Gold, Oil and the S&P 500 Index: Calm to Crisis and Back

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1 Gold, Oil and the S&P 500 Index: Calm to Crisis and Back A.G. Malliaris 1, and M. Malliaris 2 1 Economics & Finance Depts., Loyola University Chicago, Chicago, IL, USA 21 Information Systems & Operations Management, Loyola University Chicago, Chicago, IL, USA Abstract - Numerous studies have analyzed the impact of gold and oil price movements on the S&P 500 Index. The theoretical motivation of studying gold, oil and equity markets is driven by the role of energy prices as a major contributing factor to inflation as measured by both the consumer and wholesale price index, and inflation by gold. Most existing studies do not confirm robust relationships among these three assets. In this paper we take a different methodological approach. We theorize that during the past 14 years, the U.S. economy has transitioned through four regimes: the pre-crisis calm period, the bubble period, the crisis period, and the return to average growth. For each regime we study the relationships among gold, oil and equity price changes and their lagged movements. We confirm that these relationships are regime dependent. This finding confirms the empirical difficulty in finding robust rules over a large sample. Keywords: Gold, Oil, S&P 500, Forecasting, Crisis 1 Introduction Numerous studies have analyzed the impact of gold and oil price movements on the U.S. stock market as represented in the S&P 500 Index. The theoretical motivation of studying gold, oil and equity markets is driven by the role of energy prices as a major contributing factor to inflation as measured by both the consumer and wholesale price indices. Inflation in turn may be hedged by gold. These relationships are affected by the specifics of the samples used in empirical investigations. Most of the existing studies do not confirm robust relationships among these three assets. In this paper we take a different methodological approach. We theorize that during the past 14 years, the U.S. economy has transitioned through four regimes: an initial period of calm, the pre-crisis booming period, the crisis period, and the return to average growth. For each regime we study, using decision rule analytics, the relationships among gold, oil and equity price changes and their lagged movements. We confirm that these relationships are regime dependent. This finding confirms the empirical difficulty in finding robust rules over large sample. 2 Literature Review Barro and Misra [1] have studied the behavior of gold returns by developing a theoretical model motivated by the Lucas-tree model. Gold has been dominant in the financial markets during the past several centuries and is usually regarded as a hedge against inflation, political upheavals and physical disasters. Barro and Misra find from 1836 to 2011, the average real rate of price change for gold in the United States is 1.1% per year and the standard deviation is 13.1%, implying a one-standarddeviation confidence band for the mean of (0.1%, 2.1%). These authors also study the relationship of gold to other economic variables. In particular they find that the co-variances of gold s real rate of price change with consumption and GDP growth rates are small and statistically insignificantly different from zero. The implications of these negligible co-variances suggest that gold s expected real rate of return would be close to the risk-free rate, estimated to be around 1%. The volatility of the growth rate of real gold prices is small under the classical gold standard from 1880 to 1913 but high comparable to that on stocks in other periods, including 1975 to Changes in the volatility of gold prices can be partially explained by the shifting role of gold in monetary policies and changes in expected inflation. Baur and Lucey [2] also study the behavior of gold prices and distinguish between gold as a hedge versus gold as a safe haven. Gold as a hedge is defined as a security that is uncorrelated with stocks or bonds or inflation on average. This allows a typical investor to use gold as a hedge. Gold can also be used as a safe haven. A security is defined as a safe haven when it is uncorrelated with stocks or bonds or inflation in a market crash. These authors find that gold is a hedge against stocks on average and a safe haven in extreme stock market conditions. Reboredo [3] asks a much more focused question than Baur and Lucey. Reborelo asks if gold is a hedge or safe haven against oil movements. Reboredo uses an approach based on copulas to analyze the dependence structure between these two markets. Using weekly data from from January 2000 to September 2011, the author obtains the following results:. First, there is positive and significant average dependence between gold and oil, which would indicate that gold cannot hedge against oil price movements. Second, there is tail independence between the two markets, indicating that gold can act as an effective safe haven against extreme oil price movements. In a related study, Cinera, Gurdgievb and Luceyb [4] investigate the return relations between major asset classes

