STUDY ON DYNAMIC RELATIONSHIP AMONG GOLD PRICE, OIL PRICE, EXCHANGE RATE AND STOCK MARKET RETURNS
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International Journal of Applied Business and Economic Research, Vol. 9, No. 2, (2011): 145-165
STUDY ON DYNAMIC RELATIONSHIP AMONG
GOLD PRICE, OIL PRICE, EXCHANGE RATE AND
STOCK MARKET RETURNS
K. S. Sujit1 and B. Rajesh Kumar2
Abstract: The dynamic and complex relationship among economic variables has attracted
the researchers, policy makers and business people alike. This study is an attempt to test the
dynamic relationship among gold price, stock returns, exchange rate and oil price. All these
variables have witnessed significant changes over time and hence, it is absolutely necessary
to validate the relationship periodically. This study takes daily data from 2nd January 1998
to 5th June 2011, constituting 3485 observations. Using techniques of time series the study
tried to capture dynamic and stable relationship among these variables using vector
autoregressive and cointegration technique. The results show that exchange rate is highly
affected by changes in other variables. However, stock market has fewer roles in affecting
the exchange rate. In this study we tested two models and one model suggests that there is
weak long term relationship among variables.
JEL classification: C22; E3;
Keywords: Unit root tests; granger causality test, Cointegration; Vector auto regression (VAR)
INTRODUCTION
Gold was one of the first metals humans excavated. Gold as an asset has a hybrid
nature: it is a commodity used in many industries but also it has maintained
throughout history a unique function as a means of exchange and a store of value,
which makes it akin to money. After World War II, the Bretton Woods system
pegged the United States dollar to gold at a rate of US$35 per troy ounce. The
system existed until the 1971, when the US unilaterally suspended the direct
convertibility of the United States dollar to gold and made the transition to a fiat
currency system. The last currency to be divorced from gold was the Swiss Franc in
2000.
In 1833 the price of gold was $20.65 per ounce, about $415 in 2005 terms, while
in 2005 the actual price of gold was $445 – a very small change in the real price of
gold over a period of one hundred and seventy two years3
In September 2001 the price of gold was as low as $257 and a downfall of two
decades had preceded it. In the early 80’s, the price of gold was over $800 for some
days and for almost 20 years the price of gold was in a stalemate. In December
2005, gold broke the $500 barrier for the first time since 1982.
* Institute of Management Technology, Dubai International Academic City, UAE146 K. S. Sujit and B. Rajesh Kumar
In 2005, one ounce of gold can now buy only 7.7 barrels of crude oil. That’s
the least over the past 40 years - since the relationship between the prices of the
two commodities was first noticed. The average ratio over the past 40 years was
15.2 barrels of crude oil for every ounce of gold. Between 1975 and1980, when the
Organization of Petroleum Exporting Countries sharply increased the price of
crude oil for the first time, an ounce of gold could buy just over eight barrels of
crude.
As the dollar prolonged its decline in the aftermath of the 1973 breakdown of
dollar/gold convertibility, oil prices increased four-fold to nearly $12 per barrel in
1974, triggering sharp run ups in U.S. gasoline prices and a subsequent halt in
consumer demand. Gold also pushed higher during the same period, gaining about
15%.
A tumbling dollar and record oil prices were the main culprits in the 1980-82
recession. The gold/oil ratio dropped from 15.3 in January 1979 to 11.4 in August
1979 due to a doubling in oil to$29 per barrel and a more modest 30% increase in
gold.
There was a temporary spike in the gold/oil ratio from 12.5 in autumn 1979 to
21 in winter 1980. This was due to a $400 jump in gold from September 1979 to
January 1980 resulting from the Soviet Union’s invasion of Afghanistan.
In Autumn 1985, the gold/oil ratio bottomed at 10.6 after declining from a 16.9
high in February 1983 amid relative stability in both the metal and the fuel,
coinciding with a peaking fed funds rate of 8%.
Upon Iraq’s fateful invasion of Kuwait on Aug. 2, 1990, oil prices surged from
less than $21 per barrel to $31 per barrel in less than two weeks, before extending to
a then-record $40 per barrel in October. The oil price jump dragged the gold/oil
ratio by 50% to a five-year low of 10.6 in less than three months.
In December 1998, oil prices plummeted due to OPEC’s decision to increase
supplies combined with the break of Asian oil demand amid the 1997-98 market
crisis. OPFC’s miscalculation cut oil prices by more than half to $11 per barrel in
December1998, their lowest since the glut of 1986. Once again, the recession was
predicted by the gold/oil ratio’s tumble to a nine year low of 1 M in 1999.
After the outbreak of the second Iraq War in March 2003, oil prices began their
multi-year bull market, rising from $30 per barrel in March 2003 to more than $50
per barrel in March 2005. Oil ended the year at $61 per barrel, up more than 100%
over the prior two years compared to a 54% increase for gold over the same period.
The oil price moves dragged the gold/oil ratio to 6.7 % in August 2005, its lowest
level over the past 35-year history.
It is often stated that gold is the best preserving purchasing power in the long
run. Gold also provides high liquidity; it can be exchanged for money anytime the
holders want. Gold investment can also be used as a hedge against inflation andStudy on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 147
Figure 1
Source: Data collected from World Gold Council
currency depreciation. From an economic and financial point of view, movements
in the price of gold are both interesting and important. It is often argued that
investment in gold is historically associated with fears about rising inflation and/
or political risk. However, financial markets do not currently show the classic
symptoms associated with such fears.
In the context of commodities overwhelming financial assets, it is quite
interesting to study the relationship between prices of fuel and metals specifically
oil and gold. For commodities that are traded continuously in organized markets
such as the Chicago Board of Trade, a change in any exchange rate will result in an
immediate adjustment in the prices of those commodities in at least one currency
and perhaps in both currencies if both countries are “large”. For example, when
the dollar depreciates against the euro, dollar prices of commodities tend to rise
(and euro prices fall) even though the fundamentals of the markets––all relevant
factors other than exchange rates and price levels––remain unchanged. The power
of this effect is suggested by the events surrounding the intense appreciation of the
dollar from early 1980 until early 1985, during which the U.S. price level rose by 30
per cent but the IMF dollar-based commodity price index fell by 30 per cent, and
dollar-based unit-value indices for both imports and exports of commodity-
exporting countries as a group declined by 14 per cent.4
The high oil price pushed up worldwide inflation, which in turn forced the
gold price up. In 1983, the gold price climbed briefly to more than $800/oz and an
ounce of gold could buy more than 30 barrels of oil.
