




































American Finance & Banking Review; Vol. 3, No. 1; 2018 

ISSN 2576-1226    E-ISSN 2576-1234 

Impact Factor: 4.1 

Published by Centre for Research on Islamic Banking & Finance and Business   
 

 

12 

Oil Price Volatility, Exchange Rate Movements and Stock Market 

Reaction: The Nigerian Experience (1985-2017) 
 

 

Onyemachi Maxwell Ogbulu
1 

 

1
Department of Banking and Finance, Abia State University, Uturu, Nigeria 

 

Correspondence: Onyemachi Maxwell Ogbulu, Department of Banking and Finance, Abia State University, 

Uturu, Nigeria. Email: onyemachi.ogbulu@abiastateuniversity.edu.ng 

  

To cite this article: Ogbulu, O. (2018). Oil Price Volatility, Exchange Rate Movements and Stock Market 

Reaction: The Nigerian Experience (1985-2017). American Finance & Banking Review, 3(1), 12-25. Retrieved 

from http://www.cribfb.com/journal/index.php/amfbr/article/view/200 

 

 

Received: October 10, 2018                 Accepted: October 25, 2018         Online Published: November 12, 2018 

            

Abstract 

Given the observed volatility in crude oil prices in the international oil market and the role which oil and gas 

play in the Nigerian economy, this paper is an attempt to investigate the impact of crude oil prices and foreign 

exchange rate movements on stock market prices in Nigeria. In addition, the paper examined whether there is 

any volatility pass-through between the dollar price of Nigerian crude oil, foreign exchange rate of the Naira and 

stock market prices respectively. Data employed for the study are monthly values of the Nigerian Stock 

Exchange (NSE) All-Share Index (ASI), Dollar price of Nigerian Crude Oil (DPO) and the Official Exchange 

Rate of the Naira to the US Dollar (FXR) from January, 1985 to August, 2017. The methodology adopted for the 

study include the ADF unit root tests, Johansen co-integration tests, the ECM technique, Granger causality tests, 

variance decomposition as well as the GARCH(1,1) to model the volatility relationships among the variables. 

Findings reveal that there is one long-run dynamic co-integrating relationship among the variables ASI, DPO and 

FXR while the ECM results indicate that Crude oil price (DPO) significantly impact on Stock market prices. The 

Granger causality test reports a bi-directional causality relationship between ASI and DPO and a unidirectional 

causality running from FXR to ASI. The ARCH-GARCH volatility analysis demonstrates vividly that stock 

market prices in the NSE exhibit ARCH effect with a significant and positive first order ARCH term. The 

GARCH term is also positive and significant indicating that previous month’s stock market price volatility 

significantly influences current stock market volatility in the NSE. In addition, findings show that the volatility 

of dollar price of Nigerian oil (DPO) in the world oil market is significantly transmitted to the volatility of stock 

market prices in Nigeria.  The pass-through effect of the volatility of exchange rate (FXR) to the volatility of 

stock market prices is also positive and significant. These findings offer significant informational signal to policy 

makers, portfolio managers/advisors and the investing public in achieving optimal asset and portfolio profile. 
 

Keywords: Crude Oil Prices, Stock Market Price, Exchange Rates, Volatility, ARCH-GARCH,    Variance 

Decomposition. 

 
1. Introduction 

Ever since the discovery of oil in Oloibiri, Nigeria on Sunday, 15
th

 January,1956 and the coming on stream of its 

first oil field producing about 5,100 bpd in 1958, the oil and gas sector has continued to playa central role in the 

economic development of Nigeria and even in the current world economy. For instance, oil contributes about 

90% of all foreign exchange earnings of Nigeria, account for as high as 20% of GDP, 80% of total government 

revenue and about 65% of total trade. Given the level of interdependence among Nations in today’s global 

economy, fluctuations in crude oil prices in the international oil market are bound to have profound impact on 

different sectors of the economy including the stock markets and the foreign exchange markets. 

The nature and extent of this impact depends to a large extent on whether the country is an oil-importing or oil-

exporting country. For oil-importing countries, rising oil prices obviously leads to increases in production costs, 

lower output levels and lower stock returns whereas oil-exporting countries would be happy with rising oil prices 



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since this would translate to higher disposable incomes, consumption, investments and cash flows. Thus, the 

transmission mechanisms through which oil prices impact on real economic activity include both supply and 

demand channels (Ogbulu and Torbira, 2012). In addition, the magnitude of these supply-side and demand-side 

effects is in turn stronger the more the shock is perceived to be long-lasting.. 

The literature of finance is replete with several studies conducted by scholars to explore the nature of the 

relationship between changes in crude oil prices and stock markets and other key macroeconomic variables such 

as real economic growth. However, the controversy has not been settled as there is as yet no consensus on the 

raging controversy. For example, while studies conducted by authors like Muhtaseb and Al-Assaf (2017), Ono 

(2011), Iheanacho (2017), Basher and Sadorsky (2016) find significant and positive impact of oil price shocks on 

stock market returns, the works of others like Yusuf (2015), Bastianin and Manera (2014) as well as Berk and 

Aydogan (2012) found mixed results for the impact of oil price shocks on stock market volatility. 

The objective of this paper therefore is to empirically examine the nature and extent of the relationship between 

fluctuations in crude oil prices in the international oil market and stock market prices in Nigeria. In addition, the 

paper investigates whether there is any volatility relationship between crude oil prices and stock market prices 

and the extent to which volatility in crude is transmitted to stock market prices in Nigeria. 

The paper is arranged as follows. Section 1 contains the Introduction while in Section 2, we have Literature 

Review. Methodology and data are in Section 3, while Results and Discussion of Findings are presented in 

Section 4. Section 5 contains the Conclusion and Recommendations.  

