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Time-varying leverage and Basel III: a look at Canadian evidence.

Abstract Why did the conventional leverage indicators not pick up any meaningful signal of the mounting systemic risk before the subprime crisis? They remained almost unchanged in recent decades, whereas the banking landscape underwent a tremendous metamorphosis. Market-oriented banking is characterized by a new type of systemic risk, a risk which essentially evolves off the radar screen, i.e., off-balance sheet (OBS) (Calmes and Theoret Journal of Banking and Finance 34 (7): 1719-1728, 2010, 2011). In this article, we argue that the standard leverage indicators are not fitted to capture this kind of new banking risk. We introduce a new empirical framework which enables us to exploit the cyclical properties of elasticity leverage measures, while at the same time controlling for the noisy information they usually deliver, In a nutshell, thanks to the Kalman filter, we are able to compute optimal levels of bank leverage. This methodology delivers cyclical, forward-looking measures signalling systemic risk bubbles years before their burst. By properly accounting for all activities, including market-oriented banking, these time-varying leverage measures tend to systemically capture regulatory capital arbitrage and the OBS risk it entails.

Keywords Leverage * Banking * OBS activities * Liquidity * Kalman Filter

JEL C13 * C22 * C51 * G21 * G32

Introduction

The activities performed by financial institutions such as banks have changed dramatically, notably with the emergence of market-oriented banking, or "shadow banking." As a result, bank balance sheets have become increasingly complex, and the off-balance-sheet components related to fee-based activities and securitization have developed at an accelerated pace. For example, successive legislative changes allowed Canadian banks to engage in investment banking in 1987 and in trust and insurance activities in 1992. These changes led to a relative reduction in the traditional role of banks as intermediaries between lenders and borrowers, a process referred to as disintermediation. At the same time, households decreased their deposits held in financial institutions and increased their investments in stocks and bonds, which provide greater returns than deposits. Finns were also funding an increasing share of their investments directly on financial markets and were relying relatively less on loans granted by banks (Fig. 1). As a result, the volatility of bank revenues and profits increased sharply during the last decades (Calmes and Liu 2009; Calmes and Theoret 2010, 2011).

The emergence of market-oriented activities poses challenges for regulators. For the purpose of financial stability, regulatory agencies monitor banks to ensure that financial institutions are able to meet their obligations and to stay solvent. Amid concerns in the early 1980s related to low capital levels of large international banks, regulators of major industrialized countries adopted the Basel Accord to work towards higher capital levels and greater convergence in the measurement of capital adequacy. With the latest iteration of this accord, Basel III, the control of leverage will be further strengthened.

In this article, we argue that, given the new banking environment, some of the measures of leverage currently used by policy-makers and regulators to define mandatory rules are to some extent unsatisfactory at tracking bank risk. These indicators, which are based mostly on ratios of on-balance-sheet items, do not fully account for the new risk associated with market-oriented banking. For instance, the conventional measure of bank leverage, defined as the ratio of total assets to equity, has been quite stable during the period preceding the subprime crisis, despite the fact that bank risk was obviously swelling. The lack of cyclicality of this ratio stems in part from its design and also potentially from regulatory capital arbitrage (Jones 2000; Calomiris and Mason 2004; Ambrose et al. 2005; Kling 2009; Brunnermeier 2009; Cardone Riportella et al. 2010). (1)

To address this drawback, we analyze a new breed of indicators based on the broadest possible span of banking activities and rely on the degree of total leverage, i.e., an elasticity concept of leverage. Accountants and auditors often approximate leverage as a ratio of balance sheet data because analysts are usually more concerned by the long-term risk profile of financial institutions than by their short-term risk. However, in economics, leverage is fundamentally an elasticity, i.e., how changes in one variable affect another. Time-varying elasticity leverage measures, which are more sensitive to the business cycle, provide valuable complementary information to policy-makers designing mandatory rules and have proven to be useful indicators of systemic risks, i.e., risks that affect the financial system as a whole. Our analysis suggests that the leverage measures we introduce could be a useful addition to the tool kit available to regulators as they try to ensure a sound and stable financial system.

