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### Stress-Testing - Better Portfolio Mgmt

Steven P. Greiner, Ph.D.

Director of Risk, FactSet Research Systems

Agenda

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

PRESENTATION FROM FACTSET RESEARCH SYSTEMSGovernance – Ethics – Survey Results

- We are painfully aware of the public opinion towards the financial sector in the wake of continued financial crisis

All data and charts sourced from FactSet Research Systems Inc.Some Stress-Testing Methodologies

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

You run a risk report and see the VaR increase over the last several weeks and you think..............

Risk = <w*E*C*Et*wt> + <w*V(ε)*wt>

Is this risk level change caused by trades (w), exposure changes (E), or market volatility (systemic risk) itself (C)?

Observations

- 1 1/17
- 2 1/24
- 3 1/31
- 4 2/7
- 5 2/14
- 6 2/21
- 7 2/26

Recipe to Interpret Effects

- 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

All data and charts sourced from FactSet Research Systems Inc.

Recipe to Interpret Effects

- When exposures are fixed & covariance evolves, one observes impact of changing correlations
- Covariance follows VIX
- Allows observation of volatility impact

All data and charts sourced from FactSet Research Systems Inc.

Recipe to Interpret Effects

- When covariance is frozen & exposures change, one observes pricing impact
- prices detached from VIX
- Implies exposure change causes increase in risk

All data and charts sourced from FactSet Research Systems Inc.

Recipe to Interpret Effects

- Move further out to 99% Value-at-Risk
- Even stronger affect out in the tail
- Exposures dominating

All data and charts sourced from FactSet Research Systems Inc.

Recipe to Interpret Effects

- Monitor difference between 99% and 95% VaR
- Observe tail widening over time
- Though VIX muted..??
- Exposures increasing risk though volatility is stable

All data and charts sourced from FactSet Research Systems Inc.

Conclusions...What’s Happening is...

- Current 95% VaRis 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?

All data and charts sourced from FactSet Research Systems Inc.

All data and charts sourced from FactSet Research Systems Inc.Some Stress-Testing Methodologies

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 = beta1*stress + beta2*stress2 + others

4) For a given stress (i.e. -30%), compute a value of F given the applied stress & compute return estimate

Markov Chain Monte-Carlo (MCMC)

- 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

Multivariate Weibull Distributions for Asset Returns: IYannick Malevergne & Didier Sornette; Finance Letters, 2004 2(6), 16-32

Consider Bi-Modal Multi-Variate MCMC Example

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

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..

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