The rally in the gold price has been underway since April 2001. Since the current
rally is now in its tenth year, and that historically gold price rallies last no longer
than four years, this represents the most durable rally in history.148 K. S. Sujit and B. Rajesh Kumar
HIGH OIL AND GOLD PRICES – A REFLECTION
The rise of gold price in 1980 could be attributed to political reasons. At the time,
the Soviet invasion of Afghanistan, which began around Christmas 1979, was a
terrible global shock. The Soviets had just signed a “bilateral treaty of cooperation”
with Afghanistan in 1978, but by the next year relations had deteriorated. In the
midst of cold war, this action was a major setback to America which had already
been weakened by high inflation and unemployment and energy prices.
The future of the American economy and American power did not feel at all
certain. As a safe haven in times of panic and strife, gold simply reflected that fear.
However the buying panic quickly subsided and this all time peak was followed
by the beginning of a 22 year old bear market in gold.
Between 2000 and 2010, the price of gold jumped from $255 to over $1400 per
ounce. In 2009 and 2010, the inflation percentages have dropped dramatically even
dipping into deflationary levels at times. The stock market is down significantly
from its 2007 highs. The indexes are ambivalent as to direction as of late 2010. The
global economy is recovering from a recession and still on shaky ground. These
conflicting indicators create mixed signals for gold buyers. Still, it is worth noting
that gold is only 10 years into its long-term bull cycle.
Oil prices hit an all-time high of $145 a barrel in July 2008. This drove gas prices
to $4.00 a gallon. Most news sources blamed this on surging demand from China
and India, combined with decreasing supply from Nigeria and Iraq oil fields. In
fact, global demand was actually down and global supply up during that time. Oil
consumption decreased from 86.66 million barrels per day (bpd) in the fourth quarter
2007 to 85.73 million bpd in the first quarter of 2008. At the same time, supply
increased from 85.49 to 86.17 million bpd. It was also stated that commodity prices
drove up the oil prices. As investors retreated from the falling real estate and global
stock markets, they diverting their funds to oil futures .This sudden surge drove
up oil prices, creating a speculative bubble. This bubble soon spread to other
commodities. Investor funds swamped wheat, gold and other related futures
markets. This speculation drove up food prices dramatically around the world.
High oil prices were also said to be driven by a decline in the dollar. Most oil
contracts around the world are traded in dollars. As a result, oil-exporting countries
usually peg their currency to the dollar. When the dollar declines, so do their oil
revenues, but their costs go up.
COMPARISON OF GOLD, OIL IN REAL TERMS DURING THE PERIOD 1900-2010
(BASE YEAR 2009)
In real terms gold hit all time high of $1537.94 in the year 1980 .The highest oil price
of $96.91 in real terms was in the year 2008. The second highest gold price of $1208.55
was observed in the year 2010. The oil price of $95.89 in 1980 was the second highest
in the last 110 years.Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 149
Table 1
Comparison of 10 Year Average Gold, Oil Prices in1900-2010 Period
Year Real Gold Price in Real Oil Price in
dollars Dollars
1900-1909 519.74 20.18
1910-1919 398.32 19.65
1920-1929 254.84 19.89
1930-1939 451.81 14.78
1940-1949 405.36 15.42
1950-1959 277.53 14.99
1960-1969 240.18 12.17
1970-1979 490.84 38.38
1980-1989 868.09 55.37
1990-1999 505.27 26.57
2000-2010 624.06 54.97
(11 year average)
Overall (1900-2010) 459.32 26.83
The real oil prices were fluctuating over the time period. During the period
1960-1969, the oil price was the lowest in the time period 1900-2010 with an average
value of $12.17. The real gold price was also lowest during the period 1960-69 with
an average value of $240.18.The second lowest real gold prices were observed in
the period 1920-29 with an average value of $254.84 per ounce. On a closer look at
the time window of 40 years from 1930-1969, both oil and gold prices were
fluctuating in an irregular manner. The average gold prices and oil prices showed
decreasing pattern from 1940s till 1969. During this period of thirty years the average
gold prices in dollar decreased by 46.8% .In the period 1940-49 , the average oil
prices increased by 4.3% compared to the previous period of 10 years. In the 1950s
and 1960s, the average oil prices decreased by 2.79 per cent and 18.8 per cent
respectively. During the 70s and 80s the average real gold prices increased by 2.04
and 1.76 times compared to the previous period. In the 1990s the average real gold
price declined by 41.79 per cent. During the same period, the real oil prices also
declined by 52 per cent .In the 11 period of 2000 -2011, the average oil price increased
by 23.5 per cent and the gold price by approximately 107 per cent.
Over the last century and decade, the gold prices have fluctuated to the greatest
extent. The period 2000-2011 signified the highest variation in gold prices. Post
1970, the gold price fluctuations increased manifold times compared to the previous
time windows of analysis. The lowest variation in the real gold prices was observed
during the time window of 1920-1929 and 1960-1969.Compared to 1960s, the
fluctuations in gold prices increased by 872 times in the 2000s. Oil prices were very
stable in the period 1950-1959. In the 70s and 80s fluctuations in oil prices increased
to a greater extent.150 K. S. Sujit and B. Rajesh Kumar
Table 2
Variance Analysis of the 10 year Gold, Oil Prices in1900-2010 Period
Year Real Gold Price in Real Oil Price in
dollars Dollars
1900-1909 342.27 23.34
1910-1919 8252.03 29.40
1920-1929 92.94 27.73
1930-1939 14162.29 7.52
1940-1949 5805.32 3.79
1950-1959 176.13 0.38
1960-1969 98.04 0.88
1970-1979 44408.15 687.01
1980-1989 70951.82 604.70
1990-1999 6833.39 35.67
2000-2010 85572.06 489.86
(11 year average)
Overall 50441.86 396.52
REVIEW OF LITERATURE
Considerable research exists to understand the relationships or interactions among
various indicators of economic activity. Researchers have studies gold and oil
relationships with stock prices. Economic indicators included, among others,
industrial production (Flood and Marion, 2006), interest rates (Hondroyiannis and
Papapetrou, 2001), inflation (Moore, 1990), and currency rates (Amoateng and Jovad,
2004). El-Sharif. et al. (2005) found positive, often significant, relationships between
the price of oil and equity values in the oil and gas sector using data relating only to
the United Kingdom. Basher and Sadorsky (2006) reported strong evidence for the
observation that oil price risk impacts stock price returns in emerging markets.
