Capital Adequacy of Financial Enterprises
22 Pages Posted: 14 Feb 2011
Date Written: February 13, 2011
Financial entities commonly go bankrupt with disastrous consequences for individuals and society These consequences arise since bankrupt limited liability company is not responsible for losses exceeding its financial resources. Such losses are carried by unsecured creditors or, in the case of insurance companies, policy holders. Hence each limited liability entity holds an option to put losses in excess of its financial resources to other parts of the economy.
Governments may cover losses, in which case the option is often called the "taxpayer put". Business with random assets and liabilities, such as banks, insurance companies and hedge funds, are typically required to hold capital to decrease the probability of bankruptcy and make businesses acceptable to the external economy. In this paper these businesses are viewed as operating in markets with the law of two prices with sales occurring at bid prices and purchases at ask prices. The structure of bid and ask prices defines the market environment. Given the business and its regulatory and market environment, expressions are developed for the rest of the balance sheet. This includes the value of equity, the value of the implicit put option, exact expressions for the capital adequacy ratios that correct both the numerator employed in the Basel accords along with a theoretically precise formulation of the denominator or the equivalent of risk weighted assets. Computations are illustrated for two balance sheets. One with lognormally distributed and correlated assets and liabilities and the second for a business of risky loans financed by writing options on a related underlier.
Keywords: Capital adequacy ratios, acceptable risks, Basel accords, capital requirements, reserve requirements
JEL Classification: G22, G28, G38
Suggested Citation: Suggested Citation