Systemic Leverage as a Systemic Leverage as a Systemic Leverage as a

Macroprudential IndicatorMacroprudential IndicatorMacroprudential Indicator

Sang Chul RyooBank of Korea

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OutlineOutlineⅠ. Introduction

Ⅱ. Macroprudential Indicators

Ⅲ. Systemic Leverage as a Macroprudential Indicator

Ⅳ. Empirical Analysis

Ⅴ. Conclusion

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Ⅰ. Introduction

❒ The global financial crisis of 2008 has shown that initial shocks,

even if insignificant in themselves, can cause financial crisis if

they amplify within the financial system.

▶ This lesson suggests the importance of a macroprudential

policy that deals with containing the potential risk existing

across the financial system.

è We need indicators that are able to capture the systemic risk

that evolves endogenously within the system, and to identify it

at the buildup stage.

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Ⅱ. Macroprudential Indicators

❒ Criteria required for systemic risk indicator

▶ Able to signal warning of systemic risk buildup in advance

* At least one year ahead of the business cycle (BCBS)

▶ Able to capture the two main components of systemic risk -

procyclicality and interconnectedness

▶ Easily understood by regulators, thus reducing model risk and

enhancing transparency, and the data used easily accessible

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❒ Many existing indicators are calculated using financial market data.

▶ Do not identify potential risk and signal warnings but rather

reflect the risk already revealed in the markets. They therefore

fail to function as early warning indicators.

* CDS premiums and stock price indexes one year before the global

financial crisis failed to signal warnings

è In order for macroprudential indicators to effectively signal early

warnings we should construct them using balance sheet data,

which show the stages of systemic risk buildup.

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❒ The buildup of excess leverage and subsequent deleveraging in the

balance sheets of financial institutions are critical to systemic risk.

▶ For the liability side the ratio of M1 or M2 over GDP can be a

good macroprudential indicator showing system-wide liquidity.

▶ For the asset side the most frequently used indicator is the

credit-to-GDP gap.

* Systemic liquidity depends more upon the asset side than the liability

(Drehmann, Borio, Gambacorta, Jimenez and Trucharte (2010))

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<Figure 1: Credit-to-GDP and real GDP growth rate in Korea>

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▶ Figure 1 shows that the credit-to-GDP gap has some capability

as an early warning indicator.

▶ But it has a limitation in that when the financial and real

business cycles differ interpretation becomes ambiguous.

* If GDP contracts faster than credit in the downswing, the gap can increase,

signaling excess liquidity

▶ More importantly, it is a simple aggregate of the credit supplied

by individual banks, and hence does not incorporate the

interactions among economic agents.

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Ⅲ. Systemic Leverage as a Macroprudential Indicator

❒ Leverage and procyclicality

▶ Financial institutions use leverage to maximize their return on

equity (ROE), given the return on assets (ROA).

ROE (R/E) = ROA (R/A) x Leverage (A/E)

▶ Leverage is an easy way of boosting ROE when the ROA is

positive, but the opposite holds when the ROA is negative →

procyclical.

* Adrian and Shin (2009), Leverage ⇄ MTM

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❒ Leverage and procyclicality

▶ The leverage of Korea domestic banks against their asset

growth, using quarterly data from between 1993 and 2010,

shows a weakly-positive slope.

<Figure 2: Leverage management behavior of Korean banks>

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❒ Concept of systemic leverage

▶ A macroprudential indicator that can identify leverage from systemic

risk perspective is needed. For this we propose “systemic leverage”

that aggregates individual leverages and incorporates procyclicality

and interconnectedness as systemic risk factors:

Systemic leverage =

×

systemic risk factors

▶ It is not easy to capture systemic risk factors, as they are hidden

on- and off-balance sheets and can take various forms.

