Mathieu Gomes

Volatility Spillovers Between Oil Prices And Stock Returns: A Focus On Frontier Markets

Keywords: Volatility Spillovers, Oil Prices, Stock Returns, Multivariate GARCH, Diversification, Frontier Markets 1

Frontier markets are increasingly sought by investors in search of higher returns and low correlation with traditional assets. As such, it is important for financial market participants to understand the volatility transmission mechanism across these markets in order to make better portfolio allocation decisions. This paper employs a bivariate BEKK-GARCH(1,1) model to simultaneously estimate the mean and conditional variance between equity stock markets (twentyone national frontier stock indices and two broad indicesthe MSCI Frontier Markets and the MSCI World) and oil prices. We examine weekly returns from February 8, 2008 to February 1, 2013 and find significant transmission of shocks and volatility between oil prices and some of the examined markets. Moreover, this spillover effect is sometimes bidirectional.

INTRODUCTION

rude oil is probably the physical commodity that most affects the state of the economy. This impact can take place through various paths. When crude oil prices rise, cost of production of goods and services increases, and so do transportation and heating costs. This, in turn, can lead to inflationary pressures and thus restricted consumption from consumers. This produces a negative effect to capital markets, consumer confidence, and the macroeconomy as a whole. There are thus, various theoretical reasons for which oil prices can have a significant impact on financial markets, and stock markets in particular. One of them is that the value of stock prices in equity asset valuation models theoretically equals the sum of future discounted earnings expectation of companies or future cash flows. Therefore, changes in crude oil prices can directly have an impact on stock prices through the expected cash flows on the one hand, and through the discount rate on the other hand.

The first and most intuitive way through which oil prices can affect stock prices is by the channel of expected cash flows. Oil is a crucial input in the production of goods and services, and therefore, a rise in oil prices is likely to increase production costs, which in turn will reduce margins, cash flows and thus stock prices. But oil prices can also affect stock valuations through the rate that is used to discount future cash flows. Indeed, rising oil prices can create inflationary pressures that will ultimately lead to the decision-making by central banks to tighten their monetary policies and raise interest rates. This can have tremendous implications for companies as corporate investment decisions can be affected directly by changes in the discount rate. Moreover, a change in interest rates will impact company financing through higher borrowing costs and a lower market value relative to book value, which will further damage a company's ability to raise new funds. However, it is worth noting that not all companies will react the same way to changes in crude oil prices. Indeed, the direction of stock price reactions will depend on whether the company is an oil producer or an oil consumer. Oil producers will profit from an oil price increase while oil consumers will suffer from it. Overall, since the great majority of companies are oil consumers, it is logical to expect a negative effect of oil prices on stock prices.

C

Copyright by author(s); CC-BY 510

The Clute Institute

To the better of our knowledge, no previous study has examined the effect of oil price shocks on frontier markets. Our paper aims to fill this gap by making use of a rich database and innovative econometric techniques. Section 2 discusses findings of previous works on interactions between oil prices and stock markets with a specific focus on emerging markets. Section 3 introduces the concept of frontier markets. A preliminary analysis of our database is provided in Section 4. Section 5 introduces our empirical methodology. Results are discussed in Section 6, while Section 7 concludes and gives some policy implications.

LITERATURE REVIEW

A number of research papers have explicitly examined the relationship between oil markets and economic variables, such as GDP growth rates, inflation, employment, and exchange rates [START_REF] Hamilton | Oil and the macroeconomy since World War II[END_REF]; [START_REF] Gisser | Crude oil and the macroeconomy: Tests of some popular notions: Note[END_REF][START_REF] Mork | Oil and the macroeconomy when prices go up and down: An extension of hamilton's results[END_REF][START_REF] Hooker | What happened to the oil price-macroeconomy relationship[END_REF]; among others). The impact of oil price changes on the world economy is indeed large. According to [START_REF] Adelman | The economics of petroleum supply: Papers 1962-1993[END_REF], ''Oil is so significant in the international economy that forecasts of economic growth are routinely qualified with the caveat: 'Provided there is no oil shock.''' As another proof of that importance, the International Monetary Fund (2000) estimated that a US$5 per barrel price increase had tremendous effects on the state of the economy with a reduction of global economic growth by 0.3% in the following year. Surprisingly, while understanding the relationship between oil price changes and stock markets may appear crucial to energy policy planning, energy risk management and portfolio diversification, these links have only been examined recently. [START_REF] Jones | Oil and the stock markets[END_REF] were the first to test the reaction of international stock markets (Canada, UK, Japan, and USA) to oil price shocks, based on the standard cash-flow dividend valuation model. They find that for Canada and the US, this reaction can be entirely accounted for by the impact of the oil shocks on cash flows. [START_REF] Huang | Energy shocks and financial markets[END_REF], using an unrestricted Vector Autoregressive (VAR) model, show a significant link between the stock returns of certain American oil companies and oil price changes. However, there is no evidence of a link between oil prices and market indices such as the S&P 500. In contrast, Sadorsky (1999), using a Vector Autoregressive (VAR) framework, shows that oil prices play an important role in affecting economic activity. His results also suggest an asymmetric relationship, as changes in economic activity don't seem to have an impact on oil prices. [START_REF] Ciner | Energy shocks and financial markets: Nonlinear linkages[END_REF], using non-linear causality tests, provides empirical evidence that oil shocks significantly affect stock index returns in the US in a non-linear manner, and that the returns also have impacts on crude oil futures. [START_REF] Park | Oil price shocks and stock markets in the US and 13 European Countries[END_REF] show that oil price shocks have a statistically significant impact on real stock returns contemporaneously and/or within the following month in the U.S. and 13 European countries over the period running from January 1986 to December 2005 and that Norway, as an oil exporter, shows a statistically significantly positive response of real stock returns to an oil price increase.

More recently, some studies have examined the extent of oil price impacts on stock prices from a sector-bysector perspective. For example, El-Sharif et al. (2005) show that the stock returns of UK Oil & Gas companies are positively correlated to oil price increases. [START_REF] Boyer | Common and fundamental factors in stock returns of Canadian oil and gas companies[END_REF] obtain similar results for Oil & Gas returns in Canada. Arouri and Nguyen (2010), using various econometric techniques, suggest that the sensitivity of European sector stock returns to oil price changes greatly differ from one sector to another, with Oil & Gas stocks profiting from oil price increases. Similarly, [START_REF] Arouri | Further evidence on the response of stock prices in GCC countries to oil price shocks[END_REF] show that, on the basis of short-term analysis, strong positive links are found in some GCC (Gulf Cooperation Council) countries between oil prices and stock markets, and that this causality generally runs from oil prices to stock markets.

Despite various studies focusing on price spillovers between oil and stock markets, it is only recently that some attention has been paid to possible volatility spillovers between these two markets. Using a multivariate GARCH model, [START_REF] Malik | Shock and volatility transmission in the oil, US and Gulf equity markets[END_REF] find significant volatility transmission between second moments of the US equity and global oil markets. In that same study, they find that the three examined Gulf equity markets (Bahrain, Kuwait, and Saudi Arabia) receive volatility from the oil market, with Saudi Arabia featuring an interesting characteristic, i.e. a significant volatility spillover from the Saudi equity market to the global oil market, underlining the major role played by Saudi Arabia in the global oil market. [START_REF] Agren | Does oil price uncertainty transmit to stock markets?[END_REF], using an asymmetric BEKK model, finds strong evidence of volatility spillovers (albeit relatively small) from oil prices to stock markets in Japan, Norway, the UK, and the US. [START_REF] Malik | Volatility transmission between oil prices and equity sector returns[END_REF] study volatility spillovers between oil prices and

Copyright by author(s); CC-BY 511

The Clute Institute five US equity sector indices (Financials, Industrials, Consumer Services, Health Care, and Technology) and conclude in favor of significant transmission of shocks and volatility between oil prices and some of the examined market sectors.

Using a recent generalized VAR-GARCH approach to examine the extent of volatility transmission between oil and stock markets in Europe and the US at the sector level, Arouri, Jouini, and Nguyen (2011) find evidence of significant volatility spillover. Their study suggests that the transmission is usually unidirectional from oil markets to stock markets in Europe, but bidirectional in the US. [START_REF] Chang | Conditional correlations and volatility spillovers between crude oil and stock index returns[END_REF], using various econometric models, investigate the conditional correlations and volatility spillovers between the crude oil and financial markets, and find little evidence of volatility transmission between the oil market and major stock indices (FTSE100, Dow Jones, and S&P500). These results would tend to confirm that volatility transmission between oil and stock markets only occurs in some sectors.

