Assignment for Financial & Time Series
Analysis
-
Volatility in Gold Price Returns: An Investigation from
International Market
Submitted by- Group -9
Satish Kumar Boywar IM – 19/ Section C Roll no. 146
Vivek Prakash IM – 19/ Section C Roll no. 194 Rohit Gupta IM – 19/ Section C Roll no. 204
Volatility in Gold Price Returns: An Investigation from
International Market
Abstract The research was conducted in order to study the volatility in gold price returns and its
investigation. The data has been collected on daily basis for the tenure of a couple of years
starting from 1st January 2006 to 1st January 2014. The models used to run the data are;
standard deviation as a Descriptive Model, and GARCH as an Econometric Model. The
results investigate volatility. Econometrically speaking, an unequal spread of residuals is
referred as heteroskedasticity. In this research, a fast mean reversion has been observed
showing that the alpha and beta are far from 1. Based on results it was concluded that there
has been volatility in gold prices.
1. Introduction
All valued metals, such as Gold is very famous when it comes to investing. Investor buys
gold in order to have risk management, namely hedging, against the economic, currency,
social and political crises (it includes reduction in markets and the prosperity of the national
debt, foreign exchange sufficient for inflation, wars and social issues). Speculation is very
common when it comes to the investment of gold, which is the case in other markets,
including through the use of futures and derivatives.
1.1 Gold sector resumes net purchases after two decades of sales
In the period of 2010, gold‘s net buyer, for the first time in 21 years, were the official sectors.
Net official sector sales average was 400-500 tons per year from the year of 1989 to 2007. In
2008, the sales of Central Bank dropped by one half approximately and were continuously
declining and became 30 tons in the year of 2009. The official sector holds 18%, as a group,
of all above ground stock of gold. However, holding of gold is not equally distributed among
nations. The advanced economies of Western Europe and North America typically hold over
40% of the net external reserves in terms of gold, mostly gold standard legacy. Under that
regime, countries backed their currencies with gold, which led to the build-up of very large
gold reserves among the leading economies of the period. First, emerging market economies
that have been going through fast economic success have been the substantial gold buyers.
The primary reason for this has been a desire to move toward restoring a prior balance
between foreign currencies and gold that has been eroded by the rapid increase in their
holdings of foreign currencies, principally the US dollar. For this group of countries, gold has
also become an increasingly attractive means of diversifying their external reserves. As a
result, emerging market purchases of gold have made a significant impact in reducing the
quantity of gold the official sector had been supplying to the market each year. Second,
European central banks holding a significant amount of gold in their external reserves have
had a reduced appetite for sales in the wake of the financial crisis. Prior to the onset of the
financial crisis, several European central banks initiated gold sales programs in order to
rebalance their external reserve portfolios and increase their foreign currency holdings.
1.2 Rapid economic growth in emerging markets has led to large gold purchases
In 2010 several emerging market economies made large purchases of gold, led by Russia
which purchased 135 tons. Many participants of the market foresee that China might continue
buying mine production which would be local. China has a good team of experts from
domestic and from overseas advising China to continue the buying of gold. Other emerging
country purchases were made by the central banks of Thailand (16 tons), Bangladesh (10
tons), Venezuela (5 tons), and the Philippines (1.4 tons). Economic growth in emerging
markets has been very strong over the past decade, and this has resulted in rapid increases in
foreign currency reserves—either through expanding export revenues or increased foreign
exchange interventions to mitigate the strength of their rising currencies against the US
dollar. Both factors are driven by economic growth and contribute to expanding national
wealth that policy makers are eager to preserve. Throughout the financial crisis, and now
during the continuing sovereign debt concerns, emerging market central banks have
increasingly turned to gold purchase programs as a means of diversifying their reserves into
an asset with no credit or counterparty risk that provides immediate liquidity in all market
conditions. The foreign reserves across all central banks increased from $2 to $10 trillion, yet
gold as a percentage of total reserves remained at 13% across all central banks. However,
many countries that have fixed or managed exchange rates against the US dollar witnessed a
significant decline in their gold holdings in relation to their total reserves as they accumulated
more dollars in order to maintain their pegs. Beyond Russia‘s rebalancing efforts, in
2009India‘s purchase of 200 tons helped the country toward its goal of restoring the balance
between gold and foreign currencies in its total reserves.