2 using data from both the US and the UK. The authors first examine time variation in conditional correlations to determine when these variables act as a hedge against each other. The authors provide evidence on whether the dependencies between the asset classes differ during extreme price movements by using quantile regressions. Their analysis provides evidence on whether these asset classes can be considered as safe havens for each other. A key finding is that gold can be regarded as a safe haven against exchange rates in both countries, highlighting its property as monetary currency. Sari, Hammoudeh and Soytas [5] introduce the euro as an exchange rate to study its impact on gold and oil markets. These authors find that investors may diversify at least a portion of their portfolio risk away by investing in precious metals, oil, and the euro. Malliaris and Malliaris [6] investigate inter-relationships among the price behavior of oil, gold and the euro using time series and neural network methodologies. Traditionally gold is a leading indicator of future inflation. Both the demand and supply of oil as key global commodities are impacted by inflationary expectations and such expectations determine current spot prices. Inflation influences both short and longterm interest rates that in turn influence the value of the dollar measured in terms of the euro. Certain hypotheses are formulated in this paper and tested. The authors find that the markets for oil, gold and the euro are efficient but have limited inter-relationships among themselves. Narayan [7] examines the long-run relationship between gold and oil for both spot and futures markets. The author draws on the conceptual framework that when oil prices rise, they create inflationary pressures, which encourage investments in gold as a hedge against inflation. Furthermore, this paper tests for the long-run relationship between gold and oil futures prices at different maturities and finds evidence of cointegration. This implies that investors use the gold market as a hedge against inflation and also, the oil market can be used to predict the gold market prices and vice versa, thus these two markets are jointly inefficient, at least for the sample period considered in this study. Fan and Xu [8] focus on oil prices. They use endogenously determined break tests that allow for changes in both level and trend to identify four regimes. This paper has inspired the four regimes investigated in detail in our study. 3 Data This study investigates patterns in movement of London Gold, Brent Oil, and the S&P 500 from January 2000 through January Data for the S&P 500 were downloaded from finance.yahoo.com, the London Gold prices were downloaded from and Brent oil prices were obtained from After downloading, derived columns created for each series included a value standardized over the 14 year period, the percent change from yesterday to today, a 5 day moving average, the direction the series moved from yesterday to today, the number of times the series moved Up in the most recent 5 days, and concatenated directional strings of movement for 2, 3, 4, and 5 days. In addition, a column reflecting values for tomorrow was created, tomorrow s direction. An example of each of these values for the Brent Oil series is shown in Table 1. The data was divided into 4 periods, denoted as Calm, Bubble, Crisis, and After. This selection of subperiods is taken from Fan and Xu [6] and is supported from numerous analyses of the Global Financial Crisis as reported by Evanoff, Kaufman and Malliaris [9]. For each period we built separate models to investigate what movements happened together and to attempt to understand what affects tomorrow s direction for each of the three series. The dates included in each series are shown in Table 2. Table 1. Examples of Variables Names and Values for the Brent Oil Series Variable Name Sample Value BStd BPerChg B5DayMA Bdir D BNumDaysUp 2 B2Day UD B3Day UUD B4Day DUUD B5Day DDUUD BDirTp1 U Table 2. Dates for each data set. Set Begins Ends Calm 1/4/2000 3/31/2005 Bubble 4/1/ /31/2007 Crisis 1/2/2008 3/13/2009 After 3/16/2009 1/24/ Models And Results The first step in investigating these series was to look simply at the movement of each series today using Association Analysis to investigate which, if any, series typically moved in the same broad patterns within a day. Next, we look at today s movements to see if rules appear predicting tomorrow s movement. Finally, we will use both movement and numeric data based on the three series in a decision tree to forecast tomorrow s direction for each series. There were two possible outcomes for each series (Up or Down) per day. The Association Analysis model generates a set of rules that meet specific conditions. The models here were set to look for antecedents that occurred in at least 7 percent of the rows, and Consequents that were true at least 55% of the time when the Antecedent occurred. There were 6 possible

