Thesis (MBA)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: Commercial banks, investment banks, insurance companies, non-financial firms, and
pension funds hold portfolios of assets that may include stocks, bonds, currencies,
and derivatives. Each institution needs to quantify the amount of risk its portfolio is
exposed to in the course of a day, week, month, or year. Extreme events in financial
markets, such as the stock market crash of October 1987, are central issues in finance
and particularly in risk management and financial regulation.
A method called value at risk (VaR) can be used to estimate market risk. Value at risk
is a powerful measure of risk that is gaining wide acceptance amongst institutions for
the management of market risk. Value at Risk is an estimate of the largest lost that
a portfolio is likely to suffer during all but truly exceptional periods. More precisely,
the VaR is the maximum loss that an institution can be confident it would lose a
certain fraction of the time over a particular period.
The power of the concept is its generality. VaR measures are applicable to entire
portfolios - encompassing many asset categories and multiple sources of risk. As with
its power, the challenge of calculating VaR also stems from its generality. In order to
measure risk in a portfolio using VaR, some means must be found for determining a
return distribution for the portfolio.
There exists a wide range of literature on different methods of implementing VaR.
But, when one attempts to apply the results, several questions remain open. For
example, given a VaR measure, how can the risk manager test that the particular
measure at hand is appropriately specified? And secondly, given two different VaR
measures, how can the risk manager pick the best measure?
Despite the popularity of VaR for measuring market risk, no consensus has yet been reach as to the best method to implement this risk measure. The absence of consensus
is in part derived from the realization that each method currently in use has some
significant drawbacks.
The aim of this project is threefold: to introduce the reader to the concept of VaR;
present the theoretical basis for the general approaches to VaR computations; and to
introduce and apply Extreme Value Theory to VaR calculations.
The general approaches to VaR computation falls into three categories, namely, Analytic
(Parametric) Approach, Historical Simulation Approach, and Monte Carlo Simulation
Approach. Each of these approaches has its strengths and weaknesses, which
will study more closely.
The extreme value approach to VaR calculation is a relatively new approach. Since
most observed returns are central ones, traditional VaR methods tend to ignore extreme
events and focus on risk measures that accommodate the whole empirical distribution
of central returns. The danger of this approach is that these models are prone
to fail just when they are needed most - in large market moves, when institutions can
suffer very large losses.
The extreme value approach is a tool that attempts to provide the user with the best
possible estimate of the tail area of the distribution. Even in the absence of useful
historical data, extreme value theory provides guidance on the kind of distribution
that should be selected so that extreme risks are handled conservatively. As an
illustration, the extreme value method will be applied to a foreign exchange futures
contract. The validity of EVT to VaR calculations will be tested by examining the
data of the Rand/Dollar One Year Futures Contracts. An extended worked example
will be provided wherein which attempts to highlight the considerable strengths of
the methods as well as the pitfalls and limitations. These results will be compared to
VaR measures calculated using a GARCH(l,l) model. / AFRIKAANSE OPSOMMING: Handelsbanke, aksepbanke, assuransiemaatskappye, nie-finansiële instellings en pensioenfondse
beskik oor portefeuljes van finansiële bates soos aandele, effekte, geldeenhede
en afgeleides. Elke instelling moet die omvang kan bepaal van die risiko waaraan
die portefeulje blootgestel is in die loop van 'n dag, week, maand of jaar. Uitsonderlike
gebeure op finansiële markte, soos die ineenstorting van die aandelemark in Oktober
1987, is van besondere belang vir finansies en veral vir risikobestuur en finansiële
regulering.
'n Metode wat genoem word Waarde op Risiko (WoR), kan gebruik word om markverliese
te meet. WoR is 'n kragtige maatstaf vir risiko en word deur vele instellings gebruik
vir die bestuur van mark-risiko. Waarde op Risiko is 'n raming van die grootste
verlies wat 'n portefeulje moontlik kan ly gedurende enige tydperk, met uitsluiting
van werklik uitsonderlike tydperke. Van nader beskou, is WoR die maksimum verlies
wat 'n instelling kan verwag om gedurende 'n sekere tydperk binne 'n bepaalde
periode te ly.
