Examining Oil Price Dynamics

Transcription

1 Erasmus University Rotterdam Erasmus School of Economics Examining Oil Price Dynamics Using Heterogeneous Expectations Master Thesis Econometrics & Management Science In Cooperation with: PJK International by Erik Hessing Rotterdam, the Netherlands March 1, 2014 PJK International Supervisor: P.D. Kulsen Academic Supervisor: D.J.C. van Dijk Second Reader: D. Karstanje

2 Abstract In this paper we study whether financial speculators influence oil prices and if so does accounting for these speculators in the form of a heterogeneous agents model improve predictive accuracy. We find evidence for speculator activity in oil markets and compare the predictive accuracy of the HAM to that of a random walk model and a VECM, the most promising model of PJK International. Furthermore, we investigate the economic value of the models by determining which model would have been the most lucrative if we had invested based on its predictions. We conclude that the HAM and VECM are not able to beat the random walk, based on predictive accuracy, for very short (one day) forecast horizons but also find indications that the HAM might be able to outperform both random walk and VECM for medium (one month) forecast horizons. We find that the VECM has real potential in predicting the correct sign of price movements on medium investment horizons. The high predictive accuracy of the HAM and the sign prediction potential of the VECM led to mixed results in economic value for the medium investment horizons. Indicating that the choice between HAM and VECM depends on the oil product of interest. Keywords: Oil price dynamics, heterogeneous agents model, speculation in oil markets.

3 Acknowledgement I would like to thank my supervisors Dick van Dijk and Patrick Kulsen for their valuable comments and remarks, my colleagues at PJK International who have made these past months a great and educative experience. I would also like to thank Dennis Karstanje for taking the time to read this paper. Lastly, I would like to thank my friends and family who were always there for me and supported me to make the most out of this paper.

4 Contents 1 Introduction 5 2 Methodology Speculators Fundamental value Switching between Strategies Real participants The market Vector Error Correction Model Performance Measures Mean Squared Prediction Error Percentage Correct Sign Economic Value Data First Month Futures Contracts Roll-over Effect Augmented Dickey-Fuller test Descriptive statistics Stationarity & Cointegration of Oil Prices Data for VECM & PCA Atlantic & Crack Spreads Freight rates EIA Inventories Calender Spreads Foreign Exchange rates Stock Indexes World PMI Oil Fundamentals Results In-Sample Estimation Daily data Monthly data Out-of-Sample Performance Daily Data Monthly Data Conclusion 58 6 Further Research 60 3

5 CONTENTS CONTENTS Appendix A 63 A.1 Elaborate Description of Future contracts A.2 Graphs & Figures A.2.1 Fundamentalist Weight Graphs A.3 Tables A.3.1 ADF Test Statistics & Discriptive Statistics A.3.2 Daily Results A.3.3 Monthly Results A.4 Explanatory Variables A.4.1 Principal Components Analysis A.4.2 Atlantic- and Crack Spread models A.4.3 VECM

6 Chapter 1 Introduction In order to forecast price changes in financial products it is crucial to understand the cause of price movements. According to the Efficient Market Hypothesis all agents in the market behave rationally and have the same rational expectation. That is, they expect the price to reflect or return to the fundamental value of the asset. In this paper we will focus on the oil market. Oil market efficiency is rejected by Gjølberg (1985) and Moosa and Al-Loughani (1994), whom asses the efficiency of the market for oil products and crude oil futures, respectively. Sornette et al. (2009) explain this by showing that there are large differences between the fundamental value and the price of crude oil. The inefficiency of the oil market is often attributed to the existence of speculators. Fattouh et al. (2012) discuss the effect of speculation in oil markets, as a possible result of increased financialization (i.e. the increase in the variety of instruments that permit speculation in oil such as futures) of the oil futures market. They find that the main problem in literature on speculation is that it is rarely clear how speculation is defined. Resulting in the fact that they find no clear evidence in favor of speculation. However, Fattou et al. (2012) conclude that the absence of evidence for speculation does not mean that the financialization of oil futures markets does not matter. They suggest using agents with heterogeneous expectations in further research. Alquist et al. (2011) forecast the price of oil using several models based on economic fundamentals or related financial products. They obtain an 22% increase in forecasting accuracy compared to the random walk model, using a simple model based on % changes in the price of non-oil industrial raw materials. They state that there is strong evidence that not all households share the same oil price expectations (see Anderson et al. (2010)), casting doubt on standard rational expectations models with homogenous agents. The awareness of heterogeneous behavior in financial markets has led to models that are known as Heterogeneous Agents Models (HAMs). These HAMs use the heterogeneous expectations of different agents to describe and predict price movements. Ter Ellen and Zwinkels (2010) developed a simple and highly stylized heterogeneous agents model for oil prices. In which they assume two types of speculators exist, fundamentalists and chartists. Fundamentalists expect prices to return to their fundamental value whereas chartists expect price trends to continue (similar to an AR(1) model). Agents switch between these two speculator groups based on the previous performance of their respective strategies. They show that the HAM is able to outperform the random walk and VAR model on all horizons (i.e. 1 to 12 months), based on statistical performance measures like the mean squared prediction error (MSPE). In this paper we will expand on the research of ter Ellen and Zwinkels (2010). We will add an additional method to estimate the fundamental value of the oil. More specifically, in ter Ellen and Zwinkels (2010) the fundamental value is constructed using a moving average of historical and future prices. The new method proposed in this paper creates a fundamental value of oil products based on inventory and manufacturing data. Secondly, we will use the HAM to 5

7 CHAPTER 1. INTRODUCTION create predictions of price movements for very short as well as medium length investment horizons (i.e. daily and monthly). Lastly, instead of analyzing and forecasting the spot price of oil, we will focus on analyzing and forecasting the price of oil futures contracts, which are more liquid and should therefore be more open to speculation. This paper is written for and in cooperation with PJK International B.V.. PJK International is a market research, analysis and consultancy firm specializing in the petroleum industry of the ARA (Amsterdam-Rotterdam-Antwerp) region. PJK International provides its clients with market information and analysis, related to the pricing of oil products and transport costs. Among PJKs clients are major oil companies, traders, financial institutions, importers, distribution companies, transporters and consumers. PJK International does not engage in commodity trading to safeguard against conflicts of interest. The predictive accuracy of a model for oil spot prices, futures or spreads is of significant importance to PJK International. Accurate forecasts of the prices of oil products will give the clients of PJK International an important edge over their competition. In order to obtain better forecasts of the price movements of oil products PJK International has performed extensive internal research on the predictability of various oil products and the forecast accuracy of most basic models. This research includes but is not limited to; forecasting the spot-future spread using ARX/GARCH models by Akkermans et al. (2010), forecasting the returns of oil futures using Vector Error Regression Models (VECM) by Kulsen (2011) and forecasting oil futures prices using a feed-forward neural network by Tilgenkamp et al. (2012). However, this research is limited by the fact that most models created in these papers require agents to be rational and to have homogeneous expectations. The HAM model created in this paper has no such limitations and therefore provides a new and different perspective on forecasting the price movements of oil products. The VECM created in Kulsen (2011) is considered by PJK International to be its most promising model. Kulsen shows that the VECM outperforms an AR model based on the percentage correct sign performance measure. However, it fails to to outperform the AR model in predictive accuracy (i.e. (MSPE)). Kulsen(2011) states that the lack in predictive accuracy could be explained by his particular choice of out of sample period, the year 2009, which is just after the collapse of oil prices as a result of the credit crisis. Furthermore, Alquist et al. (2005) find that a suitably designed VAR model, which is similar to a VECM, tends to be more accurate than the random walk model for investment horizons up to six months In this paper we will examine, using the HAM, whether speculation has a significant effect on oil prices and if accounting for this possible speculation can result in improved out-of-sample performance. We will compare a model based on homogenous expectations with a highly stylized model which is based on heterogeneous expectations. More specifically the out of sample performance of a VECM, similar to that in Kulsen (2011), will be compared to that of a HAM. We find that, based on daily data, the HAM results are poor. The HAM either remains in the equilibrium state where fundamentalists and chartists have equal pres- 6

8 CHAPTER 1. INTRODUCTION ence in the oil market, making the HAM similar to an equally weighted combination of a model based on a moving average and an AR(1) model. Or the HAM immediately converts to a state where fundamentalists have been driven out of the market, making the HAM similar to an AR(1) model. The forecasts made by both HAMs are significantly worse than that of the random walk model. However based on MSPE the HAM, dominated by chartists, is able to outperform the VECM. The HAM performs significantly better in a monthly setting. We find that the weight distribution between fundamentalist and chartists varies significantly over time. Fundamentalist seem to dominate the market most of the time but they convert to a chartists strategy after sudden spikes and crashes. In the out-of-sample period one of the HAMs is able to outperform the VECM and the random walk model based on MSPE although no statistically significant conclusion can be made because of the small sample size. To determine the economic value of our models we calculate the total return obtained during the out-of-sample period if we had invested based on a follow sign strategy. That is, we take a long position in the contract if the forecast of our model is positive and short the contract in the case of a negative forecast. Based on our daily data sample we obtain disappointing results. The total returns are on average negative and we find that in some cases it would have been more lucrative to buy the contract and hold on to it the entire out-of-sample period (i.e. hold a long position the entire out-of-sample period). The results in our monthly sample are significantly different. We find mostly positive total returns and conclude that following our models is significantly more lucrative than just buying a contract and holding on to it. Lastly we see that the HAM has the highest economic value for 3 out of 5 oil products. While the VECM is superior for the other two. Chapter 2 discusses the methodology of this paper, in which sections 2.1, 2.2 and 2,3 give an outline of the heterogeneous agents model, section 2.4 describes the VECM and section 2.5 describes the performance measures we use to compare the HAM and VECM. Chapter 3 describes the data used in this paper. Section 3.1 describes the oil futures contracts of which we will make forecasts using the HAM and VECM. Section 3.2 gives a list of explanatory variables, used in the VECM and for the estimation of a fundamental value, and discusses why these variables influence oil prices. In chapter 4 we discuss the implications of the in-sample results of the HAM with respect to speculators in the oil market as well as compare the out-of-sample performance of the HAM with the VECM for daily and monthly forecasting. Chapter 5 concludes. 7

9 Chapter 2 Methodology This chapter discusses the methods used to make predictions of the price movements of first month oil futures contracts. The main method of interest is an heterogeneous agents model (HAM). This model is based on the underlying assumption that there are different types of agents with heterogeneous expectations active in the market. Our model combines both real and speculative market participants. We define real participants as companies that are involved in the production or consumption of oil products. Speculators are agents that have no current use for oil products and have no tangible link to the oil industry. We define 2 distinctive types of speculators; fundamentalists and chartists. Firstly, fundamentalists are agents that base their expectations on economic theory. This group believes that the asset has some intrinsic or fundamental value and expects the market price to revert to this fundamental value. The second type of agents, chartists or technical traders, base their expectations on recent price changes. They expect trends to continue in the same direction. The trading techniques used by fundamentalists are assumed to have a stabilizing (i.e. mean-reverting) effect on market prices. While chartists tend to drive prices away from their fundamental value, and as such have a destabilizing effect on market prices. Speculators are able to switch between groups based on recent performance (from fundamentalists to chartists and vice versa). Sections 2.1,2.2 and 2.3 outline the heterogeneous agents model. Section 2.4 describes the VECM and section 2.5 describes the performance measures we will use to compare the HAM and VECM. 2.1 Speculators The oil demand function of fundamentalists is based on the difference between the current price and the expected price that is, D F t = a F [E F t (P t+1 ) P t ] (2.1) where P t is the log-price of the futures contract in period t, a F is a positive parameter that represents the reaction of the demand to an expected price change. The demand of fundamentalists will increase (decrease) if they expect a higher (lower) price in the future. The fundamentalists use, among other things, some fundamental value to determine their price expectations. The price expectations of fundamentalists can be described by the following equation. E F t (P t+1 ) = P t + b F 1 (P t F t ) + + b F 2 (P t F t ) (2.2) Where F t is the log-fundamental value of the futures contract in period t. Equation 2.2 shows that fundamentalists expect price movements when the current price deviates from its fundamental value. Just like ter Ellen and Zwinkels (2010) we make a distinction between over and undervaluation; (P t F t ) + = (P t F t ) if (P t F t ) > 0 and zero 8

10 2.1. SPECULATORS CHAPTER 2. METHODOLOGY otherwise. Similarly, (P t F t ) = (P t F t ) if (P t F t ) < 0 and zero otherwise. We expect b F 1 & bf 2 to be negative and to be [ 1, 0], because fundamentalists will expect prices to decrease (increase) if the current price is above (below) the fundamental value. We distinguish between over and under valuation because research in behavioral finance and psychology has shown that investors react differently on potential gains and potential losses, Kahneman & Tversky (1979). According to their results traders are more hesitant to sell in case of overvaluation than to buy in case of undervaluation. The oil demand function of chartists is similar to the demand function of fundamentalists. Dt C = a C [Et C (P t+1 ) P t ] (2.3) in which a C is a positive reaction parameter, implying that the demand of chartists will increase (decrease) if they expect the future price to be higher (lower) than the current price. Chartists determine their price expectations based on technical analysis. However, technical analysis comes in many different forms (see Brock et al. (1992)). The characteristics of chartists, described earlier, need to be incorporated in the technical trading rule (i.e. the price expectation formula). The most common and simple technical trading rule that is in line with chartists characteristics and believes is the AR(1) specification, also used by ter Ellen and Zwinkels (2010). Chartists expectations according to the AR(1) specification are given by E C t (P t+1 ) = P t + b C 1 (P t P t 1 ) + + b C 2 (P t P t 1 ) (2.4) Similarly to equation 2.2, we make a distinction between an upward or downward trend. Chartists expect trend movements to continue in the same direction, so we expect b C 1 and b C 2 to be positive. If bc 1 > bc 2 chartists react more to price increases, and vice versa Fundamental value One of the ways we expand on the model of ter Ellen and Zwinkels (2010) is by determining the fundamental value of oil products using an additional method. We will compare the performance of this method with the method of ter Ellen and Zwinkels. We set the fundamental value equal to the 30 days (24 months) moving average (Similar to ter Ellen and Zwinkels (2010) 1 ); Determine the fundamental value by regressing the Log-Price of first month futures contracts on the principal components of the fundamental oil variables described in section ter Ellen and Zwinkels (2010) do not address the look-ahead bias in their results they calculate all their fundamental values using equation 2.5 9

