20080616 Using Duration Times Spread to …

1 Forecasting Credit Risk116 June 2008 Using Duration Times Spread to forecast Credit RiskEuropean bond Commission / VBAP atrick Houweling, PhDHead of Quantitative Credits ResearchRobeco Asset ManagementQuantitative Strategies16 June 2008 Forecasting Credit Risk216 June 2008 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model ConclusionsForecasting Credit Risk316 June 2008 How to Capture Changing Volatility? Volatility of excess returns is not constant Historical volatility is not suited to predict future volatility Using historical volatility to measure current risk means lagging the marketrolling 36m excess return volatilities US IG corporate (%)IGForecasting Credit Risk416 June 2008 Can Ratings Capture time -Varying Volatility?

2 Volatility of rating classes is not constant Using only ratings to measure current risk means lagging the marketrolling 36m excess return volatilities US IG corporate (%)AAAAAABBBF orecasting Credit Risk516 June 2008 Can spreads Capture time -Varying Volatility? When spreads are high, credit markets are more volatile and vice versa So: volatility highly correlates with spreadSpread per rating class:Volatility per rating (%)AAAAAABBB0100200300400909192939495969 798990001020304050607spread (bps)AAAAAABBBF orecasting Credit Risk616 June 2008 Why and How Should We Use spreads ?Excess returns ERover Treasuries consists of carry return ( Spread ) Spread change return ( Spread - Duration Dtimes Spread change s):which is equivalent toExcess return volatility ERcan thus be approximated by eitherorsDER ssDsER absolutespreadERD =relativespreadERDs = absolute Spread change relative Spread change absolute Spread change volatility relative Spread change volatilityForecasting Credit Risk716 June 2008 Which Spread Volatility?

3 Relative Spread change volatility is much more constant than absolute Spread change volatility Also: differences between ratings are much smallerrolling 36m absolute Spread change volatilities0510152025929394959697989900 01020304050607volatility (bps)AAAAAABBB rolling 36m relative Spread change volatilities0%2%4%6%8%10%12%929394959697 98990001020304050607volatility (%)AAAAAABBBF orecasting Credit Risk816 June 2008 Measure Excess Return Volatility per Unit DTS! Best way to measure excess return volatility is Using relative Spread change volatility Relative Spread change volatility can be estimated accurately Using historical data Duration Times Spread (DTS) can change on a daily basis, reflecting current market conditions Their product gives an estimate of current excess return volatilityAlternative interpretation.

4 Relative Spread change volatility can thus be interpreted as the excess return volatility per unit of DTS It can be estimated as the volatility of excess returns divided by DTSrelativespreadERDs = Duration Times Spread (DTS)Forecasting Credit Risk916 June 2008 From Market Level to bond Level Each month assign bonds to Duration Times Spread (DTS) quintiles and subdivide each quintile in 6 Spread buckets For each bucket, calculate the average monthly return and its time series volatility and the average monthly DTS and its time series averageDuration Times Spread vs. excess return (y) x Spread (bps)volatility (%/month) Spread Bucket 1 - LowSpread Bucket 2 Spread Bucket 3 Spread Bucket 4 Spread Bucket 5 Spread Bucket 6 - HighForecasting Credit Risk1016 June 2008 Idiosyncratic Spread Change Volatility is Also Related to Spread Level Each month bonds are assigned to 3 sector (Financials, Industrials, Utilities) x 3 Duration buckets x 6 Spread buckets We calculate the idiosyncratic Spread change as the Spread change minus the average Spread change of the bucket We estimate the standard deviation of idiosyncratic changes and the average Spread per bucket0102030405060700100200300400500600 700 Spread (bps)Volatility of idiosyncratic Spread changes (bps/month)