2. Literature Review 

2.1 Theoretical Framework 

The theoretical foundation of asset valuation can be traced to the seminal work of Gordon (1959), Lintner (1965) 

and Mossin (1966) who demonstrated that the value of an asset at any particular point in time (t) depends on the 

stream of benefits to be derived by the holder of the asset over the life of the asset. Thus, the price an asset would 

command in the market is a function of the expected stream of benefits accruable to the investor as well as the 

risk attendant on the investment. However, it has been observed by many scholars and practitioners alike that 

numerous factors both economic and non-economic, affect the price of assets in the stock market and this has 

given rise to the emergence of many theories of valuation of assets. A brief survey of these theories includes the 

Fundamentalist Approach, The Technicalist Approach, The Efficient Market Hypothesis Model as well as the 

Arbitrage Pricing Theory. 

As amply cited by Ogbulu (2012), the Fundamental approach is predicated on the assumptions that every 

security has an intrinsic value and that the intrinsic value of every security is reflected in the market price of that 

security. It is also assumed that the basic economic and fundamental facts and features about a firm or 

corporation determine the intrinsic value of securities issued by the firm or corporation. Thus according to the 

Fundamentalists, the task of the rational investor is to undertake rigorous fundamental analysis of the basic 

economic facts relating to assets to determine their intrinsic values as a prelude to identifying mis-priced assets 

in the market. Hence, armed with information on mis-priced securities the rational investor can formulate 

profitable trading rules. (Okafor, 1983), (Bodie, et al.,2008) 

On the other hand, the Technical approach dismisses the quest to obtain knowledge of intrinsic value as 

irrelevant in the buy or sell decisions of investors in the capital market. The assumptions here are that the value 

of a security is determined by the forces of supply and demand and that prices of securities are observable, 

chartable and follow recurring patterns which can be used to formulate profitable trading rules in the market. For 

the Technicalists therefore, reliance on market prices and their patterns over time would provide signals for 

timing of market transactions to optimum advantage.(Francis, 1980). 

The Efficient Market approach is anchored on the EMH which assumes that market prices of securities fully 

reflect all available and relevant information about such securities and changes in security prices are random and 

not systematic as propounded by the Technicalists. For the EMH approach therefore, there is no specific and 

recurring patterns in the behavior of stock prices which could provide the basis for formulating reliable and 

profitable trading rules. (Hirt and Block,1983) The culmination of the EMH is the single-factor CAPM according 

to which the expected return on an asset is postulated be an increasing function of the asset’s beta coefficient. 

Although some authors like Roll (1977) are of the view that the CAPM is untestable on account of the difficulty 

in finding a perfect proxy for the market portfolio, the work by Ogbulu (2012) demonstrates the use of an All-

Asset Market Portfolio to test the validity of the single-factor CAPM.          

Expectedly, the discussions and controversies that have been generated over the years on the proper meaning of 

the term “all available information” have given rise to the characterization of the EMH into three levels of 

market efficiency namely- the weak form, the semi-strong form and the strong form (Bodie, Kane and Marcus, 

2008; Ogbulu, 2009).  The weak form asserts that current market prices of securities in the capital market fully 

reflect the information implied by the historical sequence of prices of the securities. Hence, the weak form 

efficiency implies that knowledge of past prices of a security cannot be used to predict future prices of that asset 



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nor consistently secure abnormally high rates of return. The semi-strong form says that all public information 

about the securities including historical information is already fully reflected in the current prices of the 

securities hence an investor cannot use fundamental analysis of the securities to determine whether an asset is 

mis-priced or not in order to produce abnormal returns. On the other hand, the strong form states that all, not just 

publicly available information about a security is fully reflected in security prices such that even those with 

privileged or what may be considered as insider information can utilize such information to earn superior returns 

in the market. 

The Arbitrage Pricing Theory (APT) in contrast to the EMH single-factor CAPM, postulates a multifactor APT 

which generalizes the single-factor model to incorporate several other sources of systematic risk beyond the beta 

coefficient. (Ross,1976); (Chen, Roll and Ross, 1986).  

Notwithstanding the apparent contradictions inherent in these theories, it should be noted that each approach has 

its adherents and in practice many practitioners are wont to use a combination of these approaches to arrive at 

optimal decisions.  

Resting on the tenets of the Fundamentalist approach therefore, it is apposite to contend that prices of financial 

assets quoted on any stock exchange are influenced not only by firm-specific and industry factors but also by 

macro-economic, socio-economic, political and even socio-cultural factors within and outside the domestic 

economy given the inter-connectedness of many Nations today. The focus of this paper therefore is to examine 

the nature and extent of the impact of Nigeria’s crude oil price and the Naira exchange rate on stock market 

prices in Nigeria as well as investigating the volatility spillover effect from crude oil price and exchange rates to 

the stock market prices. 

2.1 Theoretical Background  

The oil price-stock market price transmission path can be traced in two ways. First is the cash flow path and the 

second relates to the wealth effect The link between oil prices and stock returns can be explored by explaining 

the channels through which the changes in oil price can affect real stock market returns. In theory, there are 

several transmission mechanisms that clarify this relation. According to the financial economic science, there are 

two main channels. First, based on a microeconomic perspective, a logical way is the channel of expected cash 

flow. Oil is an important input in the production process; therefore, higher production costs due to higher oil 

prices will adversely affect margins, cash flows and hence stock prices. Second, according to the macroeconomic 

view, oil prices may impact stock returns via the discount rate. An oil price increase often results in inflationary 

pressures. The central bank may raise the interest rate to combat these pressures (Basher and Sadorsky, 2006). 

