appreciating diversification

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:

1. Last class’s game ended with a humbling but common result, hinting at a key pillar of investing.
2. We use a few facts to dispel the recency bias that all investors carry with them.
3. They learn what the fundamental nature of stocks predicts about their individual and group behavior.
4. We widen the meaning of diversification beyond stocks, which was extremely easy to do in light of March 2026.
5. 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):

• Spreadsheet Game

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:

Measure Your Own Diversification

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

https://colab.research.google.com/github/Kris-SF/data-pipelines/blob/main/portfolio-vol/portfolio_analysis.ipynb

⚠️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.