This paper is organized as follows. We first discuss the behaviour of the standard leverages measures, present their drawbacks and describe time-varying elasticity-based leverage measures. Then, we provide the technical aspects of the simulation of our elasticity-based leverage measures using the Kalman filter, and we analyse the performance of the elasticity-based leverage measures before concluding.

Bank Leverage: A Background

Standard Leverage

In accounting and finance, leverage refers to the amount of debt--i.e., deposits and market-based financing other than equity--that banks use to finance their assets (loans, for instance). Everything else being constant, higher leverage tends to signal higher risk. In good times, leverage has a multiplicative impact on financial results (profits), while in bad times, it has a reductive effect. When a bank is highly leveraged, a small change in the value of its assets can completely wipe out its capital base and hence put it in a bankruptcy position.

The typical measure of bank leverage followed by analysts is the ratio of total assets to equity. (2) Total assets comprise all on-balance sheet items, such as loans. Equity includes common and preferred shares and retained earnings. Another common measure of leverage is the one employed by the Office of the Superintendent of Financial Institutions of Canada (OSFT) for regulatory purposes, which is equal to the ratio of total balance sheet assets plus certain off-balance sheet items and total regulatory capital (so-called Tier 1 and Tier 2). (3) Changes in the regulatory measure are closely related to those of the total assets to equity ratio.

The composition of debt in leverage measures has changed over time. Notably, the share of deposits, which are insured in the event of a bank default, has decreased. It was replaced by market-based financing (Fig. 2). This phenomenon raises the level of economic risks, and in particular, the exposure of banks to financial market conditions and to the business cycle, which, in turn, contributes to amplify the fluctuations of bank financial results (Calmes and Theoret 2010, 2011).

The Regulation of Bank Leverage and the Broader Regulatory Framework

Bank capital is regulated because it is believed that banks might otherwise hold less capital than prudence would require. Since banks benefit from explicit government safety nets like deposit insurance or from implicit governmental protection, (4) they are exposed to what is called a moral hazard problem: banks can take undue risk because they know that they are partly or completely insured against these risks. Financial regulation is in part designed to forestall such potential behaviours.

For example, in Canada, the OSFI places a limit to the assets-to-capital multiple of large banks since 1982. In 1991, the OSFI ceiling has been lowered from 30 to 20, and beginning in 2000, this limit has been set to 23 for banks meeting certain conditions. These Canadian capital standards, which supplement international financial regulation, may partly explain why the Canadian banking system is more resilient than in other industrialized countries where these capital standards are not yet implemented (Ratnovsky and Huang 2009). (5)

Limits on asset-to-capital multiples are just one of an array of financial regulations intended to promote the safety and soundness of financial institutions. At the international level, the Basel Committee on Banking Supervision has issued a number of recommendations regarding banking laws and regulations since 1988. These recommendations are followed by all the member countries including Canada, the United States, and the countries forming the European Union. There have been three Basel Accords, Basel I, II, and III since the inception of the Basel Committee, all of which were intended to replace simple regulatory leverage ratios with more complex, granular, calculations of bank capital ratios.

Basel I, the first of the Basel Accords, became effective in 1988. Under this accord, banks were required to hold at least 8 % of their risk-weighted assets in capital. Basel I was amended in 1996 to account for the increases in bank trading portfolios and better reflect market risk. (6) The Basel II accord, which emerged in 2004, allowed banks to resort to their own risk-assessment models or to external ratings to compute their regulatory capital. The implementation of Basel II was still in its infancy when the subprime crisis occurred. At the time, many authors argued that the Basel rules were responsible for the greater procyclicality of the banking system: capital requirements under internal ratings tend to increase as the economy falls into recession and decrease as the economy enters in expansion. More importantly, the rules were also unable to prevent the insolvency of many large banks. Consequently, a new Accord, Basel III, was launched in 2010 to strengthen the capital and liquidity standards.

Under Basel III, the required minimum ratio of capital is to be raised from 8.0 % to 10.5 %. The new regulation also includes a mandatory conservation capital buffer of 2.5 %, and a discretionary countercyclical buffer ranging from 0 to 2.5 %, depending on credit growth. Notably, in Basel III, a new leverage regulatory ratio is to be introduced for Tier I capital, which would be similar to the one already imposed by OSFI in Canada.