A FOCUS ON "FRONTIER MARKETS"

To the best of my knowledge, no research has so far been done about possible volatility transmission between oil markets and frontier markets (apart from GCC countries). The term "frontier markets" was coined by the International Finance Corporation (IFC), a private sector arm of the World Bank Group, in 1992 to reflect a subset of emerging market economies. Frontier markets are investable but have lower market capitalization (usually under 17% of GDP) and liquidity than the more developed "traditional" emerging markets, which makes them inherently riskier investments but also provides potential opportunities for investors to take advantage of privatizations and increased listings on local exchanges over time. As a result, they may also provide better returns. Investments in these markets are thus generally pursued by investors who are seeking higher returns, and who are willing to assume the higher level of risk associated with such markets. Among these risks are political instability, poor liquidity, inadequate regulation, substandard financial reporting, and large currency fluctuations. Apart from risks, investing in frontier markets is a smart diversification to an equity portfolio, as these markets have comparatively less correlation to developed markets, and in good times, can likely beat the returns of other markets.

Despite the growing attention to frontier markets among the investment community, very little research actually includes them. However, the contributions to this particular topic reach similar conclusions: frontier markets may offer promising diversification benefits due to low correlations with developed equity markets ( No official list of frontier markets countries has so far been established, but the number usually ranges between twenty-five and thirty countries. Oil economies often have the largest representation in frontier market indices. For example, five Gulf Cooperation Council (GCC) countries (Qatar, UAE, Oman, Bahrain, and Kuwait) currently make up about 60% of the MSCI Frontier Markets Index. Frontier markets are widely diverse in terms of income, geography and degree of economic development. For example, the GCC countries are among the richest economies globally on a per capita basis, while many of the key Sub-Saharan economies are among the poorest (the average GDP per capita of GCC economies is approximately $43,300 PPP while the average GDP per capita of the frontier Africa and Asia countries is under $2,000 PPP). But the middle class is growing in many frontier markets as improvements in logistics, better access to technology, the spread of mobile phones and better use of natural resources have begun to raise millions out of poverty while boosting consumption trends.

DATA SET

Equity market data are obtained from MSCI. In this paper, we use a set of data consisting of twenty-one national aggregate stock market indices (Argentina, Bahrain, Bulgaria, Jordan, Kazakhstan, Kenya, Kuwait, Lebanon, Mauritius, Nigeria, Oman, Pakistan, Qatar, Romania, Saudi Arabia, Slovenia, Sri Lanka, Tunisia, United Arab Emirates, Ukraine, and Viet-Nam) and two broader stock indices (MSCI Frontier Markets and MSCI World), together with a measure of the world oil price (Brent). All data are at the weekly frequency and cover a five-year period ranging from February 8, 2008 to February 1, 2013, yielding a total of 261 observations. We use weekly data because as suggested by [START_REF] Arouri | Oil prices, stock markets and portfolio investment: Evidence from sector analysis in europe over the last decade[END_REF], they appear to be less noisy than daily data, while still capturing much of the information content of stock indices and oil prices.

Copyright by author(s); CC-BY 512

The Clute Institute We can see from Table 1 that out of twenty-one national aggregate equity indices, seventeen display negative average weekly returns, which is not surprising given the characteristics of the covered period and the impact of the economic and financial crisis since 2008. The broader MSCI Frontier Markets index displays a negative average weekly return of -0.2289% while the MSCI World index exhibits a positive average weekly return of 0.0362%, largely driven by a recent bull market in the United States which represent the largest constituent of the index. The Brent posted an average weekly return of 0.2214% over the period.

At the country level, the highest weekly mean return is posted by the Sri Lanka stock market with a weekly average of 0.25% while the lowest average weekly return comes from Ukraine (-0.70%). The highest weekly return was posted by Sri Lanka on the week ranging from May 18, 2009 to May 22, 2009 (+42%), followed by Kazakhstan (+34% on the week ranging from October 27, 2008 to October 31, 2008).

Copyright by author(s); CC-BY 513

The Clute Institute

The lowest return comes from Bulgaria (-34%) on the week ranging from October 6, 2008 to October 10, 2008, followed by neighboring Romania (-29% on the week ranging from January 5, 2009 to January 9, 2009). The Brent gained up to 27% (from December 29, 2008 to January 2, 2009) while its biggest weekly drop was -22% (from December 1, 2008 to December 5, 2008). Over the whole period, the best performer was Sri Lanka with a 49% gain while the worst performer was the Ukrainian stock market, which lost approximately 90% of its value.

Weekly standard deviations range from 2.67% (Tunisia) to 6.16% (Argentina). The MSCI Frontier Markets index varied 2.53% while the MSCI World index and the Brent experienced volatilities of 3.28% and 5.10% respectively.

All return series display non-zero skewness and excess kurtosis. This feature associated with significant Jarque-Bera statistics, indicate that the returns are not normally distributed. Prior to estimating the conditional mean or conditional variance, it is sensible to test for unit roots in the series. Standard unit root testing procedures based on the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests are used. Table 2 features the results for levels (price series in logarithms) and first differences (return series) of oil and stock market price indices.

The results from the Augmented Dickey-Fuller (ADF) tests indicate that the price series are integrated of order one, except for the MSCI Frontier Markets Index, Pakistan, Slovenia (all of them at the 10% level) and Viet Nam (1% level) stock market prices, which are stationary. The Phillips Perron test reaches similar conclusions for Pakistan (10% level) and Viet Nam (1% level). Alternatively, all the return series do not have unit roots according to both tests (all at the 1% level).

Copyright by author(s); CC-BY 514

The Clute Institute We can see that all markets experienced increased volatility during 2008 due to the financial crisis. Overall, frontier markets appear to be very volatile with countries such as Argentina, Romania, and Ukraine featuring mean annualized standard deviations above 40.0%. However, the MSCI Frontier Markets index displays a mean weekly volatility of 2.53%, which is actually lower than the MSCI World's (3.28%). This tends to suggest that despite high individual volatilities, correlation between frontier equity markets is low.

Table 3 shows the correlation matrix for all considered markets. It tends to confirm the above statement, as correlations between frontier markets are indeed very low with an average value of 28.0%. The average correlation coefficient between frontier markets and the Brent is 27.6% while average correlation between frontier markets and the MSCI World index amounts to 37.4%. All these figures would tend to confirm the diversifying power of frontier markets stocks within a portfolio.

Correlations with oil are positive, suggesting that during the studied period, frontier stock markets moved together with oil prices. The highest correlation is between the MSCI World index and the oil market (0.5279). This result is expected because of the large proportion of American stocks within the index. The lowest significant correlation with oil market is obtained for Tunisia (0.1313).

Copyright by author(s); CC-BY 515

The Clute Institute

Copyright by author(s); CC-BY 516

The Clute Institute Before moving to the analysis of potential spillovers, it is interesting to examine short-term relationships between oil price changes and stock market returns. To do this, I perform a Granger causality test (for a lag equal to one) to examine the causal linkages between these series. Table 4 reports the results obtained. The results show that, in the short-run oil price shocks Granger-cause changes in stock market returns in, Jordan, Kenya, Lebanon, Oman, Qatar, Saudi Arabia, the UAE, and Ukraine (1%) and to some extent in Bahrain, Bulgaria, the Frontier Markets index, Nigeria (5%), and Viet Nam (10%). There is also evidence of causality from the Frontier Markets Index, Qatar and the UAE stock markets to oil prices.

METHODOLOGY

The GARCH-type approach has received a special interest from almost all previous studies dealing with volatility modeling and forecasting of commodities prices. When the aim is to investigate volatility interdependence and transmission mechanisms among different time-series, multivariate settings such as the CCC-MGARCH model of Bollerslev (1990), the BEKK-GARCH model of [START_REF] Baba | Multivariate simultaneous generalized ARCH[END_REF], or the DCC-MGARCH model of [START_REF] Engle | Dynamic conditional correlation: A simple class of multivariate GARCH models[END_REF] are more relevant than univariate models. Empirical results reported in [START_REF] Hassan | Multivariate GARCH model of sector volatility transmission[END_REF] and [START_REF] Agnolucci | Volatility In crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models[END_REF], among others, confirm the superiority of these models and show that they are able to satisfactorily capture the stylized facts of the commodity-price conditional volatility and the dynamics of volatility interaction.

The first step in the bivariate GARCH methodology is to specify the mean equation. Accordingly, the mean equations for oil and stock return series are given by:

(1) [START_REF] Agnolucci | Volatility In crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models[END_REF] where and are the returns between time t-1 and t on oil and stock series respectively, and are lagged returns on oil and stock series, and are long term drift coefficients, and and are error terms. Various models were tested to specify the mean equation (ARMA type) but the coefficients were not statistically significant so I ended up using the classical first order autoregressive model.

Copyright by author(s); CC-BY 517

The Clute Institute

In this paper, we use a bivariate GARCH (Generalized Auto Regressive Conditionally Heteroscedastic) model to estimate the conditional variance of oil and stock index returns. In addition, I employ the BEKK (named after Baba, Engle, Kraft, and Kroner, 1990) parameterization of the multivariate GARCH model, which does not impose the restriction of constant correlation among variables over time. The model addresses the difficulty with VECH of ensuring that the H matrix is always positive definite by incorporating quadratic forms.

