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1
Introduction
Giovanni Barone Adesi and Nicola Carcano
Abstract:Ā This chapter summarizes the motivation for managing the risks related to interest rates changes and the interest rate risk management techniques actually used by most institutions and private investors: duration vector (DV) models, principal component analysis (PCA) and key rate duration (KRD). We highlight how a number of studies conducting empirical tests of these models reported puzzling results: models capable to better capture the dynamics of the yield curve were not always shown to lead to better hedging. In this chapter, we summarize the contribution of each of the following chapters in explaining these results and proposing alternative models capable of adding value over the abovementioned traditional models both for hedging and portfolio management.
Barone Adesi,Giovanni and Nicola Carcano, eds. Modern Multi-Factor Analysis of Bond Portfolios: Critical Implications for Hedging and Investing. Basingstoke: Palgrave Macmillan, 2016. DOI: 10.1057/9781137564863.0005.
Managing the risks related to interest rates changes is a highly relevant issue for most institutional and private investors. In a broad sense, it could even be argued that interest rate risk management is the single most important global financial issue, at least in term of the involved assets, since both institutions and private individuals invest on average the majority of their assets in money-market and fixed-income instruments. Accordingly, these investors must face the issue of managing the absolute volatility of these assets. In addition, many of these investors also have to face the issue of how the value of the assets invested in money-market and fixed-income instruments changes relatively to the value of their liabilities, an issue we commonly refer to using the expression Asset and Liability Management (ALM).
When we consider the essence of the interest rate risk management techniques actually used by most institutions and private investors, we conclude that the key points of these techniques have been mostly developed a few decades ago. Of course, this does not necessarily imply that these techniques are bad or out-of-date. However, one could expect more technological advances actually applied in the framework of such a critical topic. Accordingly, the main goal of this book is to describe the value potentially added by more recent techniques to manage interest rate risk relatively to traditional techniques and to present empirical evidence of such an added value.
Managing interest rate risk implies hedging the two components of bond yields: the risk-free term structure of interest rates and the corporate bond spreads. Different techniques to hedge the risk-free term structure of interest rates have been developed over the past 40 years. Initially, academicians and practitioners focused on the concept of duration ā introduced by Macaulay (1938) ā for implementing immunization techniques. Duration represents the first derivative of the price-yield relationship of a bond and was shown to lead to adequate immunization for parallel yield curve shifts.1
The assumption of parallel yield curve shifts could be released thanks to the concept of convexity which was initially related to the second derivative of the price-yield relationship (Klotz (1985)). Bierwag et al. (1987) and Hodges and Parekh (2006) show that the usefulness of convexity is generally not related to better approximating the price-yield relationship, but rather to the fact that hedging strategies relying on duration- and convexity-matching are consistent with plausible two-factor processes describing non-parallel yield curve shifts. Further extensions of these concepts were based on M-square and M-vector models introduced by Fong and Fabozzi (1985), Chambers et al. (1988), and Nawalkha and Chambers (1997). Similarly as for convexity, most of these models relied on the observation that further-order approximations of the price-yield relationship lead to immunization strategies which are consistent with multi-factor processes accurately describing actual yield curve shifts. Nawalkha et al. (2003) reviewed these duration vector (DV) models and developed a generalized duration vector (GDV).
A second class of hedging models relied on a statistical technique known as principal component analysis (PCA) which identifies orthogonal factors explaining the largest possible proportion of the variance of interest rate changes. Litterman and Scheinkman (1988) showed that a 3-factor PCA allows capturing the most important characteristics displayed by yield curve shapes: level, slope and curvature.
A third approach relied on the concept of key rate duration (KRD) introduced by Ho (1992). According to this approach, changes in all rates along the yield curve can be represented as linear interpolations of the changes in a limited number of rates, the so-called key rates.
The interest rate risk management techniques most commonly used in practice rely on one of the three abovementioned approaches. However, a number of studies conducting empirical tests of these models reported puzzling results: models capable to better capture the dynamics of the yield curve were not always shown to lead to better hedging. This was the case of the volatility- and covariance-adjusted models tested by Carcano and Foresi (1997) and of the 2-factor PCA tested by Falkenstein and Hanweck (1997) which was found to lead to better immunization than the corresponding 3-factor PCA.
These puzzling results contributed to limit the actual use of more sophisticated yield curve models by practitioners. The second chapter of this book analyzes possible explanations for these puzzling results in the context of principal component analysis of government bond yields, whereas the third chapter extends this analysis also to duration vector and key rate duration models. In general, we find that ā once we adjust the models in order to control the exposure to model errors ā empirical results from government bond portfolios become broadly consistent with economic theory.
