Using Duration Times Spread to Forecast Credit Risk European Bond Commission / VBA Patrick Houweling, PhD Head of Quantitative Credits Research Robeco Asset Management Quantitative Strategies Forecasting Credit Risk 1
Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 2
How to Capture Changing Volatility? 0.8% rolling 36m excess return volatilities US IG corporate bonds 0.6% volatility (%) 0.4% 0.2% 0.0% 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 IG 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 market Forecasting Credit Risk 3
Can Ratings Capture Time-Varying Volatility? 1.2% rolling 36m excess return volatilities US IG corporate bonds 1.0% volatility (%) 0.8% 0.6% 0.4% 0.2% 0.0% 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 AAA AA A BBB Volatility of rating classes is not constant Using only ratings to measure current risk means lagging the market Forecasting Credit Risk 4
Can Spreads Capture Time-Varying Volatility? Volatility per rating class: Spread per rating class: 1.2% 400 1.0% 300 0.8% volatility (%) 0.6% spread (bps) 200 0.4% 100 0.2% 0.0% 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 AAA AA A BBB 0 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 AAA AA A BBB When spreads are high, credit markets are more volatile and vice versa So: volatility highly correlates with spread Forecasting Credit Risk 5
Why and How Should We Use Spreads? Excess returns ER over Treasuries consists of carry return (spread) spread change return (spread-duration D times spread change s): ER D s absolute spread change which is equivalent to ER Ds s s relative spread change Excess return volatility σ ER can thus be approximated by either absolute σ ER = Dσ spread absolute spread change volatility or relative σ ER = Dsσ spread relative spread change volatility Forecasting Credit Risk 6
Which Spread Volatility? 25 rolling 36m absolute spread change volatilities 12% rolling 36m relative spread change volatilities 20 10% 8% volatility (bps) 15 10 volatility (%) 6% 4% 5 2% 0 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 AAA AA A BBB 0% 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 AAA AA A BBB Relative spread change volatility is much more constant than absolute spread change volatility Also: differences between ratings are much smaller Forecasting Credit Risk 7
Measure Excess Return Volatility per Unit DTS! Best way to measure excess return volatility is using relative spread change volatility relative σ ER = Dsσ spread duration times spread (DTS) 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 volatility Alternative interpretation: 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 DTS Forecasting Credit Risk 8
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 average 1.75% Duration Times Spread vs. excess return volatility volatility (%/month) 1.50% 1.25% 1.00% 0.75% 0.50% 0.25% 0.00% 0 500 1000 1500 2000 duration (y) x spread (bps) Spread Bucket 1 - Low Spread Bucket 2 Spread Bucket 3 Spread Bucket 4 Spread Bucket 5 Spread Bucket 6 - High Forecasting Credit Risk 9
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 bucket 70 Volatility of idiosyncratic spread changes (bps/month) 60 50 40 30 20 10 0 0 100 200 300 400 500 600 700 Spread (bps) Forecasting Credit Risk 10
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 Conclusions Forecasting Credit Risk 11
Forecasting Credit Risk 12 Estimating Factor Returns We model a corporate bond s excess returns as S indicates whether bond i belongs to sector j in month t N is the number of sectors α s and β s are the factor returns Systematic returns are linear in DTS per sector Specific return volatility is proportional in DTS ( ) 1,, 2,,, 1 1,,, 1, 1 1,,,, 0, ~ = = = + + = t i t t i t i t i t i N j t j i t j t i N j t j i t j t i DTS N S DTS S ER γ σ σ ε ε β α
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 other Percentage of months in which Wald tests indicate significance at 95% confidence level (USIG results:) Test 1 Test 2 α s β s α s β s β s only - 78% - 41% α s and β s 97% 90% 93% 80% ER N N i, t = α j, tsi, j, t 1 + DTSi, t 1 β j, tsi, j, t 1 + εi, t j = 1 j = 1 Forecasting Credit Risk 13
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: Equal volatility for all sector intercepts (α s) Equal volatility for all sector DTS slopes (β s) Equal correlation for all pairs of (un)loaded sectors sector intercepts sector slopes sector intercepts σ 2 cov sector slopes cov σ 2 Forecasting Credit Risk 14
Calculating Tracking Error and Beta Model Risk factors have covariance matrix Σ Portfolio has exposures P to the risk factors Benchmark has exposures B to the risk factors Bet = P B Systematic Tracking Error (TE) TE is defined as the volatility of the bet s returns TE 2 = variance (P B) = (P B) Σ(P B) CAPM beta Beta is defined as the covariance of the portfolio with the market (benchmark) divided by the variance of the market beta = covariance (P,B) = P ΣB variance (B) B ΣB Forecasting Credit Risk 15
Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 16
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: 1.000 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 expost 1-month outperformance Criteria Level of risk Exceedings of tracking error multiples Discrimination of more risky and less risky portfolios Forecasting Credit Risk 17
Ex-Ante Tracking Errors Vary with Market Spread 1.1 1 0.9 0.8 Ex-ante tracking errors and market spread (IG) 90% TE bounds median TE market spread 240 220 tracking error (%) 0.7 0.6 0.5 0.4 200 180 160 140 120 100 spread (bps) 0.3 80 0.2 0.1 60 40 95 96 97 98 99 00 01 02 03 04 05 06 07 Forecasting Credit Risk 18
Ex-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 1.04 on average, but overestimations and underestimation occur frequently 10 9 8 5% percentile standard deviation 95% percentile 7 6 5 4 3 2 1 0 95 96 97 98 99 00 01 02 03 04 05 06 07 Forecasting Credit Risk 19
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 months 0.7 0.6 least risky quintile most risky quintile 0.5 ex-post volatility (%) 0.4 0.3 0.2 0.1 0 95 96 97 98 99 00 01 02 03 04 05 06 07 Forecasting Credit Risk 20
Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 21
Risk Attribution We measure the risk of Market Sectors Issuers Issues We report Total risk Risk contributions per bet Beta of the portfolio Forecasting Credit Risk 22
Tracking Error Report 1. Systematic risk 2. Specific risk 3. Beta Credit Risk Report Tracking error Systematic risk 1,14% Market 0,94% weight 0,15% weight x spread x duration 1,00% Sector 0,53% weight 0,14% weight x spread x duration 0,57% Specific risk 0,37% Issuer 0,20% Issue 0,31% Total 1,20% CAPM-beta 1,57 1 2 3 Forecasting Credit Risk 23
Attribution of Tracking Error to Sectors Sector Risk Report weight x spread x duration tracking error portfolio benchmark bet systematic specific total 1 Banking 731 330 401 0,40% 0,30% 0,50% 2 Brokerage 13 45-32 0,06% 0,03% 0,07% 3 Finance companies 3 29-26 0,04% 0,06% 0,08% 4 Insurance 121 75 45 0,07% 0,09% 0,12% 5 REITS 0 6-6 0,01% 0,01% 0,01% 6 Financial other 3 5-1 0,00% 0,01% 0,01% 7 Basic industry -5 25-30 0,05% 0,03% 0,06% 8 Capital goods 13 36-23 0,04% 0,03% 0,05% 9 Consumer cyclical -17 27-44 0,07% 0,02% 0,07% 10 Consumer non-cyclical 7 39-32 0,05% 0,06% 0,08% 11 Energy 5 7-2 0,00% 0,02% 0,02% 12 Technology 13 3 11 0,02% 0,03% 0,04% 13 Transportation -2 24-25 0,04% 0,02% 0,05% 14 Communications 85 74 11 0,02% 0,07% 0,07% 15 Other industrial 1 6-5 0,01% 0,01% 0,01% 16 Utilities 5 40-35 0,06% 0,02% 0,06% 17 Supranat./Sovereigns/Agencies 3 0 3 0,02% 0,01% 0,02% 18 ABS/Mortgages 151 0 151 0,28% 0,12% 0,30% 99 Non-corporate 81 0 81 0,13% 0,08% 0,15% Total 1.211 769 443 TE contribution 1,00% 0,53% 0,37% 0,65% Forecasting Credit Risk 24
Attribution of Tracking Error to Issuers 1. Largest overweight, not highest risk 2. Not investing in an issue is a risk as well 3. Short position (with CDS) to exploit our strong view Issuer Risk Report 3 1 2 weight weight x spread x duration tracking error Sector Subsector port BM bet port BM bet issuer TE issue TE total TE Banking Lower Tier II 1,11% 0,04% 1,07% 58 2 56 0,082% 0,121% 0,146% Banking Tier 1 2,46% 0,76% 1,69% 36 11 25 0,036% 0,075% 0,083% Banking Lower Tier II 1,97% 0,71% 1,26% 39 4 35 0,051% 0,061% 0,080% Banking Upper Tier II 0,90% 0,23% 0,67% 30 6 24 0,035% 0,063% 0,072% Banking Banking 3,07% 1,36% 1,71% 41 15 26 0,038% 0,057% 0,069% ABS/Mortgages ABS 1,06% 0,00% 1,06% 26 0 26 0,038% 0,058% 0,069% Banking Banking 2,58% 0,84% 1,74% 41 11 30 0,044% 0,051% 0,067% Banking Lower Tier II 1,03% 0,24% 0,79% 29 4 25 0,036% 0,050% 0,062% Banking Tier 1 0,78% 0,09% 0,70% 23 1 22 0,032% 0,052% 0,061% ABS/Mortgages ABS 0,79% 0,00% 0,79% 24 0 24 0,035% 0,049% 0,060% Banking Senior 1,02% 0,25% 0,76% 29 4 25 0,037% 0,046% 0,059% Insurance Life 2,09% 0,34% 1,75% 27 3 24 0,035% 0,046% 0,058% Banking Lower Tier II 2,53% 1,28% 1,26% 37 15 22 0,032% 0,048% 0,058% Finance companies Non-captive -0,17% 0,23% -0,40% 0 7-6 0,009% 0,056% 0,057% Banking Banking 2,59% 0,86% 1,73% 30 6 24 0,035% 0,042% 0,055% Banking Senior 0,98% 0,25% 0,72% 18 1 17 0,024% 0,041% 0,048% Banking Banking 0,93% 1,04% -0,11% 13 8 6 0,008% 0,046% 0,047% Banking Tier 1 1,34% 0,05% 1,29% 17 1 17 0,024% 0,039% 0,046% Banking Upper Tier II 1,79% 0,07% 1,72% 17 0 17 0,025% 0,039% 0,046% Banking Banking 3,46% 1,71% 1,76% 29 9 21 0,030% 0,034% 0,045% Brokerage Brokerage 0,00% 1,05% -1,05% 0 11-11 0,016% 0,009% 0,018% Forecasting Credit Risk
Contents Capturing changing volatility Building the risk model Testing the risk model Using the risk model Conclusions Forecasting Credit Risk 26
Conclusions Use duration times spread to capture changing volatility of Market Sectors Issuers Issues Don t use ratings! Risk model adequately captures time-varying volatility and distinguishes high and low risk portfolios Attribution to risk factors enhances insight in portfolio positioning Forecasting Credit Risk 27
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