The Why And How OF Taking “Discoverable Notes”

I have been an active note-taker for years and a fan of how meta Tiago Forte gets about the process of taking notes. Tiago’s Building A Second Brain course is very popular in productivity circles. While I have never take it, I recently came across his essay Progressive Summarization: A Practical Technique for Designing Discoverable Notes. (Link)

It’s an outstanding framework for understanding the whys and hows of taking notes. I, by accident, have arrived at a very similar system so it was interesting to see someone explain it thoroughly as only Tiago can.

This is a summary of what resonated with me.

The Why Of Taking Notes

The Right Info At The Wrong Time

What you read is good and useful and very important, you’re just reading it at the wrong time.

The challenge is knowing which knowledge is worth acquiring. And then building a system to forward bits of it through time, to the future situation or problem or challenge where it is most applicable, and most needed.


Bridging The Acquisition And Use Of Knowledge

It’s too mentally expensive, if not impossible, to internalize all or most of the information we consume. A good system is intended to bridge the time between when you discovered the information to when you use it.

At that future point, when you’re applying that knowledge directly to a real-world challenge…By the time you’re done solving a real problem with it, book knowledge has become experiential knowledge [which you carry forever].


The How Of Taking Notes

Defining The “Second Brain”

An external, integrated digital repository for the things you learn and the resources from which they come. It is a storage and retrieval system, packaging bits of knowledge into discrete packets that can be forwarded to various points in time to be reviewed, utilized, or deleted.

Designing The “Second Brain”

Goal: You are trying to triage information in an organized way. You read something you know is interesting and you want to be able to reference later.

Challenge: You need to file it quickly, make it discoverable, and emphasize why it’s important so “future you” can make sense of the notes efficiently.

Tiago says:

A note-first approach to knowledge management means we have to think about design. You are, in a very real sense, designing a product for a demanding customer — Future You. Future You doesn’t necessarily trust that everything Past You put into your notes is valuable. Future You is impatient and skeptical, demanding proof upfront that the time they spend reviewing notes will be worthwhile.

Balancing Tradeoffs

  • Discoverable: Digestible notes. So needs to be compressed
  • Understandable: Context including sources, examples, details

Getting the balance between compression and context right is not a trivial matter. When the time comes for Future You to decide whether or not to review this note, seconds count.

When you fail, you successfully sent a packet of information forward through time, but not in a state where it could survive the journey… You have to summarize the note without knowing what it will be used for.

The Progressive Summarization System

  • Layer 0 is the original, full-length source text.
  • Layer 1 is the content that I initially bring into my note-taking program. I just capture anything that feels insightful, interesting, or useful.
  • Layer 2 is the first round of true summarization, in which I bold only the best parts of the passages I’ve imported. Keywords, phrases, sentences
  • Layer 3, I switch to highlighting, so I can make out the smaller number of highlighted passages among all the bolded ones. This time, I’m looking for the “best of the best”
  • Layer 4, I’m still summarizing, but going beyond highlighting the words of others, to recording my own…restating the key points in my own words
  • Layer 5 (as needed): Remix. for a tiny minority of sources, the ones that are so powerful and exciting I want them to become part of how I think and work immediately, I remix them. After pulling them apart and dissecting them from every angle in layers 1–4, I add my own personality and creativity and turn them into something else.

My Own Accidental Version of Progressive Summarization

  • Layer 0 is usually just the link without the text which is risky since the link can break. (With Slatestarcodex site being taken down I’m experiencing this firsthand)
  • Layer 1 same as Tiago
  • Layers 2 and 3 are combined. Mix of bold and italics.
  • Layer 4 is paraphrasing often drawing connections to other ideas. While time-consuming because it requires thinking I am rewarded by an easier retrieval stage. More selective about what notes I do this with.
  • Layer 5 usually means pasting the note in other notebooks when the content has multiple contexts


Notes from Capital Allocators: Annie Duke


About Annie: Professional poker player and author of Thinking in Bets

All decisions are a bet

When you choose x you forgo y. The decision is a bet that x is a better outcome than not x.

Beliefs are formed then confirmed

Dan Gilbert’s known for happiness research but his 90s research which is lesser-known was focused on ‘belief formation’. We are hardwired to not vet beliefs since beliefs are typically perceptual. Hallucinations and mirages are rare. However, abstract beliefs that emerge from our social interactions, language, symbolism are incorporated via this same mental machinery which was really designed to assimilate perceptual beliefs.

Gilbert showed that by default we accept the belief is true BEFORE we vet it.

Research shows:

    • We often fail to later vet the belief
    • If we do vet it, we are biased
      • Kahneman’s idea of “motivated reasoning”: our beliefs drive how we vet the belief
      • Confirmation bias
      • Blindspot bias
      • Smart people are often more extreme in their biases because they rationalize with a greater repertoire
        (This was tested by first evaluating subjects’ statistical prowess then comparing how they handicap a neutral versus emotionally-charged outcome)

How do we improve?

  • Frame decisions as bets. 

    1. Assigns probabilities to outcomes
    2. Define what we explicitly are evaluating
    3. Invites others into the truth-seeking process which is also good for social reasons
      • When acting very certain we can suppress or intimidate other’s views
      • Avoid the pitfall of confusing certainty with accuracy
      • Makes the communicator more believable
      • Avoids biasing others before they start the vetting process

  • Define winning as being more accurate inoculating ourselves against self-serving bias.

    • Use Mertonian norms which comprising the ethos of science (acronym: CUDO)
      • Communism: Standardize how data is presented so members of the community cannot present the group biased picture
      • Universalism: Ideas have objective truth regardless of the messenger; “Don’t shoot the message”
      • Disinterested: Do not infect the group with your beliefs
      • Objective Skepticism: seek counterfactuals and dissent
        • In groups, use ‘red’ and ‘blue’ teams
          Red team’s function is to rebut or dissent. This instantiates a role in which being a team player is actually to challenge.

  • Be aware of our tendency to “temporally discount”.

    • A dollar today appears worth way more than in a year
    • Tonight’s wine is tomorrow’s hangover (Seinfeld’s “Day Jerry” vs “Night Jerry”)

If we associate better-calibrated beliefs with better outcomes and a happier life we should strive to be honest with ourselves while reasoning even if it sacrifices our ego/fun in the moment.

Risk Management

  • Why we fail to apply the principles of Kelly betting:

    1. Garbage In/Out: Poorly calibrating the edge and/or variance
    2. Our ability to apply rational System 1 rules are compromised when we are in an emotionally charged state (“limbic system firing”), which is when the rules matter most. “Stacking Irrationality”.

  • The merit of risk limits irrespective of risk/reward or expected value:

While irrational, they are less damaging than allowing yourself to continue betting when your “emotionally unfit”. A bias which gives us the chance to play again tomorrow when we are not emotionally unhinged is adaptive for the long-run. (Me: Reminiscent of ergodicity discussions about maximizing compounded expectation)

Tells and body language

  • Good to follow: Joe Navarro. A FBI operative specializing on body language

  • How poker players read opponents:

    1. If never faced them before, start with base rates
    2. As you learn how they bet, Bayesian update base rates
    3. Merge tells with updated probabilities

  • Signs of being relaxed vs discomfort:
    • embodied by distance from table
    • self-soothing behavior

The Antidote To Abstraction

All kids want their mama. And for good reason. Mamas are the best. It’s no contest. Of course, that doesn’t take anything away from fathers’ impacts. And if we sum the total hours fathers spend with their children I’ll bet it’s less time than they spend with mom. So in the spirit of a father’s impact-per-hour, I’ll be brief.

