Thesis (MBA)--Stellenbosch University, 2006. / ENGLISH ABSTRACT: The Omega function is a relatively newly developed performance measure, falling within the class of downside risk measures. This measure does not make any assumptions regarding the return distributions evaluated, but incorporates the actual return distribution in its calculation. The sensitivity of this measure to simulated changes within the class of stable distributions was tested, within the range of parameters that was evident in the South African investment environment. The Omega and Sharpe ratios that were calculated for these distributions were ranked and compared. Even though the rankings were similar, discrepancies did occur. On investigation it was found that these discrepancies were caused by the inability of the Sharpe measure to differentiate between increased volatility caused by higher probability weighted gains (or positive skewness) and losses, as the Sharpe ratio penalises funds for volatility. The simulated tests were extended to various distributions, which have different risk profiles and distribution shapes, and ranked. A higher incidence of ranking differences occurred due to the inability of the Sharpe ratio to differentiate between gains and losses, correctly account for the risk of positively skewed distributions and lastly due to negative Sharpe ratios, caused by the average realised returns being exceeded by the threshold (target) rate, resulting in incorrect rankings. Comparison of rankings based on the Sharpe and Omega measures was performed on the class of general equity unit trusts over a five-year period, which resulted in statistically similar rankings. In extending the evaluation over shorter periods, the ran kings were still statistically similar, even though some differences were noteworthy. As the returns became more variable, the Omega measure captured this variation and risk whilst the Sharpe ratio was unable to, as its formulation is limited to two statistics, thus losing all this additional information. Normally performance evaluation is not initiated with a detailed analysis of the return distributions in order to determine which performance measure is more appropriate. The Omega measure incorporates the distribution into the calculation, which is not the case with the Sharpe measure. Therefore, even if the distributions are normal, the Omega measure gives exacty the same result as the Sharpe measure. However, where return distributions diverge from normality, we can be certain that the Omega measure will correctly incorporate the divergence, whilst it has been shown that in certain instances the Sharpe measure does not. The Omega measure adds another dimension to risk-adjusted performance evaluation and should be incorporated in the evaluation process. / AFRIKAANSE OPSOMMING: Die Omega-funksie, wat as 'n afwaartse risikomaatstaf geklassifiseer word, is 'n relatiewe nuut-ontwikkelde prestasiemaatstaf. Hierdie maatstaf maak nie enige aannames ten opsigte van die opbrengsverdelings wat ge-evalueer word nie, maar inkorporeer die werklike opbrengsverdeling in die berekening. Die sensitiwiteit van hierdie maatstaf tot gesimuleerde veranderinge in die klas van stabiele verdelings is getoets, binne die parameters van toepassing in die Suid Afrikaanse beleggingsomgewing. Die Omega- en Sharpe-maatstawe is bereken, georden en vergelyk. Alhoewel die rangordes meestal dieselfde was, het verskille in sommige gevalle voorgekom. Hierdie verskille is veroorsaak deur die onvermoe van die Sharpe-maatstaf om te onderskei tussen verhoogde volatiliteit veroorsaak deur 'n hoer waarskynlikheidsgeweegde wins, of positiewe skeefheid en verliese. Die Sharpe-maatstaf penaliseer alle volatiliteit. Die gesimuleerde toetse is uitgebrei na alternatiewe verdelings wat verskillende risikoprofiele het en is weereens georden. Weereens was die rangordes meestal dieselfde. Die verskille wat plaasgevind het, is veroorsaak deur die onvermoe van die Sharpe-maatstaf om tussen winste en verliese te onderskei, positiewe skeefheid korrek te verdiskonteer en laastens om negatiewe Sharpe-verhoudings in die korrekte rangorde te plaas. 'n Vergelyking van die rangordes van die Sharpe- en Omega-maatstawe is gedoen op die algemene effektetrusts oor 'n tydperk van vyf jaar. Die rangordes in geheel was statisties dieselfde. Hierdie toetse is vervolgens uitgebrei om korter tydperke in te sluit, wat weereens in geheel statisties dieselfde korrelasie getoon het, maar 'n paar individuele portefeuljes se rangordes het heelwat verskil. Soos die opbrengste gevarieer het, kon die Omega-maatstaf hierdie variasies en risiko verdiskonteer terwyl die Sharpe-maatstaf nie in staat was om hierdie risiko te verdiskonteer nie, aangesien sy formulering beperk is tot twee statistieke wat 'n verlies van inligting tot gevolg het. Normaalweg word prestasie-beoordeling nie begin met 'n gedetailleerde analise van die opbrengsverdelings om te bepaal watter prestasie-maatstaf meer toepaslik is nie. Die Omega-maatstaf inkorporeer die verdeling in die berekening, wat nie die geval is met die Sharpe-maatstaf nie. AI is die opbrengsverdelings normaal, gee die Omega-maatstaf dieselfde resultate as die Sharpe-maatstaf. Waar die verdelings egter afwyk van normaal, weet ons dat die Omega-maatstaf die afwykings korrek verdiskonteer, terwyl dit bewys is dat die Sharpe-maatstaf in sekere omstandighede nie die afwykings korrek verdiskonteer nie. Die Omega-maatstaf voeg 'n verdere dimensie by risiko-aangepaste prestasiemeting en behoort dus ingesluit te word in die evauleringsproses.

