American options are not vanilla

I’ve always found it amusing that the most commonly traded options, American-style equity options contracts, are considered “vanilla”. Because they can be exercised early, their valuation is an instance of a famously difficult problem — explore/exploit. The only reason I might refer to them as “vanilla” is not for them being simple, but simply common.

The last time you bought a TV you encountered this problem — do I keep researching or pull the trigger? From shopping or channel-surfing to giant commitments like who to settle down with or businesses to pursue, the problem sits at the heart of decision-making across all domains though it tends to be more formally considered in fields like computer science, finance, game theory, and operations engineering.

💡See my notes from Brian Christian talking about Algorithms to Live By to see how explore/exploit is seen in everything from “bandit” problems to child development and learning strategies.

The Black-Scholes formula is elegant. It’s a closed-form equation that you can implement in a common financial calculator. As trainees, we programmed it into our bootcamp standard-issue 12C:

But Black-Scholes doesn’t work for American-style options.

💡If you need accessible, non-formal refreshers on Black-Scholes, see:

The equation is a factory — it takes in raw material and squeezes out a hot dog on the other side. But it has no visibility on the path between input and output. But that path is key to the core question:

What is the optimal stopping time of an American-style option?

When should we exercise the right to “stop” the option early?

While American options let you exercise anytime before expiration, you usually shouldn’t. The value of optionality (your right to wait) is typically greater than the small benefit of early exercise.

This discussion is not only useful but fun since we invoke microeconomics in real-life.

It starts with 2 key questions.

WHY would you exercise early?

  • Puts: to collect interest sooner on the short stock position.
  • Calls: to capture a dividend

WHEN is it worth it to exercise early?

We check 2 tests in sequence:

a) Is the benefit worth more than the optionality you give up?
Compare the gain from early exercise to the value of the out-of-the-money option at the same strike.

Examples:

  • Put: If a stock is $100 and you own the 120-put, you can exercise the right to sell/short the stock at $120. Is the interest you earn on the $120 until expiry worth more than the 120-call, which you are effectively selling at 0?
  • Call: Let’s say this $100 stock pays a $1 dividend and you own the 80-call. Is the 80-put, which you are giving up, worth less than the dividend?

The cost of the exercise (the time value of the option) vs its benefit (interest or dividend) is just the first step. But now you need to zero in on the when.

This is where we have to go to “marginal” cost/benefit. In other words…

b) Is one day’s cost of waiting (theta) greater than one day’s benefit (interest or dividend)?

When daily theta decay exceeds daily interest/dividend gain

Let’s get more concrete.

Stepping through the tests

We start with assumptions.

✔️Stock price = $100
✔️DTE = 60
✔️RFR (the rate you earn on cash in your account) = 5%
✔️Implied volatility = 20%
✔️ No dividends

We will analyze the 105 strike put.

I used a Black-Scholes European style calculator to compute the option values. You’re supposed to use an American calculator, but since I’m trying to explain the exercise rules, that would mask some exposition. Pointing out the European calculator’s mistakes will be better for learning.

Ok, we start with this table of our option values for each day until expiry.

Column explanations:

  • Put theo: Black-Scholes value for the 105 put given our assumptions
  • Call theo: Black-Scholes value for the 105 call given our assumptions
  • Total interest: interest you’d collect until expiry if you exercised the right to sell shares at $105. Computed as 105e^(.05 * DTE/365) – 105
  • theta from the option model
  • 1 day’s interest computed as 105e^(.05 * 1/365) – 105
  • Test 1: value of the call – total interest. This is a blunt total comparison of the put I own’s time value (represented by the call) vs the interest I’m forgoing by not exercising
  • Test 2: 1 day interest that I forgo vs 1 day optionality represented by theta. This represents the marginal comparison of the interest vs optionality for 1 day.

At 12 DTE, the European model is telling us that the 105 put is worth LESS than its intrinsic value of $5. That’s a clue!

That’s the point at which the time value of the put (ie represented by the call on the same strike…remember put/call parity means the call is “in” the put) is LESS than the interest you’d earn if you exercised early.

💡The European put can and will trade under intrinsic. The American-style option should not trade less than $5 because if it did, you would simply buy the put, buy the stock, exercise immediately and have a risk-less profit of the amount it traded under intrinsic. So if for some reason you could buy the American-style 105 put for $4.92, you’d buy the stock for $100, then exercise the put which allows you to sell the stock at $105. Between the stock and put you’ve laid out $104.92 but your proceeds from the sale are $105. You pocket $.08 with no risk.

At 12 DTE, the 105 put has passed Test 1 (interest > option value). Visually, you can see this on the upper chart. But look at the lower chart…

The lower chart is the visual of Test 2 (1-day interest exceeding 1-day optionality).

5 DTE is the point of optimal early exercise.

Let’s do this again a bit faster with the 108 strike.

Since this put is deeper ITM, the corresponding 108 call is headed to zero earlier and the interest one earns on $108 is a bit more than the interest on $105 so without working through any math we expect to exercise the 108 put sooner than 5 DTE.

For the 108 strike, Test 1 (total interest exceeds the call value) is satisfied with 55 days until expiry, but the optimal exercise point isn’t until 20 DTE.

Interest “rent” is constant; theta is NOT

The daily interest benefit is linear. It’s basically total interest divided by DTE. But you may have noticed the theta values are curved. It’s intuitive that theta for an ATM option increases in an accelerating way until expiry. After all, with 1 DTE, the ATM option is entirely extrinsic value and you know in 24 hours the time value goes to zero.

For the 108 call, it has no value several days before expiry so there’s nothing to decay. The option went through the steepest part of its depreciation days earlier. Test 2 depends on when 1d interest and 1 theta “cross”.

For reference, this is a visual of theta vs DTE for strikes of various moneyness. Remember, the stock is fixed at $100. The closer the option is to ATM, the later it experiences its steepest decay. With a week to go, the far OTM 109 call has no decay. It’s already worthless.

Optimal exercise of American calls

You exercise calls early to capture a dividend. You must be the shareholder of record on the “record date” to be entitled to the dividend. When the stock goes “ex-dividend” it means any holders of the stock are NOT entitled to the dividend.

Owning a call option does not give you rights to the dividend since you are not a shareholder. That’s why the cost-of-carry component of option pricing discounts calls by the amount of the dividend.

When a stock goes “ex”, meaning the dividend has been paid out, the shares fall by the amount of the dividend which makes sense — the balance sheet has shed X dollars per share of cash.

The owner of the call will experience the drop in share price without any dividend receipts to make up for it.

💡If a $100 stock pays a $1 dividend and the shares open at $100 your brokerage or data vendor will say the stock is up $1 on the day. Unchanged would mean the stock should open at $99. If you own a dividend-paying stock it’s not “extra” return. The company just chiseled off a piece of its value and gave it to you in cash. It’s economically a wash. If they didn’t pay you the cash the company would retain it, the enterprise value would be unchanged and your return is the same. Your cash flow is different but of course you could have sold 1% of your shares to the same effect. In fact, that’s more tax-efficient. Of course, these are all first-order mechanical considerations. The properties of companies that pay or don’t pay dividends is a separate point of debate. If you do not believe stocks fall by the amount of the dividend, meet me at the corner of Trinity and Rector. I’ll be in a trenchcoat with a suitcase of Euro-style call options to sell you on a lovely selection of fat dividend yield aristocrats.

The optimal exercise of ITM American calls is easier. Test 1 is simple. Is the dividend I’m receiving greater than the value of the OTM put I’m giving up? [Again the put value tells me the time value or optionality of the ITM call I actually own]

What about the optimal timing of the exercise?

The marginal thinking represented by Test 2 is straightforward. The benefit of exercising the call early is discrete — it’s a dividend on a specified date. If the dividend is worth more to me than the time value of the call, I shouldn’t give up the time value until the last moment I have to capture the benefit. I should exercise on the day before the stock goes ex-dividend so I’m the shareholder of record.

