links between north american exchange traded commodity ... · pdf file2 1. introduction...

Links between North American exchange traded commodity convenience yields and US Dollar denominated zero coupon inflation swap rates.

Okan Aybar*, 1 Donatien Hainaut**, 2

* Okan Aybar, École Supérieure de Commerce de Rennes

** Donatien Hainaut, École Supérieure de Commerce de Rennes

ABSTRACT

This paper investigates relationship between one year maturity convenience yields derived from North American futures contracts and the one year maturity US Dollar denominated zero coupon inflation swap (ZCIS) rates. We employ co-integration and vector auto-regressive (VAR) models as main underlying methodologies and use daily and weekly series between 2010 and 2015. We find evidence that some commodity convenience yields have long term association with ZCIS rates. Our VAR and vector error correction model (VECM) results collectively suggest more interesting results: We catch that there is short run causality running from convenience yields of commodities retaining features of short run biasedness while there is no short run causality running from convenience yields of commodities possessing aspects of unbiasedness. This inspires further research on (un)biasedness of commodity futures with at least one year maturities.

Key Words: Convenience yield, zero coupon inflation swap, risk premium, biasedness of futures price, co-integration, vector auto-regression.

JEL Classifications: Q02, Q11, Q41, E31, G13, G14

1 Corresponding author. Tel.: +33 6 43 76 57 84 - E-mail addresses: [email protected] 2 Corresponding author. Tel.: +33 2 99 54 63 63 - E-mail addresses: [email protected]

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Table of Contents 1. INTRODUCTION .........................................................................................................................................................2

2. LITERATURE REVIEW .................................................................................................................................................3

3. DATA DEVELOPMENT ............................................................................................................................................ 14

4. METHODOLOGY AND RESULTS ............................................................................................................................. 15

5. CONCLUSION .......................................................................................................................................................... 26

Acknowledgements ........................................................................................................................................................ 27

APPENDIX: ZCIS Rates vs Convenience Yield Charts .................................................................................................... 28

REFERENCES .................................................................................................................................................................... 31

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1. INTRODUCTION Inflation is a monthly economic indicator that measures the evolution of prices of a basket of all

commodities each having a specific weight. Therefore by its nature, inflation is an ex-post data. There are only few financial instruments which reflect ex-ante inflation expectations on a monthly data basis. Jarrow and Yıldırım (2003), state that, they are generally known as inflation derivatives such as inflation indexed bonds, first issued in January 1997 or inflation swap whose underlying assets are the monthly announced consumer price inflation. Thereafter, during early 2000’s, new wave of inflation derivatives, so called Zero Coupon Inflation Swaps (ZCIS), has emerged in the interbank market where professional traders reflect their ex-ante inflation3 expectations for maturity perspectives ranging from six months to five years, on a daily basis. Despite valuable implications that inflation derivatives have to offer, they are amongst the subjects that have rarely been recognized in relation with commodity prices by academia. The existing literature, eg. Schulz and Stapf (2011) mainly focus on inflation derivatives’ forecasting ability, pricing robustness, liquidity comparisons against alternative instruments such as government bonds. Our research on the other hand aims to contribute to the financial literature by defining relationship structure between commodity convenience yields and inflation derivatives.

Kaldor (1939) defined convenience yield simply as the expected return for holding a commodity during a specified period of time. Despite its long term familiarity, convenience yield is another subject on which, academic community showed little interest in defining relationship with inflation expectations using high frequency data. In addition, only rarely, has its context been extended in to issues such as convenience yield’s exogeneity to inflation, commodity supply-demand forecast and future spot price forecasting capacity. Rather, most academic researchers focused on micro-structure features of the convenience yield such as convex relationship structure with inventory levels; convenience yield’s heteroscedasticity, stochastic seasonality, mean reversion features as well as its time variability.

The contributions of this paper to the existing literature are multiple. Firstly, it is one of the first study conducted to define long and short term association between ZCIS rates and the term structure of commodities within the context of commodity convenience yields, by suggesting an econometric forecasting framework in which co-integration, vector error correction model, vector auto-regression and causality are employed.

Secondly, we assess the efficiency of ZCIS rate forecasting models by highlighting whether convenience yields of biased commodities are more robust than the convenience yields of less biased or unbiased commodities.

Thirdly, we employ daily and weekly time series which may be considered as relatively higher frequency data for observing underlying components of inflation derivatives which normally depend on monthly official announcements made by the United States (US) government in our case. In particular, depending on which commodity we focus on, we use daily and weekly series of one year maturity convenience yields of North American exchange traded commodities to explain bi-variate relationship structure and predict the subsequent daily and weekly one year ZCIS rates.

3 Underlying assets may be consumer price index (CPI), in the United States of America (US), retail price index in the United Kingdom (UK) and harmonized consumer price index in France.

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Brennan (1958), suggested that commodity convenience yields had the power to explain demand shocks. By the same token, Casassus et al. (2010) highlighted that output shocks lead to jumps in crude oil. Assuming that both supply and demand shocks have immediate effects on convenience yields, they may be incorporated in to inflation expectations. Such rationale finds support from Gosposdinov et al. (2013) who argued that commodity convenience yields provided useful information to predict not only the future spot prices but also the inflation. Therefore it could be that, convenience yields may be incorporated not only in the inflation expectations but they can also be incorporated in the ZCIS rates.

Based on the context explained above, our study attempts to answer to the following research question: Can daily and weekly one year maturity commodity convenience yields explain and predict subsequent daily and weekly one year maturity ZCIS rates within co-integration, vector error correction, vector auto-regression and causality frameworks?

This paper is organized as follows: The first section presents a literature review about general components, features and forecasting capacity of commodity convenience yields. We also discuss how convenience yields behave and what they signal under different commodity futures price biasness regimes. Second section is devoted to raw data collection of commodities and explanation of data development, convenience yield calculation and finally presentation of list of commodities we focus on. In the third section, we explain econometric methodologies, present and discuss our findings. Our concluding remarks are presented in the fourth section.

2. LITERATURE REVIEW With the objective to approach the concept of convenience yield variables and draw sound conclusions

regarding relationship structure between ZCIS rates and commodity convenience yields, we perform literature research focusing on inflation forecasting capacity of inflation derivatives, information content of commodity convenience yields, interaction between convenience yield and price volatility, convenience yields' seasonality behaviors, time dependency of convenience yields and finally implications of carry cost futures pricing theory and risk premium futures pricing theory on stochastic convenience yields.

In order to understand forecasting capacity of inflation derivatives such as ZCIS rates, one needs to understand practical aspects of inflation. Debate on whether policy makers should pay more attention to core inflation or headline inflation continues amongst academics and practitioners. De Gregorio, José (2012) argued that central banks focus on headline inflation more than core inflation, the one that excludes energy and food prices. Mija, Simion, et al. (2013) on the other hand argued that core inflation, was better indicator than headline inflation for the underlying inflationary pressures especially in emerging economies where food inflation has more significant effects. Similarly Cristadoro, Riccardo, et al. (2005) claimed that core inflation offered more accurate picture of inflation pressures in the Euro area. Researchers mentioned above proposed their conclusions on which measure of inflation required more attention. They also linked their findings on the basis of which type of economy they studied. In fact one should realize that none of those researches collectively agreed on a definitive answer as to whether core inflation or headline inflation is better indicator of actual underlying inflation pressures. Research published by Fulli-Lemaire and Palidda (2013) suggested that, covariations between core inflation and headline inflation in USA recently increased so that neither was more important as far as relationship between inflation and commodity prices were concerned. Fulli-Lemaire and Palidda (2013) reinforced their views by referencing to the case that, crude oil, a significant contributor to core

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inflation, may have been used as cross hedging vehicle against variations in both core inflation and headline inflation. Per the conclusion that crude oil price variations may be incorporated in to either measure of inflation, one can assume that inflation derivatives such as ZCIS rates may be robust for their inflation forecasting capabilities.

Many financial analysts, economists and academics from private and government sectors use the term structure of interest rates to extract information regarding how economic indicators evolve. The Federal Reserve (FED) officials use such information in efforts to predict inflationary pressures, economic growth and other major economic indicators. Research published in 1990 by Mishkin who actively contributed to the FED’s short term funding rate decisions between 2006 and 2008 suggested that the term structure of interest rates in the short end of the yield curve, the nine to twelve months period, contained information about the future path of inflation while caution may have been required for longer maturities. In their study, Schulz and Stapf (2011) concluded that although government bonds provided better information on inflation, inflation derivatives also contributed to the markets with information during normal economic times.

As Change (1998) implied, for a more concrete judgement of whether economic activity was likely to slow down or gained momentum, both the yield curve and the term structure of commodities should have reflected the same expectations. Barunik and Malinska (2015) concluded that term structure of crude oil futures prices proved to serve in similar behavior to yield curve, implying that term structure of commodities may have had similar capability to forecast prices as well as economic conditions. Market participants, namely, operators, producers, speculative traders, arbitrageurs, all infer expectations from the slope, the direction of the slope as well as the changes in the slope of the term structure. Haase et al. (2013) suggested that, variations of financing and storage costs had homogenous effects on the term structure of futures prices, allowing that futures prices shifted along the curve so that the spreads, namely the differences between futures prices of different maturities, did not change much. Nevertheless, scarcity factors, inventory variations and convenience yield may have varying effects on commodity prices along their price curve, while they may also provide useful signals regarding subsequent price actions, mean reversions, volatility and seasonality as explained in the next section.

