On Delta Hedging

Delta hedging is a trade-off between transaction costs (direct+slippage) and risk reduction. Some observations to help you think about it top-down:

  • Delta hedging is sampling prices with trades instead of simple observation

    When you compute realized volatility you choose a sampling period, say close-to-close. You can think of your delta hedges as samples. If you and I delta hedge at different prices we are sampling different volatilities. Close-to-close vol might not even correlate with our samples. So everyone’s lived experience of their attempted “market neutral” is different based on how their sampled vol compared with the implied. This is why delta hedging is bedeviling.

  • Delta hedging links implied vols to subsequent carry p/l

    Delta hedging is the link between the implied vols you trade at and the subsequent p/l you realize regardless of what some objective measure of realized spits out. If you hedge a 1 month option 2x over its life you aren’t really trading vol since hedging that infrequently is going to generate a pretty random vol compared to the vol that’s realized by conventional measures. If you are trading implied vs realized strat you are mismatched.

  • Transaction cost vs risk trade-off

    If you hedge hourly your sampled vol will land somewhere close to traditional measures of realized (assume no flash crashes or quick resolving discontinuities). But it costs you a few bps in slippage each time. Expensive. So you need to tolerate some delta, which means you don’t hedge “continuously” as the pricing models assume. How much you let your deltas run will depend on so many factors. Non-exhaustive list:

    1. Tolerable p/l variance
    2. How much gamma you have
    3. Opinion of how returns are distributed.

    Another thought. You could hedge more frequently but with a more liquid instrument like ES. So you are sampling vol more often, and saving on slippage, but increasing basis risk. (Be careful about taxes!…Futures are designated “1256” contracts and have specialized tax treatment which means you need to track p/l in different buckets for tax purposes.)

  • The reason to systematize your hedging rules

    Once you tally all the considerations you just want to systematize the hedging. Fixed time intervals, time intervals divided in proportion to volume traded, just trade on the close, every time you go to the bathroom. Whatever. Just reduce the temptation to trade emotionally.  Why?

    Cutting long gamma short and letting short gamma ride is the vol traders equivalent of being a loser in delta one trading.  Be consistent about your rules whether you are short or long gamma.

  • Be realistic about what delta is capable of hedging.

    Market making 101 — the only way to actually hedge an option is with another option.  This is especially true with low delta or tail options.

Finally…my ongoing joke is delta is the only Greek. Be short options where she expires and long where she doesn’t.

This thread was a cleaned up version of a popular Twitter thread.

What Does “Rich” Mean To You?

My Twitter following grew hand-in-hand with the newsletter. On Twitter I really just wanted 1,000 followers figuring that might be enough to crowdsource. That was a goal because Yinh and I would randomly text friends with a question to settle our own debates. I remember sitting in a cab as she blasted a group “Do you know what a solstice is?” because I claimed this was “common knowledge”.

Well I used Twitter this week for a survey.

“What number do you consider “rich”?

There are over 400 respondents by now but the poll is still open. You can see the thread and take the brief, anonymous survey here.

You can see the results here.

There’s 2 centimillionaires. 5% of respondents have a net worth greater than $10mm. And the relationship between wealth and age is fairly strong until about age 30 but then the correlation becomes much weaker. Lots of very rich 30 and 40 somethings. And there’s a 22-year-old worth $3mm. Smells like someone who has been mining ETH since high school.

The 400 respondents have a combined wealth of over $1.2b. Several people have joked that I have a valuable email list. But I did not collect email addresses. It will be interesting to see how the numbers change now that this mailing list is getting the survey. Then I’ll know just how valuable your email addresses are, muahaha!!!

Let me explain the context of this survey in the first place. It was a piggyback to my wealth tax email last weekend. A friend told me that he once read that people consider net worths 4x larger than their own to be “rich”. The reason this is interesting is you would expect that people in favor of a wealth tax would try to draw the line in relative terms since “rich” is relative. So someone worth $1mm might think $4mm should be the line, while the top respondent on our survey would draw the line at $1b.

In this case, I was trying to see if there was a relationship between a person’s net worth and what they considered rich. This sample produced a median multiple of 5. So someone with $1mm thought $5mm made you rich. Also, the median amount the entire sample considered to be rich was $5mm. That’s comforting. On average people who were worth at least $5mm considered themselves to be rich. So if you hit that mark, there’s a fair chance your neighbor’s yacht won’t actually make you feel as poor as those headlines of NYers making $750k/yr barely making ends meet will have you believe.

Many people sent me their definitions of being rich incorporating age, expenses, what makes them happy, where they live and so on. I wasn’t looking for thoughtful responses. I was looking for a gut impression. I used the word “rich” specifically for that reason. “Rich” is a child’s world. When I was a kid if another boy had that GI Joe aircraft carrier, they were automatically “rich”. It’s ironically a low-brow word. People were telling me the difference between rich and wealthy (which Chris Rock once quipped is the difference between Shaquille O’Neal and the person who signs his checks). I wasn’t interested in such nuance. Rich…first number that comes to your head. Go.

Back to the results. Of course fintwitters visualized the data. Of course fintwitters had comments. That’s the fun in this. Here’s a thread of reactions.

And as Kamil said, the best take points out that almost everyone thinks that $5mm is the bar for being rich. I’m only off by a factor of 2 when I said that $10mm was the new millionaire. In fact as of 2020, to be a 1%-er in the US a household needs $11mm!

And if you want to see net worth in the US by age as of 2020, you can find that table here.

Distributional Edge vs Carry

I had a recent discussion with a younger trader. His strategy was to sell options when IV was in the 100th percentile. 

What are some problems with this?
  • That 100th percentile depends on your lookback window and the relevance of that window is I don’t know, arbitrary. The historical distribution of IV does not need to have any relevance with respect to qualitative information you have today. Exhibit A: GME.
  • Any day when vol goes up after a 100th percentile IV day is just another 100th percentile IV day. The next day given, that you just hit 100th percentile yesterday, just doesn’t care that yesterday was a “top” compared to the days that preceded it.
  • But the biggest issue here is that selling a “high” number that you know will go down looks like distributional edge. What goes up must come down right?

High <> expensive

If something is high and you expect it to go down, there must be a countervailing force which drives the price being “high”. That’s the carry. We don’t want to sell things that are just “high”. We want to sell expensive.

So if a price is “high” we must ask: “Is it high enough relative to the carry?”

Let’s examine this idea in a few contexts.


If you sell vol at 150% and that implies a $50 straddle, it won’t matter if vol goes down to 25% if the stock gaps down $75. This is well understood already. Everyone knows vol comes down after earnings. But the p/l driver is the carry — the size of the earnings move.

Real Estate

Everyone and their grandma has seen the low cap rates in the Bay Area for the past decade. But the cap rates are so low because the carry is high…the annual appreciation. (One of my suspicions is that low cap rate properties are actually relatively underpriced. Any donkey can pull up mashvisor.com and see what screens as value. It takes more effort to find reliable drivers of growth to earn carry in “expensive” markets)


Earnings are the carry and the P/E is the directional trade. Yes, a 100 P/E stock is going to eventually have a lower P/E. Yay, directional edge!

