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Risk Settings in RiskManager:Factors to Consider forAppropriate SetupOctober 20, 2011©2011. All rights reserved. msci.com

Agenda• Introduction to Risk Settings in RiskServer• How to parameterize Risk Settings• Upcoming features for Value at Risk (VaR) calculations©2011. All rights reserved.msci.com2

Introduction to RiskSettings©2011. All rights reserved. msci.com3

Introduction to Risk Settings• Analysis & Pricing Dates• Analysis & Return Horizon• Decay Factor• Time Series Return Definitions• Pricing Model Settings• (Use upfront to Discount Bond Settings)©2011. All rights reserved.msci.com4

Risk Settings (aka Valuation Spec)• In order to run a report you need:• Positions, Statistics, Row drill-downs, Risk Settings• Risk Settings are required in any RiskServer report template• Collection of parameters that have a direct impact on the valuation, risk orsensitivity measures and stress test results of individual securities and atthe aggregate level• Fully customizable by the user©2011. All rights reserved.msci.com5

Risk Settings - Part 1©2011. All rights reserved.msci.com6

Risk Settings - Time Series Dates• Determines how much historical data to use in the risk measures• E.g. last 2 years, last 24 months, last 520 business or calendar days• A single or multiple time period: e.g. 04/01/2010 – 10/06/2011 and 01/01/2008 –31/12/2008• The order matters!©2011. All rights reserved.msci.com7

Risk Settings - Time Series Dates• Time Series Dates: 2008 + 2010 (levels and returns)time©2011. All rights reserved.msci.com8

Risk Settings - Time Series Dates• Time Series Dates: 2010 + 2008time• Historical VaR will show no difference whichever order is selected• Once a Decay Factor is used (Parametric or Monte Carlo) more weight will be given tothe latest returns so having 2008 as the latter period will result in much higher volatility• The order matters!• Usage: Revised 2008 Stress Test, Hectic Days©2011. All rights reserved.msci.com9

Risk Settings – Sampling Frequency• Sampling Frequency (Return Horizon in RiskManager version 3)• Length of returns that are taken from the historical time series data• E.g. 21 days (business days), 1 Month or end of month returns• We call these Sample Returns• Given 2 years of historical data we can extract around 24 21-day returns with nooverlapping• 2 years of data, 21-day returns and 20 days overlapping provides close to 500 21-dayreturns (not recommended due to serial correlation)©2011. All rights reserved.msci.com10

Risk Settings – Analysis Horizon• Analysis Horizon• Holding Period, VaR Horizon• 5 Day Analysis Horizon results in one week VaR numbers• Scales the returns specified in the Sampling Frequency• Does not scale the statistic directly• Always entered in Business Days• Analysis Horizon Scaling• Each Sample Return is scaled by the Analysis Horizon with Square Root of time rule• Sample Frequency = 5D, Analysis Horizon = 21D• Return21D = Sqrt(21/5)*Return5D• The Scaled Returns are used in the risk calculations as usual• Typically 5D VaR 5*1D VaR unless Parametric Methodology is applied©2011. All rights reserved.msci.com11

Risk Settings – Time Series Definitions• Allows users to specify what returns each data type shall use• Log Returns or Difference Returns• Log(P t /P t-1 ) or P t – P t-1• Useful for Time Series with small values• By default Difference Returns are only applied to Interest Rates inRiskServer©2011. All rights reserved.msci.com12

Risk Settings – Time Series Definitions• Difference Returns for CDS Spreads show more reasonable levels©2011. All rights reserved.msci.com13

Risk Settings – Decay Factor• Decay Factor – Exponentially Weighted Moving Average (EWMA)• Recent returns are given more weight the small the decay factor is• No Decay means Lambda = 1, Equal weight©2011. All rights reserved.msci.com14

Risk Settings - Part 2©2011. All rights reserved.msci.com15

Risk Settings – Currency Basket• Used to create a synthetic basket of currencies that can be used asbase/reporting currency• Example: Special Drawing Right (SDR) for the Bank of InternationalSettlements since April 2003• 1. Jan 2006: 1 SDR = USD0.632 + EUR0.41 + JPY18.4 + GBP0.0903 (to be reviewed every 5years)• http://www.bis.org/banking/bank_reporting_currency.htm©2011. All rights reserved.msci.com16