The BEKK parameterization for the bivariate GARCH(1,1) model is represented by: [START_REF] Agren | Does oil price uncertainty transmit to stock markets?[END_REF] where the individual elements for C, A and B matrices are given as:

A = B = C =
where is the conditional variance matrix, C is an upper triangular matrix of parameters, B is a 2 x 2 matrix of parameters which depicts the extent to which current levels of conditional variances are related to past conditional variances, and A is a 2 x 2 matrix of parameters that measures the extent to which conditional variances are correlated with past squared errors. In other words, A captures the effect of shocks or events on volatility. The positive definiteness of the covariance matrix is ensured owing to the quadratic nature of the terms on the equation's right hand side.

Expanding the conditional variance for each equation in the bivariate BEKK-GARCH(1,1) model gives:

As can be seen, the conditional variance of the stock market (respectively oil market) depends not only on its own past variances and innovations, but also on those of the oil market (respectively stock market). This feature permits the direct transmission of volatility and shocks from one market to another. Overall, this model allows me to capture both return and volatility spillover effects between stock and oil markets.

Under the assumption of conditional normality, the parameters of a multivariate GARCH model can be estimated by maximizing the log-likelihood function:

where θ denotes all the unknown parameters to be estimated, N is the number of series and T is the number of observations.

EMPIRICAL RESULTS

In this section, we present in Table 5 the empirical results from estimating the bivariate BEKK-GARCH(1,1) model for all pairs of oil and stock market returns and we discuss the extent of volatility transmission. There are no reported data for Bulgaria and Romania as the model was unable to converge for these two markets. The symbols *, ** and *** indicate significance at 10%, 5%, and 1% levels respectively.

Copyright by author(s); CC-BY 518

The Clute Institute Taking a close look at mean equations, we find that the one-period lagged oil returns, denoted by coefficients, never affect current oil returns significantly. For stock returns, autoregressive coefficients are usually not significant, which is in line with the efficient markets hypothesis. Exceptions are the Frontier Markets Index, Mauritius, and Ukraine, all at the 1% level. This finding tends to suggest that for these three markets, past stock realizations have some predictive power on current stock returns, which can be explained by the emerging nature of these markets (e.g., a low level of liquidity and smaller capitalizations). The constant terms for the stock returns mean equations are only significant for Kenya and the MSCI World index (both at the 1% level).

Copyright by author(s); CC-BY 520

The Clute Institute These findings are interesting as they suggest wide bi-directional transmission of both shock and volatility between oil and some frontier stock markets, but also between oil and the MSCI World Index, which is not illogical. Indeed, Arouri et al. (2011) demonstrated that the United States, which represents the major part (53.9%) of the MSCI World Index composition, feature this bidirectional relationship between oil and stock markets. Moreover, the volatility spillover effect is often strong (usually significant at the 1% level). Regarding the direction of transmission, and coefficients with statistical significance are more numerous than their and counterparts, suggesting that spillovers from oil to stock markets are more usual than spillovers going from stocks to the oil market, which is in line with the majority of previous studies. Summarizing all, direct volatility transmission between oil and stock returns is significantly present for many of the studied markets, including the MSCI World Index. Regarding the transmission's direction, shock and volatility spillovers happen more often running from oil to stock markets than from stock markets to the oil market, but there are divergences between countries, which is something to be expected given the heterogeneity of frontier market economies.

Finally, it is important to note that the set of data analyzed in this paper pertains to a very turbulent period in financial markets and that consequently, systematic factors may have played a role and biased the spillover results to some extent as spillovers usually increase during crisis periods under the effects of important financial instability and economic uncertainties.

CONCLUSION

This paper examined the transmission of shocks and volatility between oil prices and Frontier stock markets. The statistical model includes a parameterization of the conditional variance-covariance of oil price changes and stock returns, specifically the bivariate BEKK-GARCH(1,1) model, which enables the analysis of spillovers in both returns and conditional variance. Aggregate stock market data representing twenty-three frontier markets, as well as two broad equity indices (MSCI World and MSCI Frontier Markets) are used. My analysis uses weekly data from February 8, 2008 to February 1, 2013, and provides estimates of the extent to which shocks and volatility are transmitted between oil returns and the returns of Frontier equity markets (+ the MSCI World Index). My results suggest significant volatility interaction between oil and some frontier stock markets. Moreover, the spillover effect appears to be bidirectional in many markets, which is a characteristic that differs from what has been found for developed stock markets where the transmission is usually unidirectional (from oil to stock markets). However, empirical results show that the spillovers run more often from oil to stock markets.

The findings of the study offer several avenues for future research. First, the link between oil and frontier stock markets should eventually be examined over an extended period of time. Second, further evidence drawn from a deeper decomposition of spillovers (spillover, interdependence, comovements and independence) should be produced to examine the robustness of the findings. These would require more elaborate models (MCMS). Finally, hedging effectiveness could be analyzed for these markets in order to compute optimal weights and hedge ratios for oil-stock portfolio holdings. Overall, this study is of particular interest for portfolio management since it offers insight into markets that still provide valuable opportunities for portfolio diversification. In all, this paper improves our knowledge of how stock markets relate to oil prices.

  Speidell & Krohne, 2007; Jayasuriya & Shambora 2009; Berger, Pukthuanthong, & Yang, 2011).

Figure 1 :

 1 Figure 1: Weekly Returns of Broad Stock Market Indices (MSCI Frontier Markets and MSCI World) Plots of each national equity market returns are enclosed in the appendix.The following figure plots the historical weekly returns (%) of crude oil (Brent) over the studied period.

Figure 2 :

 2 Figure 2: Weekly Changes in the Oil Price (Brent)

Table 1 : Summary Statistics for Weekly Percentage Returns on Twenty-One National Stock Market Indices, Two Broad Stock Indices and the Oil Price

 1

		ARG		BAH	BRENT	BUL		FM
	Mean	-0.000392		-0.006716	0.002214	-0.005666	-0.002289
	Median	0.002725		-0.003219	0.005534	-0.002640	0.000000
	Maximum	0.190511		0.083382	0.273051	0.193988	0.072381
	Minimum	-0.264352		-0.191904	-0.223806	-0.340314	-0.141460
	Std. Dev.	0.061570		0.031999	0.051031	0.050725	0.025259
	Skewness	-0.648030		-1.713767	-0.238456	-1.161328	-1.694278
	Kurtosis	6.587412		11.23679	7.276525	11.67068	10.88979
	Jarque-Bera	158.2236		865.5709	201.3627	876.2579	801.8263
	Probability	0.000000		0.000000	0.000000	0.000000	0.000000
	Observations	261		261	261	261		261
		JOR	KAZ	KEN	KUW	LEB	MAU	NIG
	Mean	-0.002876	-0.000785	0.001149	-0.002344	-0.000651	-0.000475	-0.001280
	Median	-0.001944	-0.000461	0.002064	-0.000693	-0.002999	-0.002000	-0.000537
	Maximum	0.096996	0.339806	0.237935	0.182310	0.160940	0.117474	0.199916
	Minimum	-0.129781	-0.275896	-0.144212	-0.192224	-0.109269	-0.200252	-0.180769
	Std. Dev.	0.028759	0.055016	0.037551	0.037484	0.030326	0.034643	0.047633
	Skewness	-0.588160	0.345285	0.660617	-0.519418	1.157897	-0.561908	-0.006575
	Kurtosis	6.526772	10.74318	9.986814	9.539805	10.11749	8.666132	6.297023
	Jarque-Bera	150.3126	657.2164	549.8534	476.8495	609.2340	362.8772	118.2170
	Probability	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Observations	261	261	261	261	261	261	261
		OMA	PAK	QAT	ROM	SAU	SLO	SRI
	Mean	-0.001893	-0.001231	0.000503	-0.000461	-0.000288	-0.003351	0.002483
	Median	0.000857	0.002903	0.000849	0.007082	0.001653	-0.000979	-0.001682
	Maximum	0.118208	0.166830	0.137242	0.222458	0.144495	0.120431	0.421636
	Minimum	-0.199966	-0.238645	-0.203556	-0.293018	-0.166560	-0.197436	-0.131955
	Std. Dev.	0.033284	0.044879	0.037994	0.058200	0.038431	0.037662	0.045690
	Skewness	-1.395272	-1.124315	-0.930632	-0.819155	-0.376414	-0.979714	3.529371
	Kurtosis	11.32211	9.013421	9.588668	6.868070	6.752524	7.744587	31.31229
	Jarque-Bera	837.8604	448.2410	509.7639	191.9005	159.2990	286.5613	9259.100
	Probability	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Observations	261	261	261	261	261	261	261
		TUN		UAE	UKR	VIE	WORLD
	Mean	0.000867		-0.001789	-0.006956	-0.001192	0.000362
	Median	0.000509		-0.001154	-0.007190	-0.000214	0.002840
	Maximum	0.090079		0.230320	0.251340	0.163965	0.123224
	Minimum	-0.129134	-0.278740	-0.204843	-0.175901	-0.200515
	Std. Dev.	0.026764		0.050793	0.056337	0.050716	0.032802
	Skewness	-0.522514	-1.007268	0.197675	0.032316	-0.915448
	Kurtosis	7.223866		9.837133	5.131759	4.284099	8.946894
	Jarque-Bera	205.8977		552.5015	51.12010	17.97734	421.0553
	Probability	0.000000		0.000000	0.000000	0.000125	0.000000
	Observations	261		261	261	261	261

Table 2 : Unit Root Tests ADF test in Level ADF test in Returns PP test in Level PP test in Returns

 2 : ADF and PP tests are performed using log prices and return series. *, **, *** denote rejection of the null hypothesis at the 10%, 5%, and 1% levels respectively. Models include an intercept but no deterministic trend. The following figure plots the historical weekly returns (%) of the MSCI Frontier Markets and MSCI World indices over the studied period.

