Moontower #192


I’m still in summer travel mode but I stole some time to write homework-type post related to options. I talk about it below.

Otherwise, here are some links:

1) If you wanna follow me on Meta’s Twitter clone that they released this week:

2) With all the travel, I’ve had a chance to hang out with lots of family and friends who are not the terminally online types (sounds healthy). ChatGPT came up in a lot of convos and I thought sharing these links more broadly, especially for people that are not immersed in the discourse, might be useful.

  • 10 Ways You Can Use ChatGPT to Learn Better (Scott H Young)Scott is one of my favorite writers on all things learning. This was a good post for separating what ChatGPT is good and for. The term “word calculator” has stuck with me.
  • GPT Best Practices (Open AI)This interactive document from the creators of ChatGPT gives sugeestion and provides an in-line sandbox for you to practice yourself.

Money Angle

Continuing with the GPT resources:

ChatGPT for Finance: Promise and Peril (Dave Nadig)

Again, I’m just cherry-picking resources from writers and thinkers I trust. Dave put together a really nice guide here, and it assumes no knowledge so even if you tinker a bit some of the background he provides really helps fill in the gaps.

It opens:

Over the past month or so, my inbox and DMs have been flooded with questions about AI, in no small part due to my interview with Professor Stuart Russell at Berkeley and our recent webinar with ROBO Global’s Zeno Mercer and Resolve Asset Management’s Adam Butler. One crystal-clear pattern has emerged. Everyone wants real-world, specific examples of how AI can and can’t enter into an advisor’s, investor’s, or creator’s workflow.

I aim to please. Today, I will peel back the curtain and give concrete examples of how to use ChatGPT effectively to accelerate investment research and content creation. Meanwhile, I’ll also dispel some of the hyperbole around what ChatGPT can and can’t do.

Money Angle For Masochists

This is today’s meat. It’s a long post that includes exercises for the reader. I built it in a modular way so even if you didn’t want to go full brain damage there are useful sections that can stand alone from the whole.

What We Can Learn From Vertical Spreads (Moontower)


First, a self-indulgent remark…

I enjoy helping people learn about options. Not for instrumental reasons like the “world needs more options traders”. But in an appreciative sense — option theory is a rich toolbox for decision-making in investing and life in general. The word “decision” implies an option.

Notwithstanding, the typical person learning about options is thinking instrumentally — “how do I use these things to make money?” Of course, there’s no blog post or even book-sized answer to this question. As any craft goes, there’s basic vocabulary and principles, but these are necessary but insufficient conditions for success. You need years of trial and error to achieve competence.

Since trading/investing is a low signal-to-noise endeavor your epistemology requires strict discipline — the flip side of narrow bid-ask spreads and low-cost trading means your lack of edge can be masked for a long time. You know a loan shark is a bad deal, so you only visit Sleepy Sal as a last resort. But one broken kneecap and your LTV goes to zero. Brutal but honest. Everyone understands the deal.

Meanwhile, Robinhood administers the morphine of hidden fees to lengthen the duration of its most valuable asset — your overconfidence. Robinhood calls itself Robinhood without a hint of irony. They ate the whole wheel of cheese. I’m not even mad, I’m impressed.

Good news

At risk of pollyanna-posting, I’ll propose just getting smarter. If you have read this far you are totally capable of learning. Unsurprisingly, options discourse either tends to one of 2 poles:

  • Physics-esque math geekdom Jargon-heavy complexity certainly has a place in finance but is best ignored as a small ecological niche.
  • The “option premiums are to be sold for passive income” grift I’ve covered why this frame is nonsense ad nauseum hereherehere, and indirectly in almost all my writing.

There is a needle to be thread between these framings.

With no more than HS or even middle school math, you have enough tools to tinker and build intuition alongside your live experimentation. This homework is an example of what I’m talking about.

The purpose of this exercise

I get approached for help with options by retail traders frequently. On the one hand, it puts me in an uneasy situation — I’m not really a fan of people using their precious human capital on a machine that conspires to make you think it’s worth trying when base rates say otherwise. On the other hand, who the hell am I to discourage grown-ups who have read the disclaimers and proceed anyway. On balance, it’s a good thing that card-counting books are on the shelves even if most people who fancy themselves Ed Thorp are delusional about what it takes.