11 2.1. SPECULATORS CHAPTER 2. METHODOLOGY Moving Average The fundamental value based on a moving average is calculated using the following equation: F t = 1 N P N t N 2 +i (2.5) i=1 In which N is equal to the number of days (months) in the moving average and P t is the log price at time t. As is clear from equation 2.5 the fundamental value is an equally weighted moving average of past and future prices. This is done to produce a fundamental value which should be as close as possible to the current true value. More specifically, we make the assumption that at any current time the price deviates from the fundamental value because either information has not yet been incorporated in the current price or there has been an overreaction to past information. By taking prices over a certain window including future and past prices we intend to get as close as possible to the fundamental value, that is the value based on all available information. This methodology which is sound for in-sample estimation would lead to an obvious look-ahead bias in the out-of-sample results. We will address this by changing the way we calculate the fundamental values which would use prices which are not in our in-sample period. These fundamental values are calculated using the following equation: F t = 1 Z + N 2 Z+ N 2 i=1 P t N 2 +i (2.6) In which Z is the number of future observations left in the in-sample period with a maximum of N/2, N is the window length and P t is the log price at time t. For example, if N=24 but the in-sample period(i.e. the sample) ends 10 periods from now, Z will be equal to 10. Such that F t is the mean of 22 observations, the 11 previous prices the current price and the 10 known upcoming prices. This method of calculating the fundamental value makes sure we don t have a look-ahead bias in our forecasting results. As the last fundamental value of our in-sample period, F t will only rely on the prices P t N/2 up till P t. One could argue that the fundamental value constructed using the method described above is not theoretically a fundamental value. Possible arguments could be that because the fundamental value is based on previous and future prices market sentiment is already incorporated in this fundamental value and as such it is no longer strictly based on fundamentals (i.e. supply and demand). However, for this model to function as expected it is important to put a stabilizing group against a destabilizing group. When using this fundamental value the stabilization occurs towards the moving average instead of a true fundamental value and as such fundamentalism should be interpreted somewhat more broadly. In the next section we will discuss the construction of a theoretically correct fundamental value. 10

12 2.1. SPECULATORS CHAPTER 2. METHODOLOGY Principal Components Analysis The second fundamental value used in this paper is based on oil fundamentals. More specifically it is constructed by performing a principal component analysis on the production and supply and demand variables described in section 3.2. The number of explanatory variables is relatively large and because we are searching for a true fundamental value, which can differ from the current price according to our assumptions and research hypothesis (i.e. the existence of heterogeneous agents), we can t reject variables based on significance in an ordinary least squares or maximum likelihood regression. In order to reduce the amount of explanatory variables and with that the dimensionality and parameter uncertainty we will perform a principal component analysis. We will use the number of principal components that account for at least 95% of the variance in the original explanatory variables. We estimate parameters by regressing these principal components on the log price of oil futures. After which the log fundamental values are obtained by multiplying the parameters with the principal components. A Principal Components Analysis is defined as follows: consider X a T xn matrix of n explanatory variables and let V be the correlation matrix of X. W is an nxn orthogonal matrix of eigenvectors of V. The principal components of V are the columns of the T xn matrix P which is defined as P = XW (2.7) The original system of correlated explanatory variables has been transformed to an orthogonal system. W is ordered so that the first column of W is the eigenvector corresponding to the largest eigenvalue of V, the second column of W to the second eigenvalue of V and so on. The total variation of X is the sum of the eigenvalues of V, λ λ n. The proportion of the total variation that is explained by the first k principal components is equal to λ λ k λ λ n (2.8) We can now reduce dimensionality by setting k < n for some number of principal components k which predict a large enough proportion of the total variance. Resulting in X = P W (2.9) where P is a T xk matrix consisting of the first k columns of P and W is an nxk matrix whose columns are the first k eigenvectors. The fundamental value is then obtained by the following equation: F t = α + P t β (2.10) In which F t is the log fundamental value, P is the T xk matrix of principal components in which k is chosen so that 95% of the variance is captured and α and β(kx1) are the parameters obtained after performing the following regression: P t = α + P t β + ɛ t (2.11) 11

13 2.1. SPECULATORS CHAPTER 2. METHODOLOGY In which P t is log price. This regression is performed over the entire in-sample period to account for the best fit but exclude the chance of a look-ahead bias. Furthermore this entire process is repeated when the in-sample period changes. To be more specific, when the in-sample period changes (i.e. expanding window) we calculate new principal components and estimate new parameters Switching between Strategies Speculators are able to switch between investment strategies. They determine whether they switch or not based on the previous performance of both strategies in forecasting the price movement of oil. The performance of a strategy is measured using the squared forecasting error in the previous K>0 days/months. Optimal values for K are selected empirically by looking at the autocorrelation and partial autocorrelation of the errors and set equal to 9 days or 6 months for daily and monthly data respectively. The performance of a strategy relative to the other strategy is time varying, therefore the distribution of agents changes over time. The performance of both strategies is measured using the following equations, K A F t = [Et k 1 F (P t k) P t k ] 2 (2.12) A C t = k=1 K [Et k 1 C (P t k) P t k ] 2 (2.13) k=1 In which A F t is the conditional performance of the fundamentalist investment strategy and A C t of the chartist investment strategy. More specifically, A F t and A C t represent the squared difference between the expected prices and the realized prices (i.e. the squared error) in the previous K periods, for the fundamentalist and chartist strategies respectively. The size of A F t and A C t is negatively correlated with the performance of its respective investment strategy, that is if A F t is larger than A C t we can state that the chartist investment strategy was, on average, more accurate in forecasting the price movements in the previous K periods than the fundamentalist strategy. The fraction of fundamentalists active in the market depends on the performance of the fundamentalist investment strategy relative to the approach of the chartists. Similar to ter Ellen and Zwinkels (2010) the multinomial switching rule is given by, ( [ ( A F W t = 1 + exp φ t A C )]) 1 t A F t + A C (2.14) t Where W t is the fraction of speculators in period t that invests using the fundamentalist approach, such that 1 W t is the fraction of chartists. φ is the intensity of choice parameter, representing the extend to which the performance of a strategy determines whether it is adopted. If φ = 0 agents don t react to difference in performance between the two strategies such that W t = 1/2. φ > 0 implies that the strategy which is performing better in period t, is more broadly applied in period t + 1. Therefore, the demand of that group will carry more weight in period t

14 2.2. REAL PARTICIPANTS CHAPTER 2. METHODOLOGY 2.2 Real participants This section describes the supply and demand functions for agents that are involved in the consumption or production of oil (i.e. they have a tangible link to the oil industry). The reason we can, and should, distinguish between real agents and speculators is because the futures we are interested in are futures on an commodity. Therefore, we distinguish an investment part from the consumption part. The market supply of oil affects the price formation process. Consequently, we add real demand and supply for oil to the model. The real demand for oil depends on a component which does not depend on the oil price, and a component which represents the negative (positive) effect of a price increase (decrease) on the real demand for oil. Real demand is given by D R t = a R b R P t (2.15) in which a R is the exogenous demand for the oil product and b R represents the price sensitivity of the demand. We expect b R > 0 because an increase in price should lead to a lower demand. The supply function of oil is similar to the demand function in equation However, supply of oil is a positive function of the price and an exogenous component which does not depend on the price of oil. The supply function is given by S t = a S + b S P t (2.16) Where a S is the exogenous supply of the oil product and b S represents the price sensitivity of supply to oil prices. We expect b S > 0 because supply is a positive function of price. 2.3 The market Combining the equations presented in the previous sections we obtain the total market demand for oil products. The total market demand consists of the real demand plus the weighted average of the demand of fundamentalists and chartists. D M t = D R t + W t D F t + (1 W t )D C t (2.17) Finally, the price changes of oil products are a function of excess demand and a noise term, that is P t+1 = P t + θ(d M t S t ) + ε t (2.18) Where θ is a positive parameter which describes price adjustment according to market frictions. Combining equations 2.17&2.18 gives the final HAM, after some rewriting this results 13

15 2.3. THE MARKET CHAPTER 2. METHODOLOGY in the final model described by P t+1 = a + bp t + W t (α 1 (P t F t ) + + α 2 (P t F t ) ) +(1 W t )(β 1 (P t P t 1 ) + + β 2 (P t P t 1 ) ) W t = ( [ ( A F 1 + exp φ t A C t A F t +AC t )]) 1 (2.19) A F t A C t = N n=1 [α 1(P t n F t n ) + + α 2 (P t n F t n ) P t n+1 ] 2 = N n=1 [β 1(P t n P t n 1 ) + + β 2 (P t n P t n 1 ) P t n+1 ] 2 Where a = θ(a R a S ), b = θ( b R b S ), α 1 = θa F b F 1, α 2 = θa F b F 2, β 1 = θa C b C 1 and β 2 = θa C b C 2 This model is estimated using quasi-maximum likelihood (QML) such that autocorrelation, heteroskedasticity and possible non-normality are controlled. Quasi-maximum likelihood is similar to regular maximum likelihood, however instead of maximizing the actual log likelihood function it often maximizes a simplified form of the log likelihood function. As long as the quasi-maximum likelihood function is not overly simplified, the quasi-maximum likelihood estimates will be consistent and asymptotically normal. An easy way to perform a QML estimation is by performing a regular maximum likelihood estimation (MLE) and adjusting the standard errors. More specifically, after performing a MLE the covariance matrix is created using an equation commonly known as the sandwich formula. That is, instead of setting the covariance matrix equal to the inverse Hessian or the outer product of the gradient, the covariance matrix is created as follows: Cov = H 1 gg H 1 (2.20) In which Cov is the covariance matrix, H is the Hessian and g is the gradient (px1 with p the number of parameters). 14

16 2.4. VECTOR ERROR CORRECTION MODEL CHAPTER 2. METHODOLOGY 2.4 Vector Error Correction Model A VECM model is a VAR model with an extra feature, this feature captures the cointegration between oil futures prices. Cointegration is a relation that can exist between two series which both have unit roots. If two series are cointegrated they have similar stochastic trends, which make sure that they remain relatively close to each other. This cointegration relation can add to the forecasting ability of the model. As we will show in subsection the cointegration relation of the futures contracts can be represented by several spreads commonly used in the oil business, more specifically Atlantic and crack spreads. Both these spreads are modeled using an ARX/GARCH model with a student t distribution, that is we use ARX model for the mean and a GARCH(1,1) model to represent the volatility. y t = c + α 1 y t α k y t k + Xβ + ɛ t σ 2 t = ω + γɛ 2 t 1 + δσ2 t 1 (2.21) The Atlantic spreads are modeled using fundamental oil data from both sides of the Atlantic as explanatory variables. The specific data used consists of weekly US EIA data, ARA product stock and daily freight rate data. Data for the crack spread models consists of a level-shift variable (also used in the Atlantic crude spread), sine and cosine variables and the weekly US EIA data. The level shift variable is a variable which is zero before the first of January 2011 and one after, this variable is added to account for the increase in Crude Light supply after January 2011 In the case of daily estimation, the weekly EIA and ARA data were transformed to daily data, by updating the series when a new observation was published. That is, on the day a new observation is published the time series is updated to the published value, this value stays the same until the next publication. Furthermore, several differenced series have been created by taking a lagged series and subtracting it from the original. Differenced series have been created by taking lags going back the original frequency, in this case one week. After taking differences the same procedure is used to make the frequency of these differenced series daily. The explanatory variables for each model are selected using backward eliminations. That is, we start with all explanatory variables in the model, delete the least significant variable and re-estimate the model. We continue this procedure until all variables are significant at the 5% level. This method will also be applied to the explanatory variables for the upcoming VECMs. The Atlantic and crack spread models are constructed to create two time series that will serve as explanatory variables in the VECMs. Firstly, we will use the spread models to make daily and monthly forecasts of the Atlantic and Crack spreads. Because the spreads are directly related to the price of the futures contracts an accurate forecast of the spreads could improve the forecast of the futures contracts. Secondly, we will also use the estimation residuals as explanatory variables. These residuals are essentially the difference between the two underlying products of the spreads, after accounting for the effects of the explanatory variables. Lastly, a lagged version of the Atlantic and crack 15

17 2.5. PERFORMANCE MEASURES CHAPTER 2. METHODOLOGY spreads is also added as an explanatory variable. Series which are cointegrated are best estimated by an error correction model. In this paper we will use a VECM with a CCC-GARCH component for volatility. The VECM is given by: P t = c 1 + θp t 1 + β 1 P t β n P t n + γ 1 X 1,t γ k X k,t 1 + h t z t (2.22) where c 1 is a constant, θp t 1 is the cointegration effect, P t 1,..., P t n are lagged log oil future returns, X 1,t 1,..., X k,t 1 are exogenous variables and h t z t is the CCC-GARCH model for the residual vector. The CCC-GARCH feature captures the conditional heteroskedasticity in the residuals, which is expected to be present in oil futures return data (Kulsen 2011). Z t is a vector of standardized student-t residuals and H t is the CCC-GARCH model specified as H t = D t RD t (2.23) in which R is a kxk correlation matrix and D t a kxk matrix with h ii,t, the conditional standard deviation, on the diagonal. The conditional volatility h ii,t is modeled using a GARCH(1,1) model. The GARCH(1,1) is given by 2.5 Performance Measures h ii,t = ω ii + α ii ε 2 i,t 1 + β ii h ii,t 1 (2.24) This section describes the measures and techniques we will use to asses which model makes the most accurate forecasts. The methods we use to asses predictive accuracy are the mean squared prediction error (MSPE) and the percentage correct sign (PCS) performance measure. Furthermore, we will use Diebold-Mariano statistics (see Diebold and Mariano (1995)) to asses the significance of the difference in the squared prediction errors of the different models Mean Squared Prediction Error The MSPE is calculated using the following equation: n t=1 MSP E = (y t ŷ t ) 2 n (2.25) where y t is the realized value at period t. Whereas ŷ t is a forecast for the same period and n is equal to the total number of forecasts made, that is n is equal to the size of the out of sample period. In our case y t will be the log price difference of a first month futures contract between periods t and t-1. We will use the Diebold-Mariano (DM) statistic to compare the predictive accuracy of the different models. This statistic is created by comparing the forecast errors of 16

