MSc Business Economics
Finance Track
Master Thesis
How does the oil price risk influence stock returns in
five different countries?
Name: Qibei Qian
Student number: 11127643
Supervisor: Dr. L. Zou
Date: July 7
th, 2016
Abstract
This paper analyzes the influence of oil price shocks on stock returns in the United States, Norway, Russia, Brazil and China. Using the data from December 29th, 2009 to April 29th,
2016, the coefficients of oil price risk is found to make different contribution in the international multi-‐factor pricing model. This paper analyzes the correlation from the perspective of five typical countries and contributes economic explanation about the abnormality to the previous literatures.
Key words: Stock market risk, Oil price risk, Multi-‐factor pricing model
Content
1 Introduction ... 4
2 Literature Review ... 8
3 Methodology ... 13
4 Data and Descriptive Statistics ... 18
5 Empirical Results ... 23 6 Conclusion ... 36 Reference ... 38
1 Introduction
After World War II, petroleum took the place of coal and became the most important industry materials in the development of the modern industry. Countries which are rapidly developing are in vast demand of oil. For example, China became one of the net importer countries of crude oil in 1993 and overtook Japan to be the world’s second-‐largest consumer of oil in 2003. Table 1 and Table 2 respectively show the data of oil production and
consumption of the major regions over the world and the data of five selected countries in this thesis. Although world oil production is less than the world oil consumption in 2015, the growth of the world oil production notably exceeded the growth of the world oil
consumption in 2015 for a second consecutive year. Oil production in the North America region increased most (43.5%) over the past ten years, and the oil production of the Middle East increased most (5.4%) during the year. Oil consumption of the Asia Pacific region increased most (4.1%) in the past year while oil consumption of Brazil and China, two important developing countries were chosen as the objects of this paper, increased most over the ten years (48.7% and 73.4%). The oil consumption of the United Stated decreased 6.8% over the last ten years, which may because of the improvement in energy efficiency or the transformation of energy sources. The rapid development of new technology companies like Tesla is a good example to explain this. On the contrary, as mentioned by Bhar and Nikolova (2009), economies of emerging countries are in great demand of energy as they are experiencing a rapid economic growth as well as their inefficiency in energy using. In general, the global oil consumption increases by 1.9 million barrels per day, almost doubling the 10-‐year average amount. It is worth mentioning that the Asia Pacific contributed 74% of the 1.9 million, while China once again accounted for the largest national increase of the growth of global oil consumption (770 thousand barrels per day).
Table 1
Oil: Production in thousands of barrels per day
Region 2010 2011 2012 2013 2014 2015 2015 share of total Change 2014 -‐ 2015 Change 2005 -‐ 2015 North America 13,843 14,310 15,535 16,934 18,786 19,676 20.9% 4.7% 43.5%
South and Central America 7,348 7,401 7,322 7,344 7,605 7,712 9.1% 1.5% 5.2%
Europe and Eurasia 17,699 17,390 17,124 17,166 17,206 17,463 19.4% 1.4% -‐0.3%
Middle East 25,827 28,160 28,532 28,181 28,557 30,098 32.4% 5.4% 17.8% Africa 10,142 8,548 9,327 8,711 8,371 8,375 9.1% 0.1% -‐14.6% Asia Pacific 8,424 8,287 8,378 8,254 8,310 8,346 9.1% 0.5% 4.6% World 83,283 84,097 86,218 86,591 88,834 91,670 100.0% 3.2% 11.9% Selected Countries United States 7,550 7,853 8,883 10,059 11,723 12,704 13.0% 8.5% 84.1% Brazil 2,137 2,193 2,149 2,114 2,346 2,527 3.0% 7.9% 47.5% Norway 2,136 2,040 1,917 1,838 1,889 1,948 2.0% 3.2% -‐34.2% Russian Federation 10,366 10,518 10,639 10,779 10,838 10,980 12.4% 1.2% 14.4% China 4,077 4,074 4,155 4,216 4,246 4,309 4.9% 1.5% 18.3%
Source: BP Statistical Review of World Energy, June 2016 (www.BP.com)
Table 2
Oil: Consumption in thousands of barrels per day
Region 2010 2011 2012 2013 2014 2015 2015 share of total Change 2014 -‐ 2015 Change 2005 -‐ 2015 North America 23,518 23,330 22,926 23,365 23,418 23,644 23.9% 0.9% -‐5.9%
South and Central America 6,384 6,624 6,782 7,035 7,190 7,083 7.5% -‐2.1% 32.8%
Europe and Eurasia 19,223 19,075 18,605 18,372 18,266 18,380 19.9% 0.4% -‐9.1%
Middle East 8,201 8,455 8,770 9,011 9,353 9,570 9.8% 2.1% 45.5% Africa 3,486 3,413 3,579 3,678 3,763 3,888 4.2% 3.2% 33.3% Asia Pacific 27,954 28,893 30,001 30,588 31,119 32,444 34.7% 4.1% 32.1% World 88,765 89,790 90,663 92,049 93,109 95,008 100.0% 1.9% 12.1% Selected Countries United States 19,180 18,882 18,490 18,961 19,106 19,396 19.7% 1.6% -‐6.8% Brazil 2,721 2,842 2,905 3,106 3,242 3,157 3.2% -‐4.2% 48.7% Norway 235 239 235 243 232 234 0.2% 0.7% 4.5% Russian Federation 2,878 3,074 3,119 3,145 3,255 3,113 3.3% -‐5.2% 17.6% China 9,436 9,791 10,229 10,732 11,201 11,968 12.9% 6.3% 73.4%
Source: BP Statistical Review of World Energy, June 2016 (www.BP.com)
Compared to other commodities, petroleum plays such a crucial role in promoting the economic development all over the world, especially in developing countries. Changes in oil price always influence the global economy, which could be reflected in the stock markets. Arouri et al. (2012) attributes the impact of oil price changes on the stock market to the high fluctuations of oil price. Driesprong et al. (2008) thoroughly analyze the relationship
between changes in oil price and stock returns of several important stock markets in the world and conclude that changes in oil price could be used to forecast the stock market returns on a global scale, especially in developed countries.