A large number of studies have attempted to statistically model the determinants
of the price of gold.
Broadly these studies follow three main approaches.
Approaches Perspectives Studies
1 Models variation in the price of gold in Ariovich, 1983; Dooley, Isard and
terms of variation in main Taylor, 1995; Kaufmannand Winters,
macroeconomic variables 1989; Sherman, 1982, 1983, 1986;
Sjaastad and Scacciallani, 1996).
2 Focuses on speculation and the rationality (Baker and Van Tassel, 1985; Chua, Sick
of gold price movements and Woodward, 1990; Diba and
Grossman, 1984; Koutsoyiannis, 1983;
Pindyck, 1993)
3 Gold as a hedge against inflation with Chappell and Dowd, 1997; Ghosh et al.,
particular emphasis on short-run and 2004; Kolluri, 1981; Laurent, 1994;
long-run relationships Mahdavi andZhou, 1997; Moore,
1990; Ranson, 2005a, b).Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 151
The study by Janabi et al. (2010) explores whether the Gulf Cooperation Council
(GCC) equity markets are informationally efficient with regard to oil and gold price
shocks during the period 2006–2008 using daily dollar-based stock market indexes
dataset. The study also examines the impact of the impact of oil and gold prices on
the financial performance of the six distinctive GCC stock markets. The study finds
that GCC equity markets are informationally efficient with regard to gold and oil
price indexes.
The study by Zang et al. (2010) analyze the cointegration relationship and
causality between gold and crude oil prices. The study finds that there are consistent
trends between the crude oil price and gold price with significant positive correlation
during the sampling period. The study further suggests that long term equilibrium
between the two markets and the crude oil price change linearly Granger causes
the volatility of gold price. With respect to the common effective price between the
two markets, the contribution of the crude oil price seems larger than that of gold
price.
The study by Laughlin (1997) suggests that whether commodities fall in relation
to gold or gold rises in relation to commodities, in either case the value of gold has
risen .The study by Ashraf (2005) examines five cases in which the five instances
are noted in which a bottom gold-oil ratio coincided with falling {or negative) yield
spreads, a peaking fed funds rate, a falling dollar and eventually falling growth.
Pravit (2009) uses Multiple Regression and Auto Regressive Integrated Moving
Average (ARIMA) to forecast gold prices. The research result suggests that ARIMA
(1, 1, 1) is the most suitable model to be used for forecasting gold price in the short
term. Using multiple regression model the study suggests that that Australian
Dollars, Japanese Yen, US dollars, Canadian Dollars, EU Ponds, Oil prices and Gold
Future prices have effect on the change of Thai gold price.
The study by Larry et al. (1997) supports the hypothesis of market efficiency for
the world gold market during the 1991-2004 periods. The study also finds that the
real appreciations or depreciations of the euro and the yen against the U.S. dollar
have profound effects on the price of gold in all other currencies. Further the study
suggests that the major gold producers of the world (Australia, South Africa, and
Russia) appear to have no significant influence over the world price of gold.
The significant highlights of the study by Ismail et al( 2009) reflects the fact that
several variables like USD/Euro exchange rate , Inflation rate , Money supply (M1),
NYSE Index, S&P Poor Index and US dollar index have an influence on gold prices.
The paper by Max (2004) presents a monetary theory of nominal oil and gold
prices. It tests the model with a VAR system with a priori undetermined structural
breaks. Results with US data indicate that nominal oil and gold prices is Granger
caused by monetary factors. Also money Granger causes inflation which in turn
Granger causes output growth rate changes.152 K. S. Sujit and B. Rajesh Kumar
The paper by Mu Lan et al. (2010) uses daily data and time series method to
explore the impacts of fluctuations in crude oil price, gold price, and exchange
rates of the US dollar vs. various currencies on the stock price indices of the United
States, Germany, Japan, Taiwan, and China respectively, as well as the long and
short-term correlations among these variables. The results show that there exist co-
integrations among fluctuations in oil price, gold price and exchange rates of the
dollar vs. various currencies, and the stock markets in Germany, Japan, Taiwan
and China.
To explore whether the prices of gold were affected by inflation and other market
factors, Moore (1990) used the leading signals of inflation to test the relationship
between these leading signals and the gold prices of the New York Market since
1970. Empirical results show that, from 1970 to 1988, gold prices and the stock/
bond markets had a negative correlation, that is, when gold prices were rising, the
stock/bond markets were declining.
The paper by Ai Han et al. (2008) proposes an interval method to explore the
relationship between the exchange rate of Australian dollar against US dollar and
the gold price, using weekly, monthly and quarterly data. With the interval method,
interval sample data are formed to present the volatility of variables. The ILS
approach is extended to multi-model estimation and the computational schemes
are provided. The empirical evidence suggests that the ILS estimates well
characterize how the exchange rate relates to the gold price, both in the long-run
and short-run.
Using cointegration techniques, Eric et al. (2006) suggests that there is a long-
term relationship between the price of gold and the US price level. Second, the US
price level and the price of gold move together in a statistically significant long-run
relationship supporting the view that a one percent increase in the general US price
level leads to a one percent increase in the price of gold. There was a positive
relationship between gold price movements and changes in US inflation, US inflation
volatility and credit risk. The study also found a negative relationship between
changes in the gold price and changes in the US dollar trade-weighted exchange
rate and the gold lease rate.
