composition being uneven. The coefficients are very similar to the OLS coefficients. However, the standard errors do change a bit, and now the coefficients of Tier 1 capital (both the Basel ratio and the leverage ratio) during the crisis are significantly positive for the full sample. For large banks, as in the baseline it is only the Tier 1 leverage ratio that is significant. In the second part of the table, we show standard errors clustered by country rather than bank. Clustering by the higher level of aggregation is generally preferable (Cameron et al., 2006), but it can give rise to distortions if the number of clusters is small and the cluster size is uneven, as is the case with our sample (Nichols and Shaffer, 2007). The results are very similar to those obtained through weighted least square estimation. Finally, in the third part of the table we cluster the standard errors by quarter. Again, we find that the baseline results are not much changed, the main difference is that now the leverage ratio in crisis is significant also for the full sample.<sup>10</sup> Finally, we estimate a specification with a dummy variable that takes the value of one if a bank has been recapitalized with government funds in a given quarter (Table 9). To identify banks that received public funds we used several sources including press articles, official documents posted online, and information from central banks’ Financial Stability Report, and Treasury websites. In some countries (e.g. the U.K.) the plans were targeted to systemically important institutions, while in others (e.g. the U.S.) all banks were allowed to participate provided they fulfilled certain criteria. All in all, we identify 95 banks that were recapitalized in the full sample, of which 25 also belong to the sample of larger banks. While, the recapitalization dummy is negative and significant, indicating that stock returns for the recapitalized banks were particularly low in the quarter in which recapitalization occurred, the relationship between capital and stock returns does not change relative to the baseline.<sup>11</sup> To summarize, we find robust evidence that differences in the Tier 1 leverage ratio help explain differences in stock returns during the financial crisis in a sample of large banks. For a broader sample including all listed banks with available information, the results are more mixed: there is some evidence that capital mattered during the crisis, but the evidence is not robust, and it does not look like the market was clearly differentiating between the regulatory ratio and the leverage ratio.

# **_Why does capital affect stock returns only among large banks?_**

These results raise the question of why the leverage ratio matters for equity prices especially in the sample of larger banks. One possible interpretation is that larger banks with complex operations have more opportunities to take advantage of “regulatory arbitrage” opportunities and distort the risk exposure measure used by regulators to compute capital adequacy. Also, capital’s

> 10 Using a dataset of monthly U.S. stock prices and balance sheet variables from Daniel and Titman (2008), Petersen (2009) finds that standard errors clustered by time are much larger than standard errors clustered by firm, and recommends clustering by time. In our dataset, there appears to be little difference. Petersen also points out that clustering by time is similar to using the Fama-Macbeth regressions.

> 11 The negative coefficient of the recapitalization dummy may indicate that recapitalization diluted shareholders or that it signaled bad news about the future profitability of the bank.

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