Updated Stress Testing Features in RiskMetrics RiskManager

Transcription

1 Updated Stress Testing Features in RiskMetrics RiskManager Predictive Stress Test for the 2009 Equity Market Rally. Audrey Costabile Christopher Finger Katarzyna Siudek 1 (Marie Curie Fellow) December 1 Katarzyna Siudek was a Marie Curie Fellow at MSCI. The research leading to these results has received funding from the European Community s Seventh Framework Programme FP7- PEOPLE-ITN-2008 under grant agreement number PITN-GA (project name: RISK). The funding is gratefully acknowledged.

2 Introduction MSCI has updated the RiskMetrics RiskManager 4 stress testing library with new predictive historical stress testing scenarios. The tests were designed to help users replicate the effects of the 2009 equity market rally. The new stress tests use RiskManager s predictive stress test functionality to spread the selected shocks to other factors based on the factor covariances. This allows for more comprehensive approach than a simple test. The time frame and factor selection for the stress tests are described in the first part of this paper. In the second part we check for the numerical stability of above stress test. Scenario for the 2009 Rally Time frame selection After the 2008 crisis, markets showed significant growth in 2009, especially between March and December, when the Nasdaq grew 70%, while the S&P and DAX grew 60%. March was the month which recorded the fastest level of growth. Stress levels were selected by finding a concentration of biggest returns in similar period for all indices. March was identified as the month of fastest growth; the biggest 10-day and 22-day returns were noted in the period from early March to mid April For particular risk factors slightly different dates were used. Stress levels are summarized in Table 1 below. Table 1: Stress Levels of Risk Factors Risk Factor S&P 500 Index DAX Index FTSE 100 Index 10-day Stress Test Dates day Stress Test Dates MSCI Emerging Market Index Nikkei 225 Index Old NYMEX Light Sweet Crude Oil CDX UK Government Debt Benchmark - Zero Coupon 24M UK Government Debt Benchmark - Zero Coupon 60M MSCI Inc. All rights reserved. 2 of 13

3 UK Government Debt Benchmark - Zero Coupon 120M US Government Debt Benchmark - Zero Coupon 24M US Government Debt Benchmark - Zero Coupon 60M US Government Debt Benchmark - Zero Coupon 120M German Government Debt Benchmark - Zero Coupon 24M German Government Debt Benchmark - Zero Coupon 60M German Government Debt Benchmark - Zero Coupon 120M The selection of risk factor dates reflect the biggest changes in a similar period for all assets. This is illustrated in Tables 2-5, which show the returns for consecutive dates. The levels which were selected for the test have been highlighted. Table 2: 10-day returns for Indices, Crude oil and CDX Date CDX.NA.I G.11 60M % % % % % % % % Light Sweet Crude Oil 1M -0.60% 11.76% 24.55% 11.32% 16.63% 23.21% 15.46% 1.72% DAX Index FTSE 100 Index Nikkei 225 Index MSCI EM (Emerging Markets) in USD S&P 500 Index % % -6.06% % % % % -5.44% -8.58% % -7.47% -9.01% -3.23% -4.43% -9.58% % % -1.64% -6.38% % -8.67% -9.21% -3.28% -2.82% % -6.21% -8.01% -3.93% -4.87% -8.99% -0.23% -2.65% -2.94% -0.01% -6.93% 1.77% -4.03% -1.14% 1.40% -5.69% MSCI Inc. All rights reserved. 3 of 13