OBJECTIVES OF THE STUDY
As discussed in the review of literature that the results of interrelationship among
various important variables are varied and mixed. Reasons of these results could
be due to time period of study and the time series modeling technique used by the
studies. Hence, it is imperative to verify the relationship periodically with
sophisticate techniques. The paper explores the extent of linkages of crude oil price,
stock market returns price and exchange rate on gold prices using vector
autocorrelation and cointegration technique with the more recent data. The objective
of the study is to validate the relationship systematically.Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 153
VARIABLES AND DATA DESCRIPTIONS
The study has taken gold daily price in dollar and various other currencies data from
world gold council, S&P500 from yahoo finance website, daily crude oil price Cushing,
OK WTI Spot Price FOB (Dollars per Barrel) and Europe Brent Spot Price FOB (Dollars
per Barrel) and Trade Weighted Exchange from Thomson Reuters, Major Currencies
(DTWEXM) as a proxy of exchange rate from Federal Reserve Bank of St. Louis’s
website5. As gold prices in various currencies are in index with second January 2001as
base year we converted oil prices as in index by taking the same base period. In the
series taken there were some missing data due to holidays and other reasons, these
missing values were filled by simply forecasting using Microsoft excel.
The variations on index is calculated by taking first difference of two successive
days i.e. Vt = Pt – Pt-1, where Vt is the variation at time t and Pt and Pt-1 are the price
at time t and t-1 respectively. The time period of this study is form 2nd January 1998
to 5th June 2011, constituting 3485 observations. Appendix-3 presents the descriptive
statistics which shows that there is high value for standard deviation in all the
variables indicating variability. High Jarque-Bera shows that the series is normal.
1. Methodology
In order to examine the impact of oil price, exchange rate and stock market on gold
price Vector Autoregression (VAR) has been used. In this model all the variables
are considered to be endogenous and each endogenous variable is explained by its
lagged or past values and the lagged values of all other endogenous variables
included in the model. There are no exogenous variables in the model and hence,
by avoiding the imposition of a priori restriction on the model the VAR adds
significantly to the flexibility of the model.
The vector autoregression (VAR) is commonly used for forecasting systems of
interrelated time series and for analyzing the dynamic impact of random
disturbances on the system of variables.
The VAR approach sidesteps the need for structural modeling by modeling
every endogenous variable in the system as a function of the lagged values of all of
the endogenous variables in the system.
The mathematical form of a VAR is
yt = A1yt–1 + ... + Apyt–p + Bxt + εt
where yt is a k vector of endogenous variables, xt is a d vector of exogenous variables,
A1,... Ap, and B are matrices of coefficients to be estimated, and εt is a vector of
innovations that may be contemporaneously correlated with each other but are
uncorrelated with their own lagged values and uncorrelated with all of the right-
hand side variables.
Since only lagged values of the endogenous variables appear on the right-hand
side of each equation, there is no issue of simultaneity, and OLS is the appropriate154 K. S. Sujit and B. Rajesh Kumar
estimation technique. Note that the assumption that the disturbances are not serially
correlated is not restrictive because any serial correlation could be absorbed by
adding more lagged y’s.
STATIONARITY OF VARIABLES
A stationary time series is significant to a regression analysis based on the time
series, because useful information or characteristics are difficult to identify in a
nonstationary time series. Therefore, a nonstationary time series would lead to a
spurious regression. However, most economic time series are nonstationary in
practice. Hence, time series should be made stationary after differencing. Useful
information or characteristics can still be identified in the time series after
differencing. A time series is said to be stationary if its mean and variance are
constant and, the covariances depend on upon the distance of two time periods.
The unit root test is used to test stationarity of variables and the order of integration.
The Dicky-Fuller unit root test (DF), Augmented Dicky-Fuller unit root test (ADF)
(Dicky and Fuller, 1979) and the Phillips-Perron unit root test (PP) (Phillips and
Perron, 1988) are often used to test stationarity. For the VAR estimation all the
variables included in the model should be stationary. Table 1 presents Augmented
Dickey-Fuller (ADF) and Phillips-Perron(PP) tests at level. The result of ADF test is
presented with lag 4 and PP test is conducted with lag 8 suggest by Newey-West.
However, several other lags were also selected and the result is invariant. It is clear
that none of the values are more than Mckinnon critical values in absolute terms
hence we conclude that there is unit root present in the series. Table-2 presents the
unit root test with first difference and the results shows that all the index data
series are not stationary at the level but stationary after the first difference. In other
words all the data series are I(1) which denotes that the time series is integrated at
the first difference level.
Table 1
Unit Root Test with Level Data
Stock index
ADF with Level PP with level
Intercept Intercept and Intercept Intercept and
Trend Trend
Gold price($) 1.81(4) -0.80(4) 1.95(8) -0.74(8)
S&P 500 Index -2.18(4) -2.19(4) -2.17(8) -2.17(8)
Exchange rate -0.57(4) -2.17(4) -0.52(8) -2.19(8)
Oil price index (WTI) -1.17(4) -2.86 (4) -1.08(8) -2.74(8)
Oil price index (BRENT) -0.57(4) -2.40(4) -0.57(8) -2.42(8)
Note: *, **, *** represents the McKinnon critical values for ADF and PP at 1%, 5%, 10% levels
respectively. The values in the parenthesis are lags. For ADF the lag augmentation is on the
basis of AIC. For PP test (Newey-West suggests: 8).Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 155
Table 2
Unit Root Test with first difference
Stock index
ADF with Level PP with level
Intercept Intercept and Intercept Intercept and
Trend Trend
Gold price($) -25.92(4)* -26.05(4)* -59.53(8)* -59.63(8)*
S&P 500 Index -27.78(4)* -27.78(4)* -65.00(8)* -64.99(8)*
Exchange rate -26.14(4)* -26.15(4)* -60.56(8)* -60.56(8)*
Oil price index (WTI) -26.83(4)* -26.83(4)* -62.71(8)* 62.70(8)*
Oil price index (BRENT) -25.24(4)* -25.25(4)* -58.47(8)* -58.47(8)*
Note: *, **, *** represents the McKinnon critical values for ADF and PP at 1%, 5%, and 10% levels
respectively. The values in the parenthesis are lags. The lag augmentation is on the basis of
AIC. The values in the parenthesis are lags. For ADF the lag augmentation is on the basis of
AIC. For PP test ( Newey-West suggests: 8).
There are at least two advantages when using the first difference data series to
explain the impulse response function. Firstly, it focuses more on the increase or
decrease trend rather than the actual change. Because the first difference data series
is the increase or decrease between every two consecutive dates, a strengthening or
weakening of the trend will be detected by the impulse response function. Secondly,
it captures more information on the shocks of gold prices, because the first difference
data shows the changes in the past two days while the level data shows the changes
in one day in impulse response function.
