The Volatility of Gold

Dirk G. Baur1

School of Finance and Economics University of Technology, Sydney

First version: December 2009

Abstract

The volatility of equity returns generally exhibits an asymmetric reaction to positive and

negative shocks. Economic explanations for this phenomenon are leverage and volatility

feedback effects. This paper studies the volatility of gold and demonstrates that there is an

inverted asymmetric reaction of gold to positive and negative shocks, i.e. positive shocks

increase the volatility by more than negative shocks. The paper argues that this effect is a result

of the safe haven property of gold. Macroeconomic and financial uncertainty is transmitted

from the equity market to the gold market causing the special asymmetric reaction. The

empirical results hold for gold bullion and gold coins denominated in different currencies,

different time periods and for different distributional assumptions. Finally, we show that the

inverted volatility effect of gold can lower the aggregate risk of a portfolio for specific

correlation levels.

JEL classification: C32, G10, G11, G15, L70

Keywords: gold, commodities, volatility asymmetry, leverage effect, volatility feedback effect,

uncertainty

1 Corresponding author, address: 1, Quay Street, Haymarket, Sydney NSW 2007, Australia. Email: dirk.baur@uts.edu.au We thank Harry Tse and workshop participants at UTS for helpful comments.

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INTRODUCTION

There is a large literature studying the volatility in equity markets and its asymmetric behaviour

to negative and positive shocks. Many studies (e.g. Black, 1976, Christie, 1982 and Campbell

and Hentschel, 1992 among others) report a larger increase of volatility in response to negative

shocks than to positive shocks. This asymmetry in the reaction to shocks has been explained

with the leverage of firms and a volatility feedback effect.

Despite the importance of gold as a hedge and a safe haven asset studies investigating the

volatility of gold are rare. Tully and Lucey (2006) estimate an APGARCH model and Batten

and Lucey (2007) model the volatility of a gold futures market.2

These studies analyze some features of the volatility of gold but do not focus on volatility

asymmetry

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We hypothesize that the safe haven property of gold is an important determinant for the

volatility of gold. More specifically, if gold increases in times of falling stock markets

(especially in financial crises) investors transmit the increased volatility and uncertainty of the

stock market to the gold market. Accordingly, if the gold decreases in times of rising stock

markets investors transmit the decreased volatility and uncertainty to the gold market. This can

lead to an asymmetric reaction of the volatility of gold which is different from the effect

observed in equity markets: the volatility of gold increases by more with positive shocks than

with negative shocks.

and its importance for portfolio diversification. If the volatility of gold increases in

times of financial crises the effectiveness of gold as a hedge can be compromised. In contrast, if

the volatility of gold decreases in periods of financial turmoil the effectiveness of gold as a

hedge can be reinforced. It is thus important to analyze the volatility of gold and its reaction to

positive and negative shocks.

This paper contributes to the literature by investigating the volatility of gold for a 30-year

period for daily, weekly and monthly returns, different types of gold (e.g. gold bullion per troy

ounce and coins) and different currency denominations. In addition, the paper presents an

alternative explanation for volatility asymmetries for commodities beyond leverage and

volatility feedback used to explain volatility asymmetries in equity markets.

2 Giamouridis and Tamvakis (2001) study the relation of return and volatility in the commodity and the stock market for indices without an explicit analysis of gold, Baur and McDermott (2009) report the conditional volatility of gold for a 30-year period and analyse the safe haven hypothesis for different volatility regimes and Roache and Rossi (2009) analyse the effect of macroeconomic news on commodities and gold. 3 Tully and Lucey (2006) specify an asymmetric component in their APGARCH model but find that the asymmetry is statistically insignificant.

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The empirical results show that the volatility of gold is highly persistent and exhibits volatility

clustering. Moreover, the volatility of gold displays an inverted asymmetric reaction: positive

shocks increase the volatility by more than negative shocks. This finding supports the

hypothesis that the volatility of gold is related to the safe haven property of gold. Positive

changes in the price of gold are associated with negative financial or macroeconomic news. The

volatility and uncertainty is transmitted from the stock market or macroeconomic conditions to

the gold market leading to an increased volatility. We further show that the change in

augmented level of volatility associated with positive price changes of gold can significantly

affect the effectiveness of gold as a hedge or a safe haven. The strength of this effect depends

on the correlation between gold and the other assets in an investor’s portfolio.