But what about the carry? Earnings growth.

If earnings grow 100% per year, in 3 years that stock is 12.5 P/E if the stock price doesn’t move. How about  stocks that look like they have distributional edge if we buy them on the “low” end? We have a name for those — “value traps”. The tailwind of valuation is battling the headwind of earnings deterioration.

Implied Parameters Do Not Vary As Widely As Reality

Going back to the options example. if you sell “high” IV remember IV will rarely get higher than the range of RV because the market sets point spreads to imply mean reversion. If near term volatility explodes from 30% to 100% the market does not extrapolate this throughout the term structure.

So if you are short high IV expect negative carry. If a stock is typically 30% vol and realized shoots to 100% don’t expect IV to keep pace. You might find yourself shorting IV at the 100th percentile at say 85% vol while the stock moves 7% per day (about 112% annualized).

This dynamic holds when vol gets very low as well. Vet option traders expect to choke when they buy IV at-all-time lows. Wow, I can buy SPX weeklies for 7%! Too bad, it’s so quiet I can’t even tell if the market is open.


The big question is the speed of convergence.

If you are short that $50 straddle at 150% vol and the next day the stock is down $25, but vol halves you can hedge your negative gamma, cover some short options and win. But if you gap down $75 you lose no matter what vol does.

Profitability depend on how the speed and shape of the implied parameters (IV, P/E, cap rate) cross the carry parameters (RV, earnings, rent).

Conclusion: No Easy Trades

If IV got so high as to exceed any point on a vol cone maybe then you’d have an easy trade. Your directional tailwind (IV will probably decline) and your carry can both win. Good luck finding that.
Keep in mind:
  • Carry is the compensation for betting against mean reversion
  • Carry is the cost of betting on mean reversion

Finally, a half-joke rule I’ve had with traders I’ve worked with:

When you do your vol sorts, you sell the second highest vol on the board. You always buy the highest. This is not advice.

If the directional tailwind vs carry frontier sounds familiar it’s because I’ve talked about it before. It’s my version of EMH…The “No Easy Trades Principle”

Structuring Directional Option Trades

This post is a response to Twitter buddy @demonetizedblog

Let me take a stab at a “process” answer.


For directional trading 90% of the work happens upstream of the option expression.

The option trade construction is the most trivial part of the process. Your fundamental work should inform your opinion of the distribution. This can be compared with the implied distribution from the vol surface.

This mental process is entirely different from vol trading. Remember, you aren’t dynamically hedging. Directional trading and vol trading have totally different starting points.

[At the end of the post you’ll see when the two approaches come to the same conclusion and when they don’t. This can lead to directional traders to trade with vol traders and everyone is happy. It’s still zero-sum. It’s just that the losses can be incurred by whoever provided the liquidity to the dynamic hedger. That entity was not part of the original trade]

Ok, so when it comes to directional trading vs vol trading, you must be clear what game you are playing.

This post is about structuring directional trades.

What’s the distribution?

First, you do a bunch of fundamental voodoo and come up with a distribution of possible stock returns.

[I’ll wait]

Good. We are going to discuss options now. Relax. Take a breath. Don’t worry about fancy words like “moments of a distribution” or kurtosis. You are a fundamental investor. It’s fine to think in prices, percentages, and bets.

Now what?

Let’s establish a focusing principle.

You want the short leg of an options spread to correspond the most likely landing spot of the stock based on your analysis. If those options are the cheapest on the board you might want to consider that the option surface is not presenting you an opportunity. It agrees with you. Don’t rush over that. This is not intuitive. Many fundamental managers buy the strike of where they think the stock is going. Don’t do that. Instead let’s review some basics about distributions. Without real math.

  1. A biotech stock worth $100 might be trading for that price because it’s 90% to be 0 and 10% to be $1000. True bimodal.

    Code-switching this idea into options:

    • The 100 call is worth $90.
    • All the OTM 100 point wide call spreads are worth $10.
    • All the butterflies are zero.

      What are some courses of action here?

      Let’s say you can afford 1 100 strike call. You could have also chosen 9 900/1000 call spreads. Or 3 of the 700 calls. In this case, all the propositions are the same because the options are correctly priced.

      [Prove this to yourself. I’ll wait.]

      Cool. Now you can imagine how if some of the options were priced differently you might be able to find an alluring proposition.

  1. New stock to consider. An insurance company also trading $100. This is not a bimodal stock. Perhaps it looks more like a bell curve with a high peak shifted to the right of the forward price because a pumped up put skew is signaling strongly negative skew.

    Wait. Why does that push the peak to the right?

    Think about it. For that stock to be $100 with a long left tail, it must have a greater than 50% probability of going up. The verticals will show you that. It’s the opposite case of the biotech stock and with much less volatility.

    • If you were super bullish you might want to load up on the depressed slightly OTM calls.
    • If you were bearish but thought the left tail was not as long you might want to buy the .50d/.25 put spread to express the view by exploiting the excess skew you think the market is embedding in the OTM puts.

Just remember, options give a shape to the distribution. Not every $100 stock has the same distribution. Think about where the $100 comes from? What upside force is counterbalancing the downside? The biotech stock has a very long right tail 900% away counterbalancing a large mass of probability that’s only 100% away. The $100 stock price is nothing like the insurance company. Options allow you to express the bet you want to express. The stock price alone is too blunt.

Once you let that simmer you can start to ask yourself useful questions:

  • Would you rather own 1 atm call or more calls for a total of the same premium at a higher strike?
  • Now compare that to call spread candidates. How many call spreads can you buy and at what moneyness?

The nice thing about vertical spreads is they cancel out many of the “greeks” effectively taming your vega and gamma exposures. The bets can be thought of as binaries allowing you to make simple over/under bets. To calibrate your impression of the possible magnitude of a stock move, you consider the moneyness or how far away from stock price the chosen strikes are. The moneyness will depend on your intuition for the volatility of the stock. You will have a sense for which spreads are “close” or “far”. These are technical terms.

And since I mentioned volatility, let’s say a few words on that to help you avoid some landmines.

Is the vol cheap or expensive?

If you are a directional trader you don’t care if the right volatility for an option is 55% or 56%. You aren’t dynamically hedging. But you don’t want to go to the used-car lot without at least checking Carmax online. You can compare the implied vol to the distribution of historical realized to make yourself feel like you did diligence.

Here’s a simple way:

Compare the IV to the stock’s historical vol of a comparable tenor. So if you are considering a 6 month option look at the distribution of 6 month historical vols to see if you are on the high or low side of the range. How? Looking at a vol cone will get you a quick optical answer.

Here’s Colin Bennett’s example (with my highlight) from his book Trading Volatility:

If the recent realized volatility is elevated and you wanted to buy long-dated options it might be a poor time to buy options. You can either wait, trade structures like verticals that have little vega exposure, or even create a directional trade by selling options.

Here’s a few extras to consider when selecting an expiry:

    • The nearer the option tenor, the more event pricing matters. The event’s variance is a larger proportion of the total variance until expiration.
    • Longer dated options have takeover risk. (Cash takeovers mean your LEAP extrinsic goes to zero. Sorry.)
    • Do you plan to roll the exposure to maintain it or is there an expiration to your thesis? The more often you roll the less rebalance timing risk. This has to be weighed against trading costs.