Since both the inflation rate and interest rate, which constitute the discount rate, are influenced by oil price, it 

follows that the rise in oil price raises the discount rate, and thus, reduces the stock returns.  

In fact, the response of aggregate stock returns to oil price changes greatly depends on whether the country in 

question is an oil-importing or exporting country. For a net importer of oil, a rise in oil price puts a downward 

pressure on the country’s foreign exchange rate and upward pressure on domestic inflation rate. Because a higher 

expected inflation rate raises the discount rate, an increase in oil prices has a negative impact on stock returns 

(Huang et al. 1996). A positive impact is, however, expected on stock market in oil exporting countries as a 

reaction to a change in oil prices. The mechanism can be explained through income and wealth effects. A rise in 

oil prices raises government revenues, and public expenditure on infrastructure may increase. Furthermore, 

higher prices lead to an immediate transfer of wealth from net oil importers to net oil exporters. Government 

spending on purchasing domestic goods and services generates a higher level of economic activity and improves 

stock market returns in these countries (Bjornland, 2009). 

2.2 Empirical Literature Review 

In their paper, Lake and Katrakilidis (2009), explored the effects of oil price returns andoil price volatility on the 

Greek, the US, the UK and the German stock markets. More specifically, the authors’ research focused on the 

interactions among oil prices, its volatility, and the stock market returns as well as on the futures indices of each 

index. The volatility of the employed indices has been quantified by applying EGARCH models and the 

relationship between the variables has been examined by means of structural equation models (SEM). The 

findings from their analysis reveal that the Greek stock market index returns and the US stock market index 

returns are both sensitive to the oil price returns movements while the German and the UK stock market returns 

are not affected at all. 

In addition, Ono (2011) investigated the impact of oil prices on real stock returns for Brazil, China, India and 

Russia, the BRIC countries, over the period 1999:1-2009:9 using the multivariate VAR models. The results 

suggest that whereas real stock returns positively respond to some of the oil price indicators with statistical 

significance for China, India and Russia, those of Brazil do not show any significant responses. In addition, the 

author found statistically significant asymmetric effects of oil price increases and decreases for India but in the 

cases of Brazil, China and Russia no asymmetric effects of oil prices were detected. The analysis of variance 



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decomposition shows that the contribution of oil price shocks to volatility in real stock returns is relatively large 

and statistically significant for China and Russia. 

The paper by Muhtaseb and Al-Assaf (2017) examined whether Amman stock market returns respond 

asymmetrically to oil price fluctuations for the quarterly period 2000-2015 by applying asymmetric co-

integration. The authors employed both TAR and MTAR specification models and based on the asymmetric 

ECM, the results of their analysis provide evidence that stock returns in the Amman Stock market react to oil 

price variations in an asymmetric manner. Specifically, the findings indicate that rising oil prices have a larger 

impact on stock returns which implies that increases in oil prices have a significant effect on the behavior of 

stock market in Jordan. Hence the significant relationship between oil prices and stock returns strengthen their 

predictability power, so that appropriate strategies may be built on the basis of expected increases or decreases in 

oil prices. 

In examining the impact of oil price fluctuations on economic growth in Nigeria, Yusuf (2015) undertook a study 

to investigate the impact of oil price shocks on the Nigerian economic growth using quarterly data from 1970:1-

2011:4 while controlling for the effects of unrest in the international oil market, exchange rates and agricultural 

output. Employing the methodology of ADF unit root tests, Johansen-Joselius co-integration as well as the 

SVAR, IRF and VDC analyses, findings revealed that all the variables are integrated of order one. In addition, 

the results from the IRF and VDC analysis show that the response of oil price shocks and unrest to real GDP 

depicts both negative and positive impacts. Hence, the author concludes that oil price, exchange rates, 

agricultural output and unrest contained some useful information in predicting the future path of economic 

growth in Nigeria and recommended that the Nigerian government should diversify the economy away from oil 

to non-oil sectors as well as improving the security situation in the Niger Delta region to boost oil output and the 

economy in general. 

Furthermore, the trio of Masih, Peters and De Mello (2011) explored the empirical relationship between oil price 

volatility and stock price fluctuations in South Korea using monthly data from May, 1988-January, 2005. The 

authors adopted the multivariate VEC model incorporating the variables- interest rates, economic activity, real 

stock returns, real oil prices and oil price volatility. The results of the analysis vividly show the dominance of oil 

price volatility on real stock returns and emphasized how this has increased over time thus underscoring the 

point that oil price volatility can have profound effect on the time horizon of investment and firms need to adjust 

their risk management procedures accordingly. 

Zubair, Okorie and Sanusi (2013), in their study investigated the exchange rate pass-through to domestic prices 

in Nigeria by employing the impulse response from an estimated SVAR model of the inflation process using 

quarterly data for the period 1986-2010. The results suggest that the exchange rate pass-through is incomplete, 

low and fairly slow. In addition, the authors report that the elasticity of inflation to exchange rate changes is 

about 0.02, and that it takes about eight quarters to reach its full-impact of only 0.26. The authors further argue 

that given the large share of imports in Nigeria’s consumption basket, this surprisingly low pass-through 

indicates that importers practice the so-called pricing-to-market strategy of price setting for the Nigerian market. 

The variance decomposition analysis suggests that money supply has contributed more to Nigeria’s inflation 

process relative to the exchange rate. This suggests that policy makers must beep up efforts at achieving 

monetary stability. 