Real-world considerations

  • Early exercise decisions are directly dependent on interest rates (for puts), dividend amounts (for calls) and volatility (which influences the optionality you are surrendering when you exercise the option). Just think of the benefit you receive vs what you are giving up and what influences those quantities.
  • Stock settles T+1. If you exercise a put on Thursday, your short share proceeds from the stock hit your account Friday, meaning you collect interest over the weekend. When I started in trading, stock settlement was T+3, so Tuesdays were “put day”. That’s the day you’d exercise to capture interest over the weekend. From 2017 to 2024, “put day” was Wednesday as the standard settlement was T+2. Microstructure nerds might be aware of a famous pick-off trade in the early aughts where a SIG alum bought shares from a NYSE specialist requesting T+1 settlement knowing that the company was going to pay a giant special dividend the next day. This ended up being very expensive to the seller. And eventually, to the buyer as this maneuver landed them in court. The option world is littered with dividend shenanigans. The range of ethical codes is wide and can certainly extend to “a moral obligation to relieve dumber people of their money” or “legal fees are part of my expected value calculation”. Having spent time in the trading world, I’m not surprised to when I notice these familiar moralities in tech, but a distinction in trading is pro vs pro violence was ok, ripping off customers was killing the golden goose.
  • Sometimes companies announce a large dividend suddenly that the exchange will treat as special. Strike prices will be revised lower to account for the special dividend keeping the economic impact on options unchanged. That said, incremental changes in dividend policy are risks to option holders. Increased dividends lowers calls/raises puts all else equal.

We have an option calculator that allows you to compare the “early exercise premium” of American to European options:

https://www.moontower.ai/tools-and-games/option-pricing-calculator

Holiday coziness = backgammon

I taught both my boys backgammon this past week. This is the younger guy playing with mom.

I used to play a lot with my colleagues during the year I was a broker on the NYSE floor. Every time I came back to the “booth” (that’s the area with the phones on the sides of the exchange floor where clerks take orders from customers), I’d make a move on the Jellyfish software. When I was at Parallax, I worked with 2 of the best backgammon players in the world (one of them was the best in the world iirc) and Parallax was actually founded by Roger Low, who was a world-class player himself. Roger had retired by the time I joined so I never got to know him.

Backgammon is especially neat if you like options because the doubling cube begs you to price volatility.

💡Fun fact

When I had my phone interview with SIG (this is the round that happens in between campus interview and the final on-site) I was asked a basic question regarding the cube. Since accepting the cube doubles the stakes of the game and rejecting it forfeits the current value of the game, what is the minimum probability of winning you need to accept it?

When looking at the board you need to evaluate how risky the position is. Like how likely is the tide to turn? When you offer the cube you are selling your opponent an option and its value depends on their chance to come back. But if you offer it to them when they have no chance they will reject it and be bailed out because you have now sacrificed your own possibility of getting a gammon (double points) or backgammon (triple points) if you beat them by a large margin.

It’s a great game for kids because they get to practice dice math. I was playing last night and knew I’d win as long as my next roll wasn’t a [1,1], [1,2], [2,1], [3,3]. So the kids would first need to figure out that’s what they are rooting for and then I ask them the probability. 4 out of 36 or 1/9. Plus the little guy figured out that the 7 is the most common roll and how to count the number of ways to get each number (he was delighted by the pyramid pattern when he realized it).

We always play more games during the cozy holiday season and I’m irrationally pleased that this season it’s backgammon. I recommend it.

[Also, if you are just learning, play a bot on your phone. You learn the game very quickly getting trounced by bots. Ultimately, I’m just a casual player, I never studied it, but would just play for $5 a game with my NYSE squad. Of course, with the doubling cube and possibility of gammons that can multiply pretty quickly. The real hitters play for four and five figures per game.]

“markets vs democracies” in the wild

On Nov 26th, Imran asked his followers would what more likely to double in the next year — gold or BTC?

I looked at the result of the poll just a few hours after it was posted and it was BTC 52% to gold 48%.

By the time the poll closed with 750 votes, BTC had garnered 2/3 of the votes.

I don’t know if me a jerk had anything to do with this but when I saw that the vote was almost a coin flip I chimed in.

Focus on the last part.

The poll should be nowhere near 50/50 because you would be able to lock in a great trade by selling gold in this proposition, buying gold call spreads financed by even more expensive BTC call spreads.

This is a classic difference between markets and democracy. It’s a perfect example of the Dinosaur Markets post in real life. The markets in the options reflect the volatility and the cost of replicating these bets. Money-weighted votes are interested in the truth where opinions are cheap as sand.

It’s very difficult to have opinions that are above replacement value about liquid assets. If you’re truly good at this, then being Scrooge McDuck rich based on consistently betting on these fantastic opinions is the only proof of such a skill. Few people are rich because of a crystal ball.

A good way to make a living in finance is to find the people that voted for gold in this poll and offer to trade with them. You need to do this in the dark because if you tried to do it on a public exchange, you’d be undercut by traders competing to sell the gold proposition to these opinionated people and it would drive the price down to a non-arbitrageable price.

Public markets protect overconfident people with arbitrageable opinions from their own ignorance and stupidity. Private or non-transparent markets are nice ways to shove a vacuum hose into their bank account.

There are many places where there’s alpha in projecting your opinion. This is the stuff you spend your time on in life. Where you have self-knowledge, private info, competitive advantage, skills, taste and so on.

But when it comes to markets, remember what we learned here just a few weeks ago:

the arbitrage reflex is more profitable than the opinion reflex

Moontower #295

Friends,

First of all, here’s the slides I shared in this vid:

I hope that video was helpful. I watched it again because I think the topic is complicated, not technically, but because it’s counterintuitive. Trades like that were bread-and-butter through my pro career (and very much why I “spotted” it despite it not sticking out in the tools other than the Trade Ideas filter which is highly validating of our algorithm! I’ll allow myself to be happy about my own work for 1 second. Ok moment’s passed, let’s continue.)

Before we head on to Money Angle stuff I’ll share 2 things I enjoyed.

Fermat’s Last Theorem Documentary (link)

This 45-minute video follows the story of Andrew Wiles’ quest to prove Fermat’s Last Theorem. I didn’t know the history of the theorem or even what it stated. It claims that for any whole number exponent other than 2 there are no values of A,B,C that would satisfy Aˣ + Bˣ = Cˣ. You can’t prove this computationally because there’s an infinite number of possibilities. The proof requires mathematical logic.

Fermat allegedly had a proof but hadn’t written it down. Turns out Wiles’ proof would have been impossible for Fermat to have known (this will make sense when you watch it). Anyway, I loved it. Yinh fell asleep. YMMV.

Holiday coziness — games!

I taught both my boys backgammon this past week. This is the younger guy playing with mom.

I used to play a lot with my colleagues during the year I was a broker on the NYSE floor. Every time I came back to the “booth” (that’s the area with the phones on the sides of the exchange floor where clerks take orders from customers), I’d make a move on the Jellyfish software. When I was at Parallax, I worked with 2 of the best backgammon players in the world (one of them was the best in the world iirc) and Parallax was actually founded by Roger Low, who was a world-class player himself. Roger had retired by the time I joined so I never got to know him.

Backgammon is especially neat if you like options because the doubling cube begs you to price volatility.

💡Fun fact

When I had my phone interview with SIG (this is the round that happens in between campus interview and the final on-site) I was asked a basic question regarding the cube. Since accepting the cube doubles the stakes of the game and rejecting it forfeits the current value of the game, what is the minimum probability of winning you need to accept it?

When looking at the board you need to evaluate how risky the position is. Like how likely is the tide to turn? When you offer the cube you are selling your opponent an option and its value depends on their chance to come back. But if you offer it to them when they have no chance they will reject it and be bailed out because you have now sacrificed your own possibility of getting a gammon (double points) or backgammon (triple points) if you beat them by a large margin.

It’s a great game for kids because they get to practice dice math. I was playing last night and knew I’d win as long as my next roll wasn’t a [1,1], [1,2], [2,1], [3,3]. So the kids would first need to figure out that’s what they are rooting for and then I ask them the probability. 4 out of 36 or 1/9. Plus the little guy figured out that the 7 is the most common roll and how to count the number of ways to get each number (he was delighted by the pyramid pattern when he realized it).

We always play more games during the cozy holiday season and I’m irrationally pleased that this season it’s backgammon. I recommend it.

[Also, if you are just learning, play a bot on your phone. You learn the game very quickly getting trounced by bots. Ultimately, I’m just a casual player, I never studied it, but would just play for $5 a game with my NYSE squad. Of course, with the doubling cube and possibility of gammons that can multiply pretty quickly. The real hitters play for four and five figures per game.]