The paper is structured as follows: section I presents the empirical analysis with a description of

the data, an outline of the econometric framework, a presentation and discussion of the

estimation result and a section assessing the robustness of the results with respect to alternative

model specifications. Finally, section II summarizes the findings and concludes.

I. EMPIRICAL ANALYSIS

This part of the study describes the data in section A, the econometric model in section B and

the empirical results including a discussion and summary in section C. Section D employs

specification tests to assess the robustness of the results.

A. Data We use daily, weekly, monthly and quarterly data of different gold spot prices (per ounce) in

different currency denominations, weights (troy ounce or kg) and types (gold bullion or coins)

for a sample period of 30 years from November 19, 1979 to November 18, 2009. The number

of continuously compounded return observations is 7828 for daily data, 1566 for weekly data,

360 for monthly data and 120 for quarterly data. The data is obtained from Datastream.

< Insert table 1 about here >

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Table 1 presents the descriptive statistics of gold in US Dollar (London Bullion Market4

AM

fixing), gold in British Pound per ounce (AM official), gold in Euro per ounce (AM official),

gold per 995kg in Swiss Franc (Zurich), Gold Perth Mint per troy ounce in Australian Dollar

and Gold Krugerrand coins in Swiss Franc (Zurich fixing). The table contains four panels

(vertical direction) with returns data for daily, weekly, monthly and quarterly frequencies. The

descriptive statistics are tabulated in horizontal direction and show the mean, the standard

deviation, the minimum, the maximum, the skewness and the kurtosis of the gold returns for

each type and frequency.

The descriptive statistics show increasing average returns (mean) and risk (standard deviation)

from daily to quarterly frequencies. This pattern is weaker for the minimum of returns but

strong for the maximum return observation. The skewness increases slightly with lower return

frequencies and the kurtosis decreases from daily to quarterly return frequencies. An analysis of

the return properties within certain return frequencies (e.g. daily returns) further shows that the

currency denomination exhibits a strong impact on the returns of gold. For example, the

minimum return of gold in US Dollar is -0.1787 compared to a value of -0.1567 for gold in

British Pounds. The results for the skewness strengthen this observation with a negative value

for gold in US Dollar and a positive value of skewness for gold returns denominated in British

Pounds.5

Figures 1 and 2 provide a graphical illustration of the evolution of the different gold prices in

the sample. The figures and the table show that the currency denomination of gold has a strong

influence on the distribution of the gold returns.

There is also significant variation of specific statistics among gold returns including

the Swiss Franc and Australian Dollar denominations. For example, the average return of gold

on a quarterly basis varies from 0.13% (Krugerrand) to 2.34% (Gold in Euro) with values of

0.89% for Gold in US$ and 1.12 for Gold in British Pounds.

< Insert figure 1 about here >

< Insert figure 2 about here >

Finally, figure 3 presents a histogram of the gold return in US Dollar illustrating some features,

especially the skewness and the kurtosis of the returns also graphically.

4 London Bullion Market website: www.lbma.org.uk 5 Figure 3 presents a histogram of the gold return in US Dollar illustrating the negative skewness graphically.

5

< Insert figure 3 about here >

As a precursor to the econometric analysis of the volatility of gold, we display the return and

the squared return of gold denominated in US Dollar in figure 4. The squared return is used as a

proxy for volatility for a preliminary and descriptive analysis of volatility. The figure

demonstrates the link between returns and volatility and the occurrence of extreme returns and

high volatility. For example, in the last ten years of the sample period, four episodes of

increased volatility and extreme return shocks can be identified. The first two episodes (1999

and 2001) are relatively short compared to the second set of episodes (middle of 2005 and

2007). The last episode of increased volatility can be linked to the global financial crisis of

2007 and 2008. This period shows high volatility levels and extreme realizations of positive and

negative returns with positive returns being more frequent than negative returns.

< Insert figure 4 about here >

The proxy for the volatility of gold displays clusters of high and low volatility. A more

analytical analysis of volatility clustering, the persistence of the volatility of gold and

asymmetric effects is performed in the following section.

