Stochastic Optimization for Portfolios Consisting of Corporate Bonds in an Integrated Market and Credit Risk Framework

Abstract

High credit spreads in 2009 have attracted a lot of interest from investors seeking higher yields outside of government bonds. Investment grade corporate bonds have indeed been a popular investment in 2009. The corporate bond market today is one of the largest and most liquid of the financial markets. Corporate bonds markets can be appealing as they are generally considered safer than stocks and they often provide higher yields and more liquidity than government bonds markets.

After the World Financial Crisis central banks set interest rates at their historically low level affecting positively bonds’ prices. The question for a corporate bond portfolio manager is which decisions to take in order to hedge portfolio against volatility of interest rates. Additionally managers have to analyse the factors that affect bonds’ prices volatility and is due to credit risk.

For this reasons managers have to implement a risk management framework in order to identify the factor that affect whole portfolio value and finally optimize its value. In an integrated market and risk perspective the future value of a corporate bond portfolio is decomposed into the risk that a bond issued by a firm downgraded by rating agencies and possible drives to default, the correlation between credit events, the risk that changes occur on the average spread of exposures with the same final rating as the firm and the effect of interest rate uncertainty.

In chapter 1 we introducing the main types of bonds, analyzing how to valuate non-callable bonds and calculating their yielding and we present factors that affect bond process and price volatility when interest rates changes a bit in a parallel way.

In chapter 2 we make an introduction to risk management by referring the risks that affect corporate bond prices. Then we explain the term structure of interest rates and how we can immunize a portfolio of bonds when interest rates changes in a parallel way. Then we introduce a multi-factor model for corporate bonds and present a portfolio immunization model based on factors to protect portfolio value against non-parallel changes of interest rates, introducing the appearance of shape risk.

In chapter 3 we added an introduction of credit risk referring the main sources of credit risk in a portfolio of corporate bonds. Then we model credit risk based on a reduced-form approach which defines the default as the instantaneous likelihood of default, called the hazard rate.

In chapter 4 we present an integrated market and credit risk framework using scenario generation in order later to optimize a corporate bond portfolio using stochastic programming models. Scenario generation is a tool to model the uncertainty. We develop a model for stochastic interest rates and credit spreads based on the Hull-White algorithm. Interest rates and credit spreads stochasticity based on extended Vasicek model and we produce scenarios of interest rates and credit spreads using trinomial lattice structures which capture the correlation between interest rates and default intensities. Finally we model the correlation between default and migration.

In chapter 5 we present the necessity for Conditional Value-at-Risk as a coherent risk measure for corporate bond portfolios. The right risk measure is of paramount importance when we optimize corporate bond portfolios because of tail effects (heavy tails) in the distribution of returns that could result in significant losses and destroy portfolio efficiency. Then we present a linear program for minimizing portfolio risk using CVaR.

In chapter 6 we implement portfolio optimization models using stochastic programming in a dynamic aspect. Initially we present an anticipative model where we only take into account stochasticity in future prices without taking recourse actions. Then we present a multistage recourse model where we can take recourse decisions at the preceding time periods based on information we take at discrete time in the future. We assume that there are transaction costs when we buy or sell bonds in order to make models more sophisticated. Finally we analyze one by one the equations of multistage recourse model.

Keywords: risk management, corporate bonds portfolios, integration of market and credit risk, stochastic interest rates and credit spreads, scenario generation, stochastic optimization, anticipative model, multistage recourse model

JEL Classification: C02, C61, G11, G20, N20, Y40