  This paper reviews the economic and theoretical foundations of insolvency
risk measurement and capital adequacy rules. The proposed new measure of
insolvency risk is constructed by disentangling assets, debt and equity at the
micro-prudential firm level. This new risk index is the Firm Insolvency Risk
Index (FIRI) which is symmetrical, proportional and scale invariant. We
demonstrate that the balance sheet can be shown to evolve with a fractal
pattern. As such we construct a fractal index that can measure the risk of
assets. This index can differentiate between the similarity and dissimilarity
in asset risk, and it will also possess the properties of being self-similar
and invariant to firm characteristics that make up its asset composition hence
invariant to all types of risk derived from assets. Self-similarity and scale
invariance across the cross section allows direct comparison of degrees of risk
in assets. This is by comparing the risk dissimilarity of assets. Being
naturally bounded to its highest upper bound, (0,2], the fractal index is able
to serve like a risk thermometer. We assign geometric probabilities of
insolvency P (equity is equal or less than 0 conditional on debt being greater
than 0).