On February 16th, the four oil-‐producing countries, Saudi Arabia, Russia, Venezuela and
Qatar proposed an accord to freeze oil output and tackled a global surplus. In the following several days, both S&P 500 Index and SSE Composite Index increased a little. The oil price and the stock prices in the United States, Norway, Russia, Brazil, and China are shown in the following Picture 1. We could observe that there exists similar fluctuation after the sharp decrease in oil price in the middle of the 1000th and the 1500th observations.
Picture 1
Stock price volatility is influenced by several economic factors: macroeconomic factors, macro-‐political factors, microeconomic factors and market factors. Fluctuation in oil price could be driven by political factors, wars, and other force major in the short term. Economic factors, such as supply and demand, would affect oil price in the long term. From the oil-‐demanding side, the United States plays the most important role in influencing the oil price, as it is the largest oil-‐importing country. From the oil-‐supplying side, the limited oil production settled by the Organization of Petroleum Exporting Countries (OPEC)
straightforwardly affects the oil price. Generally speaking, an increase in oil price would increase the manufacturing cost of the company, then decrease the operating achievement, as well as the profit, and finally, reduce the stock price. The impact on the stock price comes from 1) the declines in the market value of an investment, and 2) the declines in expected stock returns, making investors have less enthusiasm towards stock market. However, as shown in the images above, there exists a probability that the oil-‐stock correlation is positive. The reason might be that both oil and stock are responding to shifts in the global demand. The relationship between oil price changes and stock returns has been discussed for several years.
This thesis is going to study the extent to which daily stock returns are correlated with changes in oil price, with the period from December 29th, 2010 to April 29th, 2016. I would
use the methodology of Basher and Sadorsky (2009) to examine the relationship in five different countries, the United States, Norway, Russia, China, and Brazil. The reason that I choose these five countries is that both China and Brazil are developing countries while the other three are developed countries. The United States, China, and Brazil are oil-‐importing countries while the Norway and Russia are oil-‐exporting countries. These five countries are different but typical in the corresponding continent. As far as I know, Russia, Brazil, and China are seldom examined in the previous literature. The United States and Norway are settled as study objects for a long period, thus in this paper, the conclusion of the study on the other three immature stock markets could be compared to the results of the two mature stock markets of U.S. and Norway.
This thesis would give a macroscopic relationship between changes in oil price and changes in stock price within the five different but typical countries. The results complement Basher and Sadorsky (2006) from the perspective of different countries and the latest data. This study would benefit individual and institutional investors who are interested in the emerging stock markets like Russia, Brazil, and China. Together with the economic
explanation, this thesis would contribute to the previous articles which mainly analyzed the developed countries in the early years.
The rest of this paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces the methodology. Section 4 presents the data. Section 5 discusses the empirical results from this analysis. Section 6 concludes the whole thesis.
2 Literature Review
At first, a famous study of Hamilton (1983) shows that almost each economic depression is related to oil production and oil price after the World War II in the United States. Mork (1994) then proves that there exists a distinct and negative relationship between the oil price and industrial production. The oil price also negatively correlates to the employment rate. Later on, many studies investigate the relationship between oil price and stock price. Chen et al. (1986) firstly state that any systematic variable that either influences the pricing operator or affects the dividends would have an impact on stock returns. Oil price is one of the systematic factors. According to the efficient-‐market theory and asset pricing theory, an increase in oil price would directly or indirectly increase the production cost of a certain firm and then influence the future cash flows and finally, affect the stock price. Changes in oil price would correlate with changes in stock prices, if both the futures market of oil and the stock market are efficient enough (Huang et al., 1996). If the market is not efficient enough, there might be lagged effect of changes in oil price on changes in stock price. On the other side, an increase in the oil price would raise the consumption cost of consumers and decrease their disposable income from the demand side. However, Chen et al. (1986) conclude that the changes in oil price have no overall effect on the return of an index, while interest rate and bond yield curve are found to be significant factors in influencing the stock returns. This statement leads to a lot of debates on the effect of oil price on stock markets.