Furthermore, Bastianin and Manera (2014) in their research paper explored the impact of oil price shocks on the 

US stock market volatility by deriving three different structural oil shock variables namely aggregate demand, 

oil-supply and oil-demand shocks which the authors related to stock market volatility using bivariate SVAR 

models, one for each oil price shock. Monthly data from February, 1973-December, 2013 were employed in the 

analysis. The findings of the study show that volatility responds significantly to oil price shocks caused by 

sudden changes in aggregate and oil-specific demand while the impact of supply-side shocks were negligible and 

insignificant.  

Using cross-country analysis, Dhaoui and Khraief (2014) examined the empirical linkage between oil price 

shocks and stock market volatility in eight developed countries namely-USA, Switzerland, France, Canada, UK, 

Australia, Japan and Singapore. Using monthly data for the eight developed countries from January 1991 to 

September 2013 and employing the methodology of EGARCH with an ARCH-in-mean model (EGARCH-M), 

findings reveal that strong negative connections between oil price and stock market returns are found in seven of 

the selected countries. Oil price changes are without significant effect on the stock market of Singapore. 

Furthermore, the authors report that on the volatility of returns, the changes in oil prices are significant for six 

markets and they have not much effect on the others. 

Berk and Aydogan (2012) in their paper investigated the impact of crude oil price variations on the Turkish stock 

market returns. The authors employed vector autoregression (VAR) model using daily observations of Brent 

crude oil prices and Istanbul Stock Exchange National Index (ISE-100) returns for the period between January 2, 

1990 and November 1, 2011. In addition, they also tested the relationship between oil prices and stock market 



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returns under global liquidity conditions by incorporating a liquidity proxy variable, Chicago Board of 

Exchange’s (CBOE) S&P 500 market volatility index (VIX), into the model. According to the authors findings 

of the variance decomposition test suggest little empirical evidence that crude oil price shocks have been 

rationally evaluated in the Turkish stock market. Rather, it was global liquidity conditions that were found to 

account for the greatest amount of variation in stock market returns. 

The work by Hamma, Jarboui and Ghorbel (2014) examined the links and interaction between oil and stock 

markets in Tunisian terms of volatility at the sector-level and secondly to determine the best hedging strategy for 

oil stock portfolio against the risk of negative variation in stock market prices.  The authors investigated seven 

sectors namely-Automobile &Parts, Banks, Basic Materials, Utilities, Industrials, Consumer services and 

Financial services using weekly data from 2
nd

April, 2005 to 12
th

 July, 2012. The methodology adopted is the 

bivariate GARCH model to capture the effect in terms of volatility in the variation of oil price on the different 

sector index, and to use the conditional variances and conditional correlation to calculate the hedging ratio and 

then determine the best hedging strategy. The empirical results obtained indicate that the majority of 

relationships are unidirectional from the oil market to Tunisian stock market. In addition, the conditional 

variance of a stock sector returns is affected not only by the volatility surprises of the stock market, but also by 

those of oil market. 

Further empirical research on sectoral impact of oil price volatility include the work by Caporale, Ali and 

Spagnolo (2015) in which the researchers investigated the time-varying impact of oil price uncertainty on stock 

prices in China using weekly data on ten sectoral indices over the period January 1997–February 2014. They 

estimated a bivariate VAR-GARCH-in-mean model and the results suggest that oil price volatility affects stock 

returns positively during periods characterized by demand-side shocks in all cases except the Consumer 

Services, Financials, and Oil and Gas sectors. The latter two sectors are found to exhibit a negative response to 

oil price uncertainty during periods with supply-side shocks instead. By contrast, the impact of oil price 

uncertainty appears to be insignificant during periods with precautionary demand shocks. 

The paper by Kang, Ratti and Yoon (2015) examined the impact of structural oil price shocks on the covariance 

of U.S stock market return and stock market volatility. The authors constructed from daily data on return and 

volatility the covariance of return and volatility at monthly frequency. The measures of daily volatility are 

realized-volatility at high frequency (normalized squared return), conditional-volatility recovered from a 

stochastic volatility model, and implied-volatility deduced from options prices. Results indicate that positive 

shocks to aggregate demand and to oil-market specific demand are associated with negative effects on the 

covariance of return and volatility while oil supply disruptions are associated with positive effects on the 

covariance of return and volatility. In addition, the spillover index between the structural oil price shocks and 

covariance of stock return and volatility is large and highly statistically significant. 

3. Methodology and Data 

3.1. Methodology 

The methodology adopted for this study is the econometric investigative enquiry which involves the application 

of regression analysis, unit root tests, Johansen Co-integration tests, the Error Correction mechanism (ECM), 

Granger causality tests and the ARCH-GARCH(1,1) model to test for  volatility effect from changes in crude oil 

price and exchange rates  to stock market prices. In addition, the paper employed the Variance Decomposition 

(VDC) analysis within an unrestricted VAR setting to examine the forecast error decomposition of the variables 

ten months into the future. 

3.1.1Model Specification 

The functional relationship describing the response of stock market prices to changes in the international crude 

oil prices and exchange rates can be stated as in equation (1) thus: 

 

ASI =  f(DPO, FXR)…………………………………………………………………….(1) 

 

While the functional model is specified as 

 

ASI   =   β0  +  β1DPO   + β2FXR  +μ………………………………………………….(2) 

 

Where: 

 ASI= Nigerian Stock Exchange All-Share Index 

 DPO= Nigerian Crude Oil Price in the international market 

 FXR= Exchange rate of the Naira to the US Dollar 

 



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The apriori theoretical expectation about the signs of the parameter coefficients are given as β1> 0 and β2<0 

given that Nigeria is an oil-exporting Nation, increase in oil prices leads to increase in aggregate income and 

cash flows and hence a bullish stock market, all things being equal. 