3 single series antecedents and 4 possible consequents per antecedent. For antecedents using two series, there were 12 possible combinations, each with 2 possible consequents. Of these possible rules, only 6 occurred in three of the periods over time. Table 3 shows all of the rules that occurred in at least three out of these four data periods. Notice that when a rule failed to apply to all four periods, they failed to work in either the Calm period or the Crisis period. But if they occurred in Calm, they also appeared in Bubble and After sets. If they did not appear in Calm, but began in Bubble, then they have continued on. The Table 3 rules can be read in the following way: If the Antecedent is True, then the Consequent is also True at least [Confidence] percent of the time. The first rule would imply If Brent Oil moved Up today, then Gold moved up today 62% of the time during the Bubble period, 58% of the time during the Crisis period, and 63% of the time in the After period. Four of the 6 rules have Brent Oil in the Antecedent. Only one rule has a consequent with the S&P series, and indication that the direction of the S&P is less likely to move with the other series in a regular pattern in the same day. Table 3. Rules appearing in three of the data sets, and the associated confidence. Confidence Ante. Conseq. Calm Bub. Cris. Aft. BDir = U GDir = U GDir = D BDir = D BDir = U and SPDir = U GDir = U GDir = U BDir = U GDir = D and BDir = U SPDir = U SPDir = D and BDir = U GDir = U The next run of the Association Analysis algorithm used today s direction of Brent Oil, Gold, and the S&P 500 as possible antecedents, and tomorrow s direction of each series as possible consequents. This is a beginning attempt to see whether or not we can forecast future direction. There were 26 possible antecedents with one, two or three series represented, and 6 possible consequents, or 26*6 = 156 possible rules. The number of rules generated by association analysis methodology were 8 for the Calm period, 39 for the Bubble period, 40 during Crisis, and 32 in the After period. Reducing the results tables to rules that occurred in at least 2 periods, we see the resulting 15 rules in Table 4. Notice that there is only one rule that repeats from the Calm period to the After period. So, directional forecasts using only knowledge of today s movements of these three series changed from the Calm to the later periods, and only one rule reappeared in the After period. Two rules carried over from the Bubble period to the Chaos period then disappeared. But, 10 pattern rules from the Bubble period are also active in the After period. That is, many relationships disappeared during the Crisis period only to return after the crisis diminished. There are two rules which appeared first in the Bubble period have continued in both of the following periods. These two longer-run rules are If the S&P moved Up today, the Gold will move Up tomorrow, and if the S&P moved Down today then it will change direction and move Up tomorrow. These two rules had the highest confidence in the Bubble period, but occurred at least 55% of the time in all later periods. Notice also that all the rules that appeared in multiple periods had consequents referring to Up movements. Table 4. Common Rules in Forecasting Antec Conseq Calm Bub Cris Aft BDir = D and GDir = D and SPDir = U BDirTp1 = U BDir = U and GDir = U BDirTp1 = U GDir = U and SPDir = U BDirTp1 = U GDir = D and BDir = U BDirTp1 = U SPDir = U BDirTp1 = U BDir = D and SPDir = U GDirTp1 = U GDir = D and SPDir = U GDirTp1 = U SPDir = U GDirTp1 = U BDir = D SPDirTp1 = U GDir = D SPDirTp1 = U SPDir = D SPDirTp1 = U BDir = D SPDirTp1 = U BDir = U SPDirTp1 = U GDir = D SPDirTp1 = U GDir = U SPDirTp1 = U We will next build a C5.0 decision tree model with tomorrow s direction as target. A C5.0 decision tree uses a non-numeric target, in this case, tomorrow s direction, and inputs can be either numeric or non-numeric. At this point, we can use many more variables as inputs because we are not restricted to only nominal values as we are with Apriori. The number of inputs for each model was 27, each of the variables listed in Table 1 for each of the series, minus the variables reflecting tomorrow s values. We built 12 of these trees, one for each of the four time periods and for each of the three data series. We used IBM s SPSS Modeler program to run each of them. The C5.0 decision tree identifies for us the variables that are most important in the decision by generating a relative importance score for each variable used in the model.