Most of the researches about the impact of oil price shocks on financial markets are based on the stock market of the United States. Jones and Kaul (1996) mainly examine the reaction of stock markets to oil shocks in the postwar period (from 1947 to 1991) and conclude that in the United States and Canada, the reaction could be explained by changes in real cash flows and changes in expected returns. In this research, Jone and Kaul (1996)
employ both current and three lagged terms of the change in the oil price as the
independent variable and find that changes in oil prices have a negative effect on real stock returns. Unlike Jones and Kaul (1996), who use the quarterly data and choose the Producer Price Index for fuel as the proxy of oil price in the regression, Huang et al. (1996) employ daily data (from 1979 to 1990) of stock prices and oil futures prices of the United States and conclude that the oil futures returns have little correlation with stock market returns, and the correlation of the volatility of the two returns are not significant either. They undertake the lead-‐lag VAR (Vector Autoregression) model to study the relationship between oil futures return and stock return, choosing the interest rate as the control variable. They also surprisingly find the first order lag term of oil futures return is statistically significant in the regression, implying the inefficiency of the market. The lead-‐lag VAR model helps to examine the interaction of the time series which consist of oil futures returns, stock returns and interest rates. Similar to Chen et al. (1986), interest rate, which here the authors choose the 3-‐month T-‐bill returns as a proxy, is employed as the control variable to test the relative relationship between changes in oil futures price and stock returns. The authors finally conclude that there exists a leading relationship or a Granger causality of the oil futures returns on stock returns of oil companies. However, there exist no such relationship between oil futures returns and broad market indices. Sadorsky (1999) uses the monthly data (from 1947 to 1996) of the United States and the VAR model to investigate the interaction between oil prices and economic variables including stock return. The author also employs the GARCH (Generalized Autoregressive Conditional Heteroskedastic) model to examine the oil price volatility and finally concludes that changes in oil prices negatively influence stock return, not vice versa. In dealing with the data, Sadorsky (1999) tests the stationarity of the time series and proves the volatility of oil price shocks affects the economy asymmetrically. Kilian and Park (2009) develop a new SVAR (Structural Vector Autoregression) model, instead of the traditional VAR model, to overcome one limitation of the previous literatures and firstly prove that the respond of real stock returns to the shocks of oil prices varies significantly, depending on whether the change of oil price is driven by the demand shock or the supply shock in the oil market of the United States. So that the investment decisions on portfolio should be adjusted in response to oil shocks, according to
the underlying cause of the oil price changes. The authors mention that an unexpected global economic expansion would boost the oil price, and it would have a consistent positive effect on the cumulative stock returns. The article takes the political disturbances in the Middle East into consideration when examines the oil shocks.
There are also many other types of research which examine the relationship between changes in oil prices and changes in stock prices in the developed countries other than the United States. For example, Park and Ratti (2008) estimate the dynamic impact of the oil price volatility on the stock returns of the United States and other 13 European countries to examine the world stock markets, using the VAR model with the monthly data from 1986 to 2005. The authors find that oil price shocks affect real stock returns contemporaneously and / or within the next month. That is, there exist lagged effect of oil price shocks on stock returns. For many of the 13 European countries, the relationship between the volatility of oil price and stock return proves to be negative within the following month. However, in the examination of Norway, it shows a statistically significantly positive reaction of real stock returns to the increase in oil price. The conclusion of the United States in this article is quite similar to Sadorsky (1999). Finally, the authors mention that the asymmetric effects of positive and negative oil price shocks on stock returns are found in the markets of the United States and Norway among all the study objectives. Faff and Brailsford (1999) uses monthly data from 1983 to 1996 and an augmented market model to examine the sensitivity of stock returns to oil prices in Australia on the industry level. They find changes in oil price significantly positively affect the stock price of oil-‐supply industries (the Oil and Gas Industry and the Diversified Resources Industry) but negatively affect the stock returns of oil-‐demand industries (the Paper and Packaging Industry and the Transportation Industry). They also mention that some firms may pass changes in oil price to customers or hedge the risk of oil price changes.
While lots of papers focus on the developed countries, some studies of stock markets in developing countries are just being done in recent years. Bhar and Nikolova (2009)四个国家 examine the impact of oil prices on stock returns and stock volatility in four emerging countries, Brazil, Russia, India, and China. The article proves that the level of impact of oil price changes on stock returns and volatility in these four countries is determined by the
degree to which the country is a net importer or a net exporter of crude oil. Ono (2011) find the effect of oil price on stock returns is statistically insignificant in Brazil. Hammoudeh and Choi (2006) use the weekly data from 1994 to 2004 and the Vector Error Correction (VEC) model to examine the relationship between six countries (the United Arab Emirates, Bahrain, Kuwait, Oman, Qatar and Saudi Arabia) of the Gulf Cooperation Council (GCC) and three global factors (oil price, S&P 500 index and T-‐bill rates), and conclude that most GCC markets would benefit from the positive shocks of oil price. Using the daily closing prices of 21 emerging markets from 1992 to 2005, Basher and Sadorsky (2006) use an international multi-‐factor model, an improvement of the Capital Assets Price Model (CAPM), and uniquely include both conditional and unconditional risk factors to examine the relationship between the movement of oil price and stock returns and find that oil price risk did significantly affect stock returns in the emerging markets of 21 countries. The authors also take account of the skewness and kurtosis as additional risk factors. This paper firstly uses the multi-‐factor model to represent a comprehensive study of how oil price risk affect the emerging market returns. However, the countries examined in the article do not include China and Russia, because the data of these two countries is not as many as other selected countries.
