Statistical modelling of private equity investments in selected emerging markets in Africa : evidence from GARCH and VAR models

Abstract

The study examines statistical properties and volatility dynamics of an emerging investment asset class, Listed Private Equity (LPE) investments, in selected markets in Africa. There has been widespread acknowledgement that traditional valuation techniques have failed to explain cross-sectional stock returns in emerging and developing markets. From the content review put forward in this study, it is evident that country-specific risk is a priced factor in investments in Africa. The study hypothesised the notion and predicated that asset returns as a product of economic rationality is followed by its statistical properties in the return distribution and volatility dynamics. The study used monthly data for LPE’s and selected country-specific data to examine the statistical properties, volatility dynamics and their relationship to country risk factors for countries that were found active in this asset class – South Africa, Ghana, Egypt and Botswana for the period 2010-2020. The study utilised the GARCH (1,1), EGARCH, TGARCH, GARCH-In-Mean, FIGARCH, FIEGARCH, DCC MGARCH, and VAR models to fit the data. These findings provide information that is used for portfolio compilation, asset pricing, and a better understanding of the structural dynamics of LPE returns, thereby laying the groundwork for the development of new valuation tools for this asset class. Three main findings were: firstly, LPEs for countries under study exhibited stylised effects in the form of volatility clustering, asymmetric effects, and leptokurtic distributions, but there is no evidence of leverage effects or structural breaks. The study found evidence that LPE’s are positively skewed with excess kurtosis. The returns for South African LPE’s are closer to normal distribution, whilst other countries exhibited non-normal distributions, typical of financial data. Egypt displayed traces of volatility associated with jump diffusions and Ghana volatility series indicated that the investment carries a risk premium commensurate with the inherent risk. The data for Botswana was stationary and was found unsuitable for further tests using GARCH modelling. Secondly, there is no evidence of data asymmetries present in the long-term volatility dynamics of the data under study. Despite the diverse economic systems in which these investments operate, their responses to positive or negative shocks are the same. This indicates that private equity investments in these African markets have homogenous dispositions in the long term; therefore, though these investments are defensive assets, geographical selection cannot be used to diversify returns. Thirdly, the study provided evidence that country-specific factors have a weak influence on the LPE’s of the data under study, refuting the hypothesis that country risk elements are a priced factor in these markets. The study makes several contributions: it is the first to examine the statistical properties and volatility dynamics of LPEs in selected African markets. Second, the thesis extends previous findings on statistical modelling by examining an unexplored market in the body of knowledge, the LPE’s in African markets, which has different dispositions to traditional asset classes. Lastly, the study adds to the LPE literature by providing valuable insights regarding LPEs in an African context, as an emerging asset class and a financing tool for economic development.

