Moontower #274

Friends,

First of all,

I want to share this amazing podcast episode recommended by musician and fellow option refugee Mat Cashman:

🎙️Bowie, Jazz, and the Unplayable Piano (Spotify)

This year is the 50th anniversary of the highest-selling jazz solo album of all time. The live performance of Keith Jarrett’s Köln concert. The concert should never have happened but in his Cautionary Tales podcast, economist Tim Harford weaves it into research that makes you stop and think about the value of variance in breaking out of local maximums. [In the episode you’ll hear about fascinating RCTs of exams given in different fonts as well as a natural experiment that occurred during the 48-hour London tube strike in 2014.]

The episode, besides being highly entertaining, strikes a similar chord to Wednesday’s post obvious subtle effect. As a matter of evolution and progress, we are long vol — we discard what doesn’t work and retain what does which is how an option works — options benefit from variance. Experimentation, contrived struggle against arbitrary constraints (when you’re guitar instructor tells you — let’s see what happens if you can only play your low E string) and shower thoughts are all non-deterministic learning or growth. The source of “alien” solutions that avail us the possibility of step-change vs incremental progress. Techniques for growth that appeal to our impulse towards coherence or explainability are sensible. But their payoff is limited because their legibility means they will also be overbid.

The willingness to take risk or look foolish or just be a bit weird is paradoxically useful when you’re trying to achieve conventional success.

[Counterrealization I haven’t fully thought out — a lot of risk-coded behavior these days is just herding and therefore is unlikely to come with the rewards you’d want for the risk.]

Harford emphasizes that “injecting randomness” into computer algorithms is common practice in a quest to avoid local maximums. I asked Gemini if RL (reinforcement learning) requires injecting randomness — lo and behold the explore-exploit problem shows up:

Reinforcement Learning (RL) extensively uses concepts of injecting randomness, primarily for the purpose of exploration.

Here’s why and how randomness is used in RL:

• The Exploration-Exploitation Tradeoff: RL agents need to balance exploiting their current knowledge of the environment to get rewards with exploring new actions and states to discover better strategies or higher rewards.
• Preventing Suboptimal Policies: Without exploration, agents might get stuck in local optima and fail to find the best possible strategy.
• Examples:
  • Epsilon-Greedy Strategy: A common method where the agent takes the best-known action most of the time (exploitation), but with a small probability (epsilon), it takes a random action (exploration).
  • Adding Noise to Action Outputs: In continuous control tasks, noise (like Gaussian noise) can be added to the agent’s action outputs to encourage exploration.

I’ve got a pile of dry-erase index cards scattered in my office as I try to organize a long essay of how explore/exploit relates to option theory and decision-making IRL — but the notes only seem to grow — especially when I come across something like this episode.

Nat’s tweet will need to haunt me for another day.

On that note — Happy Father’s Day.

This McSweeney listicle caught me yesterday morning just as I was making coffee and listening to War on Drugs on Spotify’s Fleet Foxes radio (h/t Dave Nadig):

What Your Favorite Sad Dad Band Says About You

Money Angle

 

This week we released the moontower.ai Hedge Ratio tool to both Starter and Pro subs. I recorded a video demonstrating it using Tesla (TSLA) and QQQ (Nasdaq 100 ETF).

It’s practical but also educational (for example understanding how to interpret correlation vs beta).

📌 Key Takeaways:

• The hedge analysis tool provides a visual understanding of asset relationships.
• Discover how correlation and the individual volatility of each “leg” contribute to beta.
• Learn the practical steps to convert beta into a precise hedge ratio.
• Understand idiosyncratic risk – the inherent risk that persists even after a position is hedged.
• Explore the critical impact of correlation on the overall effectiveness of your hedges.
• See how remaining risk ramps up when correlation drops below 0.85.
• Uncover how market makers leverage these concepts to reduce hedging costs while balancing “idio” risk.🧠

Chapters

00:00 – Introduction to Hedge Analysis Tool

02:42 – Understanding Beta and Correlation

06:40 – Exploring Idiosyncratic Risk

12:17 – Practical Application of Hedging Strategies

16:11 – Market Making and Delta Management

22:46 – Correlation and Risk Remaining Insights

Money Angle for Masochists

Thursday’s post the dirties are down the cleans are up took the form of an extended interview question. If you are high-volume professional vol trader, the topic of vol time is fundamental but I don’t see much written about it. I hope my posts on it fill the gap.

For non-pros it probably best serves as a bicycle for the mind or a seed of inspiration but I wouldn’t stress over it. I suspect it does since tweets like this are popular even though I’m pretty sure the engagement on them isn’t coming from a bunch of practitioners in the middle of the trading day:

Most IVs you encounter use a 365-day model. To convert to a 251-day model (or any other tenor model) you multiply by the square root of the DTE ratio.

In the spirit of Thursday’s post and the tweet, I’ll pose 2 “interview-style” questions that can be answered in seconds. They require making a reasonable assumption. I’ll give the questions here, then I’ll post an assumption as a hint after the questions for those who need help forming one. The answers are at the end of the post. (Ignore cost of carry — also if you asked about that you’re way ahead of the game).

You do not need any calculators to answer these (just mental artithmetic).

❓#1: Volatility

It’s the close on Wed. Options expiring next Tuesday and next Friday have the same dirty vol (ie the same vol in your off-the-shelf 365d model). Does one of them have a higher clean vol? Explain. List any assumptions.

❓#2: Price of a straddle

It’s Friday close. Next Friday’s ATM straddle is $5. What price is the Friday ATM straddle expiring in 2 weeks to be the same clean vol? You do not need option calculator.

 

Stay groovy

☮️

Answers to the “interview” questions

Relative to a “dirty” year where each day is treated as equal vol, a “clean” year in which variances passes more slowly over a weekend, the Tuesday expiry has less time to expiry than Friday’s ratio of clean to dirty DTE.

If the model implies the same dirty vol for Tuesday and Friday, we can infer Tuesday must have the higher clean vol bc it has relatively less vol time vis a vis a dirty model.

 

#2: The second Friday straddle must be $7.07

The approximation for an ATF straddle is .8*S*σ*√t

Since there is no cost of carry we can assume ATF straddle = ATM straddle which is what the question asks about.

We don’t know S or σ but the question asserts the same dirty vol for both Fridays.

We know there’s twice as much time to expiry for the 2nd Friday and we know the earlier Friday straddle is $5 so the second Friday straddle can be computed as

$5 * √2 since there’s 2x as much time til expiry.

So the second Friday straddle = $7.07

💡This is one of those useful trader math ideas — for a given vol the price of the straddles only varies by square root of the ratio of DTE. One of those mental arithmetic things I found myself using constantly especially with short-dated options where you’re like “if the 1-week straddle is X, the 2 week is…”. This is also a clue to the degree to which I ditch the idea of “volatility” altogether in near-dated options and “think in straddles” and move sizes. This intuition is habitual but you can also see why it has theoretical support — vega p/l is a less of an influence on short-dated options. Results mostly come down to “how much did this thing move vs how it was priced”.

Returning to the question.

The $7.07 straddle is based on the same dirty vol.

But does that translate to the same clean vol the same as the first Friday straddle?

Yes — the ratio of dirty to clean DTE is the same for both expiries!

 

Moontower Weekly Recap

Posts:

• obvious subtle effect
• the dirties are down the cleans are up