How is the optimal hedge ratio affected by the business cycle change?

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TITLE OF THESIS: HOW IS THE OPTIMAL HEDGE RATIO AFFECTED BY THE BUSINESS CYCLE CHANGE?

Burhan Denek

Thesis Supervisor: Dr. Philippe Versijp

Master Thesis

Master in International Finance

University of Amsterdam, Amsterdam Business School

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Section1: Introduction

It has been a considerable time that the world has become a unified market place thanks to economic globalization. According to Joshi (2009), economic globalization is the increasing integration of local economies via amplified cross-border movement of goods, services, technologies and capital. Benefits of economic globalization, e.g. larger free trade, bigger export markets for local producers, lower cost of capital etc., are widely recognized by almost all economies. However, drawbacks of it – such as increasing correlations and emergence of new systematic risks – started to raise greater concerns, especially after experiencing the 1997 Asia, 2000 Dot-Com Bubble and 2008 Subprime Mortgage Crises. Goldin and Vogel (2010) highlight that despite their benefits, globalization, population and economic growth create an environment where rising interdependency and complexity lead to the appearance of new systematic risks. Furthermore, Goetzmann et al. (2005) conclude that although globalization increases the investment opportunities for the international investors, this advantage is offset by increasing correlation. Therefore, managing risk and decreasing fragility against unexpected economic shocks are included in the hottest discussions of both practitioners and academicians.

One of the widely used risk management methods can be given as hedging. A hedge is designed to offset a pre-existing position by means of taking (mainly) a reverse position. Although a variety of tools can be accommodated, e.g. usage of physical commodities or usage of debt instruments, derivatives usage is the most common practice in hedging. In this thesis, the hedging tool under consideration is futures contracts.

Since eliminating the risk completely is the ultimate aim of the hedger, having a direct opposite position of the current investment in the futures market provides a perfect hedge, i.e. shorting x amount of soya bean futures while being long for x amount of soya beans. However, it is not always easy to find a hedge instrument that perfectly reflects the price movements of the exposed investment/position. For instance, Franken & Parcell (2002) state that although the US ethanol industry expands thanks to increased use of alternative fuels and low commodity prices, there is no available ethanol futures market in order to mitigate output price risk. Therefore, they investigate the usage of gasoline futures as a hedging tool in eliminating ethanol price fluctuations. As in

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Franken and Parcell (2002)’s example, when a perfect hedge instrument is not available, price risk has to be managed by a cross-hedge. Cross-hedging can be defined as hedging the exposure on an instrument, e.g. commodity, currency etc., using a different instrument with a similar price movement.

In case of a cross-hedge, choosing the suitable alternative futures contract is highly crucial since the chosen alternative should mirror the price changes in the exposed commodity, stock or currency as close as possible. Therefore, one needs to conduct a certain level of analysis, such as correlation analysis or fundamental analysis, to determine the alternative futures contract to be used for cross hedging. Blake and Catlett (1984) use correlation as the determination tool and based on the work of Anderson and Danthine (1981) conclude that correlation between cash (spot price of the exposed commodity) and futures (futures prices of the alternative commodity) is desired to be positive and as close to 1 as possible1. On the other hand, while Brooks, Davies and Kim (2006) agree that historical return correlation is a successful tool in determining the futures contract in order to reach the highest hedging efficiency during the in-sample period, they claim that for out-of-sample performance one also needs similar fundamental factors such as industry, beta, market capitalization and price to book ratio.

Second important item of the cross-hedge is determination of the optimal hedge ratio (OHR) in which the cash/futures correlation is one of the components. Hull (2012) defines the OHR as “the ratio of the size of the position taken in futures contracts to the size of the exposure” (p. 56). In the perfect hedging case, since the underlying commodity of the futures contact is exactly the same with the commodity to be hedged, the hedger would have a position in futures contracts covering x amount of y in order to hedge x amount of y. Hence the OHR would be 1. However, in the cross-hedging case, since the underlying commodity of the futures contract is not a perfect substitute for the commodity at hand, having a hedge ratio of 1 may not be optimal.

1- Anderson and Danthine (1981) claim that a stable cross-hedge can be achieved when cash/future correlation is a constant different from zero. Therefore, correlation can be either positive or negative, since in well-functioning markets shorting futures is as easy as going long. In the work of Blake and Catlett (1984), they provide examples on longing (purchasing) futures; therefore, they are

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If the OHR changes and the hedge ratio is a function of other variables (such as industry, beta (so market movements and how susceptible one is to those movements matter) and so on, it's logical, and both practically and academically relevant, to check if there is a relation with the business cycle.

