The build-up of leverage in the banking sector played a prominent role in the Global Crisis.^{1} A standard description the role of leverage corresponds with the typical profile of a financial bubble as reflected in the evolution of the banks of the Eurostoxx 50 (Figure 1). Surprisingly, the traditional measure of leverage in the banking sector does not show this profile at all (Figure 2).

**Figure 1**: Eurostoxx 50 Index

*Notes*: Monthly averages. *Source*: Bloomberg and own calculations.

**Figure 2**. Leverage ratio of Eurozone banks (Ratio of total assets to equity, number of times)

*Source*: ECB Statistical Data Warehouse and own calculations.

Shin (2010) and Adrian and Shin (2010) shed some light on this conundrum. They argue that even a stable leverage ratio may imply increased risks in the balance sheets of banking systems – both on the assets and the liabilities side – as it may conceal hyperactivity and procyclicality.

My recent research aims to improve the understanding of leverage through an alternative approach that captures the hidden risks concealed in the traditional measure of leverage (Villar Burke 2013). To this end we start with a definition.

# What is leverage?

A corporation's debt represents its obligations against anyone other than its own stakeholders. Financial leverage is a relative measure of this debt and can be expressed by a combination of two out of the three main components of a balance sheet: total assets (TA), debt (D) and equity or own resources (EQ) (see Figure 3).

**Figure 3**. Balance sheet

In principle, leverage could be expressed by any of the following formulations: TA to D, D to TA, D to EQ, EQ to D, TA to EQ or EQ to TA. However, Kahneman (2011) shows how two expressions that are mathematically equivalent may lead to different decisions. This is explained by the denominator neglect (a strong focus on the headline figure of a ratio neglecting what is in the denominator) and therefore he highlights the importance of using the right framing when translating the reality into numbers. Kahneman's findings imply that debt should be in the numerator. Therefore, any expression which includes the debt in the denominator should be discarded (implying the formulation "EQ to TA" should also be discarded as debt is included within total assets).

On top of that, ratios are usually constructed by comparing a subset of a population to the overall population. In general it is difficult to interpret ratios where one component is not contained within the other. For instance, in a group with 40 males and 60 females, one would say that 40 per cent of the group are males. Expressing the ratio by saying that there are 66% males with respect to the number of females is cumbersome and confusing. As consequence, the formulation "D to EQ" should also be discarded.

Consequently, the most appropriate formulations to measure leverage are debt to total assets (D to TA) and total assets to equity (TA to EQ). In the rest of this column, I will stick to the latter formulation (TA to EQ) as it better reveals the multiplication effect of leverage. Note that debt is included in TA – in other words, the ratio of TA to EQ is equivalent to (D + EQ) to EQ.

# The components of leverage

We have seen that leverage is the ratio between assets and equity. With the outbreak of the crisis, leverage and ‘deleveraging’ have become fashionable terms but they are not always used accurately. Deleveraging is often used to mean an ‘undesirable’ or ‘disorderly’ contraction in total assets as opposed to an expansion in equity. However, it is inexact to use the term leverage to indicate the evolution of one of its components only (unless explicitly undertaking a *ceteris paribus* analysis).

**Figure 4**. Total assets and equity of Eurozone banks

*Source*: ECB Statistical Data Warehouse and own calculations.

With a clear definition of leverage, one can analyse the evolution of its components. Between 2000 and 2008, total assets and equity expanded along a very similar path (see Figure 4), which explains the stable leverage ratio on Figure 2. The decline in leverage from 2008 onwards is explained by a combination of a more moderate expansion of assets and sustained growth in equity (Figure 5).

**Figure 5**. Total assets and equity: annual growth rates, Eurozone banks, percentage

*Source*: ECB Statistical Data Warehouse.

While the leverage ratio is a snapshot of a given moment, the process of leveraging and deleveraging is linked to the evolution of leverage over time. Most macroeconomic variables, such as prices (inflation) or GDP, are geometrical (logarithmic) in nature and expressing them in terms of growth rates is a simple tool to ‘linearise’ them. This linearisation enables comparisons to be made between economies of a different size and facilitates analysis over long periods of time. However, to compare various items within the same balance sheet, a standardisation of size is not needed. On the contrary, under an expansionary context, the computation of growth rates can introduce a downwards bias due to a continuously increasing denominator.

