Cheap(?) and easy(??) portfolio rebalancing

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…