Gold and the Dollar (and the Euro, Pound, and Yen)

Journal of Banking & Finance 35 (2011) 2070–2083

Contents lists available at ScienceDirect

Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf

Gold and the Dollar (and the Euro, Pound, and Yen) Kuntara Pukthuanthong a, Richard Roll b,⇑ a b

San Diego State University, CA, USA UCLA Anderson School of Management, CA, USA

a r t i c l e

i n f o

Article history: Received 26 June 2010 Accepted 14 January 2011 Available online 22 January 2011 JEL classification: G10 G15 F31

a b s t r a c t Usually, gold and the Dollar are negatively related; when the Dollar price of gold increases, the Dollar depreciates against other currencies. This is intuitively puzzling because it seems to suggest that gold prices are associated with appreciation in other currencies. Why should the Dollar be different? We show here that there is actually no puzzle. The price of gold can be associated with currency depreciation in every country. The Dollar price of gold can be related to Dollar depreciation and the Euro (Pound, Yen) price of gold can be related to Euro (Pound, Yen) depreciation. Indeed, this is usually the case empirically. Ó 2011 Elsevier B.V. All rights reserved.

Keywords: Commodities Exchange rate Correlation Autoregression Granger causality Dynamic conditional correlation

1. Introduction Many observers have long noted a positive relation between the Dollar price of gold and weakness in the Dollar. Except on rare occasions, the Dollar price of gold increases when the Dollar depreciates against foreign currencies. This is puzzling because it seems to imply something special about the relation between Dollars and gold. Dollar depreciation rather than the depreciation of another currency such as the Euro seems on the surface to bring a higher price of gold. But why should there be such an asymmetry? Beckers and Soenen (1984) verify the gold/Dollar inverse relation empirically and draw a strikingly asymmetric implication for US and non-US investors. They say that the correlation between the Dollar price of gold and the Dollar’s weakness implies that . . .a non-US Dollar base currency investor will have to take into account his implicit foreign exchange risk position when he invests in gold or gold-linked instruments. It turns out that the total risk of his position valued in a non-US Dollar base currency is usually lower than when it is valued in US Dollars, (p. 112). They conclude that a non-US investor will want to hold more gold because of its implicit foreign exchange hedging properties. ⇑ Corresponding author. Tel./fax: +1 310 825 6118. E-mail addresses: [email protected] (K. Pukthuanthong), [email protected] (R. Roll). 0378-4266/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2011.01.014

Sjasstad and Scacciavillani (1996) begin their paper by arguing that . . .when the Dollar depreciates against the Deutsche mark, Dollar prices of commodities tend to rise (and DM prices fall) even though the fundamentals of the markets-all relevant factors other than exchange rates and price levels-remain unchanged, (p. 879). This contention is implicitly related to the law of one price applied to gold. If the gold price is fixed with respect to some world numeraire, then its price in a depreciating currency will rise and its price in an appreciating currency will fall. The prices of gold expressed in the two currencies will move in opposite directions. But this contradicts a well-known empirical fact, which we will verify below, that gold prices are strongly positively correlated across both depreciating and appreciating currencies. After an extensive theoretical development and rigorous testing, these authors conclude that the gold price/exchange rate connection is ruled by the largest trading blocs, in particular Europe. They say, The world gold market is dominated by the European currency bloc, which possesses about two-thirds of the ‘market power’ enjoyed by all participants in that market. Accordingly, real appreciations or depreciations of the European currencies have profound effects on the price of gold in all other currencies, (p. 893). Capie et al. (2005) study the relation between the Dollar price of gold and the Pound/Dollar and Yen/Dollar exchange rate. They too confirm that Dollar gold prices tend to rise when the Dollar depre-

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

ciates. They do not consider the possibility that the same relation might prevail for gold in other currencies and those currencies’ depreciation. Generalizing beyond gold, Clements and Renee (2008) study the joint determination of the prices of ‘‘commodity currencies’’ and ‘‘currency commodities.’’ Countries that are thought to have ‘commodity currencies’’ include Australia, Canada, New Zealand, and several developing countries that are rich in natural resources. The value of commodity currencies is hypothesized to depend on commodity prices. But there is presumably bivariate causality in that the prices of currency commodities depend on the exchange rates of commodity-exporting countries. The authors find that currencies are less affected by commodity prices than commodity prices are affected by currencies. They conclude that commodity-currency research failing to account for endogeneity between currency and commodity returns may be misspecified. Sari et al. (2007) study the dynamic relations among the futures prices of oil, gold, silver, and cooper. They find a strong connection between gold and silver while copper appears to be nearly independent of movements in the prices of the other commodities. Gold and silver, but not copper, help explain the volatility of forecast errors in oil prices. In addition, exchange rates help explain the volatility in oil and metals. Since their analysis is focused on the volatility of forecast errors, their findings are particularly well suited for derivatives markets where volatility is a key valuation factor. Sari et al. (2010) investigate the relations among precious metals, oil, and the US$/Euro exchange rate. They find no long-run equilibrium relations between commodity returns and changes in the exchange rate so they suggest diversification into the precious metals in the long run. However, they also find that precious metal prices and exchange rates are closely linked in the short run (2 days) and that aftershocks occur. Lizardo and Mollick (2010) investigate the relation between oil prices and the US$. They find that increases in real oil prices lead to a significant depreciation of the US$ against the currencies of oil exporter countries including Canada, Mexico, and Russia. On the other hand, an increase in oil prices brings depreciation relative to the US$ in the currencies of oil importers such as Japan. Moreover, when oil prices increase, the US$ tends to decline relative to currencies of countries that are neither net exporters nor significant importers, such as the UK. Although our principal focus in this paper is on gold, the Appendix A here provides a similar analysis for the relations among currency depreciations and oil prices. Journalists are fond of periodically writing about gold and the Dollar. Recently, for example, Gaffen and Slater (2009) cited evidence that For the better part of this decade, the price of gold and the value of the US dollar tended to move reliably in opposite directions. . .Lately, though, gold and the dollar have been rising in tandem. . .Investors worldwide are stashing bullion. At the same time they’re buying the US dollar, (p. C1). These authors attribute the recent positive correlation by a sudden desire by global investors to flee into the safest assets, which, ironically given current conditions in the US, are alleged to be gold and the Dollar. In contrast to much of the received academic and popular literature, our contention here is that there is nothing special about the relation between the Dollar and gold. The same phenomenon occurs in other major currencies and probably in all freely convertible currencies. A rise in the price of gold in a currency is usually associated with a depreciation in the currency’s value,