Once one managed to choose the relevant futures contract and calculated the OHR at time t, the relevant hedge position can be taken for time t with a volume determined by OHR. However, keeping the futures contract the same, the OHR may change through time due to market conditions dependent components of the ratio such as cash/futures correlation: correlation between two variables is dependent on sample standard deviations of these two variables and standard deviations may change due to changing market conditions. Kroner and Sultan (1993) criticise usage of constant OHR and state that, in reality, as new information is received by the market, riskiness of cash and futures change. Therefore, it is crucial for the hedger to monitor the performance of the hedge and adjust the hedge ratio at least when there is a change in business cycle. “Business cycles are the "ups and downs" in economic activity, defined in terms of periods of expansion or recession. During expansions, the economy, measured by indicators like jobs, production, and sales, is growing in real terms, after excluding the effects of inflation. Recessions are periods when the economy is shrinking or contracting.” (Federal Reserve Bank of San Francisco, 2002).

Therefore I would like to define my thesis topic as “HOW IS THE OPTIMAL HEDGE RATIO AFFECTED BY THE BUSINESS CYCLE CHANGE?”

The aim of the thesis is finding a relationship between the OHR and business cycle. NBER US Business Cycle Turning Points data and US monthly GDP data are considered as the signaler of the state of the business cycle at a certain time1. Price changing effect of the business cycle changes on equity markets are to some extent predictable and widely studied. However, although the effect of agriculture on the business cycle is investigated, work on the effect of business cycle on agricultural

1- Thanks to availability, continuity and reliability of the US data, the research is based on the US business cycle and the US agricultural commodities market.

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commodities seems to be limited. Therefore, in order to add a value to the current literature, the invested commodity and the futures contract, which are used for cross hedging, are chosen from the US agricultural commodities market: Hay, ethanol and high fructose corn syrup are used as the cash/exposed commodity while corn futures are used as the hedging tool as in Blake and Catlett (1984)’s work.

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Section 2: Literature Review

Risk management is a constantly developing area and hedging is accepted as one of the main price-risk-mitigating tools for several decades. Therefore, there is significant number of studies in the literature about hedging. We may group these studies in three:

Studies on Hedge Effectiveness: Works under this group mainly question the

effectiveness of hedging and tries to find out if an investor (real or corporate entity) gets better off with the hedging activity. Although it seems that firm value enhancing aspects of hedging is supported more, considering the multiplicity of the market types and their dynamics (i.e. financial markets, commodity markets etc.), it shouldn’t be surprising that there is still no consensus on whether hedging has an advantageous or disadvantageous effect on investor value (i.e. a hedging activity may enhance the value of a firm investing in the financial markets, while it diminishes the value of a firm investing in the commodity markets).

The second propositon of Modigliani and Miller (1958) establishes that a firm’s weighted average cost of capital is not affacted by that firm’s leverage since a higher debt/equity ratio increases the risk of equity holders and therefore leads to a higher return on equity. We may also interpret this propositon as hedging is not going to affect the firm value as long as the shareholder can hedge as easily as the company. On the other hand, Froot et al. (1993) investigate the corporate risk management policies and conclude that hedging helps firms take advantage of new investment opportunities by means of contributing in providing sufficient internal funds. Guay and Kothari (2003) argue that derivative use is significantly small compared to the general firm risk profile; therefore, it is hard to find an empirical evidence of economic importance of derivatives usage. Lookman (2003) conducts a research on the value effects of derivatives usage of oil and gas producers and concludes that while hedging primary risks – such as a risk caused by production – leads to lower firm value, hedging secondary risks comes with a higher firm value. Bertram et al. (2003) have a study on 7,292 non-financial firms from 48 countries on the use of financial derivatives and find evidence that there is positive effect of usage of financial derivatives on a firm’s value. However, Jin and Jorion (2004) state that there is evidence that hedging doesn’t affect market values of US oil and gas producers. Kavussanos and Visvikis (2006) claim that shipping derivatives may help the

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players in the shipping sector manage their cash flows more effectively. Furthermore, Samitas et al. (2011) measure the effectiveness of hedging tools in the energy sector and find out that firms implementing hedging strategies are better off in avoiding economic problems.

Studies on Finding the Best OHR Formula: If one is convinced on the benefits of

hedging, the next step is calculating the OHR. As explained above in the introduction, having an exact match in futures markets for the exposed commodity is not always easy. In the cases that a perfect match is available one may easily have the OHR 1 and take the necessary position (i.e. being long in 1 unit of soya and going short in 1 unit of soya futures). However, if an exact match is not the case, then the futures of similar commodities need to be found in order to hedge the exposed commodity. However, in this case having the OHR 1 wouldn’t lead to optimal hedge effectiveness since the underlying commodity of the futures contact has a similar but not an exact price pattern. At this stage, the importance of calculating the OHR emerges.