3.1.2 Unit Root Test 

The Unit root test has become a popular test of the stationarity or otherwise of time series data in many 

econometric studies given the time-dependent nature of many economic variables. Some of the most popular 

tests for unit root are the Augmented Dickey-Fuller (ADF) test, the Phillips-Perron (P-P) test and the 

Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test The ADF unit root test is adopted in this study. The tests 

usually consist of estimating the regression: 

 n 

∆Yt  =  β1 + β2t  + δYt-1  + ∑αi∆Yt-1  + εt…………….(3)  

i=1 

Where εt is a pure white noise error term and ∆Yt-1 = (Yt-1 – Yt-2),    ∆Yt-2 = (Yt-2 –Yt-3), and so on with a number 

of lagged difference terms included so that the error term is serially uncorrelated to enable the researcher obtain 

an unbiased estimate of δ, the coefficient of lagged Yt-1 in equation (3) above (Gujarati and Porter, 2009). In 

testing for unit root, the null and alternative hypotheses are stated as Ho: η = 1 (unit root exists and series is non-

stationary) as against H1: η = 0 (No unit root, series is stationary). 

3.1.3 The Granger Causality Test 

The Granger causality test is used for testing the direction of causality between variables say Y and X 

(Granger,1969). The test is based on estimating the following bivariate regressions. 

 n n 

Yt=  ∑ αiXt-i + ∑ βjYt-j  + u1t ………………………………………….( 4 )   

i=1          j=1 

 

      n n 

Xt  =  ∑ δiYt-i + ∑ λjXt-j + u2t ……………………………………………(5) 

 i=1   j=1  

 

where Yt and Xt are the variables of interest while u1t and u2t are the disturbance terms assumed to be 

uncorrelated. The present study employed the Granger causality test to estimate the degree of causality between 

stock market prices, crude oil prices and exchange rates (Brooks, 2008 ).  

3.1.4 The ARCH-GARCH Test 

The development of the Autoregressive Conditional Heteroscedasticity (ARCH) model is usually attributed to 

Engle (1982) who developed the ARCH model to capture the effect of serially correlation of volatility in time 

series data according to which the ARCH model expresses conditional variance as a distributed lag of past 

squared innovations. (Goudarzi, 2013). In developing the ARCH model, the conditional return must be modeled 

first by stating the return relationship as an autoregressive AR(p) process with lags up to (p) stated as follows 

say: 

ASIt=  αo  + ∑ αt ASIt-1 + εt ……………………………………………(6)   

 

Where ASIt is current stock market price in period t. Equation (8) above implies that ASIt depends not only on 

(ASIt-1) but also on previous prices (ASIt-p). Given that the ARCH model assumes that the residuals (ε’s) have no 

constant variance, the conditional variance is modeled to incorporate the ARCH process of (ε
2
) in the conditional 

variance with (q) lagged values of the residuals (ε
2
) as stated in equation (7). 

σt
2
  =    αo  +  α1εt-1

2
 +… + αp εt-p

2
…………………………………(7) 

However, Bollerslev (1986) as well as Bollerslev, Chou and Kroner (1992) refined Engle (1982) linear ARCH 

(q) model as represented in equation (6) above to remove its long lag structure by including the lagged values of 

the conditional variance in his formulation which Bollerslev called the Generalized Conditional 

Heteroscedasticity (GARCH) model. That is, the GARCH (p,q) model specifies the conditional variance to be a 

linear combination of (q) lags of the squared residuals (ε
2
t) from the conditional return equation and (p) lags from 

the conditional variance (σt-j
2
). The GARCH (p,q) model is then written as follows: 

σt
2
=  αo  + ∑αiεt-i

2
 +  ∑βjσt-j

2
   ………………………………………….(8) 

where αi, βj>0 and  αi, βj< 1 to avoid the possibility of negative conditional variance.  

From equation (8), it means that the current value of the conditional variance is a function of a constant and 

values of the squared residuals from the conditional return equation plus values of the previous conditional 

variance. (Goudarzi, 2013).  Thus, given the standard GARCH (p,q) model, if both the ARCH and GARCH 

coefficients are significant then there is evidence of volatility in the squared series. In addition, the GARCH 

model can be utilized to model volatility clustering. If the coefficients of the ARCH and GARCH terms sum up 



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18 
 

to 1, then there is volatility clustering and confirms the presence of ARCH and GARCH effects in the variable (s) 

of interest. 

3.2 Data 

Data for the study are secondary data (monthly) sourced from the NSE official Daily Stock Market Price List of 

the NSE from January, 1985 to August, 2017. The data on Crude oil prices and Foreign Exchange Rates were 

extracted from the CBN Statistical Bulletin. The summary descriptive statistics for the data series on ASI, DPO 

and FXR are as presented in Table 1. The raw data are presented in the Appendixes. 

Table 3.1 presents the summary statistics for the variables for the period under study. The mean of ASI is 

15349.46 with a standard deviation of 15135.06. For DPO, the mean dollar price of crude oil is 38.88 US$ and 

standard deviation of 29.7US$. The mean of FXR is N90.5607 to $1 with a standard deviation of N76.3737 to$1. 

The J-B statistic for all the series show that they are all not normally distributed.  

 

Table 1: Summary Statistics (1985:1-2017:8) 

 ASI DPO FXR 

 Mean  15349.46  38.88087  90.56069 

 Median  9872.700  24.26500  111.6000 

 Maximum  65652.40  128.0800  309.7300 

 Minimum  111.3000  8.030000  0.820300 

 Std. Dev.  15135.06  29.70307  76.37374 

 Skewness  0.863020  1.024385  0.594463 

 Kurtosis  3.009841  2.789413  3.008463 

    

 Jarque-Bera  48.66207  69.28283  23.08907 

 Probability  0.000000  0.000000  0.000010 

    

 Sum  6016988.  15241.30  35499.79 

 Sum Sq. Dev.  8.96E+10  344968.6  2280683. 

