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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/70664 |
| Date | 12 1900 |
| Creators | De Wet, Ronel |
| Contributors | Krige, N., Smit, E., Stellenbosch University. Faculty of Economic and Management Sciences. Graduate School of Business. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Rights | Stellenbosch University |
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