Money Angle

On Nov 26th, Imran asked his followers would what more likely to double in the next year — gold or BTC?

I looked at the result of the poll just a few hours after it was posted and it was BTC 52% to gold 48%.

By the time the poll closed with 750 votes, BTC had garnered 2/3 of the votes.

I don’t know if me a jerk had anything to do with this but when I saw that the vote was almost a coin flip I chimed in.

Focus on the last part.

The poll should be nowhere near 50/50 because you would be able to lock in a great trade by selling gold in this proposition, buying gold call spreads financed by even more expensive BTC call spreads.

This is a classic difference between markets and democracy. It’s a perfect example of the Dinosaur Markets post in real life. The markets in the options reflect the volatility and the cost of replicating these bets. Money-weighted votes are interested in the truth where opinions are cheap as sand.

It’s very difficult to have opinions that are above replacement value about liquid assets. If you’re truly good at this, then being Scrooge McDuck rich based on consistently betting on these fantastic opinions is the only proof of such a skill. Few people are rich because of a crystal ball.

A good way to make a living in finance is to find the people that voted for gold in this poll and offer to trade with them. You need to do this in the dark because if you tried to do it on a public exchange, you’d be undercut by traders competing to sell the gold proposition to these opinionated people and it would drive the price down to a non-arbitrageable price.

Public markets protect overconfident people with arbitrageable opinions from their own ignorance and stupidity. Private or non-transparent markets are nice ways to shove a vacuum hose into their bank account.

There are many places where there’s alpha in projecting your opinion. This is the stuff you spend your time on in life. Where you have self-knowledge, private info, competitive advantage, skills, taste and so on.

But when it comes to markets, remember what we learned here just a few weeks ago:

the arbitrage reflex is more profitable than the opinion reflex

 

Money Angle For Masochists

Let’s continue on the same theme because these threads are going to become far more frequent for anyone who cares about markets. “Thinking in Bets” has a long runway, the way this country is headed, before it jumps the shark, so you might as well get used to it. From “Everything computer?” to “everything casino?”

Prediction Market Arbitrage: Using Option Chains to Find Mispriced Bets

Horse tweeted:

The moment you see a bet on a platform like Kalshi, Polymarket, or the soon-to-be Robinhood+SIG exchange, your mind should jump to the options chain.

The tweet says the Kalshi market is pricing a 9% chance of BTC hitting $250k

The options market can offer a quick sanity check. BTC is about a 55% vol. We are just being very approximate so not worrying about the term structure. I just want to show you my automatic mental response to the tweet.

Without hesitating, I pulled up the calculator on my phone and entered:

ln(250k/89k) / (.55 * sqrt(13/12))

Why?

We want to compute how many standard deviations away the $250k strike is to get a z-score which we can then convert to probability. Standard deviation depends on volatility and time. The more time or volatility you have the “closer” some percent return is. A strike that’s 100% away is extremely “far” if the asset needs to get there by tomorrow. If you have 10 years to get there, it’s not super far at all, you only need to go up 7% per year. Likewise, if an asset only varies by 5% a year, 100% is “far”, but if it moves 50% per year, 100% feels much “closer” or possible.

The formula above is simply dividing the percent return to get to the strike by the annualized volatility scaled by root(time) to find the distance.*

*Standard deviation or volatility as a quantity is proportional to the square root of time. Or you can say variance, the square of standard deviation, is proportional to time. The easiest way to remember this is to recall that when you compute the standard deviation of anything, you have an intermediate step of summing the squared deviations to get the variance, then divide by N. But to get back to the standard deviation, you take the square root of the ratio. The ratio in the intermediate step was variance/N. The final answer, the standard deviation, was the ratio of sqrt(variance) / sqrt( N). In our computations, N is replaced by time.

At the time of the tweet, BTC was 89k and there was 13 months until 2027. I assume 55% volatility.

Solving:

ln(250k/89k) / (.55 * sqrt(13/12)) = 1.80 standard deviations

We then use a standard normal table or normdist in Excel to see that 1.80 standard deviations encompasses about 96.4% of the cumulative distribution. Therefore, the probability of BTC going HIGHER than 1.8o standard deviations must be 3.6%

This is fully explained in Using Log Returns And Volatility To Normalize Strike Distances

The computation of this distance, besides being dependent on an estimate of volatility which we can borrow from the options market, assumes the asset is lognormally distributed. If you believe, as the options market certainly will if you look not at the at-the-money vol, but the far out-of-the-money call vols, that there is more positive skew than a lognormal distribution then our 3.6% estimate is too low.

But that logic is moving us in the right direction. We want to take the intel embedded in the options market when considering the price in the prediction market. We expect the liquid options market with much more volume and money behind it, to be the best guess as to the “fair price” of a proposition. If there’s an edge, it will be in the mispriced prediction market.

A prediction market bet can take a binary flavor. For example, “Probability that BTC settles above X by some date.”

It can take a “one touch” flavor. “BTC to touch but not necessarily settle above X by some date.”

Of course, “touch” is more likely than “settle” because “touch” encompasses all the times BTC settles above X, but also includes all the cases where it breaches X and falls back below X by expiry.

We can get information about the price of both binary and one-touch scenarios from the option market.

1. The Binary Bet: Price the Terminal Outcome with Vertical Spreads

Pricing: To find the true market-implied probability of the event, use the price of the spread:

Vertical spread price/Distance between the strikes ~ probability of asset expiring above he midpoint of the spread

Potential arbitrage if…the probability implied by the options chain is lower than the price offered on the prediction platform, you can buy the vertical spread and take the under in the prediction market or vice versa.

Further Reading: A Deeper Understanding of Vertical Spreads

2. The Path Bet: Account for Skew and Volatility with the One-Touch Rule

Pricing: You can estimate the path probability using the trader’s rule of thumb: take the delta of the vanilla option at that strike and multiply it by 2. This naturally takes into account the option implied skew because the delta is derived from the implied volatility at the strike.

The mechanics of an arbitrage here are complicated as it requires dynamic hedging. If that sounds interesting, perhaps you are born to be an exotic options trader. I have never tried replicating a one-touch option so while I could certainly “financially hack” a model, the main point I want to convey is that the pricing of the one-touch can be inferred from the vanilla options market.

Further Reading: one-touch

 

Stay groovy

☮️

Moontower Weekly Recap

Posts:

Prediction Market Arbitrage: Using Option Chains to Find Mispriced Bets

Horse tweeted:

The moment you see a bet on a platform like Kalshi, Polymarket, or the soon-to-be Robinhood+SIG exchange, your mind should jump to the options chain.

The tweet says the Kalshi market is pricing a 9% chance of BTC hitting $250k

The options market can offer a quick sanity check. BTC is about a 55% vol. We are just being very approximate so not worrying about the term structure. I just want to show you my automatic mental response to the tweet.

Without hesitating I pulled up the calculator on my phone and entered:

ln(250k/89k) / (.55 * sqrt(13/12))

Why?

We want to compute how many standard deviations away the $250k strike is to get a z-score which we can then convert to probability. Standard deviation depends on volatility and time. The more time or volatility you have the “closer” some percent return is. A strike that’s 100% away is extremely “far” if the asset needs to get there by tomorrow. If you have 10 years to get there, it’s not super far at all, you only need to go up 7% per year. Likewise, if an asset only varies by 5% a year, 100% is “far”, but if it moves 50% per year, 100% feels much “closer” or possible.

The formula above is simply dividing the percent return to get to the strike by the annualized volatility scaled by root(time) to find the distance.*

*Standard deviation or volatility as a quantity is proportional to the square root of time. Or you can say variance, the square of standard deviation, is proportional to time. The easiest way to remember this is to recall that when you compute the standard deviation of anything, you have an intermediate step of summing the squared deviations to get the variance, then divide by N. But to get back to the standard deviation, you take the square root of the ratio. The ratio in the intermediate step was variance/N. The final answer, the standard deviation, was the ratio of sqrt(variance) / sqrt( N). In our computations, N is replaced by time.

 

At the time of the tweet, BTC was 89k and there was 13 months until 2027. I assume 55% volatility.