18 2.5. PERFORMANCE MEASURES CHAPTER 2. METHODOLOGY different models after using some kind of loss function. The loss function used in this paper is called the squared loss function. Given that a forecast error is defined as ɛ t+1 t = y t+1 ŷ t+1 t (2.26) in which y t+1 is the realized value at t+1 and ŷ t+1 t is a forecast of that value made with information up to time t. The loss function becomes: L(ɛ t+1 t ) = (ɛ t+1 t ) 2 (2.27) The DM statistic is calculated under the null hypothesis that the expected loss of the forecast errors of one model is equal to the expected loss of the other model. More specifically: H 0 = E[L(ɛ 1 t+1 t )] = E[L(ɛ2 t+1 t )] (2.28) Against the alternative that they are not equal. Finally, the DM statistic is calculated using the Loss differential this can be represented by the following equations: d t = L(ɛ 1 t+1 t ) L(ɛ2 t+1 t ) (2.29) d DM = (2.30) 1 T vard In which d is the mean of d, T is the number of forecast errors and vard is equal to the variance of d (in case of one step ahead forecasts). Diebold and Mariano (1995) show that under the null of equal predictive accuracy. DM N(0, 1) (2.31) So that we reject the null hypothesis of equal predictive accuracy at the 10%, 5% and 1% significance level if the absolute value of the DM statistic is greater than 1,65, 1,96 and 2,58, respectively Percentage Correct Sign The percentage correct sign performance measure indicates whether a forecast made by a model has the same direction as the realized value. More specifically, it is the percentage of forecasts which have a positive (negative) sign when the realized value also has a positive (negative) sign. It is calculated using the following equation: n t=1 P CS = (sign(y t) = sign(ŷ t )) (2.32) n In which sign(y t ) is equal to 1 if y t is positive and -1 if y t is negative. Similarly, sign(ŷ t ) is equal to 1 if ŷ t is positive and -1 if ŷ t is negative. sign(y t ) =sign(ŷ t ) is equal to 1 if the signs of y t and (ŷ t ) are the same. That is, if sign(y t ) is equal to sign(ŷ t ) and 0 otherwise. Lastly, n is equal to the total number of forecasts. 17

19 2.5. PERFORMANCE MEASURES CHAPTER 2. METHODOLOGY Economic Value The economic value performance measure is the most practical of the performance measures used in this paper. That is, it is the performance measure which will matter most to investors, but perhaps less to academics. The economic value performance measure calculates the total return obtained using a certain strategy based on the forecasts made by each model. The strategy we use in this paper can be described as a follow sign strategy. That is, we take a long position in a futures contract when the one period ahead forecast is positive and short position when we expect a negative price movement. The total return is calculated over the entire out-of-sample period according to the following equation. N T otal Return = sign(ŷ t ) (y t ) (2.33) t=1 In which N is equal to the total number of out-of-sample forecasts, ŷ t is the forecast made of y t with information available at time t 1 and y t is the realized return (i.e. log(p t )-log(p t 1 )) at time t. This performance measure values sign prediction as well as predictive accuracy (i.e. minimizing the size of the forecast error). Sign prediction is accounted for by taking a long position when the one period ahead forecast is positive and shorting the futures contract when a negative price movement is expected. Similarly, predictive accuracy is valued because a wrong sign prediction when a large return is realized decreases the total return more than a wrong sign prediction when a small return is realized. This values predictive accuracy because a wrong sign forecast with a large realized return means that the forecast error is larger in an absolute sense than in the case of a small realized return ( given that we ignore the size of the forecast when the sign is incorrect). 18

20 Chapter 3 Data The data used in this paper can be divided in two groups. The first group consists of the first month futures contracts of which we attempt to predict the price movements using the heterogeneous agents model specified in chapter 2. The second group consists of the data we use in the Vector Error Correction Model and the principal components analysis. The VECM will be used as a benchmark and comparison model (see section 2.4). The principal component analysis will be used in order to calculate the fundamental value of a certain futures contract on a specific date (see section 2.1.1). 3.1 First Month Futures Contracts This paper focuses on predicting the daily and monthly price movements of the first month futures contracts of the following commodities; NYMEX crude light NYMEX RBOB (gasoline) NYMEX Heating oil ICE Brent crude ICE Gas oil The crude oil futures, Brent and Crude light, are the most liquid oil futures in the world and are considered crude oil benchmark prices for Europe and the US. RBOB gasoline futures are the only traded liquid gasoline futures. The futures are used to hedge physical gasoline positions and are considered the worldwide benchmark prices for gasoline. Gas oil and Heating oil are the same oil products, traded on the European and US futures markets respectively. Figure 3.1 shows the price time series of the first month futures contract on NYMEX crude light. The price time series of futures contracts with different underlying oil products will be used in several spreads as possible cointegration relations and explanatory variables for the return series. Figure 3.2 shows the returns time series of NYMEX crude light, the return time series will serve as dependent variables in the VECM. That is, we will attempt to forecast the return series using: a Vector Error Correction model (VECM). A more detailed description of the futures contracts and underlying products can be found in the appendix together with figures of the price and return time series. 19

21 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA Figure 3.1: NYMEX crude light prices This figure shows the daily prices of the NYMEX Crude light first month futures contract during a period ranging from the 2th of January 2007 until the 7th of May 2013 (1600 observations). The prices are in $/bbl (i.e. $ per barrel). Similar graphs for other oil products are displayed in the appendix. Figure 3.2: NYMEX crude light returns This figure shows the daily returns on the NYMEX Crude light first month futures contract during a period ranging from the 2th of January 2007 until the 7th of May 2013 (1600 observations). The returns are in percentages. Similar graphs for other oil products are displayed in the appendix Roll-over Effect The price times series of first month futures contracts are continuation price sequences. This requires that the sequences are rolled over every month, due to the fact that each month a futures contract expires and disappears. For example, if the first month futures contract is the January 2013 contract valid between 1 st of January 2013 and the 31 st of January 2013, than the first month pricing data between these two dates is the price 20

22 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA of the January 2013 contract. However, this contract expires on January 31 st so the pricing data on the 1 st of February will be based on the February 2013 contract. The switch from basing the price data on the January contract to basing it on the February contract is called a roll-over. The roll-over has two significant implications. Firstly, the difference in price between two consecutive months (i.e. the calender spread) leads to a jump in prices when the roll-over occurs. We adjust the return series to counter this effect by combining the appropriate prices to calculate the returns at the time of and one day after the roll-over (see equation 3.1). The problem of the roll-over effect also exists in price time series. To adjust for this we will create a new price time series from the adjusted returns series. This price time series will be equal to the original price time series, except for two observations each month during which the roll-over occurred. Secondly, on the days leading up to the expiration of the first month contract, the liquidity of this contract decreases. More specifically the open interest (i.e. number of outstanding contracts) of the first month contract decreases. We will use this decrease in open interest as an indicator for the time of expiration. On the day of expiration the open interest will be at a minimum followed by a sharp rise the next day, this indicates that it is time to perform a roll-over. That is, we will perform a roll-over when the open interest of the first month contract is at a minimum. The returns series are adjusted for the roll-over effect according to the following equation: r t = log( F (2) t F (2) t 1 ) for t = τ log( F (1) t ) for t = τ + 1 F (2) t 1 log( F (1) t ) else F (1) t 1 (3.1) In which τ indicates the day of expiration of the first month (i.e. spot) futures contract and F i t is the future settlement price of the ith futures contract at date t Augmented Dickey-Fuller test To determine whether time series are stationary we use the Augmented Dickey-Fuller (ADF) test. This test determines whether a time series has a unit root and is therefore not stationary. The presence of a unit root indicates that shocks to a process (e.g. a price time series) have permanent effects and that the variance depends on the time period and diverges to infinity as time increases. These properties of a unit root process can cause problems in statistical inference involving time series models. A common way to make these series stationary is to take first differences, or in case of financial products take returns. The lag order (i.e. the amount of lags) used in the ADF test is selected based on the Schwarz Information Criterion with a maximum of 24 lags. The deterministic components used in the ADF test will not be the same for each variable in the upcoming sections and will be described beneath the table with ADF test results. An intercept will be added for series with a non-zero mean. Similarly a trend variable 21

23 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA will be included if a time-series has a clear trend. The ADF test statistic is calculated using the following equations: y t = α + βt + γy t 1 + δ 1 y t δ p 1 y t p+1 + ɛ t (3.2) In which α is a constant, β the coefficient of a time trend and p the lag order of the autoregressive process. The null hypothesis of the ADF test is that γ = 0 against the alternative hypothesis of γ < 0. If a time series has no clear trend and a mean equal or close to 0 we impose the restrictions α = 0 and β = 0. Similarly, if no trend exists but the mean is not equal to 0 we impose the restriction β = 0. Under the null hypothesis this corresponds to modelling a random walk and a random walk with drift, respectively. The ADF test statistic is than calculated with the following equation: DF = γ SE(γ) (3.3) This DF statistic will be compared to the relevant critical value for the ADF test, which depends on the imposed constraints. If the DF statistic is less than the critical value, the null hypothesis of γ = 0 is rejected and we can conclude that the time series doesn t contain a unit root and as such is stationary Descriptive statistics This section compares the statistics and time series of the different oil futures contracts and returns series. Figure 3.3 shows the daily price movements of the five different 1 st month futures contracts from January 1st 2007 until the 7th of may The price movements are all very similar which implies that the returns of the futures contracts are highly correlated. This is confirmed in table 3.2 which shows the correlation and covariance between the returns of the futures contracts. ICE gas oil seems to be the least correlated with the other futures, this can be explained by the fact that trading in ICE gas oil futures closes earlier than trading in the other futures contracts, 17:30 and 20:30 respectively. However, the smallest correlation is still above 0.5. Table3.1 shows the descriptive statistics of the different returns series. It is clear that: The mean return is close to 0%. The standard deviations of the daily returns are between 1.85% and 2.54%. All return distributions have excess kurtosis, which indicates that the distributions of the returns have fat tails and as such are not normally distributed. The skewness is on average quite small and negative, except in the case of gas oil (in which it is small and positive). The autocorrelations are relatively close to zero, which is often the case in returns series. 22

24 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA There is significant autocorrelation in the squared daily returns series (see 3.4 and A.1) From figure 3.4 it is clear that there is significant autocorrelation in the volatility of Brent returns (similar patterns are visible for other oil futures time series). More specifically, the returns series seem to suffer from volatility clustering. Autocorrelations and partial autocorrelations have been computed for the squared Brent returns series (see A.1 in the appendix). It turns out that autocorrelations are present between current volatility and lags one till five. To account for these autocorrelations we will use a GARCH(1,1) for volatility (Bollerslev (1986)) when estimating our daily VECM model. Considering that the distribution of returns has excess kurtosis, is close to symmetric and that this remains true for the residuals after accounting for the autocorrelation in volatility we conclude that the distribution of the returns series is relatively similar to a student t distribution. The monthly returns series doesn t suffer form significant autocorrelation in the squared returns series, has a very small excess kurtosis and a mean close to one. Therefore the monthly VECM will be modeled using a normal distribution with no GARCH component. Figure 3.3: Prices of the different first month futures contracts This figure shows the daily prices of the first month futures contracts of five different oil products, that is the price movements of NYMEX Crude light, NYMEX RBOB, NYMEX Heating oil, ICE Brent Crude and ICE Gas oil. Firstly, a significant drop in prices can be seen at the start of the financial crises (i.e. the credit crises). Secondly, it is clear that the prices of crude oil are on average lower than the prices of refined oil products. This is to be expected as the difference in price is basically the gross margin on which refineries make their profits. 23

25 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA Table 3.1: Descriptive Statistics of the Returns of Different Oil Products NYM Crude L NYM RBOB NYM HO ICE Brent C ICE GO Mean -0,0100 0,0665 0,0102 0,0382 0,0384 Standard Dev 2,5364 2,4717 2,0674 2,2412 1,8597 Kurtosis 7,1101 5,4314 5,2012 6,9163 6,0231 Skewness -0,0075-0,2383-0,2220-0,2690 0,1010 Autocorr 1-0,0458-0,0361-0,0280-0,0748 0,0012 Autocorr 2-0,0058-0,0250 0,0049-0,0105 0,0097 This table shows the descriptive statistics of the realized returns series of the different first month futures contracts. It is clear that in contrast to a normal distribution these returns series exhibit significant excess kurtosis. Furthermore the mean is close to zero and there is a relatively small negative skewness. Table 3.2: Covariance-Correlation Matrix of the Returns NYM Crude L NYM RBOB NYM HO ICE Brent C ICE GO NYM Crude L 6,4334 4,6721 4,3412 5,0158 2,7340 NYM RBOB 0,7452 6,1093 4,0277 4,5485 2,4187 NYM HO 0,8279 0,7882 4,2743 4,1846 2,4983 ICE Brent C 0,8824 0,8211 0,9031 5,0228 2,5727 ICE GO 0,5796 0,5262 0,6498 0,6173 3,4585 The upper triangle of this table shows the covariances of the different oil products. The bottom triangle displays the correlations, the variance of each product can be found on the diagonal. Figure 3.4: Squared Brent Returns This figure shows the squared Brent returns series. This series serves as a proxy for volatility in Brent returns. It is evident from this picture that there is volatility clustering in the Brent returns series. 24