Ucwaningo luhlole izakhiwo zezibalo kanye nokuguquguquka okuguquguqukayo kwesigaba sokutshalwa kwezimali sempahla esafufusa, okungukuthi, uhlu lokulinganayo kwangasese (ULK) okwaziwa nge-(LPE) ezimakethe ezikhethiwe e Afrika. Kube nokuvunywa okusabalele ukuthi amasu okulinganisa endabuko ahlulekile ukuchaza imbuyiselo yesitoko ehlukene ezimakethe ezisafufusa nezisathuthuka. Kusukela ekubuyekezweni kokuqukethwe okubekwa phambili kulolu cwaningo, kusobala ukuthi ubungozi obuqondene nezwe elithile buyinto enenani lokutshalwa kwezimali e-Afrika. Ocwaningweni kwacatshangelwa futhi kwabikezelwa ukuthi imbuyiselo yempahla njengemikhiqizo yokuhluzeka kwezomnotho ilandelwa izici zayo zezibalo ekusatshalalisweni kwembuyiselo, kanye nokuguquguquka kokushintshashintsha. Idatha yanyanga zonke yokutshalwa kwezimali kwe-ULK kanye nedatha ekhethiwe eqondene nezwe elithile yasetshenziswa ukuze kuhlolwe izakhiwo zezibalo kanye nokuguquguquka kanye nobudlelwano bazo nezinto eziyingozi zezwe emazweni atholakale esebenza kulesi sigaba sempahla, okungukuthi, iNingizimu Afrika, iGhana, iGibithe kanye neBotswana isikhathi sonyka wezi-2010–2020. Amamodeli e-GARCH (1,1), EGARCH, TGARCH, GARCH-In Mean, FIGARCH, FIEGARCH, DCC MGARCH kanye ne-VAR asetshenziswe ukuze kulingane idatha. Okutholwe ocwaningweni kuhlinzeka ngolwazi olungasetshenziselwa ukuhlanganiswa kwephothifoliyo kanye nentengo yempahla. Okutholakele kungase futhi kube usizo ekutholeni ukuqonda okungcono kokuguquguquka kwesakhiwo sembuyiselo ye-LPE, ngaleyo ndlela kubekwe isisekelo sokuthuthukiswa kwamathuluzi amasha okulinganisa alesi sigaba sempahla. Okuthathu okutholakele okuyinhloko kube kanje: Okokuqala, ukutshalwa kwezimali kwe-ULK emazweni angaphansi kocwaningo kubonise imiphumela eyenziwe ngesitayela nangendlela yokuhlanganisa okuguquguqukayo, imiphumela ye asimetrikhi nokusatshalaliswa kwelipthokhithi, kodwa abukho ubufakazi bemithelela ezuzisayo noma ukuhlukana kwesakhiwo. Lolu cwaningo luveze ubufakazi bokuthi ukutshalwa kwezimali kwe-ULK bekugudluzwe kahle nekhithosisi eyeqile. Imbuyiselo yokutshalwa kwezimali kwe-ULK yaseNingizimu Afrika ibisondele ekusabalaliseni okuvamile kuyilapho amanye amazwe ebonise ukusatshalaliswa okungajwayelekile, okuyisimo sedatha yezezimali. IGibithe ibonise iminonjana yokuntengantenga okuhlobene nokusabalala okweqayo, futhi uchungechunge lwe-Ghana oluguquguqukayo lubonise ukuthi ukutshalwa kwezimali kwe-ULK kunengozi engqala ehambisana nobungozi obukhona. Idatha yaseBotswana ibimile futhi itholwe ingakulungele ukuhlolwa okwengeziwe kusetshenziswa imodeli ye-GARCH. Okwesibili, abukho ubufakazi be-asimetrikhi yedatha kukuntengantenga - ashukumisayo kwesikhathi eside yedatha engaphansi kocwaningo. Ngaphandle kwezinhlelo zezomnotho ezehlukene lapho lezi zimali zitshalwa khona, izimpendulo zazo ekushaqisweni okuhle noma okungekuhle zitholwe zifana. Lokhu kukhombisa ukuthi ukutshalwa kwezimali kwamasheya azimele kulezi zimakethe zase-Afrika kunesimo esifanayo esikhathini eside. Ngakho-ke, nakuba lokhu kutshalwa kwezimali kuyimpahla evikelayo, ukukhetha kwendawo akukwazi ukusetshenziselwa ukuhlukanisa imbuyiselo. Okwesithathu, ucwaningo lunikeze ubufakazi bokuthi izici eziqondene nezwe elithile zinethonya elibuthakathaka ekutshalweni kwezimali kwe ULK ngokuphathelene nedatha esacwaningwayo, okuphikisana nenkoleloze yokuthi izici zezwe ezisengozini ziyisici senani kulezi zimakethe. Ucwaningo lunikeza iminikelo eminingana. Okokuqala, ucwaningo kwaba ngelokuqala ukuhlola izakhiwo zezibalo kanye nokuguquguquka kokushintshashintsha kokutshalwa kwezimali kwe-ULK ezimakethe ezikhethiwe zase-Afrika. Okwesibili, ucwaningo lwengeza kulokho okutholwe ocwaningweni lwangaphambilini lemodeli yokubala ngoba lubandakanya ukuhlolwa kwesigaba sempahla esingahloliwe emkhakheni okhona wolwazi, okungukuthi, i-ULK ezimakethe zase-Afrika. Indlela yalesi sigaba sempahla ihlukile kulezo zezigaba zempahla evamile. Okokugcina, ucwaningo lwengeza emibhalweni ye-ULK ngokuhlinzeka ngemininingwane ebalulekile mayelana ne-ULK esimweni sase-Afrika njengesigaba sempahla esafufusa kanye nethuluzi lokuxhasa ngezimali lokuthuthukiswa komnotho.

