Moontower #336

In this issue:

• More AI uses to learn

• The resolution of uncertainty is…bearish?

• Pricing put protection without vol

Friends,

2 quick AI uses before we get to Money Angle.

Socratic Tutor | agent skill

Jane Street open-sourced a single SKILL.md that turns Claude or ChatGPT into a strict tutor. It opens with a diagnostic, scores you 0-5 on each subskill, asks one question at a time, while withholding the answer.

If you get it wrong, it asks progressively narrower questions until you find the hole in your own reasoning. Levels only go up after you prove it twice, once from cold recall, and it ambushes you with review of old material.

Regular Moontower readers will recognize traces of the methods Math Academy uses in its product from “generation” effects, to reinforcement and a nod to spaced repetition.

I beat Jane Street to publishing when I wrote this summer’s Socrates 2026 which, mother of ironies, starts with me flubbing a Jane Street-style interview question! This is the only thing I’m sure I’ve ever beaten them in, and the satisfaction of that moment is already long gone, and to make it even more pathetic, unprofitable.

More in the spirit of open-sourcing:

Every Jane Street resource on the internet | hft.md

If you hate board game rulebooks…

then we can get along. Complex eurostyle board games are no fun to learn or teach. So I recruited ChatGPT to make a custom explainer video for the rules of Brass:Birmingham with some prompts and a PDF of the rulebook.

It took a few iterations to get its “camera” to move without jerking around (but now I have the proper prompt/skill file going forward) and to sync the narration with motion. The iterating process involves having it produce a segment of the explainer to so I don’t obliterate too many tokens without helping it course-correct with my feedback.

This video is just a 30 second segment of the game’s setup phase that preceded building the full tutorial.

Money Angle

There’s No Such Thing as a Stock-Market Bubble | 4 min read

Last week, Jeff Yass, founder of Susquehanna, published an op-ed There’s No Such Thing as a Stock-Market Bubble in the WSJ. It’s the same talk he gave our office in the early 2000s.

In 1999, just as today, when share prices fall, it isn’t a delusion correcting. It’s uncertainty resolving.*

A stock price is the market’s probability-weighted guess under uncertainty. It is perfectly sensible for stock prices to soar in the context of a paradigm shift in technology, and for the most likely outcome to be a negative return or even a zero. The stock’s price is concerned with the expected value, which is probability times outcome. A tiny probability of massive upside will rationally assign a hefty valuation to the stock, but both can be true at once: a sensible expected value and a most likely outcome of zero.

But as Jeff says in the article and I’ve covered repeatedly, the options market will tell you what possible scenarios are driving the valuation. A stock price is a grainy snapshot, but an option surface is a high-definition movie with all of its strikes and expiry dates.

One of the cleaner examples of this comes from commodities pricing. Natural gas prices are vulnerable to winter squeezes. The so-called “widowmaker,” the March-April futures spread, trades as a referendum on winter supply/demand balances. From What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold:

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

Why? Because it has to balance 2 opposing forces.

1. It’s not clear how high the price can go in a true squeeze or shortage

2. The MOST likely scenario is the price collapses back to $3 or $4.

Let me repeat how gnarly this is.

The price has an unbounded upside, but it will most likely end up in the $3-$4 range.

Try to think of a strategy to trade that.

Good luck.

Wanna trade verticals? You will find they all point right back to the $3 to $4 range.

Upside butterflies, which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper), are zeros.

The market places very little probability density at high prices, but this is very jarring to people who see the jacked call premiums.

That’s not an opportunity. It’s a sucker bet.

I kept that last line in the block quote because it made me laugh. It sounds so AI, but this article was written years before ChatGPT was born, and I think Sam Altman owes me shares of OAI.

Anyway, it was comforting to see Jeff affirm 25 years later what I consider to be evergreen knowledge. So much of the value of options comes from being able to understand the shape of risk, which a 2-D stock price fails to convey.

If interested in learning more:

• I wrote about hearing that talk in Option Theory As A Pillar Of Decision-Making

• The best explanation I think I’ve done on the topic is my presentation on Excess Returns The Lie Your Stock’s Price is Telling You.

• And this week’s podcast notes with the Maymin brothers includes current, practical examples of using option surface information to inform position sizing

Money Angle For Masochists

a little exercise in proportion

Here’s a way to think about options that has nothing to do with vol.

Consider a strategy that:

1. Buys a 1-year 15% OTM put on SPX for 3% on Jan 1.

2. Puts the remaining capital in SPX

3. Every Jan 1, rebalances back into that position. So if your put expires in-the-money, you reinvest the proceeds back into SPX, if it doesn’t you sell enough SPX to buy the next year’s protection.