Solving:

ln(250k/89k) / (.55 * sqrt(13/12)) = 1.80 standard deviations

We then use a standard normal table or normdist in Excel to see that 1.80 standard deviations encompasses about 96.4% of the cumulative distribution. Therefore the probability of BTC going HIGHER than 1.8o standard deviations must be 3.6%

🔗This is fully explained in Using Log Returns And Volatility To Normalize Strike Distances

The computation of this distance, besides being dependent on an estimate of volatility which we can borrow from the options market, assumes the asset is lognormally distributed. If you believe, as the options market certainly will if you look not at the at-the-money vol, but the far out-of-the-money call vols, that there is more positive skew than a lognormal distribution then our 3.6% estimate is too low.

But that logic is moving us in the right direction. We want to take the intel embedded in the options market when considering the price in the prediction market. We expect the liquid options market with much more volume and money behind it, to be the best guess as to the “fair price” of a proposition. If there’s an edge, it will be in the mispriced prediction market.

A prediction market bet can take a binary flavor. For example, “Probability that BTC settles above X by some date”

It can take a “one touch” flavor. “BTC to touch but not necessarily settle above X by some date”

Of course, “touch” is more likey than “settle” because “touch” encompasses all the times BTC settles above X, but also includes all the cases where it breaches X and falls back below X by expiry.

We can get information about the price of both binary and one-touch scenarios from the option market.

1. The Binary Bet: Price the Terminal Outcome with Vertical Spreads

Pricing: To find the true market-implied probability of the event, use the price of the spread:

Vertical spread price/Distance between the strikes ~ probability of asset expiring above he midpoint of the spread

Potential arbitrage if…the probability implied by the options chain is lower than the price offered on the prediction platform, you can buy the vertical spread and take the under in the prediction market or vice versa.

Further Reading: A Deeper Understanding of Vertical Spreads

2. The Path Bet: Account for Skew and Volatility with the One-Touch Rule

Pricing: You can estimate the path probability using the trader’s rule of thumb: take the delta of the vanilla option at that strike and multiply it by 2. This naturally takes into the account the option implied skew because the delta is derived from the implied volatility at the strike.

The mechanics of an arbitrage here are complicated as it requires dynamic hedging. If that sounds interesting, perhaps you are born to be an exotic options trader. I have never tried replicating a one-touch option so while I could certainly “financially hack” a model, the main point I want to convey is that the pricing of the one-touch can be inferred from the vanilla options market.

Further Reading: one-touch

“dancing animals”

Option trader and professional shtpoaster P4 tweeted this quote I’ve been sitting on a for a month:

Kurt Vonnegut tells his wife he’s going out to buy an envelope:

”Oh,” she says, “well, you’re not a poor man. You know, why don’t you go online and buy a hundred envelopes and put them in the closet?”

And so I pretend not to hear her. And go out to get an envelope because I’m going to have a hell of a good time in the process of buying one envelope.

I meet a lot of people. And see some great-looking babies. And a fire engine goes by. And I give them the thumbs up. And I’ll ask a woman what kind of dog that is. And, and I don’t know. The moral of the story is — we’re here on Earth to fart around.

And of course, the computers will do us out of that. And what the computer people don’t realize, or they don’t care, is we’re dancing animals. You know, we love to move around. And it’s like we’re not supposed to dance at all anymore.”

My wife will sympathize with Kurt’s wife. I will leave the house, forget the stamps, and come back telling her about the friend I just made who works in the produce section where we just discussed apple varietals for 30 minutes. Tangos are my favorite.

I’ve always thought this was a bit of a bug. It is quite inconvenient since I easily lose track of time. But “dancing animals” is the redemption I didn’t know I needed. It’s a redemption we all need.

It is grace.

It’s a little reminder that we are messier than our identities or affiliations or goals. Your strengths contain your weaknesses. Your beliefs are self-contradicting. You thought you were so smart 10 years ago and now cringe at what you didn’t know.

And still we will try to figure it all out. And we should.

But if we ever forget that we are animals and if we forget to dance, all that we figure out will not be for us but for our sedation.

Math Sympathy

My wife started the Math Academy diagnostic on Sunday night. She couldn’t remember that if you raise a number to the 0th power, you get 1.

Her frustration instantly reminded me of being a kid and getting mad at math.

She was annoyed because she couldn’t see the intuition behind “if I multiply something by itself zero times, I get… one?”

I don’t get that either. Rather than look it up, I figured we could “prove” that this must be true based on rules that feel more visible.

Here’s how I tried to make sense of it from basics:

I asked her what 2² * 2³ was — something she could manually see as 4×8=32.

Then I said “Represent 32 using the same base of 2”.

She got 2⁵.

I had her write down what we did so far:

2² * 2³ = 2⁵

So what’s the pattern?

“That you add the exponents when you multiply?”

Right — as long as the base is the same.

But here’s the key part: she basically derived the rule herself from observation. And that matters. Most of us don’t like to accept rules “just because.”

So from there I ask what’s: 2³ * 2⁻³?

Add the exponents… 2⁰

But we know, by definition, that 2⁻³ = 1/2³

So:

2³ * 2⁻³ = 8 * 1/8 = 1

So 2⁰ MUST also be 1.

There’s no intuition here—but it follows inevitably from the basic definitions we already accept.

Back to sympathy for the learner…

She still felt annoyed even though she followed the chain. I remember being frustrated as a kid: you can see how it works, but it’s not intuitively satisfying.

As I’ve gotten older, I’ve grown more patient with “I don’t get the intuition, but I see why this rule must be true given the rules I know are inviolable.”

But when you’re young, or new to a topic, it’s easy to get bogged down by “not getting the why.” You don’t yet have the faith that a little time, a few reps, or a fresh look on another day will eventually give you that satisfying resolution in your head.

Without that faith, you feel like you’re following a recipe blindly. Which is, of course, why my wife was annoyed. She doesn’t want to rely on arbitrary memorized rules. When you feel that way, you don’t feel confident — you don’t feel like you could re-derive the rule if you needed to.

It feels like an assault on your independence or intelligence.

Anyway, this is just a thought I had because I totally commiserate with that frustration in numeracy, and this little back-and-forth dominated Sunday night’s family dinner conversation.

By the way, I still haven’t looked up “intuitive explanations for why raising numbers to the zero power equals 1,” but the proof-by-necessity — the “how could it be otherwise?” style — is satisfying enough for me not to care.

a financial death wish

A friend was asking me how to deal with a loved one who had put nearly all of his assets into a particular volatile stock and done very well. So far. The person is in their 30s with a family and my friend is concerned that if things go the other way this could be the type of thing the household might not recover from.

I asked the basic questions which of course my friend also asked. What’s your plan if the stock falls? “Probably buy more”.

Do you have a target where you’d be willing to sell any of the shares? “If it doubles again, I can retire so nothing before then.”

We can sit here and talk about risk management and yadda yadda. But I’m gonna share something personal which makes me think this has nothing to do with rational finance thought.

I’m close with people that have been taken in by pretty obvious scams. All the red flags. But the people I know are smart people. People that can compute an interest rate and all. They don’t tell me about the “great opportunity” because they know I’ll plead with them to not do it.

Predictably, they get burned. (I’m not supposed to know that because they don’t want to hear I told you so. But I know.)

They fall for this because they want to believe so badly that their better judgement doesn’t stand a chance. I’m totally nonplussed by this. It’s fascinating that we are capable of this. It explains quite a lot, good and bad, actually. But it’s not suprising if you pay attention.

But here’s the part that I found surprising and discovered on a lark.

In the aftermath of the scam, I spent 2 hours on the phone with a victim. I was standing in my kitchen of the last house. Beautiful day outside. Brutal conversation. Emotional. Just trying to make sense of it in a way where we could at least salvage some vague sense of growth out of the closure. At the tail end of our call, I asked a question that I still find peculiar but somehow felt appropriate:

“Did you need to lose that money?”

Silence.

I could hear them think.

“Maybe”.

We talked about it. There was nothing that could have been done. No warning I could have given would have talked them out of it. They admit to that.

I think about this a lot.

I told my friend whose concerned about their loved one this story. And the friend’s face dropped. They know what they’re up against.

(We actually came up with 2 proposals that he could bring to the loved one to change the shape of this death wish, we’ll see if either find reception.)

