Volatility Spillovers between World Oil Market and Sectors of BIST

Nowadays, enormous increase of production and service sectors leads to increase in demand for energy consumption. Therefore, energy and oil consumption in a variety of countries are considerably effected by energy and oil prices. International oil prices are crucial for both oil exporting countries and capital market investors as a means of volatility spillovers. This paper aims to analyze whether volatility spillovers exist between world oil market and several sector indices operating in Borsa Istanbul (BIST) 100 including energy, non-metal mineral products, and transportation using bivariate GARCH (1, 1) model. Estimation results suggest that except for non-metal mineral products sector, there are interactions between oil returns and the underlying sectors in terms of both shocks and conditional variance.


Introduction
Oil price shocks have been induced for economic recessions, financial crisis in different industries, unemployment, depression of investment through uncertainty, high inflation, low equity and bond values, trade deficits and famine.Hamilton (1983) argued that except for one, all of U.S. recessions since World War II have been taken precedence of a dramatic increase in oil crude petroleum price, typically with a lag of almost three-fourths of a year (Lizardo & Mollick, 2010).Furthermore, in the globalized era, along with the rapid increase in the information and the communication technologies, economic interaction among developed and emerging countries has been inevitable.Therefore, moving markets including oil has come into prominence as a crisis and risk transmission channel in the international arena.No doubt, this subject is more important for oil exporting countries.To this end, the crucial role of volatility spillovers revisit for investors operating in the capital markets.A recent study (Basher & Sadorsky, 2006) noticed the association between oil demand of developed and emerging countries and growth on industrial production which explicitly identifies this vital impact on modern economies.According to BP Statistical Review of World Energy (2012) data, Turkey consumes average 0.8% of the world oil annually between 2001 and 2011.During the same period; the annual oil consumption of Japan, China, India, the U.S. and the Russian Federation refers to 6%, 8.6%, 3.3%, 23.5%, and 3.2%, respectively.Statistically, the U.S. consumes nearly one-quarter of oil in the world and it is more affected by the volatility spillovers of oil prices.
The impact of the oil prices on the Turkish stock exchange index and several sub-indices (Eryiğit, 2009;Soytas & Oran, 2011;Toraman, Başarır, & Bayramoğlu, 2011) is also prominent in the existing literature.The main objective of the present paper is to explore the volatility spillovers between world oil prices and BIST 100, energy, transportation and non-metal mineral products sectors using GARCH (1, 1) model.The rest of the paper is organized as follows.Section 2 gives information about the data set and the method being used.Section 3 introduces the estimation results and discusses them in terms of implications for policy making.

Data Set
This paper utilized the data set including the daily close of the session values of BIST National Market-100 index, electricity, transportation, non-metal mineral products sub-sector indices and world oil prices between January 2, 2002 and December 31, 2012.As all the time series have a unit root, daily returns formula with respect to the existing literature can be written as where P t denotes the price index.Table 1 presents the descriptive statistics of the underlying data.As shown in Table 2, all sectors have positive average return.Moreover, since there is an ARCH effect in the time series, the application of the GARCH model is approved.p values are presented in parentheses Figure 1 illustrates the prior information about the daily returns and volatility spillovers, where clustering phenomenon was observed in parallel with the existing literature.In addition, high kurtosis values of variables in Table 1 also ensure the presence of clustering phenomenon for the underlying time series.Therefore, it can be suggested that time series have a conditional variance.
Furthermore, a simple two-equation GARCH (1, 1) vec model without exogenous influences can be illustrated as follows (Engle & Kroner, 1995): For a time period t, the log-likelihood function can be expressed where denotes the vector of all combined parameters defined in the model.Here, parameters are estimated for only variances and covariances.If the covariances (h jk,t ) are only defined by their own past values   , , j t k t   , then the number of parameters to be estimated will dramatically decrease.To this end, the diagonality is imposed on the matrices (Bollerslev, Engle, & Wooldridge, 1988).The relevant variance-covariance equations   t h are defined as the following (Engle & Kroner, 1995): In general, the number of parameters to be estimated of an N-variable vec model for each B i and C j matrices are ((1/2)N(N+1)) 2 , and (1/2)N(N+1) for diagonality.So, the total number of parameters to be estimated for a bivariate vec model as shown in Equation ( 5) and ( 6) will be twenty-two and nine for diagonality.

Results and Discussion
This paper investigates the volatility spillovers between oil market and four sectors using bivariate GARCH (1, 1) model.The relationship between oil returns and the four sectors in terms of average returns can be defined as where R 1,t and R 2,t denote oil returns and the returns of other sectors, respectively.Additionally, in Equation ( 7) and (8), t-1 and u indicate the delay and the residual, respectively.The bivariate covariance matrix can be defined as the following: In this context, a vech operator enables to transform this matrix into a single column matrix, and the final vectorial form can be described Finally, the variance-covariance structure in the underlying bivariate GARCH (1, 1) model can be written as the following: Under the assumption that u t has a conditional normal distribution, it can be estimated by the maximum likelihood method.Then, the log-likelihood will be where is assumed to combine all estimated parameters, Table 2 represents the interaction results between oil returns and the other four sectors.The convenient average and variance diagonal GARCH (1, 1) equations with respect to the corresponding parameters in Table 2, can be written as the following: Average Equations (Oil-BIST 100): Variance Equations (Oil-Non-Metal Mineral Products): Variance Equations (Oil-Transportation): For all four models being fitted, present returns of every sector were significantly affected by their own past returns.Furthermore, the relevant conditional variances were also affected by both their own past shocks and past conditional variances.In this manner, it can be suggested that volatility spillover of oil prices would play an important role on determining the future oil prices.Particularly, this situation depends on the degree of possible future shocks and volatility.Therefore, future behavior of volatility of variance will inevitably shaped by the oil production or demand.This is also valid for BIST100 and the other three sub-sectors, where their conditional variances are effected by both their own shocks and conditional variances.This interaction means that present returns may be affected by past shocks and variance volatility.Another important evidence is the significant joint conditional shocks and volatility between oil returns and electricity and transportation sectors, although no significant interaction was determined between oil returns and returns of non-metal mineral products.However, there was an interaction between oil returns and BIST100, but relatively weak interaction was observed in terms of volatility.It can be noticed that all sectors including oil returns were positively affected by their shocks and their conditional variances, which demonstrates the non-negativity of variances and a positive change will reflect the present the conditional variance in the same way.Although negative interaction was also observed, conditional variance shocks of mutual interactions and the corresponding changes on conditional covariances generally positively reflected the present covariance of returns.The analysis results may provide information for current investors to minimize their portfolio risks with respect to these interactions between oil returns and the underlying sectors.

Figure 1 .
Figure 1.Daily oil returns and BIST 100, electricity, transportation, and non-metal mineral products indices

Table 2 .
Bivariate GARCH (1, 1) model estimation results between oil returns and BIST100, electricity, transportation, and non-metal mineral products sectors