5 Forecasting Credit Risk1116 June 2008 Contents Capturing Changing Volatility Building the Risk Model Estimating Factor Returns Significance Tests Estimating Covariance Matrix of Factor Returns Measuring Risk Testing the Risk Model Using the Risk Model ConclusionsForecasting Credit Risk1216 June 2008 Estimating Factor Returns We model a corporate bond s excess returns asSindicates whether bond ibelongs to sector jin month t Nis the number of sectors s and s are the factor returns Systematic returns are linear in DTS per sector Specific return volatility is proportional in DTS()1,,2,,,11,,,1,11,,,,,0~ = = =++= tittitititiNjtjitjtiNjtjitjtiDTSNSDTSSER Forecasting Credit Risk1316 June 2008 Significance tests Data: monthly, from June 1993 to January 2006 Universes: Lehman Brothers US IG and HY index constituents Estimation method: Generalized Least Squares regression Test 1: sector coefficients are jointly different from zero Test 2: sector coefficients differ from each otherPercentage of months in which Wald tests indicate significance at 95% confidence level (USIG results:)Test 1 Test 2 s s s s s only-78%-41% s and s97%90%93%80%tiNjtjitjtiNjtjitjtiSDTSSER ,11,,,1,11,,,, ++= = = Forecasting Credit Risk1416 June 2008 Estimating Covariance Matrix of Factor Returns We robustly estimate volatilities and correlations of factor returns to calculate the covariance matrix of our risk factors We shrink the covariance matrix by assuming.

6 Equal volatility for all sector intercepts ( s) Equal volatility for all sector DTS slopes ( s) Equal correlation for all pairs of (un)loaded sectorssector interceptssector slopessector interceptssector slopes2 cov2 covForecasting Credit Risk1516 June 2008 Calculating Tracking Error and Beta Model Risk factors have covariance matrix Portfolio has exposures P to the risk factors Benchmark has exposures B to the risk factorsBet = P B Systematic Tracking Error (TE) TE is defined as the volatility of the bet s returnsTE2= variance (P B) = (P B) (P B) CAPM beta Beta is defined as the covariance of the portfolio with the market (benchmark) divided by the variance of the marketbeta = covariance (P,B) = P Bvariance (B)B BForecasting Credit Risk1616 June 2008 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model ConclusionsForecasting Credit Risk1716 June 2008 Simulation Setup We test the risk model in a Monte Carlo simulation Data: June 1993 January 2006 Universe: Lehman Brothers US Investment Grade index Portfolios.

7 Random portfolios of 80 bonds each month Covariance matrix is estimated on 60-month rolling window For each portfolio compare ex-ante Tracking Error to ex-post 1-month outperformance Criteria Level of risk Exceedings of tracking error multiples Discrimination of more risky and less risky portfoliosForecasting Credit Risk1816 June 2008Ex-Ante Tracking Errors Vary with Market Spreadtracking error (%)Ex-ante tracking errors and market Spread (IG) (bps)90% TE boundsmedian TEmarket spreadForecasting Credit Risk1916 June 2008Ex-Ante Tracking Errors Correspond Well to Ex-Post Returns Ratio of ex-post return to ex-ante tracking error should be standard normally distributed standard deviation should be 1 < 1 means risk is overestimated, > 1 means underestimation Standard deviation of ratio is on average.

8 But overestimations and underestimation occur frequently959697989900010203040506070123 456789105% percentilestandard deviation95% percentileForecasting Credit Risk2016 June 2008 Risk Model Distinguishes High and Low Risk Portfolios Each month create buckets of 20% ex-ante least risky portfolios and of 20% most-risky portfolios Calculate ex-post standard deviation of both buckets Least risky bucket indeed has lowest standard deviation in 92% of volatility (%)least risky quintilemost risky quintileForecasting Credit Risk2116 June 2008 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model ConclusionsForecasting Credit Risk2216 June 2008 Risk AttributionWe measure the risk of Market Sectors Issuers IssuesWe report Total risk Risk contributions per bet Beta of the portfolioTracking Error ReportForecasting Credit Risk2316 June 2008 Credit Risk ReportTracking errorSystematic risk1,14%Market0,94%weight0,15%weight x Spread x duration1,00%Sector0,53%weight0,14%weigh t x Spread x duration0,57%Specific risk0,37%Issuer0,20%Issue0,31%Total1,20% CAPM-beta1.

