A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy (by production of original research) in Mathematics School of Mathematics University of the Witwatersrand Johannesburg December 2012 / Generating functions and asymptotic analysis have been used in four di er- ent situations to establish new results for extremely well studied structures. Later in this thesis a more detailed individual abstract for each of these studies is provided. The four situations are: A. Durfee square areas in integer partitions. B. A study of the relationship between integer compositions and their constituent partitions by specifying the asymptotic expectation of the number of such partitions in arbitrary composition. C. Similar to B above but focusing more on the generating functions rather than on the expectations derived therefrom. D. In the area of plane partitions with additional structure imposed upon them.

Lau Ho-Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 56-57). / Abstracts in English and Chinese. / Abstract --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Comparison between APT and CAPM --- p.4 / Chapter 2.1 --- "CAPM, APT and UAPT" --- p.4 / Chapter 2.2 --- Introduction of CAPM --- p.5 / Chapter 2.3 --- Introduction of APT --- p.6 / Chapter 2.3.1 --- Assumptions and Requirements --- p.6 / Chapter 2.3.2 --- Introduction to the estimation of UAPT --- p.6 / Chapter 2.3.3 --- Limitations of classical procedures of APT --- p.7 / Chapter 3 --- Analysis of UAPT Using Structural Equation Model and Its Im- plementation in LISREL --- p.9 / Chapter 3.1 --- Introduction to SEM with LISREL Implementation --- p.9 / Chapter 3.1.1 --- The first stage of APT and the LISREL Model --- p.9 / Chapter 3.2 --- Estimation of APT by SEM --- p.12 / Chapter 3.2.1 --- Combining the two stages in classical method in APT by SEM --- p.12 / Chapter 3.2.2 --- Incorporating both observable and unobservable factors　in APT (UAPT) by SEM --- p.15 / Chapter 3.2.3 --- LISREL Implementation --- p.16 / Chapter 4 --- Simulation --- p.19 / Chapter 4.1 --- Simulation Procedure --- p.19 / Chapter 4.2 --- Results --- p.23 / Chapter 5 --- Empirical Study on Hong Kong Stock Market --- p.26 / Chapter 5.1 --- Description and source of the data --- p.26 / Chapter 5.2 --- The Goodness-of-fit Indexes in LISREL --- p.28 / Chapter 5.2.1 --- The normed fit index (NFI) --- p.29 / Chapter 5.2.2 --- The non-normed fit index (NNFI) --- p.29 / Chapter 5.2.3 --- The comparative fit index (CFI) --- p.29 / Chapter 5.3 --- The Structure of our LISREL Model --- p.30 / Chapter 5.4 --- The Five Models in the Empirical Analysis --- p.31 / Chapter 5.5 --- Results --- p.32 / Chapter 5.6 --- Conclusion --- p.33 / Chapter 6 --- Conclusion and Discussion --- p.35 / Appendix --- p.37 / Chapter A --- Example of LISREL Implementation --- p.37 / Chapter B --- Simulation Design and Simulation Result --- p.39 / Chapter C --- Result of Empirical Study --- p.50 / Bibliography --- p.56

Li Ming-Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 115-116). / Abstracts in English and Chinese. / Abstract --- p.i / Declaration --- p.iii / Acknowledgment --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Arbitrage Pricing Theory --- p.3 / Chapter 2.1 --- Model and Assumptions --- p.3 / Chapter 2.2 --- Derivation of the APT --- p.5 / Chapter 2.2.1 --- Factor Risk Premia --- p.7 / Chapter 3 --- The Classical Approach --- p.8 / Chapter 3.1 --- Factor Analysis --- p.8 / Chapter 3.2 --- The Cross-sectional Regression --- p.11 / Chapter 3.3 --- Critiques Concerning the 、APT --- p.12 / Chapter 4 --- The Structural Equation Model Approach --- p.15 / Chapter 4.1 --- Combining the Factor Model and the Pricing Equation --- p.15 / Chapter 4.2 --- Framework of the SEM with Mean Structure --- p.16 / Chapter 4.3 --- Applying the SEM Approach to the APT --- p.19 / Chapter 4.4 --- Merit of the SEM Approach --- p.20 / Chapter 5 --- Simulation Study --- p.22 / Chapter 5.1 --- Simulation Design --- p.22 / Chapter 5.2 --- Insight from the Simulation Study --- p.26 / Chapter 5.2.1 --- Factor loading. B --- p.26 / Chapter 5.2.2 --- Factor covariance matrix. Φ --- p.26 / Chapter 5.2.3 --- "Risk-free rate, rf" --- p.27 / Chapter 5.2.4 --- "Risk premium, λ" --- p.28 / Chapter 5.2.5 --- "Sample size, T" --- p.29 / Chapter 5.2.6 --- Other findings --- p.29 / Chapter 6 --- Empirical Study --- p.30 / Chapter 6.1 --- Specification of the Data --- p.30 / Chapter 6.2 --- Procedures for the SEM Approach --- p.31 / Chapter 6.3 --- Procedures for the Classical Approach --- p.35 / Chapter 6.4 --- Model Interpretation --- p.36 / Chapter 6.5 --- Difficulties Encountered --- p.37 / Chapter 7 --- Conclusion and Discussion --- p.39 / Chapter A --- Result of the Simulation Study --- p.40 / Chapter B --- Result of the Empirical Study --- p.105 / Chapter C --- LISREL Program for the Empirical Study (by the SEM Ap- proach) --- p.111 / Bibliography --- p.115

