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Cross Correlation Of Gold Prices And Exchange Rates Finance Essay

Gold is thought by many to be a currency without borders, being known around the world. While gold is influenced naturally by its supply and demand components, gold responds also to many macroeconomic factors including exchange rate and equity market. While gold provides diversification properties in a portfolio mix with equities, it also is alleged to act as a hedge against the U.S dollar as gold appears to have an inverse relationship with the currency. (Ciner, Gurdgiev, & Lucey, 2010). Cross correlation is a standard method of estimating the extent to which two series are correlated, so the main objective was to identify to which degree these two variables Gold Price in PKR and Exchange Rate (U.S. Dollar in PKR) are correlated.

Gold has provided a cushion against depreciation in the value of the dollar for two reasons. It firstly provides protection as it is a hedge against (US originated) inflation and secondly it provides a hedge against depreciation. Therefore it is not surprising that gold historically has been considered a hedge against fluctuation in the U.S. Dollar. Any depreciation in the dollar may fuel increased interest in gold due to the dilution in dollar's worth. Gold may then be considered to be the anti dollar (Capie, Mills and Wood, 2005).

In determining the extent to which gold acts as an exchange rate hedge, it is, therefore, well worth exploring the past, to see how well gold protected against currency fluctuations. That, in itself, is of interest, and it may also be of interest in the future (Capie, Mills and Wood, 2005).

Gold price has been in the centre of vivid discussions since the very beginning of economics as a science. Every recession since 1971 made these discussions severe (Ivan, 2009).

Problem Statement

The main objective of this paper was to investigate the cross-correlation between gold price fluctuation & Exchange Rate Dollar. This was estimated using econometric model of Cross correlation on yearly data from 1958-2009. Cross correlation is generally used when measuring information between two different time series. The range of the data is -1 to 1 such that the closer the cross-correlation value is to 1, the more closely the information sets are.

The US dollar exchange rate in PKR was taken as this was observed closest to the gold price in PKR. This rate was chosen as this is one of the most important foreign exchange markets that were in operation for the complete sample period, which is a yearly data from1958 till 2009 on an annual basis, had been used in the study.

Outline of the Study

The main notion to the study is to identify the underlying principles of the cross-correlation function. The degree of extend to which fluctuation in gold price & US Dollar was associated.

Hypothesis

H1: Cross Correlation of Gold Price & Exchange Rate (Dollar)

Literature Review

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 (Sjaastad, 2008). This suggested that the there is a relationship between the commodity prices and exchange rate, as the dollar was depreciating, the prices of commodity increased, and other things remaining constant.

The potential importance of this phenomenon is not limited to the major currency countries. With several minor currencies of the world being directly or indirectly tied to one of the three major currencies (the dollar, the euro, and the yen) or a currency basket, shocks to major currency exchange rates are felt not only by producers and consumers of internationally-traded commodities in major currency countries but also by many of the smaller, commodity-exporting countries in the form of inflationary (or deflationary) shocks transmitted by fluctuations in the international prices of commodities. The idea of the Australian dollar as a "commodity currency" is an example (Sjaastad, 2008). This stated that not only the commodity prices of major currency countries are affected by the shocks to major currency but also the minor currency countries are affected.

Gold price has been in the centre of vivid discussions since the very beginning of economics as a science. Every recession since 1971 made these discussions severe (Ivan, 2009).

Gold is also identified as a hedge against fluctuations in the U.S. Dollar on average, both in distressed and in normal market conditions. The properties of safe asset and hedging capabilities suggest that the dollar price of gold should increase when the bilateral exchange of the U.S. Dollar against other currencies depreciates. (Massimiliano & Paolo, 2010).

If gold is quoted in currencies other than the U.S. dollar such as sterling, it is converted using the foreign exchange rate closing price on the same day. Therefore, gold reflects the relative strength of the currency in which it is quoted. Any depreciation in the dollar may fuel increased interest in gold due to the dilution in the dollar’s worth. Gold may then be considered to be the anti-dollar (Ciner, Gurdgiev, & Lucey, 2010).

Gold is a prime candidate for a study of the effects on commodity prices of fluctuations in major currency exchange rates. A highly homogeneous commodity, gold is traded almost continuously in well organized spot and future markets. Moreover, as annual production (and consumption) of gold is minuscule compared with the global stock, the gold producing countries, not all of whose currencies are traded in organized markets, are unlikely to dominate the world gold market (Sjaastad, 2008). This stated that gold is the important variable to be considered when studying the effects on commodity prices of fluctuation in exchange rates.