The second component of bond yields which needs to be addressed by interest rate risk management techniques is represented by the corporate bond spreads. Hedging corporate bond spreads requires an understanding of the key economic factors explaining their existence and dynamics. These factors have been the focus of a substantial amount of research efforts over the last decade. Before these efforts, the prevailing opinion was the one reported by Cumby and Evans (1995): this spread is driven mainly by expected default loss and tax premium. Later research found that these factors cannot explain the cross-sectional and time series dynamics of the spread and questioned the relevance of the tax premium. Most scholars relied either on liquidity premiums or on time-varying market risk premiums to explain this credit spread puzzle.
The relevance of an aggregate ā as opposed to firm-specific ā liquidity premium for corporate bond spreads has been suggested by Collin-Dufresne et al. (2001): they find that these spreads are explained for 25% by expected default and recovery rate with the remaining 75% explained by a single factor which is not strongly related to variables traditionally used as proxies for systematic risk and liquidity. They conclude that this factor could be linked to more sophisticated proxies for liquidity.
Time-varying market risk premiums have been emphasized by Elton et al. (2001). They find that, using traditional Fama-French factors, 85% of the spread that is not accounted for by taxes and expected default can be explained as a reward for bearing systematic risk. Since the expected default loss and tax premium are relatively static, this risk premium is responsible for most of the dynamics of corporate bond spreads.
The fourth chapter of this book starts from the evidence reported by the abovementioned studies on the dynamics of corporate bond spreads in order to develop and test more advanced models for hedging corporate bond portfolios. We find that hedging strategies relying only on T-bond futures provide results which can hardly be improved by equity derivatives or Credit Default Swaps (CDS). These results may contradict common practical beliefs. Nevertheless, they are consistent with previous findings that stock market variables are less important than term structure variables to explain investment-grade bond returns and confirm recent empirical evidence of a non-default component of corporate spreads which becomes critical in times of unusual turbulences.
The fifth chapter of this book shifts the focus from pure hedging strategies to optimal portfolio construction. For many investors, analytical excess returns conform to their macro views: they wish to be exposed to any change in corporate default probabilities/recoveries, including any change correlated with changes in Treasury yields. Other investors want a corporate excess return uncluttered by the effects of correlated movements in corporate spreads and Treasury yields. This chapter focuses on presenting the techniques to implement the abovementioned investment views and on back-testing their empirical results.
Finally, the sixth chapter of the book summarizes our overall theoretical as well as practical conclusions and our key recommendations to practitioners actually engaged in interest rate risk management.
The book follows a stepwise construction approach. We start from the simplest models in Chapter 2 and gradually move towards more sophisticated models in the following chapters. In each chapter, the additional layers of complexity are firstly explained and motivated and secondly tested relying on extensive sets of empirical data.
Note
Ā Ā 1Ā Ā Ā The original formulation of duration relied on flat yield curves, but this restriction was overcome thanks to the formulation proposed by Fisher and Weil (1971). For an extensive review of how the concept of duration was developed during the last century, see Bierwag (1987).
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2
Adjusting Principal Component Analysis for Model Errors
Nicola Carcano
Abstract: Several papers which tested alternative ways of hedging against yield curve risk reported that models capturing the dynamics of the yield curve better do not necessarily lead to better hedging. We claim that the main reason for these counterintuitive observations could have been the level of exposure to the model errors and tested a generalized model of PCA-hedging which controls the overall exposure to these errors. The results we obtained both for bond-based and for swap-based hedging clearly confirm our claim. Controlling the exposure to model errors leads to an average reduction in the hedging errors of 35%. An additional, important advantage of controlling the exposure to model errors is a substantial reduction in the transaction fees implied by the hedging strategies.
Barone Adesi,Giovanni and Nicola Carcano, eds. Modern Multi-Factor Analysis of Bond Portfolios: Critical Implications for Hedging and Investing. Basingstoke: Palgrave Macmillan, 2016. DOI: 10.1057/9781137564863.0006.
The level of interest in Liability Driven Investments (LDI) and, more generally, in accurate techniques of asset and liability management has grown up significantly over the last decade. This follows a process of de-risking which has been implemented worldwide by many institutional investors. Accordingly, the approaches to effectively hedge against interest rate risk have become significantly more sophisticated than the initial models based on duration and convexity. The theories underpinning these approaches mostly rely on the concepts of key rate duration introduced by Ho (1992), of duration vectors (like the M-square model of Fong and Fabozzi (1985) and the M-vector models proposed by Nawalkha and Chambers (1997) and Nawalkha et al. (2003)) or on Principal Component Analysis (PCA).1
Hedging based on PCA is one of the most common techniques used by institutional investors to minimize the basis risk from shifts in the yield curve. In theory, accounting for the third principal component should improve the quality of hedging, since it allows to hedge also against changes in the curvature of the yield curve (this point was highlighted by Litterman and Scheinkman (1988)).
However, Falkenstein and Hanweck (1997) presented empirical evidence suggesting that hedging based on PCA should rely on two principal components rather than on three. They attributed the poor performance of three-component PCA-hedging to the instab...