SELECTION OF OPTIMAL LAG
One of the important aspect of VAR model is to select the optimal lagged term.
Traditional way of selecting the lag length was by repeating VAR model by reducing
lag length from a large lag term until 0. In each of these models, the smallest value
of the Akaike information criterion and the Schwarz criterion are used to select the
optimal lag length (Grasa, 1989; DeJong et al., 1992; Maddala and Gujarati, 2003). In
this study however, five criteria: Sequential modified LR test statistics (LR), Final
prediction error (FPE), Akaike information criterion (AIC), Schwarz criterion (SC)
and Hannan-Quinn information criterion (HQ), which have been introduced by
Lutkepohl (1993) were inspected. Similarly, the smallest value of these 5 criteria
points to the optimal lag length.
Table 3 shows the summary results of VAR lag order selection criterion. The
first left hand column shows the model for which the lag length has been selected
using The LR, FPE, AIC, SC and HQ criterion. The numbers are the smallest value
in each of criteria. Before selecting the lag length, one must consider that too short
a lag length in the VAR may not capture the dynamic behaviour of the variables
(Chen and Patel, 1998) and too long a lag length will distort the data and lead to a156 K. S. Sujit and B. Rajesh Kumar
decrease in power DeJong et al. (1992). Based on the results, the study chose four
lag to be appropriate.
Table 3
Lag-Length Selected by Different Criteria
Model for lag length with I(1) LR FPE AIC SC HQ Lag length selected
for this study
Gold($), EXCHRATE, 30 21 21 4 8 4
S&P500, WTI
Gold($), EXCHRATE,
S&P500, BRENT
GOLD(Euro), EXCRATE, 29 17 17 4 8 4
S&P500, BRENT
GOLD(Euro), EXCHRATE, 30 21 21 4 8 4
S&P500, WTI
Included observations: 3454, LR: sequential modified LR test statistic (each test at 5% level), FPE:
Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion, HQ:
Hannan-Quinn information criterion
ORDERING OF THE VARIABLES
The ordering of the variables is another crucial aspect in VAR estimation. Proper
ordering shows that current innovations in the variable that is placed first affect
the rest of the variables. At the same time, the current innovations in variables
placed towards the end are not expected to affect the variables in the beginning of
the order. The study selected the ordering of the variables by conducting pair-wise
Granger causality tests with the lag length selected by the criteria. The following
orders were selected for this study.
1. Gold ($), WTI, Exchange rate, S&P………………………..(Model-1)
2. Brent, exchange rate, WTI, Gold(euro) ……………………( Model-2)
ESTIMATION OF VAR
The coefficients obtained from the estimation of the VAR model may not be proper
to interpret directly. Hence, both impulse response functions and the variance
decomposition are used. Impulse response functions are used to trace out the
dynamic interaction among variables. It shows the dynamic response of all the
variables in the system to a shock or innovation in each variable. In other words, it
focuses more on the increase or decrease in trend rather than the actual value of the
variable. On the other hand, variance decomposition is used to detect the causal
relationships among the variables. It shows the extent to which a variable is
explained by the innovations or shocks in all the variables in the system.
The result of model 1 is presented in figure 1 and table 5. The impulse response
of model 1 shows the response to one standard deviation shock in the error termsStudy on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 157
Table 4
Pair-wise Granger Causality Tests
Null Hypothesis F-Statistic Probability
SP does not Granger Cause GOLDEURO 0.53224 0.71206
EXCH does not Granger Cause GOLDEURO 0.62378 0.64554
EXCH does not Granger Cause GOLDEURO 0.62378 0.64554
EXCH does not Granger Cause SP 0.63549 0.63717
WTI does not Granger Cause GOLDEURO 0.91018 0.45694
GOLDUS does not Granger Cause SP 1.15388 0.32927
WTI does not Granger Cause SP 1.18158 0.31676
BRENT does not Granger Cause GOLDEURO 1.31903 0.26036
GOLDEURO does not Granger Cause SP 1.40133 0.23087
EXCH does not Granger Cause WTI 2.31420*** 0.05521
GOLDUS does not Granger Cause EXCH 2.44346** 0.04462
BRENT does not Granger Cause GOLDUS 3.88093* 0.00378
SP does not Granger Cause GOLDUS 3.98387* 0.00315
GOLDUS does not Granger Cause BRENT 4.26925* 0.0019
GOLDUS does not Granger Cause WTI 6.30267* 4.70E-05
SP does not Granger Cause WTI 6.60052* 2.70E-05
EXCH does not Granger Cause GOLDUS 6.67577* 2.40E-05
WTI does not Granger Cause EXCH 7.07346* 1.10E-05
GOLDEURO does not Granger Cause WTI 7.85588* 2.70E-06
GOLDEURO does not Granger Cause EXCH 10.6839* 1.30E-08
GOLDEURO does not Granger Cause BRENT 13.0458* 1.50E-10
SP does not Granger Cause EXCH 14.3701* 1.20E-11
WTI does not Granger Cause GOLDUS 21.8512* 0
of other variables. The X axis shows the time period and the Y shows the shock in
the movement trend. The positive symbol does not mean an increase in index. It
means an increase in movement trend is strengthened. In short, a positive symbol
means a favorable effect on index and a negative symbol means an adverse effect.
It can be seen that gold in $ has positive favorable impact to a shock in WTI index
where as all remaining impacts are marginal. Similarly, the response of WTI to a
shock in Gold($) has favorable effect and it lasts for more days with lots of variations.
Response of Exchange rate to a shock in gold price index is unfavorable as it starts
from negative side. Similar unfavorable results can be seen for the response of
exchange rate to a shock in WTI and S&P as well. Response of S&P index to a shock
in WTI is favorable. It is clear from impulse response function that the shock lasts
for few days only and the intensity of response is weak.
The intensity of response can be seen from Variance Decomposition table 5.
Innovations in WTI can explain around 2.4% variations in gold price index in $. All
other innovations explain below one percent of the variation in gold price index.158 K. S. Sujit and B. Rajesh Kumar
Similarly, innovations in gold price index in $ explains around 4 to 5% variations in
WTI index. It is clear from this that both gold index and WTI index explains each
other and the percentage of variation is less.
