Abstract
Introduction: Financial markets play key role in the growth and sustainability of the economy. However, high levels of volatility in the markets may adversely affect the financial system and weaken the economy.
 Purpose: This paper examined the presence of volatility in the stock returns of the petroleum marketing sector of the Nigerian Stock Exchange using ten petroleum marketing firms quoted on the Nigerian Stock Exchange for a period of twenty-four months that is from January 2017 to December 2018.
 Methodology: The study adopted empirical research design using time series data where ordinary least squares was employed to run the analysis through the use of ARCH/GARCH models.
 Findings: Among other results, it was seen that a unit increase in volatility (VLT) will lead to 0.006916 decrease in stock returns (STR). Also, the result of R-squared implies that about eight per cent (8%) of the changes in stock returns (STR) is captured by volatility (VLT) while the remaining ninety-two per cent (92%) of the variation in the model is captured by the error term. The ARCH effect observed is statistically significant. The coefficient of the GARCH effect which is significantly positive at 5% shows that past volatility of stock market return is significant and has effect on current volatility.
 Unique Contribution to theory, Practice and Policy: The implication of this is that an increase in volatility is linked to a significant increase of returns, which is an expected result and thus conforms to economic theory. The results of static and dynamic forecasting of GARCH volatility showed that the volatility is stable. As a result, investors can hold the stock. Among other things, the author recommends that Government should make sufficient regulatory effort that will improve efficiency of stocks performance and reduce volatility aimed at boosting investors’ confidence in the petroleum marketing sector and since the various ARCH and GARCH models showed volatility movement in stock returns, Nigerian government should look for new ways to diversify the economy from dependence on oil and explore other sectors like manufacturing sector and agricultural sector to reduce volatility in the economy and the overall effect on it.
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