The Real Work Is Not In The Options

When you throw a proper punch the fist is just the delivery method. The point of contact. That’s the option expression. The real work happens from the torque in your hips. That’s the fundamental analysis behind the punch. An advantage of directional trading is you can think in discrete bets once you’ve done your fundamental homework.

Discrete trades let you:

  • Think in terms of how many bets you get paid back vs how much premium you layout and compare that to the probability your fundamental work suggests.
  • You’d like to get to a statement that looks like “I’m willing to risk 1 bet to make 3 because I think the proposition is a 50/50 shot.”
  • This establishes your expectancy and shape of the p/l.
  • Combine that info with your bankroll and now you can size the trade.

Bonus Section: Volatility Traders

I said that directional trading and volatility trading are different games. I’ll briefly talk about that.

First of all, even vol managers sometimes make discrete bets. They will “risk budget” a trade. I’m willing to spend $1mm on 150% calls for winter gas. Or whatever, you get the idea. They might even set up a separate account for tracking and attribution for this.

But really this risk budgeting or discrete framework is different from managing a relative value volatility or market making portfolio. In that environment, you are often responding to values moving around some cross-sectional trading model. You see edge, you pick it up, throw it on the pile and manage the blob. With a decent size book holding thousands of line items you are going to need 3-D goggles to slice and dice the positioning and the risk. You might not even know what you are rooting for sometimes. If you are short SPX correlation and long 200 of the 500 names then you are massively overweight vol in the 200 and you are “synthetically short” vol via the index in the other 300. Hundreds of names x hundreds of strike x hundreds of expiry and you need to bucket and compute quickly and accurately. Totally different animal from directional perspectives.

This does not mean that vol traders and directional traders don’t land on the same conclusions occasionally. A vol manager who finds a name that “screens cheap” might be looking at the same thing a fundamental manager is seeing. The fundamental manager is coming from a different vantage point, but might feel that a stock is hiding some serious upside and the nominal price of the calls are a bargain. In this case, the fundamental manager is going to struggle to find liquidity as the call options might be cheap for a few contracts but once they start calling around the street find that no market maker is willing to join the resting retail offers.

You may be wondering why the screens are so low in the first place? Why are they stale? The market maker’s dashboards are flashing green too. They know those options are cheap. But remember this is a game. They aren’t going to bother lifting the offers for a few contracts. They would rather freeroll on the possibility that some donkey overwriter who systematically sells calls without price sensitivity dangles a mid market offer. Then they’ll lift. (gratuitous “Do You Even Lift Bro?” clip)

So when do vol managers and directional traders trade with each other? All the time. Here’s 2 examples.

  1. Imagine a fundamental trader who is directionally smart but not vol savvy. They might buy calls, and the market makers who have been keeping tabs on this pattern of flow realize its predictive of a price move but has not historically beaten them to implied vol (perhaps it’s one of these dumb accounts that buys the strike of where they think the stock is going. They should probably hire a vol trader, if for nothing else to show them how to do p/l attribution). So the market makers sell the calls and overhedge the delta. Trading 101.
  2. A very common case where directional traders and vol traders are happy to trade is on vertical spreads or ratio spreads. Say a directional hedger buys put spreads. Vol traders can be happy to sell them so they can buy that tail option that the hedger gave them as the lower leg of the spread. A similar example would be a 1 x 2 ratio put spread. Say the stock is $100 and the directional trader buys the 80/75 1 x 2 put spread for a cheap or even zero premium. In their mind, they make make money all the way down to $70. They don’t start to lose money until the stock has dropped more than 30%. The vol trader has a different view. The vol trader cares about path and they know if the stock trades down to $80 quickly and vol explodes, they are going to be long vega and have ammunition to sell into the panicky vol buying. That 1 x 2 put spread is going to mark ruthlessly in the directional traders face. The directional trader didn’t respect path. Option traders are extra wary of path because they are highly leveraged businesses warehousing complex portfolios with non-linearities. There’s no better training for visualizing risk up, down, through time, across correlations, and at different speeds. The trader who honors path will often be the reason that “option that will never hit” is priced so high.

If you liked this post, consider checking out the Moontower Volatility Wiki.

The Moontower Volatility Wiki

Many beginners to options ask me and other professionals what they should read to learn options. I’ve seen this question asked enough times that I built a wiki that I can reference instead of needing to come up with an answer every time.

Voila…The Options Starter Pack (Link)

In the process of curating that I figured why not go the extra step…Introducing the Moontower Volatility Resources wiki (Link)

In addition to Moontower trading content, you will find select options content from the rest of the online vol community.

To maximize how useful this wiki there are a 2 important points.

  1. I will be keeping this wiki updated, but it is not open source. At this time, I think readers are best served knowing I’ve pre-screened submissions.
  2.  If you find a blog, book, video, interview, etc that you feel deserves to be here please submit it. I won’t guarantee I’ll include it but the benefit is we can keep this resource high quality and free of spam.

So there’s a tension involved…one side is that in order for this to be useful it can’t be a free-for-all. If you want a free-for-all there’s Reddit and Twitter and upvoting and ‘like’ buttons. This is not that. This is intended to be a reference with evergreen content subject to my standards. Like any manner of gatekeeping, I will miss things and I might let subpar stuff slide in. Sorry in advance. I’m always open to hearing suggestions/complaints. You’ll need to trust that I’m competent and care.

The other half of this tension is it requires engagement even though it’s not open-source. If you come across a source, a tool, a course or anything that fits neatly with this wiki then please share it.

Finally, here’s the excerpt from About This Wiki:
Option strategies range from directional hedging/speculation to the complexity of index dispersion portfolios and exotic structured product books. You cannot learn to trade options from reading. It is a craft and your understanding of it comes much faster when you have a position. When the feedback of the position comes in the form of mark-to-market p/l you learn what the position is sensitive to. Greeks like delta, gamma, and vega are immediately less abstract.

The good news is I believe any numerate, motivated person can learn options.

The bad news is two-fold:

  1. Experience is expensive.
  2. It is a craft best learned as an apprentice.

#1 is unavoidable. Straight talk — you will lose money learning. Guaranteed. Act accordingly. Don’t sell naked options and make sure worst-case scenarios are tolerable. Bid/asks are expensive. Sure, they might only be a few pennies, but 1 cent on a $1 option is 1% slippage. That’s 10-100x the slippage you pay to trade stock. Vast fortunes have been built on that 1% slippage. It will grind you as surely as a blackjack dealer if you play long enough without an edge.

#2 has better news. The internet in the form of blogs, podcasts, electronic brokerage and social media (esp Twitter) has never made it easier for a voracious learner to educate themselves, find mentors, and have meaningful discussions that would have been impossible even as recently as 2000 when I got into options trading.