	ARG	-1.2742	-9.9597***	-1.4877	-17.7236***
	BAH	-2.1382	-6.6618***	-1.8080	-15.2110***
	BRENT	-1.2237	-16.4203***	-1.4678	-16.4797***
	BUL	-2.4516	-5.8800***	-2.1701	-14.9115***
	FM	-2.7704*	-5.8306***	-2.4363	-14.7141***
	JOR	-1.8068	-18.1447***	-1.8263	-18.0874***
	KAZ	-2.2125	-14.8040***	-2.3390	-14.8001***
	KEN	-1.5248	-13.2526***	-1.3717	-13.4432***
	KUW	-2.4161	-15.961***	-2.4157	-15.9613***
	LEB	-0.9143	-14.9522***	-1.4812	-15.8864***
	MAU	-2.0457	-13.8381***	-2.0416	-13.9397***
	NIG	-2.3870	-14.7988***	-2.3704	-14.8091***
	OMA	-1.7742	-17.7192***	-1.8822	-17.8132***
	PAK	-2.6197*	-13.9072***	-2.6308*	-14.1896***
	QAT	-1.6244	-15.6487***	-1.7169	-15.6487***
	ROM	-2.2862	-8.7771***	-2.2802	-14.6471***
	SAU	-2.2619	-17.9140***	-2.2120	-17.9029***
	SLO	-2.5811*	-17.0239***	-2.5143	-17.1002***
	SRI	-0.8899	-13.9244***	-1.0216	-14.330***
	TUN	-2.3751	-17.0209***	-2.3728	-17.0144***
	UAE	-2.4923	-15.7630***	-2.4924	-15.8874***
	UKR	-2.1153	-7.8223***	-1.9369	-12.6360***
	VIE	-3.7097***	-13.9400***	-3.8116***	-13.9291***
	WORLD	-1.8818	-16.9366***	-1.8818	-16.9174***

Note

Table 3 : Correlation Matrix of Return Series (P-Values in Parentheses)

 3

		ARG	BAH	BRENT	BUL	FM	JOR	KAZ	KEN	KUW	LEB	MAU	NIG	OMA	PAK	QAT	ROM	SAU	SLO	SRI	TUN	UAE	UKR	VIE	WORLD
		1.0000
	ARG	--------
		-
	BAH	0.0955 (0.124)	1.0000 ---------
	BRENT	0.4347 (0.000)	0.1243 (0.045)	1.0000 ---------
	BUL	0.4679 (0.000)	0.2473 (0.000)	0.3510 (0.000)	1.0000 ---------
	FM	0.4115 (0.000)	0.4137 (0.000)	0.3979 (0.000)	0.4843 (0.000)	1.0000 ---------
	JOR	0.1724 (0.005)	0.2942 (0.000)	0.0689 (0.267)	0.3446 (0.000)	0.4710 (0.000)	1.0000 ---------
	KAZ	0.5229 (0.000)	0.0927 (0.135)	0.4805 (0.000)	0.3893 (0.000)	0.3399 (0.000)	0.1630 (0.008)	1.0000 --------
	KEN	0.2789 (0.000)	0.2260 (0.000)	0.1908 (0.002)	0.3140 (0.000)	0.3368 (0.000)	0.2931 (0.000)	0.2652 (0.000)	1.0000 ---------
	KUW	0.1969 (0.001)	0.3138 (0.000)	0.1601 (0.010)	0.1964 (0.001)	0.8057 (0.000)	0.2771 (0.000)	0.1041 (0.093)	0.1583 (0.010)	1.0000 --------
	LEB	0.3598 (0.000)	0.2351 (0.000)	0.2618 (0.000)	0.2337 (0.000)	0.3462 (0.000)	0.2122 (0.001)	0.2362 (0.000)	0.2023 (0.001)	0.1612 (0.009)	1.0000 --------
	MAU	0.2878 (0.000)	0.1912 (0.002)	0.3293 (0.000)	0.5230 (0.000)	0.4254 (0.000)	0.2800 (0.000)	0.2958 (0.000)	0.3307 (0.000)	0.1542 (0.013)	0.2046 (0.001)	1.0000 ---------
	NIG	0.0237 (0.703)	0.1204 (0.052)	0.1184 (0.156)	0.1136 (0.067)	0.2873 (0.000)	0.1065 (0.086)	0.0845 (0.174)	0.0817 (0.188)	-0.0102 (0.870)	0.1228 (0.048)	0.0614 (0.323)	1.0000 ---------
	OMA	0.2449 (0.000)	0.2584 (0.000)	0.3500 (0.000)	0.3389 (0.000)	0.6493 (0.000)	0.3331 (0.000)	0.1446 (0.020)	0.3613 (0.000)	0.4333 (0.000)	0.1411 (0.023)	0.2645 (0.000)	0.1043 (0.093)	1.0000 ---------
	PAK	0.1092 (0.078)	0.1042 (0.093)	0.0699 (0.261)	0.0595 (0.338)	0.3412 (0.000)	-0.0397 (0.523)	0.0867 (0.163)	0.0727 (0.242)	0.3256 (0.000)	0.0469 (0.451)	0.1557 (0.012)	0.0723 (0.244)	0.2457 (0.000)	1.0000 ---------
	QAT	0.2592 (0.000)	0.2707 (0.000)	0.2395 (0.000)	0.3639 (0.000)	0.7420 (0.000)	0.4510 (0.000)	0.1714 (0.010)	0.2942 (0.000)	0.5109 (0.000)	0.2906 (0.000)	0.3237 (0.000)	0.0876 (0.158)	0.5896 (0.000)	0.1181 (0.057)	1.0000 ---------
	ROM	0.4735 (0.000)	0.2418 (0.000)	0.3788 (0.000)	0.5544 (0.000)	0.5709 (0.000)	0.2066 (0.001)	0.4789 (0.000)	0.3027 (0.000)	0.3312 (0.000)	0.2670 (0.000)	0.4684 (0.000)	0.2543 (0.000)	0.3059 (0.000)	0.1646 (0.008)	0.3638 (0.000)	1.0000 ---------
	SAU	0.2664 (0.000)	0.2402 (0.000)	0.1512 (0.015)	0.3921 (0.000)	0.6058 (0.000)	0.5031 (0.000)	0.0895 (0.149)	0.2687 (0.000)	0.3608 (0.000)	0.1999 (0.001)	0.3259 (0.000)	0.1440 (0.020)	0.5179 (0.000)	0.1696 (0.000)	0.6210 (0.000)	0.2662 (0.000)	1.0000 ---------
	SLO	0.5751 (0.000)	0.1366 (0.027)	0.4708 (0.000)	0.5838 (0.000)	0.5052 (0.000)	0.3389 (0.000)	0.4543 (0.000)	0.2856 (0.000)	0.2174 (0.000)	0.2893 (0.000)	0.5061 (0.000)	0.1272 (0.040)	0.3022 (0.000)	0.0996 (0.108)	0.3074 (0.000)	0.5753 (0.000)	0.3824 (0.000)	1.0000 ---------
	SRI	0.2073 (0.001)	0.1191 (0.055)	0.2418 (0.000)	0.2168 (0.000)	0.2686 (0.000)	0.1639 (0.008)	0.2487 (0.000)	0.2307 (0.000)	0.0884 (0.154)	0.0995 (0.109)	0.3208 (0.000)	0.1149 (0.064)	0.2181 (0.000)	0.0364 (0.559)	0.1351 (0.029)	0.2327 (0.000)	0.1830 (0.003)	0.3060 (0.000)	1.0000 ---------
	TUN	0.1853 (0.003)	0.0962 (0.121)	0.1313 (0.034)	0.2344 (0.000)	0.2442 (0.000)	0.1375 (0.026)	0.1292 (0.037)	0.2188 (0.000)	0.1490 (0.016)	0.0771 (0.214)	0.1793 (0.004)	0.0833 (0.180)	0.2043 (0.001)	0.0837 (0.178)	0.0771 (0.214)	0.2321 (0.000)	0.2208 (0.000)	0.2316 (0.000)	0.1279 (0.039)	1.0000 ---------
	UAE	0.1950 (0.002)	0.3519 (0.000)	0.3156 (0.000)	0.3552 (0.000)	0.7654 (0.000)	0.4470 (0.000)	0.1912 (0.002)	0.2188 (0.000)	0.4763 (0.000)	0.2278 (0.000)	0.3670 (0.000)	0.1025 (0.099)	0.6552 (0.000)	0.2635 (0.000)	0.6333 (0.000)	0.3095 (0.000)	0.5874 (0.000)	0.3453 (0.000)	0.1921 (0.002)	0.1859 (0.003)	1.0000 ---------
	UKR	0.4063 (0.000)	0.1783 (0.004)	0.3340 (0.000)	0.4078 (0.000)	0.4157 (0.000)	0.2380 (0.000)	0.4850 (0.000)	0.2680 (0.000)	0.1776 (0.004)	0.2789 (0.000)	0.3191 (0.000)	0.1478 (0.017)	0.2779 (0.000)	0.1683 (0.006)	0.2798 (0.000)	0.4644 (0.000)	0.2829 (0.000)	0.3997 (0.000)	0.2706 (0.000)	0.1013 (0.103)	0.2787 (0.000)	1.0000 ---------
	VIE	0.2326 (0.000)	0.0916 (0.140)	0.2869 (0.000)	0.3321 (0.000)	0.3448 (0.000)	0.1906 (0.002)	0.2083 (0.001)	0.1556 (0.012)	0.1347 (0.030)	0.1418 (0.022)	0.3418 (0.000)	0.0803 (0.196)	0.2552 (0.000)	0.0017 (0.978)	0.3238 (0.000)	0.2975 (0.000)	0.2735 (0.000)	0.3664 (0.000)	0.1141 (0.066)	0.1275 (0.040)	0.2798 (0.000)	0.2780 (0.000)	1.0000 ---------
	WORLD	0.6636 (0.000)	0.0614 (0.323)	0.5279 (0.000)	0.5801 (0.000)	0.4898 (0.000)	0.1730 (0.005)	0.6027 (0.000)	0.2757 (0.000)	0.2542 (0.000)	0.3244 (0.000)	0.3860 (0.000)	0.0912 (0.142)	0.2506 (0.000)	0.1239 (0.046)	0.3186 (0.000)	0.6474 (0.000)	0.2695 (0.000)	0.6534 (0.000)	0.1561 (0.012)	0.2580 (0.000)	0.2791 (0.000)	0.4382 (0.000)	0.3204 (0.000)	1.0000 ---------

