Digitized by Kansas Correctional Industries

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Master of Management in Finance & Investment Faculty of Commerce Law and Management Wits Business School University of The Witwatersrand 2016 / The Value-at-Risk (VaR) measurement – which is a single summary, distribution independent statistical measure of losses arising as a result of market movements – has become the market standard for measuring downside risk. There are some diverse ways to computing VaR and with this diversity comes the problem of determining which methods accurately measure and forecast Value-at-Risk. The problem is two-fold. First, what is the distribution of returns for the underlying asset? When dealing with linear financial instruments – where the relationship between the return on the financial asset and the return on the underlying is linear– we can assume normality of returns. This assumption becomes problematic for non-linear financial instruments such as options. Secondly, there are different methods of measuring the volatility of the underlying asset. These range from the univariate GARCH to the multivariate GARCH models. Recent studies have introduced the Independent Component Analysis (ICA) GARCH methodology which is aimed at computational efficiency for the multivariate GARCH methodologies. In our study, we focus on non-linear financial instruments and contribute to the body of knowledge by determining the optimal combination for the measure for volatility of the underlying (univariate-GARCH, EWMA, ICA-GARCH) and the distributional assumption of returns for the financial instrument (assumption of normality, the Johnson translation system). We use back-testing and out-of-sample tests to validate the performance of each of these combinations which give rise to six different methods for value-at-risk computations. / MT2017

This thesis is concerned with a new computational study of optimal investment decisions with proportional transaction costs or capital gain taxes over multiple periods. The decisions are studied for investors who have access to a risk-free asset and multiple risky assets to maximize the expected utility of terminal wealth. The risky asset returns are modeled by a discrete-time multivariate geometric Brownian motion. As in the model in Davis and Norman (1990) and Lynch and Tan (2010), the transaction cost is modeled to be proportional to the amount of transferred wealth. As in the model in Dammon et al. (2001) and Dammon et al. (2004), the taxation rule is linear, uses the weighted average tax basis price, and allows an immediate tax credit for a capital loss. For the transaction costs problem, we compute both lower and upper bounds for optimal solutions. We propose three trading strategies to obtain the lower bounds: the hyper-sphere strategy (termed HS); the hyper-cube strategy (termed HC); and the value function optimization strategy (termed VF). The first two strategies parameterize the associated no-trading region by a hyper-sphere and a hyper-cube, respectively. The third strategy relies on approximate value functions used in an approximate dynamic programming algorithm. In order to examine their quality, we compute the upper bounds by a modified gradient-based duality method (termed MG). We apply the new methods across various parameter sets and compare their results with those from the methods in Brown and Smith (2011). We are able to numerically solve problems up to the size of 20 risky assets and a 40-year-long horizon. Compared with their methods, the three novel lower bound methods can achieve higher utilities. HS and HC are about one order of magnitude faster in computation times. The upper bounds from MG are tighter in various examples. The new duality gap is ten times narrower than the one in Brown and Smith (2011) in the best case. In addition, I illustrate how the no-trading region deforms when it reaches the borrowing constraint boundary in state space. To the best of our knowledge, this is the first study of the deformation in no-trading region shape resulted from the borrowing constraint. In particular, we demonstrate how the rectangular no-trading region generated in uncorrelated risky asset cases (see, e.g., Lynch and Tan, 2010; Goodman and Ostrov, 2010) transforms into a non-convex region due to the binding of the constraint.For the capital gain taxes problem, we allow wash sales and rule out "shorting against the box" by imposing nonnegativity on portfolio positions. In order to produce accurate results, we sample the risky asset returns from its continuous distribution directly, leading to a dynamic program with continuous decision and state spaces. We provide ingredients of effective error control in an approximate dynamic programming solution method. Accordingly, the relative numerical error in approximating value functions by a polynomial basis function is about 10E-5 measured by the l1 norm and about 10E-10 by the l2 norm. Through highly accurate numerical solutions and transformed state variables, we are able to explain the optimal trades through an associated no-trading region. We numerically show in the new state space the no-trading region has a similar shape and parameter sensitivity to that of the transaction costs problem in Muthuraman and Kumar (2006) and Lynch and Tan (2010). Our computational results elucidate the impact on the no-trading region from volatilities, tax rates, risk aversion of investors, and correlations among risky assets. To the best of our knowledge, this is the first time showing no-trading region of the capital gain taxes problem has such similar traits to that of the transaction costs problem. We also compute lower and upper bounds for the problem. To obtain the lower bounds we propose five novel trading strategies: the value function optimization (VF) strategy from approximate dynamic programming; the myopic optimization and the rolling buy-and-hold heuristic strategies (MO and RBH); and the realized Merton's and hyper-cube strategies (RM and HC) from policy approximation. In order to examine their performance, we develop two upper bound methods (VUB and GUB) based on the duality technique in Brown et al. (2009) and Brown and Smith (2011). Across various sets of parameters, duality gaps between lower and upper bounds are smaller than 3% in most examples. We are able to solve the problem up to the size of 20 risky assets and a 30-year-long horizon.