The Pitfalls of Standard Leverage

The main problem with conventional leverage measures is that they do not track bank risk very well. In particular, they are not particularly helpful as harbinger of episodes of financial and economic stress. Episodes of economic or financial stress are here identified using a Markov switching regime algorithm (MSR) which computes the probability of a stress period at any given point in time (Fig. 3). This MSR algorithm is applied to the logged Canadian Gross Domestic Product (GDP) expressed in deviation from its trend.

Figure 4 shows that during the period 2002-2007, even though bank risk was rising, the conventional leverage measures did not pick up this trend and displayed little variation. (7) The mandatory leverage proved better at capturing this rise in systemic risks, likely due to the fact that this measure, contrary to the simple asset-to-equity ratio, includes credit commitments. However, the mandatory leverage still excludes some important OBS components, notably securitization. In this sense, it does not fully capture the extent of a bank's potential economic risks.

When the mandatory leverage constraint becomes binding, the fact that these measures exclude some OBS activities implies that banks can potentially continue to take on more risks, as long as they are not reflected by on-balance sheet measures. The effective leverage can keep increasing even if this does not show up in the standard accounting measures of bank leverage.

More importantly, since some off-balance-sheet assets, as securitized assets, provide an alternative form of liquidity, banks are able to decrease their on-balance-sheet liquidity buffer in an effort to boost their return on equity. The ratio of banks liquid assets peaked at 21 % in 1996, and decreased to 11 % in the middle of 2007, concurrent with increases in market-oriented activities (Fig. 5). The decrease in on-balance-sheet liquidity, however, leaves banks more vulnerable to economic shocks, as the financial crisis that began in 2007 made clear. Also, off-balance-sheet revenues tend to be more volatile than on-balance-sheet revenues (Calmes and Liu 2009; Calmes and Theoret 2010, 2011). In short, conventional measures do not fully capture risks that may be building off-balance sheet. Our proposed leverage indicators are designed to capture this cyclical phenomenon.

Alternative Measures of Leverage

It is possible to fully capture the role played by off-balance-sheet components in the computation of leverage by resorting to an elasticity measure of leverage. In economics, the degree of total leverage is indeed defined as an elasticity, which essentially describes how changes in one economic variable affect another. As we have described, leverage ratios indicate how a change in asset prices will affect the bank's equity or solvency. If assets have a leveraging impact on equity, in principle, we should measure the resulting outcome by the elasticity of equity (E) with respect to assets (A), defined as [DELTA]E/E / [DELTA]A/A = [DELTA]E / [DELTA]A x A/E where AE is the change in equity, [DELTA]A, the change in assets, and A/E is the conventional leverage measure. This elasticity is equal to the rate of growth of equity over the rate of growth of assets, making the percentage change in equity the result of a 1 % increase in assets. In accounting and auditing, a simplifying assumption is often used, namely [DELTA]A = [DELTA]E, so that the ratio of assets to equity is equivalent to an elasticity measure of leverage. However, in the context of market-oriented banking, new assets may well be funded by additional debt or by assets sales without influencing equity, at least in the short-run. Moreover, there are many instances where the relationship between the changes in assets and the changes in equity is not really a one-for-one mapping. Indeed, if we assume that [DELTA]A = [DELTA]E, the accounting leverage measure, i.e., A/E may a priori approximate its corresponding elasticity measure. To illustrate this, assume that the initial balance sheet of a bank is the following:

The bank's initial leverage is equal to: A/E = 100/10 = 10. Now assume that the assets of this bank increase by 10 % and that the entire increase is funded by equity. We thus register the following changes in our bank's balance sheet:

In this case, the bank's equity has thus increased by 100 %. This is what the initial bank's leverage predicts. If assets increase by 10 %, equity will increase by a multiple of 10, i.e., the bank's initial leverage. (8) But only in this case, when we can safely assume that [DELTA]A = [DELTA]E, is the accounting leverage a reliable proxy of the elasticity measure and can stand for a relevant measure of bank risk.