We trust that, findings of Fulli-Lemaire and Palidda (2013), Schulz and Stapf (2011) and Barunik and Malinska (2015) may be considered as relevant academic literatures which support our research that convenience yields extracted from term structure of commodity prices, may be associated with ZCIS rates and that there may be unilateral causal relationship from commodity convenience yields to ZCIS rates. Further academic reference support this hypothesis: Although they did not refer to the convenience yield directly, Garner, (1989); Marquis and Cunningham, (1990); Cody and Mills, (1991) suggested that commodity prices were useful in predicting inflation rate. Titus and Yang (2013) re-confirmed their conclusions that commodity prices were found to be useful in predicting the inflation rate. Gosposdinov et al. (2013) took one step further and claimed that commodity convenience yields provided useful information to predict not only the future spot prices but also the inflation.

Rationale behind individual agents demanding commodities at different time frames, either on spot or forward basis, may possess valuable information when examined on a collective basis. Possessing most commodities do not yield returns. Rather there are financing and storage costs associated with possessing a commodity. Kaldor (1939) and Working (1948) introduced the concept of convenience yield which explains potential yield for owning a physical commodity. It is the yield that can be earned from holding/storing the

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commodity with the anticipation that there will be a temporary shortage of inventories. Pindyck’s (1993) suggested, convenience yields acted as temporary dividends which may have had potential to offset carry costs associated with holding a commodity. Kremser and Rammerstorfer (2010) concluded that convenience yield measures the benefits of building physical commodity inventory which allowed meeting unexpected demand. Alquist et al. (2010) claimed that the increased uncertainty sparked precautionary demand for oil to increase, such that the spot price of oil increased relative to its futures price. Pindyck’s (1993) suggested that the convenience yield was a forward looking variable that contained information not exclusive to future demands. Therefore we imply that not only the increase in the precautionary demand raises the convenience yield, expected and/or ongoing inventory scarcity may also increase spot prices relatively higher than futures prices.

Lautier (2003) acknowledged that term structure of commodities, a broader term covering concept of convenience yield, was the relationship between the spot price and the futures prices. Known also as the basis, term structure is simply calculated by subtracting the futures price from spot price. Convenience yield on the other hand is the carry cost adjusted basis, meaning that carry costs are added on top of the difference between the spot and futures prices. For example French (2005) explained convenience yield as interest adjusted spot-futures spread. Roache and Erbil (2010) calculated convenience yield in the form of interest adjusted basis by the formula “cy = (ln(St) – ln(Ft) + (rf + u)) * (t/360)”, which allowed the comparison of the current basis, as dictated by term structure of futures prices, against how much would the basis be if only measurable carry costs were applied in the futures pricing process. From these inferences, we can suggest that interest adjusted basis can be regarded and treated as the expected risk premium measured in percentage terms and is added on top of carry costs.

If market forces allow spot prices to become vastly superior to futures prices, price condition called “backwardation” evolves. If however, spot prices are lower than futures prices, price condition known as “contango” takes place. Lautier (2003) suggested, after its introduction by Keynes (1930), term structure of futures prices has neither been rejected nor validated. Nevertheless, implications of backwardation and contango conditions are adopted by practitioners and academia. In case of backwardation, buyers take the full control of market, expecting that holding on to the physical commodity will yield profit despite the accrual of carry costs. Gibson and Schwartz (1990) suggested that operators may constitute stocks, if they expected commercial advantage of building inventories due to rising expectations of stronger economic activity. Similarly, Carlson et al. (2005) hypothesized that, cash prices soared in excess of futures prices until traders were convinced that ongoing scarcity rewarded them for holding on to stocks and therefore they may started to withdraw stocks from inventories. Bessembinder (1992) argued that, high convenience yield, implying higher than normal spot price, has been an indication that investors may have been anticipating that prices could revert soon. In case of contango, market participants preferred to postpone possession of physical commodity and instead they were inclined to buy futures to fulfil their projected demand of inventory. In other words, as Carlson et al. (2005) estimated, futures premiums potentially rose to the extent of full cost of storage because should futures prices rose in excess of what carry cost rates suggested, excessive futures premiums would attract arbitrageurs to sell futures and buy spot commodities at the point where carry costs were defrayed and a possible reversal may have begun. Gibson and Schwartz (1990) referred to this condition by highlighting the case of operators who became aware of poor benefit of holding on to stocks due to expectations of slowing economic activity. Therefore since Schwartz (1997) confirmed that inventory levels were correlated with mean reversion, one may conclude that term structure of futures prices may be useful not only for forecasting economic conditions but it can help subsequent price activity.

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Convenience yield have further notable implications when studied from volatility perspective: Fama and French (1988) suggested that oil prices were more volatile than futures prices when inventories were low, supporting the Samuelson (1965) hypothesis that future prices are less variable than spot prices at lower inventory levels. Hong and Yogo (2009) supported Fama and French (1988) and Samuelson (1965) by suggesting that in case of backwardation, the volatility of cash and the nearby futures prices rose with respect to the volatility of more distant futures contracts where as in case of contango, the volatility of spot and futures prices tended to be relatively lower.

One of the most significant feature of convenience yield is its mean reversion capacity which is primarily owed to the aspect of seasonality. Mirantes et al. (2012) highlighted links between seasonality of convenience yield and inflation by concluding that convenience yields were robust in estimating commodity price seasonality and performed better than commodity prices themselves.

Futures price evolution and discovery process is dynamic allowing convenience yield to possess fractal and time dependency aspects. Brennan (1958) concluded that changing inventory levels affected expectations such that risk premium concept defined varying expectations regarding the characteristics of price reversals and risk aversion levels. That being said, Brennan’s suggestion explains why speculators become more suspicious about how much and for how long to hold on to their stocks. Sévi (2015) explained variant interaction between inventory levels and commodity prices from stochastic process perspective in that, the extent of price volatility and spot price discovery depended on the stochasticity convenience yield. Dinçerler et al. (2005) explained the varying relationship between inventories, convenience yield and the price discovery process from convexity perspective: They suggested that, in the case where risk premium theory of futures pricing was in effect, the extent of price volatility and futures price discovery depended on convenience yield that was time varying, non-monotonic and stochastic, allowing the mean reversion process to retard or expedite. This brings further implications about the capacity of convenience yield. Ataollah (1999) suggested that persistent but mean reverting convenience yield implied that the expected price did not adjust quickly. This suggestion can be interpreted as, if convenience yield does not revert quickly and remain persistent, then one may suppose that the expected prices adjust so that inflation expectations change as well. Nazlıoğlu and Soytaş (2012) supported this inference by suggesting that if prices of crude oil shifted and remained persistent at its subsequent trading range for considerable time, then they may have had indirect effect on inflation.

Whether or not a commodity futures is biased or unbiased is one of the defining concepts of our study. Samuelson (1965) was the first to consider futures prices as unbiased estimators of future spot prices. Fama (1991) proposed three forms of efficiencies so called weak form, semi-strong form, and strong form efficiency. Weak form efficiency suggested that prices followed all available information found in historical prices while semi strong efficiency suggested that prices adjusted quickly to reflect historical prices as well as the information that was publicly available. Finally strong form efficiency suggested that prices reflected not only historical prices and publicly available information but they also reflected even the private information.

Haq and Rao (2014) explained the efficiency of futures markets allowing that futures prices were essentially accurate predictions of future spot prices in the absence of risk premium variance and biasedness while prices reflected all available information symmetrically as all trading agents, including speculators, hedgers and arbitragers make rational decisions. Chance (1997) suggested that futures prices would be unbiased expectations of future spot prices if futures prices did not contain risk premium and therefore speculators would not be rewarded for their risk taking activities. Beck (2006) suggested unbiasedness was about joint hypothesis

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that market was efficient in the absence of risk premium. Chinn and Coibion (2014) stated that sufficient market liquidity and volume were essential prerequisites so that agents could freely change their positions as new information arrived. They further bound the concept of unbiasedness to forecasting ability of a futures contract. This claim finds support from Antoniou and Holmes (1996) who suggested that price discovery role of futures markets prevailed only when they were efficient. What we infer from the literature regarding efficiency of futures markets is, unbiasedness, efficiency and risk premium, are concepts that are closely linked to each other in that, lack of efficiency and presence of risk premium may drift current futures prices from what the future spot prices are ought to be, making prices may no longer be unbiased indicators of future spot prices. We can also infer that unbiasedness of futures prices is important also because it refers to fairness and accuracy of price discovery process since it refers to dissemination of useful information symmetrically allowing rational agents to remain in the market to ensure a liquid trading environment.

Literature offers many research studies that conclude contradicting results about efficiency and/or unbiasedness of futures markets. The source of such contradictions probably depend on the biasedness of analytical approaches in terms of time period, maturities, criteria of effectiveness, methodologies applied and commodities included in those studies. Pindyck (1993) concluded that, under the assumption of risk-averse market participants, futures prices were systematically biased. Danthine (1978) suggested that futures prices were biased estimates of future spot prices because of the fact that asymmetry between trading agents prevailed along with asymmetric commitments which caused the weight and balance of positions to skew. Kellard et al. (1999) assessed efficiency from co-integration point of view and highlights that in the long run spot and futures were strongly co-integrated where as in the short run subsequent changes in the spot prices could be predicted by the lagged differences of spot and futures and basis allowing agents to profit from such inefficiency.

Highlighting the fact that there are different research approaches and claims regarding efficiency and (un)biasedness of futures markets, a literature scan of commodity specific unbiasedness may provide further implications about the commodities we are involved with in this study. We therefore aim to explain how specific individual commodity futures are (un)biased and react to endogenous and exogenous factors in relation with their ability to predict future.

