A Continuous-Time Reexamination Of Dollar-Cost Averaging

The widespread practice of dollar-cost averaging (DCA) amongst the investing public, has puzzled most financial economists, ever since Constantinides [2] demonstrated the dynamic inefficiency of this strategy under very general conditions. This enduring phenomena has forced researchers, such as Statman [12], to suggest behavioral explanations for DCA's popularity, predicated on the prospect theory of Kahneman and Tversky [4].In this paper we reexamine the payoff structure of DCA via continuous-time financial mathematics and then ask the question:Is it possible to reconcile the theory and practice of dollar-cost averaging?To answer this question, we take a slightly different approach to the issue by using the tools of stochastic calculus and Brownian bridges. We demonstrate that engaging in a dollar-cost averaging strategy is akin to purchasing a zero strike arithmetic Asian option on the underlying security. In other words, people who engage in dollar-cost averaging are implicitly purchasing a path-dependent contingent claim. We then prove that the expected return from this exotic option — i.e. the DCA strategy — conditional on knowing the final value of the security will uniformlyexceedthe return from the underlying security for all sufficiently large volatilities.This leads us to argue that investorsmay bedollar-cost averaging because they have "target prices" for the underlying asset price. The strategy of dollar-cost averaging would then exceed the returns from lump-sum investing, based on their subjective conditional expectation. In fact, the more volatile the underlying security, the greater is the benefit to dollar-cost averaging — conditional on knowing the final value — which is consistent with common practice.