Technische Universität München Credit as an Asset Class - risklab

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Chapter 1 Introduction 1.1 Motivation The credit market has experienced an enormous growth over the last years. As part of the credit market, the credit derivatives market is the worldwide fastest growing derivatives market. 1 It expanded from USD 180 billion of outstanding contracts on a total notional amounts basis in 1997 to USD 5,021 billion in 2004 and to estimated USD 8,206 billion in 2006. 2 After a standardisation of credit derivative contracts and the introduction of CDS 3 indices, a revolution in terms of liquidity has taken place. The improved liquidity is only one reason why credit instruments are very attractive to investors. In addition, credit instruments, such as corporate bonds, credit derivatives and securitisations, often have an appealing risk-return profile, allowing to enhance portfolio return. Furthermore, due to the correlation structure of their returns to returns of traditional asset classes, such as stocks and government bonds, they offer high potential for diversification. Finally, they allow to manage credit risk exposure by hedging credit risk. Even knowing the potential benefits and risks of different credit instruments, many investors still have to become familiar with these instruments and have to learn how to combine them optimally with traditional asset classes, i.e. they have to know the optimal proportion of credit instruments, especially for their individual level of risk-aversion. 1.2 Objectives and Structure With this thesis, we want to contribute to a deep understanding of credit related products, particularly credit derivatives and securitisations. For this purpose, the reader shall understand the drivers and the need for credit risk transfer. He also shall understand the functionality of various products and the risks inherent in them. Furthermore, we want to give an idea of the size and the impressive development of the market. Besides, we also aim at analysing credit instruments in a portfolio context with traditional asset classes. Therefore, we introduce an asset allocation framework with a scenario- 1 See [BR04], p. 16. 2 See [Bri04], p. 5 and [Fit05], p. 1. 3 A credit default swap (CDS) is a contract in which the protection buyer pays a fixed periodic fee on the notional amount to the protection seller over a predetermined period. In exchange, the protection buyer receives a contingent payment from the protection seller, triggered by a credit event of a reference entity. 1
CHAPTER 1. INTRODUCTION based simulation of risk factors on the one hand and a simulation of default times on the other hand. Then, risk factors and default times are used to price various credit instruments. After having determined the return distribution of the government bonds, the equity index and the credit instruments, we are able to calculate optimal asset allocations with several optimisation criteria. We do not only apply traditional portfolio optimisation according to Markowitz 4 , but also optimisations, based on other criteria that are able to better capture the distinct distributional properties of credit instruments. That way, we can show that investors benefit from adding credit instruments to their portfolio, i.e. with the same level of risk they can generate a higher expected return. To reach the objectives listed above, we chose the following structure of the thesis. Chapter 2 gives a general introduction into credit risk transfer. After defining credit risk and explaining some regulatory aspects, we briefly describe traditional credit related instruments, loans and bonds. Then, we introduce the two main possibilities of credit risk transfer, credit derivatives and securitisations. We describe their functionality, the reasons for using credit risk transfer instruments, and both, chances and risks related to these markets. Finally, we give an overview on market evolution and size. In Chapter 3, single credit risk transfer instruments are explained in their basic form, but also some product variations. In particular, we introduce CDS, total return swaps, credit spread options, basket CDS, portfolio CDS, credit linked notes, collateralised debt obligations and CDS indices. In order to learn more about distributional properties of the returns of credit instruments, we analyse Lehman aggregate indices, which are fixed income indices, in Chapter 4. In Chapter 5 we introduce a model for scenario generation. It has a cascade form, incorporating macro-economic factors to simulate interest-rates and equity indices. To realistically price credit instruments, we need to take into account potential defaults. The one-factor copula approach for modelling correlated default times between reference entities has become very popular. We use this approach not only for a Gaussian one- factor copula, but also for a Normal-Inverse-Gaussian one-factor copula, which is able to produce more realistic properties for default times than the Gaussian version, such as a higher probability of joint defaults of different companies. The last section is dedicated to the pricing formulas for the credit instruments in the investment universe. In particular, these instruments are zero-coupon bonds, coupon bonds, funded CDS and funded CDS indices. Chapter 6 deals with portfolio selection. As a first step, the mean-variance approach according to Markowitz and its problems due to strict assumptions on the structure of asset returns or on utility functions is described. Then, we introduce the optimisation with the conditional value at risk as risk measure. Finally, we present the portfolio selection with the measure score taking into account an investor’s risk-aversion. In this context, we assume two representative investors, one being risk-averse and the other being risk-affine. We apply our asset allocation framework to investors in the United States in Chapter 7. At first, we present the simulation parameters, the return statistics for the instruments under consideration and the optimisation results with Gaussian and NIG default times. 4 See [Mar52]. 2
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Figure 4.2: Histogram of US aggrega
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CHAPTER 4. DATA ANALYSIS Aggregate
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4.4 Summary CHAPTER 4. DATA ANALYSI
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Definition 5.1 (Interest-Rate) CHAP
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CHAPTER 5. SIMULATION AND PRICING F
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epeat the adjusted formulas here in
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Chapter 6 Portfolio Selection After
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CHAPTER 6. PORTFOLIO SELECTION µ(x
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above definition of the VaR can als
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L� −∞ FR(r)dr = L� −∞ C
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Chapter 7 Simulation and Simulation
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CHAPTER 7. SIMULATION AND SIMULATIO
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CHAPTER 8. SUMMARY AND OUTLOOK fact
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Appendix A Mathematical Preliminari
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APPENDIX A. MATHEMATICAL PRELIMINAR
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APPENDIX A. MATHEMATICAL PRELIMINAR
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Appendix B Ratings Rating Descripti
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APPENDIX C. CALCULATION OF THE DYNA
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Appendix E List of Abbreviations AB
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BIBLIOGRAPHY [Das06] Das, S. (2006)
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BIBLIOGRAPHY [NS87] Nelson, C.R., S
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Technische Universität München Credit as an Asset Class - risklab

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