# Teaching modern portfolio theory to 10-year-olds

### By Sam Savage

It was all Michael Salama’s fault. The lead tax counsel of Walt Disney and esteemed former board member of non-profit ProbabilityManagement.org, urged us to design an investment contest for high school students based on the SIPmath™ standard. Harry Markowitz, the father of portfolio theory, had consulted on the design, and Morningstar, a leading provider of market research, had provided sample data. But we don’t have immediate access to a high school, and we end up delivering it at a couple of middle schools.

So here I am in a computer lab at Horace Mann School in Beverly Hills, Calif., with 45 minutes to explain portfolio theory to kids ranging in age from 10 to 12, before introducing the contest. I have found that teaching analytical material is easy. The hard part is getting anyone to understand it, and I am nervous. Would the middle schoolers have even heard of investments?

So I ask: “Does anyone know what stocks are?”

There is a pause. Then I am nearly knocked off my feet by a shock wave of energy. Hands waving in the air, kids jumping out of their seats, stories of parents with E-TRADE accounts, one kid saying that Apple was \$250 two years ago but is now at \$500, etc.

Well, that breaks the ice, and I charge ahead with my standard discussion of uncertainty and risk, using a cardboard game-board spinner and a giant pair of dice.

Imagine that someone spins a spinner between 0 and 1, multiplies by \$1 million, and that’s what you win (uncertainty). But you owe the loan sharks \$200,000, so a number less than 0.2 turns you into shark bait (risk). I explain histograms and ask the students to draw one for the spinner after 10,000 spins. Most draw flat, which is correct. Now for the tough one: What if someone spins two spinners and averages the results?

As I look around the room I see an 11-year-old, let’s call him Fred, whose graph is a perfect pyramid. “Why’s that?” I ask.

“Suppose there were only two outcomes,” Fred explains, “high and low. An average of low requires two lows. An average of high requires two highs. But, either high and low or low and high puts you in the middle.”

Stunned, I ask Fred to send me his complete proof of the central limit theorem, so I can compare it to that of Laplace.

I point out to the class that it is like rolling a pair of dice; there are more ways to roll a 7 than a 2 or 12. Many of my Stanford students get this wrong, and even some statisticians.

So what? Less chance of becoming shark bait when you diversify.

I now face the challenge of explaining a subject that stumps most adults: statistical dependence. “Can anyone think of a reason that two stocks would be related?” I ask.

The boy next to Fred departs his seat like a patriot missile, both arms waving. “What if two companies are rivals in the same market?” he says enthusiastically. It is clear to all that when one does well, it is probably at the other’s expense. But now Central-Limit-Fred asks for an example in which two stocks might go up and down together.

“How about Ford and Chrysler,” I suggest, “but in the case when the whole automotive market is coming back from a slump?”

This triggers a brilliant monologue from a third kid concerning the behavior of firms in competitive markets, including copy-catting, leap-frogging and so on. It kills me to do it, but I must cut off this future Nobel Laureate so we can get back on schedule.

I am humbled by the intelligence and ebullience of these kids. And then I am suddenly saddened by the realization that in a few years they will have their brains cauterized by the stultifying college application process. But I digress.

After further discussion and Excel models inspired by Markowitz’s classic 1959 book “Portfolio Selection” [1], I am ready to introduce the contest itself. The workbook, shown in Figure 1, is based on a SIP library derived from Morningstar data. Each time the portfolio is changed, a thousand trials are run, and the results are immediately displayed. The goal is to find a portfolio that minimizes the chance of losing \$5, while maintaining an average return of at least \$120.

Figure 1: The investment investment contest workbook.

So did the kids get this stuff?  Watch a 10-second video and then decide [2].

I repeated this experience at JLS Middle School in Palo Alto, Calif., with similar results. After that session a boy comes up and asks: “Can you imagine a computer program that takes a covariance matrix as input, then tells you which stocks to buy to minimize your risk?” Yes, I can.

Portfolio theory is a special case of what I call the Arithmetic of Uncertainty, which impacts us all from an early age in such common activities as waiting for the bus and running lemonade stands.

Dr. Duane Crum heads up the California branch of Project Lead the Way, a non-profit that partners with public schools, universities and other organizations to promote STEM (Science, Technology, Engineering & Mathematics) education.

“The notion of performing arithmetic with uncertainties is as foundational as the arithmetic of ordinary numbers,” Crum says. “SIPmath makes this accessible to school children, with practical lessons ranging from understanding why it is so hard to get projects done on time to deciding how many boxes of Girl Scout cookies the troop should purchase.”

ProbabilityManagement.org is actively seeking opportunities to add the arithmetic of uncertainty to the K-12 curriculum. Visit ProbabilityManagement.org to learn more.

#### References

1. Markowitz, H. M., “Portfolio Selection, Efficient Diversification of Investments,” John Wiley, 1959.