2071

not just for the Dollar but also for the Euro, Yen and Pound. Moreover, the effect happens simultaneously in all currencies. It may be hard intuitively to accept this, yet it is indeed a fact and will be proven below. In addition, gold prices in different currencies are strongly and positively correlated, not negatively correlated as in the Sjaastad/Scacciavillani scenario. This is a key to understanding the non-intuitive nature of our principal contention.

2. An exchange rate/gold price identity It will be helpful when understanding the relations among gold prices and exchange rates to consider a basic identity between covariance and variances to be described below. We first need a little notation. A log price relative between successive periods will be denoted by a symbol such as $/¥ or £/oz, which means, for example,

$=U ¼ lnf½Dollar price of Yen;ðDollars per YenÞ; in period t= ½Dollar price of Yen in period t  1g where the time units are arbitrary but are trading days in the empirical work to follow. Standard symbols are used for currencies and ‘‘oz’’ stands for ounces of gold, so similarly,

£=oz ¼ ln½ðPound price of gold in period tÞ= ðPound price of gold in period t  1Þ: The identity is written in Eq. (1) below for gold, Dollars and Yen, but it holds for any commodity that obeys the law of one price and for any pair of convertible currencies. It is

Cov½ð$=ozÞ; ð$=UÞ þ Cov½ðU=ozÞ; ðU=$Þ ¼ Var½ð$=UÞ:

ð1Þ

Proof. First note that 1 involves log price relatives, or equivalently, continuously-compounded rates of return between t  1 and t. Note also that for any positive x and y, ln(x/y) = ln(y/x) and also that var[($/¥)] = var[(¥/$)]. Thus, the first covariance in (1) can be rewritten as

Cov½ð$=ozÞ; ð$=UÞ ¼ Covf½ð$=ozÞ þ ðU=$Þ  ðU=$Þ; ½ðU=$Þg ¼ Covf½ðU=ozÞ  ðU=$Þ; ðU=$Þg ¼ Cov½ðU=ozÞ; ðU=$Þ þ Var½ðU=$Þ: The first covariance here cancels the second covariance in (1). h Although simple, identity (1) has some interesting implications for the correlations between gold prices in different currencies and corresponding exchange rates. Because the right side of (1) is an exchange rate variance and thus is strictly positive, both covariances on the left cannot be negative. If one is negative, its companion must be positive and relatively large. But there is nothing to prevent both covariances in (1) from being positive. This is an empirical issue. Note that when both covariances are positive, the Dollar price of gold is correlated with a depreciation in the Dollar relative to the Yen and also the Yen price of gold is correlated with a depreciation in Yen relative to the Dollar; i.e., gold prices go up when the currencies for both countries depreciate. The signs of both covariances on the left side of (1) can be expressed as functions of the volatility of gold returns in each currency and the cross-country correlation in gold returns. Noting that the log change in the exchange rate can be decomposed as ($/¥) = ($/oz)  (¥/oz), and similarly for its reciprocal, we have

2072

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

2.0

In this region, gold price changes are positively correlated with the depreciation of currency B but not currency A

λ = Ratio of Gold Price Change Standard Deviations (B/A)

1.8

1.6

λ

ρ

1.4

In this region, gold price changes are positively correlated with the depreciation of both currencies; (This region extends also over the entire area where the gold correlation is negative)

1.2

1.0

Observations involving the Dollar, Euro, Yen and Pound

0.8

0.6

λ ρ

In this region, gold price changes are positively correlated with the depreciation of currency A but not currency B

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ρ = Correlation of Gold Price Changes Expressed in Two Currencies Fig. 1. Gold correlation, gold volatility and currency depreciation or appreciation.

45

40

Price of Gold per Ounce, January 1, 1971=1.0

35

30

25

20

15 Pound 10 Dollar DM-Euro

5

Yen

0

Fig. 2. Gold prices in four currencies.

0.9

1.0

2073

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Cov½ð$=ozÞ; ð$=UÞ ¼ Cov½ð$=ozÞ; ð$=ozÞ  ðU=ozÞ ¼r

2 s=oz

 qrU=oz r$=oz

 1  qk; and Cov½ðU=ozÞ; ðU=$Þ ¼ Cov½ðU=ozÞ; ðU=ozÞ  ð$=ozÞ

Table 1 Gold price correlations in four major currencies. Using data from January 1971 through December 2009, daily log price relatives for gold denominated in different currencies are related. The Euro was spliced with the Deutche Mark prior to 1999. Trading days are eliminated if they are exchange holidays in any country. The remaining sample includes 8955 trading days.