    

 Observations  392  392  392 

 

4. Results and Discussion 

4.1 Unit Root Test Results 

Table 2 shows a summary of the ADF Unit root test results obtained using the E-Views version 9.0 statistical 

package. The results indicate that all the variables are integrated of order one. That is, they all become stationary 

after the first differencing. 

 

Table 2 ADF Unit Root Test Results 

Variable ADF test statistic at 1st diff Order of integration 

ASI -8.153873 1(1) 

DPO -10.615780 1(1) 

FXR -14.243390 1(1) 

Critical Values: 1% -3.447036; 5% -2.868790; 10% -2.570698 

Source: Author’s Computation 

4.2 Co-integration Test Results 

Having established that the series are integrated of the same order, it becomes plausible to apply the Johansen-

Joseluis co-integration test to determine whether there is any long-run dynamic relationship among the variables. 

In table 3, the Johansen co-integration test results are presented. The results show that there is one long-run co-

integration relationship between stock market prices, crude oil price and exchange rates for both the trace test 

and the maximum eigenvalue test. The test assumes a linear deterministic trend and was estimated with lag 

interval of 1 to 8.  

Table 3:   Johansen Co-integration Test Results 

   

Sample (adjusted): 10 392   

Included observations: 383 after adjustments  

Trend assumption: Linear deterministic trend  

Series: ASI DPO FXR    



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Lags interval (in first differences): 1 to 8  

     

Unrestricted Cointegration Rank Test (Trace)  

          
Hypothesized  Trace 0.05  

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** 

          
None *  0.062490  34.88953  29.79707  0.0119 

At most 1  0.023737  10.17525  15.49471  0.2675 

At most 2  0.002540  0.974171  3.841466  0.3236 

          
 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level 

 * denotes rejection of the hypothesis at the 0.05 level 

 **MacKinnon-Haug-Michelis (1999) p-values  

     

Unrestricted Cointegration Rank Test (Maximum Eigenvalue) 

          
Hypothesized  Max-Eigen 0.05  

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** 

          
None *  0.062490  24.71428  21.13162  0.0150 

At most 1  0.023737  9.201075  14.26460  0.2698 

At most 2  0.002540  0.974171  3.841466  0.3236 

          
 Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level 

 * denotes rejection of the hypothesis at the 0.05 level 

 **MacKinnon-Haug-Michelis (1999) p-values 

Source: Author’s computation 

 

 

 

4.3 Error Correction Model 

Having established that there exists long run relationship among the variables, the oil price-stock market price 

linkage under investigation is then specified in an ECM incorporating a four- period lagged residual. The ECM 

is employed to capture the short-run deviations of the parameters from the long-run equilibrium within the 

framework of an ARDL technique to obtain an over- parameterized ECM and then arriving at the parsimonious 

error correction result using the general - specific approach. 

Table 4: Parsimonious ECM Result 

Dependent Variable: D(ASI)   

Method: Least Squares   

Date: 09/03/17   Time: 22:25   

Sample (adjusted): 6 392   

Included observations: 387 after adjustments  

          
Variable Coefficien

t 

Std. Error t-Statistic Prob.   

          
C 92.45219 78.76416 1.173785 0.2412 

D(ASI(-1)) 0.056604 0.051333 1.102690 0.2709 

D(ASI(-2)) 0.170585 0.050269 3.393427 0.0008 

D(ASI(-3)) 0.210106 0.050362 4.171922 0.0000 

D(ASI(-4)) -0.137790 0.052094 -2.645016 0.0085 

D(DPO) 65.86481 17.39081 3.787335 0.0002 

D(DPO(-1)) 23.24333 17.79356 1.306278 0.1923 

D(DPO(-4)) -28.88898 17.53848 -1.647177 0.1004 

D(FXR) -14.95351 15.42477 -0.969448 0.3329 

D(FXR(-1)) -8.333265 15.43510 -0.539890 0.5896 



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D(FXR(-3)) -13.43361 14.72812 -0.912106 0.3623 

ECM(-1) -0.025511 0.010777 -2.367129 0.0184 

          
R-squared 0.176671     Mean dependent var 93.15098 

Adjusted R-squared 0.152520     S.D. dependent var 1628.564 

S.E. of regression 1499.235     Akaike info criterion 17.49381 

Sum squared resid 8.43E+08     Schwarz criterion 17.61656 

Log likelihood -3373.053     Hannan-Quinn criter. 17.54248 

F-statistic 7.315248     Durbin-Watson stat 1.973917 

Prob(F-statistic) 0.000000    

     
Source: Author’s computation 

 

Table 4 presents the results of the parsimonious ECM estimated using difference data of the variables. From the 

results, it is evident that changes in crude oil prices (DPO) have a significant and positive impact on stock market 

prices (ASI). Changes in foreign exchange rates are positive but not significant. The adjusted R
2
 is 

approximately 15.25% while the D-W statistics of 1.97 shows the absence of autocorrelation in the residuals. 

The ECM coefficient value of -0.0256 approximately, is appropriately signed and significant and indicates that 

the speed of adjustment of the model back to the long-run equilibrium when disturbed by any short-run shock is 

2.56% per month. 

4.4 Granger Causality Test Results 

As mentioned in 3.1.3, Granger causality test is employed to examine the direction of causality between two 

variables of interest. In Table 5 the results of the Granger causality tests are exhibited. The results report a bi-

directional causality relationship between Crude oil price (DPO) and stock market prices (ASI) while the 

causality relationship between ASI and FXR is uni-directional running from foreign exchange rates (FXR) to 

ASI. There is no significant causality relationship between FXR and DPO. 