26 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA Stationarity & Cointegration of Oil Prices This section discusses the stationarity of the price time series of the 1 st month futures contracts with the 5 different oil products, described above, as the underlying. Table 3.3 shows the results of the ADF test. The price time series of the 1 st month futures contracts all contain unit roots. In an attempt to make these series stationary we calculated the daily returns. The bottom part of table 3.3 shows the results of the ADF test performed on the daily returns series. The returns series are all stationary, therefore we will use the return series as dependent and if useful explanatory variables in the VECM. If two time series have a unit root (i.e. a stochastic trend) but they don t stray away to far from each other because they share similar stochastic trends, these time series are said to be cointegrated. Cointegrated series are best estimated using an error correction model, the cointegration relation can improve the predictive accuracy of the model. There are four spreads commonly used in the oil business to hedge or speculate that consist of combinations of the above mentioned oil products. We suspect that the spreads might represent cointegration relations, these four spreads are: The Atlantic spread of crude oil (ICE Brent Crude - NYMEX Crude Light). The Atlantic spread of gas oil (ICE Gas oil - NYMEX Heating oil). The Crack spread of gasoline (NYMEX RBOB - NYMEX Crude Light). The Crack spread of Heating oil (NYMEX Heating oil - NYMEX Crude Light). (See 3.2.1) The Atlantic spreads represent price differences between relatively similar products, produced and traded in different geological locations. The Crack spreads can be seen as the added value of refineries to the oil products (i.e. the margin on which refineries make their profits). To determine whether these spreads represent cointegration relations we perform the Augmented Dickey fuller test on the above mentioned pairs of price time series. If these spreads represent cointegration relations the results of the ADF test should indicate that they are stationary given that the price time series themselves are non-stationary. Table 3.4 shows the results of the ADF test. The results show that the Atlantic gas oil spread and the RBOB crack spread indeed represent cointegration relations between ICE gas oil-nymex heating oil and NYMEX RBOB-NYMEX crude light, respectively. However, the results also imply that the Atlantic crude spread and the Heating oil crack spread don t represent cointegration relations. This can be explained by the level shift in the Atlantic crude spread and Heating oil crack spread which occurs at the start of 2011 (see figure 3.5). If we perform the ADF test on both these spreads with data up till but not including We find that the ADF rejects the null hypothesis of non-stationarity, with p-values of 0,0001 and 0,0261 for the Atlantic crude spread and the Heating oil crack spread, respectively. This indicates that these spreads might indeed represent a cointegration relation which is disturbed by the level shift. Therefore, we will adjust the Atlantic crude spread and Heating oil crack spread by regressing on a level shift dummy variable in order to obtain residuals that don t contain a unit root. This 25

27 3.1. FIRST MONTH FUTURES CONTRACTS CHAPTER 3. DATA dummy variable is equal to 0 before the start of 2011 and 1 afterwards. After regressing on this dummy we performed the ADF test on the residuals the results can be found in the last two columns of table 3.4 which indicate that these residuals are stationary and can therefore be seen as the cointegration relation between the used price time series. This level shift can be explained by the increased production of NYMEX crude light in the US and the export ban of crude oil from the US. More specifically, at the start of 2011 the US has increased its oil production while demand remained relatively unchanged. This together with the export ban on crude oil decreased the price (stagnated the upward price trend) of NYMEX crude light. As stated above the best way to estimate a cointegrated series is by using an error correction model. The error correction model we use is the Vector error correction model (VECM) with a GARCH component for volatility, this model has been described in section 2.4. The error component (i.e. cointegration component) used in the VECM will be the (adjusted) spreads mentioned above. Table 3.3: Augmented Dickey-Fuller Test on Oil products NYM Crude L NYM RBOB NYM HO ICE Brent C ICE GO ADF Statistic -2,1413-2,0439-1,7202-1,7654-1,6295 Critical value -2,8646-2,8646-2,8646-2,8646-2,8646 P-value 0,2340 0,2772 0,4205 0,4005 0,4606 Unit root yes yes yes yes yes Returns ADF Statistic -42, , , , ,7669 Critical value -1,9416-1,9416-1,9416-1,9416-1,9416 P-value 0,0001 0,0001 0,0001 0,0001 0,0001 Unit root no no no no no Observations Indicates that an intercept was added to the ADF test. This table displays the results of the augmented Dickey Fuller test on the time series consisting of daily prices of first month futures contracts with different underlying oil products and their returns series. The top displays the results based on the prices of the futures contract, similarly the bottom part displays the results of the returns series. The time series consisting of the prices all contain unit roots, whereas the returns series are all stationary. 26

28 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Table 3.4: Augmented Dickey Fuller Test on Oil Spreads ATL Crude ATL GO RBOB Crack HO Crack ATL Crude adj HO Crack adj ADF Stat -2, , , ,0485 Critical val -2,8645-2,8645-2,8645-2,8645-2,8645-2,8645 P-value 0,2247 0,0001 0,0292 0,1946 0,0001 0,0310 unit root yes no no yes no no # Obs : Indicates that an intercept has been included in the ADF test. This table shows the results of the Augmented Dickey-Fuller test on the (adjusted) Atlantic and Crack spreads specified above. 3.2 Data for VECM & PCA This section describes the data used in the VECM and principal component analysis. We will use several fundamental (marked by the *) and financial variables with two distinctive goals in mind. Firstly we will use the fundamental variables, stated below, in a principal component analysis in an attempt to asses the fundamental value (i.e. the intrinsic value) of first month oil futures contracts. More specifically, we attempt to calculate the fundamental value of the underlying oil products which as such also represents the fundamental value of the first month futures contracts. In order to keep the amount of explanatory variables to a minimum, to counteract parameter uncertainty, we will perform a principal component analysis on these fundamental variables. Secondly, we will use all variables mentioned below, that is the fundamental and financial variables, as possible explanatory variables in a vector error correction model (VECM). The VECM will be used to make daily and monthly forecasts of the returns of the first month futures contracts. Furthermore, it will serve as the benchmark model for the HAM. To be more precise, we will create daily and monthly forecasts with the VECM and compare its performance (i.e. predictive accuracy) to the performance of the HAM model. For the prediction of the Atlantic and Crack spreads; Periodic functions. Sine and cosine variables with period of one year, an amplitude of one and zero phase shift. Freight rates. Freight rates between USG (US East Golf)-ARA(North-West Europe) and Freight rate ARA-NYH. US EIA oil data. Crude inventories, distillate inventories, gasoline inventories, refinery capacity utilization. The explanatory variables of the VECM; Forecasts of the Atlantic and Crack spreads. 27

29 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Calender Spreads. The difference between the prices of futures contract of 2 consecutive months (2 nd -1 st ), for all depend variables. The daily returns on a weighted average of the exchange rates of the worlds main oil importing countries against the US dollar: US dollar index returns. Consolidated stock index returns. That is, daily returns on a weighted average of the stock exchanges of the worlds main oil importing countries World PMI index (i.e. weighted average of the PMI indexes of the worlds main oil importing countries). one month lagged differences for the 1st 2nd and 3th month of the World PMI index. EIA international crude oil data and OPEC quota data. OECD commercial inventories, total production - total demand (World Supply) and OPEC quota data. ARA oil inventories. ARA gas oil, gasoline and total oil product inventories. US EIA oil data. EIA refinery capacity utilization. Singapore oil inventories. Both light and middle distillate inventories. IEA oil demand data. Change in IEA oil demand growth. Cushing inventories and refinery capacity utilization. Cushing is a major trading hub for crude oil (i.e. Crude Light) in Oklahoma, United States A more specific list of explanatory variables for the different models can be found in appendix A.4. In the upcoming sections we will discuss the relation between each of these variables and oil prices accompanied by an in dept analysis of the statistics of each time series Atlantic & Crack Spreads The Atlantic spreads represent the price difference between the price of an oil futures contract in Europe and in the USA. The Atlantic crude spread is created by subtracting the price of the 1 st month futures contract on NYMEX Crude Light from the price of a similar contract with ICE Brent Crude as the underlying. Similarly, the Atlantic gas oil spread is created by subtracting NYMEX heating oil from ICE gas oil. Figure 3.5 displays the daily Atlantic crude spread from the 2nd of January 2007 until May 7th 2013 (1600 observations), again clearly showing the level shift at the start of The figure for the Atlantic gas oil spread can be viewed in the appendix (see figure A.9). Crack spreads are the difference in price between oil products and crude oil and as such can be interpreted as a profit margin for refiners. Figure 3.6 displays the daily gasoline crack spread between January 2nd 2007 and May 7th 2013 (1600 observations). 28

30 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA This crack spread is created by taking the difference in price of the 1 month futures contracts of NYMEX RBOB and NYMEX crude light. Figure 3.6 shows that there is some indication of a seasonal pattern in the gasoline crack spread. An explanation for this can be that the rise in demand as a result of the US driving season causes a rise in gasoline prices relative to crude prices. This will be accounted for, when estimating the Crack Gasoline spread model, by the sine and cosine explanatory variables stated above. Figure A.10 in the appendix shows the heating oil crack spread during the same time period. We clearly see an upward trend in the heating oil crack spread, interrupted by a downward trend at the start of the credit crises, indicating an increase in heating oil prices relative to crude oil prices. Section already gave the most important reason to compute models for these spreads the so called cointegration relation, between different oil products, captured by these models. Another possible use of the Atlantic and crack spread models is to make forecasts of these spreads and use these forecasts as explanatory variables in the models for the returns on the first month futures contracts. Because these series are composed of oil product prices, the movements of these spreads are correlated with movements in oil prices. Table A.2 displays the descriptive statistics of the Atlantic and crack spreads. These statistics confirm the statements made above. The Atlantic crude spread is on average positive confirming that crude oil is indeed cheaper in the US than the EU. Both Crack spreads have relatively large positive means representing the added value of refining oil. Lastly, all spreads except for the Atlantic gas oil spread have first and second order autocorrelations higher than The lower autocorrelations in the Atlantic gas oil spread can again be attributed to the earlier closing time of ICE gas oil futures trading. Figure 3.5: Atlantic Crude Spread The Atlantic crude spread (ICE Brent Crude ($/bbl) - NYMEX Crude Light($/bbl)) from January 2nd 2007 until May 7th

31 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Figure 3.6: Gasoline Crack Spread The gasoline crack spread (NYMEX RBOB($/bbl) - NYMEX crude light($/bbl)) from January 2nd 2007 until May 7th Freight rates The Atlantic spreads are basically a comparison between 2 similar products in different geographical locations. If this spread becomes larger, in an absolute sense, it becomes more attractive to order the cheaper product no matter your geographical location. This makes sense if the price difference in oil products is larger than the cost of transportation (i.e. the freight rates). Therefore, the freight rates can have a significant effect on the Atlantic spreads. Figure 3.7 shows the freight rates for oil tankers traveling from ARA to New York or the US Gulf and from the US Gulf back to the ARA region. It is clear from this figure that the freight rates are highly correlated but do seem to differ in level. In order to asses whether these series of freight rates are stationary we perform the ADF test. Table A.3 shows the results of this test, according to the ADF test all freight rates series are non-stationary. However, because the ADF test can t account for the economic value of variables and because for two out of the three series the ADF null hypothesis is only barely not rejected, with p-values of and we choose to use level freight rates as explanatory variables. Furthermore, because the freight rates will only be used in the Atlantic spread models, which main use is to provide a series which captures the cointegration relation between oil futures, the effect of the possible unit root should be negligible in the final VECM. The descriptive statistics of these series are shown in table A.4 in the appendix, the means are relatively close, with the difference possible being caused by the difference in transporting distance, loading, unloading and other harbor fees. They all have a kurtosis close to -0.1 and high autocorrelations. 30

32 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Figure 3.7: Freight Rates The Freight rates in ($/ton) for oil tankers traveling from the ARA to New York or the US Gulf and from the US Gulf to the ARA region, for the period ranging from 1st of January 2007 until 5th of May EIA Inventories The current inventories of oil products can be used to make assumptions of short term supply and demand dynamics. Crude inventories are related to crude supply and refinery demand, whereas the inventory of oil products relates to end consumer demand and refinery supply. These inventories are related to the Atlantic and crack spreads because they provide insight in the current demand and supply of the U.S., and as such provide insight in the price movements of oil products. Another important component in the supply of crude oil, especially related to crack spreads, is the availability of operational crude oil refining capacity. The availability of crude oil refining compared to the required refining capacity should, according to economic theory, influence the price of oil products and as such influence the crack spreads. In order to capture this relation we add EIA US refinery capacity utilization data, the only refinery capacity data available, to the list of possible explanatory variables. Figure 3.9 shows the US refinery capacity utilization. To examine whether the EIA inventory (3.8) and the refinery capacity utilization data have unit roots we perform the Augmented Dickey-Fuller test. The results of this test are displayed in table A.5 in the appendix. According to the results of the ADF test each series of EIA inventory data contains a unit root, however after taking first differences the series becomes stationary. Therefore, it is advised and customary to use the first difference series of the inventory data as possible explanatory variables in the spread and error correction models. However, the ADF test doesn t account for economic value, according to economic theory the level of inventory is one of the main driving forces for price changes, because it directly relates to supply and demand. Therefore we will use a level inventory variable as well as the first difference series (i.e. the change in inventory). The results for the refinery capacity utilization data are significantly different. This 31

33 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA data is already stationary so we will use the original series of this data as an explanatory variable. The descriptive statistics of the EIA inventories and US refinery capacity can be found in Table A.6 in the appendix. Figure 3.8: EIA Inventory Levels EIA inventory data: US Crude oil, distillate and gasoline stocks from the 3rd of January 2007 until 24th of April 2013 (330 weekly observations) Figure 3.9: US Refinery Capacity Utilization This figure shows the US refinery capacity utilization from the 3rd of January 2007 until 24th of April 2013 (330 weekly observations) Calender Spreads Futures contracts with different physical delivery dates (i.e. time to maturity) are traded on commodity futures exchanges at every point in time. On the NYMEX and ICE oil futures exchanges contracts are being traded with delivery dates for every month in the future, with a maximum of three years. That is, you can buy a futures contract now and get the oil delivered any number of months from now up to three years, depending 32