Table 4 : Results of the Granger Causality Tests (P-Values)

 4

	Oil to Stocks	Stocks to Oil

Table 5 : Estimates of BEKK-GARCH(1,1) Model for Oil and Stock Returns

 5

	ARG	BAH	FM	JOR	KAZ	KEN	KUW
	Panel A: Conditional Mean Estimates
	0.0049	0.0070	0.0032	0.0044	0.0041	0.0039	0.0037
	0.0208	0.0742	-0.0645	-0.0104	0.0260	0.0202	0.0023
	0.0003	-0.0014	0.0011	-0.0016	0.0013	0.0046***	-0.0012
	-0.0774	0.0534	0.1388***	-0.0999	0.0242	0.1069	0.0698
	Panel B: Conditional Variance-Covariance Estimates
	0.0287***	0.0129	0.0122	0.0113	0.0112	0.0083	0.0118
	0.0380	0.0082	-0.0003	-0.0008	0.0084	-0.0088	0.0001
	0.0000	0.0000	0.0000	0.0024	0.0083	0.0000	0.0000
	0.4056	-0.0958	0.0494	-0.0846	0.0176	0.0472	-0.2928***
	0.6972***	-0.2349***	-0.1690***	0.1164	0.1964	0.1780**	-0.0196
	0.1187	0.2258	-0.9650**	0.0220	0.2339	0.3752	-0.0394
	-0.1441	-0.8011***	0.2192	0.3437***	0.3147	0.3456***	0.2808**
	0.7030***	-0.8600***	0.0547	-0.1990	-1.0746***	0.7539***	-0.4019**
	-0.4561	0.0960	0.3972***	0.4963**	-0.2840**	0.4195***	0.5087***
	-0.1529	-0.4031	-2.0541***	1.1711***	0.3429***	-0.9459	-1.1751***
	0.6340	-0.6055***	-0.7568***	0.2202	-0.6911***	0.5384***	-0.6911***
	LEB	MAU	NIG	OMA	PAK	QAT	SAU
	Panel A: Conditional Mean Estimates
	0.0042	0.0032	0.0027	0.0054	0.0022	0.0017	0.0022
	-0.0181	-0.0111	0.0317	-0.0475	0.0095	-0.0021	-0.0116
	-0.0012	0.0011	0.0007	-0.0001	0.0024*	0.0019	0.0014
	-0.0069	0.1981***	0.1099	-0.0303	0.1130*	0.0888	-0.0298
	Panel B: Conditional Variance-Covariance Estimates
	0.0096	0.01193**	0.0097	0.0119**	0.0067**	0.0162	0.0082
	0.0059	0.0012	-0.0039	-0.0001	-0.0050	0.0004	0.0036
	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0102
	0.2077**	0.0158	-0.2578	0.0674	0.1227***	-0.3698	-0.0813
	0.0630	0.0789	0.1450**	0.1852**	0.1612	-0.0872	0.1501
	0.1460	0.0943	0.3001	0.4959***	0.0876	0.2864	0.1799
	0.3959***	0.4275***	0.2647	0.1231	-0.7228***	0.3821	-0.6519***
	0.9300***	-0.4084***	0.8890***	0.5165***	-0.9943	-0.3150***	-0.8973***
	-0.0849***	0.4506***	0.3465	-0.3910***	-0.1515***	-0.6492	0.0394
	0.0923	-1.2326	0.1304	1.0783***	0.3999	1.1078	-0.3258
	0.9039***	-0.7103***	-0.9098***	0.8439***	0.7825	-0.2149**	-0.7324***
	SLO	SRI	TUN	UAE	UKR	VIE	WORLD
	Panel A: Conditional Mean Estimates
	0.0032	0.0025	0.0028	0.0056	0.0036	0.0034	0.0066
	0.0102	-0.0333	0.0122	-0.0498	-0.0123	-0.0395	0.0171
	-0.0033	-0.0003	0.0008	0.0024	-0.0055	-0.0017	0.0041***
	0.0184	0.1496	0.0167	0.0138	0.2076***	0.0612	-0.1053
	Panel B: Conditional Variance-Covariance Estimates
	-0.0086	0.0183	0.0036	0.0165***	0.0227	0.0069	0.0189
	-0.0133	-0.0025	0.0045	0.0009	0.0307	-0.0172	-0.0032
	0.0232	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
	0.1772	0.3630***	0.2345	0.0449	0.4033	0.1350	0.2555
	0.1453	0.0624	0.0573	0.0966	0.0496	-0.0903	0.1114

Copyright by author(s); CC-BY 519

The Clute Institute Estimates of ARCH and GARCH coefficients, which capture shock dependence and volatility persistence in the conditional variance equations, are statistically significant at conventional levels in many cases. For the stock market segment, the sensitivity to past own conditional volatility ( ) appears to be significant for fourteen series at conventional levels.

The results also suggest that the current value of conditional volatility of stock returns often depends on past unexpected shocks affecting return dynamics since the associated coefficients ( ) are statistically significant in eleven cases. Moreover, the large magnitude of GARCH coefficients suggests that conditional volatility tends to fluctuate gradually over time.

Oil price volatility behaves similarly to stock market volatility as sensitivity to past own conditional volatility ( ) appears to be significant for all series at conventional levels except for Jordan, Sri Lanka, Pakistan, and the MSCI Frontier Markets Index. Similar conclusions can be drawn regarding sensitivity to past own shocks ( ) for four countries, namely Kuwait, Lebanon, Pakistan, and Sri Lanka.

