well. But there are of course countless others.  Just Friday, as I typed this, another arose.  We had a winner to the morning news/gap in ZZZZ. Long gamma was good for about +50k.  Market opened, we start trading, stock keeps going.  25%, 30%… almost 50%.  We were hedging deltas, and then sold some gamma that was quickly awful.  We now have an Opening p/l +130k, day p/l (60k.): net +70k. The outcome is better than before, but I’m a hot mess, cursing my decisions and the stock. Better outcome, worse head space.  There are so many examples of loss aversion, many of which I’m sure you have considered during your career.  But annual comp and intraday hedging of a winner are 2… 

I’m not sure if this is at all interesting as a potential future post, but the topic fascinates me. The human brain is just not wired to properly handle these things very well.  Or, at least mine is not.

That story is the embodiment of Lawrence Yeo’s terrific Speculation: A Game You Can’t Win.

I realize the numbers my buddy is throwing around make this sound like a high-class problem. But I’ll point you to a post that will prompt you to think deeper before concluding you can’t learn from it.

  • Are You Playing to Play, or Playing to Win? (26 min read)
    Cedric Chin

    This post is fantastic on its own. You might even realize you’re a…“scrub”. But it’s a giant doorway to self-examination. It makes you wonder if you are playing to win. But, and I think this is actually unintentional, the post shows the major limitation of analogizing games to life. Check my short tweet thread before or after reading the post to see what I mean. The expression “play stupid games, win stupid prizes” comes to mind. Only you can decide what’s stupid. We are seeing this happen in real-time, with people calling this period of massive turnover and quitting the “Great Resignation”. Then again, just as we mix up bull markets with brains, there’s a good chance asset markets have pulled many people closer to “their number” and accelerated the types of questions many would usually wait another decade to wrestle with. [The nihilistic whisper in my ear, is the quickened trajectory accelerates the feeling that as we peel back one delusion we just find another. If the onion of delusions was a grand secret, its nature was typically revealed to the aged under the stacking pressure of successive self-crises. But today, that reality is creeping broadly into younger cohorts who, when they threaten to not play traditional games, seem to be serious.]

Assorted Real Estate Thoughts

An assortment of real estate things

  • An in-the-flesh example of growth vs value in real estate

    While traveling this summer we bought a house. It was a quick (that’s how I spell “impulsive”) decision. We weren’t even shopping for RE but it was one of the rare moments where Yinh and I took a look at something and arrived at the same conclusion telepathically. The home has some interesting optionality to us but the first checkbox was thinking about our downside. So we asked our local friend, who found the listing, to handicap the worst-case rent we could get for it. Feeling satisfied, we shot our shot and lifted the house.

    Turns out we underestimated the rent we could get for it by more than 40%. Within 3 days of listing it, we had 4 offers through our asking price, all guaranteed by an insurance company, a re-locating employer, or an upfront check for the whole lease term. Feeding frenzy.

    Now, the interesting part. The house is half the price of the house we rent in CA and fetches more rent than we pay here!

    What’s going on?

    This is a growth vs value thing. The house we bought is in an area where there are lots of new build permits. Supply is currently constrained because of immediate inflows of residents overwhelming capacity. But this place is nothing like the NIMBY Bay Area where home prices rightly have capital appreciation baked in. Meanwhile, where we bought has cap rates priced for carry.

    In other words, nothing to see here…markets make sense.

  • Why US Housing Prices Aren’t As Crazy As You Think (A Wealth Of Common Sense)

    This brief post by Ben Carlson provides an international perspective. It suggests that the recent surge in real estate prices is hardly a bubble and [gulp] it might even be early innings.

    This may surprise you, but compared with other developed nations, US home prices are merely playing catch-up. This is even more true when we adjust for inflation and disposable income.

    It wasn’t discussed in the post but another point suggesting RE has lagged, is US stocks have massively outperformed international markets since the GFC. This can be reassuring for those of you looking to rebalance out of stock [or crypto] gains into RE.