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❒ Components of systemic leverage

▶ Borrowing leverage (L): assets divided by equity capital

▶ Off-balance sheet leverage (l1): derivatives and contingent liabilities

in off-balance sheet transactions divided by equity capital

▶ Interconnected leverage (l2): TB & AFS securities (asset side) plus

wholesale funding (liability side) divided by equity capital

▶ FX leverage (l3): foreign currency liabilities divided by equity capital

▶ MTM leverage (l4): assets under MTM divided by equity capital

* all components are aggregate across financial institutions

log

log

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❒ Systemic leverage index

▶ Propose the systemic leverage as a macroprudential indicator

as follows:

(1)

* We do not incorporate the MTM leverage into our indicator here, as it is not

significant for domestic banks although during the global crisis MTM losses were the main driver behind deleveraging.

◼ We use the borrowing leverage (L) as base leverage and adjust

it using systemic risk components, .

* : coefficients of systemic leverage components determined by their

contribution to systemic risk

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Ⅳ. Empirical analysis

❒ Use domestic bank B/S data provided by the Financial Supervisory Service through the Financial Analysis Information Retrieval System

* Monthly, January 2001 to December 2010 for all commercial banks, local banks, special banks and foreign bank domestic branches

Figure 3 (page 15):

▶ Borrowing leverage shows no sign of systemic risk buildup before the global crisis, sharply rising since then.

▶ OBS leverage rises steadily until the global crisis.

▶ Interconnected leverage exhibits a mild rise before the global crisis, followed by a sharp decline after it.

▶ The most dramatic component is FX leverage.

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<Figure 3: Components of systemic leverage>

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<Table 1: Basic statistics for systemic leverage>

(bil. won)

Assets OBSInter. Assets

+ Liab.FX Liab. Equity Capital

mean 1,323,416 2,840,251 438,629 216,756 77,835

median 1,182,980 1,556,524 408,907 157,636 70,806

SD 444,576 2,846,790 136,441 114,479 30,484

kurtosis 0.499 0.606 0.255 0.838 0.321

skewness -1.073 -1.239 -1.418 -0.751 -1.392

min 694,023 75,757 239,068 103,680 34,293

max 2,265,143 8,334,678 663,544 495,793 131,798

observation 132 132 132 132 132

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❒ Methodology

▶ Estimate parameters with their sensitivities to procyclicality measured from their contribution to the business cycle.

A. Measurement of the business cycle

◼ Use the KOSPI stock index and the won/dollar exchange rate, because they have monthly data and move closely along with the business cycle.

◼ Construct a Markov regime-switching model with two variables and two states, S={1, 2}, where S=1 for a crisis (i.e., high volatility) and S=2 for normal times (i.e., low volatility):

(2)

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◼ Assume that the states evolve over time in accord with the first order

Markov chain, , and that the transition

probability is time-invariant.

◼ Estimate the Markov regime switching model by the maximum

log-likelihood estimation method.

◼ Infer the filtered probabilities:

▸

▸

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0.007(1.333)

-0.011(-0.350)

0.091(0.829)

-0.165(-0.433)

0.005(3.351)

0.023(1.273) 0.98

(3.50)

0.89

(0.83)738.95

-0,002(-0.348)

0.020(0.904)

0.050(0.734)

0.065(0.248)

0.000(1.253)

0.012(0.766)

* within the parenthesis is the t-test statistics, is the transition probability from state i to state j

◼ Our estimation results show that volatility for both the KOSPI and the won/dollar

exchange rate is lower in State 1 (normal state) than in State 2 (crisis state)

▸ Returns of the KOSPI and the won/dollar exchange rate, and , are

positive and negative respectively in State 1, and the opposites hold in State 2.

▸ We can therefore claim State 1 as the normal state and State 2 as the crisis state.

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B. Parameter estimation through sensitivity analysis

◼ Given the financial cycle constructed by the process of filtered probabilities,

we estimate parameters that show each component’s sensitivity to the cycle.

(3)

: filtered probability,

: components of systemic leverage

▸ Coefficient shows the sensitivity of each component to the cycle.