That does not mean that gold could no longer be a good store of value or protection against exchange rate change. But whether it is or not depends on different forces. It depends on whether, when currencies weaken, people switch to gold; and on when currencies strengthen; they become more confident about the value of currencies, and switch from gold. Even though gold no longer has any role in the monetary system of any major country, such behavior could still be sensible (Capie, Mills, & Wood, 2005).

In determining the extent to which gold acts as an exchange rate hedge, it is, therefore, well worth exploring the past, to see how well gold protected against currency fluctuations. That, in itself, is of interest, and it may also be of interest in the future (Capie, Mills, & Wood, 2005). The first is a hedge against changes in the internal or domestic purchasing power of the dollar. The second is gold is a hedge against changes in the external purchasing power of the dollar. If gold were a perfect internal hedge, its dollar (i.e., nominal) price would rise at the same rate and time as a domestic US price index. If it were a perfect external hedge, its dollar (i.e., nominal) price would rise at exactly the same rate and time as the number of units of foreign currency per dollar fell (Capie, Mills, & Wood, 2005).

Gold as hedging asset or safe haven typically focuses on the pattern of correlation. A negative (conditional or unconditional) correlation is indicative of hedging capabilities. We consider a more general approach, and shed light on properties of the relation between gold and the Dollar that have not been considered previously. In particular, we study the evolution of the pattern of contagion between the two assets across the turmoil (Massimiliano & Paolo, 2010).

The relation between gold prices and the U.S. Dollar exchange rate has been subject to intense scrutiny. In particular, a significant body of literature attributes a value to gold of safe haven or hedging capabilities against exchange rate fluctuations (Massimiliano & Paolo, 2010).

Our results suggest that gold generates stable comovements with the Dollar that have indeed persisted during the recent phases of market disruption. We also show that exogenous volatility shocks tend to generate reactions of gold prices that are more stable than those of the U.S. Dollar (Massimiliano & Paolo, 2010).

Its importance is also stressed in Machlup (1941:[21]), in which the economist takes a retrospective view on the devaluation of the USD in 1933-34, i.e. the raising of the price of gold. (Hoang, 2004)

To the best of our knowledge, Ridler and Yandle (1972) were the first to analyze the effect of exchange rate changes on commodity prices. For a given commodity, the authors started from an equilibrium situation between the world demand for imports (which depends only on the world price of the commodity in importers' currency) and the world supply of exports (which depends only on the world price of the commodity in exporters' country). They then performed comparative static to obtain the percentage change in the dollar (numeraire) price of the commodity as a weighted average of the percentage change in exporters' and importers' nominal exchange rates in terms of the numeraire currency. The authors did not explicitly consider real exchange rates or other supply and demand variables (Dominique & V., 1996). This stated in Dominique paper that the effect of exchange rate changes on commodity prices were analyze by Ridler and Yandle in 1972, in which they formed an equilibrium b/w the world demand for imports and the world supply of exports.

Sjaastad (1985) analyzed the effects of the bilateral real exchange rates among the major currencies on the real (dollar based) price of the commodity. He advanced the hypothesis that changes in the exchange rates among major currencies will cause commodity prices to fluctuate independently of the movements in the general price levels of the major countries (Dominique & V., 1996). This stated that the studies were done on the effects of exchange rates among the major currencies on dollar price of commodity.

A key feature of Sjaastad's model is that the country that has the most influence in determining the world price of a commodity is not always the country in whose currency the commodity price is denominated. One can gain insight into this with an example from the financial markets (Dominique & V., 1996).

Sjaastad and Scacciavillani (1993) applied the model developed by Sjaastad (1985) to analyze the gold market for the period 1982-90. They use a dynamic econometric specification to study the effect of fluctuations in the real exchange rate among the major currencies on fluctuations in the price of gold (Dominique & V., 1996).

The empirical analysis focuses on three large financial markets (the US, the UK and Germany) with different currencies (US dollar, UK pound and the euro) in order to examine the differences and similarities of the role of gold in these markets (Baur & Lucey, 2010).