  • A reminder that RE is a very direct bet on interest rates

    This is from an account I like and follow (as opposed to a ‘hate-follow’) @sidprabhu:

    The median home price in 2007 was ~$250k with 30y mtg at 6.5%. Assume 0 down that’s $1,580/mo. With 30y mtg at 3%, $1,580 gets you a $375k house, which is the current median price. (thread)

    I want to add another insight from @ByrneHobart paywalled letter highlighting the bond-like quality of real estate:

    The higher the price/rent ratio for a home, the higher its duration is as a financial asset, so the rates-sensitivity of big city real estate offsets a lower expected rent.

    The quote refers to the fact that while covid decimated rents in big cities, the home prices fared comparatively well. Because city cap rates are already low they are priced like high P/E growth stocks. They have high duration (ie driven by values much further out in the future) so the immediate earnings (the “rent” in the RE context) have less impact on the price than if they were value stocks which are more sensitive to the cash flow.

  • If RE prices are high but the payment is the same should we care?

    Let’s turn to @sidprabhu again. The emphasis is for the geek readers who thirst option references any way they can get ‘em:

    Some will say what’s the problem? The payment is the same. Who cares what the price is? That ignores the fact that high home prices transfer wealth intergenerationally and can decrease mobility for buyers…

    Mortgages can be prepaid. Savings can be redirected to paying down high mortgage rates early creating a risk fee rate of return. It’s much better to buy a low priced house with a high rate because you can prepay. High prices benefit sellers…Perhaps more importantly, if home prices do go down it effectively traps buyers in their home. If rates go up they lose on their home value but locking in the mark to market gain on their mortgage is very difficult…

    Want to move cities for a better job in a recession? You owe the bank the negative equity or risk damaging your credit by walking away. (thread)

    Sid’s tweets made me reconsider one of my prior takes that I called “Minimum Tick Size Frustration”:

    Real estate prices that are high are mostly annoying because they force you to put a lot of eggs in one basket. This can be true even if the prices are high but cheap (a house on Carbon Beach for $3mm is cheap even if the price is “high”). If you are worth $1.5mm and own a house worth $1mm it’s hard to diversify. Your home is 2/3 of your assets. Many homeowners are even more concentrated than that. The high price might not be a problem from an affordability point of view but it’s a problem from a risk or portfolio point of view. So when you live in a high cost of living area, the minimum acceptable house forces you to concentrate wealth more than you’d like to.

    Here’s another way to look at it. Imagine if the lowest-priced stock in the world was $50,000 a share and there’s no way to buy fractional shares. We don’t need to make a statement about whether the stock is cheap or expensive (that depends on its earnings and how many shares outstanding there are) to be frustrated that the price is high even if it’s not “expensive”. We would just be frustrated that creating a diversified portfolio would be difficult if the minimum purchase prices were so high.

    Sid’s tweets make me change my opinion that high real estate prices are “mostly annoying”. They have much worse multi-order effects, unfortunately.

  • Since the GFC, builders were slow to get their mojo back…see the replies.

Getting Less Screwed On Compensation

I’ve talked about compensation deals in the past.

For example, one of the tweets in this thread:

Anyone that has ever worked in derivs or at a mm knows what a beast comp negotiation can be. There’s a trader on both sides of the table. Both sides are pricing calls and puts, netting risks, and trying to find structures that work for both sides’ risk preferences.

In On #Voltwit Melees I wrote:

If you really want to examine incentives, think about the PMs at the fund. The non-equity owners want maximum vol since their downside is just losing their job, but their upside is a percent of their performance. Their equity-owning counterparts want the assets to stick. Notice how the non-equity-owning PM has the same incentive as the LP, not the GP.

Comp structures, just like fee structures, are about shifting incentives to create alignment. But there’s a lot of haggling under the hood that looks an awful lot like options trading. When you negotiate comp, do you ever wonder who the patsy is? Or do you think you are in the ballpark of fair value AFTER considering all the levers/scenarios?