This downwards bias can be avoided by expressing the evolution in terms of flows,^{2} which combine the information content of both absolute terms and growth rates. The relation between total assets and equity – the leverage – stands out when both series are expressed in terms of flows (Figure 6, left-hand panel); at the same time, trends and changes are clearly outlined.

**Figure 6**. Total assets and equity: net annual flows, Eurozone banks, € billion

*Notes*: Annual flows are computed as the sum of twelve consecutive months in a rolling window. "Net" refers to new transactions minus redemptions.*Source*: ECB Statistical Data Warehouse and own calculations.

When expressed in terms of flows, the evolution of total assets captures both episodes of boom and bust in a clearer way than percentage growth rates. For instance, during the run up to the crisis, flows of total assets increased fourfold (from less than €1,000 billion a year to almost €4,000 billion), while growth rates increased only threefold (from 5% to less than 15%), due to the "downwards bias" generated by a continuously growing denominator.

It could be argued that this is just a matter of scale; but the series on equity refutes this (Figure 7, right-hand panel). With the outbreak of the crisis, banks received multiple pressures to offset losses and to increase capital buffers: new regulatory requirements, stress tests, the EBA recapitalisation exercise, public capital injections to bailout banks, and so on. This reality is better captured by equity flows, which remained high (as shown by the thick dotted line in Figure 7), than by growth rates, which seem to decline from a peak in 2008 (the thin dotted line). The two dotted lines again illustrate the downward bias of growth rates.

**Figure 7**. Total assets and equity: net flows vs. growth rates, Eurozone banks

*Notes*: Annual flows are computed as the sum of twelve consecutive months in a rolling window. "Net" refers to new transactions minus redemptions.*Source*: ECB Statistical Data Warehouse and own calculations.

# The marginal leverage ratio

Flow data allow for computing an alternative leverage ratio as the relation of flows of total assets and flows of equity. This can be called the *marginal* leverage ratio as it reveals the leverage related to new activities, or *leverage* speed as it provides an indication of the leverage dynamics. In fact, the Basel III statement quoted in the first paragraph of this column speaks about "build-up of leverage" – an implicit reference to leverage dynamics and flows.

A major advantage of the marginal leverage ratio with respect to the traditional absolute leverage ratio is that the former is free from the ‘legacy’ or inertia of the overall balance sheet. Banks can embark in highly leveraged activities and conceal them under their gigantic balance sheets. The marginal leverage ratio avoids this by focusing exclusively on new activities.

Data for the aggregate of Eurozone banks show a marginal leverage ratio with more extreme values and with more drastic swings than the absolute leverage ratio (Figure 8). The evolution of this marginal leverage ratio is consistent with the dramatic effects described by Basel III for both the buildup of excessive leverage and for the quick deleveraging processes.

The comparison between the absolute and the marginal leverage ratio provides a framework for a more accurate use of the terms ‘leveraging’ and ‘deleveraging.’ Banks deleverage when their new activities have a lower leverage than their overall portfolio, in other words, when their marginal leverage ratio is below their absolute leverage ratio. This has indeed been the case since early 2008 (Figure 8). The deleveraging process has particularly accelerated since the beginning of 2013. Further investigation would be needed to disentangle the dynamics of this process. In particular, if banks are actually cleaning up their balance sheet of ‘toxic’ assets, whether they are anticipating the Asset Quality Review and Stress Test ahead of the Single Supervisory Mechanism or whether they are responding to other constraints enters into force. Particular attention could be given to the effect on credit.

**Figure 8**. Absolute vs. marginal leverage ratios

*Notes*: The *absolute* leverage ratio is computed as total assets to total equity. The *marginal* leverage ratio is computed as annual net flows of total assets to annual net flows of equity. Annual flows are computed as the sum of twelve consecutive months in a rolling window. ‘Net’ refers to new transactions minus redemptions. Last available data: July 2013.*Source*: ECB Statistical Data Warehouse and own calculations.

