TAILIEUCHUNG - Why Are there So Many Banking Crises? The Politics and Policy of Bank Regulation phần 9

Ràng buộc ngân sách mềm Không Ngụ ý Big Fail thông thường khôn ngoan định rằng các ngân hàng với số lượng lớn tiền gửi không có bảo hiểm không được phép thất bại khi sự thất bại của họ sẽ Tại ngưỡng này, giá trị vốn cổ phần của ngân hàng có một tiếp tuyến nằm ngang | CAPITAL REQUIREMENTS AND THE BEHAVIOR OF COMMERCIAL BANKS 245 portfolio for a bank having an adjusted net worth equal to K. By the arguments above we know that x K ơ K xM where xM is the market portfolio normalized in such a way that it has a unit variance . xM V-1p ơ . ơ K is a nonnegative constant equal to the standard deviation of the argument maximum of P . It is the maximum of ọ - U K Aơ ơ and in particular the mean return on x K equals p K K Aơ K . As a consequence CR K -1 7 ọp ax and Pr Ki 0 n - K n - 1 - AỌK Ị A A oXm A CR K J. Since A 0 and N increasing the proof is completed. Proposition may seem a good justification of capital requirements. Independently of the choice of risk weights a1 . aN but provided that the numerator of the ratio is adjusted to incorporate intermediation profits on deposits the capital ratio is an increasing function of the default risk. The trouble is that as soon as the capital requirement is imposed the banks behavior changes and proposition ceases to be true. This will be the subject of the next section. As a conclusion to the present section we examine the dependence of the default risk of an unregulated bank on its corrected net worth. Is CR K a monotonic function of K In other words if no capital regulation were imposed would the more capitalized banks be more or less risky than the less capitalized ones It turns out that the answer to this question depends on the properties of the utility function u. More specifically we have the following proposition. Proposition . If the Arrow-Pratt relative index of risk aversion -xu x u x is decreasing respectively increasing then the default probability of an unregulated bankis an increasing respectively decreasing function of its adjusted net worth K. 246 CHAPTER 8 Proof. By proposition the default probability of an unregulated bank is an increasing function of T K K where t K is the solution to maxT u K 1 tÍĨm and Ẩm is the random return of the market portfolio. By

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