Recently, a friend reached out for advice about a specific type of situation. I see a concern that is worth sharing more widely. A bit of background first:

The friend is a senior employee. They are not too concerned about the downside of the new opportunity they are looking at (meaning if they just earned their salary and no bonus they could tolerate that outcome…salaries tend to be a small percentage of total comp for senior employees). The friend is really interested in the opportunity for the upside so, in trader parlance, the friend wants maximum call exposure and doesn’t value the put (ie a minimum guaranteed bonus) much. I have found that employers can be flexible on these structures. If you are risk-averse they are willing to give higher minimum bonuses but take your upside. Of course, on the trading or fund management side, employees are usually in it for the big payoff so do not choose this option, especially if they have savings and can survive on their salary alone if needed.

The major points to be aware of:

  • This friend wants max upside and is not concerned about the downside of the opportunity they are considering. In fact, the friend would be taking a substantial paycut for the shot to have large exposure to the new gig’s success.
  • The nature of the gig is the friend would be launching a fund that had an AUM fee but no performance fee (it’s not a hedge fund) and the fund would be closer to systematic than discretionary.
  • The friend is focused on how to ensure they are aligned with the employer in the case that the venture succeeds.

That’s going to be tricky. Can you anticipate my warning?

Here’s what I told my friend:

You are willing to accept a large carrot on the back end to take risk on the front end. The prospective employer agrees in principle to that arrangement. If possible, the gold standard of alignment will be tying your stock awards to a trail of your efforts in the building of the new product.

The correct appearance of the trail is that it should look overly generous to you in the event that it “hits”. Remember, you took a paycut and a risk upfront. The real-time value of that trail cannot simply be weighed against your real-time efforts since the trail is a lagging indicator of your work.

You are being very clear that your situation allows you to take a risk but it’s critical that you get paid off if things work out. There is always a form of “credit risk” when structuring a deal like this in the sense that at many winning positive scenarios, on a forward-looking basis, it will always look like the right play for the employer to cut you. You are addressing this ahead of time, and want the employer to assure against the incentives it will have AFTER you have borne the bulk of the risk.

What safeguards are in place to “remember how this deal was supposed to work”?

At every review, owners can exercise the option to screw you. Insuring against that is pretty difficult. A big difference between startups and fund management is that early startup employees own true equity. This reality is harshest when things go well. I suspect some market-making firms (they are not funds but the analogy holds) could have paid every employee millions of dollars last year and still had record profits. But they didn’t. People were paid well but found out they had zero delta to the upside at some threshold.

I’m sympathetic to their employer as well. If you paid everyone what they “deserved” many would have quit having hit their FU number. And if you don’t, sure some might rage-quit, but there’s not some other employer willing to pay them more based on some outlier year. Most likely, the owners will admit to themselves, that ownership has its privileges and they are the risk-takers. An unhappy employee is free to start their own business. In fact, that’s who entrepreneurs often are…people with chips on their shoulders.

Ownership is the only true call option. Not shadow equity, where you are promised a percentage of the p/l. That’s not a stake that you can cash out to partners.

If you are in the game for upside, be careful about who writes your checks.

(Option traders know the warning well. Bonus season, despite its moniker, rarely feels like bonus-y fun. Reviews are mostly endurance tests in which you restrain yourself from flipping a desk as you read a disappointing number off a page, several times until it finally registers that it’s what was indeed intended, all the while a superior gaslights you about how good a job you did. The canyon between words and actions so wide, you might even look around to see if there’s someone else in the room. But no. They are actually talking to you.

Market-making firms are generally run by ruthless Ayn Rand worshippers. Whether they converge to this mindset as a post-hoc rationalization for their role in doing “god’s work” or start with it likely varies. I suspect it takes a certain type of person to get to the top of that profession. That person will be good at rationalizing and see wealth as evidence of being right. It’s all quite convenient.)