When [DELTA]E [not equal to] [DELTA]A, the accounting ratio A/E is no longer a proper measure of elasticity. To show this, let us assume that a portion of the increase in assets, say 5, is funded by debt. In this scenario, we have:

[DELTA]E (5) is not equal to [DELTA]A (10). In this case, the increase in equity is equal to 50 %, a multiple of 5 instead of 10, the level of the initial leverage. So when [DELTA]E [not equal to] [DELTA]A, the accounting leverage can no longer approximate its elasticity counterpart, and the elasticity measures of leverage, because they incorporate the differential ratio, are then better suited to account for the fluctuations of bank risks.

In this article, we focus on two broad measures of leverage based on elasticities. The first is the degree of total leverage (DTL), the most popular elasticity measure of leverage in the financial literature (cf. DeYoung and Roland 2001). We also consider an alternative measure of total leverage, the elasticity of bank net value (net worth) to assets. The appeal of this measure is that net value is an economic measure of wealth, a more relevant economic measure of solvency than accounting equity. As a benchmark, we also compute the elasticity of equity to assets to study the extent to which the drawbacks of the regular assets to equity ratio can be avoided with its associated time-varying elasticity counterpart. Given that total leverage measures include all activities, and in particular market-oriented banking, an additional motivation to rely on this benchmark measure is to disentangle the contribution of OBS items to leverage from the effect of the time-varying feature of our elasticity measures.

The degree of total leverage (DTL) measure is defined as the elasticity of profits ([pi]) with respect to operating revenues (OR), that is, DTL = [DELTA][pi]/[pi] / [DELTA]OR/OR, the rate of growth of profits over the rate of growth of operating income. This ratio gives the percentage change in profits following a 1 % increase in revenues. The higher this ratio, the more leveraged a bank tends to be. As in the case of leverage measured by the assets-to-equity ratio, the higher the DTL, the larger the detrimental impact a fall in operating revenues has on bank solvency, as measured by profits in this case.

Since DTL comprises the risk stemming from bank non-traditional business lines, and because these activities also impact operating revenues and profits, it can account for every banking activity, contrary to the standard leverage. Indeed, DTL provides the reaction of bank total profits to a 1 % change of its total operating revenues. It is thus an indicator of the magnifying impact of revenues on profits which takes into account all the cash-flows generated by banks, on and off-balance-sheet.

The second indicator we analyze is the elasticity of net worth with respect to assets. Net worth is the difference between bank assets and liabilities and is thus a measure of wealth, i.e., a comprehensive measure of solvency. (9) With this measure, we can compute the magnifying impact of assets on wealth and track its evolution through the business cycle. As the DTL, this measure accounts for OBS activities and can capture potential episodes of regulatory capital arbitrage.

Methodology

We consider the computation of various leverage measures: the degree of total leverage, DTL; the elasticity of net worth to assets, [[xi].sub.NW,assets] and the elasticity of equity to assets, [[xi].sub.NW,assets], assets, which serves as a benchmark (given its close link with the conventional definition of leverage). The empirical framework we introduce enables us to exploit the cyclical properties of the elasticity leverage measures, while at the same controlling for the noisy information they usually deliver. We use the Kalman-filter to smooth the behaviour of the series and compute their optimal path.

Assume the following leverage model (10):

log ([[pi].sub.t]) = [[phi].sub.1] + [DTL.sub.t]log([OR.sub.t]) + [[epsilon].sub.1]

[DTL.sub.t+1] = [[phi].sub.1] + [phi].sub.3][DTL.sub.t] + [[eta].sub.t] with [[pi].sub.t], profits; [DTL.sub.t], the degree of total leverage; [OR.sub.t] operating revenues; [[phi].sub.i] the parameters to estimate; [[epsilon].sub.t], a Gaussian noise with variance [v.sub.1t], and [[eta].sub.t] a Gaussian noise with variance [v.sub.2t]. The first equation is the measure equation while the second is the state equation. In this model, [DTL.sub.t] is the state or unobserved variable we want to estimate.