▸ The upper case h is lead time between systemic components and the cycle.

▸ Coefficient of each factor is the average over the lead time h.

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◼ For all components, the sensitivity coefficient shows a positive sign and is

significant for all values of h.

<Table 3: Sensitivity of systemic risk factors to the business cycle>

OBS leverage Inter. leverage FX leverage

h=30.021***(10.986)

0.242***(5.989)

0.317***(8.449)

h=6 0.020***

(9.363) 0.309***

(7.357) 0.229***

(5.303)

h=90.015***(5.980)

0.329***(7.418)

0.124***(2.634)

h=120.009***(3.534)

0.323***(7.209)

0.075(1.559)

***, **, * indicate statistical significances of 1%, 5%, 10% respectively, and the values in parentheses are t-test statistics.

log

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◼ We get a parameter of each factor from the simple average of the sensitivity

coefficient for the horizon h = 3, 6, 9, 12. By plugging the parameters into

equation (1), we derive the systemic leverage indicator for the Korea’s banking system as follows:

(4)

❒ Evaluation of systemic leverage as an early warning indicator

▶ Systemic leverage is, for more than one year prior to the global crisis, above its 7.70 average for the period as whole

▶ If we look at the year-on-year trend of systemic leverage growth, it reaches 15% in January 2007 and remains at around 20% for about next two years, far exceeding the average of 5.20% for the whole period.

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<Figure 5-1: Systemic leverage as an early warning indicator>

<Figure 5-2: Systemic leverage as an early warning indicator>(year-on-year growth rate)

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▶ Component of systemic leverage and its contribution to overall

systemic risk

◼ FX leverage grows most rapidly before the global crisis.

◼ Interconnected leverage makes the largest contribution.

◼ With this kind of granular analysis, we can pinpoint problem areas and

deploy surgical tools and policies in response.

◼ Its simplicity and transparency help regulators better communicate with

markets.

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<Figure 6: Systemic risk components of systemic leverage>

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▶ Markov regime-switching model with three states and one variable

∆ ∆

◼ Systemic leverage indicator issues warning signals one year ahead of both

the 2003-04 credit card crisis and the 2008 global crisis.

◼ Credit-to-GDP gap issues much weaker warning signals for both crises than

systemic leverage.

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<Figure 7: Filtered probabilities of systemic leverage, estimated from regime-switching model of 3 states and 1 variables>

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<Figure 7: Filtered probabilities of credit-to-GDP gap, estimated from regime-switching model of 3 states and 1 variables>

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Ⅴ. Conclusion

▶ Our paper proposes systemic leverage as a macroprudential

indicator, incorporating the systemic risk factors, procyclicality

and interconnectedness, into the simple borrowing leverage.

◼ We conjecture external borrowing and wholesale funding and

off-balance sheet items to be the main sources of systemic

risk in Korea.

◼ We reckon these systemic risk factors as hidden leverage that

cannot be captured by a simple aggregate indicator, e.g. the

credit-to-GDP gap.

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▶ We calculate our systemic leverage indicator using B/S data for

domestic banks in Korea, and find that it issues warning signals

in advance of financial distress.

▶ We argue that it is capable of issuing early warnings because of

two characteristics:

◼ First, it uses balance-sheet data that show the accumulation of

systemic risk.

◼ Second, our systemic leverage indicator incorporates systemic

risk components that the credit-to-GDP gap lacks.

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▶ Of course, systemic leverage cannot by itself explain all aspects of

systemic risk in the financial system.

◼ It may not provide sufficient information on credit supply relative

to the real economy. supplemented by the credit-to-GDP gap.

◼ Measures of leverage can be further complemented by market

data, for example concerning the rate of asset-price growth.

▶ For further research we may carry out some cross-country

analyses, in particular incorporating the MTM leverage.

◼ We can also use the systemic leverage indicator to determine

the macroprudential levy when implemented.