Read Charles Eisenstein’s essay The Age Of We Need Each Other (Link) (Link with my highlights)

It’s one of the best things I’ve read in a long time. I suspect different people will get different things out of it. I’ll share my own reading of it:

Its message is the antidote to all the abstraction that makes us feel helpless. If all the top-down strife is leading to daily bottoms-up anxiety this essay has a remedy.

It reminds me of the advice to break giant problems or endeavors into manageable bites. Except the giant problem is not “making a living” or “getting healthy”. It’s finding the purpose of your life. Sometimes we just don’t know what we are “supposed” to do right now. I think the answer lies right here in this essay. It affirms a timeless truth. A truth so simple it’s easy to forget:

You are, can be, or will be somebody’s world. It might just be one person. And that is not just enough. It’s everything.

Most of the people I consider heroes are people I personally know. They are unsung. And this becomes more true as I get older. I think that truth is a clue to what you are “supposed” to do.

Anyway, read the essay yourself. See what you get.

In a similar vein, I’ll share the Michael Crichton quote I keep on my main Notion dashboard.

If you want to be happy, forget yourself. Forget all of it — how you look, how you feel, how your career is going. Just drop the whole subject of you.

The quote continues.

We all know this is true because…

If you want to know how the whole essay goes check out Happiness. (Link)

You Can Mock Trade With A Deck Of Cards

Here’s a mock trading game I learned as a trainee to simulate futures and options market making. This game was commonly used as a day 1 exercise in trading class or when interviewing cohorts of college grads during recruiting “combines”.

The Futures Game

What you need:

  1. A deck of cards
  2. Nerdy friends (the more the better)
  3. A paper and pen per person to use as a tradelog


You want to deal out enough cards to players (these are the market makers) so that there is about 25 remaining in the deck. There’s some leeway here.


  • You have 6 players. So deal them each 4 cards leaving 28 cards undealt.
  • Market makers may look at their hands but don’t share info.
  • The undealt cards are known as the “public pile”. They should be evenly divided into 4 or 5 sub-piles ideally (again there’s leeway depending on how many cards there are).
  • The sub-piles are going to represent “trading days”.
  • The cards themselves are news flow which will move the futures prices.

Description of futures prices:

  • The futures are the 4 suits. There’s a club’s market, a spades market, etc.
  • The final settlement price of the futures will be the sum of the ranks of cards in the public pile. (Ace =1 thru King = 13). So the maximum any future can be worth is 911

    It’s best to define the tradeable universe to keep the liquidity centralized.

    So you could have a diamond market, a spades market, and a “reds” market (which would be an index settling to the sum of diamonds and hearts).

    How To Play

    The first trading day

    • Reveal the cards in the first public sub-pile.
    • Market makers make bids and offers for the various markets. Tight 2 sided markets should be encouraged/required. For example:John: “I’m 65 bid for Hearts and offered at 68”

      Jen: “I’ll pay 67 for 5 Hearts contracts” (perhaps Jen is holding no Hearts in her hand)

      John: “Sold you 5 at 67” (John is holding 16 points of Hearts in his hand)

    • Record all your trades on your own pad or paper:1. Which contract you bought/sold
      2. Quantity of contracts
      3. Price of contracts
      4. Counterparty

    So for example, if I paid 51 for 4 “clubs contracts” from Mary I would record that information on my paper. Mary would record her sale of the 4 contracts at 51 on her card with me as the counterparty.

    • The trading is open outcry. There are no turns.

    Settling the trading day

    1. When the trading peters out for that “day” everyone should check their trades against their counterparties to make sure there are no so-called breaks or “outtrades”.
    2. On a central eraseboard or paper the “closing price” of each market can be recorded. So if the King of clubs and 3 of clubs were revealed from the sub-pile, then clubs “settled at 15”. Clubs might have traded 53 last in the expectation that more clubs will be revealed on subsequent days.
    3. Repeat this process for all remaining tradings days

    The last settlement

    • Compute “P/L” for all trades.

    If I bought 4 clubs contracts for $51 and clubs final settlement was $63 then I made a profit of $12 x 4 or $48. Mary’s loss would match that amount for that trade.

    The total P/L of all traders should sum to zero at the end of the game.

    Options Variant

    • Either the same group or a different group of people could choose to trade calls and puts on the final settlement price of the futures.

    So if I paid 3 for Clubs 55 calls and the final settlement was $63 then I profit the difference between the $63 and the strike ($55) minus the premium I outlayed:

    $63-$55 – $3 = $5

    • You could even get fancy and trade “vol”. You could sell say 10 clubs calls and buy 5 clubs futures to hedge the delta.
    • This game is played the same way the futures game is played or in conjunction. Repeat the process for all trading days then compute P/Ls at the end. Again if there are no errors the game should be zero-sum.

Mock Trading Options With Market Makers

I got into options trading straight out of college. In 2000, the option exchanges were bustling. The Amex in NYC (where I was based), the PHLX, the P-Coast, and of course the CBOE. As a trainee, your day consisted of assisting the option market makers and specialists. Building spreadsheets, running risk reports (hitting a macro, then killing some trees), and the worst part of the job — the pre-open routine of reconciling positions and breaks. Hopefully, you’d finish before your trader sauntered into the office hungover.

During the actual trading day, your duties were pretty limited. I remember going to Cafe World at the corner of Trinity and Rector with a diagram of where my trader wanted each dish from the buffet arranged on his plate. Although you aren’t paid much you are still a liability for your first 6-12 months.

Mock Trading

Your main purpose in the cocoon phase is to learn. After the market close, you’d attend “mock” which was short for mock-trading. Mock would be led by senior traders. “Senior” basically meant a market-maker that was now “on a badge” the credential you needed to trade on the floor. You were getting taught by people that ranged from 1 to 5 years older than you which should tell you a) how start-uppy the culture and b) how much every day’s hundreds of trades added up to valuable experience quickly.

At my firm, mock was basically hunger games. You’d stand around for an hour shoulder to shoulder with 15 guys (yes it was mostly guys) in front of a dry erase board as 3 or 4 senior traders posed as brokers barking out orders and moving the stock and option prices around setting up opportunities for the trainees to spot arbitrages.

You’d have to hedge your trades (nothing like selling one of your teacher’s some puts as another teacher announced the stock bid was now 25 cents lower), lean markets based on what prevailing bids or offers were “resting” on the exchange book, read body language, remember all the verbally announced orders that might have been announced but were not in play until the stock moved. Memory, pattern recognition, and extremely fast mental math. In fact, everyone in the room would play a timed put/call parity computer game during the day to prepare (I actually trained during the tail end of the fractions era).

So for fun, I thought I’d share an example of what mock trading would be like.

