There is an active debate on how much capital banks should have. Yet establishing an 'optimal' level of bank capital is more art than science. Any conclusion is model-specific and contains a degree of judgement. The purpose of this column is to contribute to the debate by offering one more benchmark.
Basel III imposes on banks an equity-to-risk-weighted-assets ratio (risk-weighted capital) of between 8 and 12%. This is comprised of the 4.5% basic ratio, 2.5% conservation buffer, 2.5% countercyclical buffer (in upturns), and up to 2.5% surcharge on systemic banks. Some countries have higher capital requirements. Singapore imposes a 2% surcharge over Basel; the Vickers proposals in the UK call for a 3% surcharge; and Switzerland requires that its international banks hold extra 6% capital, bringing total capital requirements to 18-19%.
Historically, banks held more capital than they do today. In the early 20th century the leverage (equity-to-total-assets) ratio for US and UK banks was around 8-12% (Miles 2011). To convert leverage ratio into risk-weighted capital, the rule of thumb is to multiply it by 2; the average risk weight is 0.5 (King 2010, La Lesle and Avramova 2012). So the 8-12% leverage could correspond today to 16-24% risk-weighted capital. However that period is of limited guidance as banks were less diversified and did not have access to a well-developed safety net or deposit insurance. Leverage ratios for US and UK banks in 1950-70s were about 6.5%, corresponding to 13% risk-weighted capital. This is close to the Basel III targets.
It is hard to quantify precisely the recent, pre-crisis evolution of bank capital, because banks understated risk weights and held many exposures off-balance sheet. But a number of major global banks had leverage of only 3%, which under average risk weights would correspond to 6% risk-weighted capital. This is about a half of where they should be to satisfy Basel III.
In the academic community, many argue that banks may need significantly more capital. In a 2010 letter to Financial Times, signatories suggested that “if a much larger fraction, at least 15%, of banks’ total, non-risk-weighted, assets were funded by equity, the social benefits would be substantial.” This target is high; 15% leverage corresponds to 30% risk-weighted capital.
An exercise based on losses in past crises suggests up to 18% capital
Figure 1 plots the distribution of non-performing loan ratios in banking crises in OECD countries, according to Laeven and Valencia (2012). In most events, ratios were modest; the median is 6%. Including more extreme events, to comprise 85% of episodes (24 out of 28), gives non-performing loans of up to 19%. Episodes with even higher non-performing loans represent extreme, twin (banking-currency) crises, i.e. Korea in 1997, Turkey in 2000, and Iceland in 2008. Twin crises are rare in advanced economies; their risk can be reduced by controlling currency mismatches in banks and corporations. So we can take 19% as a historic upper bound for non-performing loan ratio in non-twin banking crises in advanced economies.
Figure 1. Non-performing loan ratio during banking crises in OECD countries
To obtain loan losses, the non-performing loan ratio should be adjusted for loss given default. There is little systematic data on loss given default. We use the estimate of Schuermann (2004) that the mean loss given default on senior secured debt in US over 1970-2003 was on the order of 50%. This means that 19% non-performing loan ratio corresponds to 9.5% loan losses. Around 1% of that can typically be absorbed by earlier provisioning. (In Spain, dynamic provisioning was able to achieve buffers of 1.5%; Saurina 2008.) This leaves loan losses net of provisions of 8.5%.
Bank equity may need to be somewhat higher than 8.5% when system-wide average losses are asymmetrically distributed among banks (i.e. some banks realise higher losses), or because banks need extra capital to continue operating after absorbing the losses. But there is also a powerful argument why equity could be somewhat lower; equity reduces bank risk-taking incentives, so well-capitalised banks are less likely to engage in strategies that lead to severe banking crises in the first place.
On balance, with a margin of safety, one could suggest that a 9% equity-to-total-assets ratio (leverage), corresponding to 18% equity-to-risk-weighted-assets ratio (risk-weighted capital) would offer banks enough capital to fully absorb most asset shocks of magnitudes observed in banking crises in OECD countries over the last 50 years.
We emphasise that this is a conservative estimate. For example, if one believes that higher bank capital has strong incentive effects, the appropriate capital target could be lower, say, 15%.
The estimate can be seen as good news. While conservative, it is not too far from the Basel III’s highest 12% ratio. It is very close to the Swiss capital requirements. And it suggests that more extreme proposals – such as those of 30% risk-weighted capital – are overkill.
It is useful to note some caveats.
- As with any estimate, there is significant model uncertainly. Losses in past crises can be a poor predictor of future losses, as bank risks can increase or decrease due to financial innovation.
- The estimate is based on losses on loans, not on the rest of bank balance sheet. 'The rest' today comprises about 50% of assets of an average large bank, half in trading assets and securities and half in cash and interbank claims (King 2010). Trading securities can have larger losses, while cash and interbank claims be safer than loans during crises. One could refine the analysis to arrive at a more precise estimate of capital needs by modelling bank asset structure with associated crisis losses and risk weights in more detail.
- We base the estimate on data for OECD countries (relevant for advanced economies). Historic losses in banking crises in emerging and developing economies were larger, due to weaker resolution tools and legal environment.