Some articles make a comparison between the oil-‐importing countries and the oil-‐exporting countries, paying less concentration on the difference between developed countries and developing countries. Generally speaking, increases in crude oil price may positively affect the economy of oil-‐exporting countries. Bjørnland (2009) concludes that a 10% increase in oil price would cause a 2.5% increase in stock price in Norway, a developed oil-‐exporting country, using the structural VAR model the linear and non-‐linear specifications in the robustness test. Park and Ratti (2008) prove that the increase in oil price significantly and positively affects the stock return. However, the conclusion is opposite to some oil-‐importing countries. By tests for asymmetric effect and nonlinear Granger causality, Wang et al. (2013) find the correlation between oil price shocks and stock returns are nonlinear and use the VAR model to inspect the dynamic linkages. They adopt the structural VAR model from Kilian and Park (2009) and conclude that the different effect of oil price shocks on stock return depending on whether the oil price shock is caused by oil-‐demand or oil-‐supply. Jung and Park (2011) study the oil demand and supply shocks on stock markets in
Norway and Korea and find the impacts on oil-‐exporting and importing countries are heterogeneous. However, most paper focus only on Norway and seldom involves other oil-‐exporting countries (Wang et al., 2013). Little attention has been paid to the newly industrialized economies in examining the effect of crude oil price changes on stock markets (Lin et al., 2014). Russia is one of the biggest oil-‐producing countries and owns most reserves of natural gas in the world. However, it is seldom studied in the existing literature.
In studying the impact of oil price shocks on stock return in China, Jin and Jin (2010) employ a two-‐factor GED-‐GARCH(1,1)-‐M model with data from 2001 to 2009, and analyze the effect of the international oil price on stock returns from 14 Chinese industries, and find that the reactions of each industry to the changes in oil price are quite different. For
example, changes in oil price positively affect the stock returns in the Oil & Gas Industry but negatively affect the Auto Industry, Construction & Materials Industry, Finance Industry, Travel & Leisure Industry and etc., and have no significant influence on stock returns in some other industries. Zhu et al. (2015) also investigate the correlation between changes in crude oil price and returns of the stock market of China on the industry level. Using the monthly data from 1994 to 2013, the authors divide the driving factors of oil price changes into cost-‐side and demand-‐side and conclude that the sensitivity to changes of oil price differs according to different industries. The article takes structural breaks and asymmetric effects into consideration. Lin et al. (2014) use the structural vector autoregressive model (SVAR) of Kilian and Park (2009), with the monthly data from 1997 to 2008, to examine the dynamic impact of oil price shocks on the stock market of the mainland of China. The authors prove that the influence of oil price shocks on stock price in China’s stock market mixes. The conclusion is quite different from the conclusion of the United States from Kilian and Park (2009). This article implies that the stock market of China is to some extent insulated from crude oil market and is just partially integrated with stock markets of other countries and the world economy, which occurs because of China’s unique regulatory environment or the rapid economic growth of China.
As mentioned above, there are already lots of arguments about the relationship between oil price and stock price. But most existing articles take the developed countries as the objects of study and analyze the effect of oil shocks on the stock market. China could be
quite different with these countries, not only because China is one of the most important developing countries, but also because of its great demand of oil since it joined the WTO in 2001 and its rapid growth of each industry. Moreover, this paper would include other four countries: 1) the United States, which is one of the biggest oil-‐importing developed
countries and is being examined from decades ago till now, could be used as the controlled object in this thesis; 2) Norway, one of the biggest oil-‐exporting developed countries, is famous for its geographical position in North part of Europe and is being studied for several times because of its uniqueness; 3) Russia, the largest oil-‐export country other than the Organization of Petroleum Exporting Countries (OPEC); 4) Brazil, one of the most important emerging countries and a typical developing country in the South America, ranks the 18th of
oil-‐importing country in the world (according to the Wikipedia) and is worth studying. Oil-‐exporting countries are more likely to benefit from the increase in oil price, while oil-‐importing countries would suffer more if the oil price increases. As far as I know, these five countries have never been examined together before. The research focused on the five different (oil-‐importing versus oil-‐exporting and developing versus developed) countries would provide a broad variety of evidence in different parts of the world and explain the correlation analysis better.