Spot The Edge

Requirements and assumptions:

  • Stay delta-neutral. If you want to buy or sell the stock you must cross the spread.
  • Options markets are all 500 up, meaning the bids and offers have 500 contracts on them.
  • Cost of carry = 0%
  • 90 days until expiration
  • You will need to know Put/Call Parity

    Call = (Stock Price – Strike Price) + Put + Cost of Carry

    Since there’s no cost of carry let’s restate this more simply:

    Call = Intrinsic + Put

Ok, here’s the option’s board:

A broker walks into the pit and announces:

I have 200 XYZ 55 straddles offered at $4.15!

I’ll get you started with a hint. Be the first person to yell: “Buy em!”

Now go figure out why.

Here are the exercises you can do with the information above.

  1. Compute the implied volatility.
  2. Find the arbitrages or best series of trades in conjunction with the broker orders that are being shouted into the pit.
  3. Report your remaining position and at what average price it was established.

    Extra credit: Compute your P/L. You may reference an option model after the mock trading session ends.

It’s all spoilers ahead so if you actually want to do this, don’t scroll further until you are done.


  • Compute the implied volatility

The approximation for the ATM straddle is given by the expression1 :

Straddle = .8Sσ√T

where S = stock price
σ = implied volatility
T = time to expiry (in years)

Let’s use mid-market of the 55 put and put/call parity to get the call price.

C = Intrinsic + P

C = 0 + $2.10 = $2.10

Since the straddle is just C + P we get $4.20 for the straddle. Plugging into the approximation:

$4.20 = .8 x $55 x σ x √.25

Solving for σ we get an implied volatility of 19%

  • What series of trades do we do?

    1. Buy 200 55 straddles for $4.15
    2. Sell 200 55 calls at $2.15
    3. Sell 400 60 calls at $1.05
    4. Buy 400 65 calls for $.05
    5. Sell 200 65 puts at $10.10
    6. Sell 3,000 shares of stock for $54.95

    Whoa. That’s a lot of trading. Because of put/call parity, traders can collapse their thinking and position by strike. A call is a put and a put is a call. You can always convert one into the other by taking the opposing delta in the underlying.

    Let’s summarize these trades by strike.

    65 Strike

    Buy 400 65 calls for $.05
    Sell 200 65 puts at $10.10


    1. Buy 200 65 calls for $.05 and sell 200 65 puts at $10.10. Buying a call and selling a put on the same strike is known as a combo. It is the same thing as synthetically buying the stock. Why? Think about it, no matter what happens you will be buying the stock for $65 at expiration. You’ll either exercise the call or be assigned on the put. But you collected $10.05 today to make that commitment so you effectively bought the stock for $65 – $10.05 today or $54.95. Sweet.

    So this can be summarized simply as buying 20,000 shares for $54.95

    2. You also bought 200 extra 65 calls for .05

    60 Strike

    Sell 400 60 calls at $1.05

    55 Strike

    Buy 200 55 straddles for $4.15
    Sell 200 55 calls at $2.15

    Since you bought 200 straddles, you bought 200 calls and 200 puts. The calls cancel out and you are left long 200 puts at a net price of $2.00 (spent $4.15 200x in straddle premia and collected $2.15 200x in call premia).

    Now remember we synthetically bought 20,000 shares for $54.95 via the 65 strike combos.

    Back to put/call parity.

    C = (S-K) + P
    C = ($54.95 – $55) + $2.00
    C = $1.95

    So the combo plus these 200 55 puts means you legged buying 200 55 calls for $1.95

  • What is our residual position and at what average price?

    Let’s do what option traders do and show the net position by strike. That’s how we see what we actually have on. It allows us to make sense of the complexity at a glance.

  • 1. First, we can see the 200/-400/200 pattern on equidistant strikes (ie they are each $5 apart). That is a butterfly. A relatively low-risk distributional trade that has very little vega, gamma, and theta with several months until expiration.

    What price did we leg it for?


    1. We bought 55 strike call synthetically for $1.95
    2. We sold 2x as many 60 calls at $1.05
    3. We bought the 65 calls for $.05

    Adding up, $1.95 + (2 x -$1.05) + $.05 = -$.10

    Negative 10 cents?

    Correct. You just legged buying a structure that can never be worth less than zero for a credit. Arbitrage.

    What is the delta of our total position?

    Option traders want to stay delta-neutral. So estimating the deltas (or having Black Scholes spit them out) we compute the delta contribution of each strike and find we must sell or short 3,000 shares to be delta neutral.

  • Extra Credit: What’s the P/L?

    Butterfly P/L

    Using a flat 19% implied vol I get a Black Scholes value of $.93 for the butterfly. We actually got paid $.10 to own it. So our theoretical profit or edge is $1.03 times 200 contracts.

    $1.03 x 200 contracts x 100 multiplier = $20,600 profit

    Combo or Synthetic Stock P/L

    We bought 20,000 shares of stock synthetically for $54.95 via the 200 65 strike combos. If the stock is marked at mid or $55.025 then we made $.075 on 20,000 shares or $1,500.

    Stock P/L

    We did need to sell 3,000 shares at $55.00 (the bid) to hedge 3,000 shares or deltas. If the stock is marked at mid or $55.025 then we lost $.025 on 3,000 shares or $75

    Total profit: $20,600 + $1,500 – $75 or $22,025!

Wrapping Up

Back in those olden days, we’d play this game after market hours but you can imagine multiple brokers shouting orders at the same time and more months than just a single expiry. We studied many different types of arbitrage relationships so we could spot mispricings from many angles.

You’d take what you learned from these games and apply it during the trading day. You’d watch how market makers and brokers in the pits reacted to different orders as you start to piece the matrix together. At my firm, the people who performed best were sent to a Philly suburb for 3 months. This was known as “class” and it was held 4 times a year. “Class” was theory and option nerd stuff until lunch then mock for the rest of the afternoon. Mock had a simulation environment with electronic overhead screens just like the exchanges and everyone held a tablet PC with stock trading software and a proper option model. This is where you started going beyond mock and getting into more game theory and real-life trading scenarios.

The faster you got into a “class” cohort the faster you got your own “badge”, P/L, and risk budget (not to mention enough comp to rent a 400 sq ft studio without a roommate).

Times have changed. The game isn’t about mental math and yelling loud and having the best memory. But this was how my intuition was built up and the lessons still permeate how I think about trading today.

Finding Vol Convexity

In this post, we will learn what it means for a position to be convex with respect to volatility.

In preparation for this post, you may want a refresher.

  • Vega is the sensitivity of a P/L to changes in volatility. This is the exposure volatility traders are taking active views on. It requires tremendous attention since changes in vol directly affect P/L via vega but also impacts or distorts the “moneyness” of all options in a portfolio. In that way, large vega exposures are signs that the risks under the hood of a portfolio are especially dynamic.

    Refresher Post: Why Option Traders Focus On Vega (Link)

  • Convexity is the idea that there are non-linear P/L sensitivities within a portfolio. The curvature of the P/L derives from the fact that the exposures change as the market moves. Option deltas are not constant. That means deltas derived from options, as opposed to deltas derived from so-called “delta one” instruments like common stock or futures, are subject to change as the market moves. Vol convexity is the same phenomenon. Instead of applying to a delta, it applies to vega.

    Refresher Post: Where Does Convexity Come From? (Link)

In Moontower style we will do this without anything more than middle school math. This 80/20 approach provides the intuition without the brain damage that only a relative handful of people need to know.

