An Explicit Option-Based Strategy That Outperforms Dollar Cost Averaging

Abstract

Dollar cost averaging (DCA) is a widely employed investment strategy in financial markets. At the same time it is also well documented that such gradual policy is sub-optimal from the point of view of risk averse decision makers with a fixed investment horizon T > 0. However, an explicit strategy that would be preferred by all risk averse decision makers did not yet appear in the literature. In this paper, we give a novel proof for the suboptimality of DCA when (log) returns are governed by Lévy processes and we construct a dominating strategy explicitly. The optimal strategy we propose is static and consists in purchasing a suitable portfolio of path-independent options. Next, we discuss a market governed by a Brownian motion in more detail. We show that the dominating strategy amounts to setting up a portfolio of power options. We provide evidence that the relative performance of DCA becomes worse in volatile markets, but also give some motivation to support its use. We also analyse DCA in presence of a minimal guarantee, explore the continuous setting and discuss the (non) uniqueness of the dominating strategy.

Optimality of Payoffs in Lévy Models

“…Observe that the improved payoff X T is no longer path-dependent due to the conditioning on S T , hence it fits into the present framework and may be enhanced further by applying Proposition 2.1. In Vanduffel et al (2012), this approach is applied to Dollar cost averaging which is shown to be outperformed by a static strategy of investing in a suitable portfolio of path-independent options. Some general comparison results for prices of path-dependent options like Asian or lookback options are given in Bergenthum & Rüschendorf (2008 …”

“…Here the aim is to determine an investment strategy C that achieves the same payoff distribution F as a given claim X but at the same time minimizes the price. In a series of papers Bernard & Boyle (2010), Bernard et al (2014), and Vanduffel et al (2009Vanduffel et al ( , 2012 give a solution of the efficient claim problem in a fairly general setting. They calculate in explicit form efficient strategies for several options in Black-Scholes markets.…”

John Doe's Old-Age Provision: Dollar Cost Averaging and Time Diversification

“…In a theoretical approach modeling stock returns as ARMA(1,1), Balvers and Mitchell [1997] show that a gradual market entry, even if the investments are not made at fixed amounts, represents a suboptimal strategy. Vanduffel et al [2012] propose a static strategy consisting of purchasing a suitable portfolio of path-independent options that will dominate LS-DCA for all risk-adverse investors. They provide evidence that the relative performance of LS-DCA is worse in volatile markets, exactly when it is supposed to be most helpful.…”

Stock Investments for Old-Age: Less Return, More Risk, and Unexpected Timing

“…In a theoretical approach modeling stock returns as ARMA(1,1) Balvers and Mitchell [1997] show that a gradual market entry, even if the investments are not made at fixed amounts, represents a suboptimal strat-egy. Vanduffel et al [2012] propose a static strategy consisting of purchasing a suitable portfolio of path-independent options that will dominate DCA for all risk-adverse investors. They provide evidence that the relative performance of DCA is worse in volatile markets, exactly where it is supposed to be most helpful.…”