Bond Duration Models And Their Applications

According to the portfolio theory suggested by Markowitz in 1952, the return and risk of investment are the two same important factors in which investors take interest. The most important feature of the modern theory of bond investment is just represented by the interest in investment risks, instead of simply pursuing the steep expecting returns from investment. Generally speaking, interest rate risk is the most important type of risk faced by bond investors. Therefore, it is the main theme in the process of bond investment to find an effective measurement and a preventive method of the interest rate risk of bonds and bond portfolios. Based on the real need of bond investment, this paper systematically illustrates the various duration models such as Macaulay duration, partial duration, key rate duration and approximate duration and so on which are used in interest rate risk management of bonds. Furthermore, we explore the applications of these models to interest rate immunization and asset-liability management. The main part of this paper has three chapters and they are structured as follows. Chapter 1 presents the basis of the theory of bond investment. This chapter mainly deals with the essential concepts and the basic theories about the bond investment, making preparations to enunciate and analyze various bond duration models in the next step. These basic contents include bond classification and the types of bond risks, the capitalization of income pricing method of bonds and the term structure of interest rates. The term structure of interest rates is the key point in this chapter. This is because its concrete shapes and shifts are closely bound up with the application and accuracy of various bond duration models. Chapter 2 discusses the bond duration models. This chapter interprets the features and computational methods of various duration models, including Macaulay duration, partial duration, key rate duration and approximate duration, in the rigid mathematical language. Macaulay duration describes the average maturity of the bond on the one hand and measures the sensitivity of the bond price to the interest rate movement on the other hand, so it is one of the important tools for interest rate risk management of bonds. Partial duration is based on the specific shape of the term structure of interest rates, and it is the measurement of the sensitivity of the bond price to the movement of some critical factor of interest rate. Key rate duration takes some key interest rates as the critical factors of the shifts of the term structure of interest rates, and it measures the sensitivity of the bond price to the movement of some key interest rate. Approximate duration of a bond is defined as the maturity of some zero-coupon bond, which has the same price and sensitivity to the interest rate movement as the original bond. From the view of computation, Macaulay duration model is relatively simple, for it only depends on the cash flows of the bond and their discounting factor. While, the computation of partial duration model or key interest duration model is related to the selection of critical factors or key interest rates. As for approximate duration model, its solution can be reached by using optimization techniques. Chapter 3 is concerned with the applications of the bond duration models. As the effective tools for bond interest rate risk management, duration models are widely used in many fields such as interest rate immunization of bond investment, asset-liability management, pension fund management, analysis of profitability with capital budgeting and so forth. This chapter lays stress on how to realize the interest rate immunization of bond investment when the interest rate moves infinitesimally by using Macaulay duration model, and the effect comparison of various duration models'application in asset-liability management. Based on the theoretical analysis and application comparison of variousduration models, the following conclusions can be drawn. 1. Macaulay duration model is the first-order linear measurement of the sensitivity of the bond price to the interest rate movement. Because there is an assumption that the yield curve is flat and its shifts are parallel implicit in this model, the relationship between the relative change of the bond price and the interest rate movement holds only when the interest rate moves infinitesimally. 2. Partial duration model is the extension of the Macaulay duration model to the general cases in which the yield curve is non-flat and its shifts are not parallel. And key rate duration model is a special partial duration model. For not depending on the assumption about the concrete form of the yield curve, these two models have more applications than Macaulay duration model. But their accuracy is closely related to the selection of critical factors. 3. Approximate duration model is a generalization of Macaulay duration model. It can be applied not only in the situation where the yield curve is flat and its shifts are parallel, but in the situation where the non-flat yield curve has non-parallel shifts. The Macaulay duration represents the mean of the bond's discounted cash flows, while the approximate duration is the median. 4. A bond portfolio's Macaulay duration is the weighted average of the Macaulay durations of the individual bonds in the portfolio. The weight of each bond's duration is the ratio of its market value to the market value of portfolio. The partial duration and the key rate duration of a bond portfolio have the same feature. 5. The approximate duration matched strategy proves more efficient than any other duration matched strategy in the asset-liability management. This is not only because it does not assume that the yield curve is flat and its changes are only parallel shifts, but because it has the optimal solution when short selling of bonds is not permitted. This paper has some significance in theory and practice by discussing bond duration models and their applications. To some degree, the introduction...