Optimal Asset allocation for South African pension funds under the revised Regualtion 28

155 Pages·2012·7.48 MB·English

Optimal Asset allocation for South
African pension funds under the revised
Regualtion 28
by
Frederik Johannes Koegelenberg
Supervisor: Mr. J.D. van Heerden
Assignment presented at Stellenbosch University in partial fulfilment
of the requirements for the degree of Master of Commerce.
Department of Statistics and Actuarial Science,
Stellenbosch University.
January 2012
Stellenbosch University http://scholar.sun.ac.za
Aan die enigste God, Jesus Christus.
Dankie Hemelse Vader vir die lesse wat ek by U kon leer en dankie dat ek kan weet dat U
altyd daar is vir my, vir my sorg en my beskerm. Jesus, U is die koning van my lewe en
ek is ten volle afhanklik aan U.
Aan my Ouers.
Dankie vir al die ondersteuning en opofferings. Dankie dat julle my geleer het van Jesus
Christus en Sy ongelooflike liefde vir my, want sonder Hom sou ek nie kon bereik het wat
ek bereik het nie.
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Abstract
On 1 July 2011 the revised version of Regulation 28, which governs the South African
pension fund industry with regard to investments, took effect. The new version allows for
pension funds to invest up to 25 percent compared to 20 percent, in the previous version,
of its total investment in foreign assets. The aim of this study is to determine whether
it would be optimal for a South African pension fund to invest the full 25 percent of its
portfolio in foreign assets.
Sevendifferentoptimizationmodelsareevaluatedinthisstudytodeterminetheoptimal
asset mix. The optimization models were selected through an extensive literature study
in order to address key optimization issues, e.g. which risk measure to use, whether
parametricornonparametricoptimizationshouldbeusedandiftheMeanVariancemodel
foroptimizationdefinedbyMarkowitz,whichhasbeenthebenchmarkwithregardtoasset
allocation, is the best model to determine the long term asset allocation strategies.
The results obtained from the different models were used to recommend the optimal
longtermassetallocationforaSouthAfricanpensionfundandalsocomparedtodetermine
which optimization model proved to be the most efficient.
The study found that when using only the past ten years of data to construct the
portfolios, it would have been optimal to invest in only South African asset classes with
statisticaldifferenceswithregardtoreturnsinsomecases. Usingthepast20-yearsofdata
to construct the optimal portfolios provided mixed results, while the 30-year period were
more in favour of an international portfolio with the full 25% invested in foreign asset
classes.
A comparison of the different models provided a clear winner with regard to a proba-
bilityofoutperformance. TheHistoricalResampledMeanVarianceoptimizationprovided
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the highest probability of out performing the benchmark. From the study it also became
evident that a 20-year data period is the optimal period when considering the historical
data that should be used to construct the optimal portfolio.
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Uittreksel
Op 1 Julie 2011 het die hersiene Regulasie 28, wat die investering van Suid-Afrikaanse
pensioenfondse reguleer, in werking getree. Hierdie hersiene weergawe stel pensioenfondse
in staat om 25% van hulle fondse in buitelandse bateklasse te belê in plaas van 20%, soos
in die vorige weergawe. Hierdie studie stel vas of dit werklik voordelig sal wees vir ‘n SA
pensioenfonds om die volle 25% in buitelandse bateklasse te belê.
Seweverskillendeoptimeringsmodelleisgebruikomdieoptimaleportefeuljeteprobeer
skep. Die optimeringsmodelle is gekies na ’n uitgebreide literatuurstudie sodat van die
sleutelkwessies met betrekking tot optimering aangespreek kon word. Die kwessies waarna
verwys word sluit in, watter risikomaat behoort gebruik te word in die optimeringsproses,
of‘nparametrieseofnie-parametriesemodelgebruikmoetwordenofdie“Mean-Variance”
model wat deur Markowitz in 1952 gedefinieer is en al vir baie jare as maatstaf vir porte-
feulje optimering dien, nog steeds die beste model is om te gebruik.
