LessonThis is a lesson restated in new words. Any figure in it is an example from the source, not this desk's record.
Portfolio weights drift because winners become a larger share of the account. The lesson compares two $10,000 books of Amazon and Apple, each started at 50 percent, using prices from 2020 through the 2022 session. One book resets to 50-50 every day. The other buys once and holds. The hold finishes at about $18,552, with roughly 40 percent in Amazon and 60 percent in Apple. The gap between the two wealth lines is the gap between the target mix and the mix you actually hold.
Why it matters
A retirement mix is a risk choice: so much in equities, so much in bonds, so much in other assets. Leaving it alone changes that choice. The lesson's illustration of a target is 30 percent bonds, 40 percent equities, and the rest in a blend such as gold or commodities. It also cites modern portfolio theory for the idea that diversification is on the order of 30 names. Two names over two years already move from 50-50 to about 40-60. A longer horizon and a longer list of holdings give the weights more room to leave their targets. The session does not say to rebalance every day. It says a skipped rebalance is a new risk profile, and it offers a monthly reset as an example of a schedule that defends the original targets.
The idea in plain words
The prices are the yfinance histories for AMZN and AAPL from 2020. Percent changes become the return series, with the first empty day removed. The lesson counts 581 return days and 582 closing prices. Daily rebalance is a dot product of the weight vector, here 0.5 and 0.5, with the return vector, plus one, then a cumulative product, scaled by 10,000. That path is the wealth of a book that earns the weighted return and then puts the weights back.
The one-time book assumes fractional shares. It spends $5,000 on Amazon and $5,000 on Apple at the first close, which is $5,000 divided by that close. Share counts then stay fixed. Wealth on any later day is the dot product of those share counts with the two closes. Plotted against the rebalanced path, the two lines look close, and they are not the same line. The lesson does not read out the rebalanced ending wealth. It does read the hold's last value: 18,552. The same last value falls out of the latest Amazon price times the Amazon shares, plus the latest Apple price times the Apple shares.
Divide each holding's dollar value by 18,552. Amazon is about 40 percent. Apple is about 60 percent, and the lesson's more granular Apple figure starts 0.59 before it rounds the pair to 40 and 60. The start was 50 and 50. Two years of price changes did the rest.
How to use it
Pull both histories, build the return matrix and the close matrix, and check the shapes. Plot the cumulative 50-50 return path times 10,000. Plot the fixed-share path on the same axes and label them. Read the last fixed-share value and split it into the two dollar holdings. Those percentages are the live weights.
The lesson's question about the space between the lines is answered by those percentages. The space is not a mystery residual. It is the wealth difference between a book that restored 50-50 and a book whose Amazon and Apple ratios were allowed to follow the prices. Extend the same measurement to any target mix you actually hold. A monthly rebalance, in the lesson's suggestion, is a reset of those percentages back to the policy mix.
What usually goes wrong
Similar wealth lines can hide a 40-60 mix. That split is the point of a picture that has not diverged wildly. The lesson asks you to imagine the same drift over 30 or 60 years, and in a tech-heavy book where one weight could become several times its start. Those are illustrations, not multiples measured in this notebook.
The hold buys at the first 2020 close. A later purchase price changes the share counts and the ending weights. Fractional shares keep the example comparable with continuous weights. The remark about 30 names is a citation of portfolio theory, not a result computed from these two stocks.
Questions people ask
What does the buy-and-hold account finish at?
About $18,552 from a $10,000 start, with the weights near 40 percent Amazon and 60 percent Apple.
What is the other line?
A daily reset to 50 percent Amazon and 50 percent Apple, built from the cumulative product of one plus the weighted return. Its ending dollar value is not stated.
Why does the lesson mention a monthly rebalance?
A month is the example cadence for putting weights back on target so the risk mix stays the one that was chosen. The session does not derive an optimal calendar.