4 % % % % % % % % % % % % % % % % % % % % % % % % % % % 4.59% 3.56% 16.69% 17.10% 5.46% 16.39% 11.46% 13.10% 16.36% 21.80% 14.48% 12.59% 2.18% 0.56% 0.33% 2.86% 2.84% -3.04% -6.33% -3.88% -1.21% 2.39% 6.87% 3.50% 4.84% -2.67% -2.10% 0.34% -5.20% -3.48% 2.00% -0.28% 2.86% -1.99% 0.01% 5.74% 2.92% 9.02% 6.57% 5.82% 13.59% 7.57% 8.05% 9.82% 9.95% 13.81% 11.75% 2.71% 4.36% 9.34% 10.22% 11.43% 9.42% 8.13% 6.89% 14.20% 14.87% 10.97% 8.84% 10.77% 13.24% 12.46% 13.12% 11.59% 15.94% 19.37% 21.64% 7.73% 5.28% 20.32% 15.68% 12.02% 7.90% 5.59% 14.97% 14.62% 12.83% 7.66% 5.74% 19.98% 16.23% 10.94% 6.32% 3.87% 13.97% 12.00% 7.85% -1.37% -2.62% 6.90% 4.04% 4.46% 2.43% 1.79% 2.02% 5.18% 2.54% 3.37% 3.96% 4.76% 6.78% 2.11% 8.37% 8.07% 9.74% 9.98% 6.42% 7.77% 4.86% 10.12% 11.60% 9.62% 4.15% 1.03% 7.82% 7.55% 1.53% 3.23% 0.49% 4.06% 5.91% 1.17% 3.19% 0.65% 1.36% 3.88% 1.39% 5.44% 1.49% 3.24% 5.49% 2.85% 6.84% 2.18% 3.91% 7.56% 4.98% 12.58% 5.87% 8.36% 14.10% 9.04% 11.56% 1.60% 9.04% 13.26% 5.47% 10.14% 0.32% 4.68% 10.86% 5.05% 5.19% -1.75% 0.41% 5.76% 3.71% 6.66% 1.57% 1.80% 4.26% 3.22% Table 3: 10-day returns for Government Bonds German Government Debt Benchmark - Zero Coupon UK Government Debt Benchmark - Zero Coupon US Government Debt Benchmark - Zero Coupon Date 24M 60M 120M 24M 60M 120M 24M 60M 120M % 1.55% 0.32% 4.60% 1.01% 2.79% % -3.70% -0.85% % 5.50% 2.86% -3.82% -1.02% 4.80% 0.85% 9.09% 8.67% % 5.55% 4.96% % -1.37% 7.31% -4.10% 5.83% 7.70% % -4.77% -2.21% % % -3.69% % -4.67% -1.42% % -2.54% -2.12% % % % -2.52% 2.19% 3.03% MSCI Inc. All rights reserved. 4 of 13

5 % -1.07% -3.17% -8.08% % -9.85% 1.30% 3.23% 3.96% % 3.72% 0.05% -4.90% % -8.70% 3.49% 5.49% 7.49% % 6.11% 1.39% -1.79% % % -0.18% -3.02% -0.35% % -3.06% -3.72% -4.04% % % -5.16% -7.72% -4.34% % 0.15% -0.31% -1.41% % % 1.07% -5.50% -3.89% % 8.08% 3.52% 5.89% % % 17.82% 6.67% 3.17% % 10.86% 4.34% 17.20% % % 18.85% 8.94% 4.59% % 8.42% 1.89% 13.78% -9.96% % % % % % 8.65% 1.47% 16.56% 3.86% % -0.59% -7.71% -6.80% % 6.90% 1.26% 5.93% 5.90% -0.83% -5.54% % -7.82% % 5.31% 2.93% -0.50% 5.59% 0.47% -5.30% % -6.57% % 6.51% 4.90% -1.68% 15.34% 6.14% -8.90% % -9.55% % 5.96% 3.19% -5.88% 14.70% 7.13% -8.13% -5.79% -3.64% % 7.71% 3.65% -3.90% 17.37% 11.80% % -7.95% -3.62% % 2.99% 0.62% -4.95% 15.69% 11.84% -7.30% -4.54% -4.27% % -2.97% -4.38% % 7.25% 5.87% % % -7.56% % -7.22% -6.91% % 6.13% 3.72% % % % % -8.48% -7.22% % 0.66% 1.12% -3.96% 3.39% 4.61% % 3.64% 3.36% -3.18% 10.66% 10.53% -0.42% 5.68% 6.56% % 11.55% 8.19% 4.38% 13.09% 12.66% 6.71% 12.00% 9.83% % 7.15% 6.70% 13.21% 13.03% 9.45% 2.48% 11.54% 9.91% % 1.03% 1.78% 14.85% 5.33% 3.52% -3.39% 6.04% 7.20% % -0.27% 2.40% 10.85% 2.22% 1.62% -1.25% -0.09% 2.70% % 0.39% 3.48% 6.66% -0.95% -0.55% 6.00% 7.46% 6.70% % 1.99% 3.21% 7.75% -0.83% 0.04% 5.83% 5.34% 6.15% % 6.01% 6.83% 15.53% 3.87% 3.00% 6.14% 5.53% 5.54% % 6.75% 6.22% 11.99% 1.08% 1.69% 9.46% 4.83% 4.93% % 5.21% 5.41% 19.41% 6.46% 3.89% 8.30% 4.83% 4.54% % -2.61% 1.29% -1.42% -4.07% -3.87% 4.19% 1.88% 2.55% % -2.32% 1.21% 5.03% -0.54% -2.12% 3.65% 2.98% 2.44% Table 4: 22-day returns for Indices, Crude oil and CDX Light Sweet Crude Oil Date CDX.NA.I G.11 60M % % % % % 1M 18.25% 36.36% 39.85% 34.32% 35.29% DAX Index FTSE 100 Index Nikkei 225 Index MSCI EM (Emergin g Markets) in USD S&P 500 Index -8.48% -7.98% 2.86% -0.67% -3.93% -4.11% -5.38% 3.93% 7.02% -0.65% -3.24% -4.09% 5.46% 7.10% -2.52% -0.92% -1.63% 8.70% 11.11% 5.65% 4.30% 0.58% 14.45% 15.72% 4.68% MSCI Inc. All rights reserved. 5 of 13

