Bank capital requirements come with important benefits and important costs. Higher capital requirements help to reduce the likelihood of future financial crises which—as we observed in 2008-2009—are extraordinarily costly in terms not only of wealth destroyed, but more importantly, households strained by unemployment. But higher capital requirements also make it costlier for banks to provide loans to businesses and households at all times; the resulting reduction in the availability of credit reduces economic output. Several academic studies have estimated the level of bank capital requirements that best trades off these benefits and costs.[1] The studies have generally followed the approach used by the Bank for International Settlements (BIS) in a 2010 paper that was an important input to the calibration of the Basel III standard for bank regulation.

First, the BIS estimated the annual probability of a financial crisis at different levels of bank capital requirements. Those estimates, combined with estimates of the cost of a crisis drawn from the academic literature, enabled the BIS to estimate the social benefit of the amount of capital available in the banking sector in terms of financial crises avoided. The BIS found that a one percentage point increase in capital requirements from pre-crisis levels reduced the annual probability of a financial crisis by about 1.5 percentage points while a similar increase from current levels reduces the probability by about 0.1 percentage points.

Second, the BIS estimated the impact on lending spreads and on GDP at different levels of capital requirements. The BIS found that, at any initial level of capital requirements, each percentage point increase in capital requirements raised loan rates 13 basis points and permanently reduced the level (not the growth) of GDP by 9 basis points.

Combining these estimates of costs and benefits, the BIS estimated the optimal level of capital requirements to be about 9 to 11 percent under their baseline set of assumption about the cost of a financial crisis.[2] Under different assumptions, the study puts the optimal level of Tier 1 capital requirements between about 8 and 13 percent.

Following a similar approach but using different estimates, two more recent studies came up with different ranges. A 2015 paper by Bank of England (BoE) economists (Brooke et al.) estimated the optimal range for Tier 1 capital requirements to be between 10 and 14 percent. A 2017 paper by Federal Reserve Economists (Firestone et al.) put the optimal range at 13 to 26 percent. As explained in a BPI blog post (see here), one important difference between the two estimates is that the BoE paper takes into account the impact of other post-crisis financial reforms on the probability and cost of a financial crisis. Most notably, the largest banks are now funded in part with debt that can be converted into equity if needed to recapitalize the institution as part of a resolution. The introduction of a credible resolution regime lowers both the probability and the cost of a financial crisis. Another important difference is that the Firestone et al. paper uses the estimated coefficients of a model that finds a statistically insignificant benefit to higher levels of capital. Thus, under this model specification higher levels of capital have a small impact reducing the probability of a crisis occurring. When those results are excluded, the upper bound of their estimated optimal range declines by about 4 percentage points.[3] Thus, the Firestone et al. would have likely yielded an optimal range that is similar to the one provided in the Brooke et al. paper if they had (1) taken into account other relevant post-crisis regulatory requirements and (2) excluded the model specification for which capital is not correlated with the probability of a financial crisis.

A 2016 paper by IMF economists took a different approach. Rather than estimating the social cost and benefit of capital regulations, Dagher et al. estimate the amount of bank capital that would have been necessary to avoid imposing costs on bank creditors or bank bailouts in past banking crises. They find that capital of 15 to 23 percent would have been necessary to absorb losses in most bank crises. As they note, the range can be interpreted as including not just equity, but also long-term —“bail in” — debt that banks have issued post-crisis pursuant to the FSB’s total loss absorbing capital (TLAC) requirement. Their estimates are determined by the losses experienced in banking crises in a wide range of countries, from Greece to Slovenia to Iceland. They estimate that about 6 percentage points of capital relative to risk-weighted assets would have been necessary to cover the losses of U.S. commercial banks in the 2007-2009 financial crisis.

Judging by these estimates, U.S. banks currently hold slightly more capital than optimal. The estimates by the BIS and BoE studies put the optimal range for tier 1 capital at about 10 to 14 percent of risk-weighted assets. The aggregate Tier 1 capital ratio of U.S. banks is about 13.5 percent; for the largest banks the figure is 13.8 percent, and both are higher than the 12 percent (mid-point of the optimal range). The largest banks also have long-term debt outstanding equal to about 10 percent of risk-weighted assets for a total loss-absorbing cushion of 24 percent, above the range the IMF study reports is necessary for banks to comfortably weather a banking crisis.

**What do equity values tell us about optimal capital?**

As a cross-check on our conclusion that banks have capital levels that are above or at the upper end of the optimal range, we calculate the market-implied probability of default for GSIBs and compare those with the maximum probabilities intended by the designers of the Basel III capital requirements.

Market implied probabilities of default are available on Bloomberg. The Bloomberg probabilities are calculated using the industry-standard “distance to default” method. In particular, using data on equity volatility, market capitalization, and leverage, the method calculates the “distance” each corporation is from having assets that are worth less than liabilities, and then converts those distances into probabilities of default using historical default experiences.