Anyway, as BTC has been dropping, this thread has been on my mind because there are a lot of cult leaders who benefit from persuasion but aren’t accountable to their followers’ families if they’re wrong.

I’ll just leave you with a tweet I sent Tuesday:

Sitting down at a table without a budget is a commitment to playing til you’re wiped out.

slow is smooth and smooth is fast

I really hope to be helpful today so bear with me as this isn’t the rosiest way to begin.

This tweet halted my scroll:

For whatever reason, AOL (what year is this?) has an unpaywalled copy of the article:

A Recipe For Idiocracy

It’s short, but let me pull an excerpt anyway:

For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment. Schools across the country have been lowering standards and removing penalties for failure. The results are coming into focus.

Five years ago, about 30 incoming freshmen at UC San Diego arrived with math skills below high-school level. Now, according to a recent report from UC San Diego faculty and administrators, that number is more than 900—and most of those students don’t fully meet middle-school math standards. Many students struggle with fractions and simple algebra problems. Last year, the university, which admits fewer than 30 percent of undergraduate applicants, launched a remedial-math course that focuses entirely on concepts taught in elementary and middle school. (According to the report, more than 60 percent of students who took the previous version of the course couldn’t divide a fraction by two.) One of the course’s tutors noted that students faced more issues with “logical thinking” than with math facts per se. They didn’t know how to begin solving word problems.

The university’s problems are extreme, but they are not unique.

The article drones on. None of it uplifting.

“We call it quantitative literacy, just knowing which fraction is larger or smaller, that the slope is positive when it is going up,” Janine Wilson, the chair of the undergraduate economics program at UC Davis, told me. “Things like that are just kind of in our bones when we are college ready. We are just seeing many folks without that capability.”

Here’s Jared’s firsthand experience as a teacher while quoting that article:

This should remind you of this quiz from 2 weeks ago…

Victor Haghani referring to the quiz (emphasis mine):

It is well-known (and disturbing) that the financial literacy of this audience is, on average, quite low – as evidenced by a mean score of 56% (yes, that would be an “F” if not graded on a curve) on the below five-question quiz, known as the “Big Five” test by researchers. A survey conducted in 2021 found that less than one third of respondents answered at least four of them correctly, the threshold researchers define as “high financial literacy.” At least as concerning as the low test scores is the fact that the scores themselves have fallen dramatically between 2009 and 2021.

Are you seeing a pattern?

The useless question is “why” all this decline. Is it the phones, social media, microplastics, fluoride, the mentality that “kindergarten is the first step to Harvard” is less about upholding standards and more about suing teachers who give bad grades (just scroll thru the results)?

Probably all of them, I don’t know.

And then you have this response to Jared from our mutual friend:

The public discourse amplified by the rich and powerful is tuned to spread to the lowest common denominator. So the average person notices that rich people sound stupid and mistakes the mask for the face. The spread of information has also made corruption more obvious. That Trump’s favors are openly for sale is celebrated by his defenders as transparency. “They were all doing this, at least now we can see it”.

Fine.

I’ll let you keep that defense, but it’s hard to hear that without also hearing “we should all be allowed to crime”. Populism brings some unintentional equilibria I suppose. [I’m warming up to the idea of paying all politicians a salary of $2mm/year but making them truly public servants. All your financial affairs on full display. The fact that Congress can insider trade tells me we are so far from accountability with teeth.]

Adam’s observation is an instance of the current hypernym: honesty is for suckers.

Don’t get me wrong. This is a permissible instinct as trust in institutions disintegrates. But we risk some baby/bathwater mistakes if we malign all institutional failure as rot from within (university-industrial complex) rather than the natural difficulty of keeping up with accelerating times (securities regulation). Human affairs, the realm of politics and coordination, don’t move as fast the electrons re-shaping power and that impedance mismatch is a source of static. But that’s not nefarious. It’s just social physics.

That was a long digression to land me back where I was headed anyway — “be dumber” is an overfit to a moment we are all struggling to understand. It’s a retreat from responsibility. A cop-out. Hopium that there’s a quick way to get above this fray, shielded from the stray bullet from any of cultural ails lurking below the seemingly healthy SPX price.

I’m sorry but you can’t fake A yourself to flourishing. The flourishing is a by-product of the wax-on, wax-off. Confidence in your competence. Having some real to offer. There’s no “getting through this moment” because life is just one of these moments after another. So tie yourself to the mast of self-efficacy and it will all feel calmer.

If you tell me we’ve gained something from the loss of standards above, I’ll listen. But what hasn’t changed is you need something to offer. Society is not your parents. It doesn’t love you unconditionally. It’s hard to make beneficial choices if basic literacy and numeracy isn’t automatic. “I’ll just ask the LLM”. Well, knowing how to ask good questions itself takes intelligence and learning.

[Personal conviction…I think the quality of someone’s questions is a strong indicator of their thinking skills. This is pretty obvious if you spend too much time on X, but a universal example is to think about the last time a child asked you a question that had you go, “Damn, smart kid”. A know-it-all like the nasal boy in Polar Express comes off as obsessive, maybe smart, definitely annoying (although not a crime). But asking the right question reveals layers. For the finance heads, it’s why Jane Street uses this prompt in interviews — see thread. To just give an answer is to misunderstand the exercise.]

Ok, so the trends in reading and math say we are less and less prepared to engage in sophisticated reasoning. And we acknowledge that reasoning is important because it’s the basis of decisions and decisions are the bridge between our internal selves and our physical experiences and conditions.

How do we reverse the trends?

I don’t have an answer for society but I do have answers for you. And your family. And your friends. (“Hey, doesn’t that scale up to society?” That’s cute, did you just arrive from Mars?)

The answer has 2 facets and since we started in the context of math we will stick with it, but I don’t think it’s limited at all to math.

1) The belief that the process of learning itself makes you smarter

We all have potential. Just like in sports. You can’t be Usain Bolt but you can always get closer to your ceiling. We choose which domains to try to move closer to our ceilings since we can’t work on everything. We prioritize based on goals. Fitness, chess, cooking.

Math and literacy touch everything, whether you want them to or not. We are all touched by deals, contracts, transactions, even if we just want to paint. Youth is the rare stage of life where there is time carved out specifically for upskilling your general-purpose machinery of abstract thought, the manipulation of symbols, and the ability to maintain a chain of ideas inside one brain. I’m not sure if the appeal of doing so is universal, but the fact that games and puzzles are not compulsory and in fact pulled, not pushed, suggests that there is something intrinsic about cognitive self-improvement. Fostering this urge requires no justification beyond “it’s fun” but it happens to have salutory effects across your mental wetware and let’s face it, your job prospects, if you insist on being purely practical.

So this gift of time that children are afforded is when the skill of skill acquisition should be taught. I emphasize this because school is treated not as a place where we acquire skills but a place to trot them out for approval. The difference is insidious. As you traverse the years, it’s not what did you master, it’s what grade did you get? There’s really no emphasis on mastery. It’s just “did you go through the motions” for most, and then for the top students, who may or may not have achieved any type of mastery (and if they did it wasn’t to the school’s credit), the school is just a sorting hat. And with grade inflation a bad one at that, making students (and their parents) feel like college admissions is plinko.

My HS diploma-only mother emphasized school because education was the path to a better life. But she specifically stressed math because she thought it literally made you smarter. Her opinion is backed by nothing but intuition and self-flattery (she was a strong math student). But Ced, whose practice and writing is maniacally obsessed with the art and science of getting good at things and separating b.s. that sounds like it works from what actually works in complex domains, sent me a link to mathematician David Bessis’ interview with Russ Roberts:

🎙️A mind-blowing way of looking at math (Econtalker)

Bessis echoes what my little immigrant mom said. In describing what we need to do differently in teaching math, he argues we must not mince words to motivate:

I think teachers should be bold. They should say, ‘It makes you smarter.’”

More:

People hate math because they view it as an IQ test that they’re failing. And, it’s not a test. It’s a technique to get smarter.

If you’re failing, it’s normal because you start. When you start any new sport, you suck at it. There’s no way you’re going to be good on Day One. Just because a two-year-old is babbling, you don’t say: Well, I guess he’ll never learn to speak, but we just won’t bother teaching him language because he’s not good at it. And yet, we do that with math. We say, ‘Well, he’s not a math person. He’s not good at math.’