B. Econometric Framework This section describes the econometric framework to assess the importance of positive and

negative returns of gold on its volatility. The model is based on Glosten, Jaganathan and Runkle

(1993) and specified as follows:

rGold,t = μ + βXt + et (1a)

ht = π + γ1 (et-1) ² + γ2 (et-1)² I(et-1<0) + δ ht-1 (1b)

The conditional mean of the return of gold is estimated by equation 1a and the conditional

volatility is estimated by equation 1b. The parameters to estimate are μ and β in equation 1a and

π, γ1, γ2 and δ in equation 1b. The constant volatility is estimated by π, the effect of lagged

return shocks of gold on its volatility (ARCH) is estimated by γ1 and a differential effect if the

return shock is negative is captured by γ2. If there is a symmetric effect of lagged shocks on the

volatility of gold γ2 is zero. In contrast, if lagged negative shocks augment the volatility by

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more than lagged positive shocks, there is an asymmetric effect which is typically associated

with a leverage effect or a volatility feedback effect. If lagged negative shocks decrease the

volatility of gold the asymmetric effect typically found for equity is inverted, i.e. positive

shocks of gold increase its volatility by more than negative shocks. The influence of the

previous period’s conditional volatility level (ht-1) on the current period is given by δ

(GARCH).

This paper focuses on the asymmetric reaction of gold returns on its volatility for two major

reasons. First, if the volatility of gold exhibits different reactions to shocks the low correlation

of gold with other assets might be compromised in certain conditions and second, the economic

explanations for asymmetric volatility for equities are not applicable for gold and commodities

in general. Financial leverage or volatility feedback cannot be the direct cause of any

asymmetry in the volatility of gold.

Equation 1a is specified with a regressor matrix X comprising additional variables that can

influence or explain any asymmetric volatility effect. Variables to be included in the regressor

matrix are lagged returns of gold, a commodity index or a stock market index with or without

an asymmetric impact on the gold return. Since the results can be influenced by the

distributional assumptions regarding the error distribution we estimate the asymmetric GARCH

model of a GARCH(1,1)-type by Maximum-Likelihood with a Gaussian error distribution and a

student-t error distribution.

C. Empirical Results This section describes the estimation results of the asymmetric GARCH model and discusses

the findings. The main findings are presented in table 2. The table contains the coefficient

estimates and t-statistics of the asymmetric volatility model parameters specified in equation

1b. The coefficient estimates are reported in horizontal direction (unconditional variance,

ARCH, GARCH and asymmetric effect) for different gold spot prices displayed in vertical

direction. The table also contains four panels (daily, weekly, monthly and quarterly) for

different return frequencies.

The coefficient estimates for daily returns exhibit highly significant ARCH and GARCH effects

(e.g. coefficient estimates of 0.0643 (ARCH) and 0.9564 (GARCH) and t-statistics of around

29 and around 700 for gold returns denominated in US Dollar, respectively). The coefficient

estimates for the asymmetric term are negative and highly significant for all gold returns in the

panel for daily data. The coefficient estimates vary from -0.0101 for gold (995kg) in Swiss

Franc with a t-statistic of -2.84 to a coefficient estimate of -0.1030 and a t-statistic of -3.77 for

gold denominated in Euro. The negative coefficient implies that negative shocks exhibit a

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smaller impact on the volatility of gold than positive shocks. In other words, positive shocks of

gold increase the volatility of gold more than negative shocks. This pattern exists for all gold

returns in the sample and across all frequencies. The magnitude of the effect increases from

high-frequency returns to low-frequency returns with the largest values for some returns at

monthly frequency. For example, the coefficient for the asymmetric term (negative shocks) is -

0.0414 for daily data and -0.1310 for quarterly data for US dollar denominated gold returns.

< Insert table 2 about here >

The asymmetric impact of positive and negative returns can also be demonstrated graphically.

Figures 6-8 present news-impact curves for gold returns denominated in US dollar, British

Pound and the Euro for daily data. One example of a news-impact curve for monthly data is

presented for gold returns in US dollar in figure 9. The news-impact curves demonstrate the

impact of lagged positive or negative returns on the contemporaneous volatility of the return

series. The lagged returns are shown on the horizontal axis and the contemporaneous volatility

is shown on the vertical axis and the curve is based on the parameter estimates of the

asymmetric GARCH model.