3 Methodology
The capital asset pricing model (CAPM), which is developed by William Sharpe (1964), John Lintner (1965), Jack Treynor (1961) and Jan Mossin (1966) based on the modern portfolio theory (MPT) by Harry Markowitz (1952), is used determine the theoretical
expected rate of return of an asset. The relationship of the expected rate of return (𝐸 𝑟# ) of
asset 𝑖 and the expected rate of return of the market portfolio (𝐸 𝑟% ) is
𝐸 𝑟# − 𝑟' = 𝛽#% 𝐸 𝑟% − 𝑟' (1)
𝛽#% denotes the sensitivity of the expected excess return of the asset to the expected
excess return of the market portfolio, 𝑟' denotes the risk-‐free rate, 𝐸 𝑟% − 𝑟' denotes
the market premium, and 𝐸 𝑟# − 𝑟' denotes the risk premium of the asset. However, the
Fama-‐French three-‐factor model is derived. The Fama-‐MacBeth regression, which works with panel data, is put forward by Fama and MacBeth (1973). The regression consists of two steps. First, the CAPM is employed for each asset to determine the asset’s beta for that risk factor. Second, all asset returns are regressed to the estimated betas to obtain the risk premium for each risk factor for a fixed period. However, this methodology omits the estimation error in the first step, which would lead to errors in the second step. Pettengill, Sundaram, and Mathur (1995) employ a conditional approach to separate positive and negative market returns to examine the difference between the expected and realized returns. A conditional relationship between realized returns and beta is determined by the sign and magnitude of the excess market returns. The relationship should be positive (negative) if the excess market returns are positive (negative).
Basher and Sadorsky (2006) derives a combination of the CAPM, which focuses on the market risk, and an international multi-‐factor model, including unconditional and conditional approaches. Both of the two models are linear. Following the methodology of Basher and Sadorksy (2006), this thesis is going to study the relationship between the stock returns of the five selected countries and three various risk factors. The empirical regression is separated to steps: 1) the time-‐series rolling regression to obtain the risk factors; 2) the cross-‐sectional regression of risk factor and excess stock returns. The advantage of the rolling regression over the standard ordinary least squares in the first step is that it could capture the potential instabilities in the coefficients of the model.
3.1 Time-‐series rolling regression
A time-‐series rolling ordinary least squares regression estimation is employed to estimate the following multi-‐factor model, in which the daily excess return of the stock market depends linearly on three risk factors: daily excess stock returns of the world stock market, returns of oil price and daily changes in the global exchange rates. Betas of the world stock market, betas of the oil prices and betas of exchange rates are estimated from the following model.
𝑅#+ = 𝛼 + 𝛽#+%𝑅
%++ 𝛽#+/#0𝑂𝐼𝐿++ 𝛽#+45𝐸𝑋𝑟++ 𝜀#+ (2)
In equation (2) 𝑅#+ denotes the daily excess return of the stock market of country 𝑖 at
return of the oil price, and 𝐸𝑋𝑟+ denotes the return of exchange rate (the fluctuation in
exchange rate). 𝛽#+%, 𝛽#+/#0 and 𝛽#+45 respectively denotes the sensitivity of the daily excess
market returns of country 𝑖 to 𝑅%+, 𝑂𝐼𝐿+, and 𝐸𝑋𝑟+. It is assumed that 𝜀#+, which
denotes the residuals, is independently and identically distributed with the mean of zero and the variance of 𝜎:.
The time-‐series rolling ordinary least squares regression estimation is employed to estimate equation (2) for each country. The rolling fixed window length is predetermined to 500 trading days, approximates trading date of a 2-‐year period. In each estimation step, ordinary least squares regression is employed, and the corresponding coefficients of the multi-‐ factor model (the constant, the world stock market beta, the oil price beta and the exchange rate beta) are recorded. Then one observation is advanced at a time, and the model is re-‐estimated again, keeping the same window length. The repeated regression stops when the last observation is regressed. As mentioned by Basher and Sadorsky (2006) that the empirical results are reasonably robust to small changes, the 2-‐year window length is chosen in this paper. By the rolling regression, the structural shocks do not have the lasting effect through the whole data range.
From the rolling regression approach, the time series of the betas of world stock market (𝛽#+%), the betas of oil price (𝛽#+/#0) and the betas of the weighted exchange rate (𝛽#+45) are
obtained for the five selected countries.
3.1 Cross-‐section regression
3.2.1 Unconditional and conditional regression
The cross section analysis could be implemented by the ordinary least square (OLS), on the basis of the dataset of daily excess stock returns of each country and the risk parameters (sensitivities) obtained in 3.1. The regression is as follows.
𝑅#+ = 𝛾<+ 𝛾%𝛽#,+>?% + 𝛾
/#0𝛽#,+>?/#0 + 𝛾45𝛽#,+>?45 + 𝜀:+ (3)
Equation (3) represents an unconditional model, examining the relationship between the daily stock returns and risk parameters. It should be noticed that the one-‐period lagged value of each risk parameter is employed to explain the daily excess return of the stock market, in order to better reflect the volatility effects of the risk factors on the stock market.