The OHR calculation is mainly divided in to two as constant and time-varying hedge ratios. Constant hedge ratio – which is constant over the time – is mainly calculated using the ordinary least squares (OLS) method. On the other hand, time-varying hedge ratio, which is varying through the time and reflecting the changes in the underlying factors, is calculated with different methods; and these different methods are majorly derived from generalized autoregressive conditional heteroskedasticity (GARCH) method. GARCH is introduced by Bollerslev (1986). As the name suggests, GARCH model is the generalized form of Autoregressive Conditional Heteroskedastic (ARCH) process, which is introduced by Engle (1982) and lets the conditional variance to change over time as a function of past errors leaving the unconditional variance remaining the same. Bollerslev (1986) accepts that the ARCH process is found to be suitable in modeling different economic anomalies such as changing uncertainty of inflation over time. However, he claims that while the GARCH process additionally permits lagged conditional variances to enter, ARCH process only specifies the conditional variance as a linear function of past sample variances. Therefore, the GARCH process permits more flexible leg structure and it allows a more tight description in many situations.

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understood that, for the time-varying (dynamic) hedge ratio calculation methods, the main comparison base is the performance of the constant hedge ratio. Then starting from this base forward, other methods are compared. Although there is a group in favor of constant hedge ratio methods, based on the majority of the literature, it is seen that time-varying hedge ratio methods outperform the constant hedge ratio based on the measure of portfolio-variance reduction.

Lien et al. (2000) compares OLS and Vector-GARCH methods. They based their comparison on examining ten spot and futures markets covering currency and stock index futures. They conclude that OLS performs better than VGARCH and comments that this result may be because of the excessively variable nature of forecasts generated by VGARCH. Bhaduri and Durai (2008) analyses three methods of constant hedge ratio calculation; OLS, vector autoregression model (VAR), vector error correction model (VECM) and one method of time-varying hedge ratio calculation; diagonal VEG multivariate GARCH. They conclude that in the long time horizon DVEC-GARCH performs better while OLS method scores better for the short time horizon. Finally, giving the complexity of the time-varying hedge ratio calculation, they suggest that one may choose OLS-constant hedge ratio method. Furthermore, Sahoo (2014) evaluates the constant and time-varying hedge ratio for several commodity futures. For the constant hedge ratio calculation he uses OLS, VAR and VECM while OLS-GARCH and bivariate-GARCH models are used for the calculation of time-varying hedge ratio. He concludes that there is no single method giving the best outcome and suggests that the hedger should use several models and try to pick the best one.

The above given studies were in favor of constant hedge ratio models or at least showing that time-varying hedge ratio models are not superior to the constant ones. On the other hand there are more studies praising time-varying hedge ratio calculation methods. The following researches can be given as examples: Bera et al. (1997) compare bivariate autoregressive conditional heteroskedastic (BGARCH) and random coefficient autoregressive (RCAR) models in calculating the time-varying hedge ratio; using daily data of spot and futures prices of corn and soybeans. They conclude that the BGARCH model is better than RCAR model. Choudhry (2003) compares constant and time-varying hedge ratio models while trying to investigate the effects of the long run relationship between stock cash index and futures index on the hedging effectiveness of

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six stock futures markets. According to the results, time-varying hedge ratio outperforms the constant hedge ratio. Chen et al. (2006) proposes a new model called range-based multivariate volatility model in order to estimate the time-varying optimal hedge ratio. They compare the results with constant hedge method and return-based multivariate GARCH model. They conclude that their model out performs both of the other methods and claim that the variance reduction of their model is 27% more than the OLS (constant) method. Choudhry and Hassan (2011) compare five different versions of GARCH models (BGARCH, GARCH-ECM, BEKK GARCH, GARCH-X and GARCH-GJR) based on the stock futures of 4 emerging countries (Brazil, Hungary, S. Africa, and S. Africa) from December 1999 to December 2009. Based on the results they conclude that BEKK model outperforms the other models during the 2 year forecast horizon while GARCH-X is the one for 1 year forecast horizon.

Studies on the Relationship between Hedging and Business Cycle: Time-varying

hedge ratio calculation methods are derived in order to insert the changing nature of the underlying parameters of the markets into the OHR. However, even these dynamic models can be inaccurate in calculating the OHR during major shifts in the markets such as changes in phases of the business cycle. Although there is a vast number of a research on hedge effectiveness and finding the best OHR formula, research on the relationship between hedging and business cycle seems limited.