Die uiteindelike resultate, verkry van die verskillende optimeringsmodelle, is gevolglik
gebruik om die optimale langtermyn bate-allokasie vir ‘n Suid-Afrikaanse pensioenfonds
op te stel. Die verskillende optimeringsmodelle is ook met mekaar vergelyk om te bepaal
of daar ‘n model is wat beter is as die res.
Vanuitdieresultatewasditduidelikdat’nportfeuljewatslegsuitSuid-Afrikaansebates
bestaanbetersalpresteerasslegsdielaaste10-jaarsedatagebruikwordomdieportefeulje
opstel. Hierdieresultateisookinmeestevandiegevallebevestigdeurmiddelvanhipotese
toetse. Deur gebruik te maak van die afgelope 20-jaar se data om die portefeuljes op te
stel, het gemengde resultate gelewer, terwyl die afgelope 30-jaar se data in meeste van die
gevalle ’n internasionaal gediversifiseerde portefeulje as die beter portefeulje uitgewys het.
In ’n vergelyking van die verskillende optimeringsmodelle is die “Historical Resampled
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MeanVariance” modelduidelikasdiebetermodeluitgewys. Hierdiemodelhetdiehoogste
waarskynlikheidbehaalomdievasgsteldemaatstafportefeuljesuittepresteer. Dieresultate
hetookgeduiopdie20-jaarperiodeasdiebestedataperiodeomtegebruikasdieoptimale
portfeulje opgestel word.
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Erkennings
Ek wil graag my opregte dank uitspreek teenoor die volgende persone:
• My studieleier, Mnr. J.D. van Heerden, dankie vir al die hulp en raad met die skryf
van die tesis en ook net vir die positiewe houding en entoesiasme teenoor die werk.
• Myinternepromotor, Prof. W.J.Conradie, virdieleidingeninsetteoordieafgelope
6 jaar van my studies.
• Chris, dankie vir die 6 jaar van vriendskap, luister, harde waarhede en ongelooflike
wyse woorde.
• Marié, Alta, Ouma Lettie, Ouma Mary en Oupa Kobus dankie vir alles wat julle vir
my beteken het die afgelope 6 jaar.
• Brigott en Morné, dankie vir al die ondersteuning en net die manier waarop julle
goed in perspektief kon stel.
• Retha en Lize-Mari, dankie vir die ongelooflike rolle wat julle in my lewe vertolk het
die afgelope jaar. Julle is awesome.
• Alma, dankie vir al die motivering, laataand koffies en daai ongelooflike glimlag.
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Ecclesiastes 11:2 (NIV)
“Invest in seven ventures, yes, in eight; You do not know what disaster may come upon
the land.”
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Contents
1 Introduction 19
1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Theoretical Overview: Asset Allocation and Optimization Models 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Why Asset Allocation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Asset Allocation Optimization Models . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Traditional Markowitz Mean-Variance (MV) model . . . . . . . . . . 22
2.3.2 Equally Weighted Portfolio (EW) . . . . . . . . . . . . . . . . . . . . 25
2.3.3 Equally-Weighted Risk Contribution Portfolios (ERC) . . . . . . . . 27
2.3.3.1 ERC Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.3.2 Theoretical Properties of ERC portfolios . . . . . . . . . . 29
2.3.3.3 Numerical solutions . . . . . . . . . . . . . . . . . . . . . . 31
2.3.4 Re-sampled Mean-Variance Optimization (RMV) . . . . . . . . . . . 32
2.3.4.1 RMV Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.5 Optimization using Value at Risk as risk measure . . . . . . . . . . . 35
2.3.5.1 OptimizationbyfittinganExtremeValueDistribution(EVD
- VaR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.5.2 Optimization Using C-VaR while incorporating Skewness
and Fat Tails . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.6 Optimization using a nonparametric optimization method . . . . . . 42
2.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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