The volatility of the exchange rates among the major currencies since the dissolution of the Bretton Woods international monetary system has been a major source of price instability in the gold market. Indeed, the instability of real exchange rates between major currencies is responsible for nearly half of the observed volatility in the spot price of gold during the 1982-90 periods (Dominique & V., 1996).

Capie, Mills and Wood (2005) analyze the role of gold as a hedge against the dollar, finding evidence of the exchange-rate hedging potential of gold (Dirk & Thomas, 2009).

While gold is usually denominated in U.S. dollars, the dollar bloc has but a small influence on the international price of gold (Dominique & V., 1996).

The major gold producers of the world (South Africa, the former U.S.S.R., and Australia) appear to have no significant influence on the world price of gold (Dominique & V., 1996).

Moreover, gold is said to be uncorrelated with other types of assets which is an important feature in an era of globalization in which correlations increased dramatically among most asset types. These components might have contributed significantly to the role of gold (Baur & Lucey, 2010).

The world gold market is dominated by the European currency bloc who possesses approximately two-thirds of the 'market power' enjoyed by all participants in the market. Accordingly, real appreciations or depreciations of the European currencies have profound effects on the price of gold in all other currencies (Dominique & V., 1996).

The authors made clear that they do not claim their empirical findings for the gold case can be generalized to other commodities (Dominique & V., 1996).

The diversification property of gold and gold’s relationship with the equity markets have been subject to significantly increased examination over the last number of years. Jaffe (1989) reported that gold, while risky in its own right, has the propensity to provide valuable diversification qualities. (Ciner, Gurdgiev, & Lucey, 2010)

While cross correlations give a first hint at the time structure of the indicators with respect to developments in industrial production they do not necessarily imply causation in the sense of Granger (1969). A more refined analysis to determine the lead of each indicator quantitatively can be performed with Granger causality tests. This test is used to see how much of the current variable Y can be explained by past values use of Y and then to see whether adding lagged values of X can improve the explanation. Thus, X is said to Granger-cause Y if the X variable is statistically significant in the equation and therefore improves the forecast of Y (Hüfner & Schröder, 2002).

In time series analysis one often used concept is Granger causality. Given a TSCM we can derive the Granger causality among the time series variables in the TSCM. Generally, Granger causality and the graphic causal models are two different concepts: Granger causality concerns the prediction power of one time series for the another, a TSCM concerns the causal relation among time series variables at each time points. (Chen, 2010).

The study of Time Series Analysis had been a subject of interest in multiple focuses throughout history from the early astronomical forecasting to the modern day economic and technological (Diebold, Kilian, & Nerlove, 2006). Time series had been an important source of analysis and forecast, Harmonic analysis had been considered one of the original most methods of forecasting time series overtime (Diebold, Kilian, & Nerlove, 2006). Time series analysis had evolved from various stages to the current automated analysis through econometrics. Automated discovery in science is a fairly recent phenomenon. It is commonly associated with the newfound capacity to collect, store and process vast amounts of data in extremely short periods of time. These capabilities come from sheer computational power and storage capability in conjunction with electronic communication, data processing and statistical analysis. Rapid information processing accelerates learning. It also enables algorithms to be implemented that automate judgments and scientific evaluations that would otherwise be made by human participants. The upshot is that empirical and experimental research could now be conducted in an automated fashion with much more limited human involvement than in the past (Phillips, 2004).

In particular, Cowan and Sergeant (1996), Lyon et al. (1999), and Brav (2000) argue that stock returns become positively crosscorrelated in large samples, causing misspecified test statistics. Specifically, calendar clustering and overlapping returns are shown to represent two main sources of crosssectional dependence. (Antoniou, Arbour, & Zhao, 2006).

Mitchell and Stafford (2000) is perhaps the only paper that examines the cross-correlation effects on the post-merger stock performance of US acquirers. In their study, however, they exclude all the overlapping observations (i.e., multiple bids) from their sample2. But we know that overlapping returns represent a major source of cross-sectional dependence and that multiple bids constitute a large part of the overall merger population (Antoniou, Arbour, & Zhao, 2006).

Using cross correlations and Granger causality estimates we determine which of the indicators has the longest lead with regard to the year-on-year growth rates of industrial production. Additionally, we analyze lead/lag structures among the indicators, taking into account differences in the publication schedule (Hüfner & Schröder, 2002).