Kroner and Sultan (1993) criticise usage of constant OHR. They state that, in reality, as new information is received by the market, riskiness of cash and futures change and this change leads to a change in OHR. As another factor, Brenner and Kroner (1995) advise that there may be cointegration1 between cash and futures prices and cointegration may result in a downward bias on OHR. Furthermore, during major shifts in the markets such as changes in phases of the business cycle, cointegration level may change and it may lead to a substantial change in OHR. Marcus and Ors (1996) conduct their research on hedging corporate bond portfolios across the business cycle and find out that the hedge

1- Brooks (2008) defines cointegration as “a set of variables is defined as cointegrated if a linear combination of them is stationary. Many time series are non-stationary but ‘move together’ over time – that is, there exist some influences on the series (for example, market forces), which imply that the two series are bound by some relationship in the long run.” (Brooks, Introductory Econometrics

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ratios of portfolios of industrial bonds differ systematically across the business cycle. Broll and Wong (2010) conclude that business cycle is an important factor in influencing a banking firm’s optimal hedging strategy. Finally, Marshall et al. (1992) try to find an answer to the question of how a firm can hedge business cycle risk using macro swaps and options.

Under the light of the stated findings, we may also conclude that commodities sectors may be sensible to the business cycle changes and, furthermore, some commodities may be more sensible to the business cycle than others, which would almost automatically lead to a different OHR at different stages in the cycle. MSCI Barra Research Bulletin (November 2009) studies the correlation of sector returns with business cycles in a global setting, using a historical data between 1976 and 2009. Based on the strength of this correlation, developed approach classifies the sectors as defensive or cyclical. They use the Organization for Economic Cooperation and Development’s (OECD) Composite Leading Indicator (CLI) series to define the business cycle state (expansion or contraction). Cyclical sectors are defined as the ones the relative performances to the market of which are positively correlated with the change of the CLI, while defensive sector performances are negatively correlated. Finally they conclude that the sectors with the strongest cyclical behavior are Industrials, Consumer Discretionary and Information Technology, while Consumer Staples, Health Care and Utilities have the strongest defensive characteristics. Furthermore, Bahardwaj and Dunsby (2013) find out that the correlation between stocks and commodities is higher during periods of economic weakness and states that the relation between correlation and the business cycle is stronger for industrial commodities. These reasearches may be considered important in showing the business cycle effect on different sectors.

As it is observed above, although there is a certain interest in the relationship between hedging and the business cycle, there is a certain amount of room for additional research. Therefore, my research takes its place under this group and it tries to find an answer to the question: How Is the Optimal Hedge Ratio Affected by the Business Cycle Change?

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Section 3: Hypothesis, Methodology and Data

In my research the null hypothesis that is tested is:

Ho= There is a relation between optimal hedge ratio and business cycle

Testing the given hypothesis is interesting for practitioners, since it adds another dimension to calculating OHR. Furthermore, it is interesting for academicians since this study provides more insight into the effects of the business cycle change on OHR.

My research is based on the early work of Blake and Catlett (1984). In their research, the authors test the use of corn futures contracts to cross-hedge both US hay and New Mexico alfalfa hay. Initially, in order to examine if corn futures are suitable contracts for cross hedging hay, they calculate correlations between United States hay and Chicago Board of Trade (CBOT) corn futures1 using monthly data from 1955 to 1981. Found correlations between US hay and corn futures contracts are between 0.828 and 0.970 and all significant at 99% confidence level. Therefore, they conclude that corn futures can be used for cross hedging hay. They pick the futures contract having highest correlation for each hay spot month. Then they form a multiple regression model (Dependent variable: Hay price, Independent variable: Related futures contract with the highest correlation) with 12 regression formulas for each month of the year. Finally, they calculate the optimal hedge ratio by conducting mentioned multiple linear regression analysis.

Although the base of my research is built on Blake and Catlett’s above-mentioned work, my research differs in certain aspects:

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1) Data selection and restrictions:

As the initial change, I test the use of corn futures contracts to cross-hedge ethanol and high fructose corn syrup (HFCS) additional to hay, while Blake and Catlett (1984) use only hay. Furthermore, data selection and restrictions of my research differ from them. In their research, Blake and Catlett (1984) collect monthly1 US hay2 spot price data from United States Department of Agriculture covering the period from 1955 to 1981. My hay data is again retrieved from the same source in line with the authors approach; however, in order to cover the most recent three major business cycles, I cover a period from January 2000 to February 2015. The major difference here is in the corn futures data selection:

In Blake and Catlett (1984)’s study, corn futures prices used are the closing prices on the first trading day of each delivery month. This method may provide an operational ease in picking the futures contract prices. However, with this method, the authors reach the same contract price for all the spot months. For instance, in their research, the price of May2015 corn futures contract is the closing price of the 1st of May; therefore, May2015 price is not dependent on the month in which the investor is, i.e. May2015 futures contract price is the same whether the investor observes the price in January or February. However, this is not the case in reality. In real life, contract prices are live and they change even daily based on time to delivery of the contract. Meaning that the price of May2015 contract in January is different than the one in February. Therefore, as a correction, in my research, futures contract prices are picked based on the hay, ethanol and HFCS spot months, i.e. for February Hay average price, the price of May2015 contract is the closing price of May2015 contract on the 15th of February3, while, for January Hay average price, it is the closing price of May2015 contract on the 15th of January. Furthermore, the authors let the investor invest in a futures contract with the expiry in the current month, i.e. if the current month is May, investor can still invest in May futures contract. However, this is not realistic since the spot hay, ethanol4 or