So it goes….my sympathies point to being helpful even if the occasional learner impales themselves. They probably would have anyway and there are more people that will be saved by either re-allocating their attention when they realize this is a grind or shed the misunderstandings that keep them plateaued.

All of this really cuts to the heart of Moontower’s approach to unlocking others: part Zen and The Art Of Options Trading, part shedding misunderstandings.

I can’t give you answers, but I can help rule out wrong answers. In that spirit, this exercise, despite its simplicity, will stimulate growth-inducing reflection.

The origin of this exercise

A reader approached me about a strategy they were exploring. It was familiar because it belonged to the class of strategies I’d describe as “harvesting”. Sell some variation of optionality (cash-secured puts, covered calls, iron condors, strangles, etc), earn steady profits.

This reader is selling downside butterflies on the SP500.

When someone has researched a strategy, they are mentally invested in confirming that it works. So right off the bat, I was heartened by the reader’s honest approach — “Kris, tell me what’s wrong with my strategy?”

It’s a fair question. But it’s not quite the right question.

  1. I haven’t done the work so I’m not in the best position to say whether the strategy is good or bad but more importantly…
  1. The “teach a man to fish” Socratic lesson is to demonstrate the implicit misunderstandings of the reader’s approach. That will lead them to higher-resolution questions that will scaffold their ability to answer the original question.

Part I: Setup

  1. The scenario that underpins the exercise and assumptions are given
  2. I hold the reader’s hand as they build a binomial tree.
  3. The reader prices options on the tree. No option models. Just arithmetic.

Interlude: Discussion About Spreads and Specifically Option Spreads

A word on spread trading in general

Every trade is based on a model of how the world works, even if that model is as basic as “stocks go up on sunny days in Chicago”. Models by definition are simplified representations of how things work.

When we spread trade (buying one instrument and selling a related instrument) we cancel out some amount of model-risk. If our stock valuation model is based on interest rates, when we buy and sell related stocks we are sterilizing the assumptions of model by letting them offset. Of course, not every stock is equally sensitive to interest rates or whatever parameters our model takes, but the principle of offsetting remains substantial.

In the work you did above, you priced options in an actuarial manner based on an easily computable distribution. In the real world, model such as Black Scholes allow us to price options with continuous distributions and with a set of assumptions about how prices evolve. Everyone knows the assumptions break down in real life but the model’s value is not in its accuracy in absolute terms but as a measure or ruler.

If you have a broken scale, it will not represent your weight accurately but it will still be useful for comparing your weight to mine. How we calibrate a function depends on the use case. Similarly, my guitar can be tuned to itself so that it can reproduce a song pleasantly. But as soon as I start playing with others we need to make sure the group is in tune.

💡A word on spread trading in options

An early lesson for options traders is the value of spreads in risk management. I can offset option risks such as exposure to delta, vega, gamma and so on by taking an opposing position in a similar option.

Vertical spreads, where you buy and sell options of different strikes in the same maturity, are terrific examples of this. They allow us to sterilize the impact of bad assumptions in the model itself by reducing the risk to simply distribution. Distributional risks are benign, like over/under bets. The max loss is known and we are insulated from risks like bad interest rate or volatility assumptions.

The closer the strikes are to each other the more the risks offset. As they get further apart the risks increase. We become more vulnerable to discontinuities in our assumptions. Imagine a $100 stock. If I told you that Carl Icahn would make a cash takeover bid of $120 IF the stock dropped below $95 (suppose he knew the board would be far likelier to accept in that scenario) then a naively continuous model would not realize that the 117 strike and 123 strike don’t have a regular relationship to one another. The distribution is not smooth between these points.

The less 2 instruments (or strikes) are related the less insulation you get from model assumptions you get from hedging.

Generally speaking, when we trade narrow vertical spreads or butterflies (which are spreads of spreads — even more insulation) we can say our position is “model-free”. Your risks are more proportional to distributional probability than magnitude which is a more benign circumstance.

Part II: Understanding Vertical Spreads and Butterflies

Quick Refresher on Vertical Spreads

  1. We price call spreads
  2. We price put spreads from the call spreads (as opposed to pricing puts first!)
    This is derived from something call an option “box” — these are usually understood in the context of an alternative to t-bills.

    But they are also the key to understanding put-call parity between vertical spreads!

