An analysis of dollar cost averaging and market timing investment strategies

In this paper we present new theoretical and practical insights into the method of dollar cost averaging (DCA) and averaging-style investment timing strategies, with a formal analysis of the problem. Firstly, we provide a rigorous mathematical formulation for studying DCA and related strategies. This provides closed form formulae for the expected value and variance of the investor’s wealth process, which mathematically proves many properties that have been documented in the literature only by empirical studies. Secondly, we prove a counterintuitive, but important, result that the frequency of DCA investment has a non-monotonic and non-trivial impact on risk, risk-return trade-off and other important performance metrics (such as the Sharpe ratio).Thirdly, we provide a method of valuing the DCA risk for models which incorporate jumps. We also provide a method of hedging DCA risk based on applying Asian options. Finally, using the PROJ method of computation, we obtain a robust and computationally efficient method for calculating standard risk measures of generic and deterministic investment strategies, such as DCA. We provide numerical experiments to illustrate our conclusions, and conduct an empirical study on the S&P500 index (from 1954 to 2019) to substantiate our results.