1- Neither daily nor weekly data is available; therefore, monthly data is used. 2- US average monthly price sourced from United States Department of Agriculture

3- Monthly hay, ethanol and HFCSprices are the average of the related month. Therefore, it seems appropriate to have the middle of the month as the reference date. If the 15th is a bank holiday; then 14th or 16th is chosen.

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HFCS1 prices are the average prices: If we accept that the mid of the month represents the average, an investor wouldn’t invest in the current month’s futures contract since the last trade date of the futures contract is the business day prior to the 15th calendar day of the contract month. In my research, investor cannot invest in the current month’s contract but in the next. Using five different futures delivery months and letting the investor invest in different months is the first approach.

Different than the above given approach and more in line with the real market dynamics, one may prefer investing in the futures contract with the highest open interest2 rather than picking different delivery months. If we assume that the contract with the “highest open interest” on average is always the same contract at any given time t, we reach the idea of continuous contract. My second approach is to use a continuous futures contract with the highest average open interest instead of using five different delivery months.

2) Regression equations:

The first Approach: Using five different futures delivery months

Blake and Catlett (1984) have 12 multiple regression equations for each month with dependent variable as hay price and independent variable as related futures contract with the highest correlation. The first approach of my research has the same; however, I insert an Optimism Dummy3 into each equation in order to measure the effect of the business cycle.

1- U.S. prices for high fructose corn syrup (HFCS), Midwest markets sourced from United States Department of Agriculture 2- “The total number of futures contracts long or short in a delivery month or market that has been entered into and not yet offset or fulfilled by delivery Also known as Open Contracts or Open Commitments. Each open transaction has a buyer and a seller, but for calculation of open interest, only one side of the contract is counted.” (CME Group)

3- Brooks (2008) explains that “dummy variables are usually specified to take on one of a narrow range of integer values, and in most instances only zero and one are used.” Dummy variables are used to denote the absence or presence of an categorical element that may effect the outcome (Brooks, Introductory Econometrics for Finance, 2008). In this thesis, it will take the value of 1 when the US economy performs well and take the value 0 when the economy performs badly.

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Correlations

As Blake and Catlett (1984) perform, a correlation calculation is conducted on the data using Eviews. Correlation tables for each cash commodity can be seen below:

Ethanol

Table 1: Correlation between Ethanol Prices and Corn Futures Prices

* The month with the highest correlation is marked with gray background.

Hay

Table 2: Correlation between Hay Prices and Corn Futures Prices

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HFCS

Table 3: Correlation between HFCS Prices and Corn Futures Prices

* The month with the highest correlation is marked with gray background.

While Jan to Dec represent each spot hay month, FMarch to FDec represent current year futures contracts and FNMarch to FNDec represent next year futures contracts. As we observe, correlations are high and significant. Furthermore, related regressions are run and all the above given correlations are found significant at 99% confidence level (only the month June of Ethanol, which is colored in red, is significant at 95% confidence level). Futures contract having the highest correlation coefficients for each cash commodity month is colored in orange and it will be used in regression. In the research of Blake and Catlett, they find May futures contract, both for the current year and the next year, optimal for all spot months; however, as can be observed from the orange colored cells in the above given correlation matrices, I found several optimal months differing based on the spot month of each cash commodity.

Regression Equations

Considering the complexity of the time-varying hedge ratio models and questionable benefits of the method compared to the constant hedge ratio models, minimum variance hedge ratio – OLS method (constant hedge ratio) is chosen.

Hull (2012) explains minimum variance hedge ratio as follows:

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the best-fit line from a linear regression of ΔS against ΔF (see Figure 1). This result is intuitively reasonable. We would expect hedge ratio to be the ratio of the average change in S for a particular change in F. The formula for the ratio is:

where σs is the standard deviation of ΔS , σF is the standard deviation of ΔF , and ρ is the coefficient of correlation between the two.

In order to calculate the OHR by linking the changes in spot prices with the changes in futures prices, a linear regression model may be employed. Corresponding regression equitation developed by Ederington (1979) is:

Rs,t = c+βRf,t +εt

Ederington (1979) indicates that the estimated slope coefficient is the variance minimizing hedge ratio (OHR). Therefore, in the above regression equation β represents hedge ratio, Rs,t andRf,t represents monthly spot and futures returns respectively.