Mapping Directional Trading To Volatility Trading

Directional Traders

Most investors are looking to profit from the direction of stocks.  Stated another way, most investors are taking active delta exposures. The size of their delta determines the slope of their P/L with respect to the market’s movement.

Directional Convexity

Some of these investors use options to make directional bets. This gives their positions convexity with respect to the changes in stock (also known as gamma). The convexity derives from the fact that their delta or P/L slope changes as the stock moves.

Volatility Traders

Now consider another, much small, class of investor. The option traders who try to keep delta-neutral portfolios. They are not seeking active delta exposure. They have no alpha in that game. Instead, they are taking active vega exposures. The size of their vega determines the slope of their P/L with respect to changes in implied volatility.

Volatility Convexity

Like the directional traders who use options, vol traders maintain convex exposures with respect to changes in the stock. Again, that’s gamma. But vol traders are much more focused on vol convexity. The reason vol traders focus on this more than directional traders is that vol traders typically run large portfolios of options across names, strikes, and tenors. These portfolios can include exotic and vanilla options. The presence of vol convexity means vol changes propagate through the entire portfolio in uneven ways. Risk managers model how vega exposures morph with vol changes.

For directional traders with just a few line items of options on their books, vol convexity is going to be much further down on the list of concerns. Somewhere in between “What’s for lunch?” and getting flamed by intern on Glassdoor.

Maximum Vega

Vol traders often think in terms of straddles. In fact, in many markets, brokers publish “straddle runs” every few hours. This is just a list of straddle prices and their implied vol per expiration.

At-The-Money Vega

A handy formula every novice trader learns is the at-the-money straddle approximation1:

Straddle = .8Sσ√T

where S = stock price
                        σ = implied volatility
                                     T = time to expiry (in years)

So if there is 1 year until expiration, the 1 year ATM straddle on a 16% vol, $50 stock is $6.40 (.8 x 50 x .16).

So if implied volatility goes up 1 point to 17% how much does the straddle change?

.8 x 50 x.17 = $6.80

So the straddle increased by $.40 for a 1 point increase in vol. Recall that vega is the sensitivity of the option price with respect to vol. Voila, the straddle vega is $.40

More generally this can be seen from re-arranging the approximation formula.

Vega = Straddle/σ = .8S√T

Ok, so we have quickly found the ATM straddle price and ATM straddle vega. Look again at the expression for the straddle vega.


There are 2 big insights here. The first can be seen from the expression. The second cannot.

  1. The vega of the ATM straddle does not depend on the level of implied vol.

    The vega only cares about the stock price and time to expiration. So whether you are talking about a $50 crazy biotech stock or a $50 bond ETF the 1-year vega is exactly the same even if the straddle prices will vary according to the implied vols.

  2. The vega of the ATM option is the maximum vega of any option in that expiry.

    This statement implies that the vega of an option varies by strike. All of the other strikes have a lower vega. They are less sensitive to vol than this one. That makes sense. This option has the greatest extrinsic value.

    (I have a confession. The maximum vega actually occurs at the 50% delta option strike, not the at-the-money or at-the-forward. I used ATM because it is more intuitive. The hand-waving should not trouble you. Going forward I will use the .50 delta option for the charts. If you need a refresher see my post Lessons From The .50 Delta OptionDon’t worry, the intuition is not going to change if you fail to appreciate the difference)

Vega Across Strikes

While we were able to compute the vega for the ATM straddle to be $.40 from the straddle approximation, how about the rest of the strikes?

For those, we need to rely on Black Scholes. You can find the formula for vega anywhere online. Let’s feed in a $50 stock, 0 carry, 16% vol, a 1-year tenor, and a strike into a vega formula. We will do this for a range of strikes.

Here’s the curve we get:

This chart assumes a single option per strike which is why the vega of the .50 delta strike is $.20 (not $.40 like the straddle vega).

The big takeaways:

  1. The vega of a non-.50d option does depend on the level of vol.
  2. There is a maximum vega any option can have and it occurs at the .50d option

The Source of Convexity

If option traders’ profits are a function of vol changes, then their vega positions represent the slope of that exposure. If the vega of the position can change as vol moves around then their position sizes are changing as vol moves around. The changes in exposure or vega due to vol changes create a curved P/L.

Let’s see how changes in volatility affect vegas.

When Vol Increases All Strikes Become Closer To .50 Delta

Here’s the vega by strike chart the same stock. The blue line assumes 16% vol across all strikes. The red line is 32% vol across all strikes.

In fact, imagine overnight, the stock’s vol doubled from 16% to 32%.

The maximum vega at any strike is still fixed at $.20, it just occurs at the new .50 delta strike. The .50 delta strike moved up $2 or about 4% but look how the vega of the options at nearly every strike increased. This is intuitive. If you double the vol then a strike that used to be 1 standard deviation away is now 1/2 a standard deviation away. All the OTM deltas are creeping closer to .50 while of course, the .50 delta option remains .50 delta.

Watch How Your Position Changes

You can start to see the reason why a position can be convex with respect to changes in vol. Imagine you were long the .50 delta option and short the way OTM 90 strike call.

  • At 16% vol the call you are long has $.20 of vega and the call you are short has 0 vega. You are unequivocally long volatility. Even if you are long 1 .50 delta call and short 10 90 strike calls you are long vol (1 x $.20 + (-10) x $0). Your portfolio’s net vega is long $.20 of vega

  • At 32% vol, the call you are long has slightly less than $.20 of vega since the .50 delta option has shifted to the right. Let’s still use $.20 to make the point. The calls you are short now possess $.05 of vega. Your new position vega computed as (1 x $.20 + (-10) x $.05) or -$.30 of vega. You are now short vol!

Your vega which represents your slope of P/L with respect to vol has changed simply by the vol changing. The higher the vol goes, the short vol you become.


  • The strikes near the meat of the distribution can only gain so much vega. Remember, maximum strike vega is only a function of spot price and time to expiry.
  • Further OTM options become “closer” to 50d. This pushes their vega up relative to the ATM option.

This chart shows vega profiles across strikes over a wider range of vols. At extreme vols lots of strikes look like .50d options!

Trade Examples

Long ATM option, short OTM option. (Long vega, short “vol of vol”)

Starting conditions:

Stock price =  $50
Implied vol = 16%


Long leg

        • 1 .50 delta call @$50.64 strike (approximately ATM)
        • Vega =$.20
        • Premium = $2.90

Short leg

        • Short 1 .14 delta call @$60 strike (approximately 20% OTM)
        • Vega = $.11
        • Premium = $.55

Summed as a vertical call spread

        • Premium = $2.90 – $.55 = $2.35
        • Vega = $.20 – $.11 = $.09
        • Note the position is long volatility

Now let’s change implied vol up and down.

It’s a busy picture. Let’s walk through the scenarios:

We start at 16% vol and increase vol

        • Call spread value increases (solid green line) because the position is long vega. Your P/L is rising since this is the position you are long.
        • However, the ATM call vega (blue dash line) stays relatively fixed while OTM call vega increases (red dashed line) causing the call spread vega (green dashed line) to decline from its initial value.
        • As vol increases your vol length is decreasing. Whoa, this looks like negative gamma with respect to vol!