 

Table 5: Granger Causality Test Results 

 

Sample: 1 392  

Lags: 2   

    
    
 Null Hypothesis: Obs F-

Statistic 

Prob.  

    
    

 DPO does not Granger Cause ASI  390  4.64971 0.0101 

 ASI does not Granger Cause DPO  10.7126 3.E-05 

        
 FXR does not Granger Cause ASI  390  3.70910 0.0254 

 ASI does not Granger Cause FXR  0.14697 0.8634 

        
 FXR does not Granger Cause DPO  390  2.70202 0.0683 

 DPO does not Granger Cause FXR  1.16005 0.3146 

        
Source: Author’s computation 

 

 

4.5 ARCH-GARCH Test Results for Volatility 

The test for the presence of volatility and its transmission effect in the crude oil price-stock market price 

relationship is modeled using the ARCH-GARCH(1,1) technique. The first step in the volatility analysis is to 

establish whether the residuals in the crude oil price-stock market price model possess any ARCH effect. Table 6 

presents the results of the heteroskedasticity test which indicates significant ARCH effect in our model. That is, 

the variances of the residuals are not constant from one period to another thus confirming the presence of high 

volatility in the series.      

 

 

 



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Table 6:  Heteroskedasticity Test: ARCH 

  

     
     

F-statistic 1714.830     Prob. F(1,389) 0.0000 

Obs*R-squared 318.7038     Prob. Chi-Square(1) 0.0000 

     
     
     

Test Equation:    

Dependent Variable: RESID^2   

Method: Least Squares   

Date: 09/03/17   Time: 22:33   

Sample (adjusted): 2 392   

Included observations: 391 after adjustments  

          
Variable Coefficien

t 

Std. Error t-Statistic Prob.   

     
     

C 5100817. 3040211. 1.677784 0.0942 

RESID^2(-1) 0.902918 0.021804 41.41051 0.0000 

     
     

R-squared 0.815099     Mean dependent var 5291325

1 

Adjusted R-squared 0.814624     S.D. dependent var 1.29E+0

8 

S.E. of regression 55612294     Akaike info criterion 38.51081 

Sum squared resid 1.20E+18     Schwarz criterion 38.53111 

Log likelihood -7526.863     Hannan-Quinn criter. 38.51886 

F-statistic 1714.830     Durbin-Watson stat 2.342716 

Prob(F-statistic) 0.000000    

     
 

Presample variance: backcast (parameter = 0.7) 

GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1) + C(7)*DPO + C(8) 

        *FXR    

     
     Variable Coefficient Std. Error z-Statistic Prob.   

     
     C -1166.007 40.83944 -28.55100 0.0000 

DPO 51.83831 3.161708 16.39567 0.0000 

FXR 109.1698 0.730276 149.4910 0.0000 

     
     T Variance Equation   

     
     C -47756.27 3360.200 -14.21233 0.0000 

RESID(-1)^2 1.060223 0.224648 4.719479 0.0000 

GARCH(-1) 0.030020 0.099226 0.302543 0.7622 

DPO 3554.836 35.39264 100.4400 0.0000 

FXR 198.9288 235.7687 0.843746 0.3988 

     
     R-squared 0.514602     Mean dependent var 15349.46 

Adjusted R-squared 0.512107     S.D. dependent var 15135.06 

S.E. of regression 10571.74     Akaike info criterion 18.24893 

Sum squared resid 4.35E+10     Schwarz criterion 18.32998 

Log likelihood -3568.791     Hannan-Quinn criter. 18.28106 

Durbin-Watson stat 0.026526    

      

    
 

The presence of volatility in the model can also be demonstrated graphically by observing the plot of the 

residuals. Fig.1 below is the plot of the residuals from equation (2). 

-40,000

-20,000

0

20,000

40,000

-20,000

0

20,000

40,000

60,000

80,000

86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 16

Residual Actual Fitted
 

 

Fig 1: Plot of residuals of oil price-stock price model 



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From the graph above, we can deduce the presence of volatility in the model where small (large) changes are 

followed by large (small) changes especially during the period 2006 to 2010. 

The next step involves the estimation of the ARCH-GARCH model to examine the nature and extent of the 

volatility relationship among the variables. In Table 7, we present the results of the estimated GARCH model 

using E-Views 9. The mean equation shows a significant and positive relationship between stock market prices 

(ASI) and crude oil prices (DPO) as well as between foreign exchange rates (FXR) and stock prices. 

The variance equation indicates that both the ARCH and GARCH terms are positive and significant meaning that 

stock market prices in the Nigerian Stock market exhibit strong volatility. It is also evident from the results that 

changes in the international crude oil price (DPO) contribute significantly to the volatility in stock market prices 

in Nigeria just as changes in foreign exchange rates (FXR) do also contribute significantly to the volatility in 

stock market prices. In addition, there is evidence of volatility clustering in the model given that the sum of the 

ARCH and GARCH terms is one (1) approximately. This implies that shocks to the conditional variance are 

highly persistent. 

Table 7: ARCH-GARCH Test Result 

Dependent Variable: ASI   

Method: ML ARCH - Normal distribution (BFGS / Marquardt steps) 

Sample: 1985M01 2017M08   

Included observations: 392   

Failure to improve likelihood (non-zero gradients) after 70 iterations 

Coefficient covariance computed using outer product of gradients 

Presample variance: backcast (parameter = 0.7) 

GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1) + C(7)*DPO + 

C(8) 

        *FXR    

          
Variable Coefficien

t 

Std. Error z-Statistic Prob.   

