System-wide risk and systemic importance:
Incomplete review of metrics and data
Nikola Tarashev, Bank for International Settlements
Cambridge, 25 September 2014
Restricted
This presentation does not necessarily reflect the views of the
BIS, the BCBS or the BCBS Secretariat.
Restricted
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
Restricted
3
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
Restricted
4
Limit the probability of failure: VaR
Tail of loss distribution (a bank’s assets)
VaR = default point
Losses absorbed by capital
Restricted
5
Prepare for / insure against costs of failure: ES
Tail of loss distribution
Losses absorbed by capital
ES  DI premium
Restricted
6
Regulatory arbitrage
 VaR: incentives for banks to hide behind a quantile
Tail of loss distribution
VaR = default point
Restricted
7
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)
Restricted
8
Contribution approach (CA) vs. participation approach (PA)
 𝑆ℎ𝑉 𝑖; 𝑁, 𝜌 =
1
𝑛
1
𝑛
𝑛𝑠 =1 𝑐 𝑛
𝑠
𝑆∌𝑖
𝑆 =𝑛𝑠
𝜌 𝑆∪ 𝑖
−𝜌 𝑆
 𝜌𝐶𝐴 𝑆; 𝑚 = 𝐸 𝐿 𝑆 𝑒 𝑆, 𝑞; 𝑚
 𝜌𝑃𝐴 𝑆; 𝑚 = 𝐸 𝐿 𝑆 𝑒 𝑁, 𝑞; 𝑚
Restricted
9
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 ?
Restricted
10
Numerical setup
 Bank-level losses:
 data on non-equity liabilities
𝐿 𝑖 = 𝜑𝑖 𝐿 𝑖
 Correlated defaults
 data on marginal PDs & asset correlations
𝐿 𝑖 =
1 𝑖𝑓 𝑟𝑖 𝑀 + 1 − 𝑟𝑖2 𝑍𝑖 < 𝛷−1 𝑃𝐷𝑖
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
 Derive distribution of system-wide losses  VaR or ES
Restricted
11
Participation vs. contribution
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
26
28
28
(100%)
(100%)
(100%)
(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
Similar message with ES
Restricted
12
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
Restricted
13
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)
Restricted
14
IB lender vs. IB borrower: the approach matters
Restricted
15
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)
Restricted
16
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
Restricted
17
Humble even with price data
Restricted
18
Bank characteristics and systemic importance
Restricted
19
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
Restricted
20