This dissertation addresses research issues in the area of interest rate risk management of default-free government bonds. The main theoretical contribution is the development of non-arbitrage permitting duration models that are independent of the underlying stochastic process of the term structure. This allows protection of the nominal value of the government bond portfolios from virtually any type of non-parallel term structure shift. Various limitations of the traditional duration theory are considered using the insights obtained from the generalized duration models developed here. For example, properties of bond convexity are considered under equilibrium conditions that make no restrictive assumptions about the stochastic processes governing the term structure. Under these conditions the analysis reveals an important link between convexity and slope shifts in the term structure. Specifically slope shifts are shown to increase the riskiness of an immunized portfolio as the convexity exposure deviates form an optimum level. Thus, high convexity is not always desirable. Limitations of the M-square model (see Fong and Vasicek (1983, 1984)) are analyzed and new scalar and vector immunization risk measures are derived that overcome these limitations. It is shown that the risk measure M-square cannot be applied to immunize a bond portfolio with short or forward positions. Second, even when short positions are disallowed, it can be shown that risk measure M-square is not unique for obtaining a lower bound on the terminal value of a bond portfolio. A vector of immunization risk measures (termed collectively as the "M-vector") is derived that allows for short positions and forward positions. Finally a portfolio theory approach to the M-vector model is presented. The duration vector of Chambers, Carleton and McEnally (1988) is found to be a limiting case of the more generalized duration models developed in this research. It is shown that the duration vector of Chambers et al. is based on a polynomial return function for bonds. This dissertation derives alternative duration vectors based on various asymptotic and non-asymptotic return functions (such as polynomial, exponential, and trigonometric functions). Multiple regression tests performed to identify the appropriate return function for government bonds find that traditional duration vector of Chambers et al. performs as well as any other return function. Finally closed-form solutions are derived for various interest rate risk measures (i.e. convexity, M-square and the duration vector) proposed in the immunization literature.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-7738 |
| Date | 01 January 1990 |
| Creators | Nawalkha, Sanjay Kumar |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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