Measuring Investment Opportunities Under Uncertainty

Abstract

In order to make sound economic decisions it is important to measure the possibilities offered by a market in relation to investments. Provided an investment scheme $S=\langle r; R_1,\dots ,R_n\rangle$, where r is a lower bound on the desired investment return and the $R_i$’s are the asset yields, the power to invest measures the capability of the scheme to fulfill requirement r. The power to invest is inspired in the Coleman’s power of a collectivity to act. We exemplify this approach considering subsets of companies from stock indexes IBEX35 and DAX. We extend the power to invest to investment schemata with imprecise yields. We prove basic relations with the precise yields case and we also show that good monotonicity properties hold. Finally, we propose an analysis, through integrals of the power function, for the case of an unspecific desired return r.

J. Castro was partially supported by the Spanish Ministry for Economy and Competitiveness (MINECO) under grant (TIN2017- 89244-R) and the recognition 2017 SGR-856 (MACDA) from AGAUR (Generalitat de Catalunya). J. Gabarro and M. Serna were partially supported by MINECO and FEDER funds under grant GRAMM (TIN2017-86727-C2-1-R) and Generalitat de Catalunya, Agéncia de Gestió d’Ajuts Universitaris i de Recerca, under project 2017 SGR 786 (ALniBCOM). M. Serna was also supported by MINECO under grant BGSMath (MDM-2014-044).