34 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA on the futures contract you buy. All these contracts can have different prices, these prices form the term-structure. Pagano and Pisani (2009) use the term-structure to forecast oil prices and conclude that futures prices can be used to forecast oil prices successfully if the model is expanded with a risk premium indicator. They use business cycle indicators like the capacity utilization of manufacturing (see and 3.2.7) as a risk premium indicator. A way to look at this term-structure is by creating (i.e. plotting) the forward curve, this is done by charting the prices of futures contracts at a certain point in time while ordering them by delivery data. A useful way to study the dynamics of the termstructure is by creating calender spreads. Calender spreads represent the difference in price between 2 futures contracts with the same underlying asset or product but different delivery dates. Futures prices are related to expectations concerning supply and demand on the delivery date. The slope of the forward curve indicates what is expected by investors, if the forward curve is upward (downward) sloping it implies that investors expect oil prices to go up (down) in the future. Calender spreads capture these expectations. Because we are interested in relatively short term forecasts, we will focus on the front end of the forward curve. That is, we will use calender spreads between the first and second month (i.e. 2 nd -1 st ) for the five oil futures contracts. Figure 3.10 shows these calender spreads. Table A.7 shows the results of the ADF test on the calender spreads. The results indicate that the calender spreads are all stationary, this is what was expected because the calender spreads are already a difference series (i.e. the difference between the prices of 2 futures contracts). Because the calender spreads are stationary we are able to use them as explanatory variables, without damaging the integrity of the results obtained by the models. The descriptive statistics of the calender spreads in table A.8 show that calender spreads are on average positive, have excess kurtosis and high autocorrelations. The calender spread of NYMEX RBOB is different from the other calender spreads, it has a negative mean and an unusually high standard deviation. A possible explanation for this could lie in the seasonality caused by the US driving season (see A.11). During, or just before, the driving season shorter futures contracts will increase in price whereas future contracts which have a delivery date close to the end of, or after, the driving season diminish in value, which creates a negative calender spread. Similarly a relatively large positive calender spread arises in a period before the driving season when the delivery date of the longer futures contract is in the driving season while the shorter futures contract delivers before the season begins. 33

35 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Figure 3.10: Calender Spreads This figure shows the calender spreads ( i.e. the difference in price between 2nd and 1st month futures contracts) for the different oil products. For the period ranging from January 2nd until May 7th Foreign Exchange rates Oil products are consumed all over the world, yet oil products are priced in US dollars. Therefore, it is likely that the US Dollar exchange rate influences oil prices. Changes in oil prices can be correlated with changes in exchange rates (see for example: Fan et al. (2008)). For computational ease we will make a weighted average of the exchange rates of the worlds main oil importing countries, the US Dollar Index (see figure 3.11). The US Dollar Index is a combination of the following exchange rates: USD/EURO USD/Chinese Yuan USD/Japanese Yen USD/Indian Rupee USD/Great-Britain Pound Each of these exchange rates has been standardized so that on the first date all exchange rates are equal to 100. This makes it easy to compare and combine the exchange rates. The weights appointed to each exchange rate are based on the total oil consumption of each country relative to the oil consumption of these five countries combined. The oil consumption figures are based on IEA data of each countries oil consumption from The weights appointed to each exchange rate are as follows: USD/EURO 43,17% 1 The Data on oil consumption for these countries can be found on 34

36 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA USD/CHY 26,73% USD/JPY 14,83% USD/INR 10,35% USD/GBP 4,92% To test whether the US Dollar Index contains a unit root we use the Augmented Dickey- Fuller test, the test results are displayed in table A.9a. Clearly the US Dollar Index contains a unit root, and is non-stationary. In order to obtain a stationary series based on the US Dollar Index we calculate the returns on the US Dollar Index. Table A.9a shows that the returns series is stationary. Therefore, we will use the returns series as an explanatory variable in the VECMs. Figure 3.11: US Dollar Index The US Dollar Index, a weighted average of the USD/Foreign exchange rates of the main oil importing countries. The observations range from 1st of January 2007 until the 7th of May 2013 (1657 observations) Stock Indexes Oil futures are traded on financial markets, the futures we investigate in this paper are traded on the NYMEX and ICE, therefore it is not unlikely that other financial markets might influence oil prices. According to Ewing and Thompson (2007) oil price co-move with several macroeconomic variables that are used to determine the business cycle, such as industrial production and stock prices. We will asses the effect of stock exchanges on oil prices by creating a weighted average of the main stock exchanges of Asia, Europe and the USA. Similar to the procedure performed in section we will base the weight for each stock index on the relative oil consumption of its respective country compared to the total oil consumption of all considered countries. The stock indexes included in the weighted average are: 35

37 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA The Nikkei stock exchange of Japan. [11,00%] The Hang Seng Index of Hong Kong (We will assign a weight to the HSI based on the oil consumption of China). [19,83%] The Sensex of India. [7,68%] The AEX of the Netherlands.[1,39%] The CAC40 of France. [4,71%] The DAX of Germany. [6,33%] The FTSE of the UK. [3,65%] The S&P500 of the USA. [45,41%] Each of these stock indexes has been standardized such that on the first day each index is equal to 1. This is done to make it easier to combine these indexes and assign the right weight to each index. The oil consumption figures are, again, based on the IEA data of each country s oil consumption in The weight assigned to each stock index is stated between brackets in the above summation. Like we did before, we will perform an ADF test to determine whether the consolidated stock index contains a unit root. Table A.10a shows the results of this test, a unit root is found in the time series of the consolidated stock index. The returns series constructed from the stock index doesn t contain a unit root and will be used as an possible explanatory variable in the VECMs. The descriptive statistics of the returns series are displayed in table A.10b. Figure 3.12: Consolidated Stock index The consolidated stock index, a weighted average of the main stock indexes of Asia, Europe and the USA. The observations range from 4th of January 2007 until the 2nd of May 2013 (1353 observations). 36

38 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA World PMI Purchasing managers indexes (PMI) are macro-economic indicators for the manufacturing sectors. They are related to industrial production and therefore to oil demand (see Ewing and Thompson (2007)) but are released much sooner than industrial production data. Purchasing managers indexes for most major economic blocks are combined in a fashion similar to the one used to combine the exchange rates and stock indexes in the previous sections. This weighted average of PMI will be called the world PMI. The world PMI consists of a weighted combination of the following PMIs: Markit Japan PMI manufacturing sector. [9,20%] Markit HSBC China PMI manufacturing sector. [16,58%] Markit HSBC India PMI manufacturing sector. [6,42%] Markit Eurozone PMI manufacturing sector. [26,78%] Markit Great Britain PMI manufacturing sector. [3,05%] ISM US manufacturing PMI. [37,97%] The weight appointed to each PMI index is stated in brackets in the above summation. Similar to the method used in sections & the weights are determined by comparing the country s or monetary union s oil consumption 2 relative to the combined oil consumption of all considered parties. The Markit and ISM manufacturing PMI data is released on the first working day of each month. The PMIs are indicator variables that range from 0 to 100 but are on average close to 50. A PMI above 50 signals economic growth in the manufacturing sector in contrast to a PMI below 50 which signals a decline in economic activity. Figure 3.13 shows the individual PMIs used to create the world PMI. From this figure it is clear that all PMIs move relatively similar although there can be a change in level, which could be caused by a difference in growth rates in the economic regions. A second explanation for the difference in levels can be found in the fact that we deal with emerging and developed economic regions. Figure 3.14 shows the weighted combination of these PMIs, the world PMI. The world PMI is a proxy for economic growth, which is basically a rate of change, and a series that revolves around the value of 50, therefore we would expect the series to be stationary. However as can be seen in table A.11a this is not the case, according to the Augmented Dickey Fuller test. A possible explanation could be that the limited sample of 77 observations is too small for the ADF test to asses whether there truly is a unit root. On the other hand, it could be that the world PMI series is truly non stationary. Therefore we will use the level as well lagged difference series of the world PMI. 2 Data on the oil consumption of the different countries can be found on the website: 37

39 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Figure 3.13: PMIs of the major economic blocks Purchasing managers indexes (PMI) of most major economic blocks. The PMI are monthly released indicators of economic growth or decline in the manufacturing sector. A PMI above 50 indicates growth, whereas a PMI below 50 indicates decline. The data ranges from the 2nd of January 2007 until the 1st of May 2013 (77 observations). Figure 3.14: The world PMI A weighted combinations of the purchasing managers indexes (PMI) of most major economic blocks. The PMIs are monthly released indicators of economic growth or decline in the manufacturing sector. A world PMI above 50 indicates growth, whereas a world PMI below 50 indicates decline. The data ranges from the 2nd of January 2007 until the 1st of May 2013 (77 observations) Oil Fundamentals The oil fundamentals are time series concerning supply and demand in worldwide oil markets. The supply chain of oil can be decomposed in three parts. Firstly, the exploration and production of crude oil, secondly crude oil refining and thirdly distribution to end consumers. Crude oil markets connect part one with part 2, oil product trading 38

40 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA markets connect part 2 with part 3 and finally oil products retail markets coordinate the distribution to end consumers. If we look at these three parts backwards we find the demand chain for oil. Demand for oil products from end consumers drives the demand in the trading market which in turn drives the demand for crude oil. Another factor that plays a significant role is the operational refinery capacity which drives the refining margins with respect to oil products. According to this analysis there are three main factors which influence oil market fundamentals: Supply of crude oil. End consumer demand. Operational refinery capacity. The supply of crude oil can and should be divided in two groups, OPEC supply and non-opec supply. OPEC supply is controlled by the cartel which issue OPEC quotas to control the market price. According to Tang and Hammoudeh (2002) OPEC production quotas are adjusted so that prices remain within a certain target price bandwidth. Non-OPEC crude supply markets have free market dynamics and behave more like normal mining limited-resource markets. Short term demand and supply dynamics in crude oil markets are related to inventories of crude oil and oil products. Crude inventories react to crude supply and demand from refineries, similarly oil product inventories are related to dynamics in end consumer demand and refinery supply. Inventory data from the OECD, the US, the ARA region (i.e. Amsterdam-Rotterdam-Antwerp region), Singapore, Cushing (the central crude oil hub in the US ) and the EIA data covered in section are used to incorporate this relation. Every month the International Energy Agency (IEA) publishes its Oil Market Report (OMR) 3. In this report they give projections of the demand growth for oil. These projections give an indication of what the general expectations are for the future demand for oil, therefore they will be included as possible explanatory variables in the upcoming models. To asses the current supply demand situation of oil products we will create the series World-net. World-net is created by subtracting the OPEC and non-opec supply from OECD and non-oecd demand, that is (OECD demand + non-oecd demand)-(opec supply + non-opec supply)=world-net. The Augmented Dickey-Fuller test results are displayed in table A.12, most fundamentals have unit roots and are therefore differenced before measuring their descriptive statistics which can be observed in table A.13. The most surprising result is the fact that the ARA gasoline inventory data doesn t contain a unit root while the other ARA inventories do have unit roots. However, this doesn t have any effect on our variable selection because like the choice we made for the EIA inventory levels we will again allow level and difference series of inventory variables. The reason for this choice is similar 3 The IEA Oil Market Reports can be found here: 39

41 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA to the one stated in section 3.2.3, the inventory level of a product is directly related to supply and demand and can therefore have a significant influence on prices. Figure 3.15: OPEC Quota This figure shows the OPEC quota in million barrels/day, for the period ranging from 1st of January 2007 until 5th of May (62 monthly observations) (a) OECD Commercial Inventories (b) US Commercial Inventories Figure 3.16a shows the OECD commercial inventory (crude + oil products) in million barrels, for the period ranging from the 9th of January 2007 until the 7th of May Similarly, figure 3.16b shows the US Commercial inventories in million barrels for the same time period. 40

42 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA (a) ARA Inventory Levels (b) Singapore Inventory Levels Figure 3.17a shows the ARA inventory levels of gas oil, gasoline and the total inventory, in kilo tons, for the period ranging from 5th of January 2007 until 2nd of May (331 weekly observations). Figure 3.17b shows the Singapore inventory levels of light and middle distillates, in million barrels, for the period ranging from 1th of January 2007 until 2nd of May (335 weekly observations) Figure 3.18: Cushing Crude Oil Inventory This figure shows the Cushing crude oil inventory levels in thousands of barrels (TB), for the period ranging from the 1st of January 2007 until May 10th 2013 (333 weekly observations). 41

43 3.2. DATA FOR VECM & PCA CHAPTER 3. DATA Figure 3.19: IEA Projected Annual Demand Growth This figure shows the projected annual demand growth, in %, by the IEA for the period ranging from 1st of January 2007 until 5th of May (77 monthly observations) Figure 3.20: World-net This figure shows the variable World-net, which represents the net demand for oil in the world, in million barrels per day. That is, World net is created by subtracting the world supply (OPEC supply + non-opec supply) from the world demand (OECD demand + non OECD demand). The data ranges from 1st of January 2007 until the 7th of May 2013 (77 monthly observations). 42

44 Chapter 4 Results In this chapter we will examine the in and out-of-sample performance of the heterogeneous agents model. In the first section we will discuss the implications of the sign and size of the estimated parameters. We will compare the parameters estimated by the HAM using different fundamental values. More specifically, we compare the parameters estimated using a fundamental value based on a moving average with parameters estimated using a fundamental value based on the principal components of the fundamental variables discussed in section 3.2. The second section compares the out-of-sample performance of both HAMs (based on different fundamental values) with the performance of the VECM and the random-walk (no change) model. The daily data sample ranges from January 2nd 2007 to the 26th of April 2013 of which January 2nd th of December 2011 will be used as the in-sample period to estimate parameters. The out-of-sample period (i.e. January 3th th of April 2013) will be used to asses predictive accuracy. One day ahead forecast are made using an expanding window of observations. That is, we first estimate parameters over the in-sample period after which we make a one day ahead forecast followed by an increase of the in-sample period by one day and a re-estimation of the parameters. This results in 275 daily out-of-sample forecasts (after accounting for discrepancies in the explanatory variables). The monthly data sample ranges from January 2000 to April We have increased the sample period in order to make tests of equal predictive ability more powerful to detect significant differences in predictive accuracy. Firstly, In order to keep the parameter estimates comparable between the monthly and daily samples we will first estimate the parameters over a sample ranging from January 2000 to December 2011, the daily parameters are robust for this change in sample period. Secondly, forecasts are made using an expanding window of observations starting with an in-sample period of January 2000-December This results in 64 monthly out-of-sample forecasts. This number of forecasts is still relatively small, however further backdating the sample would result in the loss of several explanatory variables of which no data is available before the year We will focus our in dept analysis on the results obtained for the two crude oil futures contracts (i.e. Brent Crude & Crude Light). However, similar tables and graphs for the other oil futures contracts are provided in the appendix. 4.1 In-Sample Estimation This section will discuss the parameter estimates made by the heterogeneous agents model. Firstly, we will compare the parameter estimates made using different fundamental values. Secondly, we will compare the estimates made on daily data with estimates made using monthly data (i.e. transformed daily data), in an attempt to asses whether the noise in daily data has significant effects on the parameter estimation of the HAM. 43

