Derivatives Strategies for Bond Portfolios

In this paper, we examine how standard exchange-traded fixed-income derivatives (futures and options on futures contracts) can be included in a sound risk and asset management process so as to improve risk and return performance characteristics of managed portfolios. Our results show that the non-linear character of the returns on protective option strategies offers appealing risk reduction properties in the pure asset management context. Consequently, such strategies should optimally receive a significant allocation, especially when investors are concerned with minimising extreme risks. In an asset liability management context, we also show that fixed-income derivatives in general, and recently launched long-term futures contracts in particular, offer significant shortfall risk reduction benefits. These results have potentially significant implications in the context of an increased focus on matching liability portfolios. This research is sponsored by Eurex EDHEC is one of the top five business schools in France owing to the high quality of its academic staff (104 permanent lecturers from France and abroad) and its privileged relationship with professionals that the school has been developing since its establishment in 1906. EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore concentrated its research on themes that satisfy the needs of professionals. EDHEC pursues an active research policy in the field of finance. Its “Risk and Asset Management Research Centre” carries out numerous research programs in the areas of asset allocation and risk management in both the traditional and alternative investment universes. Copyright © 007 EDHEC Introduction Interest in the use of fixed-income derivatives in asset management has perhaps never been so high, both from a pure asset management perspective and from an asset-liability management perspective. On the one hand, from a pure asset management perspective, historically low levels of long-term yields, combined with the prospect of increases in short-term rates by central banks in Europe as well as in the United States, are a strong incentive to implement strategies that aim to deliver downside protection by combining a long position in bond markets with a long position in put options. On the other hand, recent pension fund shortfalls have drawn attention to the risk management practices of institutional investors in general and defined benefit pension plans in particular, and have provided new incentives for institutional investors to use fixedincome derivatives in the management of their liability risk. "A perfect storm” of adverse market conditions around the turn of the millennium has devastated many corporate defined benefit pension plans. Negative equity market returns have eroded plan assets at the same time as declining interest rates have increased the mark-to-market value of benefit obligations and contributions. In extreme cases, this has left corporate pension plans with funding gaps as large as, or larger than, the market capitalization of the plan sponsor. For example, in 003, the companies included in the S&P 500 and the FTSE 100 index faced a cumulative deficit of $ 5 billion and £55 billion respectively, (as per surveys by Credit Suisse First Boston [ 003] and Standard Life Investments [ 003]), while the worldwide deficit reached an estimated 1,500 to ,000 billion USD (Watson Wyatt [ 003]). That institutional investors in general and pension funds in particular have been so dramatically affected by recent market downturns has emphasized the weakness of risk management practices. In particular, it has been argued that the asset allocation strategies implemented in practice, which were heavily skewed towards equities, in the absence of any protection with respect to their downside risk, were not consistent with sound liability risk management. In this context, new approaches, referred to as liability-driven investment solutions, have rapidly elicited interest from pension funds, insurance companies and investment consultants alike, following recent changes in accounting standards and regulations that have led to an increased focus on liability risk management. Such strategies, which can add significant value in terms of liability risk management, lead to an increased focus on matching investors’ portfolios via cash instruments (long-term real and nominal bonds) or via derivative instruments. From an academic perspective, while an impressive amount of research is available on issues related to bond and fixed income derivative pricing and hedging, relatively few results can actually be found on how these instruments can be used to improve an investor’s welfare in the context of portfolio strategies. This paper, as it happens, focuses on illustrating how various types of derivative securities can be used to shift the risk associated with investing in fixed income securities. We take an asset allocation perspective and assess in more detail the benefits of including bond futures and options on these futures in a fixed income portfolio. In addition to linear instruments such as futures, options have non-linear payoffs that allow investors to construct funds with skewed or dissymmetric return profiles. In comparison to simple bond index exposure, these may offer an efficient way to limit the extreme values of a portfolio return distribution. As such, our paper is closely related to a number of papers that look at optimal portfolios when investors have access to an asset and options on this asset. Based on Merton’s (1973) replicating portfolio interpretation of the Black and Scholes (1973) option pricing model, one could argue that options are redundant assets, and as a result the optimal allocation to such assets should be either indeterminate (when an investor’s expectation about parameter values match those of the markets), or infinite (when investors’ belive the derivative asset is underpriced). It should however be recognized that this result depends on the concept of dynamic completeness (see Radner [197 ] for a formal analysis), which can only be justified under a set of rather stringent assumptions that are never met in practice (continuous trading, the absence of transaction costs, leverage or short-sales constraints, constant volatility and drift of the underlying asset, symmetric information, etc). When any of these assumptions are relaxed, it can actually be shown that the introduction of derivatives would improve the welfare of investors. A first strand of the literature, initiated by Brennan and Solanki (1981), has examined the 3 4 question of optimal positioning in derivative assets from the static investor’s standpoint. The question there is to determine the general shape of the non-linear function of the underlying asset that would generate the highest level of expected utility for a given investor. Carr and Madan ( 001) extend this early work by considering optimal portfolios of a riskless asset, a risky asset and derivatives on the latter in an expected utility framework. A second strand of the literature (starting with Leland [1980] and extended by Benninga and Blume [1985]) has studied the question from a different angle: taking as given a set of standard derivatives, these papers examine the features of (static) investors’ preferences that would support a rational holding of these contracts. This paper, which sets itself apart by focusing exclusively on bond derivatives, complements existing literature by focusing on the use of derivatives, not only in asset management, but also from an asset-liability management perspective. In an attempt to focus on plain vanilla products that can readily be used by investors, we take as objects of study a set of exchange-traded fixed-income derivatives traded on Eurex, the world's leading futures and options market for euro denominated derivative instruments. The use of futures and options will be organized according to the investment process and objectives and we will examine the value of introducing derivatives both in a pure asset management context and in an asset-liability management context. The rest of the paper is organized as follows: section one introduces the theoretical model and shows how we implement it. Section two details the implementation of the investment strategies and assesses their benefits in a pure asset management context. Section three examines similar questions but from an asset-liability management (ALM) perspective. 1. The Framework In order to assess the different uses and benefits of derivatives in fixed-income portfolios in the context of a fullblown numerical experiment, one needs to generate stochastic scenarios for asset prices. The scenario generation process will be similar for the whole paper, with additional assumptions on investors’ preferences needed for some sections. In this introductory section, we therefore describe our assumptions with respect to how fixed income markets are modelled. 1.1. Choice of a Model The issue of modelling the future uncertainty is critical to any investment management problem. A stochastic forecasting model consists of multivariate time series models. While generating stochastic scenarios for stock prices can be achieved in a straightforward manner, a specific challenge related to simulating bond prices is the need to ensure the absence of arbitrage between the prices of bonds with different maturities at a given point in time. In other words, one needs to impose some restrictions on the cross-section of bond prices. This can be achieved by using a consistent model of the term structure of interest rates. Term structure models imply that changes in yields of bonds of different maturities can be expressed as a function of changes in some underlying factors. The first option would be to use an equilibrium model of the term structure. This type of model starts with diff