The Accumulation of Value Over Time

Abstract

We introduce a purely mathematical measure, Γ, of the accumulation of asset value over time that robustly measures cumulative return against market movement under whatever investment strategy is employed in buying into any given market over any period of time. Requiring no underlying assumptions about price behavior, the purely mathematical factor Γ captures the qualitative and quantitative structural elements of wealth accumulation. In direct application Γ accurately reveals the computational role and influence of volatility and mean price movement in the popular strategy of Dollar Cost Averaging. At the last Γ suggests a proportional Buy&Hold strategy that is generally more successful.

Keywords: Invest, strategy, dollar-cost-average, mathematical model

JEL Classification: G00, G11, G17, G49, M50, D11