automatic rebalancing through automatic exchange

When investing, you often want to maintain your asset allocation, which can depart from your initial allocation as specific assets increase or decrease in value. One option is to periodically check your allocation and manually transfer funds between assets (rebalance) if necessary. An added convenience is automatic rebalancing, where your investment company rebalances for you at some frequency.

However, Vanguard, one of the most popular investment companies, does not seem to support automatic rebalancing of an arbitrary asset allocation. Here's a trick you can use to achieve the same effect through automatic exchange:

Suppose you have three assets A, B, and C that you'd like to hold in the percentages a, b, and c respectively, where a + b + c = 100. All you need to do is set up 6 automatic exchanges, where A gives b percent of its value to B and c percent of its value to C, B gives a percent to A and c percent to C, and C gives a percent to A and b percent to B. In general, each asset receives a fixed percentage of each other asset, equal to the percentage of the receiving asset in the desired allocation.

The above technique rebalances exactly, but it has some problems. First, you definitely do not want to do this if there are taxes or fees associated with the transactions, since the transactions will be pretty large. (Performing the exchanges within a Roth IRA at Vanguard should still be okay.) Second, it can be a pain to set up an automatic exchange for each pair of assets you own.

Let's address both problems, though really, if you're faced with taxes or fees, you probably just want to do your rebalancing manually. However, you can decrease both the number and the size of the transactions by doing something I might call "soft rebalancing". The trick is that instead of exchanging between every pair of assets, we create a cycle of exchanges. In the above example, we could have A give to B, B give to C, and C give to A. (I'll get to the exchange amounts in a bit.) In general, if you have n assets, you only have to set up n exchanges. With soft rebalancing, you lose the ability to rebalance exactly, as we'll see.

So what are the exchange amounts? There's a slight complication, in that we can now change the rate at which rebalancing occurs, so the exchange amounts can be scaled. In the above example, A would give B proportional to 1/a, B would give C proportional to 1/b, and C would give A proportional to 1/c. In general, each asset gives up value proportional to the inverse of its percentage in the desired allocation. Again, these amounts should be scaled based on how fast you want the rebalancing to happen. At the maximum allowable rate, one of the assets will be giving up all of its value at each rebalance.

There are some problems with the cycle of exchanges scheme. Most importantly, it may take many rebalancing steps to transfer between an asset with excess value and an asset with insufficient value if the asset with insufficient value is far "downstream" from the asset with excess value. There are other schemes that address this issue, like setting up one "hub" asset and having all exchanges take place between the hub and one of the other assets (in both directions), though this scheme requires setting up about twice as many automatic exchanges.

An important point is that these exchanges must be in terms of the percent of the holdings of an asset. If the only supported exchanges are in fixed dollar amounts, automatic rebalancing is impossible. Also, I'm not sure how practical any of this is, since I have to assume that at some point Vanguard and other investment companies will offer automatic rebalancing. In the meantime though, you can use my trick if you're desperate.