Measures of risk-weighted capital are statistically insignificant, while the leverage ratio is significant at the 1% level. Contrary to the risk-sensitivity doctrine, less appears to have offered more. These results are robust to the inclusion of a broader set of macro factors, such as GDP growth and credit (Table 3). Using different methods and samples, other studies support the predictive superiority, or at least equivalence, of leverage over capital ratios (IMF (2009), Demirguc-Kunt et al (2010), Estrella et al (2000)). A second source of regulatory complexity is the definition of capital. Table 4 considers the predictive performance of a selection of measures of capital for a sub-set of banks. Two key conclusions emerge. First, simpler measures of accounting capital based on equity capital (core Tier 1) outperform broader, more complex, measures. Second, simple market-based measures of banks’ equity dominate accounting measures in their crisis-predictive performance. Simple, once again, beats complex. Put another way, consider a straight horse-race between the most complex measure of banks’ capital position (the Basel Tier 1 ratio) and the simplest (the market value of equity relative to unweighted assets). The explanatory power of the simple measure is about 10 times greater than the complex measure. However well they perform in theory or in sample, complex capital rules do not appear to have performed well in practice and out-of-sample. That is a sobering message for the architects of the Tower of Basel. (5)  Predicting bank failure – simple or complex?

(b)  In-sample performance is measured by deviance and out-of-sample performance by the mean squared prediction error. For both statistics, a lower number implies better performance. (c)  The data set excludes outlier banks with very large risk-based capital and leverage ratios. Excluded observations account for approximately 0.5% of the entire sample. 30  BIS central bankers’ speeches  Chart 9: In- and out-of-sample performance of different models of bank risk (1000 (a)(b)(c) observations)  Source: FDIC and Bank calculations. (a)  Different models estimated using 10,000 random samples of 1,000 observations each. Samples are rejected if there are no observations of bank failure. The different models are used to predict bank failure for approximately 4,300 banks out-of-sample. (b)  In-sample performance is measured by deviance and out-of-sample performance by the mean squared prediction error. For both statistics, a lower number implies better performance. (c)  The data set excludes outlier banks with very large risk-based capital and leverage ratios. Excluded observations account for approximately 0.5% of the entire sample. BIS central bankers’ speeches  31  Chart 10: Summary of out-of-sample model (a)(b) performance  Chart 11: Distribution of daily stock price (a) returns, 1928–2012  Source: FDIC and Bank calculations. Source: Bloomberg and Bank calculations. (a)  Different models estimated using 10,000 random samples of different size. Samples are rejected if there are no observations of bank failure. The different models are used to predict bank failure for approximately 4,500 banks out-of-sample.