At time t-1, estimates of [DTL.sub.t-1] of its variance, [[omega].sub.t-1], and of the coefficients [[phi].sub.i,t-i] must be provided. For instance, if t=0, we must have preliminary estimates (seed values) of [DTL.sub.0] and [[omega].sub.0]. However, since these values are unknown, we assume that [DTL.sub.0]=0 and that [[omega].sub.0] is high to account for the uncertainty related to the estimation of [DTL.sub.0]. Let us go back to time t-1 of the simulation. The three steps of the simulation are the following:

In step 1, the forecast step, the filter computes the two following forecasts: (i) [DTL.sub.t|t-1], the forecast of [DTL.sub.t] a time t-1, which is the conditional expectation of DTLt given the information available at time t-1; (ii) [[omega].sub.t|t-1] the forecast of [[omega].sub.t], at time t-1, which is the conditional expectation of [[omega].sub.t] at time t-1. These forecasts are unbiased conditional expectations computed as follows: [DTL.sub.t|t-1] = [[phi].sub.2,t-1] + [[phi].sub.3,t-1[DTL.sub.t-1]], and [[omega].sub.t|t-1] = [[phi].sub.3,t-1.sup.2][[omega].sub.t-1] + [v.sub.2, t-1]

In step 2, the revision step, new information on [[pi].sub.t] is available (time t). We can thus compute the forecast error [v.sub.t] as follows: [v.sub.t] = log [[pi].sub.t] - [[phi].sub.1,t-1] - [[DTL].sub.t-1] log([OR.sub.t-1]). The variance of [v.sub.t] represented by [[psi].sub.t] is: [[psi].sub.t] = [[log([OR.sub.t-1].sup.2])[[omega].sub.t|t-1] + [v.sub.1, t-1. We use [v.sub.t] and [[psi].sub.t] to revise [DTL.sub.t] and its variance [[omega].sub.t].

[DTL.sub.t] = [DTL.sub.t|t-1] + log ([OR.sub.t-1]) x [[omega].sub.t|t-1] x [v.sub.t]/[[psi].sub.t]

[[omega].sub.t] = [[omega].sub.t|t-1] + [log ([OR.sub.t-1])].sup.2] x [[omega].sub.t|t-1.sup.2] x [v.sub.t]/[[psi].sub.t]

The two last estimators are the conditionally unbiased estimators which minimize their variances. The Kalman filter is optimal in the sense that it is the best estimator within the class of linear estimators.

In step 3, the parameter estimation step, we resort to the maximum likelihood estimation method to estimate the parameters [[psi].sub.i]. The maximum likelihood function is: e = 1/2 [summation over t]log([[psi].sub.i]) - 1/2[summation over t][v.sub.t.sup.2]/[[psi].sub.i]. We next move to time t+1 and repeat the three steps until the end of the sample.

Results

Consistent with the recent banking episodes, we expect the Kalman-filtered elasticity measures of leverage to present an upward trend after the Asian crisis of 1997 and until 2007, just before the occurrence of the subprime crisis, as bank risk was building up during this period in the U.S. (Rajan 2005; Adrian and Shin 2010; Blanchard 2009; Rajan 2009; Nijskens and Wagner 2011), in Canada (Calmes and Theoret 2010, 2011), and elsewhere.

Before presenting our results, it is instructive to look at the behaviour of Canadian banks' net worth, which is used to build the measure [[xi].sub.NW,assets]. In contrast to equity, note that bank net worth is quite responsive to the business cycle, increasing during the rising phases of the cycle and decreasing during contractions, an attractive feature for any series used to build a leverage measure (Fig. 6). More importantly, this series is generally forward-looking in the sense that it peaks before economic downturns. Figure 7 plots the corresponding measure of leverage, i.e., the elasticity of net worth to assets. (11) First, note that [[xi].sub.NW,assets] decreases during the 1990s recession. This corresponds to the normal deleveraging process observed during economic contractions. Second, recall that before 1991, the ceiling on the Canadian mandatory leverage required by the OSFI was set at 30. This might explain the high level of [[xi].sub.NW,assets] recorded at the beginning of the 1990s and its fall thereafter. This leverage measure was quite stable at 5 from 1991 until the Asian crisis. More precisely, for every increase of 1 % in assets, net worth increased by 5 %, which represents a high degree of leverage. (12) Thereafter, during the 1997-1998 Asian crisis, the leverage measure decreased from a high of 5 to a low of -20, which suggested that banks deleveraged substantially while stock market returns plummeted around the world. After the Asian crisis, [[xi].sub.NW,assets] recovered until 2004 and returned to its pre-crisis level of 5.