According to Granger (1969), a (weakly) stationary stochastic variable X can be said to cause another (weakly) stationary stochastic variable Y if and only if the information contained in the history of X helps improve the prediction of Y when the prediction model already contains the history of Y and all other relevant information (Atuker, 2010).

Research Methods

Methods of Data Collection

The secondary source of data is used for data collection. Data of gold price (per ounce) in PKR & U.S. Dollar in PKR for 52 years (from 1957 – 2009) had been collected through various websites. It was collected from the Commodity Traders of National commodities Exchange Ltd (NCEL), www.Kitco.com, Daily Business Recorder, & Pacific Exchange Rate Service, www.exchange-rates.org, www.forex.pk.

Sample Size

Annual observations of Gold price & U.S. Dollar of Pakistan was collected for 52 years starting from 1957 to 2009 had been included in the sample size. This is considered a sufficient sample size for running econometric cross correlation test.

Empirical Findings

Grangers Causality Test

Before performing the cross correlation test, granger’s causality test is run on the variables to test the casual relation between the variables amongst each other’s. This had resulted with the evidence of a bilateral relation between variables used in the study.

Granger’s definition of causality is a pragmatic one – defined in terms of predictability.1 In the bivariate case, Granger causality from X to Y (both as defined above) can be operationalised and tested as follows (Atuker, 2010)

where: a is the constant term; b’s and g’s are parameters to be estimated; p and q are lag lengths; and et is a well-behaved error term. X does not Granger-cause Y if (Atuker, 2010)

The granger causality model is based on keeping a 3.5 F-statistic threshold to find out the casual relationship among variables. That is if any variable with a higher than 3.5 F-statistic in regards to the other variable is considered to have a casual relation of the variable in opposition with the other variable.

Following outcome are generated using e-views

Based on the granger’s causality test, variables (Gold Price in PKR & Exchange Rate: US dollar in PKR) are found with bilateral relationship, this has been noticed in this paper’s results and many previous papers. Gold price in PKR had a strong causal relation with Exchange Rate: U.S. Dollar in PKR. Also there is a strong causal relation of U.S. Dollar in PKR with Gold Price in PKR. Both have threshold higher than 3.5F- Statistic, when Granger test was run, it showed 16.7913 F-Statistic which shows a strong causal relation of Gold in PKR with U.S. Dollar in PKR and it had even more strong causal relation for U.S. Dollar in PKR with Gold Price in PKR, which was 19.2676 F-Statistic.

Cross correlation Function

After Granger test was run, Cross correlation function was applied using SPPSS. Cross correlation is a standard method of estimating the degree to which two series are correlated. Consider two series x (i) and y (i) where i=0, 1, 2...N-1. The cross correlation r at delay d is defined as (Bourke, 1996)

http://paulbourke.net/miscellaneous/correlate/xcorrelate1.gif

Where mx and my are the means of the corresponding series. If the above is computed for all delays d=0, 1, 2,...N-1 then it results in a cross correlation series of twice the length as the original series (Bourke, 1996)

http://paulbourke.net/miscellaneous/correlate/xcorrelate2.gif

There is the issue of what to do when the index into the series is less than 0 or greater than or equal to the number of points. (i-d < 0 or i-d >= N) The most common approaches are to either ignore these points or assuming the series x and y are zero for i < 0 and i >= N. In many signal processing applications the series is assumed to be circular in which case the out of range indexes are "wrapped" back within range, ie: x(-1) = x(N-1), x(N+5) = x(5) etc (Bourke, 1996)

The range of delays d and thus the length of the cross correlation series can be less than N, for example the aim may be to test correlation at short delays only. The denominator in the expression above serves to normalise the correlation coefficients such that -1 <= r(d) <= 1, the bounds indicating maximum correlation and 0 indicating no correlation. A high negative correlation indicates a high correlation but of the inverse of one of the series (Bourke, 1996).

Sjaastad considered an internationally-traded homogeneous commodity, the price of which obeys the law of one price. He assumed that worldwide there are N trading blocs, that the numeraire currency, the dollar, is the currency of bloc 1, and that each bloc's commodity excess demand depends on the commodity price deflated by the general price level and on other supply and demand variables. World market clearing condition closed the model, which yields the following reduced form equation (Dominique & V., 1996).

where pt is the logarithm of the real (dollar based) commodity price, ejt is the logarithm of the bilateral real exchange rate between blocs 1 and j , Kt groups together other supply and demand variables and 0j is the elasticity of the real commodity price with respect to the bilateral real exchange rate between blocs 1 and j . Note that the 0js are between zero and one (Dominique & V., 1996).

