Copyright © 2013 FactSet Research Systems Inc. All rights reserved. Stress-Testing - Better Portfolio Mgmt Steven P. Greiner, Ph.D. Director of Risk, FactSet Research Systems

Agenda 2 Why do Stress-Testing? Governance, that’s why!! Extreme-Event Stress-Testing Going Non-Linear: Markov-Chain MC Conclusions

3 Governance – Ethics – Survey Results PRESENTATION FROM FACTSET RESEARCH SYSTEMS + We are painfully aware of the public opinion towards the financial sector in the wake of continued financial crisis

Extreme Event Stress-Testing Practical Example 4

Some Stress-Testing Methodologies All data and charts sourced from FactSet Research Systems Inc. EXTREME EVENT 1) Begins with a risk model, you need some way of estimating correlations (covariance) across assets 2) Obtain the covariance (or factor returns) from some historical “stressed” market environment or your own innovation 3) Use this covariance to compute risks &/or these factor returns to compute returns on today’s portfolio 5

You run a risk report and see the VaR increase over the last several weeks and you think Risk = + Is this risk level change caused by trades (w), exposure changes (E), or market volatility (systemic risk) itself (C)? 6

Observations + 11/ / / /7 + 52/ / /26 7

Recipe to Interpret Effects All data and charts sourced from FactSet Research Systems Inc. Select several sequential weekly time periods Compute 95% VaR using all the combinations of actual portfolios, frozen portfolios (i.e. exposures) & covariance on those dates Choose 7 weeks: one obtains a 7 X 7 matrix of exposure changes on one axis & covariance changes on the other 8

Recipe to Interpret Effects All data and charts sourced from FactSet Research Systems Inc. When exposures are fixed & covariance evolves, one observes impact of changing correlations Covariance follows VIX Allows observation of volatility impact 9

Recipe to Interpret Effects All data and charts sourced from FactSet Research Systems Inc. When covariance is frozen & exposures change, one observes pricing impact prices detached from VIX Implies exposure change causes increase in risk 10

Recipe to Interpret Effects All data and charts sourced from FactSet Research Systems Inc. Move further out to 99% Value-at-Risk Even stronger affect out in the tail Exposures dominating 11

Recipe to Interpret Effects All data and charts sourced from FactSet Research Systems Inc. Monitor difference between 99% and 95% VaR Observe tail widening over time Though VIX muted..?? Exposures increasing risk though volatility is stable 12

Conclusions...What’s Happening is... All data and charts sourced from FactSet Research Systems Inc. Current 95% VaR is increasing mildly => Covariance isn’t resulting in the increased risk => VIX volatility signals are subdued => Rising tail risks are due to exposures changes ( spreading of difference between 99% & 95% VaR ) => Implies increasing probability of event risk Q for PM’s: WOULD YOU DO ANYTHING? 13

Markov Chain-MC Stress-Testing Practical Example 14

Correlations of “Stresses” with S&P Drawback? Correlations tie directly to linear stress-testing

Some Stress-Testing Methodologies All data and charts sourced from FactSet Research Systems Inc. MARKOV-CHAIN MONTE-CARLO 1) Begins with a risk model, you need some way of estimating correlations across assets. Use when your subject to data starvation for tail estimates 2) Generate synthesized data that matches joint probability distribution between the stress & all risk model factors...simultaneously...to populate the tail 3) Calculate the “beta(s)” between stress & risk model factors: Factor = beta 1 *stress + beta 2 *stress 2 + others 4) For a given stress (i.e. -30%), compute a value of F given the applied stress & compute return estimate 16

Markov Chain Monte-Carlo (MCMC) 17 Generates sequence of random variables from an “unknown” multi-variate probability density while incorporating the correlations from each variable with every other Sequential values tend to be auto-correlated, so delete early trials Optimize the search width parameter to achieve ~25% acceptance ratio Especially useful for re-populating “tail” density However, it requires “trial” density???

Use “Normal Projection” to create easy trial density 18 Multivariate Weibull Distributions for Asset Returns: I Yannick Malevergne & Didier Sornette; Finance Letters, (6), 16-32

Consider Bi-Modal Multi-Variate MCMC Example 19 Empirical Pairs Plots (500x5)MCMC Replicates (2500x5) QA: Run Kolmogorov-Smirnov 2-sample test that measures whether “x” and “y” are drawn from same distribution

Close Up 20 Empirical Scatter Plot MCMC Reproduction

EURUSD joint with Risk Model Factors 21

MCMC EURUSD Forex 22 Kolmogorov- Smirnov p-value is typically order of ~65%

MCMC JPYUSD Forex 23

MCMC Wheat Futures 24

MCMC Results allow for Non-Linear ST 25

Cooliolusions! Stress-Testing is good “Governance” Should be part of the investment process and requires cooperation between RM & PM Use it to complement traditional risk measures and to deploy your own insights Shouldn’t solely be based on naive inputs alone. Let your inner “Michelangelo” out, and be creative with it FactSet offers complete system.. 26

…more examples 27