We start at 16% vol and decrease vol

        • Call spread value decreases (solid green line) because the position is long vega. Your P/L is falling since this is the position you are long.
        • However, the ATM call vega (blue dash line) stays relatively fixed while OTM call vega decreases (red dashed line) causing the call spread vega (green dashed line) to increase from its initial value.
        • As vol declines your vol length is increasing. Whoa again, this looks like negative gamma with respect to vol!

Ratio Trade. Short ATM option, long extra OTM options. (Vega neutral, long “vol of vol”)

Same starting conditions:

Stock price =  $50
Implied vol = 16%

We are targeting a vega-neutral portfolio

New Portfolio

Long leg

        • Some amount of .14 delta calls @$60 strike (approximately 20% OTM)
        • Vega per option =$.11

Since the short leg has $.20 of vega and our long leg has $.11 of vega we need to buy 1.75 of the 60 strike OTM calls ($.20 / $.11) to have a net flat vega position.

        • Total vega for the long leg: $.20
        • Premium per option = $.55
        • Total premium = $.9625 ($.55 x 1.75 contracts)

Short leg

        • Short 1 .50 delta call @$50.64 strike (approximately ATM)
        • Vega = $.20
        • Premium = $2.90

Summed as a ratioed vertical call spread

        • Premium = $2.90 – $.9625 = $1.9375
        • Vega = $.20 – $.20 = $0
        • The position is flat volatility

You know what’s coming. Let’s change the implied volatility and look at the structure price. Remember you shorted the ATM option at $2.90 and bought 1.75 OTM calls for a total premium of $.9625.  

In other words, you shorted this structure for an upfront premium of $1.9375. Watch what happens to its value when you raise or lower the implied vol.

To understand why the structure behaves like this, look at the scenarios.

We start at 16% vol and increase vol

        • While both your longs and shorts increase in value, your longs pick up extra vega, while your shorts are already as sensitive as they will ever be to vega. So every uptick in vol causes the structures net vega to become long vol.
        • By being short this structure you are getting longer vol as vol increase. If your vol exposure gets longer as vol increases your exposure is convex with respect to vol.

We start at 16% vol and decrease vol

        • The opposite scenario occurs. As vol declines your short option leg has a fixed vega while your long vol leg that is OTM “goes away” as it’s vol declines. If vol is very low that call is extremely far OTM in standard deviation space. Imagine the extreme downward vol shock scenario — the stock is taken over at its current $50 for cash. All the options go to zero, the structure goes to zero, and you simply collect the premium you sold the structure at.
        • By being short this structure you are getting shorter vol as vol declines. If your vol exposure gets more short as vol falls your exposure is convex with respect to vol.

One last chart to drive it home. The green line is your P/L as vol changes. Notice that your max P/L in the vol declining scenario is $1.9375, the entire value of the structure. It is unbounded on the upside. It looks like the more familiar picture of being long a straddle! The fact that the P/L chart is curved and not linear is convexity and as we know, results from the size of exposure changing with respect to vol.

The blue line shows exactly how that vega exposure changes with respect to vol. You started vega-neutral. As vol increased you got longer. As vol fell you got shorter.

Caveats And FYIs

This was intended to be an introduction. But here’s a non-exhaustive list of “gotchas”:

  • Option surfaces usually have a skew. OTM options often trade at a premium volatility to ATM options which reduces the spread of vegas between the options. Less room for relative narrowing.
  • We haven’t talked about the cost of those premium vols. Short gamma, paying theta anyone?
  • In these examples, we shocked the vols up and down uniformly across the strikes. I’ll leave it to you to consider what adding a fixed amount of variance per strike would do to a vol surface.
  • I completely ignored the fact that as you change the vols you are changing the location of the .50 delta option, or for that matter the delta of every option. In other words, I showed fixed strike vol behavior assuming a uniform shock. Adjusting for that is recursive and frankly unneeded for the intuition.
  • Volga is the term for the sensitivity of an option’s vega with respect to vol. Volga itself changes as vol changes. That .50 delta option has starts with little sensitivity to vol. But if we crank vol higher that option moves further from .50 delta as the new .50 delta strike has moved somewhere to the right. So it follows that the old .50 delta is picking up volga, or sensitivity to vol. Again, no need to go full Christopher Nolan I’m just leaving breadcrumbs for the committed.

The main intuition I want you to get is that OTM options are sensitive to the vol of vol because their vegas can bounce around between 0 and the maximum vega. ATM options are already at their maximum vega. So structures that own extra options relative to be being short the ATM are convex in vol.


Vol convexity is important because changes in vol influence much of the greeks. Understanding the concept can be used for defense and offense. Vol directly impacts option prices according to their vega. But it also changes their vega.

Who should care?

  • Anyone who wonders how a nickel option can go to $20.

When you combine the convexity of options with respect to vol (volga) with the convexity of options due to changes in the stock price (gamma) you get nitroglycerine.

  • That segment of the market who takes active views on volatility, not direction.

Remember even when dealing with non-linear instruments, a snapshot of a portfolio at a single point in time might show it to be vega-neutral. But a photo of a car can make it look parked. Only the video can show how fast the car can move.

Hertz Roulette

In case you didn’t hear, Hertz got approval to sell $1B of common stock to the public which is bidding up its shares. Hertz however is in bankruptcy with its debt trading for less than $.50 on the dollar. Issuing stock in such a situation is unprecedented. These are unprecedented times I guess. The fact that stock traders are bidding for shares which are subordinate to debt that isn’t even going to be made whole feels awfully kangarooey.

  • Matt Levine’s write-up is funny and educational. (Link)
  • Alex Danco describes Hertz as the first example of new type of bubble — a view that the future doesn’t matter. This type of bubble is a new branch “on the financial tree of life”. He also expects this type of bubble to only happen once. (Link)

Danco’s description of the bubble dynamic in Hertz is a sign of just how meta-weird the world can feel sometimes. The dynamics of markets have become their selling point. Not their role. Automobiles were a transformative breakthrough as a transportation function. But anything that covers distance that quickly is even more fun to race and crash. To thrill-seekers, the convenience of faster transport isn’t even a secondary attribute. It doesn’t even figure into their framework of “what is a car for?”. If you find enough of those people, you have found a source of demand for the same product for different reasons. Hertz as roulette not equity. No veil of “investment” pretense.

So the question that remains — has anyone ever bought chips to play in a bankrupt casino? That’s what those new shares will be. Just don’t be the last one to cash out at the cage.

Genius Square

We’ve been playing a game called Genius Square.

The concept is simple. 2 people will play, each with their own blank board.

  • Those wooden circles are randomly placed on the board (each player gets the same coordinates on the grid). The dice allow 62,208 combinations of wood placement. Every puzzle is solvable.
  • Then ready, set, go — the first person who can fill the board with the Tetris pieces wins.
Most games last less than a minute. We’ve seen some solved in 10 seconds. It’s a perfect game to play over Zoom and can appeal to almost any age.

(Btw, the reason there are 62,208 possibilities is that you roll 5 6-sided die, 1 die with 4 distinct values, and 1 die with 2 distinct values. 6^5 x 4 x 2 = 62,208…the instructions tell you that number but it seemed weird with 7 dice until I noticed the duplicates on 2 of the dice. The values they use for the dice ensure solvability according to an algorithm that a nerd reader will probably know).