9 Credit Risk2416 June 2008 Attribution of Tracking Error to SectorsSector Risk Reportportfoliobenchmarkbetspecifictotal 1 Banking7313304010,40%0,30%0,50%2 Brokerage1345-320,06%0,03%0,07%3 Finance companies329-260,04%0,06%0,08%4 Insurance12175450,07%0,09%0,12%5 REITS06-60,01%0,01%0,01%6 Financial other35-10,00%0,01%0,01%7 Basic industry-525-300,05%0,03%0,06%8 Capital goods1336-230,04%0,03%0,05%9 Consumer cyclical-1727-440,07%0,02%0,07%10 Consumer non-cyclical739-320,05%0,06%0,08%11 Energy57-20,00%0,02%0,02%12 Technology133110,02%0,03%0,04%13 Transportation-224-250,04%0,02%0,05%14 Communications8574110,02%0,07%0,07%15 Other industrial16-50,01%0,01%0,01%16 Utilities540-350,06%0,02%0,06% ,02%0,01%0,02%18 ABS/Mortgages15101510,28%0,12%0,30%99 Non-corporate810810,13%0,08%0,15% contribution1,00%0,53%0,37%0,65%tracking errorweight x Spread x durationsystematicIssuer Risk ReportSectorSubsectorportBMbetportBMbeti ssuer TEissue TEtotal TEBankingLower Tier II1,11%0,04%1,07%582560,082%0,121%0,146% BankingTier 12,46%0,76%1,69%3611250,036%0,075%0,083% BankingLower Tier II1,97%0,71%1,26%394350,051%0,061%0,080% BankingUpper Tier II0,90%0,23%0,67%306240,035%0,063%0,072% BankingBanking3,07%1,36%1,71%4115260,038 %0,057%0,069%ABS/MortgagesABS1,06%0,00%1 ,06%260260,038%0,058%0,069%BankingBankin g2,58%0,84%1,74%4111300,044%0,051%0,067% BankingLower Tier II1,03%0,24%0,79%294250,036%0,050%0,062% BankingTier 10,78%0,09%0,70%231220,032%0,052%0,061%A BS/MortgagesABS0,79%0,00%0,79%240240,035 %0,049%0,060%BankingSenior1,02%0,25%0,76 %294250,037%0,046%0,059%InsuranceLife2,0 9%0,34%1.

10 75%273240,035%0,046%0,058%BankingLower Tier II2,53%1,28%1,26%3715220,032%0,048%0,058 %Finance companiesNon-captive-0,17%0,23%-0,40%07- 60,009%0,056%0,057%BankingBanking2,59%0, 86%1,73%306240,035%0,042%0,055%BankingSe nior0,98%0,25%0,72%181170,024%0,041%0,04 8%BankingBanking0,93%1,04%-0,11%13860,00 8%0,046%0,047%BankingTier 11,34%0,05%1,29%171170,024%0,039%0,046%B ankingUpper Tier II1,79%0,07%1,72%170170,025%0,039%0,046% BankingBanking3,46%1,71%1,76%299210,030% 0,034%0,045%BrokerageBrokerage0,00%1,05% -1,05%011-110,016%0,009%0,018% weight tracking errorweight x Spread x durationForecasting Credit Risk16 June 2008 Attribution of Tracking Error to overweight, not highest investing in an issue is a risk as position (with CDS) to exploit our strong view123 Forecasting Credit Risk2616 June 2008 Contents Capturing changing volatility Building the risk model Testing the risk model Using the risk model ConclusionsForecasting Credit Risk2716 June 2008 Conclusions Use Duration Times Spread to capture changing volatility of Market Sectors Issuers Issues Don t use ratings!