6 % % % % % % % % % % % % % % % % % % 37.12% 35.57% 23.10% 7.33% 11.02% 19.36% 25.50% 15.47% 17.00% 8.65% 6.97% 16.00% 23.90% 9.67% 10.95% 7.24% 4.31% 7.20% 7.29% 1.29% 14.96% 15.15% 9.49% 9.33% 2.85% 18.82% 19.29% 7.72% 9.29% 1.30% 15.62% 16.99% 6.67% 1.18% -3.90% 10.43% 11.00% 4.61% 6.27% 2.51% 7.15% 14.15% 8.54% 11.35% 9.10% 14.72% 22.24% 15.73% 18.73% 17.45% 20.61% 28.75% 19.83% 12.70% 10.53% 20.01% 25.06% 18.18% 17.71% 13.14% 19.16% 27.63% 22.41% 17.89% 11.32% 23.14% 26.13% 19.34% 18.04% 10.82% 21.30% 25.74% 21.97% 15.54% 7.23% 26.38% 25.85% 19.03% 14.74% 7.85% 21.53% 24.11% 18.74% 13.52% 7.32% 23.98% 24.15% 14.38% 15.26% 6.27% 16.82% 22.27% 11.23% 12.49% 2.70% 13.48% 19.31% 13.02% 15.59% 5.08% 10.14% 19.65% 11.20% 17.03% 7.56% 11.73% 18.30% 9.47% Table 5: 22-day returns for Government Bonds German Government Debt Benchmark - Zero Coupon UK Government Debt Benchmark - Zero Coupon US Government Debt Benchmark - Zero Coupon Date 24M 60M 120M 24M 60M 120M 24M 60M 120M % 13.26% 5.83% 9.91% -9.98% % % % % % 13.51% 2.31% 10.52% -9.81% % 0.68% -0.94% -1.14% % 6.19% -1.03% -3.60% % % -8.98% -9.40% -4.17% % 1.62% -2.32% -6.92% % % -8.34% % -6.30% % 11.82% 4.96% -8.69% -4.04% -2.90% -2.36% -4.91% -2.30% % 10.58% 4.59% % -5.55% -4.57% -1.00% 0.79% 1.76% % 10.15% 3.74% -5.16% -1.67% -3.71% % -7.79% -1.46% % 9.20% 3.65% -5.89% -2.57% -5.97% % % -4.98% % -1.12% -3.34% % % % % % -8.53% % -2.62% -4.27% % % % % % % % 2.08% -2.13% % % % -6.95% -9.63% -6.70% % 11.51% 2.81% 11.27% 0.84% -6.47% -0.59% -4.03% -3.06% % 12.23% 2.02% 12.30% 0.12% -7.45% 1.28% -4.11% -2.27% % 14.35% 6.58% 21.71% 19.09% 1.10% 5.56% 4.84% 4.47% % 15.91% 9.15% 16.60% 22.80% 12.67% -3.24% -1.33% 1.66% % 11.48% 10.61% 6.49% 15.17% 7.56% -3.50% -2.45% 0.53% MSCI Inc. All rights reserved. 6 of 13

7 % 6.61% 7.29% 6.36% 14.36% 4.89% -8.12% -6.06% -2.18% % 4.97% 5.50% 3.25% 14.66% 6.53% -7.40% -3.32% 1.22% % 8.13% 7.26% 2.49% 16.25% 11.19% % -4.55% 0.92% % 3.80% 1.99% 0.12% 11.01% 9.49% % -7.39% -2.66% % -0.64% -0.34% -0.98% 11.24% 7.73% % % -5.46% % -2.03% -0.20% -6.42% 8.76% 6.11% % % -4.95% % 1.11% 1.34% 3.67% 10.60% 8.12% 17.64% 20.26% 16.29% Trends reflecting the risk factor biggest changes are also illustrated in Figures 1-6 below. Figure 1: Equity Indices Figure 2: CDX North America Investment Grade Index MSCI Inc. All rights reserved. 7 of 13