1.3 Objective of The Study: To study the volatility of gold prices and its investigation in
International markets from 1st January 2006 to 1st January 2014.
1.4 Scope of The Study: By studying and investing the volatility of gold prices we can figure
out the reasons due to which there is so much fluctuations in the prices plus what measures
can be taken to maintain the price at a certain level. The investigation would tell us how
much volatility existed in gold prices during the period.
1.5 Problem Statement: ―An empirical study to investigate the volatility in gold prices from
1st January 2009 to 1st January 2014.‖
1.6 Hypotheses:
2. Literature Review According to Alptekin (2010), the research took into an account when the economy of the
world gold market remains its character as a place of conventional investment. As we can see
the up and downs in the gold prices as an indicator of market instability as whole. The
research resulted as an alternate investment according to the balance between the supply and
demand conditions which affects the economy on a vast scale. In his knowledge it was to
examine the empirical study of the instability of gold prices. The instability was tested
through ARCH LM test and GARCH (2,1) model. The result shows that the number of gold
prices was volatile and volatility was excluded. Baur, (2011) determined that by tradition
gold was a stock of worth & an inflation hedge. Gold is also viewed as a hedge against
vagueness and a harmless haven. This research proves that numerous possessions usually
related with gold are only active in a simple regression outline but significantly alteration in a
various regression outline. An expressive and econometric examination of gold and US
monetary and financial variables for once-a-month data from the period of 1979 - 2011
authenticates that gold chiefly helps as a hedge against a gentle US dollar and against
advanced commodity amounts. Gold is not a hedge against consumer rate inflation. The
observed outcome even displays that gold only lately progressed as a harmless harbor asset.
According to Baur, (2009) The reason of this paper is to observe the part of gold of
worldwide monetary scheme. We examine theory; gold indicates a harmless harbor in
contrast to shares, primary of emerging economies. A expressive analysis for the illustration
of thirty years ; 1979-2009 displays; gold as a harmless harbor used for chief European stock
markets & the United States but not for Australia, Canada, Japan & massive developing
marketplaces like BRIC nations. We even differentiate between a fragile and durable form of
the harmless harbor and argue that gold may act as a stable strength for the monetary
structure by decreasing sufferers with the face of great undesirable marketplace tremors.
Bhanot, 2006 concluded the trading of C.E Division‘s gold and silver futures contract was
boosted on Chicago Mercantile Exchange‘s Globex electronic trading arrangement, as a
fight-back against the framework of copies of these agreements from the Chicago Board of
Trade. The COMEX detected an instant stream and stable advance in market share, while
market shares of the electronic CBOT and open outcry COMEX reduced. The market worth
for normal and mini-sized contracts is greater to that of their pit-traded counterparts.
Irrespective of dropping volume share, the CBOT has a like market excellence circumstances
to the COMEX. The theoretic models of multimarket trading suggest that a translucent
electronic limit order market improves market value in whole. Also, the central market rises
as a significant midpoint for trading volume. According to Bordo in 2007 the typical gold
standard has prolonged been related with long run price loyalty. But short-run price
inconsistency controlled opponents of the gold standard to mention progresses that seem
prominently like modern varieties of price-path targeting. This object has used a dynamic
stochastic general equilibrium model to examine price dynamic forces under substitute
strategy systems. Here, a clean inflation goal proposals more short-run price dependability
than does the gold standard and, though it offerings a unit root into the value level, it hints to
as much long-term price reliability as does the gold standard for horizons that are smaller
than twenty years. Relation to these structures, Fisher's rewarded dollar decreases inflation
vagueness by an order of greatness at all horizons. A Taylor rule tips to excessive ambiguity
about inflation at long horizons. This long-run inflation ambiguity can be frequently
eradicated by giving an additional response to the unconventionality of the rate level from a
wanted path.