As a modification, we have to include the business cycle component into the above given regression equation since it doesn’t include the business cycle, while monthly spot and futures returns are included. In order to include business cycle effect into the equation a dummy variable called Optimism is inserted. Optimism dummy takes the value 1 when the US economy performs well and takes the value 0 when the economy performs badly. Value selection of the dummy variable is made manually based on the below given Figure 3.

Finally, for each regression equation, spot month and futures contract pairs are chosen based on the above given correlation tables. For instance, January hay average spot price has the highest correlation with current year’s December corn futures contract. Therefore, regression equation for the OHR of January for hay is:

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Related futures contracts for each commodity spot month are depicted below:

Table 4: Futures Contracts with the Highest Correlation for Each Spot Commodity Month

Regression equations, an example of which is given above, are built based on above given matching. Change in the coefficient β1 provides the effect of the business cycle.

The Second Approach: Using continues futures contract

Instead of having different futures contracts (i.e. March, May etc.) and finding the best futures contract for the given spot month with the help of correlation, the second approach considers that one may prefer investing in the futures contracts with the highest open interest instead of picking different delivery months. This approach is more in line with the real market behavior since the real investor majorly prefers investing in the contract with the highest open interest/volume mainly because of liquidity concerns. Continuous futures contract historical data is retrieved from Quandl.com. “Quandl's continuous contracts are created using the simplest possible roll algorithm: "end-to-end concatenation". That is to say, C1 is always the corn contract with the shortest time to expiry; C2 is the second shortest contract, and so on. On expiry date, C1 starts to point to the next future in line, and so on all the way down the strip. There's no price adjustment, and the roll dates are simply the last trading dates.” (Quandl).

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contracts (i.e. C1, C2, C3, etc.). After comparing the average open interest levels of all mentioned ten continuous contracts, C2 (the second shortest time to expiry contract) is found to have the highest average open interest. Therefore, C2 is preferred as the futures contract to be used in the regression equations. Preference of the C2 contract is also in line with the market practice since the investor may not always have the chance to invest in the futures contract with the shortest time to maturity.

Thanks to both futures and spot commodity data availability, second approach covers longer periods (Hay – January 1980 until April 2015, Ethanol - January 1982 until April 2015 and HFCS – January 1994 until April 2015).

Regression Equations

Regression equation is the modification of the first approach. Since there is only one futures contract instead of five different contracts, the main difference is that instead of having multiple (12) regressions for each spot month, there is only one regression equation for each spot commodity:

RHay= c0+ β0RC2Futures +( c1+ β1RC2Futures) x Optimism + εt

REthanol= c0+ β0RC2Futures +( c1+ β1RC2Futures) x Optimism + εt

RHFCS= c0+ β0RC2Futures +( c1+ β1RC2Futures) x Optimism + εt

As it does in the first approach, change in the coefficient β1 provides the effect of the

business cycle.

3) Defining the dummy variable:

One of the main questions is “how are we going to decide on the phase of the business cycle?”. In order to make the decision on the phase of the economy US Business Cycle Expansions and Contractions data of the National Bureau of Economic Research is used.

The National Bureau of Economic Research is a private, nonprofit research organization mainly working on the dynamics of the economy. NBER determines the official dates

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for business cycles. Below the most recent decisions of NBER on business cycle dates can be found.

Table 5: NBER US Business Cycle Turning Point Dates

Source: The National Bureau of Economic Research Web Site

Recessions start at the peak of a business cycle and end at the trough. In the above graph depicting The Conference Board's Coincident Indicators Index, it should be noted that the series rises during expansion periods (between the trough and the peak of the business cycle) and drops during recessions (between the peak and the trough of the business cycle). Therefore, Coincident Indicators Index data and NBER business cycle dates are completely in line. Under the light of above given business cycle information, table showing the value of the Optimism dummy based on the dates can be observed:

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As an aggregate measure of total economic production for a country, the gross domestic product (GDP) is one of the primary indicators used to measure the health of a country's economy. Therefore, as an alterative to the above given business cycle indication, US Monthly GDP Change is used as a second tool for determining the business cycle state. US Department of Commerce-Bureau of Economic Analysis provides quarterly US GDP information; however, my research investigates monthly data. Therefore, monthly US GDP data is retrieved from Ycharts.com.

In this approach a new variable called “GDP Deviation” is constructed by taking the difference between the GDP growth rate in a month and its long-term average.

Graph 1: US Monthly GDP Deviation

In order to observe the effect of the GDP deviation on the OHR, we need to construct new regression equations that may be observed below:

The first Approach: Using five different futures delivery months:

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Above given equation is the one for the spot month January. For each calendar month, the equation is modified.