Knetsch (2007) suggested that crude oil's price series were unsuccessful in predicting the subsequent price changes ahead and therefore elements of random walk clearly existed suggesting that crude oil market was inefficient4. In contract with Knetsch (2007) Chinn and Coibion, (2014) concluded that oil futures were unbiased and efficient in terms of reflecting the available information on a timely basis but their findings were in line as findings suggested that oil and gold underperformed for predicting the future spot prices. Their findings also suggested that gold failed to maintain its unbiasedness in particular implying that gold price could often be directed by only certain agents namely long/short hedgers, arbitragers, swap traders and large speculators. Casassus and Collin-Dufresne (2005) noted that silver as well as gold mean reverted due to negative correlation between spot prices and risk premium which depends on whether the commodity in focus was a production/consumption good or a store of value. Tang and Xiong (2012) explained the mechanics of such negative correlation as fund managers tended to construct long commodity positions in addition to stocks when risks are perceived as manageable. This correlation structure between gold and stock markets did not seem to

4 Knetsch (2007) also suggests that previous convenience yields are far more robust in predicting the subsequent prices of crude oil within 1 to 11 month perspective.

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conform to the findings of Creti et al. (2012) who suggested that gold was negatively correlated to stock market declines and level of correlation weakened when stock markets fell. The opposing suggestions of Creti et al. (2012) and Casassus and Collin-Dufresne (2005) may have indeed been result of commodity financialization. Miyazaki and Hamori (2014) explained that, acceleration of gold’s financialization lead the gold to act as a financial asset rather than a commodity. This is significant finding because financialization phenomenon may risk ability to assess effectiveness of futures contracts. This is why Büyükşahin and Robe (2014) urged the need of further research as to whether financialization posed threat or offered opportunities to market efficiency. Similar contradicting suggestions can be spotted by comparing the findings of Agyei-Ampomah et al. (2014) and Chng and Foster (2012). Agyei-Ampomah et al. (2014) found that gold was included in portfolios when crisis out broke. Chng and Foster (2012) on the other hand concluded that manufacturing firms found it convenient to stockpile gold and especially silver during good economic times. Considering that investors use publicly available information even when cross market forces are in effect, one would be inclined to believe that gold, silver and WTI crude oil are efficient and therefore unbiased from the information sensitiveness perspective. There are also other studies which claim that otherwise however. For example (Lean et al. 2010) claimed that oil markets were efficient since they found no significant stochastic dominance between the spot and futures markets. However the fact that they draw such conclusions with up to four months maturity contracts poses a question as “What would findings suggest if they were to research whether there is stochastic dominance with longer maturities of one year or more?” In fact, Chinn et al. (2001) suggested that crude oil futures with up to three month futures explained only 40% of the underlying price activity. More a more recent study done by Chinn and Coibion, (2014) claimed that in recent years there has been a period in which WTI crude oil had features of unbiasedness even when futures contracts of up to twelve months are considered while according to Dufresne (2005) gold and silver may begin to possess more and significant biasedness qualifications5.

The theory that crude oil may lack predicting power of future spot prices may be result of financialization. However, its interactions with agricultural commodities may be worthwhile to consider in efforts to understand proxy and exogenous forces that drive agricultural prices. Academic literature reveals conflicting conclusions about the effects of energy prices on agricultural commodities. Baffes, (2007) suggested that there was a pass-through structure from oil prices to the prices of agricultural commodities, metals, fertilizers and non-oil commodities. Similar to the findings of Baffles (2007), Nazlıoğlu and Soytaş (2012) reported strong evidence that there was crude oil price impact pass-through and information transmission to agricultural prices. Ciaian (2011) suggested that after 2008, crude oil and biofuels began to have significant co-integrations meaning that residuals of the regression equation model of the two are so minimal that they co-move. On the other hand, Myers et al. (2014) offered an opposing conclusion that that there was no co-movement between energy and agricultural prices in the long run. It is important to realize that most studies which suggested that there was co-movement across energy and biofuels are researches that have been conducted after financialization gained velocity after 2007. Therefore the findings of Campiche et al. (2007) which suggested that there was no co-integration between oil and grains, including corn, wheat, soybean,

5 There are conflicting conclusions as to whether crude oil futures are biased or unbiased predictors of future spot prices. Varying conclusions may have been drawn depending on which periods are studied, which methodologies are employed and which criteria such as, liquidity, prediction power or information content set the terms of (un)biasedness definition. Our study is about one year maturity convenience yield which is a function of spot and one year maturity futures prices simultaneously. In our literature research we found no conclusion suggesting that crude oil futures are unbiased in both spot/nearby futures basis as well as twelve month basis simultaneously. We therefore see crude oil futures as biased and inefficient.

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soybean oil and sugar is not surprising and this also shows how co-movement and efficiency of commodities be time varying. A recent study conducted by Avalos (2014) concluded that energy prices co-moved with food prices and highlighted that co-integration between WTI crude oil and corn was significant while there was no co-integration between crude oil and soybeans. When we consider the findings of Hakkio and Rush (1991) who claimed that efficient markets with different commodities should not have been co-integrated, we can infer that WTI crude oil and corn are inefficient markets when regarded jointly. Mckenzie and Holt (1998) supported this finding specifically for corn futures by suggesting that although corn futures market was efficient and unbiased in the long run, it showed signs of time varying risk premium, inefficiency and biasedness in the short run. Chinn and Coibion (2014) blamed increasing level of financialization of commodities for increasing co-movement between energy commodities and agricultural commodities. They claimed that although common factors affected the two commodity classes, predictability has not been enjoyed. Considering the fact that the predictive capacity of these two commodity classes showed no signs of improvement and that both classes co-moved, we can conclude that the biasedness characteristics of crude oil may have contaminated corn, wheat, soybeans, soy oil and sugar too. Algieri and Kalkuhl (2014) supported this view by referring their findings to maize, soybean and wheat futures markets. They suggested that these futures markets were not informationally efficient since investors could profit on them even when they took in to account maturities of no more than two months at any given time.

To be able to understand the links between energy and agricultural prices, ethanol deserves special attention as it may be the missing tie between the two commodity classes, namely energy commodities and agricultural commodities. Zilberman et al. (2007) supported that introduction of corn ethanol has had a significant impact on food commodity prices while Avalos (2014) concluded, oil prices became a relevant factor for ethanol. Kristoufek et L. (2012) observed that ethanol having significant relationship with oil was connected to corn, wheat and soybeans even in short term. Chng and Foster (2012) concluded further that ethanol-corn spread adjustments were more significant than adjustments between ethanol and other grains, namely wheat and soybean suggesting also that ethanol was an appropriate commodity for cross-hedging biofuels such as corn, No 11 world sugar, soybeans. In addition Dahlgran (2010) concluded that, although ethanol futures contract was thin, the market offered effective risk management chance for commercial users and producers. Also from the pricing point of view, the study suggested that with the exception of nearby contracts of up to one month, longer term maturities displayed pricing efficiency. Under the light of the above suggestions ethanol futures contracts can be regarded as effective and unbiased.

Hasan and Hoffman-MacDonald (2012) suggested that lumber futures were not rational in the sense that spot and futures prices did not converge and that there was no co-integration between the spot and futures prices during when the futures contract was actively traded. In addition they claimed that the market was too small and also only 42% of lumber production was represented at the exchange. According to claims made by Haq and Rao (2014) in regards to efficiency of futures markets, findings of Hasan and Hoffman-MacDonald (2012) suggest that lack of adequate market agents, such as hedgers, speculator and arbitragers, may lead the pricing lumber’s discovery to be biased and non-effective.

Janzen et al. (2012) concluded that cotton prices evolved mostly due to real economic activity, the precautionary demand for inventories, possible shocks to current net supply suggested that cotton was biasedly priced commodity. In addition Varangis et al. (1994) suggested that 50% of yearly volatility could be captured by US cotton futures contracts but in some cases, if hedging was not executed at the right time and in the correct

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amount then hedging may have caused risk to increase rather than risk reduction. This claim leads us to infer that efficiency of cotton is time varying and therefore cannot be regarded as efficient and/or unbiased.

Gospodinov et al. (2013) found that platinum prices were responsive to monetary policy shocks and they suggested that contractionary monetary policy announcements likely increased platinum prices implying that platinum was more reactive than proactive. Another example of how platinum was reactive to exogenous factors was provided by Chng and Foster (2012) who concluded that manufacturing firms increased their holdings of platinum and palladium holdings during good economic times when inflation expectations built up. In addition Agyei-Ampomah et al. (2014) found that industrial metals such as palladium and copper performed as a better hedging tool against possible losses in bond portfolios than gold, implying that, palladium prices rose in response to rising interest rates triggered by rising expected inflation. They also suggested that palladium, copper and lead served as a strong safe haven as they were used as a hedge against the deterioration in the credit quality during the recent financial crises. According to the findings of Arouri et al. (2013), platinum and palladium futures markets conformed to the efficiency criteria of Brealey and Myers (2003) who suggested that market were efficient provided that current prices could be forecasted by the evolution of the previous day’s prices. Chikobvu (2014) studied price evolution of platinum from the random walk hypothesis perspective and concluded that platinum futures were regarded as weak-form efficient suggesting that prices followed all available information found in historical prices. This suggests that platinum are barely unbiased. Finally Chinn and Coibion (2014) claimed that both precious and base metals were poor predictors of subsequent price changes shed a little light to the findings that platinum was barely efficient while gold and silver may not have been efficient. However, their findings lead to be more cautious regarding whether palladium was really efficient and biased or not.

Chaundri (2011) reported that copper’s demand structure was inelastic meaning that it may not have been responsive to changes in supply and demand forces. Casassus and Collin-Dufresne (2005) claimed that under the physical measure, high grade copper mean reverted as a result of time variation in risk premium implying that price discovery may have been based on biased pricing process. Chinn and Coibion (2014) confirmed this inference as they altered that high grade copper failed the test of unbiasedness in terms of squared forecast error.