While the attention is currently focused on the deleveraging process, an upper limit for the marginal leverage ratio as an early warning tool of excessive leverage could be set. The provisional proposal in Basel III implies a ceiling of around 30 to 1; however, Hoenig (2013) and Blundell-Wignall and Roulet (2013) argue that the threshold should be much lower. The leverage ceiling should be of compulsory compliance for the absolute leverage ratio, but it should only trigger an in-depth analysis when the marginal leverage ratio surpasses the threshold. After understanding the origins of a high marginal leverage ratio, authorities can decide whether or not corrective measures are appropriate.

# Additional research

While there is a vast literature on the traditional leverage ratio, the additional approach to leverage through flows presented in this column could be further investigated both at a country and bank level.

Stiglitz (2010, p. 80) shows that, in the recent financial crisis, nine American banks received $175 billion in bail-out money to compensate for nearly $100 billion in losses. At the end of the year, they paid nearly $33 billion in bonuses. While this information became available only thanks to the efforts of the New York Attorney General, the marginal leverage ratio would have probably captured those huge swings in capital (an increase due to the bail-out and a decrease due to the payment of bonuses) and triggered the alarms, provoking an in-depth analysis of their origin.

In the EU, most countries show episodes of high marginal leverage in their banking systems that could be further investigated. Data on the marginal leverage ratio and its components for EU Member States at a country level are available here.

A bank-by-bank analysis is another potential source of insights. This could be undertaken either through the financial statements published by banks or through an anonymous micro-data database. Examples of questions worth exploring would include: to what extent is the hyper-activity of banks correlated within a country? Do country aggregates conceal extreme values in specific banks? Are the episodes of extreme values in the marginal leverage ratio provoked by just a few banks within a given country or does it correspond to group herd behaviour?

*Author's note: I am grateful to Stan Maes and Maricruz Manzano for very fruitful discussions that made this paper possible. I also would like to thank the comments received from Michael Thiel, Charles Goodhart, Benjamin Angel, Sean Berrigan, Aliénor Margerit, Gérard Hirigoyen, Markus Aspegren and Marie Donnay. Jane Gimber and Nick Harrison helped to improve my English. Any remaining errors are strictly the fault of the author.
Disclaimer: The opinions and statements expressed in this column remain solely those of the author and do not necessarily reflect the views of the European Commission.*

# Bibliography

Adrian, T and H S Shin (2010), “The Changing Nature of Financial Intermediation and the Financial Crisis of 2007–2009”, *Annual Review of Economics* Vol. 2: 603-618.

Basel Committee on Banking Supervision (2011), *Basel III: A global regulatory framework for more resilient banks and banking systems - revised version June 2011*, Bank of International Settlements.

Blundell-Wignall, A, and C Roulet (2013), “Business models of banks, leverage and the distance-to-default,” OECD Journal: Financial Market Trends, 2012/2(103).

Hoenig, T M (2013), "Basel III capital: a well-intended illusion", Speech at the International Association of Deposit Insurers 2013 Research Conference. 9 April, Basel (Switzerland).

Kahneman, D (2011), *Thinking fast and slow*, London: Penguin.

Shin, H S (2010), "Financial intermediation and the post-crisis financial system", BIS Working Papers No 304.

Stiglitz, J E (2010), *Freefall: America, Free Markets, and the Sinking of the World Economy*, New York: W W Norton and Company.

Villar-Burke, J (2013), “The bonsai and the gardener: using flow data to better assess financial sector leverage”, *European Economy*, Economic Papers (500). Brussels: European Commission.

1 The Basel III agreement summarises it very clearly: "One of the underlying features of the crisis was the buildup of excessive on- and off-balance sheet leverage in the banking system. […] During the most severe part of the crisis, the banking sector was forced by the market to reduce its leverage in a manner that amplified downward pressure on asset prices, further exacerbating the positive feedback loop between losses, declines in bank capital, and the contraction in credit availability" (BCBS, paragraph 152).

2 High frequency series are embedded with seasonality. Monthly flows can be adjusted for seasonality by computing annual flows.