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Risk Settings EnhancementsMannan AbbasiDecember 2012©2012. All rights reserved. msci.com

Agenda• Volatility Scaling• Single Period Volatility Approach• Local Volatility Approach©2012. All rights reserved.2

Volatility ScalingSingle Period VolatilityApproach©2012. All rights reserved. msci.com 3

Volatility/Correlation: Old vs. New Behaviour• One look back period controls the generation of simulatedscenarios/ covariance matrix• Useful to identify historical periods from which to draw correlations,while drawing volatilities from a different period• New functionality in risk setting to decouple correlation andvolatility estimation• Existing look back period controls generation of correlation• Different volatility parameters can be specified under Volatility Scaling (singlePeriod or Local Volatility Model)©2012. All rights reserved.4

Volatility/Correlation: Parametric Analysis• Effect of additional specification• Old Settings:Σold= σ σi, j ρi j i ,j• New SettingsΣnewi, j = σ ' σ ' ρ'i j i,jΣWith T the return horizonT=oldσ ' σ 'i, jiTnewjρi,j©2012. All rights reserved.5

Volatility/Correlation: Monte Carlo• In simulation we do not work with volatilities and correlation, but with historicalscenarios, via Benson-Zangari scenario generation1. Start with historical scenarios from old settingsrd~dN(0,σ )2. Normalize them by their volatility3. Compute volatility from new settingsxdrd=σd'σ d~ N(0,1)4. Scale it into historical scenariosxd×σ'd~'N(0,σ )d5. Generate simulated P/L as usual©2012. All rights reserved.6

RiskManager Setup©2012. All rights reserved.7

Decoupling Volatility and CorrelationStandard ApproachCorrelation PeriodLast 3YVolatility PeriodLast 3YσρAsset 1 Asset 2Asset 1 2.70% 1.00 0.66Asset 2 1.80% 0.66 1.00Suitable CorrelationsCorrelation Period Jan 2004-07Volatility Period Jan 2004-07σρAsset 1 Asset 2Asset 1 2.98% 1.00 0.32Asset 2 1.41% 0.32 1.00Correlation & Volatility from Different PeriodsCorrelation Period Jan 2004-07Volatility PeriodLast 3YσρAsset 1 Asset 2Asset 1 2.70% 1.00 0.32Asset 2 1.80% 0.32 1.00©2012. All rights reserved.8

User Case: Single Period Volatility Scaling• AUD.USD vs. Commodities - 3 Years Look Back Periodρ = 0.66©2012. All rights reserved.9

User Case: Single Period Volatility Scaling• AUD.USD vs. Commodities - Low Correlation Periodρ = 0.32©2012. All rights reserved.10

User Case: Single Period Volatility Scaling• Impact on Monte Carlo VaRStandardApproachDecoupledReferenceCorrelation Period Last 3 years Jan 2004 – 07 Jan 2004 – 07Volatility Period Last 3 years Last 3 years Jan 2004 – 07VaR (MC) 95Total 292 275 235AUD.USD 1Y Forward 212 217 169S&P Commodity Index 106 101 110Diversification Benefit 26 43 44©2012. All rights reserved.12

User Case: Single Period Volatility Scaling• Impact on Predictive Stress TestsStandardApproachDecoupledReferenceCorrelation Period Last 3 years Jan 2004 – 07 Jan 2004 – 07Volatility Period Last 3 years Last 3 years Jan 2004 – 07Oil Shock -20%Total -887 -610 -511AUD.USD 1Y Forward -495 -235 -156S&P Commodity Index -393 -374 -355©2012. All rights reserved.13

Volatility ScalingLocal Volatility Approach©2012. All rights reserved. msci.com 14

Local Volatility Model• Historical VaR uses equally weighted risk-factor returns from thelookback period• These returns are applied to base market scenario to generatesimulated historical P&L’s• Historical VaR with long lookback period potentially mixes differentvolatility regimesLocal Volatility Model aims at correcting this©2012. All rights reserved.15

Example 2: Different Volatility Regimes Across TimeIs it reasonable to expect 2008-volatility in today’s market?©2012. All rights reserved.16

Local Volatility Adjustment SchemaVolatility Seed:• Hardcoded; orLocal volatilityσ dσ hσ a• Calculated from date range prior to t dAnalysis Datet d. . .th−1th. . .td + nt ar hHistorical return r h is normalized bylocal volatility σ h and scaled up by afunction of σ h and σ aLook Back Period = t d+n - t d©2012. All rights reserved.19

Local Volatility Model• Use volatilityScaling -> localVolatilityModel• Historical factor returns at any date (d) in the lookback period areadjusted to account for current volatility regime (0 ≤ p ≤1)r adjd=rd×pσ + ( 1−p)σdσda• With independent risk settings specification forσdandσa©2012. All rights reserved.20

RiskManager Setup: Local Vol with Hardcoded Initial Seed©2012. All rights reserved.21

RiskManager Setup: Local Vol with Date Range Seed©2012. All rights reserved.22

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