Using Duration Times Spread to Forecast Credit Risk


 Raymond Byron Carr
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1 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
2 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 2
3 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% 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
4 Can Ratings Capture TimeVarying 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% 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
5 Can Spreads Capture TimeVarying Volatility? Volatility per rating class: Spread per rating class: 1.2% % % volatility (%) 0.6% spread (bps) % % 0.0% AAA AA A BBB 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
6 Why and How Should We Use Spreads? Excess returns ER over Treasuries consists of carry return (spread) spread change return (spreadduration 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
7 Which Spread Volatility? 25 rolling 36m absolute spread change volatilities 12% rolling 36m relative spread change volatilities 20 10% 8% volatility (bps) volatility (%) 6% 4% 5 2% AAA AA A BBB 0% 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
8 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
9 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% 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
10 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) Spread (bps) Forecasting Credit Risk 10
11 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
12 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
13 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
14 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
15 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
16 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 16
17 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: random portfolios of 80 bonds each month Covariance matrix is estimated on 60month rolling window For each portfolio compare exante Tracking Error to expost 1month outperformance Criteria Level of risk Exceedings of tracking error multiples Discrimination of more risky and less risky portfolios Forecasting Credit Risk 17
18 ExAnte Tracking Errors Vary with Market Spread Exante tracking errors and market spread (IG) 90% TE bounds median TE market spread tracking error (%) spread (bps) Forecasting Credit Risk 18
19 ExAnte Tracking Errors Correspond Well to ExPost Returns Ratio of expost return to exante 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 % percentile standard deviation 95% percentile Forecasting Credit Risk 19
20 Risk Model Distinguishes High and Low Risk Portfolios Each month create buckets of 20% exante least risky portfolios and of 20% mostrisky portfolios Calculate expost standard deviation of both buckets Least risky bucket indeed has lowest standard deviation in 92% of months least risky quintile most risky quintile 0.5 expost volatility (%) Forecasting Credit Risk 20
21 Contents Capturing Changing Volatility Building the Risk Model Testing the Risk Model Using the Risk Model Conclusions Forecasting Credit Risk 21
22 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
23 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% CAPMbeta 1, Forecasting Credit Risk 23
24 Attribution of Tracking Error to Sectors Sector Risk Report weight x spread x duration tracking error portfolio benchmark bet systematic specific total 1 Banking ,40% 0,30% 0,50% 2 Brokerage ,06% 0,03% 0,07% 3 Finance companies ,04% 0,06% 0,08% 4 Insurance ,07% 0,09% 0,12% 5 REITS ,01% 0,01% 0,01% 6 Financial other ,00% 0,01% 0,01% 7 Basic industry ,05% 0,03% 0,06% 8 Capital goods ,04% 0,03% 0,05% 9 Consumer cyclical ,07% 0,02% 0,07% 10 Consumer noncyclical ,05% 0,06% 0,08% 11 Energy ,00% 0,02% 0,02% 12 Technology ,02% 0,03% 0,04% 13 Transportation ,04% 0,02% 0,05% 14 Communications ,02% 0,07% 0,07% 15 Other industrial ,01% 0,01% 0,01% 16 Utilities ,06% 0,02% 0,06% 17 Supranat./Sovereigns/Agencies ,02% 0,01% 0,02% 18 ABS/Mortgages ,28% 0,12% 0,30% 99 Noncorporate ,13% 0,08% 0,15% Total TE contribution 1,00% 0,53% 0,37% 0,65% Forecasting Credit Risk 24
25 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 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% ,082% 0,121% 0,146% Banking Tier 1 2,46% 0,76% 1,69% ,036% 0,075% 0,083% Banking Lower Tier II 1,97% 0,71% 1,26% ,051% 0,061% 0,080% Banking Upper Tier II 0,90% 0,23% 0,67% ,035% 0,063% 0,072% Banking Banking 3,07% 1,36% 1,71% ,038% 0,057% 0,069% ABS/Mortgages ABS 1,06% 0,00% 1,06% ,038% 0,058% 0,069% Banking Banking 2,58% 0,84% 1,74% ,044% 0,051% 0,067% Banking Lower Tier II 1,03% 0,24% 0,79% ,036% 0,050% 0,062% Banking Tier 1 0,78% 0,09% 0,70% ,032% 0,052% 0,061% ABS/Mortgages ABS 0,79% 0,00% 0,79% ,035% 0,049% 0,060% Banking Senior 1,02% 0,25% 0,76% ,037% 0,046% 0,059% Insurance Life 2,09% 0,34% 1,75% ,035% 0,046% 0,058% Banking Lower Tier II 2,53% 1,28% 1,26% ,032% 0,048% 0,058% Finance companies Noncaptive 0,17% 0,23% 0,40% ,009% 0,056% 0,057% Banking Banking 2,59% 0,86% 1,73% ,035% 0,042% 0,055% Banking Senior 0,98% 0,25% 0,72% ,024% 0,041% 0,048% Banking Banking 0,93% 1,04% 0,11% ,008% 0,046% 0,047% Banking Tier 1 1,34% 0,05% 1,29% ,024% 0,039% 0,046% Banking Upper Tier II 1,79% 0,07% 1,72% ,025% 0,039% 0,046% Banking Banking 3,46% 1,71% 1,76% ,030% 0,034% 0,045% Brokerage Brokerage 0,00% 1,05% 1,05% ,016% 0,009% 0,018% Forecasting Credit Risk
26 Contents Capturing changing volatility Building the risk model Testing the risk model Using the risk model Conclusions Forecasting Credit Risk 26
27 Conclusions Use duration times spread to capture changing volatility of Market Sectors Issuers Issues Don t use ratings! Risk model adequately captures timevarying volatility and distinguishes high and low risk portfolios Attribution to risk factors enhances insight in portfolio positioning Forecasting Credit Risk 27
28 Disclaimer All copyrights patents and other property in the information contained in this document is held by Robeco Institutional Asset Management and shall continue to belong to Robeco Institutional Asset Management. No rights whatsoever are licensed or assigned or shall otherwise pass to persons accessing this information. This document has been carefully prepared and is presented by Robeco Institutional Asset Management. It is intended to supply the reader with information and reference on Robeco Institutional Asset Management's specific capabilities and it is to be used as the basis for an investment decision with respect to this capability. The content of this document is based upon sources of information believed to be reliable, but no warranty or declaration, either explicit or implicit, is given as to their accuracy or completeness. This document is not intended for distribution to or use by any person or entity in any jurisdiction or country where such distribution or use would be contrary to local law or regulation. The information relating to the performance is for historical information only. Past performance is not indicative for future results Forecasting Credit Risk 28
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