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This paper reviews the economic and theoretical foundations of insolvencyrisk measurement and capital adequacy rules. The proposed new measure ofinsolvency risk is constructed by disentangling assets, debt and equity at themicro-prudential firm level. This new risk index is the Firm Insolvency RiskIndex (FIRI) which is symmetrical, proportional and scale invariant. Wedemonstrate that the balance sheet can be shown to evolve with a fractalpattern. As such we construct a fractal index that can measure the risk ofassets. This index can differentiate between the similarity and dissimilarityin asset risk, and it will also possess the properties of being self-similarand invariant to firm characteristics that make up its asset composition henceinvariant to all types of risk derived from assets. Self-similarity and scaleinvariance across the cross section allows direct comparison of degrees of riskin assets. This is by comparing the risk dissimilarity of assets. Beingnaturally bounded to its highest upper bound, (0,2], the fractal index is ableto serve like a risk thermometer. We assign geometric probabilities ofinsolvency P (equity is equal or less than 0 conditional on debt being greaterthan 0).

On the Fractal Geometry of the Balance Sheet and the Fractal Index of Insolvency Risk