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System-wide risk and systemic importance:Incomplete review of metrics and dataNikola Tarashev, Bank for International Settlements

Cambridge, 25 September 2014

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This presentation does not necessarily reflect the views of the BIS, the BCBS or the BCBS Secretariat.

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Roadmap

1. Two competing metrics of aggregate risk: VaR and ES

a. have different statistical properties

b. are suited for different purposes

2. Systemic importance: what if data were not an issue?

a. different measures for different purposes

b. common misunderstandings

3. Data: an important driver of analyses of system-wide risk and systemic importance

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Choice of metric: rarely motivated by objectives

Two types of metrics: for portfolio risk & system-wide risk.

Quantile-based: e.g. Value-at-Risk (VaR)- robust estimation- elicitable, if data sample is known

Tail expectations: e.g. Expected Shortfall (ES)- coherent: well-defined capital optimization

problems- limits arbitrage

But these metrics serve very different purposes VaR: attain an acceptably low probability of distress ES: prepare for the fallout of distress

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Limit the probability of failure: VaR

VaR = default point

Losses absorbed by capital

Tail of loss distribution (a bank’s assets)

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Prepare for / insure against costs of failure: ES

ES DI premiumESLosses absorbed by capital

Tail of loss distribution

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Regulatory arbitrage

VaR: incentives for banks to hide behind a quantile

VaR = default point

Tail of loss distribution

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From system-wide risk to systemic importance

Shapley value: an allocation methodology & disciplining device

Satisfies appealing criteria. Captures how the interaction of players creates risk

Tarashev, Borio and Tsatsaronis (2010)

A popular alternative is a special case

Aumann-Shapley value, applied to ES or VaR = marginal ES, popularised by Acharya et al (2009)

Another popular alternative falls in a different category:

CoVaR, popularised by Adrian and Brunnermeier (2008)

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Contribution approach (CA) vs. participation approach (PA)

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Participation in tail events vs. contribution to systemic risk

Participation approach charge premia for insuring against losses in tail events

Contribution approach penalise banks for raising the risk in system

Does it really matter which one you choose ?

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Numerical setup

Bank-level losses: data on non-equity liabilities

Correlated defaults

data on marginal PDs & asset correlations

Derive distribution of system-wide losses VaR or ES

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VaR example

Low common-factor loading High common-factor loading

CA PA CA PA

Group A 34.34% 0.0% 28.15% 100%

Group B 65.66% 100% 71.85% 0.0%

Total VaR 26

(100%)

26

(100%)

28

(100%)

28

(100%)

Note: Each panel refers to a different banking system. VaR is measured in cents per dollar exposure to the system. The first two rows report the systemic importance of each group of banks, as a share in system-wide VaR and as measured by the approach specified in the column heading. For all banks, 𝑃𝐷= 0.27%. The number of banks in each groups and their respective sizes (as a share in the total system size) are as follows: 𝑛𝐴 = 5, 𝜑𝐴 = 0.07, 𝑛𝐵 = 5, and 𝜑𝐵 = 0.13. The common-factor loadings are 𝑟𝐴 = 𝑟𝐵 = 0.60 (low) and 𝑟𝐴 = 𝑟𝐵 = 0.724 (high).

Table 1

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Similar message with ES

Participation vs. contribution

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Need to remain mindful of causality

A measure of system-wide impact (CoVaR idea): quite useful from a policy perspective in practice: E(systemic distress | individual distress)

Think of the stylized banking system from above. To fix ideas: different PDs; identical exposures to common risk factor, etc.

Which bank is designated as most systemically important? The bank with lowest PD Intuition: if the safest bank is in trouble because of

common risk factor, other banks must also be in trouble.

Spurious causality misleading message

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Data availability: a factor in the metric design

Data on interlinkages in the system: Interbank network is a key driver of system-wide

risk. Different approaches to measuring systemic

importance treat interbank borrowers and lenders differently.

Drehmann and Tarashev (2013)

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IB lender vs. IB borrower: the approach matters

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Price data

Rely on markets to convey information about interconnectedness, in reduced form.

Data are rich: despite few direct observations in the tail of interest … EVT techniques possible

Tarashev and Zhou (2013)

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Empirical setup

Sample of 50 largest banks with CDS data

Data:

Balance sheet data banks’ size

CDS spreads LGD, tendency to default with others

Moody’s KMV EDFs PDs

Systemic event ≡ when losses exceed 15% of system size

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Humble even with price data

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Bank characteristics and systemic importance

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Cited papers

Tarashev, Borio and Tsatsaronis (2010): “Attributing systemic risk to individual institutions”, BIS Working Paper 308.

Drehmann and Tarashev (2013): “Measuring the systemic importance of interconnected banks”, Journal of Financial Intermediation, v. 22, iss 4.

Tarashev and Zhou (2013), “Looking at the tail: price-based measures of systemic importance”, BIS Quarterly Review, June