Classifying yield spread movements in sparse data through triplots

Thesis (PhD)--Stellenbosch University, 2020.ENGLISH SUMMARY : In many developing countries, including South Africa, all data that are required to calculate the fair values of financial instruments are not always readily available. Additionally, in some instances, companies who do not have the necessary quantitative skills are reluctant to incorporate the correct fair valuation by failing to employ the appropriate techniques. This problem is most notable with regards to unlisted debt instruments. There are two main inputs with regards to the valuation of unlisted debt instruments, namely the the risk-free curve and the the yield spread. Investigation into these two components forms the basis of this thesis. Firstly, an analysis is carried out to derive approximations of risk-free curves in areas where data is sparse. Thereafter it is investigated whether there is sufficient evidence of a significant change in yield spreads of unlisted debt instruments. In order to determine these changes, however, a new method that allows for simultaneous visualisation and classification of data was developed - termed triplot classification with polybags. This new classification technique also has the ability to limit misclassification rates. In the first paper, a proxy for the extended zero curve, calculated from other observable inputs, is found through a simulation approach by incorporating two new techniques, namely permuted integer multiple linear regression and aggregate standardised model scoring. It was found that a Nelson Siegel fit, with a mixture of one year forward rates as proxies for the long term zero point, and some discarding of initial data points, performs relatively well in the training and testing data sets. This new method allows for the approximation of risk-free curves where no long term points are available, and further allows for the determinants of the yield curve shape by considering other available data. The changes in these shape determining parameters are used in the final paper as determinants for changes in yield spreads. For the second paper, a new classification technique is developed that was used in the final paper. Classification techniques do not easily allow for visual interpretation, nor do they usually allow for the limitation of the false negative and positive error rates. For some areas of research and practical applications these shortcomings are important to address. In this paper, classification techniques are combined with biplots, allowing for simultaneous visual representation and classification of the data, resulting in the so-called triplot. By further incorporating polybags, the ability of limiting misclassification type errors is also introduced. A simulation study as well as an application is provided showing that the method provides similar results compared to existing methods, but with added visualisation benefits. The paper focuses purely on developing a statistical technique that can be applied to any field. The application that is provided, for example, is on a medical data set. In the final paper the technique is applied to changes in yield spreads. The third paper considered changes in yield spreads which were analysed through various covariates to determine whether significant decreases or increases would have been observed for unlisted debt instruments. The methodology does not specifically determine the new spread, but gives evidence on whether the initial implied spread could be left the same, or whether a new spread should be determined. These yield spread movements are classified using various share, interest rate, financial ratio, and economic type covariates in a visually interpretive manner. This also allows for a better understanding of how various factors drive the changes in yield spreads. Finally, as supplement to each paper, a web-based application was built allowing the reader to interact with all the data and properties of the methodologies discussed. The following links can be used to access these three applications: - Paper 1: https://carelvdmerwe.shinyapps.io/ProxyCurve/ - Paper 2: https://carelvdmerwe.shinyapps.io/TriplotSimulation/ - Paper 3: https://carelvdmerwe.shinyapps.io/SpreadsTriplot/AFRIKAANSE OPSOMMING : In baie ontwikkelende lande, insluitend Suid-Afrika, is al die inligting wat benodig word om die billike waardes van finansiële instrumente te bereken, nie altyd geredelik beskikbaar nie. In sommige gevalle is ondernemings, wat nie oor die nodige