Regarding volatility transmission between oil and stock markets, there can be observed that conditional volatility of stock markets is sometimes affected by innovations in the oil market as indicated by the significance of the coefficients for Argentina, Bahrain, Kenya, Nigeria, Oman, and the MSCI Frontier Markets Index. This seems to suggest that a shock originating from the oil market generally has an impact on stock market volatility in these markets. This is not illogical given the economic structure of these countries, in which the energy (Argentina, Bahrain, Nigeria, Oman, FM index) and financials sectors (Kenya, FM index) account for big proportions of GDP. The highest value is found for Argentina. This can be explained by the importance of the manufacturing sector within its economy (20% of the countries' GDP). Moreover, the country is an oil producer and petroleum products account for about 10% of its exports.

In addition, there is evidence suggesting that past volatility of oil markets affect current stock market volatility as indicated by significant coefficients for twelve series. The highest coefficient measuring the volatility spillover from oil to stock markets is found for the MSCI Frontier Markets Index, which is not surprising given the importance of oil-centered economies within the index with Kuwait, Qatar, Nigeria, and the United Arab Emirates accounting for 65.29% of its composition. Moreover, if we take a look at the index sectorial composition, we see that Financials, Industrials and Energy account for 69.58% of its constituents. These are sectors for which we usually document significant volatility spillovers with oil for fundamental reasons (oil is an input for Industrials, and has an impact on consumer and investor confidence, as well as on monetary policy, thus affecting financials). The second highest coefficient is found for Jordan, which despite not being an oil exporting country is heavily dependent on oil for its transportation and industrial sector (approximately one fifth of its GDP), both major consumers of petroleum products.

Interestingly, the statistical significance of the (three cases) and (seven cases) coefficients in the conditional variance equation for oil returns suggests that the oil market volatility is influenced by changes (shocks and volatility) that occurred in some frontier stock markets. The highest (volatility transmission) coefficient is found for the MSCI World index while the highest (shock transmission) coefficient is found for the MSCI Frontier Markets index. Strangely, is also significant for Jordan, which is unexpected. Further studies would be needed to investigate this relationship but this probably results from its geographical situation. Indeed, immediate proximity with countries such as Iraq or Saudi Arabia probably induces comovements between stock markets of these countries, which appear as spillovers.

AUTHOR INFORMATION

Mathieu Gomes is a commodity index structuring analyst at BNP Paribas. He holds a Master's degree in financial markets and a Master's degree in management from the Université d'Auvergne, Clermont-Ferrand, France. His research interests include commodities, investment strategies, and financial economics. E-mail: mathieu.gomes@gmail.com Dr. Anissa Chaibi is a researcher at IPAG Business School, France. Her research areas are development economics, finance, and econometrics. Her most recent articles are published in refereed journals such as Economic Modelling, Energy Policy and Journal of Applied Business Research. E-mail: anissa.chaibi@ipag.fr (Corresponding author)

Copyright by author(s); CC-BY 521

The Clute Institute


Mathieu Gomes

Harvesting Commodity Curve Premia Through Roll-Yield Differentials

).

).

, short hedgers supply usually exceeds long hedgers demand and futures prices therefore embed a discount that is a compensation for insurance against future spot price risk, i.e. futures prices are downward-biased estimates of future expected spot price as commodity producers are willing to forgo part of their expected profits in order to lock their margins. This discount is

aimed at inducing speculators to take long positions on the futures market and restore equilibrium. [START_REF] Hicks | Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory[END_REF] shared this view, emphasizing the "congenital weakness" of inventory holders relative to consumers, notably because consumers have alternatives (substitute products) and as a result are less vulnerable to price increases than producers to price drops.

Another way to view it is through Kaldor's theory of storage [1939] which links the term structure of futures prices to the level of inventories. According to this theory, futures prices should equal spot prices plus the cost of carry (storage, insurance and interest forgone) less the convenience yield. The convenience yield is defined by [START_REF] Brennan | The Supply of Storage[END_REF] as "the advantage (in terms of less delay and lower costs) of being able to keep regular customers satisfied or of being able to take advantage of a rise in demand and price without resorting to a revision of the production schedule". In other words it represents the "comfort" of possessing stocks in periods of low inventories. The theory of storage thus posits that when the convenience yields exceeds the cost of carry, futures prices will be lower than spot prices, a situation referred to as backwardation. The convenience yield is therefore positively correlated with the spot price and negatively correlated with inventory levels. This approach makes sense: inventories act as a buffer for commodities supply when there is a spike in demand. If demand increases faster than supply, inventories will begin to decrease and will eventually reach a level at which they will no longer serve this function, at which point the market will have to offer an incentive to storage holders to promote the build-up of inventories. A downward sloping or backwardated term structure provides this incentive.

Backwardation translates into a positive implied roll-yield, which means that rolling a futures long position on this commodity should generate a profit (the contract sold will be worth more than the newly bought contract) provided the term structure remains stable. The opposite situation (upward sloping forward curve, negative implied roll-yield) is referred to as Contango.

Following this, commodities in backwardation should tend to outperform because of 1) a tendency for spot price appreciation and 2) positive roll-yield or positive carry. This intuition has been confirmed by previous studies. [START_REF] Erb | The Strategic and Tactical Value of Commodity Futures[END_REF] use the term-structure signals of 12 commodities to implement a simple strategy that goes long the 6 most backwardated commodities and short the 6 most contangoed commodities and find greatly improved Sharpe ratios compared to long-only strategies. [START_REF] Fuertes | Tactical Allocation in Commodity Futures Markets: Combining Momentum and Term Structure Signals[END_REF] expand on this strategy by assessing the sensitivity of the term structure profits to the roll return definition and the frequency of rebalancing.

The performance of these strategies suggests that the commodity term-structure is a good predictor of future performance. However, it is important to keep in mind that commodity futures excess returns can be broken down into two components, Spot return (sometimes called Price return) and Roll return, and that the term structure has a strong predictive power on Roll returns [START_REF] Nash | Backwardation of Commodities and Returns on the GSCI Investment[END_REF]; [START_REF] Gorton | Facts and Fantasies about Commodity Futures[END_REF]), not so much on spot returns, which are much more volatile. The consistency and persistence of roll-returns come from the fact that the shape of commodity forward curves is primarily driven by fundamental factors that tend to adjust slowly over time.

According to these elements, it is therefore interesting to investigate how a strategy aiming at isolating this roll-return (i.e. neutralizing the spot return) would behave.

HEDGING SPOT RETURNS BY TARGETING CORRELATED COMMODITIES

The term-structure of commodity futures is shaped by the interaction of interest rates, fundamental factors such as inventory and seasonality as well as by the diversity of market participants (producers often seek to hedge on longer maturities while consumers or processors usually hedge their purchases over shorter horizons). As previously explained, this forward curve provides a consistent source of return but expected roll-returns can be hurt by violent spot price moves. In order to reduce this spot price risk, it makes sense theoretically to take long and short positions within sub-groups of highly correlated commodities. Indeed, the hedging of spot returns made possible by the concomitant buying and selling of correlated commodities should result in the monetization of the difference in roll-yields generated by a long position entered on a more backwardated (or less contangoed) curve and a short position entered on a less backwardated (or more contangoed) curve. In other words, doing so should make it possible to capture the carry differential (provided the term structure remains stable) between the targeted commodities and therefore to extract a "purer" curve premium.

In order to test this hypothesis, we create groups of correlated commodities (see Exhibit 1). Within each of these sub-groups, long positions will be entered on commodities exhibiting the highest level of backwardation and short positions will be entered on those exhibiting the highest level of contango. 2 pairs will be selected from the industrial metals complex as this group includes 5 commodities. As a result, the strategy will be long 8 commodities and short 8 commodities. The created basket will be equally weighted and leveraged twice (long 100%short 100%).

If all commodities in a given group are in backwardation (contango), the strategy will go long the most backwardated (least contangoed) commodity and short the least backwardated (most contangoed) commodity. For each commodity, the degree of backwardation/contango (denoted 𝑌 𝑡 ) is measured between the first nearby contract and the contract one year ahead, using the following formula:

EXHIBIT 1. COMMODITY SUB-GROUPS

𝑌 𝑡 = [log 𝑃 𝑡,𝑛 -log 𝑃 𝑡,𝑑 ] × 365 𝑁 𝑡,𝑑 -𝑁 𝑡,𝑛 (1)
where 𝑃 𝑡,𝑛 is the price of the nearby contract at time t, 𝑃 𝑡,𝑑 is the price of the distant contract, 𝑁 𝑡,𝑛 is the number of days between time t and the maturity of the nearby contract and 𝑁 𝑡,𝑑 is the number of days between time t and the maturity of the distant contract. According to this equation, a negative 𝑌 𝑡 will imply a contangoed term structure while a positive 𝑌 𝑡 will imply a backwardated term structure. Using the one-year ahead contract instead of a closer one allows to reduce seasonality bias often encountered in some commodities. The strategy will be invested on nearby commodity rolled indices which are described in the next section.