I was fortunate to discover options trading right as I graduated college. I joined Susquehanna (SIG) and learned how to think about options, risk, and trading from Jedis. Their curriculum and methods for teaching were so comprehensive, tested, and systematized that it was a massive source of competitive advantage. The cared deeply about cultivating talent. They did not care if you knew what an option or interest rate was when they hired you. They looked for drive and aptitude only since they were secure in their ability to teach everything you needed to start managing a portfolio in as few as 18 months out of college.

I am not a math whiz. I was one of the <5% of hires who got a higher score on verbal than math SAT. Options intimidate many people simply because of the Greek letters and the math behind the models. I get it. I’m intimidated by math whizzes too. I have no more than HS Calc BC math education and a single stats course in undergrad. But the truth is, you don’t need to be able to derive Black-Scholes any more than billiards champ needs to know physics. Don’t get me wrong — the intuition behind the models is critical but the bar to acquire that is much lower than a math degree.

Much of my writing is an attempt to bring the reader to an intuition of the math in the same way that I was taught. I hope it’s even more accessible since my own weakness in math makes it easy to imagine being in the average reader’s shoes.

This wiki sits in that sparse space in-between the basics you might learn from the Series 7 and the nerdom that is derivatives structuring at a French bank. This is that mushy practical area in-between sophisticated retail and professional vanilla options user. It is an area, that will become more popular thanks to the boom in retail option activity and r/WSB. The vig and risk of options is going to weed out many of the new tourists but the few who persevere and have a deeper thirst to learn should find this wiki helpful.

And for the finance professionals who use options directionally but do not “trade volatility”, the resources found here might be just the bridge you need to understand volatility surfaces a bit better. This can improve your trade expressions, risk management, timing and ultimately executions.

If you have feedback, my door is always open.


A Former Market Maker’s Perception of PFOF

It feels like payment for order flow controversies flare up every few years. When I see some of the takes I know how marine biologists felt after Jaws hit the cinemas in 1975.

Except they didn’t have Twitter to scream into.

I’m going to assume you already know what payment for order flow is.

If you need the basics, A16’s Alex Rampell and Scott Kupor have you covered. (Link)
If you want the GOAT of high finance’s version, here is the Matt Levine post I shared last week. (Link)

Now if you stop at Levine’s post I’d forgive you. There’s really no following that guy. But now that I’ve said that, you own the downside of reading further and if I say anything useful here I’m in-the-money.

I think my experience qualifies me to hopefully add some perspective to the discussion. I have been trading options for 21 years with the first half of those years on the floor. Even though I’ve been trading prop for the past decade I’m a dyed-in-the-wool market-maker. You can take the dog off the floor, but you can’t take the floor out of the dog. (Full disclosure: I used to work for SIG who was an early payer for order flow, but I had no insight into that side of their business).

An Image Problem

Payment for order flow sounds terrible. It sounds like payola. Greasing the radio DJ to get your record played on-air. That’s a bribe to the regional gatekeeper. There’s widespread misconception that when Citadel pays for flow it’s attempting to use the info to front-run the order. This is a dizzying misconception.

No trader thinks front-running random retail flow makes any sense.

Write that on a chalkboard 50x please.

The Nature of Adverse Selection

Drive it home: no trader thinks front-running random retail flow makes any sense.

In fact, the opposite is true. The entire basis of trading against retail flow is that it is a random mix of buys and sells and not autocorrelated. You want to trade against your drunk uncle Sal who has a good feeling about the Jets this Sunday. We call this “dumb” flow. Sorry, but that’s what it’s called.

On the other hand, we refer to institutional flow as “smart flow”. Not because it knows which direction the stock is going to go, although this can be the case as anyone who has been contra to SAC flow back in the day can attest. The reason we don’t want to trade against the flow is that it’s autocorrelated. 1,000 shares is the tip of an iceberg. Nobody eats just one chip just as nobody buys just 1,000 shares.

The options equivalent is putting someone up on a trade, only to have them reload 5 minutes later. This past fall, Softbank string-raised tech calls every day for a couple weeks. Masa-son is not smart paper, but he has a big stack. Truthfully, the threshold to be an undesirable counterparty is surprisingly low. I remember hearing a SIG trader at a conference a few years after I left. He mentioned that their studies had shown that the adverse selection of an options trade went up dramatically once it was greater than 16 lots.

Let’s understand this. Consider a pro-rata exchange where your limit bid is on equal standing with other limit bids but your fill is proportional to your size. So let’s say you are bidding $1.25 for 100 option contracts and the total bid quantity is 1000. If a retail sized order sells the bid for 10 contracts, you get filled on 1 because your size was 10% of the total displayed size. The pro-rata system (vs maker-taker which is a queue based on speed) incentivizes traders to show far more liquidity than they really want to. They don’t want to get their whole bid hit but they need to show size to be entitled to any reasonable percentage of the incoming orders. When an order sweeps the book, banging out the displayed size on the bid, the market makers are instantly sad. They know they are on the wrong side of a “smart” order.

The possibility that the flow you trade against is adverse, smart, institutional – whatever you want to call it – has a deep implication. You make a wider market than you would have if you could just tell the difference between the adverse flow and the random retail flow.


The brokers have realized they can segment the market between orders that can be facilitated on tighter spreads and those that require wider quotes. Liquidity has a price. Without PFOF, spreads need to be cushioned by the probability that an order is institutional. Instead, PFOF creates a tiered market where the cost of liquidity is proportionally aligned with the risk on a per trade basis. Retail traders get better fills. There’s less deadweight loss.

Institutional traders might complain, but its an illusion that they should have gotten the price that a retail trader should get. The risk business is not the widget business. You don’t get volume discounts.

“The opportunity to trade against random flow” as a source of revenue is a bit abstract. You are already familiar with price discrimination in other domains.

  • Casino’s attracting whales.

    Casinos don’t like card counters, they want customers that have positive LTV in the long run. They like whales and the type of people who buy books titled “The Fool-Proof System To Beating Roulette”. Casinos are paying for order flow when they offer complimentary suites and blacked out SUVs to and from McCarran.

  • Ad tech

    What is the internet but reams of data on customers being sold to the highest bidder so platforms (the brokers in our analogy) and in turn vendors (the Citadels) more can more efficiently convert sales (trades)?

  • Financial products

    Good driver discounts on auto policies. Life insurance physicals. Credit checks for loans. Price discrimination based on risk is the norm not the exception.

  • Retail

    As a broke 20 year old I used to frequently buy and return products at GNC. Yes, you can return a half-used tub of creatine. GNC started keeping tabs as a policy. I get it. The Ponderosa wishes it could turn away Joey Chestnut.


The discourse around PFOF has an air of monopoly sentiment. Maybe not in the Standard Oil sense of the world. There’s more firms than Citadel. You have Virtu, G1 (SIG), Two Sigma, Wolverine. It looks more like OPEC.

But there’s a big difference. These are not natural monopolies or crony handouts. Contrast the dynamic with payola. Payola was a scam that worked because the value of the bribe to the briber (the record label) was very low compared to the payoff of getting radio exposure. Meanwhile the value of the bribe was substantial to the receiving DJ who was paid a conventional salary despite being the caretaker of a government monopoly — airwaves.