kwantitatiewe vaardighede beskik nie, teësinnig om die regte billike waardasie te bereken deur nie-toepaslike tegnieke te gebruik. Hierdie probleem is veral opvallend ten opsigte van ongenoteerde skuldinstrumente. Daar is twee hoof insette met betrekking tot die waardasie van ongenoteerde skuldinstrumente, naamlik die risiko-vrye kromme en die opbrengskoersspreiding. Die ondersoek na hierdie twee komponente vorm die basis van hierdie tesis. Eerstens word ’n analise uitgevoer om benaderings vir die risiko-vrye kurwes af te lei in areas waar die data skaars is. Daarna word ondersoek gedoen om vas te stel of daar voldoende bewyse is van betekenisvolle veranderinge in die opbrengskoersspreiding van ongenoteerde skuldinstrumente. Ten einde hierdie veranderinge te bepaal, is ’n nuwe metode wat gelyktydige visualisering en klassifikasie van data moontlik maak, ontwikkel - genaamd tri-stipping-klassifisering met poli-sakke. Hierdie nuwe klassifikasietegniek het ook die vermoë om wanklassifikasiekoerse te beperk. In die eerste artikel word ’n benadering vir die uitgebreide nul-kromme bereken uit ander waarneembare insette. Dit word gevind deur middel van ’n simulasiebenadering deur twee nuwe tegnieke, naamlik gepermuteerde heelgetal meervoudige liniêre regressie en totale gestandaardiseerde model-telling, te gebruik. Dit is gevind dat ’n Nelson Siegel-passing, met ’n kombinasie van een jaar vooruitkoerse as benaderings vir die langtermyn nulpunt, en ’n mate van weglating van die aanvanklike datapunte, relatief goed in die leer en toetsing van datastelle presteer. Hierdie nuwe metode maak voorsiening vir die benadering van risiko-vrye krommes waar geen langtermynpunte beskikbaar is nie. Dit maak ook voorsiening vir die komponente van die opbrengskrommevorm deur ander beskikbare data in ag te neem. Die veranderinge in hierdie vormbepalingsparameters word in die finale artikel as komponente vir veranderinge in opbrengskoersspreidings gebruik. In die tweede artikel word ’n nuwe klassifikasietegniek ontwikkel wat in die finale artikel gebruik word. Klassifikasietegnieke laat nie maklik visuele interpretasie toe nie, en maak gewoonlik ook nie die beperking van die vals negatiewe en positiewe foutkoerse moontlik nie. Hierdie tekortkominge is belangrik vir sommige navorsings- en praktiese toepassingsareas. In hierdie artikel word klassifikasietegnieke gekombineer met bi-stippings, waardeur die data gelyktydig visueel voorgestel en geklassifiseer word, wat die sogenaamde tri-stipping tot gevolg het. Deur poli-sakke in te bring, word die vermoë om foute in die wanklassifikasie te beperk geïnkorporeer. ’n Simulasie-studie sowel as ’n toepassing word word geïllustreer. Dit toon aan dat die metode soortgelyke resultate lewer in vergelyking met die bestaande metodes, maar met ekstra visualiseringsvoordele. Die artikel fokus slegs op die ontwikkeling van ’n statistiese tegniek wat op enige veld toegepas kan word. Die toepassing wat byvoorbeeld verskaf is, was op ’n mediese datastel. In die finale artikel word die tegniek op veranderinge in opbrengskoersspreidings toegepas. In die derde artikel word veranderinge in opbrengskoersspreidings ondersoek en word dit deur middel van verskillende ko-variate ontleed om te bepaal of betekenisvolle daling of stygings by ongenoteerde skuldinstrumente waargeneem word. Die metodologie bepaal nie die nuwe spreiding spesifiek nie, maar lewer ’n bewys of die aanvanklike geïmpliseerde spreiding dieselfde gelaat kan word, of dat ’n nuwe spreiding bepaal moet word. Hierdie opbrengskoersspreidingbewegings word op ’n visueel interpretatiewe wyse geklassifiseer met behulp van verskillende aandeel-, rentekoers-, finansiële verhouding- en ekonomiese tipe ko-variate. Dit gee ook ’n beter begrip van hoe verskillende faktore die veranderinge in opbrengskoerse beïnvloed. Ten slotte, aanvullend tot elke artikel, is ’n webtoepassing gebou wat die leser in staat stel om met al die data en eienskappe van die metodologieë wat bespreek is, te eksperimenteer. Die volgende skakels kan gebruik word om toegang tot hierdie drie toepassings te verkry: - Artikel 1: https://carelvdmerwe.shinyapps.io/ProxyCurve/ - Artikel 2: https://carelvdmerwe.shinyapps.io/TriplotSimulation/ - Artikel 3: https://carelvdmerwe.shinyapps.io/SpreadsTriplot/Doctora

A Geneaology of Correspondence Analysis: Part 2 - The Variants

In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analysethe association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development ofcorrespondence analysis across all areas of research