The Second Approach: Using continues futures contract

RHay= c0+ β0RC2Futures + β1RC2Futures x gdp_deviation + εt

Change in the coefficient β1 provides the effect of the business cycle in both of the

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Section 4: Empirical Results and Discussion

The first Approach: Using five different futures delivery months

Since multiple futures contracts are available for each spot month of the subject commodities (i.e. hay, ethanol and HFCS), the initial step was to determine the futures contract having the highest pricing information for each of the spot month through a correlation analysis. The correlation results for each commodity are given above on pages 13 and 14. Under the light of these results, optimum futures contract for each spot month were picked (highlighted in orange). Then each spot month for each commodity was regressed against the optimum futures contract; first including the effect of the business cycle changes thru the dummy variable and GDP deviation, then without the effect of the business cycle chances by removing the dummy variable and GDP deviation.

For the classical linear regression model (CLRM), in order to be able to estimate the parameters, and to interpret the coefficients of the model, for all t=1,…,T following assumptions need to hold:

1. E (εt|Rf,t) = 0 (orthogonality)

2. var (εt) = σ2 < ∞ (homoscedasticity)

3. cov (εt , εs) = 0 for all s≠t (no residual autocorrelation)

4. εt ~ N (0, σ2) (normality)

Brooks (2008) interprets above given assumptions as: Orthogonality: The errors have zero mean

Homoscedasticity: The variance of the errors is constant and finite over all values of Rf,t

No residual autocorrelation: The errors are linearly independent of one another Normality: that εt is normally distributed

The first assumption is the most essential one to hold. If it doesn’t hold, there is no longer a regression since the coefficients of the model cannot be interpreted. If the following three assumptions do not hold, the coefficient estimators may be biased, standard errors may be wrong and the test statistics may be unreliable.

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The problem occurs when the model omits one or more important underlying variables and this causes biased coefficients.

In this study it is assumed that orthogonality and normality holds. In order to overcome serial correlation1 and heteroskedasticity2 in the error terms, regressions are conducted with robust standard errors (Newey-West estimator). Regression outcomes for each commodity are presented below while the full tables can be observed in the Appendix.

ETHANOL

Table 7: Ethanol Regression Results Summary – Without Business Cycle Effect

* “Multiplier” values, given in all the tables of the regression results, provide the number of tons of the subject commodity to be covered by 1 paired futures contract under the calculated OHR.

In the first equation, Jan_Eth represents the January Ethanol spot price, while FDec,

1- Serial correlation, also known as autocorrelation, is the correlation between a time series and the lagged versions of itself over serial time intervals.

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which is the optimal contract for the January Ethanol spot price, is the value of CBOT December corn futures contract in USD. It is important to be reminded that each corn futures contract stands for 5,000 bushels of corn. Since the value of a corn futures contract is quoted in cents per bushel, value of one futures contract was calculated by dividing contract price by 100 (in order to find the USD value for one bushel) then multiplying by 5,000. This method can be observed in Blake and Catlett (1984)’s work as well.

Coefficient of FDec, provides us the optimum hedge ratio. We may interpret the result as: in order to hedge 1 ton of hay, 0.018 current-year December corn futures contract is needed. From another angle, 1 current-year December corn futures contract would cover 56 tons of Ethanol. Meaning that, “Multiplier” values (1/C(2)), given in all the tables of the regression results, provide the number of tons of the subject commodity to be covered by taking a long position in 1 paired futures contract under the calculated OHR (if the sign of the multiplier is negative then the investor shorts 1 paired futures contract in order to cover “multiplier” tons of the subject commodity).

In order to understand the effect of the business cycle changes on the OHR, it is beneficial to examine the results of the regression equations, which do not include the effect of the business cycle changes, first. We may call these regression equations “bare regression equations”. As it is observed from the above given table, statistics for C(2), which provides the OHR, are significant at least at 95% confidence level but majorly at 99% confidence level. From these results we may derive the solution that used corn futures contracts carry OHR information at significant levels. However, would the business cycle effect be the ommitted variable? Therefore, would adding business cycle effect as an additional variable increase the significany level of the OHR?

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Table 8: Ethanol Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

In the above given regression equations, the coefficient C(4) reflects the effect of the dummy, which reflects the business cycle effect. Although in the first months, the results of C(4) are significant at even 99% confidence level; in the following months the significancy levels decrease substantially until October. The above picture signals an inconsistent behavior. Therefore, in order to have a deeper understanding, it may be beneficial to test the business cycle effect via another business cycle indicator such as GDP deviation.

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Table 9: Ethanol Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

Above given table provides the results of the regression equations including GDP deviation as the signaler of the business cycle changes. The coefficient C(3) provides the effect of GDP deviation, while multiplier (1/C(3)) provides the numarical effect of GDP deviation on the OHR, in the same way explained above. In all of the twelve months, t and prob. values indicate that the C(3) effects are not significant at neither 99% confidence level nor at 95% confidence level.