According to Bordo, 2003 , in this research the old gold standard had being long related with
long-run price steadiness and short run price. The short run price instability has directed the
censors to recommend modifications that have observed ample like modern varieties of price-
path leveling. This paper had used an actual stochastic overall steadiness model in order to
study price dynamics under alternate policy. In the model, an inflation aim offers more short-
run value steadiness than does the gold standard and, though it grants a unit root into the price
level, and even it has engaged to as much long-term price reliability as does the gold standard
for horizons which are shorter than 30 years. Fisher's reimbursed dollar decreases price level
and inflation vagueness by an order of scale at all horizons. The traditional gold standard has
long been linked with long-run price steadiness. But short-run price indiscretion led censors
to suggest expansions that look typically like modern types of price-path targeting. This
examination has used a vibrant stochastic overall equilibrium model to examine price
dynamics under extra policy structures. Here, an inflation target delivered more short-run
price constancy than does the gold standard and, though it grants a unit root into the price
level, it hints to as much long-term price constancy as does the gold standard for horizons
smaller than thirty years. Fisher's rewarded dollar decreases price level and inflation
vagueness with an order of greatness at altogether prospects. According to Chernyshoff
(2007) this study is an acceptance of the gold standard strengthens or contracts
macroeconomic unpredictability. Followers believed so, critics believed not, and theory deals
indistinct infrastructures. A rigid exchange-rate system like the gold standard might edge
monetary jolts if it ties the hands of policy makers. But any conclusion to leave exchange-rate
elasticity might conciliation shock preoccupation in a world of real shocks and insignificant
stickiness. A simple model displays how an absence of elasticity can be eminent in the
broadcast of standings of trade shocks. Indication on the association between real exchange
rate unpredictability and terms of trade variability from the late nineteenth and early
twentieth century discoveries a pretentious alteration. The old-style gold standard engrossed
shocks, but the interwar gold standard didn‘t, and this past pattern suggests that the interwar
gold standard wasn‘t a upright rule assortment.
According to Coudert (2011) in this investigation, they look into the role of gold as a
harmless haven. They stretched the current writings in 2 means. First, they study crunch
stages consecutively distinct by recessions and bear markets. Second, ARMA-GARCH-X
model has been used to evaluate conditional co-variances between gold and stocks returns.
The regressions where run on monthly data for gold and numerous stock market indices.
They originated that gold succeeded as being a safe haven against all the stock indexes. The
outcome demonstrations that it holds for crunches named as recessions or bear markets, as
the covariance between gold and stocks returns is observed as negative or null in all
circumstances.
According to Demidova-Menzel (2007), this research observes the main forces for gold
investment. Since 2000 the prices of gold has increased considerably, considering gold an
inspiring add-on to a portfolio. As gold futures have negative roll yields, gold pool books are
measured by great credit risk and physical care of gold means great transaction costs, Xetra-
Gold may be the greatest well-organized way to enter the market. Xetra-Gold is a creation
shaped by the Deutsche Börse in the period of 2007, which is well-ordered like a security but
can be switched into physical gold any while. In the portfolio context gold has had a positive
inspiration on Euro and USD portfolios between the tenure of 2000 and 2006 because of
considerable yields and little correlation to other assets. But, this has not been factual for
nearly all other ages, the association was continuously low but the returns of gold were
approximately zero, which supersedes the positive alteration consequence. According to
Desquilbet, (2004) this research is regularly sustained that (CBs) and (GSs) are alike in that
they are rigid monetary rules, the two basic structures of which are great credibility of
monetary authorities and the existence of automatic adjustment mechanism. This article
contains a comparative analysis of these two types of systems both from the viewpoint of the
sources and mechanisms of generating credibility, and the elements of operation of the
automatic adjustment mechanism. Confidence under the GS is endogenously driven, while it
is exogenously determined under the CB. CB is a much more asymmetric system than GS
although asymmetry is a typical feature of any monetary system. The absence of credibility is
typical for peripheral nations and cannot be overcome totally even by ―hard‖ monetary
systems. Hammoudeh (2010) has determined that in this paper volatility and correlation
dynamics in price returns of gold, silver, platinum and palladium explores the corresponding
risk management implications for market risk and hedging. VaR examines the downside
market risk linked with investments in valuable metals, and to design ideal risk management
policies. They figured the VaR for chief valuable metals using the calibrated Risk Metrics,
different GARCH models, and the semi-parametric Filtered Historical Simulation approach.