Faculty of Commerce, Law and Management University Of Witwatersrand 07 September 2016 / The purpose of this study is to identify whether the Law of One Price theory holds across bitcoin exchanges in different countries given the uniquely defining characteristics of bitcoin. This was explored using Johansen’s Cointegration to extract the economic relationship between the time series sampled. It was demonstrated in the results that the Law does not always hold, however this was dependent on which bitcoin exchange is being used. Prices across the same bitcoin exchanges were likely to hold because of similar transaction costs and the ease of trading. For the time series where the Law of One price did not hold, the explanatory factors could include the bitcoin market illiquidity and purposeful disequilibrium. Bitcoin is a fairly new concept and has been press-worthy in the finance, economic and technological spheres. In South Africa, awareness of the digital currency is low, as is an understanding of its features and the impact on the economy as well as society as a whole. This study therefore aims to explore bitcoin in a finance context, in terms of the Law of One Price, while briefly gaining an understanding of the digital currency itself. / MT2017

Choy Man Wah Minnie. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 83). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Analysis of APT using SEM --- p.3 / Chapter 2.1 --- The APT model --- p.3 / Chapter 2.2 --- The structural equation model approach --- p.5 / Chapter 3 --- Incorporating stochastic constraints into the SEM analysis of APT --- p.8 / Chapter 3.1 --- Introduction --- p.8 / Chapter 3.2 --- Bayesian analysis of stochastic constraints --- p.9 / Chapter 3.3 --- Three types of structures for T I --- p.10 / Chapter 3.3.1 --- Case 1: T = (σ2Imxm --- p.10 / Chapter 3.3.2 --- "Case 2: r is a diagonal matrix with diagonal elements σ2j for = 1， …,m" --- p.13 / Chapter 3.3.3 --- Case 3: Γ is a general positive definite matrix --- p.14 / Chapter 3.4 --- Estimation of parameters using the Mx program --- p.16 / Chapter 4 --- Empirical study on Hong Kong stock market --- p.17 / Chapter 4.1 --- Information of data --- p.17 / Chapter 4.2 --- Source of data --- p.17 / Chapter 4.3 --- Lisrel model with exact constraints --- p.19 / Chapter 4.3.1 --- The resultant model --- p.20 / Chapter 4.4 --- Lisrel model with stochastic constraints --- p.21 / Chapter 4.4.1 --- Result --- p.22 / Chapter 5 --- Simulation study --- p.35 / Chapter 5.1 --- Simulation design --- p.35 / Chapter 5.2 --- Simulation procedure --- p.40 / Chapter 5.3 --- Simulation result --- p.41 / Chapter 5.3.1 --- Sample size --- p.41 / Chapter 5.3.2 --- Analysis methods (constraints) --- p.42 / Chapter 5.3.3 --- Factor loadings --- p.43 / Chapter 5.3.4 --- Factor correlation matrix --- p.43 / Chapter 5.3.5 --- Risk premia --- p.43 / Chapter 5.3.6 --- Overall result --- p.44 / Chapter 6 --- Conclusion and discussion --- p.45 / Appendices --- p.46 / Chapter A --- Simulation result - Mean --- p.47 / Chapter B --- Simulation result - Bias --- p.56 / Chapter C --- Simulation result - RMSE --- p.65 / Chapter D --- Mx input script --- p.74 / Chapter D.l --- Stochastic constraints Case 1 --- p.74 / Chapter D.2 --- Stochastic constraints Case 2 --- p.77 / Chapter D.3 --- Stochastic constraints Case 3 --- p.80 / Bibliography --- p.83