Made available in DSpace on 2010-04-20T20:51:08Z (GMT). No. of bitstreams: 3 154942.pdf.jpg: 18952 bytes, checksum: 23e574558dce7d0f2a386af838a81bbe (MD5) 154942.pdf: 506907 bytes, checksum: 04eae2214c9bdd57e0cbeb2bb4459728 (MD5) 154942.pdf.txt: 81444 bytes, checksum: 047630fc773c90c68757120835adddab (MD5) Previous issue date: 2006-02-15T00:00:00Z / Mutual funds performance evaluation is, traditionally, made using Sharpe Ratio that considers only the first and the second moments of the return distribution (mean and variance), but it requires assumptions on the normality of the returns distribution and on the investor’s utility function as quadratic. However, it is well known that a quadratic utility function is inconsistent with investor behavior and some funds, like hedge funds, have returns distributions far from a normal distribution Keating and Shadwick (2002a, 2002b) proposed a new measure called Omega that incorporates all the moments of the distribution, and has the advantage of requiring no assumptions on the returns distribution or on the utility function of a risk averse investor. The purpose of this work is to verify if this measure has a greater forecast power than other performance measures, like Sharpe and Sortino Ratios. The empiric study indicated that Omega measure makes a ranking, most of the time, different from the other measures. Despite the portfolios constructed with Omega have had an average return greater than the average return of the portfolios constructed using the other measures, in almost all the tests, this difference of averages of returns was significant only in some cases. In spite of this, there is a light indication that Omega measure is the most appropriate for the use of investors when is made the performance evaluation of mutual funds. / A avaliação de desempenho de fundos de investimentos é, tradicionalmente, realizada utilizando-se o Índice de Sharpe, que leva em consideração apenas os dois primeiros momentos da distribuição de retornos (média e variância), assumindo as premissas de normalidade da distribuição de retornos e função quadrática de utilidade do investidor. Entretanto, é sabido que uma função de utilidade quadrática é inconsistente com o comportamento do investidor e que as distribuições de retornos de determinados fundos, como os hedge funds, estão longe de serem uma distribuição normal. Keating e Shadwick (2002a, 2002b) introduziram uma nova medida denominada Ômega que incorpora todos os momentos da distribuição, e tem a vantagem de não ser necessário fazer premissas sobre a distribuição dos retornos nem da função de utilidade de um investidor avesso ao risco. O objetivo deste trabalho é verificar se esta medida Ômega tem um poder de previsibilidade maior que outras medidas de avaliação de desempenho, como o Índice de Sharpe e o Índice de Sortino. O estudo empírico indicou que a medida Ômega gera um ranqueamento, na maioria das vezes, relativamente diferente das outras medidas testadas. Apesar das carteiras formadas com base na medida Ômega terem gerado um retorno médio maior que o retorno médio das carteiras formadas pelas outras medidas em praticamente todos os testes, esta diferença entre as médias dos retornos só foi significativa em alguns casos. Mesmo assim, há uma leve indicação de que a medida Ômega é a mais apropriada para utilização do investidor ao fazer a avaliação de desempenho dos fundos de investimentos.