As expected. Fig. 7 also shows that this measure of leverage is forward-looking in the sense that it tracks the increase in bank risk throughout the period, a pattern largely undetected by the conventional risk measures (Fig. 4). The components of the conventional leverage measures are subject to a regulatory ceiling and hence their fluctuations are constrained in economic expansions. On the other hand, the components of [[xi].sub.NW,assets] are not regulatory constrained and can display a greater variance and more sensitivity to the business cycle than those of the standard measures. Since one of the aims of Basel III is to better address the procyclicality of the banking sector, [[xi].sub.NW,assets] appears to be particularly useful in trying to achieve this objective.

Considering our second elasticity-based measure of leverage, the DTL, let us first look at the behaviour of the bank profits series, the rate of growth of profits being the DTL numerator (Fig. 8). As net worth, the profits series seems forward-looking and quite sensitive to the business cycle and to financial crises. But there are big spikes in this series, which is not the case for the net worth series (arguably a smoother series.) The corresponding DTL measure is reproduced in Fig. 9. First note that its mean value of 2 (estimated over the period 1997-2010) suggests that the effective leverage is higher than what the standard leverage indicates. (13) Furthermore, the behaviour of DTL is quite consistent with its [[xi].sub.NW,assets] counterpart. In particular, DTL tracks the increasing trend in bank risk detected with [[xi].sub.NW,assets].

The last leverage measure we propose in this study is the one selected as a benchmark to analyze our two elasticity measures: the elasticity of equity to assets, [[xi].sub.EQ,assets]. As expected, compared to the other two measures, the benchmark fluctuates much less, its volatility being bounded in an interval ranging from 0 to 0.6 (Fig. 10). The most straightforward explanation for this finding is that even though [[xi].sub.EQ,assets] is a time-varying measure, it does not properly account for OBS activities, hence its lack of variability. In this respect, note that the outperformance of our alternative measures cannot only be attributed to their elasticity design, since the benchmark measure is itself based on the same elasticity formulation. Instead, the superiority of our indicators must also stem from the fact that they are based on more comprehensive variables.

Nevertheless, as a measure of systemic risks, the [[xi].sub.EQ,assets] measure has still a more appealing profile than its corresponding assets-to-equity ratio. For example, this indicator is definitively moving on an upward trend before the subprime crisis and, similarly to our alternative leverage measures, [[xi].sub.EQ,assets] is somewhat sensitive to the business cycle. In this respect, the peaks observed in [[xi].sub.EQ,assets] are similar to those of the DTL filtered series.

Conclusions

Accounting leverage ratios like the one proposed by Basel III, present serious shortcomings. Indeed, they may not fully reflect off-balance-sheet activities and therefore underestimate the risks associated with individual institutions, and, when aggregated, fail to capture adequately the levels of risk building up in the economy. Contrary to the accounting leverage measures, our findings about the behaviour of elasticity measures of leverage, i.e., the DTL and the elasticity of net worth to assets, show that these indicators are forward-looking measures of risk in the sense that they can account for the build-up of risk before a crisis or a recession. In that respect, the elasticity of net worth to assets peaks before economic downturns. Contrary to our elasticity measures, many indicators of financial and economic stress, like the Federal Reserve Bank of St-Louis measure or the VIX, do not track risk before a crisis, remaining low and quite stable before an economic downturn or crisis. Moreover, our elasticity measures of leverage efficiently track the deleveraging process which takes place during a crisis: banks returning to their traditional activities which are less risky than the off-balance sheet ones. Even the benchmark we use in this paper, the elasticity of equity to assets, monitors bank risk better than its accounting counterpart, the assets to equity ratio, which is akin to the ratio proposed by Basel III to regulate bank capital. Finally, our elasticity leverage measures are not subject to regulatory capital arbitrage, as is the case for the accounting measures, which tend to remain stable during expansion periods as banks move funding from on to off-balance sheet.