Risk Settings – Time Series Type Settings• Mean Reversion• Only Applicable in Counterparty Credit Exposure Reports• Some time series empirically show mean reverting behaviour such as Interest Rates, CDSSpreads and Implied Volatilities• User can define after what period a time series shall revert back to its mean©2011. All rights reserved.msci.com17

Risk Settings – Liquidity Fraction• The fraction of daily volume that if sold off will not affect market price• Example: Average Daily Volume 5mln shares, Liquidity Fraction 10%Selling 500,000 shares within a day will not affect the market price• Liquidity fraction is used in the statistics• Liquidity Horizon• Liquidity Adjusted VaR• Average Daily Volume is populated in the Terms and Conditions for most equities• Default Value is 0.1 (10%)©2011. All rights reserved.msci.com18

Risk Settings – Liquidity Fraction, Issuer Mapping Rules• Mapping table of CDS Spread curve to Issuer Name• Used for Jump To Default stress test only• What happens to the position or portfolio if an issuer defaults©2011. All rights reserved.msci.com19

Risk Settings – Pricing Model Settings• Pricing Model settings – to modify underlying analytics of models• Convertible Bond Settings – Step Length Scalar• The CB model uses an equity tree that has a node on each cash flow or option (call/put) day• Entering Scalar as 2 will half the step size and therefore double the number of nodes in the tree• Use reasonably with Monte Carlo statistics, useful for Present Value and Delta• Generic Bond – Implied Spread Floor• Puts a floor on the Credit Spread (Issuer OAS + Idiosyncratic OAS)• Credit Spread = Max (Floor, Issuer OAS + Idiosyncratic OAS)©2011. All rights reserved.msci.com20

Risk Settings – Other• Other options• Use Cash when out-of-range client Price• If calibration fails the user-entered price will be ignored and the difference between model and user price willbe added as CASH.• Use Upfront to discount bond transformations• Upfront returns calculated based on 1-U from U• By default the ‘shift method’ is used to adjust upfront price: add spread*term 1)1)See Section 3 of Measuring CDS Value at Risk,©2011. All rights reserved.msci.com21

Parameterize RiskSettings©2011. All rights reserved. msci.com22

How to Parameterize Risk Settings• Sample Frequency• Decay Factor• Time Series Dates©2011. All rights reserved.msci.com23

Sampling Frequency, Analysis Horizon and Time Series Dates• Ideally for 1 Month Holding Period use monthly returns over a longerperiod of time• Problems to consider:• lack of monthly returns in case of some equities (newly listed)• Higher sample error• What Decay Factor will capture the best volatility estimate• Overlapping of data not recommended, because autocorrelation violates the assumptionof independent returns (OLS regression in stress tests requires error terms to beuncorrelated)©2011. All rights reserved.msci.com24

Sampling Frequency, Analysis Horizon and Time Series Dates• Example: There are 24 independent monthly returns over 2 years• Historic Simulation• Only these 24 returns will be used in calculating the historical risk measures (VaR, CVaR,Marginal Var, Standard Deviation, …)• Small sample size, higher standard error• Decay Factor is not taken into account• Parametric method• Only the above 24 monthly returns will be used to generate the Covariance Matrixtaking the decay factor into account• Higher margin of error• Decay factor is used, which one should be used, concept of Half Life©2011. All rights reserved.msci.com25

Sampling Frequency, Analysis Horizon and Time Series Dates• Monte Carlo Simulation• Bootstrapping method applied to the same 24 monthly returns from the previousexample to generate N independent identically distributed returns 3)• Decay Factor is used• Common method for capturing 1-month VaR©2011. All rights reserved.msci.com26

Sampling Frequency, Analysis Horizon and Time Series Dates• For Historic and Parametric methodology often daily returns (SamplingFrequency) are used with the required Holding Period (Analysis Horizon)• Problem with this is that correlations between different geographical markets may notbe captured properly, weekly sampling frequency over 2 years or more is used in thiscase• A good example to illustrate this is looking at the Nikkei 225 and S&P 500 equity indices.They are in different geographical regions and not uncorrelated.©2011. All rights reserved.msci.com27

