In this issue:
- The “three pitches” rule and a lazy man’s framework for getting in shape
- Things that popped from the Investment Beginnings Lesson #4 — Risk
- Made you an easy online tool to see how much diversification benefit you get from your holdings
Friends,
A couple of good articles that stood out before we get to Money stuff.
How to Apply Pixar’s “Three Pitches” Rule | 3 min read
David Epstein spent a lot of time with Ed Catmull in researching his recent book Inside the Box. He shares a neat practice from Pixar. Directors aren’t allowed to bring one idea, they must develop three. We often fixate on our first idea even though it’s usually not our best (the “creative cliff illusion”). Epstein applied this in writing the new book by writing three different openings for every chapter. Nine of twelve chapters ended up using attempt #2 or #3. He admits this is tedious, but leads to better quality. I’d add that LLMs can ease some of that burden or augment the process by asking them to consider more ideas beyond the 3 you generate yourself.
The Lazy Man’s Guide to Actually Getting in Shape | 60 min read
Jonathan doesn’t publish often these days, but it’s worth subbing; otherwise, you’ll miss a treatise like this. This is 16,000 words, but Jon tells you upfront that you can just read the bolded sentences for a fast version. It’s a moneyball lens on fitness with a decision process that generalizes to any wicked domain, wellness, of course being one of the most wicked. A lot of examples of “think in probabilities”, “make +EV bets with limited downside”, “via negativa”, and toggling confidence when multiple lenses validate an idea (ie personal experience, expert track record, math, what works empirically, science).
Money Angle
This week, I hosted class #4 of the Investment Beginnings for local kids aged 12+.
The series’ materials are here:
https://notion.moontowermeta.com/investment-beginnings-course
This is the specific material for class #4:
- Slides
- Spreadsheet Game (File:duplicate to have your own editable copy)
I also created a web version of the game:
☀️🌧️Sun/Rain Game
While I’ve been doing the series for kids, I think a lot of adults could even benefit. The overall arc of the presentation:
- Last class’s game ended with a humbling but common result, hinting at a key pillar of investing.
- We use a few facts to dispel the recency bias that all investors carry with them.
- They learn what the fundamental nature of stocks predicts about their individual and group behavior.
- We widen the meaning of diversification beyond stocks, which was extremely easy to do in light of March 2026.
- We play a game that makes the implications for portfolios concrete.
While moontower readers span a wide range of investment experience (although overall quite interested in investing and money), here are a few ideas that I hope are presented in ways that might augment even your understanding or at least help you explain to learners in your life.
The most naive strategy is hard to beat
The kids spent Class 3 picking stocks based on a bunch of variables they could sift through, only for the equal-weight benchmark to beat everyone except the team that contrarily concentrated in the highest momentum company that is very much still an enigma to the market (TSLA).
The equal-weight strategy which I just called a monkey (although it’s not random, just dumb) beat 2/3 of the 15 individual stocks themselves.
The reason you shouldn’t be surprised that the naive strategy is hard to beat
Companies eventually die, but indexes shed them before they are in hospice.
Only 17% of the original S&P 500 companies from 1957 survived 50 years. The average company lifespan on the index was 33 years in 1964 — it’s now under 20. Kodak invented the digital camera in 1975 and buried it because of the innovator’s dilemma.
In a crash, stocks remember they’re all stocks.
Diversification works differently in good years than bad ones. In the class data, stocks spread widely in bull years. Then we looked at Jan 2022 to Jan 2023: 13 of 15 stocks fell together, the spread collapsed.
I didn’t want to lean into the word correlation, but I noticed a different way to convey the same idea. The inter-quartile range (IQR) of annual returns was smallest in the worst years. This chart is rich with insight. Notice the IQR’s visually but also how the equal-weight portfolio performed relative to the individual stock and median stock returns each year:
These observations are non-CAPM ways to arrive at the familiar language of diversifiable risk (company-specific stuff you can eliminate for free) and systematic risk (market-wide stuff you can’t diversify away but do get paid to carry). The crash revealed which was which.
If we zoom out from stocks alone, we see a race where the leaders change each year
The Novel Investor quilt shows 15 years of annual returns ranked best to worst across 9 asset classes. The diversified portfolio, that gray-ish bar, never wins a year nor comes in last. Note commodities, gold and BTC are absent from the series.
How do you think they would influence the gray portfolio?
The Sun/Rain Game
This leads to a game where we can build some intuition about the role of non-stock assets in a portfolio.
If you look at the sheet you can see how the kids actually did (I changed the kids names to letters):
The game’s punchline is that owning the anti-correlated asset despite it having a worse expected return than the “good” asset leads to a better long-term portfolio.
