I have been learning about investments lately and encountered a concept called rebalancing. Rebalancing means exchanging assets to achieve a target allocation. For instance, suppose you resolve to hold 80% of your investments in stock and 20% in bonds. If you buy assets in those proportions and let them grow, the stock is likely to outperform the bonds. Your mix might drift to something like 90/10, and you need to rebalance.

In a typical investment portfolio, it’s not hard to figure out how to do this: In the example above, you would exchange 1/9th of the stocks for bonds. But the complexity escalates if your target allocation has more than two categories, or you hold a large number of mutual funds which themselves span multiple categories (consider a catalog of retirement strategy funds that contain different mixes of stocks and bonds).

For this post, let’s overthink things a bit and consider the general case of portfolio rebalancing with $n$ funds and $m$ asset categories. What’s the “cheapest” way to rebalance—how can you do it in the fewest transactions? And can we make “AI” (note: not actually AI) find the answer for us instead of eyeballing it?

If you’re reading this, I finally updated the backend of the site to use a new framework—from Jekyll to Hugo. I also took the opportunity to redo the homepage a bit. I don’t have as many blog-post-shaped thoughts as I used to, so I reduced the post previews to just links to create room for more freeform content.

The Hugo migration was a bit of work because I took my time and did it the fun way. The old version of the site used Jekyll and had accrued a lot of Jekyll’s “isms,” along with weird conventions of my own. I wrote a custom content migration script to transform Jekyll tags automatically where possible and flag for manual attention where needed.

I think/hope it worked. Old post links will redirect you to the new URLs. For RSS subscribers, depending on how your reader is configured, you may pick up a new copy of every post; you can just mark as read everything before today’s date.

I read a comment stating that git (a tool programmers use to collaborate on code, sort of like Word’s Track Changes) is not a version control system but a “system for creating a version control system.”

That got me thinking about other such “metasystems” I use, and the frustration that arises when one expects a mere system and instead gets the meta thing.

I recently learned about PageRank, the original Google algorithm for ranking webpages. It works by constructing a Markov chain on links between pages and computing the stationary distribution. The stationary probability of a given page measures the page’s centrality in the web, an index of popularity.

I wanted to try implementing the algorithm myself and fiddle with a few Rust libraries, so I wrote a script that runs PageRank on interviews from the People and Blogs series. P&B interviews are a tidy dataset for the algorithm, because Manu always asks interviewees to recommend other blogs, then he uses these recommendations to pick subsequent interviewees. This means the graph is well connected despite its small size.

I was going to share the results here, but ranking blogs by popularity seems against the spirit of the indie web ethos, so you’ll have to run the program yourself. (But to make it clear I’m not covering anything up, let me acknowledge that my interview is in a 61-way tie for last place, with all the other blogs that had no links to them.)

A few observations from this exercise below.

Owen Lacey blogged about a reality game show called Are You the One? in which contestants win a prize by guessing the soulmate ordained for them by the show’s producers. Specifically, there are $n$ men and $n$ women, and each one has an unknown “perfect” match; to win the prize, the contestants (as a group) must pair everyone up correctly.

During each episode, the contestants get two kinds of clues:

1. Truth Booth, where the contestants submit a single couple and learn whether that couple is a perfect match.
2. Match Up, where the contestants submit a matching (assigning everyone to a couple) and learn the number (but not the identity) of perfect matches present in their matching.

The game ends after Match Up if all $n$ couples in the matching are correct. Definitely check out Owen’s post, which has a better (and illustrated!) explanation of the rules.

Below, I present an efficient algorithm for playing Are You the One. It exploits both the informational clues and contestants’ intuitions to find perfect matches quickly. With modest assumptions on the quality of players’ intuitions, my algorithm wins by episode 10 in 100% of simulated seasons.