¼ r2U=oz  qrU=oz r$=oz  k  q where r¥/oz and r$/oz are the standard deviations of the Yen and Dollar log gold price changes, respectively, k is their ratio, (k r¥/ oz/r$/oz), q denotes the correlation between the Dollar and Yen log gold price changes and the symbol  means ‘‘has the same sign as.’’ If the cross-currency gold correlation q happens to be negative, both covariances in (1) are positive. They are both also positive when q is positive and q < k < 1/q. The first covariance is negative and the second one positive when k > 1/q while for k < q, they again have opposite signs but the second one is negative. As we have already seen, both covariances cannot be negative. The respective regions with differing covariance signs are shown in Fig. 1. An equivalent expression to (1) can be obtained by considering a bivariate regression of the gold price log return on the log exchange rate relative. The slope coefficients from such regressions are, of course, the ratios of the covariances on the left of (1) and the variance on the right, so the slope coefficients must satisfy b$|¥ + b¥|$ = 1. This is simply another way to write the identity (1). If the bs are both positive, they must also both be less than 1.0. If q¥/oz,¥/$ denotes the correlation between the Yen price of gold price and the Yen exchange rate per Dollar, then b¥|$ = q¥/oz,¥/$(r¥/ oz/r¥/$). Since q¥/oz,¥/$ is bounded by ±1, b¥|$ will be less than one in absolute value unless the gold price is more volatile than the exchange rate. But our identity stipulates that b$|¥ + b¥|$ = 1 and since r¥/$ = r$/ ¥, another way to write the identity is q¥/oz,¥/$r¥/oz + q$/oz,$/¥r$/ oz = r¥/$. Now suppose the volatility of gold is similar in both Yen and Dollars. If these volatilities are equal, then q¥/oz,¥/$ + q$/oz,$/ ¥ = r¥/$/r¥/oz < 2, so the exchange rate volatility can be no larger than twice the volatility of gold. Of course, if the correlations are relatively modest, this upper constraint on exchange rate volatility is far from binding. When the law of one price holds for any other commodity, the identity (1) is also valid for the Dollar and Yen prices of that commodity. Usually, the law of one price holds fairly closely for any item whose physical presence is not an essential attribute of ownership and there are no impediments to capital flows. Gold is a good example but others include financial assets traded in both markets, such as cross-listed shares, and other precious metals or gemstones. 3. Data All the data used hereafter are downloaded from DataStream, a division of Thomson Financial. The sample period extends from January 2, 1971 through December 10, 2009, the latest available date at the time of downloading. The gold bullion price is the New York fixing at the close of trading each day. This is established at approximately the same time as exchange rates between the US Dollar and the Euro,1 Yen, and Pound. Relying on the law of one price, the US Dollar price of gold is converted into the other three currencies simply by multiplying through by the Dollar exchange rate per subject currency. Similarly, exchange rates among the non-Dollar currencies are obtained by dividing the Dollar price of one currency by another. 1

Prior to 1999, the Deutche Mark replaces the Euro as the latter began trading only on January 1, 1999.

Euro/oz Yen/oz Pound/oz

US$/oz

Euro/oz

Yen/oz

.8828 .8823 .9012

.8808 .9295

.8610

Table 2 Volatilities and kurtoses of gold prices and foreign exchange rates. Daily standard deviations of gold log price relatives and log exchange rate relatives are calculated from January 1971 through December 2009 inclusive. Daily log relatives are equivalent to continuously-compounded daily returns and are expressed as percent per day. Exchange rate reciprocals are identical since volatilities of logs are invariant with respect to sign. Excess kurtosis is the daily fourth moment divided by the standard deviation to the fourth power minus 3.0. The last panel reports the excess kurtosis of GARCH(1,1) residuals. The Euro was spliced with the Deutche Mark prior to 1999. Trading days are eliminated if they are exchange holidays in any country. The remaining sample includes 8955 trading days. Gold

Exchange rate Dollar

DM-Euro

Yen

(A) Standard deviation (%/day) Dollar 1.341 DM-Euro 1.339 Yen 1.405 Pound 1.337

0.649 0.669 0.595

0.673 0.502

0.726

(B) Excess kurtosis Dollar 26.6 DM-Euro 25.5 Yen 23.1 Pound 25.8

5.23 8.89 4.38

7.40 9.71

7.94

2.42 6.72

3.34

(C) Excess kurtosis of GARCH(1,1) residuals Dollar 4.76 DM-Euro 15.4 7.62 Yen 16.4 8.29 Pound 13.9 4.07

We also downloaded the daily closing values for the S&P500, DAX 30, TOPIX, and FTSE All Shares indexes. These are used to identify suspected holidays. If the index value in any of the four countries is identical to five decimal places on successive days, the second date is suspected to be a holiday in that country and not used in the calculations for any country. This assures simultaneous valid observations.2 4. Results Fig. 2 plots gold prices expressed in each currency over the sample period. Two aspects are apparent after a casual ocular inspection. First, there is a net increase in the price of gold that diverges across countries because of differing exchange rate appreciations. The Japanese Yen appreciated the most over these 39 years relative to the other currencies, so the Yen price of gold has the lowest overall increase. This was followed in order by the increases of gold prices expressed in the DM-Euro, Dollar, and Pound. Second, gold price changes are highly correlated across countries and display significant volatility. The strength of cross-country correlations in gold prices is verified for the entire sample in Table 1, which uses daily log price relatives of gold. Every correlation exceeds .86 and two are above .9. 2 We repeated the calculations using all posted values on DataStream and also eliminating suspicious holidays only for the suspected country. The results are virtually identical in all respects.

2074

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Table 3 Gold prices and exchange rates. Correlations and slope coefficients are reported from bivariate regressions between daily log gold price relatives in different currencies and daily log changes in exchange rates. These are equivalent to continuously-compounded daily returns. Prior to 1999, the Deutche Mark replaces the Euro. The data extend from January 1971 through December 2009, a total of 8955 non-holiday trading days. The slope coefficients conform to identity (1) in the text; sums of the off-diagonal pairs are 1.0. For example, the Euro/oz-Dollar coefficient, .4958, and the US$/oz-Euro coefficient, .5042, sum to unity. Gold