Phuputso e hlahlobile dintho tse ikgethang tse amanang le dintlha tse hlaloswang ka dipalo le boemo ba diphetoho tse sa tsitsang le tse sa lebellwang tsa tlwaelo ya mmaraka ya ho phahama le ho theoha ka potlako e kgolo, ya matsete a moruo o holang, a tshwanang ka dintho tse itseng le ho sebetsa ka ho tshwana mmarakeng, a bitswang mofuta wa ho tsetela kgwebong ya poraevete e sa hwebeng mmarakeng wa diabo (LPE) mebarakeng e kgethilweng Aforika. Ho bile le kananelo ya batho ba bangata ya hore mekgwa ya boholoholo ya ho fumana boleng ba setoko e hlolehile ho hlalosa dipoello tse fapaneng tsa ditoko tse fapaneng ka nako e itseng mebarakeng ya moruo wa dinaha tse holang. Ho tswa tekolong botjha ya dikahare tseo ho buuwang ka tsona phuputsong ena, ho a bonahala hore kotsi ya naha e itseng e tswalwa ke ditheko tsa matsete Aforika. Phuputsong, ho bile le mohopolo le kakanyo ya hore dipoello tsa diasete e le dihlahiswa tse molemo haholo mothong di latelwa ke dintho tsa tsona tse ikgethang tse amanang le dintlha tse hlaloswang ka dipalo mmoho le boemo ba diphetoho tse sa tsitsang le tse sa lebellwang tsa tlwaelo ya mmaraka ya ho phahama le ho theoha ka potlako e kgolo. Datha ya kgwedi le kgwedi ya matsete a LPE le datha e kgethetsweng naha e itseng di sebedisitswe ho hlahloba dintho tse ikgethang tse amanang le dintlha tse hlaloswang ka dipalo le boemo ba diphetoho tse sa tsitsang le tse sa lebellwang tsa tlwaelo ya mmaraka ya ho phahama le ho theoha ka potlako e kgolo le kamano ya tsona le mabaka a amanang le kotsi ya ho tsetela naheng e itseng le boholo ba ho hloka botsitso bo ka tswalang tahlehelo ya ditjhelete dinaheng tse fumanweng di le sehlopheng sena sa matsete a tshwanang ka dintho tse itseng le ho sebetsa ka ho tshwana mmarakeng, tseo e leng Aforika Borwa, Ghana, Egepeta le Botswana dilemong tsa 2010–2020. Dimotlolo tsa GARCH (1,1), EGARCH, TGARCH, GARCH-In-Mean, FIGARCH, FIEGARCH, DCC MGARCH le VAR di sebedisitswe ho tshwanela datha. Lesedi le fumanweng la phuputsong le fana ka lesedi le ka sebedisetswang ho etsa potefolio le ho bala sekgahla sa poello e lebelletsweng aseteng kapa letseteng. Lesedi le fumanweng le ka boela la ba bohlokwa hore ho be le kutlwisiso e kgolo ya diphetoho tsa tlhophiso ya dipoello tsa LPE, tse fanang ka tlhophiso ya ntshetsopele ya disebediswa tsa tlhahlobo e ntjha ya sehlopha sena sa diasete. Lesedi le fumanweng la dintlha tse tharo tse ka sehloohong e ne e le le latelang: La pele, Matsete a LPE a dinaha tse fuputswang a bontshitse dikameho tse entsweng hore di shebahale ka mokgwa o itseng oo e seng wa tlhaho wa boholo ba tlhokeho ya botsitso bo amanang le boholo ba phetoho e etsahalang e fetohang le nako, boholo ba tlhokeho ya botsitso bo eketseha haholo ha ditheko di theoha ho feta ha ditheko di phahama ka palo e lekanang le kgonahalo e kgolo ya datha e fapaneng le tse ding, empa ha ho a ba le ntho e bontshang kamano e mpe pakeng tsa poello le tlhokeho ya botsitso bo amanang le boholo ba phetoho e etsahalang kapa phetoho e sa lebellwang tlhophisong ya datha eo