Actuarial Research Centre (ARC) PhD Studentship Output
Actuarial ResearchCentre (ARC)PhD studentship outputThe Actuarial Research Centre (ARC) is the Institute and Faculty of Actuaries’ network of actuarialresearchers around the world.The ARC seeks to deliver research programmes that bridge academic rigour with practitioner needsby working collaboratively with academics, industry and other actuarial bodies.The ARC supports actuarial researchers around the world in the delivery of cutting-edge researchprogrammes that aim to address some of the significant challenges in actuarial science.
EMPIRICAL STUDIES IN CORPORATE CREDITMODELLING; LIQUIDITY PREMIA, FACTORPORTFOLIOS & MODEL UNCERTAINTYbyPaul René Frank van LoonSubmitted for the degree ofDoctor of PhilosophyDepartment of Actuarial Mathematics and StatisticsSchool of Mathematical and Computer SciencesHeriot-Watt UniversityMarch 2017The copyright in this thesis is owned by the author. Any quotation from the report oruse of any of the information contained in it must acknowledge this report as the sourceof the quotation or information.
AbstractInsurers match the cash flows of typically illiquid insurance liabilities, such asin-force annuities, with government and corporate bonds. As they intend to buycorporate bonds and hold them to maturity, they can capture the value attached toliquidity, without running the market liquidity risk that is associated with havingto sell bonds in the open market. During the long consultation period dedicated tothe mark-to-market valuation of insurance assets and liabilities for the Solvency IIregulatory framework, CEIOPS noted the importance of the accurate breakdown ofthe credit spread into its components, most notably the credit and non-credit (i.e.liquidity) components. In this thesis we review many modelling efforts to isolate theliquidity premium and propose a reduced-form modelling approach that relies on anew, relative liquidity proxy.Challenging the status quo when it comes to active and passive investment strategies, products and funds, Exchange Traded Funds and ‘smart-beta’ products provideinvestors with straightforward ways to strategically expose a portfolio to risk drivers,raising the bar for traditional investment funds and managers. In this thesis, weinvestigate how traditional sources of equity outperformance (alpha), such as smallcaps, low volatility and value, translate to UK corporate bonds. For automatedtrading strategies in corporate bonds, and those with specific factor exposure requirements in particular, transaction costs, rebalancing and an optimal turnoverstrategy are crucial; these aspects of building factor portfolios are explored for theUK market.Since the financial crisis, mathematical models used in finance have been subject to a fair amount of criticism. More than ever has this highlighted the needof better risk management of financial models themselves, leading to a surge in‘model validation’ roles in industry and an increased scrutiny from regulatory bodies. In this thesis we look at stochastic credit models that are commonly used byinsurers to project forward credit-risky bond portfolios and the model uncertaintyand parameter risk that arises as a result of relying on published credit migrationmatrices. Specifically, our investigation focuses on two violations of the Markovianprocess that credit transitions are assumed to follow and statistical uncertainty ofthe migration matrix.
AcknowledgementsFirst of all, I would like to thank Professor Andrew Cairns and Professor AlexanderMcNeil for providing guidance on the research conducted during my time as a PhDcandidate. Regular discussions with both Andrew and Alex have been instrumentalover the last three and a half years. Their expertise has been of great benefit in aidingmy understanding of some technical aspects of my studies and their enthusiasmhelped shape the direction of my research. Their comments on the initial draftcontributed to an improved final thesis.Secondly, I would like to thank Alex Veys from Partnership Assurance. Notonly have Partnership supported my PhD studentship financially, regular meetingswith Alex during the first year of the PhD deepened my understanding of corporatebond markets and shaped the direction of the research going forward. I am grateful for the time I got to spend with Alex and the rest of the investment team atPartnership’s offices during the summer of 2014. During this time I was fortunateenough to have the opportunity to discuss my progress with many industry expertsincluding Etienne Comon from GS Asset Management, Paul Sweeting from JPMAsset Management, Albert Desclee from Barclays Capital and others.I also wish to extend my gratitude to the Institute and Faculty of Actuaries andthe Actuarial Research Centre for their support throughout my PhD. In particular Iwould like to thank Kevin and Sarah from the IFoA, who have been ever so helpful inaccommodating conference speaking opportunities in Washington, Kuala Lumpur,Beijing, Dublin and many places around the UK. I thank Con Keating for invitingme to present some of my work to the CISI Bond Group in September 2014.Finally, I would like to thank my family for their support. I am grateful toMarijke, Eric, Megan and Mark for their constant love, support and encouragementthroughout the years.i