Different risk management tactics are recommended, and the finest methodology for
calculating VaR based on conditional and unconditional statistical tests is acknowledged. The
economic importance of the consequences is emphasized by considering the daily capital
charges from the projected VaRs. The risk-reducing portfolio weights and dynamic hedge
ratios between different metal groups are also examined.
Acording to Kearney, 2008. Nearby 90% of the decrease in gold prices over the decade of the
1990s - from $393 in the beginning of 1990 to $286 in early 2000 - occurred after early 1995.
Whereas gold prices were dropping, the usage of derivative instruments by the gold mining
industry improved promptly. Conventionally, such activity would not be expected to affect
gold prices. In this paper, we examine the likely influence of derivatives on the gold market.
The research results propose that the use of derivatives by gold producers, whether it was to
hedge against the risk of decreasing gold prices probably pushed gold prices below what they
would have been based upon historical contacts. Conversely, when gold producers reduced
their net derivative positions over the April 1999:IV to January 2006 period, this de-hedging
seems to have helped improved gold prices back toward levels stable with longer run
fundamentals. Kearney, (2009) has concluded in this paper that gold and platinum prices are
positively linked over 1985-2006. So far, over smaller sample stages the link fluctuates from
positive to negative in the period of 1996-2001 and back. The purpose of this research was to
analyse whether this shift is the result, at least in part, of the rapid increase in forward sales
by gold producers, which led in the influence of considerably dropping gold prices in the
second half of the 1990s. The non-neutral short run impacts of derivatives on gold prices. The
outcomes demonstrates decreasing gold prices are related with great net upsurges in forward
sales, whereas increasing gold prices are linked with decreasing forward sales or producer
dehedging. According to Marzo, (2010), they have examined how the connection of gold
prices and the U.S. Dollar had been impacted by the current chaos in financial markets. They
have used spot prices of gold and spot bilateral exchange rates against the Euro and the
British Pound to analyze the pattern of instability spillovers. They have also projected the
bivariate structural
GARCH models planned by Spargoli e Zagaglia (2008) to gauge the causal links of
instability fluctuates in the two assets. They also applied the tests for change of codependence
of Cappiello, Gerard and Manganelli (2005). They recognized the capability of gold to
produce constant co movements with the Dollar exchange rate which have endured the latest
levels of market disruption. Their results even disclosed that exogenous rise in market
insecurity have inclined to generate reactions of gold prices that are extra steady than those of
the U.S. Dollar.
3. Methodology In order to investigate the volatility in International gold markets, gold prices data consists of
daily observation from January 1st 2006 to 1st January 2014 will be considered. We will be
studying and analyzing the volatility in gold price returns, for this we will be referring
different books on economics, research plans and articles, magazine, newspapers. However,
data will be collected from internet. We will also gather quantitative data and will try to
present it in the most appropriate manner and for that We will be using GARCH model,
charts, tables and different graphs and use of SPSS and Microsoft Excel software.
3.1 Data and Variables
To conduct this research, secondary data is collected. The data has been retrieved from
daily frequency. Variable in this study are the gold prices.
3.2 Sample
The time that will be focused for the sample is 1st January 2006 to 1st January 2014.
3.3 Models
The models which will be used to conduct this study are; Descriptive Model and
Econometric Model.
3.3.1 Gold Return
Since we are observing daily data of gold , we are going to get daily log returns for the
markets incorporated in our sample. The formulation for log returns is:
where,
Rt = gold returns at time‗t‘
Pt = gold price at time‗t‘
Pt-1 =gold price at 1st lag of time‗t‘.