Following Pettengill et al. (1995) and Basher and Sadorsky (2006), the conditional relationship between excess returns of the stock market and risk factors is taken into consideration, to examine the daily excess stock returns in bullish and bearish markets more accurately. From Sadorsky (1999), Park and Ratti (2008) and Zhu et al. (2015), changes in oil price also have asymmetric effects on stock returns. The unconditional approach is modified to the conditional approach as follows.
𝑅#+ = 𝛾<+ 𝛾%@𝐷+>?% 𝛽#,+>?% + 𝛾%> 1 − 𝐷+>?% 𝛽#,+>?% + 𝛾/#0@ 𝐷+>?/#0𝛽#,+>?/#0
+𝛾/#0> 1 − 𝐷+>?/#0 𝛽#,+>?/#0 + 𝛾45𝛽#,+>?45 + 𝜀C+ (4)
In Equation (4), the dummy variable 𝐷+>?% takes the value of 1 (0), indicating that the
daily excess return of world stock market is positive (negative). Thus by Pettengill et al. (1995), 𝛾:%@ and 𝛾:%> are reasonably expected to have positive and negative signs
respectively. Similarly, the dummy variable 𝐷+>?/#0 takes the value of 1 (0), indicating that
the return of oil price is positive (negative). 𝛾/#0@ and 𝛾/#0> are expected to have positive
and negative signs for an oil-‐exporting country and to have the inverse signs for oil-‐importing countries.
𝑯𝟎𝟏: 𝛾
:%@+ 𝛾:%>= 0, symmetry between up and down world stock markets;
𝑯𝟏𝟏: 𝛾
:%@+ 𝛾:%>≠ 0, asymmetry between up and down world stock markets.
𝑯𝟎𝟐: 𝛾
/#0@ + 𝛾/#0> = 0, symmetry between up and down oil changes;
𝑯𝟏𝟐: 𝛾/#0@ + 𝛾/#0> ≠ 0, asymmetry between up and down oil changes.
3.2.2 Unconditional and conditional regression with the total risk factor
In the capital asset pricing model (CAPM), market risk (systematic risk) is the risk that affects all investments, most of which are either economic or politic (e.g. recession, interest rate etc.). However, systematic risk cannot be diversified if the investor invests in distinct assets. Diversifiable risk (unsystematic risk), on the other hand, is more firm specific (e.g. lawsuits, labor trouble etc.). The sum of systematic risk and unsystematic risk is known as the total risk. When making investment decisions, investors are suggested to pay attention to the total risk of the certain asset. Standard deviation is one of the commonly used measurements of risk. In this thesis, the variance of the daily market returns is employed as the total risk (𝑇𝑅#,+>?) for country 𝑖. 𝑇𝑅#,+>? is gathered based on the same rolling
models including the total risk factor are displayed as follows. The hypotheses are the same as hypotheses in 3.2.1.
𝑅#+ = 𝛾<+ 𝛾%𝛽#,+>?% + 𝛾 /#0𝛽#,+>?/#0 + 𝛾45𝛽#,+>?45 + 𝛾+L𝑇𝑅#,+>?+ 𝜀M+ (5) 𝑅#+ = 𝛾<+ 𝛾%@𝐷 +>?% 𝛽#,+>?% + 𝛾%> 1 − 𝐷+>?% 𝛽#,+>?% + 𝛾/#0@ 𝐷+>?/#0𝛽#,+>?/#0 +𝛾/#0> 1 − 𝐷 +>?/#0 𝛽#,+>?/#0 + 𝛾+L@𝐷+>?% 𝑇𝑅#,+>?+ 𝛾+L> 1 − 𝐷+>?% 𝑇𝑅#,+>? (6) +𝛾45𝛽#,+>?45 + 𝜀N+
3.2.3 Unconditional and conditional regression with skewness and kurtosis
Skewness and kurtosis indicate that the data are not normally distributed, which are significantly important to financing and investing. So that more and more advanced economic analysis models examine the skewness and kurtosis of the data (Harvey and Siddique, 2000 and Bekaert et al., 1998). Skewness is used to measure the asymmetry of the probability distribution around the mean. Positive (negative) skew indicates the tail on the right (left) side is longer or fatter than the left (right) side. Kurtosis (the volatility of volatility) measures whether the data are heavy-‐tailed or light-‐tailed compared with a normal
distribution. The distribution of data tends to have fat (thin) tails if the kurtosis is more (less) than three. Generally speaking, most investors are risk-‐averse. With the mean and variance constant, investors prefer portfolios with positive skewness (mean is larger than median) because of the large chance of small loss and the small chance of large gain. Assets with lower kurtosis are preferable because higher kurtosis indicates more likelihood of either extremely large or extremely small returns of the portfolios. The following equation (7) and (8) respectively express the model conditional and unconditional relationship between the daily stock returns and risk, including the explanatory variable of skewness.