You cannot teach mathematics to kids who are convinced that your mathematical ability is something that is static… A combination of confusion about the nature of mathematics, and confusion about how the brain operates, and confusion about the origin of the shocking gap of abilities that are visible on a given day in a given high school makes us believe that this thing is entrenched and you’re not going to be able to change it. But it’s not true.

The failure of teaching mathematics—and it’s something that has been going on for not just centuries, but actually millennia—is the failure to admit that we do things in our head. We play with our intuition, we play with images, and these things have traditionally not even been discussed as being part of mathematics.

At school, you enter the room with your intuition, and the teacher is telling you that your intuition is wrong; and you reach your conclusion that intuition is bad and that you’re stupid. But, the thing is, it’s wrong, but it’s not going to be wrong forever. You will gradually evolve your intuition if you confront it with this very special apparatus that is logical formalism.

Mathematics is a technique that, if you learn how to master the technique itself, you will develop your intelligence; you will utilize your brain in a way that you would not be able to otherwise.

But this is really cutting to the heart of my mother’s hunch, which she couldn’t articulate:

I knew when I was a mathematician that what was really interesting to me was not the mathematics: it’s that kind of meta-cognition that you have to learn to become a mathematician. And this is the topic of the book. What do you do inside your head when you become better at mathematics?

It’s worth mentioning that much of the interview is spent on intuition and what Bessis, playing on Kahneman, calls System 3 thinking:

Whenever you catch your intuition red-handed being wrong at something, don’t throw that away. Don’t reject the intuition… Explore it. Try to unpack it… do back and forth until they agree. It may take you five minutes, one hour, a day, a week, a year, 10 years, 50 years.

Bessis argues that this process of confronting incorrect intuition is a uniquely valuable habit because it creates a highly memorable learning stimulus. This rings so true personally. When something goes wrong, when you are snapped out of autopilot, or surprised, the lesson you learn sticks with you.

His last inversion, namely, that math is not a test of smartness but it makes you smarter is a hokey story of being intimidated when Bessis noticed legendary mathematician Jean-Pierre Serre in the audience. After the Bessis talk, Serre said he’d need to repeat the talk because he “didn’t understand a word of it”. Serre was being sincere. Bessis noticed that most people would not admit to incomprehension so easily. And while it’s much easier to do so if you are Serre, whose capabilities are beyond reproach, Bessis wondered:

“Maybe with that attitude, you can become Jean-Pierre Serre.”

Ok, so the first step to improving our abilities in math (or literacy) is believing it’s possible and worthwhile.

The next step is to know how to actually acquire the skills.

2) Skill development is not the same as education

School is time-based education. You do X in 4th grade, Y in 5th and so forth. There’s some acceleration but it doesn’t stretch as far as individual variation because the range would be too wide to contain in a single classroom. The compression hurts not only the top performers but the bottom performers who are hanging on for dear life only to be waved through to the next grade, where the deficiencies compound.

Skill development is rooted in learning science. You are far more likely to have encountered its prescriptions in sports or music than school. I encapsulate a lot of that information in The Principles of Learning Fast. But today I want to zoom in specifically on our foundations because it’s an actionable target if you are insecure about your knowledge and how to go about learning to mastery since you may have never realized that was an option. How could you have realized that…there’s a test tomorrow you need to study for even though you don’t understand the material from last week’s test, right? It’s not your fault but hopefully what you’re about to learn can serve you and your loved ones going forward.

I’m going to let Alpha School’s Joe Leimandt be the messenger. The following flow comes from an interview he did with Patrick O’Shaughnessy.

🎙️Building Alpha School, and The Future of Education (Colossus)

1) Knowledge is hierarchical

Most of knowledge is hierarchical where it’s based on foundation. Algebra is basically advanced fraction manipulation. Fractions is multiplication and division. And you can just keep going down the tree where you have to actually learn bottom-up and have mastery.

2) Well, what is mastery?

Think of a sports analogy like in basketball. If you’re the point guard and you lose the ball 30% of the time going down the court, the coach is not going to be like, hey, let’s work on the alley-oop. They’re going to be like, okay, let’s get back to the basics and master the basics so you can get down the court.

Have you mastered the basics? How good are you? We always talk about in standard school, there’s a whole set of things that 70%—you’re passing, you don’t know 30% of the material, and then they move you on to more advanced things.

This is pretty obvious stuff. You know how this feels:

3)The Swiss Cheese Problem

The problem’s not the algebra, it’s the prior knowledge… if you’re pushing people up and they’ve only learned 70 or 80% of the curriculum, you should think it’s like Swiss cheese. It’s like you’re building a foundation with all these holes. And then eventually as you get high enough, it just gets too much and it collapses and you can’t learn anymore.

4) Going Back to 3rd Grade

If you’re doing fractions and you haven’t mastered division, you’re going to sit there and say, God, this fraction problem is really hard. But the real issue is, well, just go back and learn your division and then the fraction’s going to be easier.

We have one student who was, this is sort of a unique, an extreme example and I hesitate to say it but we had a student who was 740 on the math SAT and in looking they were making careless errors. Some of the problems they were overloading working memory and for whatever reason the student didn’t have fluency of multiplication and division tables. So we literally sent her back to third grade math.

We’re the only school in the world who will take a 740 math SAT student go back to third grade, send back and she got a 790, a 790. And it’s that kind of thing where when you talk about the science of learning and just I say it this way, the parent and the student in this case were not excited that their 740 math student is being given third grade problems. That can’t be the issue, but it is. It is, because you’re overloading the working memory and she’s just making careless mistakes.

My eldest is 12. I keep telling him that the form on his basketball shot is off. He finally asked me to show him a video of him shooting. After seeing it, HE decided he wanted to correct it. He understands it’s a step back to go forward. I gave him tremendous praise for the decision because it’s not easy to make choices like that. It’s an investment in the bigger picture

[He’d like be able to make the HS team and it’s gonna be competitive. His current shot won’t cut it, especially since I don’t expect he’ll be very tall.]

My wife is going to start Math Academy because she sees the kids’ work and, well, there’s lots of swiss cheese in her knowledge. She decided that didn’t sit well with her. The kids asked her what level of math she’s gonna rebuild from and while the diagnosttic will place her, she has no shame about however far it suggests. The 12-year-old would bet he’s ahead and she’s not taking the other side of that.

Everyone is anxious about time. Finish so you can get to the next thing and the next thing. I’m very sympathetic. Things just feel like a race. Business is often a race. It’s hard to backfill expertise or keep up with all the cool new stuff when you’re putting out fires. So I don’t know to what extent we as adults can choose mastery for ourselves. I don’t pretend to know your constraints. But when it comes to the kids, I urge you to think about this stuff. You know what it’s like to have swiss-cheese in your foundation. Holes are not totally avoidable. But rushing to check off “done” is training for a life of cramming. Of seeing a stimulus to grow as an obstacle to relaxation rather than an opportunity to expand your capacity to offer something to others.

That’s a real goal. Not a fake one. Getting there takes as long as it takes for you. But once you’re there you can’t be shaken because the foundation is rock solid. The title of today’s letter is hook to remind you:

Slow is smooth, and smooth is fast

There’s no shortcut to smooth.

Moontower#294

Friends,

I really hope to be helpful today so bear with me as this isn’t the rosiest way to begin.

This tweet halted my scroll:

For whatever reason, AOL (what year is this?) has an unpaywalled copy of the article:

A Recipe For Idiocracy

It’s short, but let me pull an excerpt anyway:

For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment. Schools across the country have been lowering standards and removing penalties for failure. The results are coming into focus.

Five years ago, about 30 incoming freshmen at UC San Diego arrived with math skills below high-school level. Now, according to a recent report from UC San Diego faculty and administrators, that number is more than 900—and most of those students don’t fully meet middle-school math standards. Many students struggle with fractions and simple algebra problems. Last year, the university, which admits fewer than 30 percent of undergraduate applicants, launched a remedial-math course that focuses entirely on concepts taught in elementary and middle school. (According to the report, more than 60 percent of students who took the previous version of the course couldn’t divide a fraction by two.) One of the course’s tutors noted that students faced more issues with “logical thinking” than with math facts per se. They didn’t know how to begin solving word problems.