ACADEMIC REGISTRYResearch Thesis SubmissionName:Paul Renee Frank van LoonSchool/PGI:Mathematics and Computer ScienceVersion:Final(i.e. First,Resubmission, Final)Degree Sought(Award andSubject area)Doctor of PhilosophyDeclarationIn accordance with the appropriate regulations I hereby submit my thesis and I declare that:1)2)3)4)5)*the thesis embodies the results of my own work and has been composed by myselfwhere appropriate, I have made acknowledgement of the work of others and have made reference towork carried out in collaboration with other personsthe thesis is the correct version of the thesis for submission and is the same version as any electronicversions submitted*.my thesis for the award referred to, deposited in the Heriot-Watt University Library, should be madeavailable for loan or photocopying and be available via the Institutional Repository, subject to suchconditions as the Librarian may requireI understand that as a student of the University I am required to abide by the Regulations of theUniversity and to conform to its discipline.Please note that it is the responsibility of the candidate to ensure that the correct version of the thesisis submitted.Signature ofCandidate:Date:SubmissionSubmitted By (name in capitals):Signature of Individual Submitting:Date Submitted:For Completion in the Student Service Centre (SSC)Received in the SSC by (name incapitals):Method of Submission(Handed in to SSC; posted throughinternal/external mail):E-thesis Submitted (mandatory forfinal theses)Signature:Date:Please note this form should bound into the submitted thesis.Updated February 2008, November 2008, February 2009, January 2011ii
Contents1 Motivation to the PhD Thesis11.1Regulatory Environment of the Liquidity Premium in Solvency II . .21.2Rise of ETFs and Smart Beta Products . . . . . . . . . . . . . . . . .61.3Financial Risk of Non-Financial Risks: Model Risk . . . . . . . . . .92 Quantifying the Liquidity Premium on Corporate Bonds142.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1Liquidity Proxies . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.2Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.3CDS-based Approach . . . . . . . . . . . . . . . . . . . . . . . 242.2.4Structural Model Approach . . . . . . . . . . . . . . . . . . . 282.3Description of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . 372.4Descriptive Analysis of Credit Spreads . . . . . . . . . . . . . . . . . 432.52.62.4.1Timeline Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 452.4.2Descriptive Analysis of Market Data . . . . . . . . . . . . . . 48Modelling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.5.1Modelling Methodology. . . . . . . . . . . . . . . . . . . . . 532.5.2Modelling the Bid-Ask Spread . . . . . . . . . . . . . . . . . . 542.5.3Modelling the Credit Spread . . . . . . . . . . . . . . . . . . . 552.5.4Credit Spread of Perfectly Liquid Bonds . . . . . . . . . . . . 56Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.6.1Modelling Bid-Ask Spread . . . . . . . . . . . . . . . . . . . . 572.6.2Modelling Credit Spread . . . . . . . . . . . . . . . . . . . . . 62iii
2.6.32.72.8Liquidity Premium Estimates . . . . . . . . . . . . . . . . . . 66Additional Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . 702.7.1Alternative Liquidity Proxy Specification . . . . . . . . . . . . 712.7.2Robustness of Credit Spread Measure . . . . . . . . . . . . . . 742.7.3Investigating RBAS Properties . . . . . . . . . . . . . . . . . 77Bank of England’s Structural Model . . . . . . . . . . . . . . . . . . . 802.8.1Quick Model Overview . . . . . . . . . . . . . . . . . . . . . . 813 Quantitative Factor Investing in the UK Corporate Bond Market 843.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.1.1Review of Credit Specific Literature . . . . . . . . . . . . . . . 873.2Description of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3Methodology & Risk Factors . . . . . . . . . . . . . . . . . . . . . . . 913.3.13.4Single-Factor Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . 983.4.1Non-Normality of Factor Returns . . . . . . . . . . . . . . . . 983.4.2(Risk-adjusted) Measures of (Out-)performance . . . . . . . . 1003.4.3(Risk-adjusted) (Out-) Performance of Factor Portfolios . . . . 1023.4.4Turnover & Transaction Costs . . . . . . . . . . . . . . . . . . 1073.4.53.5Risk Premia Factors . . . . . . . . . . . . . . . . . . . . . . . 923.4.4.1Choice of Factor Tolerance . . . . . . . . . . . . . . . 1083.4.4.2Annualised Performance Measures . . . . . . . . . . 110Illiquidity Factor as Liquidity Premium . . . . . . . . . . . . . 112Multi-Factor Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . 1143.5.1Benefits of Natural Crossing and Reducing Trading Costs . . . 1234 Model Uncertainty & Parameter Risk in Stochastic Credit Models1244.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.2Review of Modelling Methodologies . . . . . . . . . . . . . . . . . . . 1274.2.1Review of Credit Ratings as a Markov Chain . . . . . . . . . . 1284.2.1.1Finding a Generator for Public Migration Matrices . 1314.2.1.2From Published Matrix to Valid Generator . . . . . . 132iv