𝑅#+ = 𝛾<+ 𝛾%𝛽#,+>?% + 𝛾/#0𝛽#,+>?/#0 + 𝛾45𝛽#,+>?45 + 𝛾OP𝑆𝐾𝐸𝑊#,+>?+ 𝜀T+ (7) 𝑅#+ = 𝛾<+ 𝛾%@𝐷 +>?% 𝛽#,+>?% + 𝛾%> 1 − 𝐷+>?% 𝛽#,+>?% + 𝛾/#0@ 𝐷+>?/#0𝛽#,+>?/#0 +𝛾/#0> 1 − 𝐷 +>?/#0 𝛽#,+>?/#0 + 𝛾OP@𝐷+>?% 𝑆𝐾𝐸𝑊#,+>?+ 𝛾OP> 1 − 𝐷+>?% 𝑆𝐾𝐸𝑊#,+>? (8) +𝛾45𝛽#,+>?45 + 𝜀U+
Equation (9) and (10) are the conditional and unconditional relationship incorporating the kurtosis.
𝑅#+ = 𝛾<+ 𝛾%𝛽#,+>?% + 𝛾/#0𝛽#,+>?/#0 + 𝛾45𝛽#,+>?45 + 𝛾PV𝐾𝑈𝑅𝑇#,+>?+ 𝜀X+ (9)
+𝛾/#0> 1 − 𝐷+>?/#0 𝛽
#,+>?/#0 + 𝛾PV@𝐷+>?% 𝐾𝑈𝑅𝑇#,+>?+ 𝛾PV> 1 − 𝐷+>?% 𝐾𝑈𝑅𝑇#,+>? (10)
+𝛾45𝛽#,+>?45 + 𝜀
Y+
Here 𝑆𝐾𝐸𝑊#,+>? and 𝐾𝑈𝑅𝑇#,+>? are respectively the relative skewness and kurtosis
risk factors and are obtained in the same way as the total risk factor (𝑇𝑅#,+>?) in 3.2.2. The
hypotheses are the same as hypotheses in 3.2.1. The model including all the risk factors is not favorable because of the multicollinearity across the different risk factors.
4 Data and Descriptive Statistics
The variables constructing this paper consist of 1) daily closing oil price; 2) daily closing stock index prices of five selected countries (United States, Norway, Russia, Brazil and China); 3) daily closing prices of the world index; 4) trade weighted exchange rate; 5) the
three-‐month Treasury Bills rate.
The dataset covers the period from December 31, 2006, to April 29, 2016, for a total of 1652 daily observations. The data from 2008 to 2009 are excluded to get rid of the
unexpected impact of the Global Financial Crisis on the relationships between oil market and the stock market. Compared to Basher and Sadorsky (2006), a shorter but more recent dataset is emoloyed in this paper.
4.1 Daily return of oil price
As several existing articles (Hammoudeh and Choi, 2006; Jin and Jin, 2010 and Zhu et al.,2015) indicate that West Texas Intermediate (WTI), which is the underlying commodity of New York Mercantile Exchange’s (NYMEX) oil futures contracts, is a grade of crude oil used as a benchmark in oil pricing. This paper also employs the daily closing price of WTI crude oil futures contract as the proxy of oil price. The data could be gathered from the FRED
Economic Data1. Daily oil returns (𝑂𝐼𝐿
+) are presented as the log difference2 in oil prices
(𝑃𝑂+), which is expressed as dollars per barrel.
𝑂𝐼𝐿+ = ln ]^]^_`a_ ×100% = ln 𝑃𝑂+− ln 𝑃𝑂+>? ×100% (11)
1 https://research.stlouisfed.org/fred2/series/DCOILWTICO/downloaddata 2 The log change is more precise than the percentage change: ∆ ln 𝑋
4.2 Daily return of stock price
The data for this paper consist of the daily closing index prices of five selected countries (the United States, Norway, Russia, Brazil, and China) and the World Index (𝑊𝐼#+) of the
Morgan Stanley Capital International (MSCI). The proxy of index stock price of each country is listed in Table 3. The available data could be collected from DATASTREAM.
Table 3
Proxies of stock price of selected country Country Index
Currency
United States S&P 500 Standard and Poors (S&P) US Dollars
Norway OSEAX Oslo Exchange All-‐Share Index Norwegian Krone
Russia MICEX
Russian Ruble
Brazil BOVESPA Sao Paulo Stock Exchange Brazilian Real
China SSE Shanghai Stock Exchange Composite Index Chinese RMB
The daily closing index prices are presented in the country’s home currency. So in order to avoid the impact of the currency risk as well as benefit the investors who own U.S. dollar to trade, all the index prices are converted to U.S. dollar by merging and calculating with the daily exchange rates in STATA. The exchange rates of the five countries over the period are available on DATASTREAM. 𝑃𝑆#+∗ represents the stock index in the form of each home
country’s currency at time 𝑡. 𝐸𝑋#+ represents the value of one U.S. dollar in terms of the
currency of country 𝑖 at time 𝑡. Calculating by the following formula, stock index prices settled in dollars of country 𝑖 are obtained.
𝑃𝑆#+ = 𝑃𝑆#+∗/𝐸𝑋#+ (12)
Then, the daily log stock returns of each country (𝑆𝑅#+) and the daily log stock return of
the world stock market (𝑆𝑅%+) are both settled in U.S. dollar.
