Constantinides's Argument

Another day, another article about dollar-cost averaging. I just finished skimming through "A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy" by George Constantinides. The core argument there is quite devastating, I feel, and can be explained at an intuitive level without any of the mathematical apparatus from the paper.

To set the stage first note that although we've talked about dollar-cost averaging as a strategy for shifting money from a safe investment (cash) to a risky investment (stocks), an adherent of dollar-cost averaging should equally well recommend the same approach when moving from stocks to cash (or, in general, from any asset class to any other asset class). The core argument still applies: you want to enhance your chances of getting a "fair" price for the stock and not run the risk of a bad price by happening to be very unlucky in your choice of the day for the lump sum transition. Whether you happen to be buying or selling the stock, the logic is the same.

Second, note that we've implicitly been assuming all along that there are no transactions costs of any sort. We can instantly and without cost shift any part of our portfolio from one asset to another without paying commissions, capital gains tax, or anything like that. Of course, this is an idealization, but it seems like a harmless one. Certainly the proponents of dollar-cost averaging don't argue that the reason the approach works is because of transaction costs. (If anything, transactions costs hurt the case for dollar-cost averaging since you have more transactions.)

Now consider two investors John and Mary. John has inherited $1,000,000 in cash while Mary has inherited $1,000,000 in stock. Let's call that point in time t0. They have identical preferences as far as risk and return and each feel their optimal long-term allocation is 50% stocks and 50% cash. If we subscribe to dollar-cost averaging, at t0 John should move a little money into stocks and Mary should move a little money into cash. But clearly they will still have different portfolios: John will still be mostly in cash, and Mary will still be mostly in stocks.

Now here's where the trap closes on the hapless DCA proponent. Observe that John and Mary are really in equivalent positions at t0. By our assumption above of no transaction costs, Mary can move all her money from stocks to cash at t0 without any cost (and vice versa for John). If Mary can transition freely and instantaneously to John's portfolio at t0, and John can transition freely and instantaneously to Mary's portfolio at t0, how can they possibly have different optimal investment strategies to pursue at t0?

To put it another way, suppose we can quantify John's utility at t0 (after he readjusts his portfolio as per DCA) as Uj,0 and Mary's utility at t0 as Um,0. This utility will be a function of the expected return and volatility of their portfolio going forward from t0. If Uj,0 > Um,0 then you have to wonder why Mary doesn't just shift all her money to John's portfolio at t0 which would give her utility Uj,0. Likewise if Um,0 > Uj,0. The only way we don't get a contradiction is if Uj,0 = Um,0 but in general that is not going to be the case - a 95% allocation to stocks and a 95% allocation to cash will not offer identical utility.