One of the interesting finding of Variance Decomposition is about exchange
rate which is largely explained by innovations in gold index (10%), WTI (3%) and
S&P (1%). This can also be seen from the impulse response function discussed above.
In case of S&P index the innovation in WTI index explains around 2% of the
variations in S&P index.
In model 2 the study used a different ordering of variables and replacing WTI
index with Brent index and instead of gold index in $ the model used gold price
index in euro. The result is more or less similar. Innovations in Brent index explain
around 6 to 7% variations in Exchange rate. S&P index explains around 1.5% and
gold index in euro explains just 1% variations in exchange rate. This can also be
seen from the trend in impulse response figures mentioned in figure 2.
Engle and Granger (1987) pointed out that a linear combination of two or more
non-stationary series may be stationary. If such a stationary, or I(0), linear
combination exists, the non-stationary (with a unit root), time series are said to be
cointegrated. The stationary linear combination is called the cointegrating equation
and may be interpreted as a long-run equilibrium relationship between the variables.
The study further investigated whether or not the variables in our model are
cointegrated? For this the study used Johansen’s (1991) maximum likelihood
method. The result of cointegration test is presented in the below mentioned table.
However, the study could not find any cointegration among variables in the first
model where as in the second model there is just one cointegrating equation showing
weak long run relationship among variables.
CONCLUSION AND DISCUSSIONS
Gold historically combated losses that occurred during the period of inflation, social
unrest and war. When stock prices fell financial advisors were expected to advise
investors to maintain a position in gold during the period. Conversely during boom
times, gold investments often decreased in value as stock prices increased like in
1990s. Some investors believed that gold prices had no portfolio risk aversion value
and can be treated like any other commodity whose price changes were strictly
determined by supply and demand. During times of oil price uncertainty, oil
investments emerged as a risk deterrent in the context of inverse relationship with
stock market movement. In the currency market, exchange rates are often predicated
on the health of a country’s economy. If the economy is robust and growing, the
exchange rates for their currency reflect that in higher value.The simple relationship
between currencies through a single common commodity does not exist and the
interconnection between gold prices, exchange rates and oil prices are all complex
in nature. There are many factors on which the prices of gold and crude oil mayStudy on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 159
depend upon: government policies; budget, inflation, economic and political
condition of the country etc.
This paper aims to establish and validate the dynamic relationship of
commodities prices involving gold and crude oil with exchange rate and stock
index. The paper uses daily time series data to explore the impact of fluctuations
and interrelationship among crude oil price, stock market returns and Trade
Weighted Exchange Index which is computed by taking major Currencies
(DTWEXM) and gold price. The link between variables which determine the oil
and gold prices variation and their relation with economic activity have been
explored in empirical research. But studies involving the relationship between oil
prices, gold prices, exchange market and stock market returns are limited. This
paper aims to demonstrate systematically the dynamic relationship among gold
price, oil price, exchange rate and stock market returns using Vector auto regressive
(VAR) technique.
The study used two models to show the dynamic relationship. The first model
takes gold index in US dollar and in second model gold index in euro. In order to
add variety we have taken WTI [Cushing, OK WTI Spot Price FOB (Dollars per
Barrel)] in the first model and Brent [Europe Brent Spot Price FOB (Dollars per
Barrel)] in the second model. The ordering of variables is done on the basis of
Granger causality test. The result shows that exchange rates have a direct influence
on gold prices; oil prices and stock market index. The variance decomposition
implies that the largest portions of total variations in exchange rate comes from
innovation in Gold index, WTI and S&P stock market index. The dynamic effects of
the impulse response also suggest the same in terms of the relationship of exchange
rate with respect to gold prices, oil prices, stock market index returns and inflation.
It is clear from the analysis that fluctuations in gold prices are largely dependent
on gold itself rather than oil and other indices. But gold price fluctuation affects the
WTI index. Most of the variables taken in this study affects exchange rate in some
way or the other. Out of which gold plays an important role with largest variation
of 10%. However, gold price in euro turned out to be less affected by the indices
taken.
Gold prices are typically denominated in US dollars and this implies that the
exposure gained from buying /selling gold is influenced by changes in the exchange
rate for US dollars. Changes in exchange rate through changes in costs and revenues
will have direct impact on profits and thus impact stock returns. However, gold
index in euro fails to show similar effects on exchange rate as the shock in gold
price in euro explains just 1% of the variations in exchange rate.
It is often observed that with higher oil prices, the currency of oil exporting
countries rise in value and that of oil importing countries decrease in value. The
most profitable trades are those between that of a country that exports oil vs a
country that depends on oil. Canada is among the largest oil exporting nations.160 K. S. Sujit and B. Rajesh Kumar
The increasing oil exports can be compared with the strengthening of Canadian
dollars over a period of time. Similarly Japan’s reliance on Oil imports make it
vulnerable to oil price fluctuations which would lead to drop in yen value. The
result of this study shows that a shock in WTI and Brent, used as a proxy of oil
price, causes 3% and 6-7% fluctuation in exchange rate respectively.
The study also verified the presence of cointegration among variables and found
that there is one cointegrating equation in second model. This shows that there is
weak long run relationship among variables. (See Appendix 2).
Notes
1. Eric J. Levin & Robert E. Wright, Short run and Lon run determinants of the price of gold ,
World Gold council Research Study No. 32 , 2006.
2. Larry A. Sjaastad, Fabio Scacciavillani, “The Price of Gold and the Exchange Rates,” Journal of
International Money and Finance, December, 1996.
3. http://research.stlouisfed.org
References
Ai Han, Shanying Xu, Shouyang Wang (2008), Australian Dollars Exchange rate and Gold Prices :
An Interval Method Analysis , 7th International Symposium on Operations Research and its
Applications (ISORA’08) , Lijiang China, Oct 31-November 3.
Amoateng, Kofi A. and Kargar, Jovad, (2004), “Oil and Currency Factors in Middle East Equity
Returns”, Managerial Finance, Vol. 30 (3), 2004, 3-16.
Ariovich, G., (1983), The Impact of Political Tension on the Price of Gold, Journal for Studies in Economics
and Econometrics, Vol. 16, pp. 17-37.