- We assume that all absorption capacity has to be provided by bank capital – equity. In practice, some can be provided by contingent capital – a debt security that contractually converts into equity well ahead of bank distress. Some recent policy initiatives focus on 'bail-inable' debt, which the government can haircut during crises (Zhou et al. 2012). But haircutting bank debt risks exacerbating a crisis, so it is unclear whether relying on the absorption capacity of bail-inable debt is optimal from an ex ante perspective.
- The estimate is a target for bank capital at the peak of the cycle. When the economy is slow or contracting, bank capital requirements could be lowered to facilitate lending and recovery.
Overall, we hope that notwithstanding these caveats this simple calculation may provide a useful benchmark for thinking about optimal capital levels.
The costs of higher capital are modest in steady state, but adjustment is a challenge
If one uses the losses in past crises as a gauge for 'optimal' bank capital, what would be the cost associated with higher capital levels?
There are two ways to calculate the effect of higher capital on the bank’s cost of funding. One is to keep the costs of bank’s debt and equity exogenous. Assume that the required return on bank equity is 15%, and the cost of bank debt is 5% (3% net of tax shield). Then an increase in the bank’s risk-weighted capital ratio by one percentage point, equivalent to a shift of 0.5% of funding from debt to equity (given the average risk weight of 0.5), would increase the weighted average cost of capital by six basis points. This type of analysis is used by Elliott 2009 and BCBS 2010; it produces the highest possible costs.
Another way is to base on the Modigliani-Miller proposition that the banks’ overall cost of funding should not increase with higher equity (as equity and debt become safer and cheaper; Admati and Hellwig 2013), except for the tax shield effect. Then – under similar assumptions – an increase in the bank’s risk-weighted capital ratio by one percentage point would increase the weighted average cost of capital by just one basis point. Under additional departures from Modigliani-Miller, the cost can be somewhat higher: Kashyap et al (2010) suggest up to 2.25 basis points for a one-percentage-point increase in risk-weighted capital.
Thus, the costs of higher bank capital in steady state are modest. An increase in bank capital requirements by six percentage points from the Basel’s 12% to our very conservative 18% would increase the banks’ cost of funding (and hence the lending rates) by about 13.5 basis points under the Kashyap et al (2010) estimate. And in the case where Modigliani-Miller does not hold (exogenous costs of debt and equity) the increase would be 36 basis points.
While the high level of bank equity is not prohibitively costly in steady state, the costs of raising bank capital quickly may be substantial. Issuing new equity has underwriting and adverse selection costs. Reducing dividends to boost retained earnings may lead to declines of bank capitalisation and weaken confidence. But the main risk is that banks can increase capital ratios by cutting lending. Aiyar et al (2013) show that about a half of banks’ short-term response to an increase in capital requirements occurs through a contraction of balance sheet. This means, for example, that an increase in capital requirements from 10% to 11% (by one percentage point, equivalent to 10%) could reduce lending associated with the highest risk weights (e.g. non-financial corporate lending) by as much as 5%. So the adjustment cost cannot be neglected.
This suggests that banks should increase their equity over a period of time, backloaded to the time when economic growth accelerates. For Europe, this may be another argument for the European Stability Mechanism support to banks in distressed countries (Dell’Arricia et al 2013).
Author's note: The views expressed are those of the author and do not represent those of the IMF. I thank Charles Calomiris, Stijn Claessens, Luc Laeven, Srobona Mitra, and others for helpful comments. All errors are mine.
Admati, A and M Hellwig (2013), The Bankers' New Clothes: What's Wrong with Banking and What to Do about It, Princeton University Press.
Aiyar S, C Calomiris and T Wieladek (2013), "Does Macro-pru leak?" Journal of Money, Credit and Banking, forthcoming.
BCBS [Basel Committee on Banking Supervision] (2010), "An assessment of the long-term economic impact of stronger capital and liquidity requirements".
Dell’Ariccia G, R Goyal, P Koeva-Brooks and T Tressel (2013), "A Banking Union for the Eurozone", VoxEU.org 5 April.
Elliott, D J (2009), "Quantifying the effects on lending of increased capital requirements", Brookings Institution Working Paper.
Kashyap A K, J C Stein and S Hanson (2010), "An analysis of the impact of substantially heightened capital requirements on large financial institutions", Working Paper, Harvard University.
King, M R (2010), "Mapping capital and liquidity requirements to bank lending spreads", BIS Working Paper 324.
La Lesle, V and S Avramova (2012), " Revisiting risk-weighted assets", IMF Working Paper 12/90.
Laeven, L and F Valencia (2012), "Systemic Banking Crises Database: An Update", IMF Working Paper 12/163.
Miles, D (2011), "What is the optimal leverage for a bank?", VoxEU.org, 27 April.
Saurina, J (2009), "Loan loss provisions in Spain. A working macroprudential tool", Revista de Estabilidad Financiera 17, 11-26.
Schuermann, T (2004), "What do we know about loss given default?" Federal Reserve Bank of New York.
Zhou J, V Rutledge, W Bossu, M Dobler, N Jassaud and M Moore (2012), "From bail-out to bail-in: mandatory debt restructuring of systemic financial institutions", IMF SDN 12/03