Chen (2009) claimed that, unleaded gasoline proved to be a good indicator of both inflation and future spot prices. In addition to the findings of Chinn (2009), Chinn and Coibion (2014) suggested that gasoline and heating oil futures prices could be used to find subsequent prices and that they were unbiased predictors of future spot prices across all horizons except natural gas which failed to possess effectiveness properties.

After extensive discussion of commodity specific (un)biasedness, we also discuss two main approaches for futures pricing, the carry cost hypothesis and the risk premium hypothesis, both of which constitute integrity of our discussion and scientific knowledge we offer.

According to the model of carry cost hypothesis, the spot and futures prices of commodities, respectively denoted by St and FT-t are linked by the following relation. The simple model of carry cost hypothesis based futures pricing formula is as follows3:

Ft,T = St * e(rf + u – cy) * (t/360) (1)

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where, “Ft,T”, “St”, “rf”, “u” and “cy” point out respectively futures price, spot price, the risk free rate, the cost of carry and the convenience yield.

If carry cost hypothesis is the driving theory behind an observed futures price, then one would assume that market agents follow an inductive pricing process by adding carry cost factors such as spot interest rates, physical maintenance costs and current spot supply and demand balance which is associated with convenience yield on top of spot prices. In this case agents’ concern would be nothing else to estimate the subsequent changes on these factors.

By the same token, Vansteenkiste (2011) symbolized risk premium hypothesis as6:

Ft, T – St = Et (ST) – St - rp (2)

From the above symbolization, one can derive risk premium based futures pricing formula as:

Et (ST) = St * e(rf + u – cy) * (t/360) + rp (3)

where, “Et (ST )” represents today’s, “t”, expected futures price for delivery at time “T”

Chance (1997) stated that although futures prices are generally regarded as unbiased expectations of future spot prices, expectations may sometimes lead futures prices to imply financing and storage costs different than what they actually are. While this is the case, agents expect a future spot price by incorporating current carry costs and then adjusting them with a risk premium component, marked as “rp” in the expectation hypothesis theory model presented in the above formula where risk premium is function of potential variations in all factors incorporated in carry cost hypothesis futures pricing such as the risk free rate, cost of storage and the convenience yield as well as all other exogenous macro factors that may directly or indirectly influence discretionary expectations on a collective basis while making this whole process a deductive approach. For example agents would need to forecast the nature of interaction between the convenience yield and risk premium before they apply risk adjustment. We infer this from Gorton, Hayashi and Rouwenhort (2008) who assumed the level of inventories were negatively related to the required risk premium of commodity futures. Such inference can also be based on Brennan (1958) who suggested that in case where current inventory levels rise, the risk premium may be less significant. The underlying variance of the interaction between current inventory levels and the risk premium may be the reason why convenience yield is time varying, non-monotonic and stochastic as Dinçerler et al. (2005) suggested.

Implications of futures pricing paradigms are significant. Gospodinov and Ng (2011) stated that carry cost hypothesis based pricing model and expectations hypothesis based pricing model implicitly define convenience yield and risk premium respectively. This may imply the following: If carry cost hypothesis based futures pricing is dominant, convenience yield would have straightforward and significant impact on the spot price in the form of, for example precautionary demand, and then futures price would be calculated by

6 Chance (1997) also explains expectations based futures pricing as summation of Futures price plus risk premium and theory is symbolized as St + (rf + u) + rp = Et (ST), where, “Et (St)”, “St”, “rf”, “u” and “rp” represent today’s (t) expected futures price at time “T”, today’s (t) spot price, today’s (t) risk free rate, cost of storage and risk premium applicable for the forecasted period respectively.

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incorporating risk free interest rate and physical cost of holding the commodity. If, on the other hand, risk premium hypothesis is the underlying theory behind the observed futures market prices, then agents would need to forecast not only the potential changes in the factors associated with carry cost hypothesis such as convenience yield, interest rates and storage costs but also they would need to consider all other exogenous macro factors that may potentially affect the expectations on future spot price of a commodity whilst complicating the entire pricing process.

When risk premium and carry cost hypothesis are compared, one can infer that the underlying factors and their inferences may be different and therefore futures price may be fairly different depending on which futures pricing hypothesis is in effect. This view is supported when findings of Roache and Erbil (2010) and Lautier (2009) are considered. Roache and Erbil (2010) suggested that expectations in future path of inventories may lead the futures price curve to change significantly while Lautier (2009) described convenience yield as being positive and deterministic function of the spot price. While convenience yield and expectations have independent and exclusive effects on spot and forward prices, they mutually interact and have significant effects on the price basis. Alquist et al. (2010) implied that precautionary demand of oil caused by rising convenience yield, was also associated with uncertainty of future excess demand. This is supported by Gospodinov and Ng (2011) who suggested that implications of futures prices driven by carry cost hypothesis and expectations hypothesis are tied by how convenience yield and expectations are mutually correlated. In particular, they suggested that in a case where inventories of a commodity are down and convenience yield was up, spot price of a commodity exceeded the expected futures price implying that convenience yields and future spot price expectations may have exclusive effects on spot-forward differential, namely, the basis although they are correlated with each other.

To sum up, we infer that, per carry cost hypothesis, the convenience yield is more primarily affected by the variations in spot prices while per risk premium hypothesis, convenience yield is primarily affected by variations in futures prices. That being said, convenience yield of a commodity, extracted from futures prices that are discovered by risk premium hypothesis pricing in which expectations are in full effect, would contain different information than the convenience yield that is extracted from futures prices that are discovered by carry cost hypothesis pricing. Therefore convenience yields that are calculated from a futures contract that is biased may have different capacity than the convenience yield derived from a futures contract that is unbiased. Fama and French (1988) supported this argument by suggesting that current and expected spot prices are influenced directly by the current and future commodity demand respectively. We also infer that although implications of convenience yield and future spot price expectations signal similar changes in price basis, one can conclude that carry cost hypothesis is more associated with the variations in current convenience yield while risk premium theory is linked to expected supply and demand forces which are exposed to endogenous as well as exogenous pricing factors.

As the final remark of our literature review, we analyze which time horizon deserves attention so that our bi-variate analysis of ZCIS rates and commodity convenience yields produce scientifically significant and practically useful results. There are two theoretical frameworks which support our decision of studying commodity convenience yield-ZCIS rate relationship on a one year perspective. Armesto et al. (2005) acknowledged that commodity futures with 6-9 months maturities rise in parallel to surprise increased in the federal funds rate target. They added that futures prices tend to fall back to their original levels after such moves if market participants believe that rise in the federal funds rates may be effective enough to mitigate future inflationary expectations. Study also suggested that, in the case where inflation expectations became

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persistent and remain elevated, commodity futures did not mean revert soon as expected. This study gives a clear understanding that, in addition to traditional carry cost based, no-arbitrage futures pricing framework, commodity prices may also be explained by risk premium theory which claims that market participants may impose their expectations on futures prices as well as on the convenience yield. If we link this inference with the findings of Söderlind et al. (1997) who claimed that extracting short term inflation risk premium expectations from 6-9 month forward rate curve were inadequate, then conducting analysis on a time frame that is more than nine month, such as one year makes sense under the assumption that inflation risk premium is also reflected on the term structure of commodities.

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3. DATA DEVELOPMENT Global financial turmoil that started late 2008 caused major structural breaks, extraordinary volatility

and major imbalances in prices and this continued until 2010 only after which markets calmed down and returned to relatively normal conditions. As Schulz and Stapf (2011) concluded that, inflation derivatives failed to discover price effectively due to turbulences caused by global financial crisis that erupted after autumn 2008. In this context, we decided that, data between 2007 and 2010 could contain so much noise that they could lead our econometric findings to become spurious and not match with the economic and financial theory. Therefore we employed the data set that was completely available between the period of February 2010 and August 2015.

Convenience yield is not a readily available data but it can be extracted from carry cost model futures pricing formula as shown below.

Ft, T = St * e(rf + u – cy) * (t/360) (4)

solving for “cy”, we get

cy = (rf + u - (lnFt,T - lnSt)) * (t/360) (5)

After downloading price data with appropriate maturities from Bloomberg, Reuters and Interactive Data terminals, we constructed a daily and weekly data set of one year maturity convenience yields. We calculated convenience yields based on the formula presented above. Since not all commodities trade on the same dates at all times, we assured that all different convenience yields correspond to common trading day. We did the same for weekly data series that were based on last trading day that is common to all convenience yield series of the week.

Since only few commodities have reliable spot price and that none of them has centralized spot physical carry cost data available on a daily basis, we used nearby futures contracts which generally mature in, more or less, 20 days as the spot price, St. As far as futures price, Ft, is concerned, we used the futures contracts that have more or less 12 additional months after the expiration of nearby futures contracts. For example, in the case of crude oil, we used nearby futures contracts which generally have around 22 days before its maturity and the futures contracts that have 13 months till its maturity. This way, we were able to capture the one year spread between the nearby future price and the far future price; the one year physical carry cost and the one year financing cost information on a forward to forward basis.

As far as one year interest rate is concerned, we used one year London Interbank Offered Rate (LIBOR). It would be more precise to calculate and use the one month maturity LIBOR forward rate agreement for twelve months period by interpolating the one month period spot LIBOR rate and the thirteen months period spot LIBOR rate. However the difference between the one year spot LIBOR and one month maturity LIBOR forward rate agreement for twelve months is just minimal enough to neglect and avoid such procedure.