I don’t think it’s surprising that high fixed cost industries settle into oligopoly-type hierarchies. The competitive forces are so strong that they double as high barriers to entry. The HFT-firms here are not defending natural monopolies. They are the survivors of the trading game who invested heavily in technology early. @hidenotslide explains in his recent post about another storied traded firm, DRW:

This brings me to my first point – firms who embraced HFT early in its evolution are today’s kings. Of the 10-20 firms that make up the bulk of high frequency trading profits, a large majority were launched before the 2008 financial crisis and many even prior to 2000. Because superior technology leads to direct competitive advantages in HFT, barriers to entry have become insurmountable over the last decade as companies have invested in ever faster exchange connections & market data feeds. A 2017 paper from researchers at Cornell & Penn argues this exact point – newer, smaller entrants that engage in HFT can survive, but they don’t get anywhere near the share of profits that larger, more established firms enjoy.

What’s absent from the narrative is how tall the pile of bodies these firms stand atop. I should know. I used to be able to work five hours a day (NYMEX alum holla) and make a lawyer’s wage. And in some years, a law partner’s carry too. Well, if you were smart you saved your money and realized it wasn’t going to last. The days of “locals” (ie wildcat market-makers) is long gone.

Many of the small firms, who saw the writing on wall and had an appetite for the long game, plowed money back into massive technology capex. Most of them just earned the right to say they lost to the best. In some cases they found small, profitable niches where they play the role of suckerfish. Respect to them, even this was not easy.

How about the remaining firms? The private giants the media likes to call “shadowy”. They were the ones who were most adept at assembling teams of software and hardware engineers working with game-theory geniuses to devise algos in a cat-and-mouse battle with competitors. The ones who stayed step-for-step with the exchanges who themselves were experimenting with matching engine rules, data, product listings and connectivity in their own battles for market share.

The truth is progress is cutthroat.

I remember the days before decimalization where you could make $5 wide verticals 3/8 wide. Today that same vertical is a choice market and the market maker gets paid the equivalent of an inter-dealer broker commission or about 25 cents. On a 3/8 wide market the market maker used to earn nearly $18.75 (or 50% of 3/8)! My business partner and I always marvel at the innovation and how little vig a trader is willing to accept to flip million dollar coins. It’s such a flex for capitalism. So much so that how good these firms are is chalked up to monopoly and not that fact that they are the survivors of the capitalism’s most brutal tournament.

How Survivorship Bias Makes Firms Look Like Monopolies

Perhaps I should not be surprised at the monopoly sentiment. Some of you will nod. “How can they make money every day?” First, I’m not sure they do, but even if they did that’s hardly a red flag. Casinos might make money every day so long as they can open. They’re not monopolies. Worrying that financial firms make money everyday is conflating market makers with investment managers because they traffic in the same products. But one of them is a customer and the other is a supermarket. With tiny supermarket margins per trade. And high fixed costs. If volumes dried up, the losses would show up even if the margins stayed flat.

A stronger, but still naïve argument, that they were monopolies would come from noticing that these 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. Now you are blowing away less coordinated competitors who were quite content to earn their hundreds of percent a year and retire early once the markets got too tight for them to compete.

SIG was playing the long game. 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.


Thus far I’ve only pushed back against the idea that PFOF is somehow nefarious. It is a form of price discrimination. The price discrimination is economically sensible when we price liquidity. There is a cost to having someone trade with you at the exact moment you want to trade. If you are a retail trader, that cost is tiny and we can thank technology and the competitive drive of very smart people to undercut one another so they can be the best bid for your business.

If you are an institutional trader that cost is higher. And it should be. Your cost to trade should be compared to your historical cost to trade. Not against what a retail trader’s costs are. I’d be shocked if an apples-to-apples TCA showed that this cost has increased over time. My null is the cost to trade for everyone has collapsed but probably more for retail.

I don’t have any strong opinions as to whether PFOF is the best equilibrium. One could argue we should have a single central order book, but then the exchange would have a monopoly. Plus it’s not obvious to me that the centralization of liquidity serves the heterogenous interests of all economic stakeholders across countries, regulatory regimes, strategies, time zones, and instruments.

We could entertain more incremental tweaks to the current architecture. For example an auction every minute or shorter trading hours to centralize liquidity in time but not venue. There’s probably some efficient frontier of tradeoffs. Nothing about PFOF looks villainous from my understanding of markets so if it lies along that frontier I would not be surprised.

And perhaps now you won’t be either.

How Options Confuse Directional Traders

2017 was a historically low-vol year, rewarding options sellers despite selling lower option premiums as the year progressed. Like they found a broken slot machine at the Cosmo. It wasn’t until the Feb 2018 “volmageddon” in exchange-traded VIX products, that retail discovered the dangers of selling options.

In the past year, retail, led by r/WSB, is back in the deep end of the options pool. This time they brought swimmies — they are only buying options. This limits their losses to the premiums.

As opposed to professional vol traders, most people use options as a way to bet on direction. You buy a put to bet on a stock going down and you buy a call to bet on a rally (or an “up” — a term coined by my doctor friend who always used to make fun of us finbros who talked about “puts and ups” all the time when we were in training). I tend to dissuade people for messing with options unless they have a very specific risk to hedge or if their speculative thesis is well-defined. Since options expire you need to be right not just on direction but timing as well. There’s a lot of ways to lose, get lured into trading more, and generally chop yourself up.

I’m going to demonstrate how you can lose money despite being very “right”. For good measure, we’ll extend the conversation to how hedging can actually increase your risk. Let’s jump in.

An Option Lesson

The recent action in GME justified the cigarette warning label I put on options. If the option user doesn’t appreciate the role implied volatility plays in an option price, then Benn’s tweet is mystifying:

Put options increased in value as the stock went up.

Then, with the stock on the way down @mark_dow tweets:

Put options lost value as the stock collapsed.

My kids would chalk this up to “opposite day” (apparently a modern holiday where kids wear pajamas to school). Alas, there is a more boring explanation:

Implied volatility increased as the stock price increased and fell as the stock price fell.

Pro Version

If you are eager, we can drill down a bit.

  • The option’s “vega” dominated its delta in both cases. The vega tells us how much the option’s price will change as the volatility rises or falls.
  • “Vanna” represents the sensitivity of the option’s delta to volatility — a second order effect. As the vol increased, the OTM option deltas increased. This is notable because it is a positive feedback loop. As the stock and vol both increase on the way up, market makers have to buy more stock to hedge. On the way down, it is stabilizing as the vol decreasing means the option delta decreases and market makers need to be “less short” to hedge the puts…it’s stabilizing because this offsets the negative gamma effect from being short puts in the first place. This one is tricky because the vanna effect is dampening the vanilla gamma effect.
  • Then there’s “volga” which is how the option’s vega changes with respect to vol. This is yet another second order effect of vol (I’ve written about that here). It feeds right back into vanna and acts as a reinforcer on the way up and a stabilizer on the way down (since spot and vol are positively correlated. We’ll get to this correlation later).
  • There are higher order Greeks than “vanna” and “volga”. Ironically, they are only known by the French. Don’t ask.