Exchange rate, currency of gold price per Dollar

Euro

Yen

Pound

Correlation US$/oz Euro/oz Yen/oz Pound/oz

.2440 .2401 .3317 .2164

Dollar

Euro

Yen

Pound

0.5042

0.3033 0.3018

0.5140 0.5126 0.6764

Slope coefficient, b

.3345 .1831

.1513 .1516

.2282 .1923 .3495

.1756

Fig. 1, which was introduced in Section 2, displays the three distinct regions where gold price returns and currency depreciation have particular signs. The region q < k < 1/q is characterized by a positive correlation between gold price changes and currency depreciation. All four countries in our sample are located within this region; (q is taken from Table 1 and k is computed from the standard deviations in the first column of Table 2, Panel A). This is not surprising given that the volatilities of gold returns are similar in the four currencies. The rather high gold correlations, however, place the countries close to the edge of the region and one might well imagine that other countries could lie outside and thus exhibit a positive relation between gold prices and currency appreciation, unlike the Dollar, Euro, Yen and Pound. Table 2, Panel A reveals also that gold’s daily return volatility is roughly twice the size of the daily exchange rate return volatility. As discussed in Section 2, when gold price volatility is the same in two countries, there is a constraint on exchange rate volatility. It can be no larger than twice the volatility of the gold return. However, as shown in Table 2, exchange rate volatility does not even approach this upper bound, which implies that correlations between gold returns and exchange rate returns are not that large. Panel B of Table 2 reports excess kurtosis, the standard measure of tail thickness relative to a Gaussian distribution.3 All the excess kurtoses are positive, thus indicating fat tails or, put more simply, relatively frequent extreme observations. Sample skewness (not reported) is close to zero for all series, so the extreme observations are in both tails. Notice that excess kurtosis is considerably larger for gold returns than for exchange rate changes. One well-known cause of thick tails is non-constant volatility. Even if returns are conditionally Gaussian, movement in the variance over the sample will make the unconditional distribution appear to have thicker tails than Gaussian. We assess the extent of this effect by first fitting a standard GARCH(1,1) process to the variance and then examining the excess kurtosis of the GARCH residuals. If the GARCH model properly accounts for movements in the variance and the returns are indeed conditionally Gaussian, then the GARCH residuals would have little remaining excess kurtosis. Panel C of Table 2 reports these results. First, notice that for gold returns, the GARCH residuals have much smaller excess kurtoses than the raw returns, but they still have some. For some of the exchange rate changes, there is little reduction in kurtosis between GARCH residuals and the underlying series and some residuals (e.g., the Dollar/DM-Euro exchange rate change) actually have moderately larger excess kurtosis. For the Yen/Pound and Yen/DM-Euro, however, the reduction is substantial though there still remains some indication of thick tails even in these distributions. 3 Excess kurtosis is the ratio of the fourth sample central moment to the fourth power of the sample standard deviation minus three. Its expectation is zero for a Gaussian distribution.

0.4958 0.6967 0.4860

0.6982 0.4874

0.3236

There are two possible explanations: (1) a GARCH(1,1) process does not capture the full richness of volatility movements in these series or (2) thick tails are not entirely attributable to non-constant volatility, or both (1) and (2). Fortunately, since we focus mainly on correlations, thick tails might be less problematic than in many some applications; correlations are of course bounded between 1 and +1. Hence, the probability distributions of the correlation coefficients will possess all higher moments. Hence, according to the central limit theorem, repeated observations of the sample correlation coefficient drawn from independent and identically distributed observations should be asymptotically Gaussian. We also examined the return series for non-stationarity by subjecting them to an augmented Dickey/Fuller unit roots test. In all cases, the hypothesis of a unit root was rejected with a p-value of 0.0001 or smaller. Not surprisingly, these daily log change series are decidedly stationary. The left section of Table 3 reports correlations between gold returns and exchange rate returns over the entire sample. All the correlations are positive but rather modest in magnitude, ranging from about .15 to about .35. The average is .23. Since each correlation is positive, the results confirm that over 39 years taken in their entirety, gold prices in every currency tended to rise simultaneously with a depreciation in that same currency. There is nothing unique about the Dollar in this regard. In fact, correlations between the Dollar price of gold and the Dollar’s depreciation against the Yen and Pound are below average; (the correlation against the Yen is the smallest in the table). The Yen is at the other end of the spectrum; the Yen price of gold is correlated more than .3 with Yen depreciation against the Dollar, Euro and Pound. Note that these correlations are independent of long-term trends in the rate of appreciation or depreciation. The Yen appreciated materially against the other three currencies over the entire sample period, but when it did depreciate, the Yen gold price tended to be more closely connected to the depreciation. The right side of Table 3 reports slope coefficients (bs) from bivariate regressions of gold returns on exchange rate returns. As the table’s heading point out, the identity discussed in Section 2 is satisfied in every case. The sum is exactly 1.0 for the two bs in symmetrically-positioned off-diagonal cells. Note also that the bs are uniformly larger than the corresponding correlations, which is necessarily true when the volatility of gold returns is larger than the volatility of exchange rate returns, as it is in every case (Table 2, Panel A). Finally, all the bs are positive, again indicating that gold prices are related to depreciation in every currency. Although the previous results show that the gold price rises when the currency depreciates over the entire 1971–2009 period, there might have been material deviations from this pattern during particular sub-periods. Assessing this possibility is tricky, though,

2075

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Panel A. Within Calendar Years, 1971-2009 0.7 0.6 0.5 0.4

Correlation

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 1971

1976

1981

1986 DM-Euro

1991 Yen

1996

2001

2006

Pound

Panel B. Daily Dynamic Conditional Correlation

0.7

0.5

Correlation

0.3

0.1

-0.1

-0.3

-0.5 1971

1976

1981

1986

1991

1996

2001

2006

Fig. 3. Correlation between Dollar gold return and Dollar depreciation.

because statistical error can creep in when the number of observations is reduced. Even though the true correlations might be uniformly positive, their sample estimates could at times be opposite in sign. As a compromise between estimation error and

true variation, we decided to compute the correlations in two different ways. First, we computed the correlation within each calendar year. The number of simultaneous non-holiday observations varies between 220 and 237 depending on the year. Second, from

2076

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Panel A. Within Calendar Years, 1971-2009 1