Asharaf Laidi, (2005), Gold, Oil and Dollar Repercussions, Futures, December, page 36-38.
Baker, S. A., and van Tassel, R. C., (1985), Forecasting the Price of Gold: A Fundamentalist Approach,
Atlantic Economic Journal, Vol. 13, pp. 43-51.
Basher, Syed A. and Sadorsky (2006), Perry, “Oil Price Risk and Emerging Stock Markets”, Global
Finance Journal, Vol. 17 (2), 224-XXX.
Chappell, D. and Dowd, K., (1997), A Simple Model of the Gold Standard, Journal of Money, Credit and
Banking, Vol. 29, pp. 94-105.
Chen, M. C. and Patel, K. (1998), House Price Dynamics and Granger Causality: An Analysis of
Taipei New Dwelling Market, Journal of the Asian Real Estate Society, 1(1), pp. 101-126.
Chua, J., Sick, G. and Woodword, R., (1990), Diversifying with Gold Stocks, Financial Analysts Journal,
Vol. 46, pp. 76-79.
DeJong, D. N., Nankervis, J. C., Savin, N. E. and Whiteman, C. H. (1992), The Power Problems of Unit
Root Test in Time Series with Autoregressive Errors, Journal of Econometrics, 53(1-3), pp. 323-
343.
Diba, B. and Grossman, H., (1984), Rational Bubbles in the Price of Gold, NBER Working Paper: 1300.
Cambridge, MA, National Bureau of Economic Research.
Dicky, D. A. and Fuller, W. A. (1979), Distribution of the Estimators for Autoregressive Time Series
with a Unit Root, Journal of the American Statistical Association, 74(336), pp. 427-431.
Dooley, M. P., Isard, P. and Taylor, M. P., (1995), Exchange Rates, Country-specific Shocks and Gold,
Applied Financial Economics, Vol. 5, pp. 121-129.Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 161
El-Sharif, Idris; Brown, Dick; Burton, Bruce; Nixon, Bill; and Russell, Alex,(2005), “Evidence on the
Nature and Extent of the Relationship between Oil Prices and Equity Values in the UK”, Energy
Economics, Vol. 27 (6), 2005, 819-XXX.
Engle, R. F., & C. W. J. Granger (1987), Cointegration and Error-correction Representation, Estimation
and Testing. Econometrica, Vol. 55, pp. 251-276.
Eric J. Levin & Robert E. Wright, (2006), Short Run and Lon Run Determinants of the Price of Gold ,
World Gold Council Research Study No. 32.
Flood, Robert, and Marion, Nancy, (2006), “Stock Prices, Output, and the Monetary Regions”, Open
Economies Review, Vol. 17 (2), 147-173.
Ghosh, D. P., E. J. Levin, P. Macmillan and R. E. Wright and (2004), Gold as an Inflation Hedge?,
Studies in Economics and Finance, Vol. 22, No. 1, pp. 1-25.
Global Market Research Report September 2010, Deutsche Bank.
Grasa, A. A. (1989), Econometric Model Section: A New Approach. Kluwer Academic, Boston.
Gujarati, D. N. (2003), Basic Econometrics. Gary Burke, New York.
Hondroyiannis, George and Papapetrou, Evangelia, (2001), “Macroeconomic Influences on the Stock
Market”, Journal of Economics and Finance, Vol. 25 (1), 2001, 33-50.
Ismail Yahya, Shabri, (2009), Forecasting Gold Prices using Multiple Linear Regression Method,
American Journal of Applied Sciences 6(8), 1509-1514.
Janabi, Mazin A. M., Hatemi. J., Abdul Nasser, Irandoust, Manucheh (2010), International Review of
Financial Analysis, Jan 2010, Vol. 19, Issue 1, p. 47-54.
Johansen, S. (1991), “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector
Autoregressive Models,” Econometrica, Econometric Society, Vol. 59(6), Page 1551-80.
Kaufmann, T. and Winters, R., (1989), The Price of Gold: A Simple Model, Resources Policy, Vol. 19,
pp. 309-318.
Kolluri, B. R., (1981), Gold as a Hedge against Inflation: An Empirical Investigation, Quarterly Review
of Economics and Business, Vol. 21, pp. 13-24.
Koutsoyiannis, A., (1983), A Short-Run Pricing Model for a Speculative Asset, Tested with Data from
the Gold Bullion Market, Applied Economics, Vol. 15, pp. 563-581.
Larry A. Sjaastad, Fabio Scacciavillani (1996), “The Price of Gold and the Exchange Rates”, Journal of
International Money and Finance, Dec. 1996; reprinted in Meher Manzur (ed), Exchange Rates,
Interest Rates and Commodity Prices, Edward Elgar, 2002 and in Moonjoong Tcha (ed), Gold
and the Modern World Economy, Rouledge 2003.
Laughlin, J. Laurence, Gold and Prices Since (1887), Quarterly Journal of Economics, Apr987, Vol. 1,
Issue 3, p. 319-355.
Laurent, R. D., (1994), Is There a Role for Gold in Monetary Policy? Economic Perspectives, 18, 2-14.
Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.
Maddala, G. S. and Kim, I. N. (1998), Unit Root, Cointegration, and Structural Change. Cambridge
University Press, United Kingdom.
Mahdavi, S. and S. Zhou, (1997), Gold and Commodity Prices as Leading Indicators of Inflation:
Tests of Long-Run Relationship and Predictive Performance, Journal of Economics and Business,
Vol. 49, pp. 475-489.
Max Gillman, Anton Nakov, (2004), Monetary Causality of Oil and Gold Prices, Central European
University Working Paper.
Moore, Geoffrey H. (1990), “Gold Prices and a Leading Index of Inflation”, Challenge, Vol. 33 (4),
1990, 52-57.162 K. S. Sujit and B. Rajesh Kumar
Mu-Lan Wang, Ching-Ping Wang Tzu-Ying Huang, (2010), Relationships among Oil Price, Gold
Price, Exchange Rate and International Stock Markets International Research Journal of Finance
and Economics, Issue 47 Euro Journals Publications.
Phillips, P. C. B. and Perron, P. (1988), Testing for a Unit Root in Time Series Regression, Biometrica,
75(2), pp. 335-346.
Pindyck, R. S., (1993), The Present Value Model of Rational Commodity Pricing, Economic Journal,
Vol. 103, pp. 511-530.
