A Self Propagating Measure for the 'Cumulative State of Market Incompleteness'

What is it about?

Ideally, every asset that is valued in markets simultaneously is priced with reference two risks, namely first, the risk portended by the timing of the valuation (the valuation uncertainty risk) and secondly, the risk that is specific to the parameters of the asset (the individual asset risk). Suppose two assets seek to list in a market, say a stock market. This study shows that, feasibly the ranking of valuation uncertainty risk either coincides with, or is dichotomous to the ranking of individual asset risk. For concreteness, conditional on the sequence with which the two assets arrive in the market, for each asset, there exists the feasibility of two non-coinciding valuations. For additional concreteness, the formal theory demonstrates that the individual asset risk is non-collapsible into the valuation uncertainty risk, and vice versa, with the outcome neither of abstraction from asset risk nor abstraction from valuation uncertainty risk is amenable to the generation of robust valuations. If the two assets are to be robustly priced, there is arrival at the necessity of a valuation rubric that desensitizes asset valuations to the sequence with which assets arrive in markets. The formal theory infers that the objective is achieved if there is arrival at a robust measure for valuation uncertainty risk that is conditioned on the state of the market. Refer to said measure as the measure for the 'Cumulative State of Market Incompleteness (CSI)' and denote the measure, M. In presence of a conditioning of the quality of an asset on M, the resulting valuation is robust to any sequence in the context of which the asset arrives in the market. Given an asset must be valued prior to the feasibility, to wit, it is incorporated into the Capital Asset Pricing Model (CAPM), clearly M cannot be a CAPM portfolio. More importantly, with the one-factor CAPM established to be inherently inefficient (see for example, Gibbons 1982), the one-factor CAPM lacks robustness as a proxy for M. Further, since a market index is an index of returns, not an index of risk, there is not any market index that suffices as a proxy for M. At the present time, as such there does not exist any measure or proxy for M in markets, particularly stock markets. For the mathematical representation of the CSI, that is, M, as such evidence that it is a self propagating measure, see the study Abstract. In stated respect, note that were M not to be self propagating, the claim that it is a pricing measure would be bogus.

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Photo by Linus Mimietz on Unsplash

Photo by Linus Mimietz on Unsplash

Why is it important?

At the present time, M does not exist in any market. In absence of a measure and proxy for M, the extent to which asset valuations for two different assets, A and B which arrived in a market at times, t and t+1, respectively are consistent with each other cannot robustly be determined. In stated respect, note that a proxy does not coincide with a measure. A measure is a concept, e.g. as in this study, the Cumulative State of Market Incompleteness, that is, the CSI. A proxy is a specific variable that is motivated as an empirical proxy for a concept. Given a specific variable first has to be shown, theoretically to be adequate to a representation of the CSI, then be simulated to show it is robust, the search for a specific proxy for the CSI resides outside of the scope of the current study.

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