Beyond the short run: The longer time scale volatility of investment value

Abstract

Fund and other investments often exhibit longer run volatility associated with macroeconomic or other dynamics to an extent inconsistent with the efficient market accumulation model. Volatility and performance models or metrics based on one period returns or simple extensions can fail to pick up this up, resulting in suboptimal investment policies, or welfare losses if exit happens to be forced at the wrong time. We show how to use wavelet analysis to resolve problems of detection, attribution and welfare measurement, including assigning volatility metrics and path risk, while dynamic value at risk ideas can be applied to establish clearance points relative to any benchmark comparator path. Generalisations of the spectral utility function can guide investment policy or be used to design optimal portfolios. The methodology is primarily intended for long-term funds management, though it could potentially be used to design portfolios that capitalise on shorter swings.