Capital structure and risk acceptability

Capital structure is designed to maximize security valuation in two price markets when acceptable risks form a convex set. The valuation functions used are financial in the sense of increasing the value by a dollar of claims with access to an additional dollar. Such valuation functions require the specification of rebate functions for the probabilities testing acceptability. A specific rebate function termed RADICAL is introduced that delivers closed form solutions for conservative valuations. Applications are first illustrated on stylized random variables. They are followed by results based on risk neutral distributions observed in options markets. Median equity levels fall from 14% to 10% for 45 underliers over the period 2015 to 2023 as the cone of acceptable risks is enlarged to promote greater risk taking. The equity levels are observed to peak in early 2020.