CISS – A Portfolio-Theoretic Framework for the Construction of Financial Stress Indexes

1. CISS – A Portfolio-Theoretic Framework for the Construction of Financial Stress Indexes Manfred Kremer European Central Bank Presentation at the Conference of European Statistics Stakeholders (CESS), Budapest, 21 October 2016 The views expressed are those of the authors and do not necessarily reflect those of the ECB or the Eurosystem.

2. Outline • Introduction • Statistical indicator design • Basic setup • Raw stress indicators • Normalisation • Aggregation • Final indicator • Basic indicator properties • Resume and research programme Goody - Cross-country spillovers

3. 1. Introduction • What is the CISS about, and why is it distinct? • Composite Indicator of Systemic Stress (pronounced “KISS”); • Novel “financial stress index”, i.e. a composite indicator quantifying the current state of instability in the financial system by aggregating a number of individual stress indicators into a single statistic • “thermometer”, no “barometer”; • Focuses on measuring systemic financial stress(stress ≈ risk ex-post) • Conceptual design builds on the notion of systemic risk “Systemic risk can be defined as the risk that instability becomes so widespread within the financial system (‘horizontal view’) that it impairs its functioning to the point where economic growth and welfare suffer materially (‘vertical view’).”(de Bandt and Hartmann, 2000); • Systemic stress or instability operationalised by applying portfolio theory to the aggregation of robustly normalised individual stress indicators.

4. 2. a) Basic setup • Ideally, CISS should capture strains in every part of the financial system, weighted by its systemic importance  obviously impossible. • Proposed basic statistical framework (applied to euro area data): • identify the (five) main aggregate financial market segments covering the main flows of financial funds; • populate each market segment with an identical number (three) of representative (ideally complementary) raw stress indicators; • apply probability integral transform to homogenise raw indicators; • compute a time-varying matrix of rank-correlations between the transformed indicators and … • … use the correlations to aggregate the transformed indicators into the composite index (the CISS) based on basic portfolio-theory.

5. 2. b) Raw stress indicators “You can’t see the wood for the trees”

6. 2. c) Normalisation • Raw stress indicators transformed by applying probability integral transform: • implementation involves order statistics: replace each value of the raw indicator xt by its ranking number r, scaled by the sample size n (equivalent to empirical CDF) • yields a set of standard uniform distributed indicators • recursive transformation over expanding samples to preserve “real-time” character • trades off consistency and (likely) gains in statistical robustness against loss of information from abandoning the cardinal scale of the original units of measurement.

7. 2. c) Normalisation (cont’d) • Probability integral transform: example case

8. 2. d) Aggregation: Portfolio-theoretic framework • Individual indicators aggregated into composite indicator based on portfolio theory • Compute system-wide stress analogous to portfolio risk in a static CAPM framework • Simple two-asset example: • General n-asset case:

9. 2. d) Aggregation: Portfolio-theoretic framework • Applied to CISS: • replace asset risk (σi) with transformed individual stress measures (si); • portfolio risk (σp2 or σp) then yields our composite stress index (CISS). • Two avenues to introduce systemic risk features: • time-varying cross-correlations collected in correlation matrix t  widespread instability, interconnectedness • segment-specific “market shares” wi ,t in the “portfolio” of stress measures si ,t  systemic importance (size, flows, real impact, …).

10. 2. c) Aggregation: CISS formula

11. 2. d) Aggregation: Time-varying cross-correlations • Time-varying cross-correlations • computed as exponentially weighted moving averages (EWMA) • time-varying version of Spearman’s rank correlation

12. 2. d) Aggregation: Time-varying cross-correlations

13. 2.e) Final indicator: correlation impact CISS equals (square of) weighted average of subindexes if all elements of the matrix t take the value of one, i.e. if all subindexes are perfectly correlated (special case, upper bound).

14. 3. Basis indicator properties • Difficult to assess whether a financial stress index performs well both in absolute terms (What is a good indicator?) and in relative terms (Which indicator is better?) • Systemic risk is an elusive and complex phenomenon • Many degrees of freedom in constructing composite stress indicators • Severe data constraints limiting the reliability of empirical analysis (crises are “rare events”, lack of statistical degrees of freedom in “horse races”). • Assess the CISS’s performance in absolute terms: • Statistical stability and … • … economic plausibility of its information content.

15. 3. Properties: Statistical robustness • Historical signals of the CISS very robust to the arrival of new information (no “event re-classification problem”) • Example for CISS with recursion starting in January 2002

16. 3. Properties: Statistical robustness (cont’d) • The signals received from a “conventional” state-of-the-art financial stress index (FSI) shows signs of instability over time • The “event re-classification problem” can become severe.

17. 3. Properties: CISS and crisis events Euro area CISS and major financial stress events (weekly data; 2 Jan. 1987 – 7 Oct. 2016)

18. 4. Resume and research programme • CISS is a distinct financial stress index that focuses on capturing the systemic dimension of stress and on statistical robustness, the latter an essential property if the indicator shall be updated for monitoring purposes on a regular basis. • Ongoing work to compute CISS for a broader set of countries. • Ongoing work to compute CISS for individual euro area countries with cross-country indicator comparability by applying the probability integral transformation not only across time but also across countries. • Ongoing work on CISS applications in macro-econometric models to assess aggregate effects of financial instability.

19. Goody – Cross-country spillovers CISS for major economies Brexit vote

20. Goody – Cross-country spillovers (cont’d) Stronger stress spillovers from China (forecast error variance contributions in %) Note: Spillovers computed within the VAR forecast error variance decomposition framework suggested by Diebold and Yilmaz (2012). VAR with 4 lags of weekly data for the euro area, US, UK and Chinese CISS.

21. RESERVE SLIDES

22. 2. b) Raw stress indicators • Features of financial stress: • Increased uncertainty (e.g., about asset valuations or the behaviour of other agents); • Increased investor disagreement (differences of opinion); • Stronger information asymmetries (intensifying problems related to adverse selection and moral hazard); • Increased risk aversion, e.g. lower preferences for holding risky/illiquid assets (flight-to-quality / flight-to-liquidity). • Stress features bring about typical stress symptoms: • Increased volatility; wider default and liquidity risk premia; market dry-ups for risky financial instruments etc. • For our purpose, stress symptoms are captured by fairly standard raw stress indicators: • Largely price-based indicators available at high frequencies without delay and with relatively long data histories.

23. 2. b) Raw stress indicators (cont’d) • Raw stress indicators grouped into 5 market segments: • Money market (MM): realised volatility of 3-month Euribor; spread Euribor/T-bill (3-month maturity); recourse to the marginal lending facility at the ECB. • Bond market, sovereign and non-financials (BM): realised volatility of 10-year Bund; spread corporate AAA versus government bonds; 10-year interest rate swap spread. • Equity market, non-financials (EM): realised volatility of equity returns; CMAX; stock-bond correlation • Financial intermediaries (FI): realised volatility of idiosyncratic returns of the banking index; spread A-rated financials/non-financials; CMAX interacted with book-price ratio for the financial sector equity index. • Foreign exchange (FX): realised volatility of US/EUR, JPY/EUR, GBP/EUR.

24. 2.e) Final indicator: Weighted average of subindexes represents upper bound

25. 2.e) Final indicator: Decomposition chart

26. 3. How different from alternative fear gauge?

27. US CISS