But this is so unintuitive that I got a student’s question wrong during the discussion!
I’ll explain the mistake here.
A student asked if we played the game for 100 years instead of just 20 years, if owning the good asset ONLY would have led to the best return. I initially said no, then corrected myself and said yes because it has the higher expected return.
But I was right the first time. The answer is definitely NO.
It comes down to the fact that the good asset has an expected arithmetic return of +5%, BUT it has a negative expected CAGR or geometric return.
The math:
The company is 50/50 to return+40% or -30% in any given year.
.5 x 40% + .5 x -30% = +5%
But over 2 years, you expect 1 up, 1 down. Compounding math:
1.4 x .7 = 98%
You expect to lose 2% over a 2-year sequence of about 1% per year.
Formally, we compute the expected CAGR by multiplying (note how the arithmetic or single period return is added):
1.4^(1/2) * .7^(1/2) – 1 = .9899 -1 = -1%
[The exponents represent the probability of each outcome. If there were 3 outcomes, you’d have 3 terms and the exponents sum to 1.]
In the long run, the good asset destroys value. So you do not want to concentrate in it despite its superior expected arithmetic return.
The CAGR is being killed by volatility drag, which is the asymmetry of the fact that if you lose 30% you need to return 42.9% to get back to even, but the “up” years only return 40%. You are falling behind over time.
The bad asset returns -10% half the time and +8% half the time. It’s a “worse” asset, but it’s less volatile. Taking this quality to its extreme, isn’t this what cash is?
In arithmetic terms, our average return if we allocate to each asset equally is +2% (50% x 5% + 50% x -1%). But that portfolio is less volatile because one stock zigs when the other zags. The diversification cuts the volatility MORE than it cuts the expected return, leading to a better risk/reward!
If we rebalance each year back to an equal-weight portfolio, we “pull” the expected CAGR closer to the expected arithmetic return. It’s the only way we can get close to eating those expected arithmetic returns. Otherwise, they don’t really exist for you over time.
This table is worth staring at:
Here’s a message one of the dads sent me after the class:
Money Angle for Masochists
I made you a tool to compute your portfolio vol and see how much the cross-correlations between your holdings have been reducing total vol from the vol that the individual assets contain. You can tinker by adding ETFs of other asset classes to your equities (ie GLD or USO or TLT etc) to see how they affect the volatility.
If you just want inspiration for an idea, use the tool to compare the Mag 10 index (MGTN) realized volatility with the average realized volatility of its holdings. The index is conveniently equal-weighted, 10% in each name.
Two ways to try this on your own portfolio:
🌐To run in your browser
⚠️Just push through the warning it spits off
The output will includes metrics and charts:
🖥️To run locally
git clone <https://github.com/Kris-SF/data-pipelines.git>
cd data-pipelines/portfolio-vol
pip install -r requirements.txt
jupyter lab portfolio_analysis.ipynb
Either way, edit the WEIGHTS dict and the START / END dates, then Run All.
An Explicit Solution to Black-Scholes Implied Volatility | Wolfgang Schadner
For the past 50 years, implied vols were calculated from option prices and other option inputs numerically. Simple versions use Newton-Raphson or bisection searches. The idea is to “guess” what the implied vol is, call that g*, see what option price that produces, split the difference, and repeat the recipe until you arrive at a price that is within a fraction of a cent of the market price. This method is used because there’s no closed form going from price → vol, only vol → price.
This SSRN paper came out this week and made the rounds quickly. It offers a closed-form approximation, alleging it recovers IV to machine precision ~3.4x faster than the current best-in-class. If it holds up under wider testing in the wild, it’s the kind of thing that ends up in textbooks.
From My Actual Life
My youngest turned 10 yesterday. I wrote him a letter just as I did for my eldest when he turned 10. It can be hard to remember what your kids are like at every phase. But also, it can be hard to remember where you’re at mentally at those ages. You hope the letter becomes a gift they cherish when they are older and can relate to being an adult writing to their child. But looking back at the letter myself will be a time capsule gift for my future self too.
This is an instance of a belief I have come around to as they’ve gotten older. A lot of what I think I do for them I really think is for me. I want to be around them selfishly more so than I think my presence is as important as I’d like to believe.
The possibility that kids do more for you than you for them is better left as a self-effacing end to having children rather than something to weigh before having them. Don’t tell the optimization maxxers.
This Week In The Options Trench
This week Eirk and I disentangle the source of amplified profits and losses
Stay groovy
☮️