금융기관 통합의 도산확률 및 시스템리스크 확대 효과

The purpose of this paper is twofold. The first is to show that integrating two financial institutions into one may give rise to an increase in the probability of default (PD) of the resulting integrated one. This is because while cash flow in the asset side after integration tends to exhibit reduced volatility due to diversification effect from less than perfect correlation existing between the two ex ante cash flows, total liability obligation remains to be the simple summation of the two existing liability obligations. The reason why reduced volatility in the post integration cash flow gives rise to greater default probability can be understood by referring to the mean preserving contraction (MPC) or mean preserving spread (MPS) working reversely. When two distributions each governing cash flow of a financial institution are combined, the resulting distribution becomes less volatile than any of the two original distributions under certain conditions. This can be understood as an MPC or a reverse MPS. It then follows that the cumulative probability of realizing a certain value of asset side cash flow when such a value is greater than the mean value is greater under the post integration distribution which is less volatile. Here, the cumulative probability corresponds to the default probability. Accordingly, the default probability gets larger under the post merger distribution if the combined liability amount turns out to be greater than the mean value of asset side payoffs. As a matter of fact, such a situation is not uncommon for financial institutions with high leverage ratios. In this respect, the current paper is the first to point out the possibility that integration of financial institutions gives rise to lower volatility in the asset side returns but increased default probability on the part of the integrated institution. Such being the case, risk diversification effect deemed beneficial in modern portfolio theory turns out to be largely responsible for increased default probability in this paper. Maybe, a devil in disguise. The second purpose of the paper is to analyse the impacts of integration of financial institutions on systemic risk of an economy. For this purpose, we define systemic risk to be simultaneous default of more than a certain (say, majority) number of financial institutions (or a certain proportion of market share thereof). As mentioned above, such integration will increase the default probability of the integrated institution given high leverage ratios. Since there will be a smaller number (or a greater concentration) of financial institutions with increased default probability as a result of such integration, it is likely to result in greater such systemic risk. The results of the paper allow two implications. First, regulation against integration of financial institutions would contribute to a decrease in systemic risk as it would potentially prevent an increase in the default probability of a financial institution. As a matter of fact, this provides a clear rationale for a stronger capital requirement against the so-called ‘Too-Big-To-Fail’ or ‘Systemically Important Financial Institutions (SIFI),’ initiated by the Financial Stability Board after the 2008 Global Financial Crisis. Second, merging any two private commercial banks or integrating any two policy banks would increase the default probability and thus give rise to greater deadweight costs for the society or fiscal burden on the part of the government.