DATA SET

Futures market data are obtained from Datastream and span the period ranging from January 28 th 2002 to September 15 th 2014. It consists of closing prices for nearby contracts as well as distant contracts (one year ahead) for the 19 commodities already presented. The commodities series are constructed using the S&P GSCI roll schedule and positions are rolled over 5 days from the 5 th to the 9 th business day of each month (20% each day). The strategy performances reported in this paper will be excess return performances, i.e. collateral returns will not be taken into account.

Open Interest data used later in this study come from the CFTC Aggregated Commitment of Traders Report.

PERFORMANCE ANALYSIS

In order to assess the risk-adjusted returns of the back-tested strategies, we use the following multi-factor model -previously used by [START_REF] Fuertes | Tactical Allocation in Commodity Futures Markets: Combining Momentum and Term Structure Signals[END_REF]:

𝑟 𝑠,𝑡 = 𝛼 + 𝛽 1 𝐵𝑂𝑁𝐷 + 𝛽 2 𝐸𝑄𝑈𝐼𝑇𝑌 + 𝛽 3 𝑀𝐴𝑅𝐾𝐸𝑇 + 𝜀 𝑠,𝑡 (2)
where 𝑟 𝑠,𝑡 is the return of the strategy being examined, 𝐵𝑂𝑁𝐷, 𝐸𝑄𝑈𝐼𝑇𝑌 , and 𝑀𝐴𝑅𝐾𝐸𝑇 are the excess returns on the Lehman Aggregate US total return bond index, the S&P500 composite index and the S&P GSCI (Goldman Sachs Commodity Index) respectively and 𝜀 𝑠,𝑡 is an error term. Significant positive 𝛼 would mean that performance is not just compensation for bearing some type of risk (passive return). average maximum drawdown for the four rebalancing frequencies is -16.36%, much lower than the average figure for the four classic TS strategies (-27.61%).

EXHIBIT 2. SUMMARY STATISTICS

This leads to much more consistent returns over time as can be seen on Exhibit 5.

Annualized returns for the roll strategy are much more stable than for the classic TS strategy, even during the recent period in which many commodities strategies have achieved disappointing performances (Exhibit 4). Over the period studied, the strategy only posted one negative annual return (in 2008).

EXHIBIT 5. YEARLY ANNUALIZED RETURNS FROM FEB-02 TO SEP-14

The comparison is even more staggering when we look at maximum drawdown figures (Exhibit 6). As mentioned in the introducing paragraph, we see that targeting roll-yield differentials allows to greatly reduce drawdowns compared with a classic term-structure strategy. This can be easily explained by the market neutral nature of the strategy as opposed to the directional nature of the classic term-structure strategy.

Exhibit 3 shows the coefficient estimates resulting from equation (2). For the classic TS strategies, we can see that coefficients related to the S&P GSCI are always positive and statistically significant, which is in line with the results of previous studies. Coefficients associated with the equity market are also significant but negative for the classic TS strategies. We can also emphasize that returns of the classic TS strategies are not related to the bond market. Finally, their alphas are positive and usually significant.

If we turn our attention to the roll strategies, we notice that their alphas are all positive and significant. On average, they earn an annualized gross alpha of 6.69%. More importantly, none of the other coefficients are statistically significant, implying that the performance of these strategies is not mere compensation for bearing equity, bond or commodity risks. In other words, the performance of the roll strategy does not come from passive exposure to traditional risk factors or "Betas" but instead results from the active features of the strategy.

EXHIBIT 6. YEARLY MAXIMUM DRAWDOWNS FROM FEB-02 TO SEP-14

The results presented above are gross of transaction costs but these have been shown

to be small (Locke and Venkatesh [2007]), especially for liquid futures as those used in our strategy. Even if we pick the high-range estimate of Locke and Ventakesh (0.033%) and use the strategy annual turnovers reported in Exhibit 2, the average annualized alpha stands at 5.65% (penalized by the very high turnover of the daily-rebalanced strategy).

Exhibit 7 reports the Pearson correlation coefficients between the returns of the backtested strategies and those of traditional asset classes. Overall, correlations with T-bills, bonds, stocks and the US dollar index are either very low or non-significant. In line with the results of As suggested by [START_REF] Fuertes | Tactical Allocation in Commodity Futures Markets: Combining Momentum and Term Structure Signals[END_REF], this positive relationship between traditional TS strategies and the S&P GSCI is probably due to the relatively high weighting of energy commodities within this index (approximately 70%), associated with the fact that these commodities are often long picks in term-structure based strategies because of their typically backwardated forward curves. However, we see that the correlation coefficients between the roll strategies and the S&P GSCI are not statistically significant, which is consistent with our risk-adjusted analysis.

EXPOSURE TO ALTERNATIVE RISK FACTORS

Given the low correlation usually observed between traditional assets and commodity futures [START_REF] Bodie | Risk and returns in commodity futures[END_REF]), the BOND and EQUITY factors previously used and which emanate from traditional asset pricing models may not be appropriate to assess the performance and our strategy. We thus build an alternative pricing model aimed at capturing the fundamentals of the term structure based on the hedging pressure hypothesis [START_REF] Cootner | Returns to speculators: Telser vs. Keynes[END_REF]; [START_REF] Hirshleifer | Hedging pressure and future price movements in a general equilibrium model[END_REF]) and the theory of storage [START_REF] Brennan | The Supply of Storage[END_REF]). The proposed asset pricing model (Equation 3) includes benchmarks based on hedging pressure [START_REF] Basu | Capturing the Risk Premium of Commodity Futures: The Role of Hedging Pressure[END_REF]) and on term structure [START_REF] Erb | The Strategic and Tactical Value of Commodity Futures[END_REF]) in addition to the traditional factors (bond, equity and commodity markets).

𝑟 𝑠,𝑡 = 𝛼 + 𝛽 1 𝐵𝑂𝑁𝐷 + 𝛽 2 𝐸𝑄𝑈𝐼𝑇𝑌 + 𝛽 3 𝑀𝐴𝑅𝐾𝐸𝑇 + 𝛽 4 𝐶𝐴𝑅𝑅𝑌 + 𝛽 5 𝐻𝐸𝐷𝐺𝐼𝑁𝐺 + 𝜀 𝑠,𝑡

where 𝑟 𝑠,𝑡 is the return of the strategy being examined, 𝑀𝐴𝑅𝐾𝐸𝑇 stands for the excess return of the S&P GSCI (Goldman Sachs Commodity Index), 𝐶𝐴𝑅𝑅𝑌 is the excess return of the classic TS strategy examined in the previous section (rebalanced monthly) and 𝐻𝐸𝐷𝐺𝐼𝑁𝐺 is the excess return of a monthly-rebalanced strategy that takes long and short positions on commodity futures based on the activity of hedgers (commercial participants) and speculators (non-commercial participants). More precisely, to compute this factor, we base our methodology on [START_REF] Basu | Capturing the Risk Premium of Commodity Futures: The Role of Hedging Pressure[END_REF] and use a double-sort:

1) First, we split the cross section of commodities -using a 50% breakpointinto Low HP and High HP according to the average hedging pressure of hedgers over the past 4 weeks.

According to Hirshleifer's hedging pressure theory [1990], contracts with hedger's low hedging pressure are presumably backwardated (and their price is thus expected to increase) while those with hedger's high hedging pressure are presumably contangoed (and their price is thus expected to decrease).

2) Then, we combine the positions of hedgers with those of speculators by buying the 30% of Low HP for which speculators have the highest average hedging pressure over the previous 4 weeks and selling the 30% of High HP for which speculators have the lowest average hedging pressure over the previous 4 weeks. We can see from Exhibit 8 that the coefficients associated with the CARRY and HEDGING factors are both statistically significant, implying our strategy performance results partially from exposure to classic term-structure and hedging pressure risk premia. That being said, exposure to these factors explains only a very small part of the strategy returns and alpha remains significant with annualized values ranging from 5.82% to 6.17%.

SENSITIVITY TO ALTERNATIVE YIELD MEASURE

As explained in a previous section, we computed term-structure's degree of backwardation/contango using the first nearby contract and the contract one-year ahead in order to avoid seasonality bias encountered in some commodities. For the sake of robustness,

we now examine what performance the strategy would yield if the degree of backwardation/contango were computed using the annualized slope between the first and second nearby contracts. This alternative strategy specification (denoted Roll Strategy Alt.) leads to slightly different results (Exhibit 9). Overall, annualized mean returns are higher, ranging from 6.91% to 7.46%. However, this comes at the cost of a higher level of volatility (8.77% on average compared with 7.09% for the strategy using one-year measures). This increased variability leads to slightly lower Sharpe ratios (ranging from 0.81 to 0.88). Maximum drawdown figures are also higher on average even though they remain much lower than for classic TS strategies. Turning to the risk-adjusted performance analysis (Exhibit 10), we notice that the strategy still generates consistent alpha (from 4.40% to 5.81%). Interestingly, the 𝑀𝐴𝑅𝐾𝐸𝑇 factor becomes significant, indicating some degree of exposure to the broad commodity market. The coefficients associated with the 𝐶𝐴𝑅𝑅𝑌 factor are higher than when using one-year ahead contracts, indicating a higher exposure to the term-structure risk premium. Finally, the 𝐻𝐸𝐷𝐺𝐼𝑁𝐺 factor remains significant.