Vol traders care about these cross-currents because of how they accelerate or dampen the price of options. These effects alter hedging flows which change buying and selling pressures. Outputs become inputs so each sub-cycle in the process looks like a foreshock to something bigger, or the aftershock to something dissipating.

This might sound theoretical or academic but it’s the nuts and bolts of managing volatility portfolios. An option book with many names, maturities, and strikes looks like an amorphous blob until you use these concepts to give it shape. Once it has shape you can recognize what kind of animal it is. You can predict how it might respond to different scenarios. The measurable risk is how it will react to the market’s movements. The stock is going to do stuff. That’s a given. You are not allowed to be surprised by that fact.

The real concern is if the portfolio, this animal under your care, acts outside your range of expected behavior.

Normie Version

Rest easy. That was utter overkill for investors or even casual option punters. To understand why puts got cheaper on a selloff, you just need this picture:

It is a beautiful and simple visual intuition constructed by @therobotjames.

  • The purple bell curve is the distribution of GME stock when it’s trading for 600% vol and $200.
  • The green bell curve is the distribution of GME stock when it’s trading for 400% vol and $90.


Despite the higher stock price, the purple curve imputes a higher probability of the stock going below $20 because the distribution is much wider at 600% vol than at 400% vol. The impact of the vol totally dominates the moneyness, or distance, the stock is away from the strike. Another way to say this is “the $20 strike is closer to $200 than it is to $90” if the volatility is that much higher when the stock is $200. This is easier to understand if we simply make the volatility disparity wider. Imagine a govt bond that trades for $100 par and a stock that trades for $200. Nobody would be shocked if the 50 strike put for the stock was worth more than the 50 strike put for the bond.


I can see you scratching your head. In GME, we are talking about the same exact asset at 2 points in time with a contradicting proposition: namely that the probability of the stock dropping below $20 when the stock is $200 is higher than when the stock is $90!

This paradox is an illusion that happens whenever you have the benefit of hindsight. You don’t know which of these prices is the true odds. You can only trade with the information you had at the time. You cannot arbitrage the relative pricing between the 2 states of the world that we have the luxury of seeing in the rearview. Looking back you can say that the stock’s chance of going below $20 was underpriced when it was trading $90 or that it was overpriced when it was trading $400 but you couldn’t make those claims at the time. They only seem paradoxical when compared to each other.

At this point, I suspect retail traders, curious as to why they won to buying puts on the rally and lost to buying puts on the selloff, developed some understanding of vol dynamics.

Hopefully the tuition wasn’t too steep. Not all lessons are as cheap as a defined option premium.

The Expensive Option Lesson Pros Learn

Professional option traders adjust option greeks for spot-vol correlation. In the GME-case the correlation is positive just as it is in agricultural commodities. As the price increases, the vol increases. Most markets have a negative spot-vol correlation. The VIX falls when the SPX rallies. This is also true in the oil market. A supply of options hits the market during rallies as large hedgers overwrite calls.

To adjust for this, option traders will model a negative spot-vol correlation or “vol beta”. For example, suppose your ATM call option typically has a 55% Black-Scholes delta. you might model a 50% delta only, knowing that if the future goes up $1, your call option probably won’t increase by $.55 since implied vol will fall. (In fact, one of the ways to know if the counterparty you are quoting was a bank or not was by the delta the broker wanted to use on delta-neutral structures. Banks often quoted with Black-Scholes deltas while prop shops used deltas which incorporated vol betas, effectively lowering all call deltas).

When you model vol beta you are usually making a trade-off between hedging local behavior of common moves versus more unusual sized moves which will break the spot-vol correlation, in turn upending calibrated deltas. If a skirmish broke out in the Strait of Hormuz and oil ripped 10% higher I would not expect volatility to fall. Therefore, you also need to consider a matrix of outcomes.

(This is a hypothetical picture which tells us if oil rallied 10% and vol increased 50% we would lose money. Note that if vol fell in accordance with a vol beta we would have made money).

Even with respect for local and jump spot-vol correlations, you can still be caught off-guard. In nat gas, I’ve underestimated just how GME-like its vol surface can change. I’ve seen put prices not budge despite a 20% selloff in an underlying. If you are running a hedged book and have any long futures against the puts you enjoyed the full drawdown in futures without any offset from the puts. Enough to make a burly man cry.

The idea that “you only risk your premium” when you buy options is only true if you do not hedge. It’s diabolical to get crushed on a supposedly neutral position. Why? Because, you thought you were hedged. This tricked you into buying more puts than you would have if you didn’t hedge.

(All basis trades have this dangerous property. The illusion of being hedged induces you trade bigger or use leverage to push a small edge.)

Qualitative Appreciation For Spot-Vol Correlation

The GME put holder who lost money on a sell-off now understands how the change in implied volatility explains the loss. Regrettably, this is like being told you missed a flight because you were late. It’s just a mechanical explanation. What you really want to know is why did volatility come in as much as it did? In option trader terms, “why did the vol beta outperform or underperform in the first place?”

The beta itself will have quite a bit of variance since a price can follow many paths to a destination. Those paths will each be a sample of unique realized volatility. Did the price grind to X or did it gap to X? The realized beta will vary from your projected one depending on the path and the market’s interpretation of that path. If the stock gaps down due to a specific bit of news (for example news that a big short is done covering or the company issuing more shares) the gap can actually be vol-reducing as the market interprets the news as “stabilizing”. If the gap comes with no explanation, then the market might interpret this data point as another mystery piled on an already burning heap of confusion. The market will presume that the crazy stock might just rip back up again. In this case, the vol might hold up better on a sell-off that occurs without a reason in contrast to the the prior case where the reason had the narrative effect of curtailing the upside.

So in the GME case, most of the reasons the price can go down are stabilizing. We expect options to be sold in response to a sell-off, and for the vol to decline. But “most of the reasons” does not mean 100% of the reasons so there is a probabilistic distribution to what the realized spot-vol correlation could be. And that’s why we still have surprises.

The Beauty Of Options

Ultimately, options help to “complete” a market. A simple stock price is just the expected value of a stock (equity risk premia and arbitrage pricing theorists are welcome to have a cage match over that statement. I’ll be out back selling beer). By imputing more information than a one-dimensional expected value, option surfaces give us a richer picture of expectations. What’s considered stabilizing, and what’s considered unthinkable are encoded in options markets.

There’s a silver lining to the WSB obsession with options. Some of these people who showed up for a thrill will stick around to learn how to listen to how a vol surface whispers.

Adding My .02 To The WSB Insanity

r/WallStreetBets. GME. AMC. Citadel. Ken Griffin. Steve Cohen. Melvin. Matt Levine.

Wait, Matt Levine?

Yes, Matt Levine. Just read everything he wrote this week for staging this entire topic.

My work here is done.

…Ughh fine. I’ll address a few subtexts.

Feedback Risk

The simplest observation from the hedge fund Melvin’s plight is their bet size was too large. They underestimated both volatility and liquidity. These are not uncommon mistakes.

Morgan Housel explains by analogy:
Forecasting when a species might go extinct is hard because whatever is causing a species to die off rarely progresses at the same rate. It can speed up in the blink of an eye in ways that surprise people.