0.8

Correlation

0.6

0.4

0.2

0

-0.2

-0.4 1971

1976

1981

1986

Dollar

1991

Yen

1996

2001

2006

Pound

Panel B. Daily Dynamic Conditional Correlation 0.8

Correlation

0.6

0.4

0.2

0

-0.2

-0.4 1971

1976

1981

1986

1991

1996

2001

2006

Fig. 4. Correlation between DM-Euro gold return and DM-euro depreciation.

daily data over the entire time period (8955 days), we computed the Engle’s (2002) dynamic conditional correlation (hereafter DCC).4 The results are plotted in Figs. 3–6 for the Dollar, DM-Euro, Yen and Pound, respectively. In each figure, the correlation is depicted between the log gold return in the subject currency and that currency’s daily log depreciation. Panel A of each figure plots the cor-

4 The DCC was computed using the ‘‘integrated’’ method. See Engle (2002, equation 17). He refers to this as the ‘‘DCC LL INT’’ estimator; see Engle (2002, p. 342.)

relation for each calendar year while Panel B presents the dynamic conditional correlation. Not surprisingly, the correlations are usually positive, but only the Yen has no negative calendar year correlation; the DCC for the Yen does fall below zero slightly around 1976 and with respect to depreciation against the Dollar in the first half of the 1980s. For the Dollar, there are negative calendar year sample correlation estimates around 1974–1975 and 1991–1992. This is matched by the DCC values near the same periods and, with respect to depreciation against the Yen, in the second half of the 2000 decade.

2077

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Panel A. Within Calendar Years,1971-2009 1 0.9 0.8

Correlation

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1971

1976

1981

1986

Dollar

1991

DM-Euro

1996

2001

2006

Pound

Panel B. Daily Dynamic Conditional Correlation 0.75 0.65 0.55

Correlation

0.45 0.35 0.25 0.15 0.05 -0.05 -0.15 1971

1976

1981

1986

1991

1996

2001

2006

Fig. 5. Correlation between Yen gold return and Yen depreciation.

The DM-Euro has negative calendar year estimates around 1981. However, the DCC, particularly with respect to depreciation against the Yen, was negative more often (but for shorter periods). The Pound also had some negative calendar year correlations around 1981, in 1991 (against the DM) and in 2006–2007. Again, such negative correlations were more frequent according to the DCC but they were of shorter duration. The asymptotic standard error of the correlation coefficient is approximately T1/2, where T is the sample size; this is around

.066 for a typical annual sub-sample of 230 daily observations. Hence, the observed annual sample correlation would have to be less than .132 to conclude that it is statistically significantly negative at a conventional level. Using the actual number of daily observations in each calendar year, the observed correlation was two standard errors less than zero nine times over the 4(3)(39) = 468 country/exchange rate/ year possibilities. These occasions were as follows: The Dollar in 1975 against the Pound and in 1991 against the Yen; the Euro in

2078

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Panel A. Within Calendar Years, 1971-2009 1

0.8

Correlation

0.6

0.4

0.2

0

-0.2

-0.4 1971

1976

1981

1986 Dollar

1991 DM-Euro

1996

2001

2006

Yen

Panel B. Daily Dynamic Conditional Correlation

0.8

0.6

Correlation

0.4

0.2

0

-0.2

-0.4 1971

1976

1981

1986

1991

1996

2001

2006

Fig. 6. Correlation between Pound gold return and Pound depreciation.

1979 against the Dollar, in 1980 against the Yen and in 2007 against the Dollar and Yen; the Pound in 1980 against the Dollar and Yen and in 1991 against the Euro.5 As mentioned already, the Yen never had a negative computed value. Nine ‘‘significantly’’ negative correlations in 468 attempts represent roughly 1.9% of the country/exchange rate/years, which could happen merely by chance. At the other extreme, Table 4 reports the percentage of sample years when the correlation is positive and at least two standard errors above zero. By chance, this would happen less than 2.5% of the time, but the results in Table 4 show reveal something very differ-

5

For each of these same instances and for no others, the bivariate slope coefficient (b) had a t-statistic algebraically less than 2.

Table 4 Percentage of significant positive correlations between gold prices and currency depreciation. Correlations are computed during each calendar year, 1971–2009 inclusive, between the log price relative of gold in a currency and the depreciation of that currency against other currencies. This table reports the percentage of years out of 39 possible that the correlation is positive and two standard errors above zero. Gold

Exchange rate, currency of gold price per Dollar

US$/oz DM-Euro/oz Yen/oz Pound/oz

71.8 79.5 69.2

DM-Euro

Yen

Pound

69.2

56.4 64.1

61.5 64.1 94.9

92.3 74.4

69.2

2079

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Dollar Gold Return and Dollar Depreciation against- the DM-Euro 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 1971

1976

1981

1986 Average DCC in Year

1991

1996

2001

2006

Correlation during Year

Fig. 7. Simple correlation vs. average dynamic conditional correlation Dollar Gold Return and Dollar Depreciation against the DM-Euro.

Table 5 Fraction of days that the dynamic conditional correlation is positive. Engle’s (2002) dynamic conditional correlation (DCC) is computed between daily gold returns in four currencies and that each currency’s daily depreciation (log change) against the others. The table reports the percentage of days for which the DCC is positive. There are 8955 trading days in the sample, which spans 1971–2009. Gold

Exchange rate, currency of gold price per Dollar (%)

US$/oz DM-Euro/oz Yen/oz Pound/oz

Table 6 Autoregressions of daily gold returns and daily changes in exchange rates. The dependent variable is the daily log price relative of gold expressed in four currencies or the daily log relative of the Dollar price of three currencies. Two lagged values of the dependent variable are the explanatory variables. Coefficients are reported with accompanying t-statistics in parentheses. There are 8955 daily returns in the sample.