4 After Crisis Bubble Calm After Crisis Bubble Calm Relative importance scores sum to 1 for each model and indicate the relative impact each variable has on determining the final model output value. Tables 5a, 5b, and 5c show these scores for each period and each Target. Table 5a. Brent Oil Tp1 target Input B2Day 0.05 B3Day B4Day B5Day 0.24 B5DayMA Bdir 0.06 BNumDaysUp BPerChg BStd 0.03 G2Day G3Day G4Day 0.04 G5Day G5DayMA 0.09 Gdir 0.07 GNumDaysUp 0.06 GPerChg 0.01 GStd 0.17 SP2Day SP3Day SP4Day 0.06 SP5Day SP5DayMA 0.05 SPDir 0.02 SPNumDaysUp SPPerChg SPStd Columns with no values indicate that the model was not able to find any useful variables and always predicted a single direction for every day. Of the 12 models, three failed to generate discriminating models. These were Gold in the Calm period, and the S&P 500 in both the Bubble and After periods. This leaves 9 models with information about variable importance. In these models, we see that eight of the variables are used in at least three of the models. Of this group, three variables are based on Brent Oil (the Brent standardized value, the Brent percent change and the Brent 4-day directional pattern), one is derived from Gold (the 5-day directional pattern of Gold), and the remaining four are derived from the S&P closing value (the S&P percent change, the S&P standardized value, the S&P 5-day moving average, and the S&P 5-day directional pattern). The variable most used, that was identified as important in 6 of the models, was the 5-day pattern of directional movement in the S&P, with a relative impact ranging from.33 to.95. That is, the model looks at a week s pattern of S&P movement and this accounts for at least one-third of the variable importance in two-thirds of the models, two from the Oil group, three in the Gold group, and one in the S&P group. This is an interesting variable because it is longer term (or, older) information and its influence occurs more often in oil and gold than in the S&P. In addition to the impact of each of the variables, we are interested in the accuracy of forecast for each of the three models. Table 6 contains the counts for each Target variable during each of the periods. Here we have the predicted Tp1 (tomorrow) variable direction in the columns and the actual variable direction in the rows. We ask whether the correct predicted directions outnumber the incorrect ones for each target in each period. Looking, for example, at tomorrow s Brent Oil direction as the target, BDirTp1, we see that, in the Calm period the model predicted Down correctly 285 times and incorrectly 169 times. When predicting up, there were 334 incorrect predictions, and 503 correct ones. Table 5b. Gold Tp1 target. Input B2Day 0.06 B3Day 0.07 B4Day B5Day B5DayMA 0.11 Bdir 0.21 BNumDaysUp BPerChg 0.02 BStd G2Day 0.04 G3Day G4Day G5Day 0.3 G5DayMA 0.07 Gdir GNumDaysUp GPerChg 0.09 GStd 0.16 SP2Day 0.01 SP3Day 0.19 SP4Day SP5Day SP5DayMA SPDir SPNumDaysUp SPPerChg SPStd

5 After Crisis Bubble Calm Table 5c. S&P 500 TP1 target. Input B2Day B3Day 0.01 B4Day 0.12 B5Day 0.44 B5DayMA 0.08 Bdir BNumDaysUp 0.08 BPerChg BStd G2Day G3Day G4Day 0.14 G5Day G5DayMA Gdir GNumDaysUp 0.11 GPerChg GStd SP2Day 0.02 SP3Day SP4Day SP5Day 0.57 SP5DayMA SPDir 0.06 SPNumDaysUp SPPerChg 0.01 SPStd 0.02 Table 6. Matrix showing Actual vs Predicted counts of series directional movement per period. Act Predicted Calm Bubble Crisis After BDir Tp1 Dn Up Dn Up Dn Up Dn Up Dn Up GDir Tp1 Dn Up Dn Up Dn Up Dn Up Dn Up SPDir Tp1 Dn Up Dn Up Dn Up Dn Up Dn Up Inspecting each prediction pair across the two rows for Brent oil, we see that during the calm, bubble, and crisis periods, the number of correct predictions outnumbered incorrect predictions in each of these. In the After period, where the C5.0 methodology failed to generate a model, we see that the number of incorrect predictions dominated. For Gold tomorrow, GDirTp1, we have in every period, model predictions where the number of correct forecasts are greater than the incorrect ones. For the S&P target, SPDirTp1, models failed to be generated in two of the periods, bubble and after. For the periods where C5.0 was able to generate a model, calm and crisis, both models were correct more than incorrect in each direction. In the periods for bubble and after, the models predicted only one direction for every day (up). It happened that a majority of the days were up, so these also show more correct than incorrect predictions. Another way to look at the forecast numbers is by the percent of times each model was correct, whether in predicting and up or a down direction for tomorrow. Table 7 displays these percentages. Table 7. Percent of correct forecasts in each model. Calm Bubble Crisis After BDirTp GDirTp SPDirTp During the crisis period, every target was predicted correctly more than 80% of the time. In the other periods, correctness ranged from a low of 53% to a high of 70%. During the calm period, predictive