There are more than sixty commodity futures available in the North American commodity futures space. In our entire dataset, we have daily and weekly convenience yield series of 24 North American exchange traded

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commodities7 staring from February 2010 until July 2015 and August 2015 for weekly and daily series respectively.

4. METHODOLOGY AND RESULTS Stationarity assessment of commodity convenience yields and ZCIS is prerequisite for appropriate

application of co-integration and/or VAR process. Appropriate co-integration requires non-stationarity at levels and stationarity at first order differences, I (1), while VAR requires that variables are stationary at either level and at first difference in our study. In co-integration case we also expect both dependent and independent variables to be non-stationary at level. According to Engel and Granger (1987), only then we can sensibly assess residuals of their co-movement and make accurate drawings regarding stationarity results of residuals. In case of VAR we need all variables to be stationary because without them being stationary at the same time does not allow researchers to determine a regression equation in which the dependent variable is produced by an apparent comprehensive generating process. As simplified by the regression equation below, a simple approach that leads to stationary testing, also known as unit root testing is presented.

Yt = β1Yt-1 + ℇt (6)

provided that β1 is low (less than 100%) and statistically significant and that the variance of residual, ℇt, cluster does not exceed one sigma (67%)

Our main unit root testing framework is Augmented Dickey-Fuller Test (ADF Test). Specifically, we employed AR (1) model of Augmented Dickey-Fuller Test. We specified our test credentials with an intercept α0, allowing that sum of all changes are non-zero and that they drift overtime. Accordingly we assumed time trend component, β0t in the model. In addition, due to the stochastic (random walk) nature of financial data we added error term, ℇt in the equation below:

Yt = α0 + β0t + β1Yt-1 + ϴ1ΔYt-1 + ϴ2ΔYt-2 + … + ϴpΔYt-p + ℇt (7)

such that, H0: β1=1, that, the time series Yt is non-stationary; H1: β1<1, that, the times series Yt is stationary

and also that

H0: β0=0; that mean and auto-covariance of the series do not depend on time; H1: β0≠0, that mean and auto-covariance of the series depend on time according to Dickey-Fuller t-statistics

For ADF test to be applied, “the term “p” expressed in formula 7 needs to be determined. Therefore we used Akaike information criterion to calculate the “p” at which the sum of error squares of the model is minimum.

As the secondary unit root testing methodology we employed Philips-Perron Test to understand if results of stationarity conforms to each other or not. Unlike the ADF test in which Akaide information criteria is essential to determine lags of time series differences so that regression equation of ADF test does not suffer from serial correlation and heteroscedasticity, Philips-Perron test does not require determination of appropriate 7 West Texas Intermediate crude oil, unleaded gasoline, heating oil, natural gas, ethanol, copper, palladium, platinum, gold, silver, wheat, corn, oat, soy meal, soy oil, cocoa, coffee, sugar, cotton, lumber, orange juice, lean hog, live cattle.

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lags. In Philips-Perron approach, the fact that it uses a modified t-statistics table adjusted for serial correlation and heteroscedasticity, makes it easy and worthwhile to apply in our research. Although both tests alter almost same results, double checking the accuracy of stationarity of series plays a significant role in performing our series of analysis appropriately and draw concrete and accurate conclusions.

Using ADF and Philips-Perron stationary testing methodologies, we tested and on Table 1, we presented the test results of daily and weekly stationarity of ZCIS rates as well as daily and weekly convenience yields of all the commodities we mentioned in the data section. According to visual examination of series, we processed our analysis based on three regression assumptions which are random drift and intercept, only intercept and finally, neither intercept, not drift.

It is important to note that in some cases it is unclear as to whether a series is stationary or non-stationary. Sometimes different indicators and diagnostics of one methodology contradict within each other. In some cases, two different methodologies may suggest different results or sometimes results may appear to be just shy of the critical probability threshold levels. In fact there are ongoing discussions about stationarity testing in academia. One area of concentration is in regards to ADF testing methodology which we employed as our principal stationarity testing approach. As opposed to conclusions made by Dickey and Fuller (1979), Glynn et al. (2007) and Brooks (2002) claimed that ADF testing may not have been effective especially when calculations suggested that time series were barely stationary. Brooks (2002) suggested that, the effectiveness of the tests was low if the process were found to be stationary with a root close to the non-stationary boundary. In this case, if the variables in the regression model are not stationary, then it can be proved that the standard assumptions for asymptotic analysis may not be valid. In other words, the usual “t-ratios” will not follow a t-distribution, so we cannot validly undertake hypothesis tests about the regression parameters. Given such uncertainties about the efficiency of ADF testing, we have made discretionary decisions based on R2 results, how far critical probability levels are close to threshold levels of one indicator of same or different method. In case where we made decisions based on our discretion, we explained them as end note under Table 1, where we summarize our findings of stationarity of our daily data series and the weekly data series as below:

Table 1: Augmented Dickey-Fuller and Philips-Perron Stationary Tests

Variables (Convenience Yields) Regression Model Difference Level ADF t-statistics 1 Philips-Perron t-statistics Probability (Significance Level) 3 Status

Daily Weekly Daily Weekly Daily Weekly Daily Weekly

Zero Coupon Inflation Swap Trend and Intercept Level -2,6854 -3,2943 -2,6546 -2,9176 0,2428 0,0693 NS NS

First Difference -12,0820 -12,625 -38,7113 -12,6089 0,0000 0,0000 S S

Unleaded Gasoline Trend and Intercept Level -3,0364 -3,3942 -3,0928 -3,3008 0,1226 0,0541 NS NS


Heating Oil Trend and Intercept Level -2,1765 -1,2465 -2,8618 -3,1299 0,5018 0,8981 NS NS


Palladium 4 No Intercept, No Trend Level -1,7757 -1,0383 -1,9775 4 -1,5603 0,0720 0,2693 NS 4 NS

First Difference --18,6085 -7,3653 -50,0165 -21,7557 0,0000 0,0000 S S

Ethanol, 2 Trend and Intercept Level -3,6958 -3,4228 2 -4,0413 -3,74512 0,0229 0,0504 S NS 2


Wheat 6 Trend and Intercept Level -3,3457 -3,7060 -3,4462 -3,6966 0,0594 0,0234 NS 6 S


Oat Trend and Intercept Level -2,9803 -3,1696 -3,1654 -3,1525 0,1381 0,0199 NS S

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WTI Crude Oil Trend and Intercept Level -1,4750 -1,3259 -1,3770 -1,7052 0,8378 0,8794 NS NS


Cotton Trend and Intercept Level -2,2751 -2,2377 -2,3347 -2,2299 0,4468 0,4668 NS NS


Coffee Trend and Intercept Level -3,1005 -2,9434 -3,1162 -2,9692 0,1065 0,1505 NS NS


Corn Trend and Intercept Level -2,6376 -2,5977 -2,6242 -2,4587 0,2635 0,2818 NS NS


No 11 World Sugar 7 Trend and Intercept Level -2,7247 -4,0702 -2,7911 -3,2676 0,2266 0,0078 NS S 7


Live Cattle Trend and Intercept Level -3,8131 -3,9238 -3,9240 -3,8769 0,0161 0,0123 S S


Soy Meal 5 Trend and Intercept Level -2,3155 -1,6309 -3,4221 5 -2,8789 0,4246 0,7784 NS 5 NS


Natural Gas Trend and Intercept Level -2,4774 -2,8335 -2,7672 -2,7745 0,3394 0,1865 NS NS


Silver Trend and Intercept Level -2,7087 -2,5927 -2,6386 -2,6820 0,2331 0,2840 NS NS


Cocoa Trend and Intercept Level -5,1632 -3,5860 -5,9774 -5,4781 0,0001 0,0328 S S


High Grade Copper No Intercept, No Trend Level -3,4008 -3,3060 -3,6065 -3,6067 0,0007 0,0010 S S


Lumber Trend and Intercept Level -3,6944 -3,5004 -3,4698 -3,4618 0,0230 0,0413 S S


Platinum Intercept Level -5,4503 -5,0700 -10,2801 -6,8072 0,0000 0,0000 S S


Gold Trend and Intercept Level -4,6522 -3,7835 -5,0451 -4,9040 0,0008 0,0188 S S


Orange Juice Trend and Intercept Level -4,0303 -4,0124 -4,1125 -3,9901 0,0081 0,0093 S S


Lean Hog No Intercept, No Trend Level -2,6014 -2,6703 -2,0385 -2,2879 0,0090 0,0076 S S


Soy Oil Trend and Intercept Level -3,9090 -3,7625 -3,7977 -3,8907 0,0119 0,0199 S S


Observation period: February 22nd, 2010 – August 21st, 2015 covering 1387 daily time series and 287 weekly time series.

“NS” stands for Non-stationary; “S” stands for Stationary.

Lags determined by Akaike Information Criterion.

All convenience yields are of one year maturity.

1 Critical Values for Augmented Dickey Fuller Stationary Test and Philips-Perron Stationary Test.

Significance Level Trend and Intercept Intercept Only No Trend, No Intercept 1% -3.9905 -3,4530 -2,5730 5% -3,4256 -2,8714 -1,9419

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2 Philips-Perron adjusted t-statistic of -3,7451 suggests that Ethanol’s weekly series are stationary at level whereas ADF Tests show that it is non-stationary. Since ADF Test’s R2 is 0,0959 while Philips-Perron Test’s R2 0,0507, our decision was to accept the suggestion of ADF Test which lead us to assume the data as non-stationary at level.

3 Probability corresponds to ADF Test.

4 Philips-Perron t-statistics oppose the suggestion of ADF t statistics in that Philips-Perron test claims that daily series of palladium convenience yield are stationary where as ADF tests claim that they are non-stationary. Since R2 of ADF test is 7,08% and Philips-Perron test is 0,5%, we decided that Palladium’s daily convenience yield series are non-stationary at level.