The university’s problems are extreme, but they are not unique.

The article drones on. None of it uplifting.

“We call it quantitative literacy, just knowing which fraction is larger or smaller, that the slope is positive when it is going up,” Janine Wilson, the chair of the undergraduate economics program at UC Davis, told me. “Things like that are just kind of in our bones when we are college ready. We are just seeing many folks without that capability.”

Here’s Jared’s firsthand experience as a teacher while quoting that article:

This should remind you of this quiz from 2 weeks ago…

Victor Haghani referring to the quiz (emphasis mine):

It is well-known (and disturbing) that the financial literacy of this audience is, on average, quite low – as evidenced by a mean score of 56% (yes, that would be an “F” if not graded on a curve) on the below five-question quiz, known as the “Big Five” test by researchers. A survey conducted in 2021 found that less than one third of respondents answered at least four of them correctly, the threshold researchers define as “high financial literacy.” At least as concerning as the low test scores is the fact that the scores themselves have fallen dramatically between 2009 and 2021.

Are you seeing a pattern?

The useless question is “why” all this decline. Is it the phones, social media, microplastics, fluoride, the mentality that “kindergarten is the first step to Harvard” is less about upholding standards and more about suing teachers who give bad grades (just scroll thru the results)?

Probably all of them, I don’t know.

And then you have this response to Jared from our mutual friend:

The public discourse amplified by the rich and powerful is tuned to spread to the lowest common denominator. So the average person notices that rich people sound stupid and mistakes the mask for the face. The spread of information has also made corruption more obvious. That Trump’s favors are openly for sale is celebrated by his defenders as transparency. “They were all doing this, at least now we can see it”.

Fine.

I’ll let you keep that defense, but it’s hard to hear that without also hearing “we should all be allowed to crime”. Populism brings some unintentional equilibria I suppose. [I’m warming up to the idea of paying all politicians a salary of $2mm/year but making them truly public servants. All your financial affairs on full display. The fact that Congress can insider trade tells me we are so far from accountability with teeth.]

Adam’s observation is an instance of the current hypernym: honesty is for suckers.

Don’t get me wrong. This is a permissible instinct as trust in institutions disintegrates. But we risk some baby/bathwater mistakes if we malign all institutional failure as rot from within (university-industrial complex) rather than the natural difficulty of keeping up with accelerating times (securities regulation). Human affairs, the realm of politics and coordination, don’t move as fast the electrons re-shaping power and that impedance mismatch is a source of static. But that’s not nefarious. It’s just social physics.

That was a long digression to land me back where I was headed anyway — “be dumber” is an overfit to a moment we are all struggling to understand. It’s a retreat from responsibility. A cop-out. Hopium that there’s a quick way to get above this fray, shielded from the stray bullet from any of cultural ails lurking below the seemingly healthy SPX price.

I’m sorry but you can’t fake A yourself to flourishing. The flourishing is a by-product of the wax-on, wax-off. Confidence in your competence. Having some real to offer. There’s no “getting through this moment” because life is just one of these moments after another. So tie yourself to the mast of self-efficacy and it will all feel calmer.

If you tell me we’ve gained something from the loss of standards above, I’ll listen. But what hasn’t changed is you need something to offer. Society is not your parents. It doesn’t love you unconditionally. It’s hard to make beneficial choices if basic literacy and numeracy isn’t automatic. “I’ll just ask the LLM”. Well, knowing how to ask good questions itself takes intelligence and learning.

[Personal conviction…I think the quality of someone’s questions is a strong indicator of their thinking skills. This is pretty obvious if you spend too much time on X, but a universal example is to think about the last time a child asked you a question that had you go, “Damn, smart kid”. A know-it-all like the nasal boy in Polar Express comes off as obsessive, maybe smart, definitely annoying (although not a crime). But asking the right question reveals layers. For the finance heads, it’s why Jane Street uses this prompt in interviews — see thread. To just give an answer is to misunderstand the exercise.]

Ok, so the trends in reading and math say we are less and less prepared to engage in sophisticated reasoning. And we acknowledge that reasoning is important because it’s the basis of decisions and decisions are the bridge between our internal selves and our physical experiences and conditions.

How do we reverse the trends?

I don’t have an answer for society but I do have answers for you. And your family. And your friends. (“Hey, doesn’t that scale up to society?” That’s cute, did you just arrive from Mars?)

The answer has 2 facets and since we started in the context of math we will stick with it, but I don’t think it’s limited at all to math.

1) The belief that the process of learning itself makes you smarter

We all have potential. Just like in sports. You can’t be Usain Bolt but you can always get closer to your ceiling. We choose which domains to try to move closer to our ceilings since we can’t work on everything. We prioritize based on goals. Fitness, chess, cooking.

Math and literacy touch everything, whether you want them to or not. We are all touched by deals, contracts, transactions, even if we just want to paint. Youth is the rare stage of life where there is time carved out specifically for upskilling your general-purpose machinery of abstract thought, the manipulation of symbols, and the ability to maintain a chain of ideas inside one brain. I’m not sure if the appeal of doing so is universal, but the fact that games and puzzles are not compulsory and in fact pulled, not pushed, suggests that there is something intrinsic about cognitive self-improvement. Fostering this urge requires no justification beyond “it’s fun” but it happens to have salutory effects across your mental wetware and let’s face it, your job prospects, if you insist on being purely practical.

So this gift of time that children are afforded is when the skill of skill acquisition should be taught. I emphasize this because school is treated not as a place where we acquire skills but a place to trot them out for approval. The difference is insidious. As you traverse the years, it’s not what did you master, it’s what grade did you get? There’s really no emphasis on mastery. It’s just “did you go through the motions” for most, and then for the top students, who may or may not have achieved any type of mastery (and if they did it wasn’t to the school’s credit), the school is just a sorting hat. And with grade inflation a bad one at that, making students (and their parents) feel like college admissions is plinko.

My HS diploma-only mother emphasized school because education was the path to a better life. But she specifically stressed math because she thought it literally made you smarter. Her opinion is backed by nothing but intuition and self-flattery (she was a strong math student). But Ced, whose practice and writing is maniacally obsessed with the art and science of getting good at things and separating b.s. that sounds like it works from what actually works in complex domains, sent me a link to mathematician David Bessis’ interview with Russ Roberts:

🎙️A mind-blowing way of looking at math (Econtalker)

Bessis echoes what my little immigrant mom said. In describing what we need to do differently in teaching math, he argues we must not mince words to motivate:

I think teachers should be bold. They should say, ‘It makes you smarter.’”

More:

People hate math because they view it as an IQ test that they’re failing. And, it’s not a test. It’s a technique to get smarter.

If you’re failing, it’s normal because you start. When you start any new sport, you suck at it. There’s no way you’re going to be good on Day One. Just because a two-year-old is babbling, you don’t say: Well, I guess he’ll never learn to speak, but we just won’t bother teaching him language because he’s not good at it. And yet, we do that with math. We say, ‘Well, he’s not a math person. He’s not good at math.’

You cannot teach mathematics to kids who are convinced that your mathematical ability is something that is static… A combination of confusion about the nature of mathematics, and confusion about how the brain operates, and confusion about the origin of the shocking gap of abilities that are visible on a given day in a given high school makes us believe that this thing is entrenched and you’re not going to be able to change it. But it’s not true.

The failure of teaching mathematics—and it’s something that has been going on for not just centuries, but actually millennia—is the failure to admit that we do things in our head. We play with our intuition, we play with images, and these things have traditionally not even been discussed as being part of mathematics.

At school, you enter the room with your intuition, and the teacher is telling you that your intuition is wrong; and you reach your conclusion that intuition is bad and that you’re stupid. But, the thing is, it’s wrong, but it’s not going to be wrong forever. You will gradually evolve your intuition if you confront it with this very special apparatus that is logical formalism.

Mathematics is a technique that, if you learn how to master the technique itself, you will develop your intelligence; you will utilize your brain in a way that you would not be able to otherwise.

But this is really cutting to the heart of my mother’s hunch, which she couldn’t articulate:

I knew when I was a mathematician that what was really interesting to me was not the mathematics: it’s that kind of meta-cognition that you have to learn to become a mathematician. And this is the topic of the book. What do you do inside your head when you become better at mathematics?