𝑆𝑅#+ = ln ]h]hi_
i,_`a ×100% = ln 𝑃𝑆#+− ln 𝑃𝑆#,+>? ×100% (13)
𝑆𝑅%+ = ln jki_
jki,_`a ×100% = ln 𝑊𝐼#+− ln 𝑊𝐼#,+>? ×100% (14)
4.3 Risk-‐free rate
In this thesis, the rates of the 3-‐month Treasury Bills (T-‐Bills) are employed as the risk-‐free rates. As one of the most marketable money market securities which are issued by
the U.S. government, T-‐Bills are affordable to individual investors and are widely regarded as the least risky Wealth Management Products all over the world. The variable is noted as 𝑟'+
and is used for the calculation of the excess return. The data could be collected from the Board of Governors of the Federal Reserve System3.
4.4 Daily excess return
The daily excess return, the dependent variable which is indicated as 𝑅#+, is calculated
by subtracting the rate of the 3-‐month T-‐Bills (𝑟'+) from the daily log return of the stock
market index (𝑆𝑅#+) of each country 𝑖. In order to get the daily excess return of the world
index of MSCI (𝑅%+), the same procedure is taken by subtracting the rate of the 3-‐month
T-‐Bills (𝑟'+) from the daily return of the world index (𝑆𝑅%+). The daily excess return of the
world index of MSCI is regarded to be the world market excess returns in the multi-‐factor model.
𝑅#+ = 𝑆𝑅#+− 𝑟'+ (15)
𝑅%+ = 𝑆𝑅%+− 𝑟'+ (16)
4.5 Daily return of exchange rate
Adler and Dumas (1983) proves that the international investors face exchange risk if purchasing power parity is violated. While the asset pricing model requires the assumption of purchasing power parity, the exchange rate risk should be considered to be an additional risk factor as an independent variable in the international multi-‐factor asset pricing formula. Instead of the Trade Weighted U.S Dollar Index: Major Currencies (DTWEXM)4, the Trade
Weighted U.S. Dollar Index: Broad (DTWEXB)5 is chosen to approximate the exchange rate
in this thesis, because China, Brazil, and Russia are taken as study objectives. The Trade Weighted U.S. Dollar Index (TWDI) aggregates and summarizes information contained in a collection of foreign exchange rates of U.S. trading partners. The main objective of TWDI is to summarize the appreciation (an increase of the index) and depreciation (a decrease of the index) of U.S. dollar against foreign currencies. So the log change of the Traded Weighted
3 http://www.federalreserve.gov/econresdata/
4 Major currencies index includes Canada, Japan, United Kingdom, Switzerland, Australia, Sweden and the Euro
Area.
5 Broad currencies index includes countries in DTWEXM, Mexico, China, Taiwan, Korea, Singapore, Hong Kong,
Malaysia, Brazil, Thailand, Philippines, Indonesia, Israel, Saudi Arabia, Russia, Argentina, Venezuela, Chile and Colombia.
U.S. Dollar Index could be employed as the proxy for fluctuations in exchange rates (𝐸𝑋𝑟+).
The data could be collected on Federal Reserve Economic Data6.
𝐸𝑋𝑟+ = ln ljmkljmki_
i,_`a ×100% = ln 𝑇𝑊𝐷𝐼#+− ln 𝑇𝑊𝐷𝐼#,+>? ×100% (17)
4.6 Descriptive statistics
The summary of the data is provided in Table 4. The average of daily excess return in the five countries ranges from -‐0.1520% (Brazil) to -‐0.0439% (United States). All of the five selected countries have negative average daily excess stock returns. However, compared with the standard deviation, the average daily excess stock returns are quite small. Standard deviation, used as the unconditional risk measurement, shows that stock markets of all the five countries are more volatile than the world market index, because each standard deviation of the five countries is larger than the standard deviation of the world stock market (0.9154). Among the five countries, the highest level of risk is observed in Brazil, with the maximum of standard deviation (1.8968), while the United States is the least risky country, with the minimum of standard deviation (1.0049). The stock market of Russia owns the largest range of daily excess return (22.7422%) while the United States owns the
smallest one (11.5476). Skewness measures the asymmetry of the probability distribution. Statistics in Table 4 indicate that none of the daily excess stock returns follows the
symmetric distribution. The daily excess stock returns of Brazil skews to the right (the right tail is longer, and the mass distribution is concentrated on the left side) while the daily excess stock returns of the other four countries skew to the left (the left tail is longer). The statistics of kurtosis indicate the probability of appearance of extreme values in the dataset is relatively high. All the daily excess stock returns of the five countries exhibit a high degree of kurtosis, larger than three and known as leptokurtic, and indicate each one produces more outliers than the normal distribution. It could be explained that all the five stock markets have a comparatively great possibility of extremely large or extremely small stock returns, especially the stock market of China which fluctuates significantly during the chosen period. Skewness and kurtosis of stock returns are separately added into the international multi-‐factor pricing model to test whether each of those could be an additional risk factor.
