On the mitigation of valuation uncertainty risk: the importance of a robust proxy for the “cumulative state of market incompleteness”

Suppose the same set of assets enters a primary market in either a monotone decreasing or monotone increasing sequence of asset risk. This study shows that the errors that attend the valuations of those assets in the context of the two different orderings are noncoincident. The sequence in which new assets arrive within a market is thus a source of valuation uncertainty risk. The formal theory shows that both asset risk and valuation uncertainty risk are mitigated if investors condition valuations of new assets on a dynamically evolving intertemporal mechanism that has parameterization as an explicit robust measure for the “cumulative state of [market] incompleteness” (CSI). Theoretically, relative to every preceding state, the CSI is a sufficient measure for the severity of market-conditioned valuation uncertainty risk. Although the derivation of a specific measure for the CSI is beyond the scope of this study, the formal theory arrives at three mathematically specified risk metrics that approximate the properties of the CSI. Let q and M denote, respectively, the individual initial public offering quality and the CSI. The CSI has the explicit parameterization Mt = ⋃ts=1(qs | Ms-1), as is expected of any well-defined measure, is self-propagating.