The graphs illustrate that positive returns of gold have a larger impact on its volatility than

negative returns. The asymmetry is not only significant statistically (see table 2) but also

graphically. Since the news-impact curves are plotted for relatively conservative values of the

gold returns compared to their extremes as shown in table 1, the graphical representation

demonstrates the magnitude of the asymmetric effect in terms of the volatility change. For

example, the volatility of the daily gold return in US Dollar is 0.015 for shocks equal to -8%

and exceeding 0.4 for shocks equal to +8%.6 Hence, the increase in volatility with positive

shocks is almost three times (2.81) larger than the increase in volatility with negative shocks.7

< Insert figure 6 about here >

< Insert figure 7 about here >

< Insert figure 8 about here >

6 The estimated volatility ht is multiplied by 1000. 7 The ratio is lower if standard deviations (square root of the estimated volatility) are used for comparison.

8

< Insert figure 9 about here >

The results demonstrate that the volatility of gold exhibits an inverted asymmetry of positive

and negative shocks relative to the asymmetry found for the volatility in equity markets. Since

financial leverage and volatility feedback cannot explain this effect, we argue that the effect is

related to the safe haven property of gold. If the price of gold increases in times of financial or

macroeconomic uncertainty (see Baur and McDermott, 2009), investors buy gold and transmit

the volatility and uncertainty to the gold market. The price and the volatility of gold increase

simultaneously. If the price of gold decreases in tranquil times investor sell gold thereby

signalling that financial and macroeconomic uncertainty is low. This leads to a smaller increase

of volatility compared to the positive gold price change.

The difference of the asymmetric reaction of gold compared to stocks can also be characterized

as follows. While negative return shocks in equity markets signal “bad” news and positive

return shocks imply “good” news, it is the other way around in the gold market. Positive shocks

in the gold market imply “bad” financial and macroeconomic news and negative returns in gold

mean “good” news. Hence, in relation to the title of the work by Campbell and Hentschel

(1992), a study of volatility of the gold market could also be entitled “Bad News (in the gold

market) is Good News”.8

One could reason that the inverted asymmetric volatility effect is not related to the safe haven

effect of gold as argued above but a typical finding for commodities. Table 3 presents the

estimation results of an asymmetric GARCH model for different metal commodity indices and

one general commodity index. The commodities covered are industrial metals, copper, nickel,

zinc, aluminium and a general commodity index (S&P GSCI commodity spot index). The

coefficient estimates for the asymmetric effect show a negative coefficient for all indices except

the aluminium index. Hence, the inverted asymmetry can also be observed for commodities.

However, the magnitude of the effects is relatively small and four out of six estimates are

statistically insignificant. For comparison, the average coefficient estimate of the asymmetric

effect for daily gold returns is -0.0460 and -0.0087 for commodities. The gold average

(including gold coins) is around five times larger than the average coefficient estimate for

commodities.

8 This could also be related to a quote by John Updike “The beauty of gold is, it loves bad news.” (Harry “Rabbit” Angstrom – Rabbit is Rich as quoted in the Economist, February 26th 2009). This quote was used to refer to the safe haven property of gold, i.e. that the price of gold increases in response to negative shocks in the stock market.

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This finding demonstrates that there is a specific effect not fully captured by the safe haven

property under the assumption that only gold exhibits this characteristic. However, it is also

possible that commodities are also used as a safe haven asset by investors but that the effect on

gold is stronger.

< Insert table 3 about here >

Finally, existing research supports the argument that the safe haven property of gold is

responsible for the specific type of volatility asymmetry. The findings of Roache and Rossi

(2009) demonstrate that the volatility of gold increases with positive gold shocks. The authors

report that gold is very sensitive to adverse macroeconomic news.