85.07 91.75 86.86

DM-Euro (%)

Yen (%)

Pound (%)

89.19

81.09 82.50

86.78 93.69 97.96

98.89 85.80

Lag 1 day

Lag 2 days

Adjusted R-square

0.0384 (3.631)

0.0092 (0.871)

0.0013

DM-Euro/oz

0.0547 (5.175)

0.0290 (2.746)

0.0034

Yen/oz

0.0348 (3.291)

0.0094 (0.888)

0.0011

Pound/oz

0.0397 (3.752)

0.0110 (1.042)

0.0014

0.0019 (0.183)

0.0000

Gold returns US$/oz

85.34

ent. For every currency, there is a highly significant positive relation between gold prices and currency depreciation in the majority of years. This even happens over 90% of the time for the Yen price of gold and depreciation of the Yen against the Euro and Pound. The dynamic conditional correlations (DCCs) present a somewhat different picture. First of all, as Figs. 3–6 clearly show, the DCCs are extremely volatile and exhibit some extreme movements over rather short periods. For example, the correlation between the British Pound gold return and the Pound’s depreciation against the DM changes from around 0.377 on September 16, to +0.543 on July 29, 1993; the correlation then falls back to 0.0841 by the end of the year. Nonetheless, the general pattern of the DCCs agrees well with the calendar year correlations; annual averages of the DCCs are close to simple calendar year correlations. This is illustrated in Fig. 7, where the calendar year simple correlation is plotted alongside the average DCC for the same calendar year. Fig. 7 is just an example, the Dollar gold return and the Dollar depreciation against the Euro, but the other cases show a similar close connection. Short-term excursions of the DCCs from longer-term averages are indeed impressive, but as reported in Table 5, the DCCs are po-

Exchange rate changes $/DM-Euro 0.0139 (1.315) $/Yen

0.0039 (0.365)

0.0223 (2.110)

0.0003

$/Pound

0.0606 (5.736)

0.0027 (0.255)

0.0035

sitive most of the time. The DCCs are positive on at least 80% of the sample days for all currencies and more than 90% of time for the Yen.6 Hence, based on the calendar year correlations and the DCCs, it seems safe to conclude that gold prices and currency depreciation usually go together for each of these currencies. To this point, we have examined only daily gold returns in various currencies and simultaneous daily movements in exchange 6 The DCC is positive on almost 99% of the sample days for the Yen gold return and the Yen’s depreciation against the DM-Euro.

2080

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Table 7 Granger causality from vector autoregressions. The table contains p-values that indicate if the column variable Granger causes the row variable. When the dependent variable is a gold return, two lagged daily gold returns in the same currency are included on the right side of the VAR to control for microstructure bid/ask bounce (not shown). When the dependent variable is an exchange rate change, three lagged values of the gold return in the denominator currency (the non-dollar currency) are included. For all exchange rate changes, three daily lags are included. The p-values are for a joint test that all three daily lags together are significant. Significance at the 1% level or better is indicated by an asterisk. There are 8955 time series observations in the original sample. Dependent variable

Gold return

$/DM-Euro

Gold returns being caused by column variable US$/oz 0.0000⁄ DM-Euro/oz 0.0440 Yen/oz 0.0030⁄ Pound/oz 0.0010⁄ Exchange rate changes being caused by column variable $/DM-Euro 0.2000 $/Yen 0.9630 0.1500 $/Pound 0.2410 0.0010⁄

$/Yen

$/Pound

0.7770 0.9610 0.0270 0.9920

0.0420 0.1090 0.1760 0.0000⁄

0.1910

0.4330 0.1870

0.3580

rates. Although it is not germane to our principal message, it seems worthwhile to briefly document the relations among of various leads and lags of these variables. To this end, we first look for microstructure phenomena in the daily returns, specifically the bid/ask bounce induced by successive daily transaction prices executing at one side or the other of the spread. A simple univariate autoregression suffices for this purpose and is presented in Table 6 for each of the four daily gold returns and three daily changes in exchange rates.7 The gold returns all display significant negative coefficients at the first daily lag, a definite indication of the bid/ask bounce. Note, however, that the adjusted R-squares of these autoregressions are miniscule; so the seemingly significant t-statistics are mainly due to the enormous sample size (8955) and probably have little economic relevance. The exchange rate changes do not display the same negative first-order lagged effect, which is likely attributable to small spreads in foreign exchange trading. Indeed, the $/Pound change has a seemingly significant positive first-order lagged coefficient while the $/Yen has second-order positive significance. Again, however, the trivial R-squares reveal that economic significance is lacking. Lead/Lag relations among the base series whose univariate autocorrelations are given in Table 6 could normally be examined with a vector autoregression (VAR). There are two reasons, however, to be cautious in such an approach. First, the gold return correlations are quite high (Table 1) so putting several of them on the right side of a VAR would result in a material degree of multicollinearity. Second, microstructure issues such as the bid/ask bounce illustrated for the gold returns in Table 6 might conceivably mask more economically meaningful relations. In an effort to finesse these problems, we decided to estimate a partial VAR in which not every variable appears lagged on the right side of every equation. This still allows us to ascertain whether currencies lead gold or vice versa. Table 7 reports Granger causality tests from our partial VAR system. When a gold return is the dependent variable, the right-side explanatory variables include three daily lagged values of all three exchange rate log change plus two lagged values (not reported) of the dependent variable to control for microstructure bid/ask bounce. The number of lags is sufficient according to the Akaike information criterion. 7 Since exchange rates in all combinations of currencies are simply computed from the Dollar/other base rates, there is no need to examine separately autocorrelations of every currency combination.