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

A technique called gaussian temporal factor analysis (gaussian TFA) proposed by Xu in 2000 may be used to test the APT model under the mild assumption that the efficient market hypothesis (EMH) is violated. We are motivated to investigate statistical behaviors of the gaussian TFA model. / According to a recent survey by Cochrane (1999), the multi-factor APT model is gaining popularity and recognition over CAPM by the investment community. While empirical evidence shows that mutual funds can earn average returns not explained by the CAPM by following a variety of investment styles, this anomaly could be captured by APT which includes the single-factor CAPM as a special case. Yet, three aspects of APT still cannot be tested in practice. / First, a systematic testing package is proposed for testing gaussian TFA in six dimensions, including factor number, factor loadings, residuals correlations and autoregressive conditional heteroscedasticity (ARCH) effects, economic significance and factor independence, using financial data in Hong Kong. Particularly, a new hypothesis testing approach is proposed for statistically testing independence. / In the finance literature, an objective way to judge whether an asset pricing model is misspecified is by statistical tests. In the past, both the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) have been the subjects of extensive tests. / Second, we investigate two extensions of the gaussian TFA model in view of ARCH in driving noise residuals. We test the extended models for ARCH as well as other aspects to ensure model specification adequacy. Furthermore, we find that ARCH effects are not quite significant driving noise residuals of the macroeconomic modulate independent state-space model. This may be due to long-term modelling of the market. / Third, we test gaussian TFA from the practical point of view in financial prediction and portfolio management. For prediction, we introduce the gaussian TFA alternative mixture experts (ME) approach for forecasting. For adaptive portfolio management, we derive the gaussian TFA adaptive algorithm for implementing the Sharpe-ratio based adaptive portfolio management under different scenarios. Empirical results reveal that APT-based portfolio management techniques are in general superior to return-based techniques. / by Kai-Chun Chiu. / "July, 2003." / Adviser: Lei Xu. / Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4451. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 113-125). / 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 dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / School code: 1307.

A thesis submitted to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of the Witwatersrand in fulfilment of the requirements for the degree of Master of Commerce (M.Com) in Finance, Johannesburg June 2017 / Traditional finance theory surrounding the risk-return relationship is underpinned by the CAPM which posits that a single risk factor, specifically market risk, is priced into asset returns. Even though it is a popular asset pricing model, the CAPM has been widely criticised due to its unrealistic assumptions and the APT was developed to address the CAPM’s weaknesses. The APT framework allows for a multitude of risk factors to be priced into asset returns; implying that it can be used to model returns using either macroeconomic or microeconomic factors. As such, the APT allows for non-traditional factors, such as investor sentiment, to be included. A macroeconomic APT framework was developed for nine countries using the variables outlined by Chen, Roll, and Ross (1986) and investor sentiment was measured by the FEARS index (Da, Engelberg, & Gao, 2015). Regression testing was used to determine whether FEARS is a statistically significant explanatory variable in the APT model for each country. The results show that investor sentiment is a statistically significant explanatory variable for market returns in five out of the nine countries examined. These results add to the existing APT literature as they show that investor sentiment has a significant explanatory role in explaining asset prices and their associated returns. The international nature of this study allows it to be extended by considering the role that volatility spill-over or the contagion effect would have on each model. / XL2018

Xiong, Liying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leave 34). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Hong Kong Horse Racing Market and Models in Horse Racing --- p.3 / Chapter 2.1 --- Hong Kong Horse Racing Market --- p.4 / Chapter 2.2 --- Models in Horse Racing --- p.5 / Chapter 3 --- Probit Regression Model Incorporating with Public Estimates --- p.9 / Chapter 3.1 --- Estimation under No Particular Conditions --- p.10 / Chapter 3.2 --- Estimators under Particular Condition --- p.15 / Chapter 4 --- Prediction and Testing --- p.23 / Chapter 4.1 --- Prediction of Win Probability --- p.24 / Chapter 5 --- Conclusion --- p.32 / Bibliography --- p.34

The impact of political and economic events on the asset pricing model described by the arbitrage pricing theory (APTM) was examined in order to establish if they had caused any changes in its specification. It was concluded that the APTM is not stationary and that it must be continuously tested before it can be used as political and economic events can change its specification. It was also found that political events had a more direct effect on the specification of the APTM, in that their effect is more immediate, than did economic events, which influenced the APTM by first influencing the economic environment in which it operated. The conventional approach that would have evaluated important political and economic events, case by case, to determine whether they affected the linear factor model (LFM), and subsequently the APTM, could not be used since no correlation was found between the pricing of a risk factor in the LFM and its subsequent pricing in the APTM. A new approach was then followed in which a correlation with a political or economic event was sought whenever a change was detected in the specification of the APTM. This was achieved by first finding the best subset LFM, chosen for producing the highest adjusted R2 , month by month, over 87 periods from 20 October1991 to 21 June 1998, using a combination of nine prespecified risk factors (five of which were proxies for economic events and one for political events). Multivariate analysis techniques were then used to establish which risk factors were priced most often during the three equal subperiods into which the 87 periods were broken up. Using the above methodology, the researcher was able to conclude that political events changed the specification of the APTM in late 1991. After the national elections in April 1994 it was found that the acceptance of South Africa into the world economic community had again changed the specification of the APTM and the two most important factors were proxies for economic events. / Business Leadership / DBL