45 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS Daily data The HAM is based on the differences between lagged log-prices and log-prices with logfundamental values. Table 4.1 shows the descriptive statistics of these 2 series. Table 4.1 clearly shows the difference between the fundamental value based on the moving average (fundamental value (1)) and fundamental value based on principal components (fundamental value (2)). Fundamental value (1) stays significantly closer to the log-price than fundamental value (2), which can be concluded from the difference in minimum and maximum and the increased standard deviation for fundamental value (2). This is to be expected as fundamental value (1) is directly based on log-price whereas fundamental value (2) is based on current supply and demand, which should only be completely equal to log-price if one makes the assumption of fully rational and efficient markets, which goes against the main assumption made in this paper: the existence of heterogeneous agents in the market. Similar results are obtained for gasoline (i.e RBOB), gas oil and heating oil as can be seen in tables A.14 and A.15 in appendix A.3.2. The in-sample parameter estimates for crude oil are displayed in table 4.2. Generally it can be seen that a and b are never significant indicating that the real demand and supply for oil keep each other in balance. More specifically, the positive price movement after an increase in real demand is almost immediately offset by an increase in real supply followed by a negative price movement. The speculative fundamentalists and chartists do show significant coefficients although results vary significantly based on the approach, to calculating the fundamental value, of the fundamentalists. The parameters estimated using fundamental value (1) are all of the hypothesized sign. More specifically, we observe that both α 1 and α 2 are negative and significant. This indicates that there are investors in the market which base their expectations on the discrepancy between the price of first month crude oil futures and its fundamental value. The negative sign shows that fundamentalists have a stabilizing effect on oil prices. Furthermore, since α 2 > α 1 we can conclude that fundamentalists react more to an overvaluation than an undervaluation of oil. Chartists in this market show destabilizing behavior as β 1 and β 2 are both larger than 0. When prices decrease they expect that they decrease further. Similarly, after a price increase another price increase is expected. However, chartists seem to have less effect than fundamentalists on positive price movements of crude oil, as only the β 2 parameter for crude light oil is significant. Indicating that chartists only significantly influence the price in the case of a declining trend. The speculator parameters estimated using fundamental value (2) are significantly different than those previously discussed. Fundamentalists have much less effect on crude oil prices, that is only in the case of an overvaluation of the Crude Light futures contract do fundamentalists have a significant impact on the price. This is a stabilizing effect as α 2 < 0. Similarly, chartists also have a limited effect on crude oil prices. More specifically, in the case of Brent Crude oil chartists respond to a positive price trend indicated by β 1 which is significant at the 10% level. Furthermore β 1 < 0 suggesting that chartists expect a trend reversal, and as such have a stabilizing effect on oil prices. De Jong et al. (2009) explain this by stating that the probability of a correction towards the fundamental value could increase as the distance to the fundamental value increases. So 44

46 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS the fact that chartists have a stabilizing effect could be contributed to a large difference between the current price and its fundamental value. The intensity of choice parameter φ indicates whether agents switch between strategies by choosing the strategy which performed best in the last 9 days. This parameter is highly significant in the case of fundamental value (2) indicating that speculators are very likely to switch to the more accurate strategy. In contrast to the φ obtained using fundamental value (1) which is not significantly different from 0. In order to gain insight into the weight distribution between speculators (i.e. fundamentalists and chartists) figures 4.1a and 4.1b display the daily fundamentalist weight in Brent crude oil for fundamental value approaches 1 (Moving average) and 2 (PCA), respectively. The fundamentalist weight for fundamental approach 1 is similar for all examined oil products. More specifically, the value is always more or less equal to 0.5. This can be attributed to the small, and not significant, intensity of choice parameter, φ, obtained using this fundamental value strategy. This intensity of choice parameter indicates the responsiveness of agents to the difference in performance of fundamentalist and chartist strategies. In the case of fundamental value approach 1, agents are relatively unresponsive to the difference in performance of both strategies. This could be because those strategies are very similar. More specifically, based on daily data a strategy using a moving average of thirty days maybe too similar to the chartist strategy (AR(1)) resulting in traders being indifferent when choosing between these strategies. This indifference leads to both strategies being applied by an equal amount of speculators in the oil market, making the model similar to an equally weighted combination of a model based on a moving average and an AR(1) model. Contrary to fundamental value approach 1, the fundamental value obtained using approach 2 is relatively different from the original price series. As can be seen in figures 4.1b and 4.2b, these fundamental value time series represent a more stable intrinsic value of the prices. That is the time series has lower peaks and higher falls than the original price time series. In most cases (i.e. Brent, heating oil and gas oil) this results in a very high intensity of choice parameter. Indicating that traders react very quickly to differences in performance of the strategies. Consequently, we see that basically all traders move away from the fundamentalist strategy and become chartists because the chartist strategy is significantly more accurate, most of the time, making the HAM similar to an AR(1) model. This could also be driven by the fact that switching occurs based on the performance in the previous nine days. In a sense that, fundamental approach 2 provides a more stable intrinsic value, based on weekly and monthly data, which doesn t account for daily price swings. Therefore, fundamental approach 2 might be more viable in a monthly setting. The conflicting results obtained for Crude Light and RBOB may be misleading. Figures 4.2b and A.13b do indeed show a positive weight for fundamentalists in the market. However, the estimated parameters for these oil products indicate that the fundamentalists in this market hardly react to the difference between the price and their estimate of its fundamental value. With the exception of the Crude Light α 2 parameter, these parameters are not significant. More specifically, α 1 and α 2 are relatively close to 0 indi- 45

47 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS cating that the price impact of fundamental analysis with oil being over or undervalued is very limited. Table 4.1: Crude Oil In-sample Statistics Brent Crude Light P P-F1 P-F2 P P-F1 P-F2 (1) (2) (3) (4) (5) (6) Mean 0,0004-0,0002 2,82E-04 0,0004-3,1E-05 3,10E-04 Max 0,1271 0,1392 0,5649 0,1641 0,2019 0,5055 Min -0,1095-0,1771-0,4641-0,1307-0,2175-0,4803 Standard dev 0,0242 0,0340 0,2218 0,0278 0,0398 0,1941 Kurtosis 6,1801 4,5650 2,2247 7,2928 5,7408 2,6450 Skewness -0,1746-0,1396 0,2772 0,0989-0,2554 0,1850 # of Observations This table shows the descriptive statistics of the daily time series created using crude oil data for the in-sample period, January 2nd th of December Columns 1 and 4 show the statistics of the first difference of the log price of the first month futures contracts. Columns 2 and 5 the difference between the log-price and fundamental value (1) (i.e. the 30 days moving average). Similarly, Columns 3 and 6 the difference between the log-price and fundamental value (2) (a forecasted series using fundamental data). 46

48 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS Table 4.2: HAM parameters for crude oil Brent Crude light FV (1) FV (2) FV(1) FV (2) (1) (2) (3) (4) Real demand/supply a -0,0040 0,0012-0,0051-0,0244 (-0,3243) (0,0687) (-0,3516) (-1,2455) b 0,0013-0,0002 0,0016 0,0049 (0,4839) (-0,0668) (0,4867) (1,1068) Fundamentalist α 1-0,6011-1,5656-0,5766 0,0025 (-6,3968) (-0,8288) (-7,0709) (0,1480) α 2-0,4764-5,6168-0,4870-0,1779 (-5,9578) (-0,4246) (-6,0093) (-2,7991) Chartist β 1 0,0587-0,0868 0,0936-0,1318 (0,5746) (-1,6722) (0,8927) (-1,4361) β 2 0,1682-0,0449 0,2395-0,0051 (1,6259) (-0,9332) (2,2312) (-0,0536) Switching φ 0,0612 6,1793 0,0076 1,9979 (0,2667) (2,9516) (0,0131) (4,2414) Statistics Mean Weight 0,4993 0,0024 0,5000 0,4312 # of Observations Logl 3003, , , ,989 Parameter estimates of the model given by equation 2.19 for both the moving average fundamental value and PCA fundamental value using daily data ranging from January 2nd 2007 to December 30th 2011.,,, denotes significance at the 10,5 and 1% level, respectively. T-statistics 1 are denoted between brackets 1 Standard errors are computed using the Derivest program for matlab which can be obtained from: 47

49 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure 4.1: Brent Crude Fundamentalist Weight Displays the daily time series of the fundamentalist weight for the two different fundamentalist approaches to Brent Crude oil. (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure 4.2: Crude Light Fundamentalist Weight Displays the daily time series of the fundamentalist weight for the two different fundamentalist approaches to Crude Light oil Monthly data In this section we discuss the in-sample parameter estimates and the weight distribution between speculators, based on a monthly data sample. Table 4.3 shows the statistics of the time-series used in the HAM for Brent and Crude Light oil. Similar to the daily statistics, fundamental value (1) stays closer to the log-price than fundamental value (2), however in this monthly data set these differences are a lot smaller. More specifically, in the daily time series the max deviation from the log-price of fundamental value (2) was two to five times as large as that of fundamental value (1). Whereas in the case of this monthly data set the max deviation of fundamental value (2) is not even two times as large as that of fundamental value (1). Similarly in the case of the standard deviation, in the daily sample the standard deviation of the difference between the log 48

50 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS price and fundamental value (2) is about 6 times larger than the standard deviation when using fundamental value (1). In the case of the monthly sample this difference has been reduced to the standard deviation using fundamental value (2) being only two times as large as that of fundamental value (1). This could indicate that in a monthly setting fundamental approach 2 results in a more accurate fundamental value, that is a fundamental value closer to the current value of oil. This should make fundamental approach 2 more attractive to speculators with a monthly investment horizon. Table 4.4 shows the in-sample parameter estimates for crude oil based on monthly data. Similar to the results obtained for the daily data we again see that the parameters of real supply and demand are not significant. More interesting are the different results obtained for speculator coefficients. Contrary to the daily results we see that fundamentalist coefficients are hardly significant for both fundamental values however, this could be caused by the relatively small sample size. More specifically the fundamentalist coefficients based on fundamental value one are all relatively close to being significant at the 10% level, this could indicate that fundamentalists do have an effect on monthly crude oil prices, but with this small sample size its difficult to make statistical conclusions. The results obtained for chartist coefficients are also different in this monthly setting. We find that chartists have a significant effect on crude oil prices. Chartists in this market show destabilizing behavior which is only significant for price decreases. That is, chartists only significantly influence crude oil prices when there is a declining trend during which they expect prices to decline further. Lastly, we see that, in contrast to the daily results, the intensity of choice parameter is significant, at least at the 10% level, for all fundamentalist approaches to crude oil. Figures 4.3 and 4.4 display the monthly weights of fundamentalists and chartists, using different fundamental value approaches, for Brent crude oil and Crude light oil, respectively. The results obtained here are very different than those in the previous section. Similar to the results in the previous section fundamental approach 1 leads to very similar weight distributions for all examined oil products. However, in contrast to the previous section, the fundamentalist weight varies over time. This can be attributed to the higher intensity of choice parameter. Indicating that based on monthly data agents are changing strategies based on difference in performance. On average fundamentalist dominate the market except for periods containing sharp rises and crashes during which a significant part op the fundamentalists adopt a chartist strategy. The results obtained using fundamental approach 2 are different for crude oil and refined oils(i.e. RBOB, Gas oil and Heating oil ). For crude oil the results are very similar to those obtained using fundamental value (1). The weight distribution between speculators varies significantly over time. The intensity of choice parameter is significantly larger resulting in more variation in speculator weights. More specifically, speculators are more open to changing strategy when there is a difference in performance, resulting in a very volatile weight distribution. The opposite is true for refined oils (see A.30 and A.31). Speculators active in refined oils seem to have a high status quo bias (not willing to change strategies). The intensity of choice parameters are very small and as a result the weight distribution between fundamentalists and chartists remains close to 49

51 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS 0.5 at all times. This could be a explained by the lack of speculators in these markets. Compared to the parameter estimates for crude oils we see that the a and b parameters are significantly larger, and with larger T-values, indicating that real investors have a larger influence on the price of refined oils compared to crude oils. The lack in statistical significance of the coefficients of these parameters could just be a results of the small sample size. Table 4.3: Crude Oil In-sample Statistics Brent Crude Light P P-F1 P-F2 P P-F1 P-F2 (1) (2) (3) (4) (5) (6) Mean 0,0099-0,0071 0,0024 0,0089-0,0072 0,0022 Max 0,2545 0,5737 1,0297 0,2602 0,5686 1,0096 Min -0,4074-0,5162-0,8771-0,3948-0,5978-0,9108 Standard dev 0,0949 0,1654 0,3368 0,0971 0,1699 0,3302 Kurtosis 5,0578 5,4034 3,6253 4,2961 5,7116 3,8280 Skewness -0,8580 0,0143 0,2389-0,6909-0,2025 0,2736 # of Observations This table shows the descriptive statistics of the monthly time series created using crude oil data for the in-sample period, January December Columns 1 and 4 show the statistics of the first difference of the log price of the first month futures contracts. Columns 2 and 5 the difference between the log-price and fundamental value (1) (i.e. the 24 months moving average). Similarly, Columns 3 and 6 the difference between the log-price and fundamental value (2) (a forecasted series using fundamental data). 50

52 4.1. IN-SAMPLE ESTIMATION CHAPTER 4. RESULTS Table 4.4: HAM parameters for crude oil Brent Crude light FV (1) FV (2) FV(1) FV (2) (1) (2) (3) (4) Real demand/supply a -0,0143 0,0445-0,0294 0,0583 (-0,2009) (0,6951) (-0,3675) (0,7961) b 0,0109-0,0047 0,0146-0,0079 (0,6029) (-0,2933) (0,7191) (-0,4339) Fundamentalist α 1-0,6422-0,1161-0,5808-0,1349 (-1,6131) (-1,2773) (-1,6808) (-1,2226) α 2-0,3691 0,0011-0,5499 0,0137 (-1,5453) (0,0209) (-1,5499) (0,1888) Chartist β 1 0,1877 0,0952 0,0155 0,0272 (0,4885) (0,3750) (0,0437) (0,1277) β 2 1,1279 0,7283 1,1292 0,6253 (4,2462) (3,4576) (4,2141) (3,1715) Switching φ 1, ,1237 1,4373 9,6009 (1,7822) (2,0363) (1,9493) (1,6792) Statistics Mean Weight 0,5405 0,5663 0,5437 0,5396 # of Observations Logl 139, , , ,6390 Parameter estimates of the model given by equation 2.19 for both the moving average fundamental value and PCA fundamental value using monthly data ranging from January 2000 to December 2011.,,, denotes significance at the 10,5 and 1% level, respectively. T-statistics are denoted between brackets 51