Regression results for Hay and HFCS support above findings as well.

HAY & HFCS

Results of the Hay and HFCS “bare regression equations” are in line with the results of ethanol. Values of C(2) are significant at 99% confidence level. Meaning that the OHR values are significant.

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Table 10: Hay Regression Results Summary – Without Business Cycle Effect

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Table 12: Hay Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

Table 13: HFCS Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

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Similar to the ethanol results, the coefficient C(4) (business cycle effect) values for both Hay and HFCS are significant in the earlier months; however, get into a decreasing trend until October. These results are again inconsistent.

Table 14: Hay Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

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Table 15: HFCS Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

It is observable that the dummy variable, based on the NBER US Business Cycle Turning Point Dates, contains a higher level of information than GDP deviation especially in hay since the regression results including dummy variable, on average, produce more significant results than the ones including GDP deviation. However, the reality for both of the business cycle indicators is that adding them, as an additional variable doesn’t produce reliable results.

The Second Approach: Using continues futures contract

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Table 17: Ethanol Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

Table 18: Ethanol Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

Table 19: Hay Regression Results Summary – Without Business Cycle Effect

Table 20: Hay Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

Table 21: Hay Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

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Table 23: HFCS Regression Results Summary – With Business Cycle Effect – Optimism Dummy is based on NBER US Business Cycle Turning Points

Table 24: HFCS Regression Results Summary – With Business Cycle Effect – US Monthly GDP Change as the Business Cycle Indication

Regression results including the continous futures contract instead of having multiple delivery months derive us to the similar results. While “bare regression” results of C(2) are significant at 99% confidence level, results produced by the models with the business cycle variables are not significant.

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Section 5: Conclusion

This study aimed to find a relationship between the optimal hedge ratio (OHR) and the business cycle. While NBER US Business Cycle Turning Points data and US monthly GDP data were considered as the signaler of the state of the business cycle, Hay, Ethanol and High Fructose Corn Syrup were used as the cash/exposed commodity. Then, each spot month for each commodity was regressed against corn futures based on two methods: Using five different corn futures contracts vs. one continuous corn futures contract as the hedging tool.

Each regression method is ran twice; first including the effect of the business cycle changes through the dummy variable (binary based on NBER US Business Cycle Turning Points data) and GDP deviation, then without the effect of the business cycle chances by removing the dummy variable and GDP deviation.

Results suggest that business cycle changes do not have a reliable and significant effect on the OHR although some minor effect is observed on certain months, especially in the results of the regression equations including NBER US Business Cycle Turning Points data as the business cycle signaler. However, these effects are inconsistent and not reliable.

It is observed that usage of simple linear regression model, which has only the spot commodity price change as the dependent variable and the futures contract price change as the independent variable, produces significant OHR values. This implies that cross-hedge with these instruments is therefore possible. However, since adding business cycle effect does not significantly improve the results, it should be also considered that coefficients may be biased and standard errors may be wrong. This may mean that the models still ommit one or more fundamental variables. Therefore, additional variables would help having more accurate OHR values.

Although this study couldn’t reach its aim and find a relation between the OHR and the business cycle, it may still be useful for academicians and practitioners. In the search of finding better OHR with the means of additional variables, researchers may ommit the business cycle change and they may save considerable time. Reasearchers, instead of

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using constant hedge ratio, may also consider using time-varying hedge ratio in order to cover the changes in the underlying factors. Therefore, a GARCH based regression model rather than simple linear regression model may be more suitable. Futhermore, different agree-commodities or different sectors may be studied.

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Appendix

Regressions Results for Ethanol

January – Without Business Cycle Effect January – With Business Cycle Effect

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February – Without Business Cycle Effect February – With Business Cycle Effect

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March – Without Business Cycle Effect March – With Business Cycle Effect

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April – Without Business Cycle Effect April – With Business Cycle Effect

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May – Without Business Cycle Effect May – With Business Cycle Effect

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June – Without Business Cycle Effect June – With Business Cycle Effect

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July – Without Business Cycle Effect July – With Business Cycle Effect

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August – Without Business Cycle Effect August – With Business Cycle Effect

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September – Without Business Cycle Effect September – With Business Cycle Effect

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October – Without Business Cycle Effect October – With Business Cycle Effect

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November – Without Business Cycle Effect November – With Business Cycle Effect

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December – Without Business Cycle Effect December – With Business Cycle Effect

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The Second Approach: Using continues futures contract:

Without Business Cycle Effect With Business Cycle Effect

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Regressions Results for Hay

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November – Without Business Cycle Effect November – With Business Cycle Effect

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Regressions Results for HFCS

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