    The value of a put spread must be equal to:

    The difference between the strikes – the value of the call spread

    To see why, consider the following structures:

    • Long the 100 call, short the 100 put No matter what happens at expiration, you will be buying the stock for $100.
      • If the stock expires above $100, you will exercise the call
      • If the stock expires below $100, you will be assigned on the put

        This position acts exactly like a long stock position and in fact is often referred to as “synthetic stock” or “combo”.

        Let’s consider the opposite position on another strike.

    • Short the 105 call, long the 105 put This is short synthetic stock. No matter what happens, at expiry you will be short the stock at $105. You are short the 105 “combo”.

      Ok, combining these ideas:

      • Long the 100 combo
      • Short the 105 combo
    notion image

    Net result: At expiry, you will buy the stock for $100 and sell it at $105.

    This structure is known as a “box”

    Of course, if you expect to make $5 profit on expiration, in a world where there is no free money, you can expect this structure to cost you the present value of $5 today.

    I can see you wondering “Kris, what the heck does this have to do with put spreads?”

    Look at the picture again.

    notion image

    A box can be decomposed into:

    Long the 100/105 call spread


    Long the 105/10 put spread

    The sum of these structures must equal the value of the box which equals the distance between the strikes!

    Re-arranging: Box – Call Spread = Put Spread

    In our example, the 100/105 call spread is worth $1.85.

    Box – Call Spread = Put Spread

    $5 – $1.85 = $3.15 = 105/100 put spread

    You can use this identity to price all the put spreads simply from knowing the call spreads!

  3. We dive into the pricing of butterflies and appreciate them for what they really are: a spread of spreads!

Part III: Reasoning About Strategies and Extraplolating To Decision-Making In General

This tutorial was a response to a reader who wanted to know if their butterfly selling strategy was sound.

We built a simple binomial stock model to underpin pricing for calls, puts and vertical spreads. Ideally, this exercise, should have helped the reader to isolate what types of questions they to consider to hone in on their ultimate question:

“Does selling butterflies make sense?”

If those questions remain hard to infer then hopefully the subsequent Socratic discussion will help. The flow of the questions should be helpful to anyone engaged in a repeated strategy.

  1. Through a series of exercises, we study the risk and reward of vertical spreads and butterflies
  2. We conclude with inferences and discussion. I’ll re-print 2 sections of that here.

Why you should resist the seduction of high hit rate strategies

If a strategy has a high hit rate, it is operating on a highly skewed trade. Your high hit ratio tells you nothing about whether this strategy is profitable in the economic sense of the word. It takes a very long time/large sample to learn anything about how well you calibrated on low probability events. If something you believe to be a 1% probability is actually a 2% probability you are wrong by 100%. That will be reflected in the payoff space — something that you are accepting 50-1 odds for should demand 100-1 odds. If you insist on conflating positive expectancy with hit rates you could save yourself the headache and just run a martingale strategy in a casino. You’ll have negative edge but you’ll probably win and at least you’ll get some free drinks and a hotel room. I’m not arguing that you have negative expectancy on your skewed strategy, but the burden of proof is on you to prove otherwise and the point is that the more skewed the payoff of the strategy is the worse the epistemological foundation for your conclusions. Which means you can never really push. And if you know today, that you are building a strategy you can’t push too hard, then the question is it worth pursuing in the first place (it’s a bit meta but it feels like another tree with conditional probabilities at the nodes).

Addressing the original reader

The reader who reached said something I’ve heard in various forms:

”I’m selling downside because the market drifts upwards”

By having this exercise mimic this idea by biasing the coin probability to the upside and then pricing the spreads we can see that the market is already assigning a lower probability to the downside.

In real-life, implied skew makes the put spreads worth less; this exercise kluges that. So when you sell those put spreads using “markets go up” logic you are doing the same thing as someone bets on the Nuggets because they’ll probably win — brah, it’s already in the price. Your job is to find why the price is wrong.

From My Actual Life

On my 35th birthday, Yinh and I rolled into the hospital in SF to induce the birth of our first kid. He was stubborn and didn’t want to share a birthday — he came the next day.

This coming week we will celebrate Zak’s 10th birthday. I’ll save the sappiness for the letter I will give him. But as I reflect on the caboose end of the years where his mother and I are the center of his world, the tension of preserving his joy and innocence while preparing him for the future feels like it’s about to go up a notch.

Still, if it wasn’t confusing that would be its own source of worry.

Stay groovy!



I’ll be in LA Thursday with my boy Khe.

Come hang out

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