5 ADF Test suggests soy meal convenience yield is stationary with a significant t-statistic whereas Philips-Peron Test suggests that soy meal convenience yield is stationary with only barely significant t-statistic. Therefore we decided to assume that series are non-stationary as ADF test proposes.

6 ADF Test proposed that Wheat’s daily convenience yield series are non-stationary with an R2 of 2,82% while Philips-Perron Test suggested that the series are stationary by only a negligible margin and R2 of 0,87%. Therefore we regarded the series as non-stationary.

7 ADF Test proposed that Sugar’s weekly convenience yield series are stationary with an R2 of 8,91% while Philips-Perron Test suggested that the series are non-stationary by only a negligible margin and R2 of 2,44%. Considering that ADF Test’s R2 is higher and that probability is significantly low, We decided to accept suggestion that series are stationary.

ADF and Philips-Perron stationarity tests suggested that daily convenience yield series of copper, cocoa, lumber, ethanol, platinum, gold, orange juice, lean hog, live cattle and soy oil are all stationary both at level and at first difference. ADF and Philips-Perron Tests also suggested that daily series of ZCIS rates, crude oil, heating oil, palladium, gasoline, wheat, oat, cotton, coffee, corn, sugar, soymeal, natural gas and silver convenience yields become stationary only when they are first differenced.

ADF and Philips-Perron stationarity tests further suggested that weekly convenience yield series of wheat, oat, sugar, live cattle, cocoa, copper, lumber, platinum, gold, orange juice, lean hog and soy oil are stationary both at level and at first difference while weekly series of ZCIS rates and gasoline, heating oil, palladium, ethanol, crude oil, cotton, coffee, corn, soy meal, natural gas and silver convenience yields become stationary they are first differenced.

These results are important since they play key role in determining whether we use co-integration or VAR methodology to define characteristics of co-movement process between ZCIS rates and commodity convenience yields.

Co-integration is a well-defined process where two or more non-stationary independent variables, Yt and Xt are studied to conclude whether they have statistically significant linear relationship with low residuals and a statistically significant Beta constant. If this is provided, then difference between the variables, Yt and Xt must produce an error term or residual, εt, is stationary. Least square regression can be used to explain further how the process conforms to least squared standard regression model, “Yt = α + β Xt + εt”, by focusing on error component.

εt = Yt – α – β Xt (8)

In particular, if Yt and Xt co-move or co-integrated, then the residual, εt, should be stationary which can be tested by Augmented Dickey-Fuller Test.

In finance and economics, due to high volatility, structural breaks and economic shocks, most long term time series of prices and/or rates are non-stationary at level. They tend to have unit roots due to significant

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trends, seasonality factors and major unexpected shifts across time. However researches expect that two or more variables which are non-stationary at level become stationary when they are differenced at the same order in order to apply co-integration. (Johansen, 1991)

Employing bi-variate unrestricted Johansen cointegration testing, we assess co-movement capacity between daily ZCIS rates and daily series of one year maturity convenience yields of appropriate commodities, namely, gasoline, heating oil, palladium, wheat, oat, crude oil, cotton, coffee, corn, sugar, soy meal, natural gas and silver. We also assessed the co-movement capacity between daily weekly one year maturity ZCIS rates and weekly series of one year maturity convenience yields of gasoline, heating oil, palladium, ethanol, crude oil, cotton, coffee, corn, soy meal, natural gas and silver. We derive this list from Table 1 in which commodities are labeled as stationary or non-stationary at level and at their first difference on both daily and weekly basis. In Table 2, results and details of pairs that are co-integrated and displayed.

Table 2: Unrestricted Johansen Co-integration Tests

ZCIS Rate vs Trace Test Results

Trend Assumption Lags 1 Eigenvalue Trace Statistic 2 Probability Null Hypothesis 3 Number of Co-integrations

Heating Oil D Intercept and No Trend (ND) 4 lags 0,0123 21,6386 3,21% Rejected 1

Unleaded Gasoline D No Intercept or Trend (ND) 3 lags 0,0097 14,5517 2,08% Rejected 1

Palladium D Intercept and No Trend (LD) 1 lag 0,0174 27,6021 0,05% Rejected 1

Wheat D No Intercept or Trend (ND) 6 lags 0,0087 13,4131 3,27% Rejected 1

No 11 World Sugar D No Intercept or Trend (ND) 3 lags 0,0075 13,9809 2,61% Rejected 1

Crude Oil D Intercept and No Trend (LD) 7 lags 0,0100 16,4912 3,53% Rejected 1

Ethanol W No Intercept or Trend (ND) 1 lag 0,0632 20,1001 0,21% Rejected 1

Unleaded Gasoline W No Intercept or Trend (ND) 1 lag 0,0462 15,1764 1,62% Rejected 1

Heating Oil W Intercept and No Trend (ND) 1 lag 0,0600 24,1203 1,40% Rejected 1

Palladium W Intercept and No Trend (ND) 1 lag 0,0546 23,3783 1,80% Rejected 1

WTI Crude Oil W Intercept and No Trend (LD) 1 lag 0,0442 15,8057 4,49% Rejected 1

Cotton W Intercept and No Trend (LD) 4 lags 0,0475 16,4344 3,60% Rejected 1


“D” corresponds to “daily time series”. “W” corresponds to “weekly time series”. “ND” corresponds to “No Deterministic”. ”LD” corresponds to “Linear Deterministic”.

All convenience yields are of one year maturity.

Threshold for probability is 5%.

1 Lags are determined by Akaike Information Criterion.

2 Trace Statistics Threshold Levels for 5% confidence are 20.2618 and 12.3209 for “restricted constant trend” and “no deterministic trend” assumption.

3 Null Hypothesis: “There is no co-integration.”

As seen on Table 2, our co-integration test results suggest that daily series of heating oil, unleaded gasoline, palladium, wheat, sugar and WTI crude oil convenience yields with one year maturity are co-integrated with daily series of one year maturity ZCIS rates. We also find that weekly series of ethanol, unleaded gasoline, heating oil, palladium, WTI crude oil and cotton convenience yields with one year maturity are co-integrated with weekly series of one year maturity ZCIS rates.

From the co-integration perspective, this finding suggest that, there is enough evidence to conclude that non-stationary or time trending variations of ZCIS rates can be estimated by the regression equation which

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includes lagged variations of ZCIS rates and commodity convenience yields in focus with significant and persistent precision, while beating the null hypothesis that there is no co-integration and leaving only marginal room for error which is not more than five percent of the whole testing period.

Once we know which commodity convenience yields have long term association ship with ZCIS rates, specifications of long and short term association ship and the co-movement characteristics can be further analyzed by Vector Error Correction Model (VECM).

Johansen (1998) suggests that VECM should be employed in order to define the short term causality between co-integrated dependent and independent variables. VECM and VAR are similar concepts in that both models used lagged values each having correlation coefficient to estimate the most recent value.

Yt = α0 + β1Yt-1 + β2Yt-2 + β3Yt-3 + … + βpYt-p + ℇt (9)

With the assumption that variables are non-stationary at level and become stationary at first difference and that difference between variables are super consistent8, then VECM can be modeled as follows:

ΔYt = α0 + βΔXt ± λµt-1 + ℇt (10)

where,

“α0” explains vector of constant,

“β” explains short run shock effects on differenced lagged terms,

“λ” explains error correction term (ECT) or long run correction of the variables and can have negative and positive values,

“µt-1” is “(Yt-1 - Xt-1)”,

“ℇt” explains vector of errors.

Long term correction or adjustment coefficient, λ, may have positive or negative values. It is vital that for error correction to validate a reversal to long term equilibrium, error correction term has to have negative value. If the ECT is positive, one can conclude that there is no long run causality running from the independent variable to dependent variable and that both variable drift independent of each other. If ECT is negative and is proven to be reliable long term estimator thanks to low probability rejecting the null hypothesis, that λ ≥0, then ECT may suggest there is long term causality between dependent and independent variables, which in our case are ZCIS rates and individual commodity convenience yields respectively.

VECM model also provides information regarding short term causality. Performing WALD test to test whether the null hypothesis that all short term coefficients marked with µ collectively are not equal to zero is rejected. For such rejection to be significant, the null hypothesis that “There is no causality running from independent variable to dependent variable” is rejected thanks to low probability of null hypothesis being true.

8 As suggested by Stock (1987), super consistency is validated when one lagged variables (Yt-1 and Xt-1) of typical bivariate regression model, Yt = α0 + βXt + ℇ, can estimate next actual observed, Yt and Xt, values using ordinary least squares method with minimum errors, ℇ, that are stationary. It can be modeled as, ℇt = Yt - α0 - βXt where ℇt~I(0).

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In case null hypothesis is not rejected, then it is concluded that variables, the commodity convenience yields in our case, known as endogenous actually are regarded as exogenous variables having no direct link to the dependent variable, ZCIS rates.