Fun Analogy Between Combinations and a Correlation Matrix

Just some math fun because I noticed a random observation this week while thinking through 2 unrelated problems.


If you recall the formula for a combination where n is total items and r is how many you are choosing from the set:

So if you have 12 musical notes how many 3 note chords can you create?

12! / (3! * 9!) or 220.

If you have spent time playing games the combination formula is as ingrained as the Pythagorean theorem (We are doing some backyard remodeling, I literally needed to compute a hypotenuse this weekend so Pythagoras was top of mind).

Anyway, here’s the random thing I noticed.

Suppose the question was how many 2 note chords can we create out of 12 notes? Well, a correlation matrix answers the same question when r = 2. A correlation matrix is a bunch of pairs. Pairs are just combinations of 2.

Look at the matrix. The grey boxes are just double-counting the green ones. A,E is the same chord as E,A. And the diagonal axis is not a pair so they don’t count either. So if you add up the green boxes you get 66 boxes.

But if we used the combination formula you also get 66 because 12! / (2! x 10!) = 66

Very neat. This makes sense. Let’s break it down.


If you need to compute a combination of 12 notes choosing 2 you can just visualize the matrix.

  1. Start with 12 x 12 boxes = 144
  2. Subtract 12 diagonal boxes to arrive at 132.
  3. Divide by 2 because of double counting. 66.

    Generalizing that process. (N²-N)/2 or N(N-1)/2

To prove that it’s equivalent you can notice that:

C(N,2) = N!/ ((N-2)! x 2)

Substitute N!/(N-2!) for N(N-1). That is kosher since 12×11 is the same as 12!/10!

So N!/ ((N-2)! x 2) == (N²-N)/2


With permutations, we say that “order matters”. A,D and D,A are distinct. They must be counted as 2 pairs, not just 1. So if you go back to the correlation matrix you start with the N² terms and subtract the N diagonals. You’re done! No need to divide the duplicates by 2 since A,D and D,A both need to be counted as distinct pairs.

To check you can look at the permutation formula which is the same as the combination formula but you don’t need to divide by r. You don’t need to divide out the number of ways the chosen items can be re-arranged as you do with the combination formula which doesn’t care about order.

So the permutation formula says there are 12×11 permutations or 132. Same as the matrix method which says there are 144 pairs minus 12 diagonal boxes.

When it comes to music chords permutations might be the more relevant count if you consider chord inversions.

One last trick

Remember when you were summing the green boxes…the columns were made of 11 boxes, 10 boxes, 9 boxes and so on…

Here’s the trick to summing the numbers 1 through N or in this case 1 thru 11.


So 11×12/2 = 66

Let’s try another. Sum the numbers 1 through 100.

100×101/2 = 5050

Why does this work?

Pair the ends off.

100 + 0
99 + 1
98 + 2
97 + 3
…continue until 51+49

What do you end up with:

  • 50 pairs summing to 100
  • The middle “50” left over.

    50×100+50 = 5050.

That maps to (N/2) x N+1 or “the middle number occurs N + 1 times”. That 1 term is the “middle 50”.

The first time I encountered that question was playing a game that required us to sum the ranks of a suit of cards. So Jacks are 11, Queens 12, Kings are 13 and Aces are 1s. So 13 total ranks.

What’s the sum of 1 to 13?

Perhaps another time I will explain how we used to mock trade options on the sum of ranks of cards held in people’s hands as cards were “flopped” into collective view. (Susq alum are having flashbacks to “after-work mock” now).

On Police Reform

As protests flooded the streets in the wake of George Floyd’s murder, I pulled together a stream of thoughts in my weekly letter. One of the questions I wondered aloud about was what standard police should be held to. In tweet form:

One of my readers who I chat with responded with illuminating insights on the topic. It turns out he/she had quite a background in law enforcement with a good view into local and Federal practices. As is our national habit, the discourse on police has quickly become politically polarized. Polarization is obscuring the massive degree of nuance endemic to the rich topic of law enforcement. This friend felt compelled to write down his/her thoughts and iterated on the essay over many sessions. I pushed for it to be published but the demands of this person’s current profession require anonymity. So I asked to share it on Moontower preserving anonymity. I don’t have a big platform but I’m happy to share this with those of you who do follow. Thanks to my guest and of course to you for reading.

We have a valuable opportunity to change right now but we are running the risk of not realizing powerful change due to a false equivalency in the dominant narrative.


1. What Can You Do Today to Help Create a More Just Society

2. What is the False Equivalency and Which Key Stakeholder is Missing?

3. Worldview and Caveats

4. Race and Fatality in Police Encounters

5. A Baseline for Police Violence

6. Understanding Violent Encounters and Human Limitations

7. Societal Considerations

8. Concluding Thoughts


What Can You Do Today to Help

Before expanding on the false equivalency and its effect, here are some initiatives that I think will, you know, just help make society a little bit better for everyone. No need to look at it through a political ideology, just look at it and say gee, this would help a lot of people. Think of it as trying to move society closer towards John Rawls’ Justice as Fairness without making any normative judgments about the current state of affairs.

  • Immediate: Help support bail for underprivileged people. Poor people that can’t afford bail often lose their jobs while waiting for trial, even if found innocent later. I recommend the Bail Project.
  • Immediate: Support legal assistance so that disadvantaged groups are more likely to get good legal representation. Anyone who has ever seen Lionel Hutz in action knows what I mean.
  • Medium Term: Anything that helps support educational and healthcare disparities between communities. If you aren’t sure, go to CharityNavigator and sort by 4-star charities.
  • Medium Term: Take away the power police unions have to protect police officers from losing their job even after multiple complaints. This is a sticky situation because it then brings the wider circle of public unions under scrutiny. Here is a nice overview of the potential problems.
  • Policy questions to ponder: ending the criminalization of drugs. Over policing of disadvantaged areas. The militarization of the police.
  • I also feel the need to caveat this with the following: When I first wrote this, I forgot to say anything about George Floyd? Why? Because I’ve thought about this problem deeply for years, so Floyd might be the catalyst for me sharing my thoughts, but not the catalyst for me taking an interest in this narrative, that happened a long time ago. Every cop that I know thought the murder of George Floyd was just that, murder. It was heartless, bizarre, and without explanation. 

What is the False Equivalency and Which Key Stakeholder is Missing? 

We have a valuable opportunity for change and we might fail to capitalize on it. We are missing a critical opportunity to communicate about some very real issues as a society. What’s happening instead? We are screaming past one another with ideology and frameworks. Some very positive changes have occurred but what I fear is that the current narrative completely alienates and vilifies one key group that’s going to be needed in our fight for a more just society.