About the intraday volatility modeling, the limitations and potential problems of using Andersen & Bollerslev's approach are addressed and distinct modifications are proposed to tackle the corresponding issues. The first suggestion is about the utilization of the interaction between the intraday periodicity and the heteroskedasticity while the second is about the modified normalization for the estimation of the intraday periodicity. / Furthermore, it is demonstrated that the inclusion of overnight variance can improve the prediction accuracy of the Chicago Board of options Exchange (CBOE) volatility indexes (VIX and VXD) under specific weight combinations. The findings contradict the common perception that overnight return does not contain useful information for daily volatility modeling. / On the other hand, the third suggestion is about the inclusion of overnight information for the estimation of daily volatility. This study explores the possibility of incorporating the overnight variance indirectly through the use of linearly combined daily volatility estimators. The empirical results demonstrate that the inclusion of overnight variance can produce substantial influence when the minimum-variance constraints are relaxed. Besides, the influence is revealed to be not monotonic as an increase of the overnight proportion does not necessarily produce a larger influence. / The proposed modifications are tested with different ARCH structures, including GARCH(1,1), FIGARCH(1,d,1) and HYGARCH(1,d,1), by using simulated data and market data. Apart from studying the 1-step-ahead out-of-sample performance, several multiple-step-ahead forecasting results are also addressed. Under the same level of model flexibility (parameterized portions), our proposed modifications always outperform the original method in both in-sample fitness and out-of-sample performance on various forecasting horizons. / This research study investigates three new considerations for improving the performance of volatility modeling of financial returns. Two of them are related to the intraday volatility modeling and the other one is about the use of overnight information for daily volatility modeling. / Chu, Chun Fai Carlin. / Adviser: Kai Pui Lam. / Source: Dissertation Abstracts International, Volume: 73-04, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 180-186). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Yu Lian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 81-84). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.4 / Chapter 3 --- An Index Tracking Model with Downside Chance Risk Mea- sure --- p.12 / Chapter 3.1 --- Statement of the Model --- p.13 / Chapter 3.2 --- Efficient Frontier --- p.16 / Chapter 3.3 --- Application of the Downside Chance Index Tracking Model --- p.29 / Chapter 3.4 --- Chapter Summary --- p.34 / Chapter 4 --- Index Tracking Models with High Order Moment Downside Risk Measure --- p.35 / Chapter 4.1 --- Statement of the Models --- p.35 / Chapter 4.2 --- Mean-Downside Deviation Financial Index Tracking Model --- p.38 / Chapter 4.3 --- Chapter Summary --- p.45 / Chapter 5 --- Numerical Analysis --- p.45 / Chapter 5.1 --- Data Analysis --- p.45 / Chapter 5.2 --- Experiment Description and Discussion --- p.48 / Chapter 5.2.1 --- Efficient Frontiers --- p.48 / Chapter 5.2.2 --- Monthly Expected Rate of Return --- p.50 / Chapter 5.3 --- Chapter Summary --- p.52 / Chapter 6 --- Summary --- p.54 / Chapter A --- List of Companies --- p.57 / Chapter B --- Graphical Result of Section 5.2.1 --- p.61 / Chapter C --- Graphical Result of Section 5.2.2 --- p.67 / Chapter D --- Proof in Chapter 3 and Chapter4 --- p.73 / Bibliography --- p.81

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Behavioural theories of finance and economics have received little academic attention until recently. Nevertheless, behavioural theories of investor behaviour can be directly applied to categorization of investors and prediction of future behaviour. The purpose of characterizing and predicting future behaviour is to ensure allocation of appropriate corporate resources to meet the needs of clients as effectively as possible. This research specifically focuses on segmentation and predictive modeling of retail clients at Phillips, Hager & North Investment Management Ltd. Segmentation is undertaken through cluster analysis of investors based on transactional and performance data. Subsequent logistic regression and seemingly unrelated regression models are developed to determine if investment personality - through Know-Your-Client (KYC) information - and demographics have an explanatory and predictive relationship with future investor behaviour.

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