We run VECM for those commodity convenience yields that are co-integrated with ZCIS rates to highlight the long term and short term causality running from individual commodity convenience yields to ZCIS rates. Our findings are presented in Table 3 as below:

Table 3: Estimates of Long Term Adjustments and Short Term Causalities

ZCIS vs Long Run Adjustment Estimates

Decision 2

Short Term Causality Estimates

Error Correction Term Probability Lags 1 Chi-Square Test P Value Decision 3

Heating Oil D -0,0048 4,93% Significant 4 lags 83,81% No short term causality

Unleaded Gasoline D 0,0002 87,09% Non-significant 3 lags 13,11% No short term causality

Palladium D 0,0005 56,81% Non-significant 1 lag 35,40% No short term causality Wheat D -0,0009 55,35% Non-significant 6 lags 22,93% No short term causality

No 11 World Sugar D 0,0002 1,58% Significant 3 lags 65,30% No Short Term Causality

WTI Crude Oil D -0,0103 0,57% Significant 7 lags 1,42% Short term causality exists

Ethanol W -0,0043 57,55% Non-significant 1 lag 59,42% No short term causality

Unleaded Gasoline W 0,0037 62,09 Non-significant 1 lag 15,08% No short term causality

Heating Oil W -0,0277 3,57% Significant 1 lag 19,65% No short term causality

Palladium W -0,0037 59,77% Non-significant 1 lag 28,86% No short term causality

WTI Crude Oil W -0,0504 0,72% Significant 1 lag 17,48% No short term causality Cotton W -0,0501 0,51% Significant 4 lags 8,30% No short term causality Observation period: February 22nd, 2010 – August 21st, 2015 covering 1387 daily time series and 287 weekly time series.

“D” corresponds to daily time series. “W” corresponds to weekly time series.

Threshold for all probabilities is 5%.


2 Null Hypothesis: There is no long run causality.

3 Null Hypothesis: There is no short run causality.

Results of daily series highlight that there is long run causality running from convenience yield of heating oil and of crude oil to daily ZCIS rates since their signs of error correction term, which is the coefficient of co-integration model, are both negative and significant with probability of 4,93% and 0,57% respectively. Despite significant results, in the case of heating oil convenience yield, error correction term is so small that, convergence takes 208 (1/0.0048) trading days which may not be realistic time frame to be considered by practitioners. In case of crude oil which also has significant error correction term, convergence takes 97 (1/0.0103) trading days.

There is also long term causality running from wheat's convenience yield to ZCIS rates however, since its probability suggests to accept the null hypothesis that "There is no long run causality" we can conclude that the likelihood of short term adjustment is not significant.

Error correction term for gasoline, palladium and sugar proves that there is no long run causality running from the convenience yield of these commodities to ZCIS rates due to the fact that their sign of correction term is positive and therefore no adjustment towards the equilibrium can be expected.

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In addition to long term causality, we also tested short term causality running from the lagged convenience yields of selected commodities to ZCIS rates. In particular, we applied Wald Test to suggest whether there is short term causality running from the lagged series of convenience yields to ZCIS rates. We found that since Chi square probabilities of all convenience yields exceed the 5% threshold to accept the null hypothesis that "There is no short run causality." we conclude that there is no short term causality except for crude oil's convenience yield. We find that there is short term causality running from WTI crude oil's convenience yield to ZCIS rates as seven lags of convenience yield collectively forecast when price may converge with equilibrium with small margin of error.

When weekly series are regarded we add more information to our findings. We conclude that there is significant long term causality running from weekly series of crude oil, heating oil and cotton to ZCIS rates as all have negative value of coefficient with probability less than five percent, 0,72%, 3,57% and 0,51% respectively. However we also find that convenience yield of ethanol and palladium are not significant although their error correction term suggest that there may be long term causality running from their convenience yield to ZCIS rates. In addition we suggest that there is no long run causality running from convenience yield of gasoline to ZCIS rates as its error correction term is positive. Finally Wald Test suggests that there is no short term causality running from any convenience yield in focus to ZCIS rates since their chi square probabilities are above the 5% probability threshold above which null hypothesis that “There is no short run causality” is accepted.

In order to decide if our regression models are acceptable, we performed residual serial correlation test, Breusch-Pagan-Godfrey’s residual heteroscedasticity test and Jarque-Bera’s residual normality. Results are presented on Table 4 as below:

Table 4: Estimates of Residual Serial Correlation, Breusch-Pagan-Godfrey Heteroscedasticity and Normality Tests

Residual Serial Correlation Breusch-Pagan-Godfrey Heteroscedasticity Test Normality Testing

Variables Lags 1 Chi-Square Test P Value Decision 2 Chi-Square Probability Decision 3 Jarque-Bera Probaility Decision 4

Heating Oil D 4 lags 0,15% Serial correlation exists 1,80% Heteroscedasticity exists 0,00% Not normally distributed

Unleaded Gasoline D 3 lags 0,04% Serial correlation exists 11,34% No heteroscedasticity 0,00% Not normally distributed

Palladium D 1 lag 37,81% No serial correlation 0,30% Heteroscedasticity exists 0,00% Not normally distributed

Wheat D 6 lags 61,55% No serial correlation 14,20% No heteroscedasticity 0,00% Not normally distributed

Sugar D 3 lags 0,65% Serial correlation exists 3,71% Heteroscedasticity exists 0,00% Not normally distributed

WTI Crude Oil D 7 lags 36,21% No serial correlation 0,00% Heteroscedasticity exists 0,00% Not normally distributed

Ethanol W 1 lag 70,50% No serial correlation 91,74% No heteroscedasticity 0,00% Not normally distributed

Unleaded Gasoline W 1 lag 42,56% No serial correlation 64,03% No heteroscedasticity 0,00% Not normally distributed

Heating Oil W 1 lag 54,28% No serial correlation 76,06% No heteroscedasticity 0,00% Not normally distributed

Palladium W 1 lag 52,90% No serial correlation 52,41% No heteroscedasticity 0,00% Not normally distributed

WTI Crude Oil W 1 lag 17,64% No serial correlation 3,79% Heteroscedasticity exists 0,00% Not normally distributed

Cotton W 4 lags 23,85% No serial correlation 0,22% Heteroscedasticity exists 0,00% Not normally distributed


“D” corresponds to daily time series. “W” corresponds to weekly time series.



2 Null Hypothesis: ”There is no serial correlation.”

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3 Null Hypothesis: “There is no heteroscedasticity in the residual.”

4 Null Hypothesis: “Residuals are normally distributed.”

Jarque-Bera’s residual normality testing suggests that none of our regression equation’s residual is normally distributed. Residual serial correlation tests conclude that residuals of VECM regression models built for heating oil, unleaded gasoline and No 11 world sugar on daily basis have serial correlation. This suggests that these models need to be adjusted and improved. Breusch-Pagan-Godfrey Heteroscedasticity Tests indicate that VECM regression models built for heating oil, palladium, No 11 world sugar and WTI crude oil daily convenience yield as well as VECM regression models built for weekly series of WTI crude oil and cotton convenience yield also need to be adjusted and improved so that efficient and sound forecasting can be done though VECM regression equations.

As a summary of our co-integration analysis, VECM analysis and diagnostic tests, we find that weekly series of heating oil is the best performer amongst other commodities for long run prediction of weekly ZCIS rates since its error correction term is significant to suggest that there is long run causality running from its weekly convenience yield to weekly ZCIS rates. Also the fact that heating oil's VECM regression equation shows no sign of serial correlation and heteroscedasticity, we can conclude that regression model is reliable despite that residuals are not normally distributed.

Other VECM regressions suggest a mixed picture in that despite promising diagnostics that there is neither serial correlation, nor heteroscedasticity, daily and/or weekly convenience yields of such commodities either do not have significant long run or short run relationship with daily and/or weekly ZCIS rates. It is important to note that only daily convenience yield of crude oil that has significant long and short run relationship simultaneously yet its diagnostics suggest otherwise.

As part of our analysis, we also employ VAR model to estimate regression equations that explain the dynamics between ZCIS rates and commodity convenience yields.

Typical VAR with intercept model can be written as :

Yt = α0 + β1Yt-1 + β2Yt-2 + β3Yt-3 + …+ βpYt-p + ℇt (11)

where,

“Yt” is at time t, a combination vector of independent individual variables at different p lags (t-p),

“β” values are correlation coefficients or amount and direction of impact factors of each independent variable at “p” lags,

“α0” vector of constant,

“ℇt” is vector of errors.

The above independent variable may be endogenous as well as exogenous factors affecting all other endogenous factors while endogenous factors amongst themselves can also affect each other. In our model, we use lagged series of convenience yield of a single commodity and the lagged series of ZCIS rates to estimate ZCIS at time “t”, therefore we are involved with endogenous factors which are lagged convenience yields.

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Engel and Granger (1987) suggested that if all series were not stationary while some are stationary, VAR results would be misleading. We therefore employed first differenced daily and weekly data series all of which were found stationary according to ADF and Philips-Perron stationarity tests, as presented in Table 1. This allowed appropriate application of bi-variate VAR process as well as Granger Causality Tests which we explain in the next section.

While performing VAR analysis, we paid special attention to selecting appropriate number of lags for commodity convenience yields and ZCIS rates. Lee (1997) stated that an arbitrary selection of lags may lead estimation to be biased or weakly efficient. Supporting conclusion is presented by Hafer and Sheehan (1989) who claimed that efficiency and accuracy of VAR models depended on correct lag selection. Therefore we adopted and used Akaike information criteria, a widely used and accepted method of defining the number of lags to include in our VAR models.

Based on the conclusions that ADF and Philips-Perron stationarity tests provide, we constructed two separate databases, daily and weekly, in which we added level series of convenience yields which are found stationary at level. In addition we added the first differenced series of ZCIS rates as well as the convenience yields that become stationary when first differenced to ensure that our daily and weekly database contains only stationary series for the purpose of running VAR and Granger Causality Tests appropriately.

One other important prerequisite of Granger Causality is that both variables, dependent and independent variables should be covariance stationary and while both are stochastic at the same time. This implies that variables can drift while magnitude of covariance between variables remains predictable. Once this given, Granger Causality can be run to simply test whether lagged values of Yt and Xt explain dependent variable Yt with less variation of error term, compared to the error term in the regression equation in which lags of only Yt are incorporated. If the condition that error term in the first equation is less than the latter, ℇ1t<ℇ2t, then one can conclude that Xt Granger causes Yt.