ho sebetswang ka yona. Phuputso e bontshitse hore matsete a LPE a fetotse tsela eo a tsamayang ka yona hantle le ho ba le ntlha ya datha e itseng e fapanang haholo le dintlha tse ding. Dipoello tsa matsete a LPE a Aforika Borwa di ne di batla di le kabo e tlwaelehileng ha tsa dinaha tse ding di bontshitse dikabo tse sa tlwaelehang, e leng ntho e tlwaelehileng ka datha ya ditjhelete. Egepeta e bontshitse mehlala ya ditheko tse hlokang botsitso tse namang ka mahlakore a mangata, mme tatellano ya ditheko tse hlokang botsitso tsa Ghana e bontshitse hore matsete a LPE a na le sekgahla se phahameng sa poello eo o ka e lebellang diaseteng tse nang le kotsi e kgolo se lekanang le boemo ba kotsi e sa rarollwang. Datha ya Botswana e ne e tsitsitse le ho fumanwa e sa lokela ho ho etswa diteko tse ding tse sebedisang motlolo wa GARCH. Ntlheng ya bobedi, ho ne ho se na bopaki ba ho se lekalekane ha datha boemong ba nako e telele ba diphetoho tse sa tsitsang le tse sa lebellwang ba datha eo ho fuputswang ka yona. Ho sa kgathalatsehe hore matsete ana a na le tshusumetso efe ditseleng tse fapaneng tseo ho hlahiswang le ho tsamaisa dintho ka yona, dikarabelo tsa oona diketsahalong dife kapa dife tse sa lebellwang tse bang le kameho ya tshohanyetso e ntle kapa e mpe, di fumanwe id tshwana. Hona ho bontsha hore matsete a kentsweng dikhamphaning tse sa hwebeng mebarakeng ena ya Aforika a diabo a ba le ditlhophiso tse tshwanang ka mora nako e telele. Kahoo, le ha matsete ana e le diasete tse fanang ka moputso o tsitsitseng ka nako e telele, tlhahlobo ya diaterese tsa batsetedi e ke ke ya sebedisetswa ho thibela kotsi ka ho aba matsete ditumellanong tse fapaneng tsa ditjhelete. Ntlheng ya boraro, phuputso e fane ka bopaki ba hore dintho tse amang tlhahiso ya naha e itseng di na le tshusumetso e fokolang matseteng a LPE a mabapi le datha e fuputswang, ho hanana le mohopolo wa hore dintho tse nang le kotsi ya ho tsetela naheng e itseng ke ditjeo tsa tlhahiso ya ntho e nngwe mebarakeng ena. Phuputso e na le dintho tse ngata tseo e di etsang. Ya pele, phuputso e bile ya pele ya ho hlahloba dintho tse ikgethang tse amanang le dintlha tse hlaloswang ka dipalo boemong ba diphetoho tse sa tsitsang le tse sa lebellwang matseteng a LPE mebarakeng e kgethilweng ya Aforika. Ya bobedi, phuputso e tlatsetsa lesedi le fumanweng patlisisong ya nako e fetileng ka ho ithuta le ho fihlela diqeto tse utlwahalang ka datha, ka hore e hloka tlhahlobo ya dintho tse eso fuputswe, tse sebetsang ka ho tshwana mmarakeng, leseding, mehopolong le makaleng a thuto e itseng, ke hore, LPE mebarakeng ya Aforika. Ditlhophiso tsa sehlopha sena sa matsete a sebetsang ka ho tshwana mmarakeng se fapana le dihlopha tsa boholoholo tsa matsete a sebetsang ka ho tshwana mmarakeng. Ya ho qetela, phuputso e tlatsetsa lesedi dingolweng tsa LPE ka ho fana ka kutlwisiso ya bohlokwa e mabapi le LPE boemong ba Aforika e le sehlopha sa matsete a qalang ho ba teng a sebetsang ka ho tshwana mmarakeng le dintho tse thusang ho etsa tjhelete ya ho ntshetsa moruo pele.