Say an elephant is being hunted for its tusk. The rate of hunting often massively speeds up over time, cascading into a frenzy that pushes a mildly at-risk species into quick extinction.

It’s simple: As the number of elephants declines, tusks become rare. Rarity pushes prices up. High prices make hunters excited about how much money they can make if they find an elephant. So they work overtime. Then fewer elephants remain, tusk prices rise even more, more hunters catch on, they work triple-time, on and on until the number of hunters explodes as everyone chases the last herd of elephants whose super-rare tusks are suddenly worth a fortune.

Forecasting models that don’t appreciate how frantic the last-minute hunt can become “give a false sense of security when managing large harvested populations,” the researchers wrote. A species’ endangerment starts slow, then picks up, gets a little faster, then boom … spirals into a disaster seemingly overnight. Supply and demand are intuitive; realizing how quickly supply and demand can go from linear to exponential is not.

Feedback loops – where one event fuels the next – often lead to that kind of bewilderment.

Find a feedback loop and you will find people who underestimate how crazy prices can get. (full post)
A Thought Exercise For Outsourcing Liquidity Risk

A portfolio manager shorting a stock will size a position not just based on price target and conviction but based on the risk relative to bankroll and relative to the liquidity. There are conventional ways to do this. Volume, days-to-cover, variance, 90s nostalgia factor (kidding on that one…worrying about that going forward is like closing the barn door after the horse escaped). While these inputs inform a sizing decision, the bottleneck in the risk management process is not in the sizing. It’s in the remedy when your sizing turns out to be wrong. Eventually it will be. Your plan needs to tolerate that eventuality.

Most plans are to cut risk by buying back some percentage of your shorts. This is like trading with a stop. You are constructing an option since you cover as the stock goes against you and you add as the stock goes in your favor (remember if you short a stock and it falls, to maintain exposure as a percentage of AUM you need to short even more).

The problem with this plan is it is soft optionality. It’s not the same as buying a hard option like a deep ITM put, or buying an OTM call to hedge your short position. Hard options protect you from gap risk. You know, that thing that happens when a stock is halted. Or when the US goes to sleep. Or when a gamma squeeze creates a massive imbalance.

To improve risk management, managers should at least entertain the question: “if I wanted to buy X amount of deep ITM puts instead of shorting shares how much would it cost?”

The answer to that question comes from market-makers who sit in the middle of the marketplace. They hoover up market intel to synthesize a price so you can know exactly how much it costs to express your view with a hard option. Sure, that price embeds a consultation fee in the form of a vig, but at least they are on the hook for mispricing. Not you.

A market maker’s job is to price the spread between soft optionality and hard optionality by gauging the liquidity required to dynamically hedge. Market makers are also in highly competitive, low margin businesses. If you pass on their price for the hard optionality you must ask yourself…”is my assessment of the liquidity/gap risk that much better than theirs OR are their margins excessive?”

At the very least, you can consider this reasoning a sanity check before you size up a big short.

Brokerages are in the Credit Business

The conspiracy theories around Robinhood suspending trading in GME can be cut to shreds with both Occam’s and Hanlon’s razors. RH and any broker for that matter are clearly desperate once they resort to cutting off their customers. The customers are the lifeblood.

Sure Citadel pays RH for order flow, but that relationship is downstream of RH having customers in the first place. Just because RH’s checks come from Citadel, not from the Yolo’ing redditors directly, doesn’t mean Citadel comes before the customers. After all if Citadel didn’t pay RH another market maker would slide right in to that spot. To think the customers come second to Citadel is to confuse accounting for economics. It’s breathtaking to imagine this kind of naivety.

What created a situation so dire that RH had to anger its mob? A good ole’ fashioned credit crunch.

I’ll let Byrne Hobart explain not just the dynamic but why RH had to “explain it poorly”:
A simple model of a stock brokerage is that it’s an almost fully-reserved bank. The brokerage has clients, the clients have positions, and in one sense each position is an asset on the broker’s balance sheet, while the customer’s ownership of that position is a liability. So your broker is a sort of bank, that takes deposits in dollars, but also in shares of IBM, treasury bonds, far-out-of-the-money call options on AMC. Normally, this bank tanks very little risk, but there are a few things that can go wrong: trades take time to settle, which creates a brief liability mismatch. Brokers put up collateral to ensure that, in the event that they go out of business before the trade completes, their customers won’t lose their assets. When trade volume rises, and the volatility of the assets rises, this creates a larger demand for collateral.

This is, day-to-day, a problem brokers are able to manage. Their capitalization needs don’t change that much. But when users are all piling into the same volatile trades, the need for capital rises suddenly. As a result, Robinhood stopped processing trades in GameStop, except trades to unwind existing positions. (As did several other brokerages: Interactive Brokers, WeBull, and Public, for example.)

This story certainly sounds sinister; it matches the appearance of strings getting pulled in order to bail out hedge funds. But the brokers’ actions also look like the actions of any financial intermediary faced with a sudden increase in uncertain obligations. (And there were not stories about brokers like Vanguard and Fidelity, which have fewer day-traders, blocking GameStop trades.) When volatility is high, brokers often act in their own interest. This has happened before: one major short-selling firm was basically shut down mid-crisis because their prime broker raised margin requirements. (The prime broker in question denies much of this.) While it’s rare in the US, brokers can go under because of client losses. FXCM, for example, had many clients who were borrowing the Swiss franc to fund other currency bets. It was a stable currency with low rates, until the Swiss gave up on keeping it stable and allowed it to float; it instantly rose 45%, wiping out many clients many times over and forcing FXCM to get rescued by a larger financial institution, and to rescue many of those clients in turn.

Which doesn’t excuse Robinhood, WeBull and the rest. They communicated inaccurately, but not poorly, because an accurate description of the problem was “We’re more of a bank than we realized, and we’re in danger of insolvency.” And that would lead to a run on the bank—and definite insolvency. WeBull’s CEO did clarify this later on, and with enough time to digest it, and new funding from their venture backers, the bank-run risk is minimal.

The brokerage experienced a familiar technology problem — a rapid increase in capital requirements for scaling infrastructure when user growth explodes compounded by a frumpy problem as old as time — the need to raise more collateral.

The combination of these forces should be more than enough to satisfy the explanation with the least and most likely assumptions. If this theory is still not as compelling as blaming Citadel let me ask a question — if you were Ken and owned a machine that printed cash would you rather turn the machine off for a few days or would you try to forge the bills you aren’t able to make jeopardizing the entire future of the printing press?

Please. You don’t make foie gras out of the golden goose.

The Big Guy Vs Little Guy Debate

If conspiracy theories weren’t enough, then we get the ambulance chasers.

AOC, Chamath, and the Barstool meatball.

Right on cue and impossibly aligned proving that the arc of moral outrage bends towards grift.

Unable to resist the warm embrace of Twitter hearts and re-tweets, this band showed up to promote the populist WSB underdog David vs hedge fund elite Goliath narrative. Ranjan Roy dispels that framing handily. Not to take anything away from Roy, but anyone with a clue how trading works knows that framing is nonsense.


A hypothetical.