The p-values in Table 7 are for a joint test that all lags taken together significantly Granger cause the dependent variable. For gold returns, we see that the Dollar exchange rate against the DM-Euro Granger causes gold returns expressed in dollars, Yen, and Pounds and marginally (p-value of 0.044) in DM-Euros. The $/Yen exchange rate Granger causes the Yen gold return with marginal significance (p-value: 0.027) while the $/Pound exchange rate change Granger causes the Pound gold return and marginally causes the Dollar gold return (p-value: 0.042). This general pattern is that lagged values of exchange rate changes are influential for future gold returns in the same currency. Note that the $/Yen exchange rate has no significance except for the Yen gold return and the $/ Pound exchange rate is not significantly related to the gold return in DM-Euros or in Yen. These results are somewhat surprising because they suggest that the gold market is not perfectly semi-strong form efficient. However, even though the p-values reveal the ability to forecast future gold returns, there is not much economic potential for profit because the explanatory power is extremely low. The pseudo-R Squares in the gold return equations of the VAR range from .0023 to .0038. The bottom three lines of Table 7 report Granger causality test for predicting exchange rate changes. In these equations, no lagged values of the dependent variable were included but three lags of the gold return in the denominator currency (the non-dollar currency in the exchange rate), were added. There is much less evidence of predictability for exchange rate changes as compared to gold returns. Only one variable is statistically significant: the $/ DM-Euro exchange rate change for predicting the $/Pound exchange rate. None of the lagged gold returns and no other lagged exchange rate change is significant. Overall, there is little evidence of economically meaningful lagged relations among exchange rate changes and gold returns except for the microstructure bid/ask bound in the latter. This contrasts sharply with highly significant contemporaneous correlations among gold returns in different currencies and between gold returns and depreciation in the same currency, the main object of our study.

5. Conclusions Many previous authors have noted that gold prices in Dollars are correlated with weakness in the Dollar relative to other currencies. Intuitively, this seems to suggest something asymmetric because weakness in the Dollar is the same as strength in the other currency. Is there something special about the Dollar? Actually, the intuition is wrong. Over any calendar interval, the gold price expressed in a currency can be associated with weakness in that currency and, over the same interval, a similar relation with the same sign can hold for gold prices and weakness in other currencies. Indeed, we find empirically that not just the Dollar, but also the Euro, Yen and Pound, displayed the same negative association over the entire period from 1971 through 2009 – a higher gold price was correlated with a weaker currency for all of them. Occasionally, gold and a particular currency temporarily depart from their usual negative relation. In the 468 country/exchange rate/year possibilities in our data, the relation was significantly reversed (at the 5% level) on only nine occasions, about 1.9% of the time. This never happened for the Yen, but it did occur twice for the Dollar, four times for the Euro8 and three times for the Pound, mostly in different years. 8 Actually, it happened twice for the Deutche Mark, which we spliced to the Euro when the latter appeared in 1999.

2081

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

The dynamic conditional correlation (DCC) of Engle (2002) conforms well to this overall pattern. The DCC is positive on over 80% of the sample days for all countries and over 90% of the time for the Yen. The bottom line is that gold returns in a currency are associated with currency depreciation most of the time for the countries examined here. Gold prices expressed in different currencies are highly correlated, around 0.9 using daily gold returns in the four major currencies studied here. Gold prices are moderately correlated with the price of foreign currency (i.e., with weakness), around .15–.35. Rarely, an estimated correlation during a sub-period is positive between gold and a currency’s strength, but this might be due to sampling error and the episode does not last long. In most periods, gold is associated with weakness in a currency, regardless of country (among the four countries examined here). Acknowledgements We are most grateful for detailed suggestions from Stephen Ross and for comments from Michael Brennan. We are thankful for financial supports from Inquire UK and College of Business Administration, San Diego State University. Appendix A. Oil and the Dollar (and the Euro, Yen and Pound) Many previous readers have wondered whether similar relations hold between exchange rate changes and other commodities traded in the global market. To check this, crude oil comes to mind as a possibly good candidate. The spot prices of crude oil, however, are reluctant to change very often. Oil spot prices in Dollars are constant for years at a time in the early part of our gold sample (the 1970s and early 1980s). In later periods, the Dollar price of spot crude oil is less constant but rarely changes on a daily basis. Consequently, it seems sensible to use an oil futures price rather than a spot price. Data are available daily for the shortest-term crude oil futures settlement price on the New York Mercantile Exchange beginning March 30, 1983. This is the longest series we are able to find for oil prices that has daily variation. It contains 6163 trading days. Fig. A.1 plots the oil price in four currencies over the available sample. The legend on the right side identifies the currencies plot-

Table A.1 Oil price correlations in four major currencies. Using data from March 1983 through December 2009, daily log price relatives for oil denominated in different currencies are related. The Euro was spliced with the Deutche Mark prior to 1999. Trading days are eliminated if they are exchange holidays in any country. The remaining sample includes 6163 trading days.

Euro/bbl Yen/bbl Pound/bbl

US$/bbl

Euro/bbl

Yen/bbl

.9639 .9635 .9672

.9622 .9809

.9547

ted from the highest price (in Dollars) to the lowest price (in Yen) at the ending date in December 2009. Clearly, these series are very highly correlated, a fact that is verified by the correlations in Table A.1. All correlation exceeds 95%. These correlations are all somewhat larger than the corresponding ones for gold reported in Table 1 of the paper. Oil prices are also considerably more volatile than gold prices as can be seen by comparing the first columns of Table A.2 and Table 2 of the paper. The exchange rate volatilities in Table A.2 differ from those in Table 2 simply because the time periods are different. Table A.3, a companion for oil to Table 3 of the paper for gold, shows that oil does not always satisfy the same conditions. Note

Table A.2 Volatilities of oil prices and foreign exchange rates daily standard deviations of oil log price relatives and log exchange rate relatives are calculated from March 1983 through December 2009 inclusive. Daily log relatives are equivalent to continuouslycompounded daily returns and are expressed as percent per day. Exchange rate reciprocals are identical since volatilities of logs are invariant with respect to sign. The Euro was spliced with the Deutche Mark prior to 1999. Trading days are eliminated if they are exchange holidays in any country. The remaining sample includes 6163 trading days. Oil

Dollar Euro Yen Pound

2.443 2.509 2.558 2.487

Exchange rate Dollar

Euro

Yen

0.672 0.682 0.613

0.653 0.477

0.695

5.0

Oil Price per Barrel, March 30, 1983 = 1

4.5 4.0 3.5 3.0 Dollar

2.5

Pound DM-Euro

2.0

Yen 1.5 1.0 0.5 0.0

Fig. A.1. Oil prices in four currencies.