4.2.1.34.2.24.3Review of Default Probability and Credit Spreads . . . . . . . 137Ignoring Complexities in the Rating Process . . . . . . . . . . . . . . 1434.3.1Rating History . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.3.1.14.3.2Evidence for Downward Momentum . . . . . . . . . 146Time Inhomogeneity . . . . . . . . . . . . . . . . . . . . . . . 1484.3.2.14.4Historical Data . . . . . . . . . . . . . . . . . . . . . 135Evidence for Time-Inhomogeneity . . . . . . . . . . . 1514.3.3Interaction between Rating Drift and the Business Cycle . . . 1554.3.4Statistical Uncertainty . . . . . . . . . . . . . . . . . . . . . . 1574.3.5Stochastic Credit Model & Calibration . . . . . . . . . . . . . 1594.3.6Calibrating the Market Price of Risk . . . . . . . . . . . . . . 1604.3.6.1Calibration of a CIR process . . . . . . . . . . . . . . 1614.3.6.2Likelihood Function . . . . . . . . . . . . . . . . . . 1624.3.6.3Initial Estimates using OLS . . . . . . . . . . . . . . 163Empirical Results using Monte Carlo Simulation . . . . . . . . . . . . 1644.4.1Simulation of Rating Process. . . . . . . . . . . . . . . . . . 1644.4.2Empirical Results of the Simulated Portfolios . . . . . . . . . 1664.4.3Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 1715 Closing Remarks & Directions for Future Research1735.1Quantifying the Liquidity Premium on Corporate Bonds . . . . . . . 1735.2Quantitative Factor Investing in the UK Corporate Bond Market . . 1775.3Model Uncertainty & Parameter Risk in Stochastic Credit Models . . 181A Appendix to Chapter 2184B Appendix to Chapter 3186C Appendix to Chapter 4188Bibliography189v
List of Tables2.1Joint distribution of successive price changes (conditional on no newinformation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2Average of daily standard deviations by variable and rating class.Note that Duration and Notional Amount are logged variables in themodel.3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Risk and Return measures (excess returns, gross of transaction costs)for all factor portfolios over the period October 2003 - July 2014.3.2. . 104Monthly turnover and excess returns (gross and net) over durationmatched Gilts for each of the factor portfolios. . . . . . . . . . . . . . 1083.3Annualised volatility estimates using different scaling parameters;scaling under the assumption of independence,and the scaling factorunder the assumption of an estimated AR(1) process. . . . . . . . . . 1123.4Risk and return characteristics of Liquidity factors constructed onsubsets of the bond universe data. . . . . . . . . . . . . . . . . . . . . 1133.5Pearson correlation between excess returns over duration-matchedtreasuries for factor portfolios and the market portfolio. . . . . . . . . 1153.6Pearson correlation between the outperformance over the market portfolio for all seven factor portfolios. . . . . . . . . . . . . . . . . . . . . 1153.7Optimised factor portfolio weights in percentages under each of thestrategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119vi
3.8Comparing two simple weighting schemes, equal weighted (WE ) andinversely proportional to variance (WI ), to the risk and return metricusing the optimal portfolio weights (WO ). Each scenario is evaluatedhere using a difference risk or return metric; the portfolio weights WOvary for each of the scenarios, whereas the weights for WE and WIare fixed by definition. . . . . . . . . . . . . . . . . . . . . . . . . . . 1203.9Portfolio weights for the optimal portfolio and the portfolio that meetsthe similarity criterion, but is least similar, for each of the strategies. 1214.1Migration matrix published by Moody’s in their annual default study(Moody’s Investor Services, 2011) . . . . . . . . . . . . . . . . . . . . 1334.2Comparison of methods of conversion from published annual migration matrix to generator and back. . . . . . . . . . . . . . . . . . . . 1354.3One-year CTMC benchmark migration matrix estimated on all ratingevents from US-based issuers (1980 - 2002). . . . . . . . . . . . . . . . 1374.4Possible migrations under the extended state space are marked withan ’X’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.5Long term average migration matrix of 5-year transition probabilitiespublished by Moody’s in their annual default study (Moody’s InvestorServices, 2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464.6Best estimates of the default probability for all ratings and states andthe corresponding 99% confidence interval.4.7. . . . . . . . . . . . . . 