Suppose there are 15 courses of actions one can take. 5 are illegal, 5 more are unethical. That leaves 5 acceptable actions. It feels like our collective calculus is moving to a rule of “if it’s legal, why not?”

The ethics ozone layer between what’s legal and what we should do is fully depleted. The air is irrevocably polluted. I’m not pointing fingers solely on daytraders who are openly coordinating behavior in ways that stun anyone who has ever sat through securities compliance training. There is a sense that the game is rigged and while I think the specific targets in these trading examples are misdirected, it certainly feels that way in a broader sense. Especially when we consider the runaway examples of inequality I’ve discussed recently.

My full thoughts on this are out of scope here, but I couldn’t help but chime in on this @skelecap & @SuperMugatu thread.

Sticking It To The 1%

The most populist development in the story is not daytraders getting rich. Sure, a few will, but when you turn GME into one of the top 10% of stocks by market cap you are also guaranteeing a large cohort of bagholders. Since, ya know, math.

The real damage will be to savers in a story that will rhyme with this:

Random Thoughts on Leitner’s Upside Digitals, Time Horizon, and WSB

Some thoughts on Jim Leitner’s interview on MacroHive:

  • My favorite idea from the pod: the discussion of replacing equity allocation with digital calls. He talks about buying say 5 year 100% OTM digital for 7 cents on a dollar. You should listen for his full reasoning but it rhymes with Warren Buffet’s thoughts on option pricing which is ultimately the difference between no-arb risk neutral derivs pricing and odds implied if you believe in an equity risk premium. (Alpha Architect blog)

    Let me add to that.

    Indulge this lazy theory as to why Leitner’s idea might be correct for a technical reason he can probably feel more than explain. Suppose we quintiled the broad market by valuation. Whatever metric, the US is in the highest partition. I would not be surprised if stock replacing your equity exposure with options would have been historically a good trade conditioned on extreme valuation. Not because you win more, but because you lose less when the markets roll over. And of course that means you can rebalance with a better hand after a drawdown. Total CAGR improves.

    I’ll go a step further. Why might the market might price the vol too cheap on those OTM calls? Perhaps a very expensive market exhibits autocorrelation on longer time frames (ie monthly vs weekly returns). In other words, momentum prevails. The momentum can lead to cheap implied to realized vol ratios in the same way that a stock that rallies 1% per day for 20 straight days will have been a bargain buy at 16% implied vol.

    So when Jim gets 13 to 1 on that digital, perhaps the true odds conditioned on an expensive market are 8 to 1 or 10 to 1. Again, this is a lazy musing, I would love to see if there’s any work out there on this.

    This whole exercise is the upside version of Spitznagel’s point about conditioning convex trades based on valuation. The piece very much flies in the face of anti-timing arguments and it’s quite robust to how expensive the convexity actually is. See Universa’s Those Wonderful Tenbaggers (Link)

  • Jim’s discussion of BTC was ok but prompted a discussion with Yinh about our BTC holdings (which you can presume is small since I still fly coach):

    1. Your time horizon should dictate the dashboard of metrics that informs your decision.

    2. Disagreements about the “right” price are always a disagreement about time horizon. That’s what makes a market.

    One of the points he made was about PayPal making it easy to buy BTC was bullish. This kind of argument is simultaneously insightful and deranged because it is reflexively Ponzi but also right. The “horizon” field is left blank and for the investor to fill in.

  • Jim’s book recs:

    1. The Checklist Manifesto

    Doctors make lots of decisions under uncertainty and Gawande’s book has many transferrable lessons to investment processes.

    2. Superforecasting

    Predictions should have time horizons and a confidence interval. Score yourself and over time you will improve.

  • Other recs:

    1. Keep a journal of trades and the reasoning behind them. Your future self will thank you.

    2. Open a play account where the money isn’t make or break. His is $100k. This account absorbs the trades which come from “feeling the need to do something”. For your real accounts, most of the time you should sit on your hands.


  • WSB gets emotional on Mad Money (5 min vid)

    Last week I wrote Is Social Harmony The Last Collateral?It was a post that regrettably resonated with many of you. Not to be dark (narrator: it’s dark), but this re-purposed Joker clip expresses the same message as my post but even better. Where I put “dentist”, it put “millennial”. The framing is more desperate and nihilistic than my post, but I reluctantly admit, it is probably more in touch. It shares my sense that the GFC was an even more watershed moment than it seemed at the time.

  • Made my first financial meme. Look how grown-up I am. (link)

Tech Bubble Insights

The below links are all related.

  • Lessons from the tech bubble (thread)

    Last year, I spent my winter holiday reading hundreds of pages of equity research from the 1999/2000 era, to try to understand what it was like investing during the bubble…

    This thread is a humble reminder that the collapse of the tech bubble in 2000 wasn’t really a surprise. This reminds me of funds using derivatives to bet against the housing bubble leading up to 2008. Many were too early and found themselves squeezed by bank counterparties for more collateral until they had to puke their positions to stronger hands. It would be like filling in the right Powerball numbers for the wrong week.

    Right idea x wrong timing = Wrong

  • What happened if you Invested in all the pets.coms (thread)

    If you purchased $1 of all 1997 IPOs on 12/31/97, $1 of all 1998 IPOs on 12/31/98, and $1 of all 1999 IPOs on 12/31/99 at their respective market weights on those days (then did nothing), how much is that $3 worth as of 9/30/2020? *$3 invested in the Russell 3000 is worth ~$14.

    Jake’s thread dives into a complete answer. So try to answer before clicking the link.

    In case you care, my approach to the question:

    I started with some assumptions and estimates. For example, how many IPOs happened in each vintage (I guessed 100), what was a typical IPO market cap (I guessed $1B), and knowing that AMZN was a 1997 vintage I made the super conservative assumption that the other presumed IPOs (100 per vintage) all went to zero. So if AMZN IPO’d at $1B it’s up 1560x which means your portfolio, even with 299/300 companies being zeros, went up 5x or about 8% CAGR since the late 90s. I guessed a better survival base rate would be 10% of the IPOs, which meant realistically there are 30 surviving companies. If they were an order of magnitude less successful than AMZN they would have returned 150x each bringing the total “IPO portfolio” closer to 20x. So I took the over. I’d give myself a C.

    The poll prompted a lot of questions for me. Like what is the correlation between survival, returns, and market cap at IPO? For example, how much more likely is a top quintile market cap IPO to survive? Has the relationship meaningfully changed over time? Do companies’ ability to stay private for longer change the return prospects of IPOs long term?

  • Gorilla Game Investing (summary)

    This book is a framework for investing when a disruptive technology has been identified but the competition is wide open. Imagine buying all the companies and then selling the losers as they go down and re-balancing into the winners. This can make sense if the industry has winner-take-all dynamics. To me the strategy looks like you are trying to construct a long option on the company that will own the TAM. That re-balance strategy even looks like negative gamma…buying the rallying stock and selling the losers.

A giant realization everyone should appreciate from all these links…most companies go to zero. Single stocks have positive skews. Indices are just baskets of stocks with a rebalancing strategy. Indices have a negative skew. I try not to miss chances to reinforce your intuition of portfolio theory.