Systemic Risk, Crises, and Macroprudential Regulation (The MIT Press) by Peydró José-Luis & Laeven Luc & Freixas Xavier
Author:Peydró, José-Luis & Laeven, Luc & Freixas, Xavier
Language: eng
Format: epub
Publisher: The MIT Press
Published: 2015-07-02T16:00:00+00:00
The One-Factor Merton Model A second point to emphasize is that if the risks of individual loans are independently distributed, the law of large numbers assures that the probability of bankruptcy tends toward zero when the number of loans tends to infinity, provided that the expected return on the loan is larger than the average cost of capital, that is, that banks are profitable ventures. This means that in such a world of independently distributed losses, the expected losses are covered by the interest rate charged on the loan.
This academic exercise allows us to define capital as differing from provisions. Indeed risks related to the independent risks of each loan, the expected losses, should be covered by the interest rate charged on the loan and accounted for as provisions. Capital should, instead, be defined as the amount to cover unexpected correlated risks.5
The independently distributed losses case implies that any realistic model of banks’ risks should be based on common factors simultaneously affecting all loans. The Basel approach takes the simplest possible model when it postulates the existence of a single (macroeconomic) factor that, as a first approximation, could be thought of as GDP growth. This is the rationale for having banks’ capital requirements that constitutes a buffer against the risk in this single systemic factor and is different from provisions.
In a world of specialized banks there is no unique measure of risk for each asset, as the portfolios the banks hold are different and have sector-specific risk. The risk of a specific Irish mortgage for an Irish bank that has 60 percent of its portfolio invested in this type of loan is therefore higher than for a German bank that has 2 percent of its portfolio invested in Irish mortgages. So the single-factor model cannot take this feature into account. Finally, notice that the single-factor model is an approximation. If there were several macroeconomic factors, the risk weights for each financial product would depend on the proportion of the different macroeconomic factors a bank portfolio embodies (Gordy 2003).
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