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 nn funds and mm 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?