The maximum probabilities of default intended under Basel III are provided in two white papers from the BIS and the Fed that describe the calibration.[4] There are three components to the core capital requirements under Basel III. The minimum requirement of 4.5 percent of risk-weighted assets was calibrated so that a bank passing the requirement would have no more than a 1 percent chance of failing each year. To that level, banks are additionally required to hold a 2.5 percentage point “capital conservation buffer” (CCB) calibrated to equal the decline in capital the median large bank has typically experienced during periods of economic stress. Lastly, global systemically important banks (GSIBs) are required to hold additional capital intended to lower their probabilities of default to compensate for the systemic costs of their failure.

The GSIB capital surcharges are calculated using each bank’s systemic risk score, a largely ad hoc combination of bank characteristics, as a proxy for the systemic costs of failure. The GSIB surcharges are essentially set to reduce the probabilities of default to the allowable probability of a non-GSIB times the ratio of the non-GSIB and GSIB’s systemic risk scores. For example, if the reference bank score is 100 and the GSIB’s score is 500, the GSIB’s allowable probability is 0.20 percent (1 percent times 100 divided by 500).

How do market-implied probabilities compare with the Basel III intended maximum probabilities? They are much lower. To make the comparison, we have to address each of the three components of the capital requirements. In short, we compare each GSIB’s market-implied probability of default after absorbing a 2.5 percentage point reduction in its capital ratio to its allowable probability of default-adjusted for its systemic score.

To address the CCB, we adjust the market-implied probabilities. We recalculate the probabilities of default for each GSIB under the assumption that the bank incurs losses that consume its entire capital conservation buffer. Prior to making any adjustment, the average market-implied annual probability of default for the GSIBs averages 0.05 percent. That is, investors with money on the line judge that the average GSIB has a 50-50 chance of failing over the next 1400 years. To make the CCB adjustment, we assume each bank’s common equity declines by 2.5 percent of risk-weighted assets, and that the bank’s equity/book ratio remains unchanged. The probability of default for the 8 U.S. GSIBs after adjusting in this way for the CCB averages 0.09 percent.

To account for the GSIB surcharge, we adjust the 1 percent target maximum allowable annual probability of default under Basel III.[5] Specifically, for each GSIB, we multiply that probability by the ratio of the reference non-GSIB’s systemic risk score under Method 2 (100) divided by the GSIB’s Method 2 score as of October 2018, which range from 215 to 728. We use the Method 2 score, which was designed by U.S. bank regulators, rather than the Basel-designed Method 1 score, because the Method 2 score is used to set U.S. bank capital requirements and because it is more conservative. The maximum allowable annual probability of default for the GSIBs averages 0.24 percent.

Combining the two figures, we conclude that even after the substantial decline in stock prices and increase in volatility that has occurred over recent months, the average GSIB market-implied probability of default of a GSIB after having used its CCB is two-fifths the maximum allowable probability intended under Basel III. If we assume that Basel III was intended to set capital levels optimally, then, by this metric, banks have capital ratios that are substantially higher than optimal.

In the case of the 16 U.S. banks with more than $100 billion in assets that are not GSIBs, the calculation becomes simpler because the intended maximum allowable annual probability of default is 1 percent in each case. For those banks, their market-implied probabilities of default, after factoring in a 2.5 percentage point reduction in capital ratios average 0.05 percent, one-twentieth the maximum allowable level of 1 percent (see also footnote 5). Thus, non-GSIBs also appear to have capital ratios that are significantly higher than optimal, by the Basel Committee’s standard.

*Disclaimer: The views expressed in this post are those of the author(s) and do not necessarily reflect the position of the Bank Policy Institute or its membership, and are not intended to be, and should not be construed as, legal advice of any kind.*

^{1} High capital requirements also tend to push risk to holders (corporates, non-bank financials) less able to manage it, and especially given post-crisis legal changes, where regulators have less ability to provide support. These studies do not attempt to include this potential cost.

^{2} These results convert the pre Basel III TCE/RWA units used in the 2010 paper to post Basel III CET1/RWA units using the conversion factor of 0.78 provided in a subsequent BIS working paper (WP 591). The original range published in the 2010 paper is 12-14 percent.

^{3} We would like to thank Simon Firestone and Ben Radish for providing us this information.

^{4} “Calibrating regulatory minimum capital requirements and capital buffers: a top-down approach, Basel Committee on Banking Supervision,” October 2010, and “Calibrating the GSIB surcharge,” Board of Governors of the Federal Reserve System, July 20, 2015.

^{5} As discussed, 1 percent was used to calibrate the 4.5 percent minimum capital requirement. Because Basel III also includes the CCB and, for GSIBs, the GSIB surcharge, the combined maximum allowable annual probability of default is much lower.