Pravit Khaemusunun (2009), Forecasting Thai Gold Prices, http://www.wbiconpro.com/3-Pravit-.pdf
Ranson, D., (2005a), Why Gold, Not Oil, Is the Superior Predictor of Inflation, London, World Gold
Council.
Ranson, D., (2005b), Inflation Protection: Why Gold Works Better Than “Linkers”, London, World
Gold Council.
Sherman, E. J., (1982), New Gold Model Explains Variations, Commodity Journal, Vol. 17, pp. 16-20.
Sherman, E., (1986), Gold Investment: Theory and Application, New York, Prentice Hall.
Sherman, E. J., (1983), A Gold Pricing Model, Journal of Portfolio Management, Vol. 9, pp. 68-70.
Sjaastad, L. A. and F. Scacciallani, (1996), The Price of Gold and the Exchange Rate, Journal of Money
and Finance, Vol. 15, pp. 879-897.
Zhang, Yue-Jun, Wei Yi-Ming (2010), The Crude Oil Market and the Gold Market: Evidence for co
integration, Causality and Price Discovery, Resource Policy, Sep, Vol. 35 Issue 3, p. 168-177, 10p.
Appendix 1
Figure 1: Impulse Response of Model 1Study on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 163
Table 5 (Model-1)
Forecast Error Variance Decomposition (%)
By Innovations in
Variables explained Steps DGold($) D(WTI) D(EXCH) D(SP)
1 100 0 0 0
DGold($) 2 97.00953 2.408574 0.393806 0.188092
4 96.98881 2.421412 0.39538 0.1944
6 96.98757 2.422423 0.395554 0.194452
10 96.98756 2.422431 0.395555 0.194453
1 4.670554 95.32945 0 0
D(WTI) 2 4.663751 94.67627 0.050133 0.609842
4 5.062611 94.27301 0.053657 0.610724
6 5.063766 94.27158 0.053687 0.610964
10 5.063767 94.27158 0.053689 0.610968
1 9.983431 2.23718 87.77939 0
2 9.781681 2.787204 86.1912 1.239914
D(EXCH) 4 9.941507 2.785671 85.99585 1.276976
6 9.941585 2.785948 85.99544 1.277026
10 9.941587 2.78595 85.99544 1.277026
1 0.008423 2.075613 0.038329 97.87763
2 0.018852 2.315957 0.05435 97.61084
4 0.135892 2.360765 0.080636 97.42271
D(SP) 6 0.136756 2.36091 0.080687 97.42165
10 0.136758 2.360919 0.080688 97.42164
Figure 2: Impulse Response Function of Model 2164 K. S. Sujit and B. Rajesh Kumar
Table 5
Forecast Error Variance Decomposition (%)
By Innovations in
Variables explained Steps DBrent D(EXCH) D(SP) D(Gold euro)
1 100 0 0 0
D(Brent) 2 98.62662 0.000708 0.875632 0.497042
4 98.53315 0.025586 0.887106 0.554161
6 98.50023 0.025581 0.886875 0.587312
10 98.49773 0.025582 0.886853 0.58984
1 7.020575 92.97942 0 0
D(EXCH) 2 6.859108 90.87158 1.482127 0.787188
4 6.862712 90.65788 1.513882 0.965527
6 6.859721 90.6117 1.513137 1.01544
10 6.859481 90.60431 1.513019 1.023191
1 0.849647 0.006429 99.14392 0
2 0.872523 0.020691 99.00461 0.102177
D(SP) 4 0.874946 0.024881 98.95489 0.145287
6 0.87506 0.024898 98.94581 0.15423
10 0.875116 0.024898 98.94366 0.156322
1 0.005985 0.477452 0.048912 99.46765
2 0.337606 0.323116 0.034116 99.30516
D(Gold euro) 4 0.527258 0.317051 0.035738 99.11995
6 0.545922 0.311951 0.036908 99.10522
10 0.552228 0.311683 0.036944 99.09915
Appendix 2
Model-1 Eigen value Null Hypothesis LR Statistics Critical value
(trace Statistic) 5% 1%
With linear deterministic 0.005249 r=0 33.73766 47.21 54.46
trend in data 0.002991 r≤1 15.42402 29.68 35.65
0.001341 r≤2 5.000186 15.41 20.04
9.47E-05 r≤3 0.329490 3.76 6.65
No deterministic 0.004646 r=0 31.13455 39.89 45.58
trend in data 0.002370 r≤1 14.92975 24.31 29.75
0.001870 r≤2 6.673186 12.53 16.31
4.56E-05 r≤3 0.158786 3.84 6.51
Model-2
With linear deterministic 0.034052 r=0 133.8935* 47.21 54.46
trend in data 0.002477 r≤1 13.32966 29.68 35.65
0.001076 r≤2 4.699122 15.41 20.04
0.000274 r≤3 0.953587 3.76 6.65
No deterministic 0.029008 r=0 117.5548* 39.89 45.58
trend in data 0.002812 r≤1 15.11391 24.31 29.75
0.001522 r≤2 5.312087 12.53 16.31
0.0000032 r≤3 0.011303 3.84 6.51
In model-1 L.R. rejects any cointegration at 5% significance level. In model-2 L.R. test indicates 1
cointegrating equation(s) at 5% significance levelStudy on Dynamic Relationship among Gold Price, Oil Price, Exchange Rate and Stock Market Returns 165
Appendix-3
Descriptive Statistics
BRENT WTI GOLDUS GOLDUK EXCH SP
Mean 206.3528 181.0425 208.0798 185.8706 88.8861 1189.999
Median 170.014 151.7772 153.23 125.59 85.9542 1187.7
Maximum 621.4621 538.0254 568.42 515.33 113.0977 1565.15
Minimum 38.8391 38.82636 92.72 86.7 68.2405 676.53
Std. Dev. 124.5562 103.6308 122.6771 114.2451 12.0476 181.5427
Skewness 0.808646 0.783732 1.082158 1.38956 0.207448 -0.16822
Kurtosis 2.971085 3.001649 3.054802 3.717136 1.799332 2.387342
Jarque-Bera 379.9334 356.7687 680.63 1196.195 234.329 70.94109
Probability 0 0 0 0 0 0
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