3.3.2. Measures of Dispersion state how spread out the facts is around the mean. Measures
of dispersion are specifically supportive when data are normally distributed, i.e. thoroughly
look like the bell curve. The utmost mutual measures of dispersion follow.
1. Variance is specified as the addition of the squares of the differences between each
observation and the mean, that amount is divided with the sample size. For populations, it‘s
considered with the square of the Greek letter sigma (��). For samples, it‘s considered as
the square of the letter s (��). Consequently it is a quadratic appearance, i.e. a number
upraised to the second power, variance is the 2nd moment of statistics. Variance usage is‘nt
much common than standard deviation. It can be used if we want to subordinate the
contradiction of two or more sets of interval data. The more the variance, the more spread out
the data.
Formula for sample population:
2. Standard deviation is stated as the positive square root of the variance, i.e. μ for
populations and s for samples. Basically it is the average difference among observed values
and the mean. The standard deviation is used when stating dispersion in the a like units as the
original measurements. It is used more commonly than the variance in testifying the degree to
which data are spread out. Standard deviation is a widely used measurement of irregularity
used in statistics and probability theory. It shows how much dissimilarity there is from the
"average" (mean, or expected value). A low standard deviation specifies that the data points
tend to be very close to the mean, while high standard deviation specifies that the data are
spread out over a great range of values. Hypothetically, the standard deviation of a statistical
population, data set, or probability distribution is the square root of its variance. It is
algebraically easier however virtually less strong than the average absolute deviation. A
beneficial feature of standard deviation is that, not like variance, it is articulated in the same
units as the data. Standard deviation is frequently used to measure confidence in statistical
inferences. In science, researchers usually report the standard deviation of experimental data,
and only effects that fall far outside the range of standard deviation are measured statistically
significant – normal random error or disparity in the measurements is in this way notable
from causal disparity. Standard deviation is also very important in finance, where the
standard deviation on the rate of return on an investment is a measure of the volatility of the
investment.
Formula for sample population;
Where;
s=sample standard deviation
n= sample size
x= observations
3.3.3 Econometric Analysis
3.3.3.1 GARCH (p,q) Model
Generalized Autoregressive Conditional Heteroskedasticity model was revealed by Bollerslev
(1986). The GARCH volatility function shows the results of a GARCH stochastic, or random,
unpredictability model as applied to a historical time series of the price of an asset. GARCH
can be used to assess the impulsiveness of bonds, stocks, currency exchange rates, fund‘s
returns or commodities. GARCH supports to examine for patterns of inconsistency between
the historical volatility and the implied volatility. Such inconsistencies can suggest chances
for instability trading. GARCH can also be used for foreseeing variance study. GARCH is a
statistical model used by financial institutions to evaluate the instability of stock yields. These
facts are used by banks to help conclude what stocks will possibly deliver greater earnings,
also to estimate the yields of existing investments to help in the planning procedure. There
are several variations of GARCH, that includes NGARCH correlation, and also IGARCH that
limits the unpredictability parameter. Each model can be used to accommodate the definite
qualities of the stock, industry or economic state. In that situation, the GARCH (p, q) model
(where p is the order of the GARCH terms and q is the order of the ARCH terms ) is given by
GARCH (1,1) model specification
The Generalised Autoregressive Conditional Heteroskedasticity model was developed
independently by Bollerslev in 1986. There are 2 dispersed lags used to clarify inconsistency
under GARCH models, one on past squared residuals to capture great frequency effects or
news about volatility from the earlier period measured as lag of the squared residual from
mean equation, and second on lagged values of variance itself, to have long term influences
For GARCH (1, 1):
Where:
In the GARCH (1, 1) model, the variance probable at any given data is a mixture of a long
run variance and the variance probable for the previous period, adjusted to take into account
the size of the previous period‘s detected shock. In the GARCH model estimates for financial
asset yields data, the sum of coefficients on the lagged squared returns and trailing
conditional variance is very near to one. This infers that shocks to the conditional variance
will be extremely persistent and the occurrence of quite long remembrance but being less
than one it is still mean reverting. Although instability takes a long time, it eventually gets
back to the mean level of instability, just like a pendulum which detects and moves to and fro
motion about its mean position. It infers that existing information has no effect on long run
forecast. Long run average variance is that is only relevant when
4. Result and Discussion
4.1 Gold Price Return chart
The above graphs show unequal spread (variance) for Gold Prices from 1st January 2006 to 1st
January 2014. Econometrically speaking, unequal spread of residuals is referred to as
hetroskadastity.
