Money Math

How I Teach Middle Schoolers To Build Stock Portfolios

If you construct a portfolio from 2 stocks and one is $100 and the other is $10, buying a share of each means the first will dominate your portfolio’s risk, assuming they have the same volatility.

If you have $100,000 to invest, you can balance the risk by equal-weighting the holdings: $50k into each stock. You buy 500 shares of A and 5,000 shares of B.

But what if they aren’t the same volatility?

Equal-weighting means the most volatile stocks determine performance. If your $100,000 is split equally between the 2 stocks and A moves 10% per day while B moves 1% per day, you aren’t diversified. Stock A will mostly determine your returns.

We can achieve more balance via equal-risk-weighting, which adjusts how many dollars go into each stock based on its volatility.

Weight each stock by 1/vol:

Stock A gets 1/10
Stock B gets 1/1.

Divide by the total (1/10 + 1 = 1.1) and you get about 9% in A and 91% in B. Stock A is 10x as risky, so it gets about 1/10th the dollars.

On $100,000 that’s roughly $9k of A and $91k of B, corresponding to

91 shares of A
9,100 shares of B

Compared to the equal-dollar portfolio, the equal-risk portfolio requires you’d sell about 409 shares of A and buy about 4,100 shares of B, moving roughly 41% of your total portfolio value from the jumpy stock to the calm one.

No masochism for the kids but in case you’re interested…

Equal risk weighting is the starting point for so-called risk parity weighting. The difference is that instead of only considering the volatility a holding adds to the portfolio, the correlation is considered. A stock highly correlated with the rest of your portfolio contributes a lot of risk, while an anti-correlated one does a better job diversifying and reducing total portfolio risk. The effect can be so strong that even a highly volatile but anti-correlated stock can reduce total risk.

Computing a correlation-aware risk contribution requires a full covariance matrix and an optimizer — i.e., a guess-and-test calculator — to find the portfolio weights, since there’s no closed-form solution. If the kids can grok equal vol-weighting I feel like I’ve done my job, and they can discover risk parity on their own if they’re so inclined.)