Yt = β1Yt-1 + … + βpYt-p + ϴ1Xt-1 + …+ ϴpXt-p + ℇ1t (12)

Yt = β1Yt-1 + … + βpYt-p + ℇ2t (13)

Same equation may be true vice versa as:

Xt = β2Yt-1 + … + βpYt-p + ϴ2Yt-1 + … + ϴpYt-p + ℇ2t (14)

Xt = β2Yt-1 + … + βpYt-p + ℇ3t (15)

If ℇ2t<ℇ3t, then one can conclude that Yt Granger causes Xt.

In order to confirm significance of such relationship, Beta terms’ significances are tested via F-tests with the null hypothesis that Beta=0. If the null hypothesis is rejected according to 5% threshold, then such probability can be estimated.

We run VAR analysis in which all commodities with appropriate data and ZCIS rates are included to capture any significant short term causality between ZCIS rates and the convenience yields of individual

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commodities. Wald tests suggested that, with probabilities of less than 5 percent, null hypothesis that “Commodity’s Convenience yield does not cause ZCIS Rate.” are rejected for daily series of WTI crude oil, high grade copper, corn, lumber and silver as well as for weekly series of platinum, cotton and silver convenience yields. Therefore we conclude that convenience yields of commodities mentioned in Table 5 have significant forecasting ability to capture movements in daily ZCIS in the short run.

Table 5 also summarizes our findings of Granger Causality tests which suggest that daily convenience yields of the commodities mentioned in the table all granger cause ZCIS rates.

Table 5: Estimates of Vector Auto Regression Model and WALD Tests and Granger Causality Test

ZCIS vs Wald Test Granger Causality Test (From Convenience yields to ZCIS Rate)

Lags 1 Probability Decision 2 f-statistic Probability Decision 3

Crude Oil D 7 1,65% Crude oil causes ZCIS Rates 2,4500 1,69% Crude Oil Granger Causes ZCIS Rates

Copper D 1 2,34% Copper causes ZCIS Rates 5,1393 2,35% Copper Granger Causes ZCIS Rates

Corn D 2 4,77% Corn causes ZCIS Rates 3,0433 4,80% Corn Granger Causes ZCIS Rates

Lumber D 2 0,22% Lumber causes ZCIS Rates 6,1358 0,22% Lumber Granger Causes ZCIS Rates

Silver D 1 1,57% Silver causes ZCIS Rate 5,6322 1,59% Silver Granger Causes ZCIS Rates

Platinum W 2 1,19% Platinum causes ZCIS Rate 4,5032 1,19% Platinum Granger Causes ZCIS Rates

Cotton W 4 2,91% Cotton causes ZCIS Rate 2,7389 2,91% Cotton Granger Causes ZCIS Rates

Silver W 5 0,75% Silver causes ZCIS Rate 3,0953 0,88% Silver Granger Causes ZCIS Rates




2 Null hypothesis: “Commodity’s Convenience yield does not cause ZCIS Rate.”

3 Null hypothesis “Commodity’s Convenience yield does not Granger Cause ZCIS Rate.”

We finally realize and note that short term estimates of VAR regressions provide better results than short term estimates of VECM regression equations in the absence of diagnostic tests. However as shown on Table 6, only VAR regression equations built from weekly series of platinum and silver convenience yields enjoy being free from residual serial correlation and residual heteroscedasticity, while rest of the VAR regression equations suffer from serial correlations as well as heteroscedasticity. Therefore whether our VECM regression equations or VAR regression equations work more efficiently becomes unclear in the presence of diagnostic tests.

Table 6: Estimates of Serial Correlation, Breusch-Pagan-Godfrey Heteroscedasticity and Normality Tests

Serial Correlation Breusch-Pagan-Godfrey Heteroscedasticity Test Normality Testing

Variables Lags 1 Chi-Square Test P Value Decision 2 Chi-Square Probability Decision 3 Jarque-Bera Probaility Decision 4

WTI Crude Oil D 7 61,91% No Serial Correlation 0,04% Heteroscedasticity Exists 0,0000 Not Normally Distributed

High Grade Copper D 1 76,04% No Serial Correlation 0,04% Heteroscedasticity Exists 0,0000 Not Normally Distributed Corn D 2 9,27% No Serial Correlation 0,00% Heteroscedasticity Exists 0,0000 Not Normally Distributed Lumber D 2 27,45% No Serial Correlation 0,00% Heteroscedasticity Exists 0,0000 Not Normally Distributed Silver D 1 62,82% No Serial Correlation 0,00% Heteroscedasticity Exists 0,0000 Not Normally Distributed Platinum W 2 11,01% No Serial Correlation 43,57% No Heteroscedasticity 0,0000 Not Normally Distributed Cotton W 4 51,91% No Serial Correlation 1,16% Heteroscedasticity Exists 0,0000 Not Normally Distributed Silver W 5 64,95% No Serial Correlation 13,95% No Heteroscedasticity 0,0000 Not Normally Distributed Observation period: February 22nd, 2010 – August 21st, 2015 covering 1387 daily time series and 287 weekly time series.

26



2 Null Hypothesis: “There is no serial correlation.”

3 Null Hypothesis: “There is no heteroscedasticity in the residual.”

4 Null Hypothesis: “Residuals are normally distributed.”

5. CONCLUSION Convenience yield is income expected to be earned for holding a commodity with the anticipation that

there will be a temporary shortage of inventories. Extracted from the differential between the spot and futures prices of a commodity, it contains information that allows researchers to understand some important underlying forces in the economy such as interest rates, current supply and demand balance and direction of commodity prices in the short to medium run as well as inflation expectations. With this respect convenience yield has been prominent amongst policy makers, hedge fund managers and commercial users such as producers and users of the commodity in focus.

We calculated daily as well as weekly series of one year maturity convenience yields from a list of 24 commodities traded at North American futures exchanges and studied their bi-variate relationship with one year maturity US Dollar denominated Zero Coupon Inflation Swap rates in econometric frameworks namely, co-integration, vector error correction model, vector-autoregressive model and Granger Causality in an effort to understand if convenience yields are appropriate tools to help predict ZCIS rates.

Our findings of co-integration analysis suggest that daily convenience yields of heating oil, unleaded gasoline, palladium, wheat, No 11 world sugar and WTI crude oil, and as well as the weekly convenience yields of ethanol, unleaded gasoline, heating oil, palladium, WTI crude oil and cotton are co-integrated with ZCIS rates, implying that they have long term association and tend to co-move.

Vector error correction model results conclude that, none of the convenience yields that are co-integrated with ZCIS rates exhibit short term causality with the exception of daily convenience yield of WTI crude oil. However, daily convenience yields of heating oil and the weekly convenience yields of heating oil, WTI crude oil and cotton exhibited signs of long term causality. Despite their significance we also conclude that mean reverting process takes long time, 208 days for heating oil, 97 days for WTI crude oil. Finally our VECM analysis revealed that daily convenience yields of unleaded gasoline, palladium and No 11 world sugar and weekly convenience yield of unleaded gasoline does not even exhibit long term causality due to the fact that their error correction terms are in positive values.

We also applied VAR models to discover bi-variate relationship structure between ZCIS rates and the daily and weekly convenience yields of 24 different commodities. We found that VAR results are far more robust than VECM results. We found that daily convenience yield series of WTI crude oil, silver, high grade copper, corn and lumber convenience yields exhibit statistically significant causality with daily ZCIS rates. In addition weekly series of platinum, cotton and silver exhibit statistically significant causality with daily weekly ZCIS rates. All mentioned daily and weekly commodity convenience yields also granger caused daily and weekly ZCIS rates.

When residual diagnostics for our VECM and VAR regressions are considered, VECM diagnostics suggest that only weekly convenience yield of heating oil has statistically meaningful long term relationship while VAR diagnostics suggest that weekly convenience yield of platinum and silver have significant long and short term

27

causality with weekly ZCIS rates. Nevertheless our VECM and VAR model conclusions can be improved by modifying their underlying formats in further studies.

One of the most interesting finding we discovered was, VAR regression equations which were involved with the convenience yields of the biased commodity futures produced more robust results than VECM regression equations that were involved with the convenience yields of unbiased and inefficient commodity futures. In fact, this finding is not surprising since one would normally expect to discover stronger relationship between convenience yields of biased commodities that are priced based on expectations and the ZCIS rates which by their nature already are priced based on pure expectations. However our conclusion needs confirmation by a series of additional researches. (1) a reformulation of our regression models to improve residual diagnostics in order to enrich our list of appropriate commodities whose convenience yields signal more reliable results, (2) an extensive research of multi methodology supported conclusions suggesting which commodity futures contracts with maturities of at least 12 months possess features of effectiveness and unbiasedness9, (3) a research that discusses the effectiveness of ZCIS rates should be conducted in order to confirm our inferences.

Acknowledgements The support from my family, Associate Professor Serda Selin Öztürk, Professor Doctor Firuzan Esin and

Figen Şentürk are gratefully acknowledged.

9 Funk et al. (2008) suggests, data period and analytical tools used to conduct the analysis determine whether a market is efficient.

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APPENDIX: ZCIS Rates vs Convenience Yield Charts Evolution of daily ZCIS rates and daily convenience yields of commodities in focus between February 22nd, 2010 and 21st August, 2015

29

Evolution of weekly ZCIS rates and weekly convenience yields of commodities in focus between February 26th, February, 2010 and August 21st, 2015:

31

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