148Persistence and default probability conditioned on the state of theeconomy across rating categories. . . . . . . . . . . . . . . . . . . . . 1544.8Best estimates of the default probability and the corresponding 99%confidence interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1584.9Quarterly transition matrix for three economic regimes, defined byGDP growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.10 Value-at-Risk relative to the benchmark matrix with standard modelparameters (Benchmark). . . . . . . . . . . . . . . . . . . . . . . . . . 171vii
B.1 Long-term credit migration matrix, estimated by Service in their Annual Default Study of 2014. . . . . . . . . . . . . . . . . . . . . . . . 186C.1 Sector and geographic areas of firms included in the dataset (%). . . . 188viii
List of Figures2.1The Annual Benchmark Spread is based on the difference in annualyield between a bond and the corresponding benchmark bond. Abenchmark bond is chosen as to minimise the difference in maturity(remaining life) between a bond and its reference.2.2. . . . . . . . . . 43Daily average Credit Spreads (and 5th and 95th quantile) over timefor Financial/Non-Financials and the four investment grade ratingcategories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.3Average Credit Spread by Rating (on a logged y-axis) over time,annotated with a non-exhaustive selection of events during the ‘creditcrunch’. Tick marks indicate the start of the year. . . . . . . . . . . . 452.4Descriptive analysis of market data: number of issuers (top left), totalnotional amount outstanding (top right), average duration by rating(bottom left and the proportion of the bonds universe issued fewerthan twelve months ago.) . . . . . . . . . . . . . . . . . . . . . . . . . 482.5Exploratory Analysis of a selection of available analytical values andtheir change over time (top), coupled with the way in which somebivariate relationships vary over time (centre, bottom). . . . . . . . . 502.6Stylised representation of bond yields, illustrating the challenge toestimate yield curve C in order to extract liquidity premia. Yieldcurves: A- risk free (e.g. gilts); B- as A plus expected default losses;C- as B plus credit risk premium; D1,2 - as C plus liquidity premiumand bid/ask spread; E1,2 - as D but higher bid/ask spread. . . . . . . . 532.7Beta parameters (β) for log duration, grouped by Financials and NonFinancials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58ix
2.8Beta parameters (β) for log Notional (left) and Seniority indicator(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.9Beta parameters for the Age Category indicator (left) and CapitalTier (LT2) indicator (right). . . . . . . . . . . . . . . . . . . . . . . . 602.10 The weekly duration coefficient, β, for Non-Financial Issuers (left)and Financials (right) for all four rating categories. . . . . . . . . . . 612.11 Gamma coefficient for Non-Financials (left) and Senior (right) bondindicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.12 Gamma coefficient for Non-Financials across rating categories. . . . . 632.13 Gamma coefficient for log Duration (NF) on the left and RBAS onthe right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.14 Gamma coefficient for Coupon (left) and Collateralized indicator (right). 652.15 Variation of the coefficient of determination, R2 , for the credit spreadsmodel over time (weekly) and by rating category. . . . . . . . . . . . 662.16 Decomposition of credit spread (left) for A-rated bonds of average liquidity into a liquidity and non-liquidity component; Liquidity component of credit spread (middle) in basis points and the liquiditycomponent of credit spread as a proportion of total credit spread(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.17 Time-varying nature of four weekly quantiles of daily liquidity premium distributions, in basis points (left) and in proportion of spread(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.18 Monthly estimates of median liquidity premia across rating category.692.19 Predicted liquidity premia for constant bond over time (left), for various degrees of liquidity (right). . . . . . . . . . . . . . . . . . . . . . 702.20 Shown on the same scale, the bid-ask spread for all IG ratings, bothFinancial and Non-Financial issuers, increased dramatically duringthe financial crisis. . . . .
The Actuarial Research Centre (ARC) is the Institute and Faculty of Actuaries’ network of actuarial researchers around the world. The ARC seeks to deliver research programmes that bridge academic rigour with practitioner needs by working collaboratively with academics, industry and other actuarial bodies.
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