53 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure 4.3: Brent Crude Fundamentalist Weight Displays the monthly time series of the fundamentalist weight for the two different fundamentalist approaches to Brent Crude oil. (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure 4.4: Crude Light Fundamentalist Weight Displays the monthly time series of the fundamentalist weight for the two different fundamentalist approaches to Crude Light oil. 4.2 Out-of-Sample Performance In this section we will compare the forecasting performance of the HAM to that of a VECM and a random walk model. The VECMs created for the different dependent variables can be found in the appendix in sections A.3.2 and A.3.3 for daily and monthly models, respectively. An interesting result in the estimation of these VECMs on the different data sets (i.e. daily and monthly) is that the VECMs created using the daily data set have more financial explanatory variables (e.g the consolidated stock index) and auto regressive terms, whereas the monthly data set results in VECMs with more fundamental explanatory variables (e.g. ARA inventories). This could result from the frequency in which the original data is observed. The financial data often has a daily frequency, whereas the fundamental data has either a weekly or monthly frequency. This 52

54 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS makes the fundamental data less useful in daily time-series estimation. The random walk model expects no price changes. That is, the forecast made by the random walk model is a price change of 0. Therefore, the MSPE of the random walk will be equal to the mean of the squared price changes in the out of sample period. The percentage correct sign (PCS) performance measure is not relevant to this random walk model because the model makes no sign predictions. Similarly, the economic value performance measure is also not relevant to the random walk model. To obtain benchmark values of the economic value performance measure, we have replaced the random walk model by a strategy where the investor holds a long position in the first month futures contract during the entire out-of-sample period. More specifically, the investor holds a long position in the first month futures contract closes his position just before expiry and buys the new first month futures contract (i.e. he performs a roll-over). He keeps performing roll-overs till the end of the out-of-sample period Daily Data The forecasting results for the daily data set are displayed in tables 4.5, 4.6 and 4.7. Table 4.5 shows the mean square prediction error (MSPE) and the percentage correct sign (PCS) performance measures of the daily forecasts. The Diebold-Mariano test statistics, which indicate whether the difference between the squared error of two time series is significant, are displayed in table 4.6. The results presented in these tables indicate that the HAM using fundamental value one (HAM(1)) is significantly outperformed by all other models, especially concerning MSPE. The Diebold-Mariano test statistics on the first three rows are all positive and significant, even at the 1% level (except when compared to the VECM forecasts for CL and RBOB), which indicates that the squared forecasting errors of the other models are significantly smaller. The fact that the HAM(1) is outperformed by the HAM(2) is remarkable because the HAM(2) is in this state a nested model of the HAM(1), given that the fundamentalist weight is close to 0. A possible explanation for this could be that the effect of fundamentalists in the HAM(1) negatively impacts predictive accuracy. More specifically, the forecasts made by the fundamentalists might be less accurate than those of the chartists, however this difference isn t large enough for fundamentalists to convert to chartists resulting in suboptimal forecasts. In contrast to the HAM(1), the HAM(2) is able to significantly outperform the VECM for all dependent variables except RBOB. This result is similar to what Kulsen (2011) obtained because the HAM(2), when there are no fundamentalists in the market, is similar to an AR(1) model. However, like the HAM(1), the predictive accuracy is still less than that of the random walk model. The Diebold-Mariano statistics comparing HAM(2) with the random walk model are all positive indicating that the forecast errors of the HAM(2) are larger. Although this difference is only significant for heating oil, we must conclude that the random walk model has made the most accurate daily forecasts based on MSPE. When one considers the PCS performance measure there is no clear winner. More specifically, the HAM(1) has the highest PCS for 2 out of the 5 dependent variables 53

55 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS (i.e. Crude light and Heating oil). Similarly, the HAM(2) outperforms the other models based on PCS for RBOB, whereas in the case of Brent and Gas oil the VECM is the most reliable sign predictor. The economic value (i.e. total return when using a follow sign strategy) results are displayed in table 4.7. Table 4.7 shows the total and mean returns over the entire out-ofsample period. We find that the model which obtains the highest total return depends on which futures contract is considered. More specifically, the highest return for Crude Light is obtained when the HAM(1) model is used. The HAM(2) obtains the best return for Brent and the VECM for gas oil. Lastly, we find that the highest economic value for RBOB and heating oil is obtained by simply going long in the first month futures contract during the entire out-of-sample period. The relatively good performance of the long investor can be explained by the percentage of positive returns (PPR) in the out of sample period. The PPR in the out-of-sample period are shown in table A.18 in the appendix. We see that the PPR are higher than the PCS of our models for all but gas oil. This indicates that just going long in the futures contract during the entire out-ofsample period is more accurate, based on sign prediction, than following the predictions made by our models. We find that most of the total returns are negative which can be explained by the relatively low PCSs of our models. When calculating the total returns based on a follow sign strategy the PCS is the percentage of price movements which have a positive effect on the total return. As such, a high PCS is often an indicator of a large total return. However, PCS is not the only criteria considered when calculating economic value (total return). An example of this is the fact that the total return of Brent when using the HAM(2) is significantly larger than when the VECM is used, while the PCS of the VECM is larger. This can be explained by the fact that not all returns have equal size. More specifically, it is possible for a model to obtain high total returns when the PCS is relatively low if the model correctly predicts the signs of the returns which are large (in an absolute sense) compared to other returns. Table 4.5: One Day Ahead Forecasting Results HAM VECM Random Walk Funda Value (1) Funda Value (2) MSPE PCS MSPE PCS MSPE PCS MSPE Brent 3,15E-04 44,73% 2,29E-04 49,45% 2,48E-04 50,18% 2,27E-04 Crude Light 3,65E-04 50,18% 2,93E-04 46,18% 3,20E-04 48,73% 2,88E-04 RBOB 5,57E-04 47,27% 4,65E-04 48,00% 4,82E-04 45,09% 4,61E-04 HO 2,45E-04 48,36% 1,99E-04 44,73% 2,11E-04 48% 1,94E-04 GO 2,02E-04 42,55% 1,58E-04 49,82% 1,31E-04 65,82% 1,24E-04 # of Observations This table shows the mean squared prediction error and percentage correct signs. of the forecasts made by the different models examined in this paper. The forecasting period ranges from January 3th 2011 until the 26th of April

56 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS Table 4.6: Diebold Mariano Test Statistics Brent Crude Light RBOB HO GO HAM(1) & HAM(2) 5,0544 3,3542 2,8258 4,1751 4,5630 HAM(1) & VECM 3,6985 2,1345 1,8875 2,7791 6,9980 HAM(1) & RW 4,8726 3,9653 2,7272 4,3983 5,0259 HAM(2) & VECM -2,0430-2,0683-1,0277-2,0823 3,3938 HAM(2) & RW 0,5197 0,9014 0,4475 1,7824 0,9091,,, denotes significance at the 10,5 and 1% level. Diebold-Mariano statistics, based on a squared error loss function, comparing the predictive accuracy of the models examined in this paper for each oil product. Table 4.7: Economic Value: Total Returns and Mean Daily Returns HAM VECM Long Funda Value (1) Funda Value (2) Total mean Total mean Total mean Total mean Brent -0,3465-0,0013 0,2294 0,0008-0,1237-0,0004-0,0448-0,0002 Crude Light 0,1166 0,0004 0,0734 0,0003-0,4654-0,0017-0,0679-0,0002 RBOB -0,2074-0,0008-0,1216-0,0004-0,5306-0,0019 0,0713 0,0003 HO -0,0216-0,0001-0,2791-0,0010-0,4394-0,0016-0,0022-0,0000 GO -0,2331-0,0008 0,2419 0,0009 1,3349 0,0049-0,0684-0,0002 This table shows the total and mean (daily) returns obtained by the different models over the entire out of sample period. Which ranges from January 3th th of April 2013 (275 observations). The last 2 columns show the results obtained if an investor would have held a long position in the contract during the entire out of sample period Monthly Data Tables 4.8, 4.9 and 4.10 show the one month ahead forecasting results based on the monthly data set. The MSPE and PCS of the monthly forecasts are displayed in table 4.8, whereas table 4.9 shows the Diebold-Mariano statistics. The results of the economic value performance measure (the total and mean returns) are displayed in Table 4.10 The results in table 4.8 indicate that based on MSPE the HAM(2) is the best model. The MSPEs of the HAM(2) are smaller than all other models, with the exception of the VECM and random walk (RW) model forecasts of Crude Light which are close to equal. The DM statistics in table 4.9 also indicate similar conclusions. The bottom two rows contain only negative values, ignoring the previously stated exceptions, indicating that the squared forecast errors made by the HAM(2) are smaller than those of the VECM and RW model. Similarly, the first row only contains positive values which means that the squared forecast errors of the HAM(1) are larger than those of the HAM(2). However, even though the DM statistics indicate that one model might have a higher predictive accuracy than the other based on the sign of the statistic, these differences in predictive 55

57 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS accuracy are almost never significant. This lack of significance could be contributed to the small amount of out of sample forecasts. That is, even though it could be that one model has a significantly higher predictive accuracy than another model, we can t make statistical conclusions because of the small out-of-sample period. The PCS performance measure displayed in table 4.8 shows that on average the VECM performs the best in predicting the correct sign of the price changes. The PCS statistics of the VECM are all larger than 50% with most closer to 60% this indicates that the VECM might have real potential in sign forecasting. Table 4.10 shows the total returns over the entire out-of-sample period when a follow sign strategy is used. The results are very different than the results obtained in the daily sample. We see that the total returns are on average positive and that the highest returns are obtained by two models. Following the predictions of the HAM(2) leads to the highest returns in Brent, Crude Light and gas oil. Similarly, the VECM earns the highest total returns in RBOB and heating oil. These results are close to what we expect based on the MSPE and PCS displayed in 4.8. We see that the HAM(2) has the smallest MSPE and the VECM has the largest PCS. As these performance measures both have an effect on the economic value it is logical that these models obtain the highest total return. Furthermore, we see that the differences in PCS values of the HAM(2) and VECM are significantly larger in the case of RBOB and heating oil, the oil products for which VECM has the highest economic value. This shows that lack in predictive accuracy of the VECM is compensated by the higher accuracy in sign prediction. The results obtained for Crude Light are remarkable in the sense that the MSPE is lower and the PCS is higher when forecasts are made with the VECM compared to the HAM(2) yet the economic value of the HAM(2) is significantly higher. Similar to the explanation we gave in the daily section, we attribute this to wrong sign predictions of the VECM for relatively large returns (e.g. the returns during the 2008 market crash). To illustrate this see figure A.12 in the appendix. It clearly shows the impact of predicting the wrong sign for relatively large returns on the economic value. Table 4.8: One Month Ahead Forecasting Results HAM VECM Random Walk Funda Value (1) Funda Value (2) MSPE PCS MSPE PCS MSPE PCS MSPE Brent 0, ,00% 0, ,56% 0, ,69% 0,0092 Crude Light 0, ,00% 0, ,25% 0, ,38% 0,0104 RBOB 0, ,38% 0, ,00% 0, ,19% 0,0144 HO 0, ,19% 0, ,88% 0, ,38% 0,0081 GO 0, ,75% 0, ,25% 0, ,25% 0,0088 # of Observations This table shows the mean squared prediction error and percentage correct signs. of the forecasts made by the different models examined in this paper. The forecasting period ranges from January 2008 until April

58 4.2. OUT-OF-SAMPLE PERFORMANCE CHAPTER 4. RESULTS Table 4.9: Diebold Mariano Test Statistics Brent Crude Light RBOB HO GO HAM(1) & HAM(2) 1,3459 0,9637 0,7257 1,8581 1,4694 HAM(1) & VECM 0,5841 1,1391 0,1538 0,9649 0,7076 HAM(1) & RW 1,3960 1,1506 0,4391 2,1348 1,6030 HAM(2) & VECM -1,6254 0,1419-0,4317-2,0123-1,9710 HAM(2) & RW -0,5451 0,2906-0,4672-0,0870-0,2685,,, denotes significance at the 10,5 and 1% level. Diebold-Mariano statistics, based on a squared error loss function, comparing the predictive accuracy of the models examined in this paper for each oil product. Table 4.10: Economic Value: Total Returns and Mean Monthly Returns HAM VECM Long Funda Value (1) Funda Value (2) Total mean Total mean Total mean Total mean Brent 0,1404 0,0022 0,8128 0,0127-0,5090-0,0080 0,0674 0,0011 Crude Light 0,0164 0,0003 1,0050 0,0157-0,0788-0,0012-0,0788-0,0012 RBOB 0,7983 0,0125 0,2138 0,0033 1,4211 0,0222 0,1078 0,0017 HO -0,6767-0,0106-0,0774-0,0012 0,3625 0,0057 0,0675 0,0011 GO -0,4428-0,0069 0,7834 0,0122 0,3185 0,0050 0,0095 0,0001 This table shows the total and mean (monthly) returns obtained by the different models over the entire out of sample period. Which ranges from January April 2013 (64 observations). The last 2 columns show the results obtained if an investor would have held a long position in the contract during the entire out of sample period. 57