8 Figure 3: Crude Oil MSCI Inc. All rights reserved. 8 of 13

9 Figure 4: German Government Bonds and DAX Figure 5: UK Government Bonds and FTSE Figure 6: US Governmental Bonds and S&P MSCI Inc. All rights reserved. 9 of 13

10 Scenario Definitions The selection of risk factors for the stress tests includes major indices: S&P 500, FTSE 100, German DAX, Japan Nikkei and an emerging market MSCI index. Due to the character of the preceding 2008 crisis, credit risk was found to be an important factor. For this reason the CDX investment grade index was added as an important credit derivative used to hedge credit risk. Interest in less risky assets was observed during that period and is expressed by including German, UK and US government bonds. Finally, increasing prices of crude oil were also identified as an important factor. Table 6: Stressing Risk Factors Risk Factors 10-day Stress Test 22-day Stress Test S&P 500 Index 21.64% 22.41% DAX Index 13.12% 18.73% FTSE 100 Index 11.59% 17.45% Nikkei 225 Index 20.32% 23.14% MSCI Emerging Market 19.37% 28.75% NYMEX Light Sweet Crude Oil 21.80% 25.50% MSCI Inc. All rights reserved. 10 of 13

11 CDX UK Government Debt Benchmark - Zero Coupon 24M UK Government Debt Benchmark - Zero Coupon 60M UK Government Debt Benchmark - Zero Coupon 120M US Government Debt Benchmark - Zero Coupon 24M US Government Debt Benchmark - Zero Coupon 60M US Government Debt Benchmark - Zero Coupon 120M German Government Debt Benchmark - Zero Coupon 24M German Government Debt Benchmark - Zero Coupon 60M German Government Debt Benchmark - Zero Coupon 120M % % 17.20% 21.71% % 19.09% % 1.10% 18.85% 5.56% 8.94% 4.84% 4.59% 4.47% 23.52% 29.04% 10.86% 14.35% 4.34% 6.58% Numerical stability Introduction To ensure numerical stability of the calculations we use the theory of pseudo inverse. Pseudo inverse is a generalization of the regular inverse that allows us to achieve stable results in regression problems. The details for this methodology are described in other MSCI paper (include links/reference here) - Predictive stress test for Gulf War 2, Tech Wreck 2000 and 8 Major Global Indices Monthly Worst. Diagnostics of numerical stability (respective dates). Roughly speaking we will claim that a matrix is well-conditioned if its regular and pseudo inverse are identical. For this we check if all singular values of the matrix are greater than some certain threshold. The threshold is equal to (maximal singular value of the matrix)*(matrix dimension)*(machine epsilon). MSCI Inc. All rights reserved. 11 of 13

12 Results The numerical stability for the stress tests introduced in this paper have been analyzed. For We tested the covariance matrices for two different risk settings, one based on daily data from last year and the other based on monthly data from the last 5 years (both from late November ). In Table 6 below we present detailed results. Table 6: Stress Test Numerical Stability Stress Test Risk Setting Condition Number 2009 Rally 1 year daily returns 5 year monthly returns Max Singular Value Min Singular Value Tolerance Threshold Result E-08 Well conditioned E-06 Well conditioned A condition number of the order is not considered to be too high. The relative error in the data is smaller than the matrix condition number multiplied by machine epsilon. Since machine epsilon is of order analyzed matrices were found stable. Moreover, they also comply with the stricter criteria based on pseudo inverse theory, as all of singular values are greater than required threshold. Client Service Information is Available 24 Hours a Day clientservice@ Americas Europe, Middle East & Africa Asia Pacific Americas Atlanta Boston Chicago Montreal Monterrey New York San Francisco Sao Paulo Stamford Toronto (toll free) Amsterdam Cape Town Frankfurt Geneva London Madrid Milan Paris Zurich (toll free) China North China South Hong Kong Seoul Singapore Sydney Tokyo (toll free) (toll free) (toll free) Notice and Disclaimer This document and all of the information contained in it, including without limitation all text, data, graphs, charts (collec tively, the Information ) is the property of MSCl Inc. or its subsidiaries (collectively, MSCI ), or MSCI s licensors, direct or indirect suppliers or any third party involved in making or compiling any Information (collectively, with MSCI, the Information Providers ) and is provided for informational purposes only. The Information may not be reproduced or redisseminated in whole or in part without prior written permission from MSCI. The Information may not be used to create derivative works or to verify or correct other data or information. For example ( but without limitation), the Information many not be used to create indices, databases, risk models, analytics, software, or in connection with the issuing, offering, sponsoring, managing or marketing of any securities, portfolios, financial products or other investment vehicles utilizing or based on, linked to, tracking or otherwise derived from the Information or any other MSCI data, information, products or services. The user of the Information assumes the entire risk of any use it may make or permit to be made of the Information. NONE OF THE INFORMATION PROVDERS MAKES ANY EXPRESS OR IMPLIED WARRANTIES OR REPRESENTATIONS WITH RESPECT TO THE INFORMATION (OR THE RESULTS TO BE OBTAINED BY THE USE THEREOF), AND TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, EACH INFORMATION PROVIDER EXPRESSLY DISCLAIMS ALL IMPLIED WARRANTIES (INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES OF MSCI Inc. All rights reserved. 12 of 13

