Dynamic Linkage amongst Oil, Gold, Exchange Rates and Stock Markets in Africa: Evidence from Volatility of Major African Economies

: In this work, we study whether the price fluctuations amongst exchange rates, stock and commodities markets are dynamically influentially linked and dependent within African economies, as there is a dearth of literature on this subject. The study models monthly price changes amongst these markets between the years 2000 and 2019 using a copula based DCC GARCH framework for a sample of twenty highest ranked African economies by nominal GDP. The results show evidence of time varying co-movement amongst these markets that tend to increase during times of turbulence in sampled markets. Dynamic relations are found to be quantitatively and relatively substantial for economies of Egypt, South Africa, Tanzania, Libya and Zambia. The results from this study would improve the risk management decisions by investment managers, individual investors and investment regulators.


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Commodity trading is a strategic and globally prominent economic activity that is used 14 on a micro and macroeconomic level for reasons such as generating income, industrial input, 15 commercial demand and managing various risks. Africa is a commodity rich continent in which 16 the extractive industry plays a crucial role and this is because a number of its constituents have relate an economy's currency to its stock market. The "flow-oriented" model suggests that, 1 changes in exchange rates affect an economy's stock market through changes emanating from 2 relative price and demand for domestic goods arising from international trade and competitive- 3 ness. International competitiveness impacts economic output, income and investment decisions 4 that pertain to future cash flows, affecting the present value of stock prices (Dornbusch and 5 Fischer 1980). The "stock-oriented" model suggests that, trading activities in the equities mar- 6 ket affect the wealth of individuals who timeously balance their portfolios and stock holdings 7 by changing their demand for means to transact and trade globally, such as financial assets in 8 the form of money. The resulting change in money supply and demand equilibrium affects 9 interest rates, hence allowing for misalignment in exchange rates markets (Branson 1981;10 Frankel 1983). Though the relationship between real exchange rate misalignment and eco-11 nomic growth exists, there are certain optimal real exchange rate threshold levels at which 12 undervaluing or overvaluing a currency can be associated with either positive or negative eco-

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This paper uses a copula based dynamic conditional correlation GARCH approach to ex- 16 amine whether there is a possibility of a dynamic influential and dependence relationship 17 amongst commodities, currencies and equities in African economies. The study uses crude oil 18 and gold as commodity market proxies because of their prevalence in the African economies' 19 exports market. The study also uses exchange rates and stock markets of African economies 20 that were the highest ranked by income over the sample period spanning 2000 and 2019. The 21 results from the studied relationship mainly add to the existing understanding and offer broader 22 insights on the impact commodity price fluctuations have on each other and on economic var-23 iable shocks especially for developing economies that are price takers with moderate or high 24 total export concentration consisting of commodities. Also, the inclusion of gold in the analysis gives weight to the ability of this paper to make concluding remarks regarding commodities 1 exported in the African continent. 2 2. Literature review 3 Researchers have over the years rationalised the linkages between commodities and per-4 tinent economic variables that are influential to economic performance especially that of de-5 veloping and in transit economies. Pindyck and Rotemberg (1990) were amongst the first to 6 argue that, within the commodities market, linkages in the form of co-movements exist even 7 amongst unrelated commodities. However, the co-movements in the commodities market does 8 not imply that there exist homogeneity in the overall market's risk and return structure (Erb  Tessema and Gurara (2014); and Behmiri and Manera (2015) however further offered addi-11 tional insights by arguing that in varying sample periods and market segments, exogeneous 12 global factors such as economic shocks, natural disasters and wars tend to influence co-move-13 ments in the commodities market. Varying frameworks and sampling approaches have shown 14 that the commodities' market also influence economic variables including exchange rates and 15 stock markets. Filis, Degiannakis and Floros (2011) using a dynamic conditional correlation 16 (DCC) GARCH framework, find negative time varying influential relationship from changes 17 in oil prices towards stock markets that is similar for both importing and exporting economies. 18 Wang, Wu and Yang (2013) using a structural vector autoregressive (VAR) approach find that 19 the response relationship is conditional on whether the economy is an exporter or importer of 20 oil. Reboredo and Ugolini (2016) show how the size of an oil shock plays a role in the influence of crude oil in the modelling stages either as an endogenous or exogenous variable can show varying conclusions to the impact and relationship it has with stock markets, while that of crude 1 oil and currency is similar regardless of oil treatment. Crude oil has been shown to have a 2 negative co-movement relationship also with exchange rates of most economies. For instance, 3 Yang et al. (2018) and Bedoui et al. (2018) show that with the exception of Japan, there is a 4 negative relationship between crude oil and currency using GARCH-type models by sampling    Securities and Iress. Error! Reference source not found. is a basic statistics view of the sam- 16 pled univariates and offers statistics on the data's degree of asymmetry, kurtosis and p-values 17 of results from two normality tests, Jarque-Bera (JB) of Bera and Jarque (1981) and  Wilks (SW) of Shapiro and Wilk (1965). Based on the skewness (asymmetry), kurtosis (lepto-1 kurtic), SW and JB tests; none of the sampled variables can be regarded as being normally 2 distributed. Serial dependence and stationarity in the data are tested using, respectively, the  of each sampled variable can be expressed as an ARMA ( 1 , 0) as follows:

Materials and Methods
2 can be expressed respectively using the GJR and exponential GARCH as follows: (2) 2 where: 3 − is an indicator variable that represents asymmetric and leverage effects In equation (3) and ∝ capture the size and sign effects respectively and represent asym-6 metric effects. The standard GARCH can be represented by removing the leverage effect pa-7 rameters in either equation (3) or equation (4). The ARCH (∝ ) and GARCH (δ j ) terms both 8 represent the persistence of the conditional variance while ARCH (∝ ) term represents the short 9 run effect of past innovations on the variance at time t. The following conditions are made for 10 the standard and GJR GARCH models to be stationary and ensure positiveness of conditional 11 variance: In univariate models, there are cases where the persistence of the conditional variance is where ~ ( , ) as follows: where: In the definition of constant c, Γ(. ) represents a Gamma function, 2 < < ∞ and −1 < 7 < 1.  ̅ is a vector of standardised residuals and has each element defined as fol-5 lows:  ̅ is a symmetric matrix representing the unconditional mean of and is 7 made of weighted average of the unconditional variance-covariance matrix of 8 the estimators (VCE) of the standardised residuals. 9 After the estimation of the varying marginal distribution families, the parameters are 10 transformed into using the probability integral transformation process to allow for their com-11 parability. The transformed parameters are fitted in a C-MGARCH model with their joint de-12 pendence structure estimated by a copula. A copula is a function that couples a multivariate 13 joint distribution function with its marginal distributions that are uniformly distributed (Nelsen, 14 1999). According to Sklar (1959), for an n-dimensional joint distribution function, 15 = ... , with margins 1 , 2 , . . . , there exists an n-dimensional copula Ç ∶ 16 [ , ] → [ , ], such that for all ∈ ( ℝ ∪ {±∞} )

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The estimation process uses R's rugarch and rmgarch packages of Ghalanos (2013). The 6 models used for the marginal distributions and their estimations are shown in Table 2 and Table   7 3 (a and b), respectively. The exponential and GJR GARCH better model 59% of the sampled  In Tables 3 (a) and 3 (b), the following applies: *** =>Statistical significance at 10%; ** => 17 statistical significance at 5% and* => statistical significance at 1%. priate and a goodness of fit test for the Student-t copula. The results in Table 4 show that, at a 4 5% level of significance, Kenya variables' dependence structure requires a time varying copula 5 while that of Ethiopia, Libya, Nigeria, Sudan, Tanzania and Tunisia would require a different 6 copula other than the Student t copula. We fit a dynamic dependence structure using a Student 7 t copula DCC-GARCH and report in Table 5 the estimates of the joint scalar parameters which 8 are useful in determining the dynamic dependence pattern. At a 5% level of significance the 9 results of Table 5 show that not all the scalar parameters are significant, and that the constant 10 correlation assumption would fit the dynamic dependence process of economies of: Angola,

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We report on the period average for the all economies in Table 6 and present a visualisa-21 tion of the dynamic dependence from Figure A1 to Figure  crises for both commodities. These changes, as DRC is a copper exporter, could be signals of 15 changes in production additives price and a co-movement in the commodity markets in general. 16 The currencies of Libya (oil and diamonds) and Angola (oil and gas) have a negative co-move- (cocoa). The BRVMCI has relatively low dependence to both oil and gold. 16 The results presented on the relationship amongst the variables are conditional on the 17 economy as they are not consistent. In general, the findings around gold and oil association Zambia.

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The results initially show asymmetric impact from positive and negative past shocks of 14 an asset to both their future counterparts and volatility; however, this impact is also found to 15 be associated with and dependent on behaviour in other markets. Dependence from price fluc- 16 tuations amongst the sampled markets is time varying and evolves at a scale around the average 17 dependence measure for most economies but has relatively larger shifts for the economies of We would like to appreciate the teams from Botswana Stock Exchange, Egypt Stock Exchange, 5 and Johannesburg Stock Exchange for the data they entrusted with us to use as part of the 6 analysis for this paper. Stock Markets: Evidence from Emerging African Economies. Applied Economics 52 (18) (3): 705-30. Figure 1 Please see the Manuscript PDF le for the complete gure caption Figure 2 Please see the Manuscript PDF le for the complete gure caption Figure 3