Die waarde van die konsep lê in die algemene aard daarvan. WoR metings is van
toepassing op portefeuljes in dié geheel en dit omvat baie kategorieë bates en veelvuldige
bronne van risiko. Soos met die waarde van die konsep, hou die uitdaging om WoR
te bereken ook verband met die algemene aard van die konsep. Ten einde die risiko
te bepaal in 'n portefeulje waar WoR gebruik word, moet metodes gevind word waarvolgens
'n opbrengsverdeling vir die portefeulje vasgestel kan word.
Daar bestaan 'n groot verskeidenheid literatuur oor die verskillende metodes om WoR
te implementeer. Wanneer dit egter kom by die toepassing van die resultate, bly
verskeie vrae onbeantwoord. Byvoorbeeld, hoe kan die risikobestuurder aan die hand
van 'n gegewe WoR-maatstaf toets of die spesifieke maatstaf reg gespesifiseer is? Tweedens, hoe kan die risikobestuurder die beste maatstaf kies in die geval van twee
verskillende WoR-maatstawwe?
Ondanks die feit dat WoR algemeen gebruik word vir die meting van markrisiko, is
daar nog nie konsensus bereik oor die beste metode om hierdie benadering tot risikometing
te implementeer nie. Die feit dat daar nie konsensus bestaan nie, kan deels
daaraan toegeskryf word dat elkeen van die metodes wat tans gebruik word, ernstige
leemtes het.
Die doel van hierdie projek is om die konsep WoR bekend te stel, om die teoretiese
grondslag te lê vir die algemene benadering tot die berekening van WoR en om die
Ekstreme Waarde-teorie bekend te stel en toe te pas op WoR-berekenings.
Die algemene benadering tot die berekening van WoR word in drie kategorieë verdeel
naamlik die Analitiese (Parametriese) benadering, die Historiese simulasiebenadering
en die Monte Carlo-simulasiebenadering. Elkeen van die benaderings het sterk- en
swakpunte wat van nader ondersoek sal word.
Die Ekstreme Waarde-benadering tot WoR is 'n relatief nuwe benadering. Aangesien
die meeste opbrengste middelwaarde-gesentreer is, is tradisionele WoR-metodes
geneig om uitsonderlike gebeure buite rekening te laat en te fokus op risiko-maatstawwe
wat die hele empiriese verdeling van middelwaarde-gesentreerde opbrengste akkommodeer.
Die gevaar bestaan dan dat hierdie modelle geneig is om te faal juis wanneer
dit die meeste benodig word, byvoorbeeld in die geval van groot markverskuiwings
waartydens organisasies baie groot verliese kan ly.
Daar word beoog om met behulp van die Ekstreme Waarde-benadering aan die gebruiker
die beste moontlike skatting van die stert-area van die verdeling te gee. Selfs
in die afwesigheid van bruikbare historiese data verskaf die Ekstreme Waarde-teorie
riglyne ten opsigte van die aard van die verdeling wat gekies moet word, sodat uiterste
risiko's versigtig hanteer kan word. Ten einde hierdie metode te illustreer, word
dit in hierdie studie toegepas op 'n termynkontrak ten opsigte van buitelandse wisselkoerse.
Die geldigheid van die Ekstreme Waarde-teorie ten opsigte van WoR berekenings
word getoets deur die data van die Rand/Dollar Eenjaartermynkontrak
te bestudeer. 'n Volledig uitgewerkte voorbeeld word verskaf waarin die slaggate en
beperkings asook die talle sterkpunte van die model uitgewys word. Hierdie resultate
sal vergelyk word met 'n WoR-meting wat bereken is met die GARCH (1,1) model.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/52189 |
| Date | 12 1900 |
| Creators | Ganief, Moegamad Shahiem |
| Contributors | Biekpe, N., Stellenbosch University. Faculty of Economic & 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 |
| Format | 102 p. : ill. |
| Rights | Stellenbosch University |
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