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Title: Dynamic models of semi-variance
Author: Bond, S. A.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2001
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The semi-variance is a measure of downside risk originally suggested by Markowitz (1959). More correctly termed a second order lower partial moment, it captures the volatility of a series below a target rate of return. Under a certain set of conditions, use of the variance provides the same result as using semi-variance. However, when there is asymmetry present in the distribution of returns and in the preferences of individuals, semi-variance is preferred. Despite the potential of such risk measures, little previous work has examined the most suitable form for a dynamic (conditional) model of a lower partial moment. A number of approaches to this problem suggest themselves, such as a regime model, distribution based model or even an OLS model. The development and evaluation of such models forms the central focus of this dissertation. After an introduction in Chapter 1, Chapter 2 introduces the concept of semi-variance in detail and provides a comparison of the sample properties of the estimators for semi-variance and variance. Furthermore, Chapter 2 develops an expression for the size of the relative (in)efficiency of the sample semi-variance under the assumptions of symmetry and asymmetry of returns. The subsequent three chapters consider the form of a conditional semi-variance model. Chapter 3 develops a family of regime models of downside risk based on the SETAR ARCH model (Tong 1990). The models developed are found to outperform GARCH models and are able to explicitly identify the semi-variance. The use of asymmetry conditional density functions in GARCH models is the focus of Chapter 4. More specifically, Chapter 4 develops a GARCH model based on the double gamma distribution. This distribution has the added advantage that the conditional semi-variance can be identified from the parameters of the density function. The model is applied to a set of foreign currencies with mixed results.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available