13 ORIGINALITY, ACCURACY, TIMELINESS, NON-INFRINGEMENT, COMPLETENESS, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE) WITH RESPECT TO ANY OF THE INFORMATION. Without limiting any of the foregoing and to the maximum extent permitted by applicable law, in no event shall any Information Provider have any liability regardin g any of the Information for any direct, indirect, special, punitive, consequential (including lost profits) or any other damages even if notified of the possibility of such damages. The foregoing shall not exclude or limit any liability that may not by applicable law be excluded or limited, including without limitation (as applic able), any liability for death or personal injury to the extent that such injury results from the negligence or wilful default of itself, its servants, agents or sub -contractors. Information containing any historical information, data or analysis should not be taken as an indication or guarantee of any future performance, analysis, forecast or prediction. Past performance does not guarantee future results. None of the Information constitutes an offer to sell (or a solicitation of an offer to buy), any security, financial product or other investment vehicle or any trading strategy. MSCI s indirect wholly-owned subsidiary Institutional Shareholder Services, Inc. ( ISS ) is a Registered Investment Adviser under the Investment Advisers Act of Except with respect to any applicable products or services from ISS (including applicable products or services from MSCI ESG Research Information, which are provided by ISS), none of MSC I s products or services recommends, endorses, approves or otherwise expresses any opinion regarding any issuer, securities, financ ial products or instruments or trading strategies and none of MSCI s products or services is intended to constitute investment advice or a recommendation to make (or refrain from making) any kin d of investment decision and may not be relied on as such. The MSCI ESG Indices use ratings and other data, analysis and information from MSCI ESG Research. MSCI ESG Research is produced by ISS or its subsidiaries. Issuers mentioned or included in any MSCI ESG Research materials may be a client of MSCI, ISS, or another MSCI subsidiary, or the parent of, or affiliated with, a client of MSCI, ISS, or another MSCI subsidiary, including ISS Corporate Services, Inc., which provides tools and services to issuers. MSCI ESG Research materials, including materials utilized in any MSCI ESG Indices or other products, have not been submitted to, nor received approval from, the United States Securities and Exchange Commission or any other regulatory body. Any use of or access to products, services or information of MSCI requires a license from MSCI. MSCI, Barra, RiskMetrics, ISS, CFRA, FEA, and other MSCI brands and product names are the trademarks, service marks, or registered trademarks or service marks of MSCI or its subsidiaries in the United States and other jurisdictions. The Global Industry Classification Standard (GICS) was developed by and is the exclusive property of MSCI and Standard & Poor s. Global Industry Classification Standard (GICS) is a service mark of MSCI and Standard & Poor s. About MSCI MSCI Inc. is a leading provider of investment decision support tools to investors globally, including asset managers, banks, hedge funds and pension funds. M SCI products and services include indices, portfolio risk and performance analytics, and governance tools. The company s flagship product offerings a re: the MSCI indices which include over 120,000 daily indices covering more than 70 countries; Barra portfolio risk and performance analytics covering global equity and fixed income markets; RiskMetrics market and credit risk analytics; ISS governance research and outsourced proxy voting and reporting services; FEA valuation models and risk management software for the energy and commodities markets; and CFRA forensic accounting risk research, legal/regulatory risk assessment, and due -diligence. MSCI is headquartered in New York, with research and commercial offices a round the world. MSCI Inc. All rights reserved. 13 of 13