Parameterize Risk Settings• Nikkei 225 vs S&P 500, daily and weekly returns• Total data used 01/01/2010 – 31/12/2010• Graph of log returns for May 2010• Using weekly returns is more in line with expectationsCorrelations over 1 yearDaily Weekly0.22 0.74©2011. All rights reserved.msci.com28

Decay Factor• Compare Decay Factors• Used to indicate how much many returns are used in the volatility calculations• Decay H = 0.5, half-life H• Half-life of 3 months means that the weight in the return 3M ago is half that of the return with the biggestweight (last return)• Another way to look at decay factor is to associate it with number of returns that makeup a given percentage of estimated volatility©2011. All rights reserved.msci.com29

Decay Factor• Daily Sampling Frequency used• With Decay Factor 0.94, the last 74 daily returns make up 99% of volatilityfor that risk factor©2011. All rights reserved.msci.com30

Decay Factor• Returns as function of Decay Factorλ=0.94 0.991.0• λ=1, No Decay, Equal weighting• λ=0.94, 99% of volatility is made of the last 74 returns©2011. All rights reserved.msci.com31

Risk Setting choices• Aim: Good estimation of Volatility and Correlations• Assumption that sample mean is zero• Reduce standard error of the estimate• Reduce standard error for all risk factors, not just one• Only one decay factor is applied to all risk factors• Empirical methods can be used to determine a suitable Decay Factor©2011. All rights reserved.msci.com32

Risk Setting choices• Root Mean Square Error• Reducing Root Mean Square Error implies a good estimate• This is a good statistical process for a single estimate, but we need to find a stableParameter that works without having to update the single decay factor on a daily basis©2011. All rights reserved.msci.com33

Risk Setting choices - Stability• Stability is important• Risk managers should not have to update their Risk Settings on a daily basis• Need to find stable parameters that provide good forecasts• The higher the decay factor, the smoother history of volatilities©2011. All rights reserved.msci.com34

Risk Setting choices - Stability• Optimal Decay Factors based on volatility forecasts (RMSE criterion)©2011. All rights reserved.msci.com35

Risk Setting choices - Stability• Define• N number of time series (480), t i is the i th root mean square deviation(RMSE) associated with• Relative Error• Weight• Optimal Decay Factor• Optimal Decay Factor is average of individual optimal decay factorsweighted by individual forecast accuracy©2011. All rights reserved.msci.com36

Risk Setting choices - Stability• In case of 0.94 decay only the last 75 observations will have an effect onthe risk measures• With 0.94 using 1 year or 10 years of daily returns should make nosignificant difference to Parametric or Monte Carlo VaR, but processing willbe slower in the latter case (not linear though)©2011. All rights reserved.msci.com37

Risk Setting choices - Stability• Further points• Using Decay Factor is appropriate for current volatility estimation of non-stationaryreturns• Apply daily sampling frequency with the required analysis horizon for standalonevolatility measures• 5-Day returns is a common way of capturing correlations across geographical markets• Square root of time rule is applied to the returns, not directly to VaR• Select appropriate length of history, not too little, but also not too much©2011. All rights reserved.msci.com38

Useful Features forVolatilityCalculations©2011. All rights reserved. msci.com39

Research and Development• Decoupling of Volatilities and Correlations• Event-Driven VaR©2011. All rights reserved.msci.com40

Research and Development• Decoupling of Correlations and Volatilities• Currently a single decay factor and sampling frequency applied are to all risk factors forvolatility and correlation calculations• R&D are looking at allowing one sampling frequency for correlation calculations andanother sampling frequency for volatility estimation• A planned stress test overhaul will also focus on using more suitable correlations in thepredictive stress test regressions©2011. All rights reserved.msci.com41

Research and Development• Event-driven VaR• EWMA is a way to estimate volatility to be used in VaR• Research and Development is looking at using Implied volatility surfaces to forecastfuture volatility, this is a more market-driven forecast and should be more useful forLong Term VaR©2011. All rights reserved.msci.com42

References1. Measuring Value at Risk, Catherine O’Neil, April 20102. RiskMetrics Technical Document, 19963. A general approach to calculating VaR without volatilities andcorrelations, Benson & Zangari, 19974. Updated Stress Testing Features in RiskMetrics RiskManager, Sept 2011©2011. All rights reserved.msci.com43

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