     
     

C -861.9789 49.69672 -17.34478 0.0000 

DPO 36.40032 3.200040 11.37496 0.0000 

FXR 100.1106 0.689781 145.1340 0.0000 

     
     
 Variance Equation   

          
C -38153.37 6898.508 -5.530670 0.0000 

RESID(-1)^2 0.985343 0.192599 5.116042 0.0000 

GARCH(-1) 0.125656 0.050631 2.481799 0.0131 

DPO 2355.079 450.4689 5.228061 0.0000 

FXR 580.9129 109.5096 5.304677 0.0000 

     
     

R-squared 0.424575     Mean dependent var 15349.46 

Adjusted R-squared 0.421616     S.D. dependent var 15135.06 

S.E. of regression 11510.44     Akaike info criterion 18.20694 

Sum squared resid 5.15E+10     Schwarz criterion 18.28799 

Log likelihood -3560.561     Hannan-Quinn criter. 18.23906 

Durbin-Watson stat 0.022134    

     
     

Source: Authors computation 

4.6 Variance Decomposition Analysis 

To further our investigation, the variance decomposition analysis was undertaken to examine the response of 

stock market prices emanating from own shocks and also from shocks in crude oil prices and foreign exchange 

rates within an out of sample period of ten months. In Tables 8, we show the results of the VDC obtained from 

the unrestricted VAR estimation of the model. 

The results in Table 8 indicate that own shocks from stock market prices (ASI) account for 100% of the forecast 

variance decomposition in the first month in the future and none is attributable to the other variables and steadily 

decreases to 98.68 % in the 10
th

 month. In the 10
th

 month for example, shocks emanating from DPO and FXR 

account for the remaining 1.32% in the variance decomposition of ASI. 



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23 
 

The first panel in the graph in Fig 2 amplifies the variance decomposition of ASI due to shocks from ASI and the 

other variables. 

Table 8: Variance Decomposition Test Results 

          
 Variance 

Decomposition 

of ASI: 

    

 Period S.E. ASI DPO FXR 

     
     

 1  1582.229  100.0000  0.000000  0.000000 

 2  2372.300  98.97639  0.936641  0.086969 

 3  2982.137  98.48131  1.399620  0.119073 

 4  3475.070  98.33504  1.553430  0.111530 

 5  3887.317  98.35498  1.553003  0.092016 

 6  4241.111  98.44049  1.480838  0.078667 

 7  4550.743  98.53915  1.378907  0.081947 

 8  4825.831  98.62279  1.269258  0.107947 

 9  5073.153  98.67554  1.164028  0.160430 

 10  5297.680  98.68792  1.070191  0.241888 

     
 

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent ASI var iance due to ASI

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent ASI var iance due to DPO

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent ASI var iance due to FXR

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent DPO var iance due to ASI

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent DPO var iance due to DPO

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent DPO var iance due to FXR

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent FXR var iance due to ASI

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent FXR var iance due to DPO

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent FXR variance due to FXR

Variance Decomposition

 

Fig 2: Graph of Variance Decomposition of ASI 

4.7 Discussion of Findings 

The results from the parsimonious ECM indicate that changes in crude oil prices (DPO) significantly and 

positively affect changes in stock market prices (ASI) in Nigeria. Foreign exchange rate movements are 

appropriately signed but not significant. The above ECM results when taken with the Granger causality results 



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24 
 

which show a bi-directional causality relationship between ASI and DPO underscores the fact that there is a 

strong and significant relationship between crude oil prices and stock market activities. The uni-directional 

causality from FXR to ASI suggests that activities in the foreign exchange market also influence prices in the 

stock market. These findings are in consonance with the results of the studies carried out by Kang, Ratti and 

Yoon (2015), Zubair, Okorie and Sanusi (2013) as well as an earlier work by Ogbulu and Torbira (2017). 

Furthermore, the results of the volatility test using the GARCH (1,1) model vividly confirm the presence of 

ARCH effect in the ASI-DPO model. The mean equation shows that both DPO and FXR are positive and 

significant just as the variance equation depicts that both the ARCH and GARCH terms are significant and 

positive. The implication is that both the previous month’s squared residual (volatility) and the previous month’s 

residual (volatility) of stock market prices (ASI) significantly and positively influence the current month’s 

volatility of the Nigerian stock market. In addition, both DPO and FXR contribute significantly to the volatility 

of stock market prices in the Nigerian context. The observed results also indicate the presence of volatility 

clustering in the market. The results of the forecast variance decomposition of ASI emanating from own 

innovations dominate those of DPO and FXR within the forecast period of 10 months. These results agree well 

with earlier results from the works of Basher, Alfred and Sadorsky (2010) and Berk and Aydogan (2012). 

5. Conclusion and Recommendations 

This paper set out to investigate in the main the nature and extent of the relationship between crude oil prices and 

stock market prices in Nigeria with foreign exchange rate movements as a control variable. In addition, the paper 

sought to explore the nature of the volatility relationship between crude oil prices and stock market prices in 

Nigeria using the GARCH (1,1) model. The findings of the paper vividly indicate that changes in crude oil prices 

in the international oil market significantly affect stock market prices in Nigeria. On volatility, it is evident that 

crude oil prices and foreign exchange rates contribute significantly to the volatility of the stock market in 

Nigeria. 

In the light of the above results, it is recommended that investors in the Nigerian stock market should always 

incorporate information emanating from the international oil market and the Nigerian foreign exchange market in 

their investment-decision process. Given the observed significant relationships between crude oil prices and the 

stock market including the presence of volatility pass-through in the markets, it is apt for policy makers in 

Nigeria to design and sustain investment-friendly policies that would help in boosting oil production. The issue 

of security, infrastructure and energy are of paramount importance in achieving this goal. 

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