Since the last crisis, there has been an increased recognition that regulation should take an holistic view of the financial system, instead of focusing on individual institutions. Our leverage measures could be used as complimentary indicators of rising systemic risks in financial systems, prompting regulators to take a closer look at various indicators of such risks, potentially leading to further regulation interventions.

Acknowledgments We would like to thank the participants at the 74th Meeting of the International Atlantic Economic Society and particularly Joseph Macri for discussing our paper in the session on macroeconomic theory. We also thank John Williams for helpful discussion on market-oriented banking, and Celine Gauthier, Etienne Bordeleau, Robert DcYoung, Pierre Sarte, Georges Pennacchi, Finn Poschman for their valuable comments on an earlier version. Finally we thank the Chair CIFO for its financial support.

Published online: 2 June 2013

[c] International Atlantic Economic Society 2013

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(1.) Regulatory capital arbitrage refers to strategies that allow banks to take advantage of differences between the actual economic risks they face and how those risks are calculated for regulatory purpose. For instance, banks can move risks off-balance sheet, which will reduce their capital requirements, while still maintaining an exposure to these risks.

(2.) For instance, this is the measure reported in the bank quarterly results published by the Canadian Bankers Association.

(3.) The off-balance sheet items comprise all direct contractual exposures to credit risk such as letters of credit, sale and repurchase agreements, and other credit contingencies. Importantly, the measure excludes some OBS components like securitization or trading income.

(4.) Well expressed in the adage "too big to fair.

(5.) Another explanation for Canadian banks relative resilience is that that they resort less, on average, to market-based funding than their counterparts in other countries (Bordo et al. 2011).

(6.) As opposed to banks' book portfolios which comprise loans and are related to credit risk.

(7.) The balance sheet leverage of US commercial banks was also quite stable during the period preceding the subprime crisis and even decreased for Japanese banks.

(8.) Conversely, when assets decrease by 10 %, equity also decreases by a multiple given by the initial level of leverage.

(9.) Net worth corresponds to the measure of equity, but excludes the shares issued by the bank. Net worth may be assimilated to accumulated profits by a bank and is thus much more cyclical than equity.

(10.) To write this section, we adapted the procedure explained in James and Webber (2000), and in Harvey's (1989) textbook, a classic on the subject.

(11.) We use National balance sheet accounts provided by CAN SIM, a Statistics Canada's database. Data on bank assets and net worth are available since 1990, the longest sample at our disposal, the time series used to compute our other leverage indicators being only available after 1997.

(12.) Compared to a level below 2 for periods of low regime (low volatility for economic or financial variables).

(13.) The accounting leverage measure was quite stable around 20 during this period, which did not signal abnormal risk in the banking system. By contrast, an elasticity above 2 signals significant leverage changes. Indeed, for each increase of 1 % in operating revenues, profits increase on average by 2 %.

P. Bergevin

C.D. Howe Institute, 67 Yonge Street, Toronto, Ontario, Canada

C. Calmes

Chaire d'information financiere et organisationnelle, Ecole des sciences de la gestion (UQAM); Laboratory for Research in Statistics and Probability, LRSP, Universite du Quebec (Outaouais), 101 St-Jean-Bosco, Gatineau, Quebec, Canada

e-mail: christian.calmes@uqo.ca

R. Theoret

Ecole des sciences dc la gestion, Universite du Quebec (Montreal), 315 est Ste-Catherine, Montreal, Quebec, Canada

R. Theoret

Chaire d'information financiere et organisationnelle, Ecole des sciences de la gestion (UQAM), Universite du Quebec (Outaouais), Gatineau, Canada

Assets  Liabilities

100     Debt: 90
        Equity: 10
Assets  Liabilities

110     Debt: 90
        Equity: 20
Assets  Liabilities

110     Debt: 95
        Equity: 15
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Comment:Time-varying leverage and Basel III: a look at Canadian evidence.
Author:Bergevin, Philippe; Calmes, Christian; Theoret, Raymond
Publication:International Advances in Economic Research
Article Type:Report
Geographic Code:1CANA
Date:Aug 1, 2013
Words:5747
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