correctness was close to 60% for each target. In the bubble period, the predictive value dropped for the S&P, but rose for both oil and gold. In the crisis period, it was easier to predict all series direction tomorrow. Then after the crisis, all numbers dropped significantly. We used two models, Association Analysis and C5.0 Decision Tree, to construct predictions for tomorrow s direction in Brent oil, Gold, and the S&P 500. Association analysis can only be used when there are rules that get triggered, while the decision tree model can be applied on any day. Comparing Table 4 confidence numbers to Table 7 percent of correct forecast numbers, we see that the C5.0 model was a clear winner in the crisis period. Using association analysis only on days when rules were triggered would have significantly limited your trading opportunities, and on these days, the confidences were much lower than the correctness of the decision tree models. In the After period for the SPTp1 target the association analysis rules only referred to the Up direction, and the decision tree model only predicted Up. Confidence and correctness percents were very similar. The Calm period decision tree model was correct about 60% of the time. 5 Conclusions When searching for inter-relationships between two or among several assets or economic variables, regression and time series techniques are often employed. Inter-relationships among gold, oil and equities have attracted numerous studies and results are

6 often sample dependent. The literature in this area proposes the hypothesis that oil prices contribute to inflation and such inflation induces further increases in the price of gold. When inflation is mild, the valuation of equities is not affected; however, increased inflation affects equity returns. In this paper we follow association analysis to investigate changing inter-relationships among gold, oil and equities during evolving regimes. In particular, looking backwards since the beginning of 2000, we identify four regimes called the calm period from January 4, 2000 to March 31, 2005; the bubble period of April 1, 2005 to December 31, 2007; the crisis period of January 2, 2008 to March 13, 2009 and finally the after the crisis period of March 16, 2009 through January 24, For each of these periods we perform three searches. First, we investigate the series of gold, oil and equity daily price direction, up or down, using Association Analysis to investigate which, if any, series typically moved in the same broad patterns within a day. Next, we look at today s movements to see if rules appear predicting tomorrow s movement. Finally, we will use both movement and numeric data based on the three series in a decision tree to forecast tomorrow s direction for each series. There are numerous finding since there are four periods with three searches in each but the key finding of this work is that during the crisis period the inter-relationships among gold, oil and equities were the strongest as judged by the effectiveness of prediction, followed by the bubble period. In contrast both during the calm or after the crisis period, the inter-relationships weakened. Our results are informative because they highlight that within a very long time series sample uniform interrelationships hardly persists; instead these inter-relationships evolve depending on the specific characteristics of the sequence of regimes. If regimes are characterized by low volatility and thus financial calmness the idiosyncratic markets characteristics of each asset prevail and thus reduce interdependencies; however, when financial turmoil emerges, it dominates idiosyncratic characteristics and inter-relationships strengthen because asset prices become highly correlated. [6] Malliaris, A.G. and Mary Malliaris (2013), Are Oil, Gold and the Euro Inter-related? Time Series and Neural Network Analysis, Review of Quantitative Finance and Accounting, 40, pp [7] Narayan, Paresh Kumar (2010), Gold and Oil Futures Markets: Are Markets Efficient, Applied Energy, 10 pp [8] Fan, Ying and Jin-Hua Xu, (2011), What Has Driven Oil Prices Since 2000? A Structural Change Perspective, Energy Economics, 33, pp [9] Evanoff, D., George Kaufman and A.G. Malliaris (2012), Editors, New Perspectives on Asset Bubbles, Oxford Univerity Press, New York. 6 References [1] Barro, Robert and Sanjay Misra (2013), Gold Returns, NBER Paper No [2] Baur, Dirk G. and Brian M. Lucey (2010), Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold, The Financial Review, 45, pp [3] Reboredo, Juan (2013), Is Gold a Hedge or Safe Haven Against Oil Price Movements?, Resources Policy, 38, pp [4] Cinera, Cetin, Constantin Gurdgievb, Brian M. Luceyb (2013), Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates, International Review of Financial Analysis, 29, pp [5] Sari, Ramazan, Shawkat Hammoudeh and Ugur Soytas (2010) Dynamics of Oil Price, Precious Metal Prices, and Exchange Rate, Energy Economics, 32, pp