Exchange_rate_RS with Gold_Price_RS

Cross Correlations

Series Pair: Exchange_rate_RS with Gold_Price_RS

Lag

Cross Correlation

-10

0

-9

-0.03

-8

0.022

-7

0.048

-6

0.07

-5

0.092

-4

0.056

-3

0.244

-2

0.23

-1

0.403

0

0.621

1

0.217

2

-0.003

3

-0.024

4

-0.03

5

0.032

6

-0.049

7

0.267

8

0.468

9

0.327

10

0.34

Cross Correlation Function when testing U.S. Dollar in PKR with Gold Price in PKR shows different behavior at different lags. Lag 0 shows that cross correlation was 0.621 which was significant and it showed that there was association between gold price in PKR of current year and US Dollar in PKR in current year. Lag 1 showed that Current year (year 0) exchange rates: US Dollar in PKR has an association with year 1 gold price in PKR. Lag 2 showed that current year US Dollar in PKR has no association with year 2 gold prices in PKR. Lag 3 showed that current year US Dollar in PKR has again no association with Gold prices in PKR. Lag 4 showed that current year US Dollar in PKR has again np association with Gold prices in PKR of 4th year. Lag 5 showed that current year US Dollar in PKR has negligible or no association with Gold prices in PKR of 5th year. Lag 6 showed that current year US Dollar in PKR has no association with Gold prices in PKR of 6th year. Lag 6 showed that current year US Dollar in PKR has again no association with Gold prices in PKR. Lag 7 which has cross correlation 0.267 showed that current year US Dollar in PKR has an association with Gold prices in PKR of 7th year. Lag 8 which has cross correlation 0.468 showed that current year US Dollar in PKR has an association with Gold prices in PKR of 8th year. Lag 9 which has cross correlation 0.327 showed that current year US Dollar in PKR has an association with Gold prices in PKR of 9th year. Lag 10 which has cross correlation 0.34 showed that current year US Dollar in PKR has an association with Gold prices in PKR of 10th year.

Lag -1 which has 0.403 cross correlation showed that year 0 (current year) US Dollar in PKR has an association with Gold prices in PKR of last year. Lag -2 which has 0.23 cross correlation showed that current year US Dollar in PKR has an association with Gold prices in PKR of 2nd last year. Lag -3 which has 0.244 cross correlation showed that current year US Dollar in PKR has an association with Gold prices in PKR of 3rd last year. Lag -4 which has 0.056 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 4th last year. Lag -5 which has 0.092 cross correlation showed that current year US Dollar in PKR has an association with Gold prices in PKR of 5th last year. Lag -6 which has 0.403 cross correlation showed that current year US Dollar in PKR has an association with Gold prices in PKR of 6th last year. Lag -7 which has 0.07 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 7th last year. Lag -8 which has 0.022 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 8th last year. Lag -8 which has 0.022 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 9th last year. Lag -9 which has -0.03 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 9th last year. Lag -10 which has 0.0 cross correlation showed that current year US Dollar in PKR has no association with Gold prices in PKR of 10th last year.

If it is to summed up then the Current year at lag 0, the US Dollar in PKR has an association with Gold price in PKR at 1 year after (lag 1), 1 year back (lag -1), 2 year back (lag -2), and 3 year back (lag -3), and then no association till lag 6 and then positive association till lag 10.

Conclusion and Discussion

The study investigated cross correlation analysis on the U.S. Dollar in PKR and Gold Price in PKR. The Granger’s Causality Test was run to see the causal relation between the variable among each other and the Cross Correlations test was run to check the degree to which both the variable are correlated. The purpose of the study was to investigate the cross correlation between gold price and US Dollar. The study encompassed data for 5 decades (i.e. 1957 – 2009).

Grangers Causality Tests suggested that variables (Gold Price in PKR & Exchange Rate: US dollar in PKR) are found with strong bilateral relationship which means that they both caused each other.

Cross Correlation suggested that US Dollar in PKR were significantly correlated overtime with Gold Price in PKR. And considering previous year it is not significantly associated. A close relationship exist between US dollar in PKR and Gold price, as there was no such lag in which they are negatively associated.

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