Probabilistic Studies of Different Investment Strategies

Abstract

<p>Lump Sum (LS), Dollar Cost Averaging (DCA), and Value Averaging (VA) are among the most popular investment strategies. However, conflicting conclusions on their relative performances have been given in the literature due to the use of different time periods of data and simulations. We propose an alternative investment strategy called Threshold Control (TC) based on statistical process monitoring. The idea is that the investor only makes portfolio moves when its market value is far above or below the target value set by the investor. TC can be viewed as a generalization of both LS and VA, and provides more flexibility to the investor. We present theoretical results for the mean returns and standard deviations of returns for the four strategies under the independent and identically distributed (i.i.d.) model for the stock return. This model includes, as special cases, the i.i.d. t distribution model and the discrete-time versions of the famous geometric Brownian motion model and the double exponential jump-diffusion model. We also present numerical results on the performances of these investment strategies for the i.i.d. t distribution model, the geometric Brownian motion model, and the double exponential jump-diffusion model; and simulation results for the stochastic volatility model. The results show that setting the appropriate target return rate (target value) is critical to successful investing. This implies that the investor needs to have a good understanding of the valuations and expected returns and risks of the assets in which he or she invests.</p>