A Continuous-Time Re-examination of the Inefficiency of Dollar-Cost Averaging

Abstract

Ever since the landmark article by Constantinides (1979), the academic literature has been decrying the inefficiency of the investment strategy known as dollar-cost averaging (DCA). In fact, despite more than twenty years of damning evidence, DCA remains as popular as ever amongst the press and individual investors. The purpose of this article is to re-examine DCA, but using tools from continuous-time option pricing. We believe that this framework yields additional and previously undocumented insights into the nature of DCA. Our main results are as follows: (1) We show that the end-of-period stochastic payoff induced by DCA--although neither normal nor lognormal--is identical in distribution to the stochastic payoff of a derivative security known as a zero strike (zepo) arithmetic Asian option. (2) Standard results in continuous-time finance theory dictate that--given the inefficiency of DCA--one can always construct a constant proportions continuously rebalanced portfolio that will stochastically dominate DCA, in a mean variance framework. We add to this by showing that for typical volatility and drift rates, one can construct a static buy-and-hold portfolio that will stochastically dominate DCA, in a mean variance framework. By typical conditions, we mean that the underlying assets volatility is lower than some--relatively large but known--critical threshold that depends on the drift rate. This enables us to quantify and display the inefficiency of DCA by 'moment matching' to a static buy-and-hold strategy. In other words, we 'moment match' the variance and then solve for the implicit loss in expected return, and vice versa, we 'moment match' the expected return and then solve for the excess variance. Furthermore, we confirm--to a first order of approximation--that the nominal Sharpe ratio from DCA is reduced by 13%, compared to any buy-and-hold strategy. However, if the volatility and drift rates are not typical, we show that the Sharpe ratio of DCA is higher than the Sharpe ratio of any buy-and-hold strategy. (3) Finally, using techniques from the theory of Brownian bridges, we compute the expected payoff induced by DCA, conditional on knowing the final value of the underlying security. We are thus able to prove--among other properties--that when the underlying security ends-up exactly where it started, the expected payoff from DCA is uniformly better than lump-sum investing. The magnitude of this conditional benefit to DCA, increases with higher volatility of the underlying security.