 On a national level, what is the false equivalency? It is the following: “a complex and long line of historical inequalities and oppression have created a system with inherent racism” is considered equivalent and just as true as the following state “the police are racist.” The first statement is substantiated, the second one really is not. Why do I think this clarification is important? Because you can disarm a lot of hostility in the discussion between the left and the right once you tweak the narrative to allow for this nuance, and maybe we can work on changes that in theory many of us support. The heart of the argument is thus bound up in these three points:

  1. Is there a complex and long line of historical inequalities, oppression, and racism that have surreptitiously and latently made the experiences of minorities in the legal and law enforcement realms to be different than mainstream populations? Yes. This is racism.
  2. Are police officers en masse a group of racists proactively attempting to discriminate against minorities solely due to their minority status? No.
  3. If you accept both points 1 and 2 it allows for constructive dialogue. Also, if you want real reform it makes a whole lot more sense to have the police as partners in that effort and not adversaries. If you vilify the police and blame them for every ugly aspect of the system, threaten their lives, and cut their funding etc. are you going to on average get better or worse qualified people applying to be police officers?

I think most people right now agree on point #1 above, so let me spend some time on point #2 and help explain parts of the law enforcement job that often go unexplained to the general public, to the detriment to all of us in this discussion.

Worldview and Caveats

I’ve already shared some of this writing with friends and was attacked for it, so let me try to be clear upfront and say: I think there are very real problems in society. The outcomes under the current state are discriminatory and there are entire segments of the population crying out saying they haven’t been heard and have been suffering from racism. We should do everything we can to help them. The pain and psychological trauma of literally living one’s entire life in this manner is are burdens that I cannot even begin to fathom.

Race and Fatality in Police Encounters

Three studies from progressive academics concluded the following:

  1. Journal of Politics, research from Shea Streeter of Stanford University1 has shown that, if you compare blacks and whites coming into contact with the police under similar circumstances, they have a virtually equal likelihood of being killed. “The reason why so many police killings of African Americans have sparked outrage is that, at least to many, the circumstances of those interactions did not appear to warrant lethal force. A jarring implication of my research is that an analogous proportion of white decedents are also killed by police under similarly dubious circumstances.”
  2. Proceedings of National Academy of Sciences – Officer characteristics and racial disparities in fatal officer-involved shootings2. “We did not find evidence for anti-Black or anti-Hispanic disparity in police use of force across all shootings, and, if anything, found anti-White disparities when controlling for race-specific crime. While racial disparity did vary by type of shooting, no one type of shooting showed significant anti-Black or -Hispanic disparity.”
  3. Ronald Fryer of Harvard University – An Empirical Analysis of Racial Differences in Police Use of Force3: On the most extreme use of force – officer involved shootings – we find no racial differences in either the raw data or when contextual factors are taken into account. We argue that the patterns in the data are consistent with a model in which police officers are utility maximizers, a fraction of which have a preference for discrimination, who incur relatively high expected costs of officer-involved shootings.
  4. Unrelated to fatal force situations, but also worth reviewing4 if you are interested in these meta-studies: 85-90% of all racial groups who called 911 for help felt they behaved properly

I think this broadly helps frame a discussion where we can dispense with the false equivalency and agree on points 1 and 2 above.

A Baseline for Police Violence

There are over 800,000 law enforcement officers in the US5. In any given year there are approximately 63 million unique interactions between a civilian and a police officer in the United States (source: US Department of Justice6). Police shootings are cataloged and scrutinized by media and the Department of Justice. The FBI has entire divisions dedicated to investigating civil rights violations of local police departments. The Washington Post has a widely publicized police database7 which broadly proclaims that “black Americans are killed by police is more than twice as high as the rate for white Americans.”

If we are looking for clearly objectionable police behavior and bias let’s filter this down and specifically look only at shootings of unarmed people and not shootings involving some kind of weapon. Filter the database for 2019 and we see 1,004 people. Filter it again for “Unarmed” and the number drops by 99% to 56 people. Of those 56 people: 25 were white, 15 were African American, 11 were Hispanic, and 5 were other.

There are pretty broad studies from Harvard and Michigan State University that conclude that at least when it comes to fatal force the police are not biased by race8. What I think is clear is that minorities are more likely to have contact with police, and more likely to be prosecuted for a crime than white people under similar circumstances. So here you have the paradox of points 1 and 2 on display: as a minority you are more likely to have a police encounter purely based off the demographics of communities and deployment of police assets (point 1 above systemic factors) but once that encounter starts you are of equal or even less likely to be killed than a white person (see footnote 4) i.e. point 2 above police officers, in general, aren’t biased in their application of fatal force.

Everyone forgets to look at police officers though – the other side of the coin. 48 police officers were killed in 2019, 40 were white, 7 were African American, and 1 was Asian. This means that if you are an unarmed African American as part of the general population in 2019 you die at the hands of police at a rate of approximately 15 per 37.1 million compared to African American police officers who died at a rate of 7 per 106,400. (800,000 police officers, of which 13.3% are African American9, compared to 12.6% of the general US population).

So even if you assume every unarmed killing (more on that later – use of force, tactics, and the fact a police officer never knows who is armed or not) is entirely without any reasonable cause you have a fatality error rate in 2019 for all citizens, regardless of color, of 56 people per 63 million unique police to citizen interactions per year. Or a rate of .00009%. I think one is one too many but when you have 800,000 people making decisions in 63 million encounters some of which are bound to involve making decisions under conditions of risk, violence, and uncertainty, I would imagine that error rate is broadly representative of the error rate in any human endeavor.

Understanding Violent Encounters and Human Limitations 

“As your heart rate goes up, your tunnel vision can get narrower and your auditory exclusion can increase.” 

— Dave GrossmanOn Combat: The Psychology and Physiology of Deadly Conflict in War and in Peace

Everyone sits back and looks at the situation and likes to think about what they might have done. Here are some realities for the people that have seen too many movies. You can start with the first 3 listed in this article: 15 Things The Police Wish The Public Knew About Law Enforcement10:

  1.   The police aren’t martial arts or even hand to hand combat experts.

    “People have been conditioned by TV to believe that a properly trained police officer of any size can take down a person of superior size and strength11, quickly, almost effortlessly, without the use of weapons, and without any injury to either party. This is not true. Few cops are expert martial artists. The defensive tactics training12 they receive is fairly perfunctory. Struggles often result in injured joints, lacerations, concussions and other injuries to both parties. There is lots of cursing and screaming involved. The cops usually win, but only because they can get enough cops on the scene to overwhelm the adversary.

    The reality of it is this: if you get physical with a police officer they are going to assume their life is in mortal danger. If at any point you can hit them hard enough to stun them, or are able to grab their weapon, their assumption is that you are going to kill them. So this is why you see multiple police officers tackle and hit people at times – they aren’t experts in hand to hand combatives, they are going to use numbers and brute force to bring the situation under control as quickly as possible.

  2.  Performance Under Stress: During a stressful event the human capacity to think and even respond with coordinated physical movements is reduced.