Follow Up To “The R Word”

Last week I shared The “R” Word.

The post was about trying to reframe a career in a sustainable way. In a way that aligns with how our idiosyncratic energies work. Aligned with the types of people we want to be around.

The largest payoff to this isn’t immediately obvious. It relieves the pressure to build a nest egg with an overengineered margin of error. Instead of relying on assumptions of things that are out of your control like returns and inflation you choose to rely on your human capital.

The key is that you will still be excited to employ your ability and the returns that come from being a willing perma-learner. You won’t have a strong desire to stop working since you chose a stroll that forgives you for meandering instead of a sprint. A sprint taxes you not just physically, but mentally, by making you think there’s only one way to win. Racing is insidiously expensive because it directs your gaze to a finish line. A bizarre approach to life, since tomorrow is never guaranteed.

The post led to many responses (it’s the most reactions I’ve gotten from a post, especially as a percentage of total views). Many of you are thinking deeply about the same topic. I’ve had a few young people respond. I am impressed at how deliberate they are about their long-term strategy. I was never that mature. Unsurprisingly, most of the responses came from finance/trading folks of similar age as me. Many extremely financially successful or downright rich. Some of them have been sick of their profession for years but in the absence of a roadmap can’t pry themselves away from stacking more chips.

I keep thinking about this. I keep coming back to a half-baked thought but I’ll blurt it out and you can finish it in your own oven. It could be a wasteful or irresponsible thought. Or it can unlock more thoughts and break inertia. I take zero responsibility, blame, or credit for what you do with it.

You will never walk away from money without a reason. But money is not fungible with risk. Actually it’s a risk-absorber. For many, the feeling of a life well-lived requires risk. If you accumulated more money than you need, you have sterilized a lot of risk. And you’ve sterilized the feeling of being alive. There are many types of risky pursuits. Some are fun but not meaningful. Some are meaningful but not fun. And everything in between.

Before making any changes to your life think about:

  • The size of risk you need to feel engaged
  • The nature of the risk you need (where is it on the fun/meaningful spectrum?)  

With the answers to these questions, you will know whether you just need a new hobby…or if you need “a man to come through the door with a gun”.

Finally, I’ll point you to 2 terrific related posts that have lingered for me.

  • The Path (5 min read)
    Chris Wong

    Excerpt with my emphasis:

    For me, The Path started when I began my career in finance in 2002. Actually, I’ve probably been on The Path even longer, since middle school. Get good grades, get on the honors track, do extracurriculars. Get into a good college. Get a good job. Get promoted. Get a better job. Get promoted. Get a better job. Get promoted.By the time I turned thirty, I had begun to question The Path.

    The real reasons were that the money was good and The Path was a siren’s call to a life of comfort. The money to me was security and optionality. But I wasn’t using the optionality to do anything and because I had already stopped spending money on things I didn’t enjoy, I had a degree of financial security. Why be inauthentic to myself in order to pursue goals that didn’t interest me? In finance, the answer to the interview question “Why do you want this job?” is a dirty open secret. You are not allowed to say money. Even though that is everyone’s real answer. You must make up an answer to prove that you are not a masochistic psychopath. I couldn’t lie anymore. The only reason to stay in this job was money, but to me cash was the applause of Performance Art and I would rather put on my own show in an empty theater.

  • Speculation: A Game You Can’t Win (More To That)
    Lawrence Yeo

    Risk aversion is the idea that a loss of X hurts more than the joy of winning X. That means the profession of investing has an emotional volatility drain that wears us down. This short post will similarly resonate with traders. If you are not a trader and it resonates, I’d suggest you are misallocating your time.

    Excerpt from Lawrence’s post:

    …financial freedom isn’t about money, it’s about attention. The less you have to think about money, the more free you actually are. Speculation is the antithesis of that statement.

    Read the whole post here.