4.2 Econometric Analysis
GARCH (1, 1) is applied through software. All three parameters of GARCH (1, 1) model are
significant for all markets as which means long run variance, 1st lag square returns, and
trailing variance are significantly explaining the conditional variance.
GARCH(1,1) estimation of Gold Price Returns
Omega = 3.33902299574238E-06
Alpha = 0.1034
Beta = 0.8910
All coefficients that are omega, alpha and beta values are significant as t – statistics is greater
than 2 and probability value is less than 0.05 for all coefficients. Hence, overall the model is
significant. Furthermore, the sum of parameters supposed to be either 1 or approaches 1.
W a B a+b w+a+b LRAV
0.000003 0.1034 0.8910 0.9944 0.9944 0.014457
-40.0%
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%Daily Returns
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
Mar/
06
Sep
/06
Mar/
07
Sep
/07
Mar/
08
Sep
/08
Mar/
09
Sep
/09
Mar/
10
Sep
/10
Mar/
11
Sep
/11
Mar/
12
Sep
/12
Mar/
13
Sep
/13
Standard Deviations : 10-day MA s(k)
Actual 10-day MA Standard Deviation
0.0%
5.0%
10.0%
15.0%
20.0%Aug 20/08 - Jan 100 market-day window
Long run average variances (LRAV) for the gold price returns are also calculated (using
which has derived 0.014457 which is 1.4457% of LRAV.
Since the sum of coefficients for both market returns‘ is less than 1, which is required to have
a mean reverting variance process. The process of mean reversion gets slower, as the sum of
coefficients gets closer to 1. As result shows that highest mean reversion value, that is 0.978.
5. CONCLUSION
Yes! There is volatility. From the test it shows a significant result and a positive sign that
volatility exists. While the econometric debate on the short range or long range nature of
dependence in uncertainty still goes on and it might never come to an end but these financial
models provides with a motivation to analyze the volatility and hence providing a useful
complement to econometric analysis and more research needed to make a complete
conclusion and recommendation that be given to the investor and reader. After being a source
of significant supply, central banks became net buyers in the gold market in the year of 2010.
Emerging market economies that have been going through fast economic success have been
the substantial gold buyers in order to diversify the external reserves. In the intervening time,
central banks of Europe, which for two decades had been selling gold, have almost, clogged
their sales in the wake of the financial European sovereign debt crunches. These two forces
have considerably reduced the supply of gold to the market.
The official sector tends to be highly risk averted and even the public remains concern all the
time regarding the fiscal and monetary conditions, any sales of gold, especially from the
progressive economies are likely to remain small. Meanwhile, emerging markets continue to
build large external reserves, to provide them with security in the face of ever challenging
market conditions. With the importance of gold universally reaffirmed by central banks,
developing economy‘s central banks are expected to endure buying Gold in order to conserve
state‘s treasure and to promote better market stability financially. Central banks continues to
be dedicated to the significance of gold and its importance in upholding strength and sureness
as they have been for many years.
6. Areas of Further Research Having conducted this research has given a valuable insight yet certain areas supposed to be
incorporated, these are:
To incorporate leverage effect by applying many other financial and economic model.
Impact of Gold prices on Inflation and with global stock market.
To compare volatility in bullish and bearish trend of different time eras.
To follow exponential smoothening techniques and forecast how would or it might
react due to economic role.
Investigate the Supply and demand of gold in detail.