EXHIBIT 9. SUMMARY STATISTICS (ALTERNATIVE YIELD MEASURE)

EXHIBIT 10. RISK-ADJUSTED PERFORMANCE (ALTERNATIVE YIELD MEASURE)

To sum up, using the annualized slope between the first and second nearby contracts to build the strategy (i.e. not accounting for seasonality) leads to slightly lower risk-adjusted performance by moderately increasing volatility, adding some degree of exposure to the commodity market and increasing exposure to the classic term-structure premium. However, exposure to examined risk premia remains very low and the strategy still generates significant alpha.

CONCLUDING REMARKS

This paper introduces a new way to systematically invest in commodity futures and provides risk and performance analysis. Building on the fact that buying backwardated commodities and selling contangoed commodities generates abnormal returns over the long run, we modify the strategy in order to reduce its sensitivity to spot price movements. We do so by targeting roll-yield differentials between highly correlated commodities i.e. buying the most backwardated/least contangoed one(s) and selling the most contangoed/least backwardated one(s) within these sub-groups and we compare the performance of this strategy with a classic term-structure strategy. We test for various rebalancing frequencies and show that this approach creates significant alpha and greatly improves Sharpe ratios. More importantly, the strategy returns are not related to either the commodity, equity or bond markets, resulting in a strategy that is truly market neutral. Moreover, the alpha generated does not result from passive exposure to term-structure or hedging-pressure based benchmarks.

In addition, the performance of the strategy appears to be remarkably stable even during the recent past. This point is worth emphasizing as the majority of commodity based strategies have suffered during this period.

These findings are of particular interest for asset managers since they offer insights into new ways of diversifying a portfolio and generating consistent alpha irrespective of broad market moves, especially at a time when the merits of holding a commodity exposure within an asset portfolio has been challenged. Overall, it improves our knowledge of commodity futures returns.

ENDNOTE

I would like to thank an anonymous referee for providing me with many valuable comments and suggestions on a previous version of this manuscript. I also thank Patricia Bonnett (from the editorial team) for her help during the submission process.

  For robustness purposes, we test four versions of the strategy (denoted roll strategy) featuring monthly, bi-weekly, weekly and daily rebalancing respectively. For each frequency, we also create simple Term Structure strategies (denoted TS strategy), simply buying the 8 most backwardated commodities and selling the 8 most contangoed commodities. Rebalancing occurs the last day of the month for the monthly rebalanced strategy, every two Friday for the bi-weekly version, every Friday for the weekly-rebalanced version and every day for the dailyrebalanced version.Exhibit 2 reports summary statistics for these various strategies. We can see that regardless of the rebalancing frequency the roll strategy systematically yields higher Sharpe ratios than the classic TS strategies. This is explained by the much lower volatility obtained as a result of partially neutralizing spot price movements.

		Monthly rebalancing	Bi-weekly rebalancing	Weekly rebalancing	Daily rebalancing
		Roll strategy	TS strategy	Roll strategy	TS strategy	Roll strategy	TS strategy	Roll strategy	TS strategy
	Annualized	0.0673	0.0951	0.0654	0.1306	0.0698	0.1268	0.0683	0.1184
	return
	T-statistic	3.2582	1.8582	3.1406	2.3838	3.3882	2.3321	3.3095	2.1832
	Annualized	0.0709	0.1812	0.0715	0.1825	0.0706	0.1815	0.0707	0.1816
	volatility
	Sharpe ratio	0.9499	0.5247	0.9147	0.7156	0.9889	0.6988	0.9652	0.6517
	5-day 95% VaR	-0.0144	-0.0393	-0.0148	-0.0392	-0.0142	-0.0386	-0.0147	-0.0388
	Skewness	-0.1166	0.0079	-0.1544	-0.0536	-0.1339	-0.0260	-0.1054	-0.0830
	Excess Kurtosis	1.1197	0.7700	1.3852	0.9934	1.5110	0.8990	1.3170	0.9731
	Best month	0.0688	0.1504	0.0679	0.1578	0.0696	0.1498	0.0708	0.1608
	Worst month	-0.0607	-0.1076	-0.0613	-0.1262	-0.0653	-0.1050	-0.0640	-0.1055
	Maximum	-0.1314	-0.2800	-0.1697	-0.2606	-0.1753	-0.2891	-0.1778	-0.2746
	drawdown
	% positive	58.94%	54.30%	63.58%	58.28%	64.90%	58.28%	60.26%	56.95%
	months
	Turnover p.a.	17.1665	16.4879	24.0513	21.9298	31.4351	27.6946	53.7702	42.1996
	EXHIBIT 3. RISK-ADJUSTED PERFORMANCE
		Monthly rebalancing	Bi-weekly rebalancing	Weekly rebalancing	Daily rebalancing
		Roll strategy	TS strategy	Roll strategy	TS strategy	Roll strategy	TS strategy	Roll strategy	TS strategy
	Annualized 𝛼	0.0664	0.0803	0.0654	0.1246	0.0690	0.1220	0.0668	0.1141
	(3.310) -0.0342 (-1.0310) EXHIBIT 4. PERFORMANCE OF CTA INDICES FROM 2010 TO 2013 (1.5826) (3.2337) (2.4331) 𝐵𝑂𝑁𝐷 -0.0045 (-0.0541) -0.0597 (-1.7836) 0.0030 (0.0349) 𝐸𝑄𝑈𝐼𝑇𝑌 0.0005 -0.0737 0.0034 -0.0823 12% Barclays CTA Index	(3.4583) -0.0515 (-1.5606) 0.0110	(2.3909) -0.0189 (-0.2236) -0.0776	(3.3405) -0.0307 (-0.9271) 0.0110	(2.2337) -0.0158 (-0.1865) -0.0702
		(0.0722)	(-4.3233)	(0.5029) HFRX Macro: Commodity Index (-4.7800)	(1.6446)	(-4.5212)	(1.6365)	(-4.0873)
	𝑀𝐴𝑅𝐾𝐸𝑇 6%	0.0008 (0.1475)	0.1122 (8.0717)	0.0016 (0.2802) Newedge Commodity Trading Index (Trading) 0.0943 (6.7163) -0.0018 (-0.3357)	0.0790 (5.6508)	0.0009 (0.1640)	0.0793 (5.6658)
	Note: The table reports coefficients estimates for equation (2). Significance t-ratios are in parentheses. Bold denotes significance at the 5% level or better.
	0%
	-6%
	-12%
	Sources: BarclayHedge, HFRX, Newedge
	The roll strategies also feature much lower maximum drawdowns compared with classic TS
	strategies and the proportion of positive months is systematically higher for the roll strategies
	(61.92% on average compared with 56.95% for the traditional TS strategies). The lowest
	maximum drawdown is achieved by the monthly rebalanced roll strategy (-13.14%) and the

  Hedging pressure for a category (commercial or non-commercial participant) is defined as the number of long open interest in that category divided by the total number of open interest in the category.

	EXHIBIT 8. RISK-ADJUSTED PERFORMANCE (ALTERNATIVE FACTORS)
		Monthly	Bi-weekly	Weekly	Daily rebalancing
		rebalancing	rebalancing	rebalancing
		Roll Strategy	Roll Strategy	Roll Strategy	Roll Strategy
	Annualized 𝛼	0.0585	0.0582	0.0617	0.0596
		(3.0178)	(2.9645)	(3.1860)	(3.0639)
	𝐵𝑂𝑁𝐷	-0.0360	0.0622	-0.0538	0.0321
		(-1.1211)	(1.5125)	(-1.6786)	(0.9972)
	𝐸𝑄𝑈𝐼𝑇𝑌	0.0077	0.0100	0.0178	0.0176
		(1.8462)	(1.5035)	(2.7227)	(1.6905)
	𝑀𝐴𝑅𝐾𝐸𝑇	-0.0360	0.0004	0.0041	0.0037
		(-0.5872)	(0.0674)	(0.6736)	(0.6116)
	𝐶𝐴𝑅𝑅𝑌	0.0994	0.0905	0.0929	0.0911
		(14.5848)	(13.0958)	(13.6557)	(13.3218)
	𝐻𝐸𝐷𝐺𝐼𝑁𝐺	0.0205	0.0273	0.0247	0.0169
		(2.4058)	(3.1600)	(2.9079)	(1.9794)
	𝑅 2	0.0667	0.0576	0.0621	0.0572

Note: Significance t-ratios are in parentheses. Bold denotes significance at the 5% level or better.