2082

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

Table A.3 Oil prices and exchange rates. Correlations and slope coefficients are reported from bivariate regressions between daily log oil price relatives in different currencies and daily log changes in exchange rates. These are equivalent to continuously-compounded daily returns. Prior to 1999, the Deutche Mark replaces the Euro. The data extend from March 1983 through December 2009, a total of 6163 non-holiday trading days. The slope coefficients conform to identity (1) in the text; sums of the off-diagonal pairs are 1.0. For example, the Euro/bbl-Dollar coefficient, .8657, and the US$/bbl-Euro coefficient, .1343, sum to unity. Oil

Exchange rate, currency of oil price per Dollar

Euro

Yen

Pound

Correlation US$/bbl Euro/bbl Yen/bbl Pound/bbl

.0368 .2307 .2984 .1972

.0581 .1408 .2403

.0320 .0678

.2063 .0543

Table A.4 Percentage of significant positive correlations between oil prices and currency depreciation. Correlations are computed during each calendar year, 1983–2009 inclusive, between the log price relative of oil in a currency and the depreciation of that currency against other currencies. This table reports the percentage of years out of 27 possible that the correlation is positive and two standard errors above zero. Exchange rate, currency of oil price per Dollar US$/bbl Euro/bbl Yen/bbl Pound/bbl

81.5 88.9 81.5

Euro

Yen

Pound

18.5

7.4 37.0

14.8 59.3 77.8

55.6 37.0

0.8657 1.1140 0.7756

.0593

that the correlations for oil (in the left side of Table A.3), are uniformly smaller than those for gold (in Table 3). One correlation, for the Dollar price of oil and the Dollar/Yen exchange rate, is even negative. In this instance, oil price increases (in Dollars) are associ-

Oil

Dollar

Euro

Yen

Pound

0.1343

0.1140 0.2438

0.2244 0.7233 0.8064

Slope coefficient, b

25.9

0.7563 0.2767

0.1936

ated with an appreciation of the Dollar with respect to the Yen. However, the negative correlation is only marginally significant even if all sample days are mutually independent of one another. Moreover, the associated t-value is below 2.0 in only one of the 27 sample years considered independently. Over all countries and exchange rates, negative correlations occurred eight times in 4(3)27 = 324 country/exchange rate/year possibilities, a rate of only 2.47%, which probably indicates mere random happenstance. With respect to significant positive correlations, Table A.4, a companion to Table 4 of the paper, reports the percentage of calendar years when the oil prices in a currency are positive and two standard errors above zero. The picture here is very different than for gold. In particular, the Dollar price of oil is not often associated with significant Dollar depreciation. There is another contrast as well: oil prices in Euros, Yen, or Pounds are associated with a depreciation of these three countries against the Dollar in more than 80% of the calendar years. Against other currencies though,

1.05

In this region, oil price changes are positively correlated with the depreciation of currency B but not currency A

1.04

λ = Ratio of Oil Price Change Standard Deviations (B/A)

1.03

λ

1.02

ρ

1.01

1.00

In this region, oil price changes are positively correlated with the depreciation of both currencies; (This region extends also over the entire area where the oil correlation is negative)

Diamonds indicate observations involving the Dollar, Euro, Yen and Pound

0.99

0.98

λ ρ

In this region, oil price changes are positively correlated with the depreciation of currency A but not currency B

0.97

0.96

0.95 0.950

0.955

0.960

0.965

0.970

0.975

0.980

0.985

ρ = Correlation of Oil Price Changes Expressed in Two Currencies Fig. A.2. Oil correlation, oil volatility and currency depreciation or appreciation.

0.990

0.995

1.000

K. Pukthuanthong, R. Roll / Journal of Banking & Finance 35 (2011) 2070–2083

there is much less significance. There is no such asymmetry for gold. Fig. A.2 is a companion to Fig. 1 of the paper but the scale has been enlarged to reveal the far right side of the plot, where all the data points lie. Notice that two points lie outside the region of positive relation between commodity price changes and currency depreciation. These correspond to the Dollar price of oil and, respectively, the Dollar/Yen exchange rate and the Yen/Dollar exchange rate. In summary, gold has significantly higher correlation than oil with currency depreciation for each of the four currencies considered here. But although oil’s correlation is weaker than gold’s, it is rarely negative. However, the Dollar price of oil is not often significantly positive either (not shown). Oil prices rises in other currencies are more often associated with that currency’s depreciation, particularly against the Dollar, but the effect is much smaller for depreciation against the other currencies.

2083

References Beckers, S., Soenen, L., 1984. Gold: more attractive to non-US than to US investors? Journal of Business Finance and Accounting 11, 107–112. Capie, F., Mills, T., Wood, G., 2005. Gold as a hedge against the dollar. Journal of International Financial Markets, Institutions, and Money 15, 343–352. Clements, K., Renee, F., 2008. Commodity currencies and currency commodities. Resources Policy 33, 55–73. Engle, R., 2002. Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350. Gaffen, D., Slater, J., 2009. Dollar, gold are suddenly inseparable. Abreast of the Market Column, Wall Street Journal, March 16, pp. C1–C2. Lizardo, R., Mollick, A., 2010. Oil price fluctuations and US dollar exchange rates. Energy Economics 32, 399–408. Sari, R., Hammoudeh, S., Ewing, B.T., 2007. Dynamic relations between oil and other commodity futures prices. Geopolitics of Energy 29, 1–12. Sari, R., Hammoudeh, S., Soytas, U., 2010. Dynamics of oil prices, precious metal prices, and exchange rates. Energy Economics 32, 351–362. Sjasstad, L., Scacciavillani, F., 1996. The price of gold and the exchange rate. Journal of International Money and Finance 15, 879–897.