    What you get is brute force gross motor function moves. Let’s talk about people’s reaction under stressful situations13 for people who have never been a knockdown drag-out fight or have not been shot at:

      • During a stress event, the SNS is activated and adrenaline, chemicals, and hormones are dumped from the adrenal glands and immediately sent out to the areas of the body needed to primarily support the survival effort. At 145 heart beats per minute (BPM), most people lose complex motor skills, meaning those manual dexterity skills necessary to do several things at once or in unison.
      • At 175 BPM, the pupils dilate and flatten and visual narrowing occurs – or what is referred to as tunnel vision – and since the visual system is the primary sensory system for the brain it becomes increasingly difficult to focus and track objects and targets.
      • In the auditory system, hearing shuts down or is diminished significantly at around 115 BPMs and that is why many people say they didn’t hear anything during a life-threatening stress event.
      • The brain is ultimately affected as well. At 175 BPM, it is not uncommon for someone to have problems recalling what just occurred. This is sometimes referred to as “critical stress amnesia.” Immediately after an event, a person may only recall 30 percent of what happened with memory gradually increasing over many hours.
      • At 185-220 BPM, most people will go into a state of “hyper-vigilance.” This is also commonly known as the “deer in the headlights” or “feedback mode” where a person repeats non-effectual actions or having irrational behavior like moving from behind the protection of a building during a gunfight.
      • Lastly, at a mere 115 BPM, fine and complex physical motor skills become less available and effective. Pulling the trigger of handgun correctly, aiming on target or manipulating handcuffs or other tools becomes increasingly difficult to do. This is in direct contrast to the gross motor skills which become enhanced such as those parts of the body needed to fight or flee.

  3.  Split Second Decision Making14: Why It Can Look So Bad After The Fact
    • Go back and re-read the effects of stress on the body and the impact on motor skills and brain function. The average gunfight is over in seconds which means there is not often time for conscious thought. When people receive weapons training they are usually taught to 1. Aim center mass of a target because even when you are aren’t under stress it’s nearly impossible to hit an appendage such as an arm or leg and 2. Keep shooting until the target goes down. Why? Because sometimes getting shot actually doesn’t stop someone from coming at you. I refer to this Apple podcast: Mike Day: Navy SEAL, Shot 27 Times and Never Quit15 who was shot 27 times and still managed to take out his attacker.
    • So when you read some incendiary article that police shot someone 30 times, what they aren’t saying is that it’s not like the police had a meeting before and decided how who was going to shoot how many bullets, the entire event probably transpired in 5 seconds with no time to coordinate, and each officer drew their weapon as they were trained to do and shot repeatedly until the individual went down. Furthermore, given the effects of stress on the body, each officer was probably not even aware of what the other people around them were doing at the time.

Examples of the Types of Decisions Officers Make: I’ve spoken to people about the death statistics for police officers and the response is so what, they signed up for that job. Well, the counterpoint is that you’ve implicitly admitted then than it’s inherently dangerous and violent. Why is that an important acknowledgment? Because to understand police violence you need to understand what kinds of situations they are confronted with and how they are trained to react.

    1. Hint: it’s not easy16 and unless you’ve undergone the training17 it’s really easy to read an after the fact headline and become enraged. Footnotes 8 and 9 are really worth going to in order to get a feel for this.
    2. Two quick summary stories from my use of force training: in one class we watched bodycam videos of police shootings and voted after on if the use of force was appropriate. On one of them, the person was running, stopped, turn around really quickly and pulled a gun out. He was shot and killed. 100% of the class voted it was an appropriate shooting. They slowed the tape down and showed us the pictures after, it was a very young man and the gun was actually a cell phone.
    3. It’s not easy when it’s happening in real-time speed and your stress hormones are flooding your system – vision narrows and your brain just reacts at times without time even for conscious thought. In the virtual simulator, I was in a shoot or no-shoot decision and I shot a lady. To me, it looked like she was pointing the gun at another officer to her right. They let the video play through and it turns out she was putting the gun down, I just had a bad angle. It’s terrifying to me how hard it is to make decisions in these scenarios.
    4. Look at this scenario18 and how fast it plays out – and the officers have the benefit of daylight and helicopter telling them what the person is doing. The reality is you never know who19 has a gun – I carried a concealed weapon and was able to draw it and fire two shots into a target at close range in under 2 seconds
    5. What is the takeaway when you combine these split-second scenarios with human decision making under stress: Police officers are taught that action beats reaction – so if he/she even thinks you are reaching for something that might harm them they are going to attempt to react faster than you and shoot. If you want to see why officers often react the way they do, or attempt to react with a strong level of force to head off any resistance right up front just go on youtube and drop in something about traffic stops gone wrong. Things go from okay to getting shot at in a literal second. A lot of the posturing and domineering behavior is done in hopes to dissuade someone from even thinking about taking that road.
  1. The Damage of a Bad Media Narrative20 “Atlanta Police Officer Shoots a Black Man Dead at the Fast-Food Drive-Thru” That’s the headline, people are already protesting. The police officer has already been fired and the mayor forced the police chief to resign. You read further details: the man had passed out in his car and was blocking the drive through so police were called. He got out of his car, started wrestling with the officers, managed to take one of their tasers, and was firing it at them, and only at that point did they shoot him. None of that is in the media, instead the officer is fired and the police chief is forced to resign. Any intelligent police officer that can find work elsewhere right now is going to do so and you are going to be left with less qualified and capable candidates. This entire narrative is making the situation more volatile and more error prone rather than the opposite.

Societal Considerations

 Large datasets and false homogeneity: First point and counterpoint: Large sets of numbers hide the truth at times. If you have never worked in law enforcement it’s hard to realize that the police are not a monolithic organization. Police departments are like church parishes – each one has its own culture, leadership, training department, demographic make-up, funding sources, etc. This view enables the following conclusions 1. Don’t just look at the national level averages and say there is no problem. On the other hand 2. The fact that departments vary widely should also make people hesitant to condemn the police en masse as some collective hive mind bent on discrimination. What is clear is that you give police departments a lot of power and authority – hiring practices should come under the ultimate scrutiny.

Lack of Narrative and Effect: Well what about the other side of the story when police are entirely wrong in their actions? I think that is put on display every day, what people don’t understand is what police officers are confronted with daily and just how quickly they have to decide under pressure. When you routinely vilify the police and incite hatred towards them without understanding the demands of their job and how these kind of things can occur you are creating a real problem in the sense that no reasonably intelligent person is going to want to become a police officer and the quality of your candidate pool is going to go down drastically. This will likely make all of the above problems worse over time and not better. There is a very real human element to this that is hidden by the dominant narratives.

“All Cops Are Bad Because They Don’t Turn in The Bad Cops”: People are dismissed from law enforcement agencies all the time – it’s just not publicized. I worked for a smaller agency and over the course of four years just in my local office we dismissed 4 individuals from internal investigations, from low ranking to very high ranking. They didn’t do anything criminal, or even overtly wrong in some cases, but they were judged to have a character not appropriate to law enforcement. That being said, there is a lot of evidence piling up that police unions are a very large problem because they protect officers from complaints and the officers cannot get fired. So even if a fellow officer or citizen files multiple complaints, nothing happens21. We didn’t have a union so people could be dismissed at any point.

Concluding Thoughts

Let’s stop turning police officers into the scapegoat for all the underlying societal problems that nobody wanted to address before. You need a holistic and systemic approach. Reach out to local police departments and include them in the discussion, support politicians to change the laws they have to enforce, support charities that help ensure equal treatment in the justice system. But if you keep vilifying and blaming the police for the entire system you are only going to get less qualified and less astute police officers moving forward, and that will be to the detriment of all of us. The current narrative is largely inaccurate, it’s also damaging.

Breaking Barriers United on Defunding The Police (Link)

Jay Stalien on Being a Beat Cop in Urban America (Link)

Humanizing the Badge (Link)