It’s worth mentioning that much of the interview is spent on intuition and what Bessis, playing on Kahneman, calls System 3 thinking:

Whenever you catch your intuition red-handed being wrong at something, don’t throw that away. Don’t reject the intuition… Explore it. Try to unpack it… do back and forth until they agree. It may take you five minutes, one hour, a day, a week, a year, 10 years, 50 years.

Bessis argues that this process of confronting incorrect intuition is a uniquely valuable habit because it creates a highly memorable learning stimulus. This rings so true personally. When something goes wrong, when you are snapped out of autopilot, or surprised, the lesson you learn sticks with you.

His last inversion, namely, that math is not a test of smartness but it makes you smarter is a hokey story of being intimidated when Bessis noticed legendary mathematician Jean-Pierre Serre in the audience. After the Bessis talk, Serre said he’d need to repeat the talk because he “didn’t understand a word of it”. Serre was being sincere. Bessis noticed that most people would not admit to incomprehension so easily. And while it’s much easier to do so if you are Serre, whose capabilities are beyond reproach, Bessis wondered:

“Maybe with that attitude, you can become Jean-Pierre Serre.”

Ok, so the first step to improving our abilities in math (or literacy) is believing it’s possible and worthwhile.

The next step is to know how to actually acquire the skills.

2) Skill development is not the same as education

School is time-based education. You do X in 4th grade, Y in 5th and so forth. There’s some acceleration but it doesn’t stretch as far as individual variation because the range would be too wide to contain in a single classroom. The compression hurts not only the top performers but the bottom performers who are hanging on for dear life only to be waved through to the next grade, where the deficiencies compound.

Skill development is rooted in learning science. You are far more likely to have encountered its prescriptions in sports or music than school. I encapsulate a lot of that information in The Principles of Learning Fast. But today I want to zoom in specifically on our foundations because it’s an actionable target if you are insecure about your knowledge and how to go about learning to mastery since you may have never realized that was an option. How could you have realized that…there’s a test tomorrow you need to study for even though you don’t understand the material from last week’s test, right? It’s not your fault but hopefully what you’re about to learn can serve you and your loved ones going forward.

I’m going to let Alpha School’s Joe Leimandt be the messenger. The following flow comes from an interview he did with Patrick O’Shaughnessy.

🎙️Building Alpha School, and The Future of Education (Colossus)

1) Knowledge is hierarchical

Most of knowledge is hierarchical where it’s based on foundation. Algebra is basically advanced fraction manipulation. Fractions is multiplication and division. And you can just keep going down the tree where you have to actually learn bottom-up and have mastery.

2) Well, what is mastery?

Think of a sports analogy like in basketball. If you’re the point guard and you lose the ball 30% of the time going down the court, the coach is not going to be like, hey, let’s work on the alley-oop. They’re going to be like, okay, let’s get back to the basics and master the basics so you can get down the court.

Have you mastered the basics? How good are you? We always talk about in standard school, there’s a whole set of things that 70%—you’re passing, you don’t know 30% of the material, and then they move you on to more advanced things.

This is pretty obvious stuff. You know how this feels:

3)The Swiss Cheese Problem

The problem’s not the algebra, it’s the prior knowledge… if you’re pushing people up and they’ve only learned 70 or 80% of the curriculum, you should think it’s like Swiss cheese. It’s like you’re building a foundation with all these holes. And then eventually as you get high enough, it just gets too much and it collapses and you can’t learn anymore.

4) Going Back to 3rd Grade

If you’re doing fractions and you haven’t mastered division, you’re going to sit there and say, God, this fraction problem is really hard. But the real issue is, well, just go back and learn your division and then the fraction’s going to be easier.

We have one student who was, this is sort of a unique, an extreme example and I hesitate to say it but we had a student who was 740 on the math SAT and in looking they were making careless errors. Some of the problems they were overloading working memory and for whatever reason the student didn’t have fluency of multiplication and division tables. So we literally sent her back to third grade math.

We’re the only school in the world who will take a 740 math SAT student go back to third grade, send back and she got a 790, a 790. And it’s that kind of thing where when you talk about the science of learning and just I say it this way, the parent and the student in this case were not excited that their 740 math student is being given third grade problems. That can’t be the issue, but it is. It is, because you’re overloading the working memory and she’s just making careless mistakes.

My eldest is 12. I keep telling him that the form on his basketball shot is off. He finally asked me to show him a video of him shooting. After seeing it, HE decided he wanted to correct it. He understands it’s a step back to go forward. I gave him tremendous praise for the decision because it’s not easy to make choices like that. It’s an investment in the bigger picture

[He’d like be able to make the HS team and it’s gonna be competitive. His current shot won’t cut it, especially since I don’t expect he’ll be very tall.]

My wife is going to start Math Academy because she sees the kids’ work and, well, there’s lots of swiss cheese in her knowledge. She decided that didn’t sit well with her. The kids asked her what level of math she’s gonna rebuild from and while the diagnosttic will place her, she has no shame about however far it suggests. The 12-year-old would bet he’s ahead and she’s not taking the other side of that.

Everyone is anxious about time. Finish so you can get to the next thing and the next thing. I’m very sympathetic. Things just feel like a race. Business is often a race. It’s hard to backfill expertise or keep up with all the cool new stuff when you’re putting out fires. So I don’t know to what extent we as adults can choose mastery for ourselves. I don’t pretend to know your constraints. But when it comes to the kids, I urge you to think about this stuff. You know what it’s like to have swiss-cheese in your foundation. Holes are not totally avoidable. But rushing to check off “done” is training for a life of cramming. Of seeing a stimulus to grow as an obstacle to relaxation rather than an opportunity to expand your capacity to offer something to others.

That’s a real goal. Not a fake one. Getting there takes as long as it takes for you. But once you’re there you can’t be shaken because the foundation is rock solid. The title of today’s letter is hook to remind you:

Slow is smooth, and smooth is fast

There’s no shortcut to smooth.

Money Angle

A friend was asking me how to deal with a loved one who had put nearly all of his assets into a particular volatile stock and done very well. So far. The person is in their 30s with a family and my friend is concerned that if things go the other way this could be the type of thing the household might not recover from.

I asked the basic questions which of course my friend also asked. What’s your plan if the stock falls? “Probably buy more”.

Do you have a target where you’d be willing to sell any of the shares? “If it doubles again, I can retire so nothing before then.”

We can sit here and talk about risk management and yadda yadda. But I’m gonna share something personal which makes me think this has nothing to do with rational finance thought.

I’m close with people that have been taken in by pretty obvious scams. All the red flags. But the people I know are smart people. People that can compute an interest rate and all. They don’t tell me about the “great opportunity” because they know I’ll plead with them to not do it.

Predictably, they get burned. (I’m not supposed to know that because they don’t want to hear I told you so. But I know.)

They fall for this because they want to believe so badly that their better judgement doesn’t stand a chance. I’m totally nonplussed by this. It’s fascinating that we are capable of this. It explains quite a lot, good and bad, actually. But it’s not suprising if you pay attention.

But here’s the part that I found surprising and discovered on a lark.

In the aftermath of the scam, I spent 2 hours on the phone with a victim. I was standing in my kitchen of the last house. Beautiful day outside. Brutal conversation. Emotional. Just trying to make sense of it in a way where we could at least salvage some vague sense of growth out of the closure. At the tail end of our call, I asked a question that I still find peculiar but somehow felt appropriate:

“Did you need to lose that money?”

Silence.

I could hear them think.

“Maybe”.

We talked about it. There was nothing that could have been done. No warning I could have given would have talked them out of it. They admit to that.

I think about this a lot.

I told my friend whose concerned about their loved one this story. And the friend’s face dropped. They know what they’re up against.

(We actually came up with 2 proposals that he could bring to the loved one to change the shape of this death wish, we’ll see if either find reception.)

Anyway, as BTC has been dropping, this thread has been on my mind because there are a lot of cult leaders who benefit from persuasion but aren’t accountable to their followers’ families if they’re wrong.

I’ll just leave you with a tweet I sent Tuesday:

Sitting down at a table without a budget is a commitment to playing til you’re wiped out.

Stay groovy

☮️

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