59 Chapter 5 Conclusion In this paper we examined whether speculators effect oil prices and if so whether accounting for this effect could improve predictive accuracy. To determine and account for speculator activity in oil markets we adopted the simple and stylized heterogeneous agents model developed by Ter Ellen & Zwinkels (2010). Using this model we studied whether fundamentalists and chartists speculators effect oil prices. Fundamentalists develop their price expectations based upon a fundamental value whereas chartists expect price trends to continue. Furthermore fundamentalists can change to chartists and vice versa based on the performance of their respective strategies in the past. To expand on the heterogeneous agents model we developed a more realistic way of creating the fundamental value on which fundamentalists base their price expectations, by creating a time series which accounts for variations in supply and demand of oil but leaves out most other components. We created this time series by performing a principal component analysis on supply and demand data for different oil markets. We fit these principal components on the actual prices after which we multiplied the parameters with the principal components to obtain the fundamental value time series. Focusing on crude oil, after estimating the parameters of this heterogeneous agents model and calculating their statistical significance to oil price movements based on a daily data set. We found that speculators are indeed active in oil markets and have a significant impact on oil prices. Based on daily data we found the real supply and demand, defined as the supply and demand of agents who are involved in the consumption or production of oil, cancel each other out and as such don t significantly effect the daily price swings of oil. The speculator parameter estimates highly depend on the choice of fundamental value. If we use a fundamental value similar to the one introduced by Ter Ellen & Zwinkels (2010) we find that fundamentalists have a significant impact on crude oil prices. More specifically, we see that fundamentalists have a stabilizing effect on crude oil prices, that is they expect prices to converge to their fundamental value, which in this case is based on a moving average. However when we use our new fundamental value, described above, we find that only in the case of an overvaluation of Crude Light oil do fundamentalists have a significant impact on the price. For both fundamental values chartists seem to have very little effect on prices. With the main difference being that chartists have a destabilizing effect when we use the moving average fundamental value and a stabilizing effect in case of the principal component fundamental value. The weight distribution between fundamentalists and chartists also varied significantly based on the fundamental value. The moving average fundamental value led to an equally weighted distribution of fundamentalists and chartists whereas the pca fundamental value drove all fundamentalists out of the market making the HAM similar to an AR(1) model. The speculator parameter estimates obtained using a data set with a monthly frequency are significantly different. All results obtained with this monthly set are somewhat limited because of the small sample size. More specifically, the small sample size makes it difficult to make statistically significant conclusions, however the indications 58

60 CHAPTER 5. CONCLUSION observed using this data set are still worth mentioning. In this monthly setting the significance of the parameter estimates is similar for both fundamental values. We see that fundamentalist coefficients are not significant. However we do see that the T-values based on the moving average fundamental value are close to significant at the 10% level indicating that fundamentalists might affect oil prices in that setting. Chartists results are also similar for both fundamental values. Chartists show destabilizing behavior but their influence on price changes is only significant for a declining price trend. The weight distribution between fundamentalist and chartist speculators in this monthly setting is significantly different than that in the daily setting. We see that the weights for crude oil fluctuate overtime with the weight distribution being more volatile for the HAM with the pca fundamental value. The opposite is true for refined oils in which there is no fluctuation in weights between fundamentalists and chartists when using the pca fundamental value. We attribute this to the lack of speculators in these markets and find that real supply and demand play a more significant role. To see whether accounting for heterogeneous agents would increase forecasting performance we compared the forecasts made by the HAMs to that of a random walk model and a VECM, which serves as the most promising model developed by PJK international. We asses predictive accuracy by calculating the mean squared prediction error (MSPE) and the percentage correct sign (PCS) performance measures. We find that based on MSPE both HAMs and the VECM are outperformed by the random walk model when making one day ahead forecasts. Based on PCS no model consistently outperforms the others. In a monthly setting the HAM using the pca fundamental value had on average smaller MSPEs, when making 1 month ahead forecasts, than the other models yet these difference were almost never statistically significant when compared to the random walk. This lack of significance could be attributed to the small amount of out-of-sample observations and therefore these smaller MSPEs could be considered an indication of higher predictive accuracy. The VECM showed significant promise in forecasting the correct sign with the PCS being higher than 50%, with most closer to 60%, for all oil products. We studied the economic value of the models by calculating the total return obtained, during the out-of-sample period, if we had invested based on a follow sign strategy. In the daily sample we found that the economic value of our models was rather disappointing given that the total return was on average negative. Furthermore, we found that in some cases it was more lucrative to simply buy a contract and hold on to it the entire out-of-sample period than follow the predictions of our models. The results in the monthly data set were significantly different. We obtained mostly positive total returns and found that following the predictions of our models was significantly more lucrative than buying a contract and holding on to it. Lastly, we found that for 3 out of 5 oil products the HAM had the highest economic value. Followed by the VECM which was the most lucrative in the other 2 cases. 59

61 Chapter 6 Further Research The research in heterogeneous agents models is relatively new and still ongoing, as such many questions still need to be answered. First would allowing more types of agents improve model fit and predictive accuracy? More specifically, would increasing the types of agents and as such the types of investment strategies agents can choose from improve the performance of the HAM? As we have seen from this study changing the way one group of speculators thinks has significant impacts on the predictive accuracy of the HAM. Therefore, it might be interesting to see what happens when new agents enter the market or similar to our study agents have other price expectations. Another question that arises is will more complicated trading rules for fundamentalists and chartists improve performance. For example if we had used the VECM forecasts as price expectations for the fundamentalist traders would that have increased or decreased the performance of the HAM? Lastly, what would happen if we asses the performance of a strategy using a different performance measure. To be more specific, what if agents didn t switch strategies based on the MSPE in the past like in this study, but on a measure which,also, accounts for sign prediction like economic value? 60

62 Bibliography [1] R. Alquist, L. Kilian, R. Vigfusson, Forecasting the Price of Oil, HandBook of Economic Forecasting, May 5, 2011 [2] Anderson, S., Kellogg, R., J. Sallee, What Do Consumers Know (or Think They Know) About the Price of Gasoline?, mimeo, Department of Economics, University of Michigan, 2010 [3] W.A. Branch The Theory of Rationally Heterogeneous Expectations: Evidence From Survey Data on Inflation Expectations, The Economic Journal, 114, , July, 2004 [4] W.A. Brock, J. Lakonishok, B. LeBaron, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance 47, , [5] E. de Jong, W.F.C Verschoor, R.C.J Zwinkels, Behavioral Heterogeneity and Shift- Contagion: Evidence from the Asian Crisis, Elsevier, Journal of Economic Dynamics and Control, 33, , November, 2009 [6] F.X. Diebold, R.S. Mariano, Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 13, , 1995 [7] S. ter Ellen, R.C.J Zwinkels, Oil price dynamics: A behavioral finance approach with heterogeneous agents, Energy economics 32, , March 18, 2010 [8] B.T. Ewing, M.A. Thompson, Dynamic cyclical comovements of oil prices with industrial production, consumer prices, unemployment, and stock prices, Energy Policy 35, , [9] Y. Fan, H. Tsai, Y. Wei, Y. Zhang, Spillover effect of US dollar exchange rate on oil prices, Journal of Policy Modeling, vol. 30, issue 6, pages , [10] B. Fattouh, L. Kilian, L. Mahadeva, The Role of Speculation in Oil Markets: What Have We Learned So Far?, forthcoming: Energy Journal 34(3), 2013 [11] O. Gjølberg, Is the spot market for oil products efficient?, Energy economics 7, , 1985 [12] L. Tang, S. Hammoudeh An empirical exploration of the world oil price under the target zone model, Energy economics 24, [13] C.H. Hommes, Heterogeneous Agent Models in Economics and Finance, Handbook of Computational Economics, Volume 2, 2006 [14] I.A. Moosa, N.E. Al-Loughani, Unbiasedness and time varying risk premia in the crude oil futures market, Energy economics 16, , 1994 [15] P. Pagano, M. Pisani, Risk Adjusted Forecasts of Oil Prices, European Central Bank, Working paper series, no 999,

63 BIBLIOGRAPHY BIBLIOGRAPHY [16] D. Sornette, R. Woodard, W.-X. Zhou, The oil bubble: evidence of speculation, and prediction, Physica A 388, , 2009 Internal Papers of PJK International B.V. [17] L. Akkermans, C. Engelen, A. de Ridder, E. Salet, Forecasting the spot-future spread for oil products, March 8, 2010 [18] P. Kulsen, Forecasting models for oil prices, September 2, 2011 [19] A. Tilgenkamp, B. Spruijt, M. Jansen, Y. Yang, Predicting oil futures using advanced forecasting techniques,

64 Appendix A A.1 Elaborate Description of Future contracts Light crude oil is a liquid petroleum and it s first month futures contract is traded on the NYMEX commodity exchange. The price of this futures contract is widely regarded as a proxy for the cost of imported crude oil. The futures contract is quoted in US dollars per barrel and the contract size is equal to a thousand barrels. Reformulated Gasoline Blendstock for Oxygen Blending (RBOB) is the trading classification of gasoline futures on the NYMEX. These futures are quoted in US dollars per gallon with a contract size of gallons equal to 1000 barrels. An interesting pattern is visible in the daily price movements of the RBOB one month futures contract displayed in figure A.1 in the appendix. A clear shark teeth pattern is visible in the price of the futures contract, with the exception of the period just before and after the initial crash of the credit crisis. An explanation for this can be found in the US driving season. During the US driving season the demand for gasoline goes up which forces the prices of the futures contracts to increase as well. When the driving season is over demand and consequently prices drop again, resulting in a seasonal pattern. Heating oil is a liquid petroleum product used as a fuel to furnaces and boilers in buildings. Heating oil is mostly used in the northeastern USA. Heating oil futures contracts are traded on the NYMEX, the contract is quoted in US dollars per gallon with a contract size of gallons which is equal to 1000 barrels. To make it comparable with gas oil ($/ton), which is basically the same product, we convert heating oil prices in $/gallon to prices in $/ton the conversion factor we use is equal to (i.e. $/gallon =$/ton) as shown by Kulsen (2011). Brent Crude oil is a trading classification of sweet light crude oil extracted from the Brent oilfield, in the North Sea. Brent is the leading global price benchmark for Atlantic crude oils. Two thirds of the world s internationally traded crude oil supplies are priced based on the price of Brent. Brent Crude futures were originally traded on the open outcry International Petroleum Exchange in London, but as from 2005 it has been traded on the electronic IntercontinentalExchange (i.e. ICE). Similar to the NYMEX Crude light futures contract, these contracts are also quoted in US dollars per barrel with the contract size being equal to a thousand barrels. Gas oil is the European equivalent of heating oil. The gas oil futures contracts are traded on the IntercontinentalExchange (ICE). The futures contracts are quoted in US dollar per metric ton, and the contract size is equal to one hundred metric tonnes. 63

65 A.2. GRAPHS & FIGURES APPENDIX A. A.2 Graphs & Figures Figure A.1: NYMEX RBOB prices This figure shows the daily price movements of NYMEX RBOB first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The prices are in $/gall (i.e. $ per gallon) Figure A.2: NYMEX RBOB returns in % This figure shows the daily returns on the NYMEX RBOB first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The returns are in percentages. 64

66 A.2. GRAPHS & FIGURES APPENDIX A. Figure A.3: NYMEX heating oil prices This figure shows the daily price movements of NYMEX heating oil first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The prices are in $/ton. Figure A.4: NYMEX heating oil returns This figure shows the daily returns on the NYMEX heating oil first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The returns are in percentages. 65

67 A.2. GRAPHS & FIGURES APPENDIX A. Figure A.5: ICE brent crude oil prices This figure shows the daily price movements of the ICE Brent crude oil first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The prices are in $/bbl (i.e. $ per barrel). Figure A.6: ICE brent crude oil returns This figure shows the daily returns of the ICE Brent crude oil first month futures contract during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The returns are in percentages. 66

68 A.2. GRAPHS & FIGURES APPENDIX A. Figure A.7: ICE gas oil prices This figure shows the daily price movements of ICE gas oil during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The prices are in $/ton (i.e. $ per ton). Figure A.8: ICE gas oil returns This figure shows the daily returns of ICE gas oil during a period ranging from the 2nd of January 2007 until the 7th of May 2013 (1600 observations). The returns are in percentages. 67

69 A.2. GRAPHS & FIGURES APPENDIX A. Figure A.9: Atlantic Gas Oil Spread The Atlantic gas oil spread (ICE Gas oil($/ton) - NYMEX Heating oil($/ton)) from January 2nd 2007 until May 7th Figure A.10: Heating Oil Crack Spread The Heating crack spread (NYMEX Heating Oil($/bbl) - NYMEX crude light($/bbl)) from January 2nd 2007 until May 7th

70 A.2. GRAPHS & FIGURES APPENDIX A. Figure A.11: RBOB Season Pattern This figure shows the average price of futures contract than expire at the end of the month. These average are calculated over the period ranging from January 2007 until April (a) Monthly Returns Obtained by the HAM(2) and VECM (b) Total Returns obtained by the HAM(2) and VECM Figure A.12: Monthly and Total Returns of the HAM(2) and VECM for Crude Light This figure shows the monthly and total returns obtained by an investor if he would have invested in first month Crude Light futures according to the predictions of the HAM(2) and VECM using a follow sign strategy. The realized return (i.e. the price movements of the futures contract) is not visible in figure A.12a because it is equal to the return of the VECM. In this case the VECM made only positive forecasts for the out-of-sample period. 69

71 A.2. GRAPHS & FIGURES APPENDIX A. A.2.1 Fundamentalist Weight Graphs Daily (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.13: RBOB Fundamentalist Weight Displays the daily time series of the fundamentalist weight for the two different fundamentalist approaches to RBOB (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.14: Heating Oil Fundamentalist Weight Displays the daily time series of the fundamentalist weight for the two different fundamentalist approaches to Heating oil. 70

72 A.2. GRAPHS & FIGURES APPENDIX A. (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.15: Gas Oil Fundamentalist Weight Displays the daily time series of the fundamentalist weight for the two different fundamentalist approaches to Gas oil. Monthly (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.16: RBOB Fundamentalist Weight Displays the monthly time series of the fundamentalist weight for the two different fundamentalist approaches to RBOB 71

73 A.2. GRAPHS & FIGURES APPENDIX A. (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.17: Heating Oil Fundamentalist Weight Displays the monthly time series of the fundamentalist weight for the two different fundamentalist approaches to Heating oil. (a) Moving Average Fundamentalist Weight (b) PCA Fundamentalist Weight Figure A.18: Gas Oil Fundamentalist Weight Displays the monthly time series of the fundamentalist weight for the two different fundamentalist approaches to Gas oil. 72