Ask Claude to backtest it for, say, 25 years. It only needs the SPX prices on every Jan 1 because we are not using market-based pricing for the put. We’re just saying it costs 3%

Then compare the performance to just owning SPY unhedged.

The exercise provides a confidence interval for: what premium would you be happy to pay for the put so that you could skip diversifying and just hold 100% SPY plus the insurance policy?

If you run this exercise, you’ll find for anyone with a typical risk preference*:

At 1% it’s a no-brainer.

At 5% it’s meh.

*It’s a bit chaotic to throw the phrase “risk preference” into that sentence so freely, but you can, in the spirit of upgrading your context, learn a lot from Elm Wealth’s whitepaper How We Invest

I posted that thought exercise on X and received a reply I really liked:

The Option Premium

@theoptpremium

@KrisAbdelmessih You don’t even need the backtest to see where it lands. 3% a year for 25 years is 75% of your starting capital spent on insurance. In that stretch, a 15% out-of-the-money put paid off meaningfully in 2008, a little in 2002 and 2022, and nothing in the other 22 years. Add it up…

@theoptpremium · Nov 6, 2026 · View on X

It’s a great example of the type of on-the-fly reasoning one develops when they don’t have the luxury of time.

I’ll rephrase the tweet’s approach in my own way, showing my logic at every step.

1. Which years had a point-to-point return of -18% (the put’s breakeven) or more?

• 2001 or 2002. One of those years, I can’t remember, but if the put paid, it was very small.

• 2008. I’d guess the market was down ~40%, so the put paid (40-18)/3 or about 7x

• 2020. Oh wait, the market didn’t actually finish lower iirc. The put didn’t pay out.

• 2022, it might have paid a small amount

2. Estimating net losses on the put

Let’s be conservative and say the put broke even in the wake of the dot-com era and 2022. So the put loses its full value in 22 years, pushes in 2 years, and makes 7x one-time.

Net net, you lost 15 out of 25 bets or 60% of your premium. If the put costs 3%, the hedge pulls down your arithmetic return by 1.8% per year.

3. What does this mean for the strategy?

Back of the envelope, I’d guess your annual arithmetic return on a naked SPX position for the past generation has been close to 10% and lop off about 1.3% for vol drag* to get a CAGR ~8.7%

This put cost you another 1.8% per year, leaving you with about 8.2% arithmetic but a touch less vol drag because it lowered your volatility. It’s a bit crunchy to import the savings from a 2008 tail event into volatility, which is more descriptive of a distribution’s meat, but a 40% move in variance space is nearly 10x bigger than a typical 15% move, so if you think of 2008 as 10 years, then the GFC represents about ⅓ of the sample in variance time.

Notice, the put doesn’t erase 2008, but it makes the loss much smaller. Without the put, 2008 was down 40%, but with the put, your loss caps at -18%.

Now measure each version as a miss from an average year:

• Unhedged, the average year is about +10%, so −40% is a 50-point miss.

• Hedged, the average year is about +8%, so −18% is a 26-point miss.

Variance cares about miss squared.

50² = 2500.

26² ≈ 676.

676 is about ¼ of 2500.

So the hedged 2008 carries about ¼ of the variance the unhedged 2008 did.

In other words, the put removed ¾ of 2008’s variance!

Since 2008, a single year, carried about ⅓ of the whole sample’s variance, the put removed about ¼ (¾ of ⅓) of the total variance.

I’m going to repeat this for tedious emphasis:

Removing ¾ of the variance for a single giant year out of 25 years removed ¼ of the total variance

¾ of the total variance remains, but since vol is the square root of variance, we need to compute √0.75 ≈ 0.87.

87% of the volatility remains, so vol goes from 16% to about 14%.

Vol drag is half of vol squared: ½ × 0.14² ≈ 1%.

So we get 8.2% arithmetic return with the put minus ~1% of vol drag and we end up with a CAGR of about 7.2%

The put cost 1.8% per year, but because it reduced drag as well, it only lops ~1.5% from CAGR. This represents somewhere between a third and a half of historical equity risk premium. Whether this is worth it or not is in the eye of the beholder, but it doesn’t sound like puts, which we expect to have a premium, are egregiously high.

4. What if the put only cost 1%?

We’ll stay conservative and say you push in 2002 and 2022. But in 2008 you make (40-16)/1 or 24x on the puts. You basically break even on owning the puts and cut off your left tail!

You get better at this the more you practice, but moving in between risk, return, and payoff scenarios like this should not only be fun but inoculate you from the viral disease of fuzzy thinking

Stay groovy

☮️