Giamouridis and Tamvakis (2001) provide alternative explanations for the inverted asymmetric

effect of the commodity volatility. The authors argue that the volatility pattern can be explained

with the fact that exchange-based commodity trading is directly linked to the underlying

physical asset. We believe that the introduction of exchange-traded funds (ETFs) on

commodities and gold has undermined the direct link the authors are referring to. If the direct

link weakened with the introduction of ETFs and other investment vehicles, the strength of the

asymmetric effect should have strengthened in recent years. Such an effect will be investigated

in a sub-sample analysis potentially displaying structural changes through time in section D.

Portfolio diversification effects

The inverted asymmetry of volatility contains an important implication for portfolio

diversification. If gold is used as a diversifier or a hedge against financial or macroeconomic

uncertainty it can decrease the risk in terms of expected return due to the negative correlation

(e.g. see Baur and Lucey, 2009) but increase the volatility of a portfolio in times of financial

market turmoil. This effect can compromise the low or negative correlation effect gold

demonstrates with other assets in such periods. Table 4 shows that the change in the total

portfolio variance caused by an increased volatility of gold depends on the correlation

coefficient. If the correlation between stocks and gold is negative (-0.2 for portfolios 2 - 4 in the

table), the increased volatility of gold leads to a negative reaction in the portfolio variance due

to the covariance term which dominates the individual variance contribution of gold.

< Insert table 4 about here >

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This finding implies that the inverted asymmetric volatility pattern of gold strengthens the safe

haven effect. The results show that there are too components of the effect, a correlation effect

primarily affecting the returns and a covariance affect which lowers the aggregate risk of a

portfolio through an increasing covariance effect comprising both the decreased correlation and

the increased volatility reaction.

D. Specification Issues This section studies the robustness of the results with respect to alternative model

specifications. First, we discuss the importance of the distributional assumptions. Second,

alternative mean equation specifications and their influence on the asymmetric effect are

assessed. Third, a sub-sample analysis examines the stability of the parameters through time

including a specific investigation of the global financial crisis of 2007 and 2008. Fourth,

estimation results of the asymmetric effect for gold coins are reported. Finally, differences in

estimates based on a symmetric GARCH(1,1) and an asymmetric GARCH(1,1) model are

assessed.

The estimation results reported above are based on the distributional assumption that returns

follow a Gaussian distribution. If the asymmetric GARCH model is re-estimated using a

student-t distribution, the results can be summarized as follows. The average degree of freedom

is around 6 across all types of gold returns and frequencies. The coefficient estimates for the

term governing the volatility asymmetry are slightly lower. For example, the coefficient

estimate for daily gold returns denominated in US Dollar changes from -0.0414 to -0.0387.

Similar changes can be observed for the other return series. Larger changes can be observed for

the estimated standard errors of the coefficient estimates and the t-statistics. The errors increase

significantly (two to three times) reducing the t-statistics by a similar magnitude. However, this

affects only estimates of lower frequency gold returns (monthly and quarterly data) in terms of

statistical significance since the t-statistics for daily and weekly returns are relatively high in

the benchmark model.

The model was re-estimated with different exogenous variables in the mean equation to assess

the impact of such variables on the volatility asymmetry. We used the S&P500 stock market

index and an interaction term with a dummy variable capturing only negative stock market

returns in the mean equation. Alternatively, lagged gold returns and lagged negative gold

returns were specified in the mean equation. The alternative mean equations demonstrated that

the volatility equation is not significantly affected by the specification of the mean equation.

A related issue is the inclusion of exogenous variables in the volatility equation. The inclusion

of the squared return of the S&P500 and an interaction term with a dummy for negative returns

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does not change the volatility asymmetry of gold. The estimates were obtained with an iterative

ordinary least-squares estimation.9

To examine the stability of the model parameters we divide the 30-year sample period in three

sub-periods of ten years each. We perform the estimation for daily data for US Dollar, British

Pounds and Australian Dollar (Perth Mint) denominated gold returns. We restrict the analysis to

the series with the full number of observations. The remaining gold return series are available

for shorter periods only. The sub-sample estimation results show stable ARCH and GARCH

parameters for gold in US Dollar and slightly decreasing ARCH parameters (from 0.1412 in the

first sub-sample to 0.0870 in the third sub-sample) and increasing GARCH parameters (from

0.8655 to 0.9349) for gold in British Pounds. The ARCH and GARCH parameters for gold in

Australian Dollar exhibit some variation across sub-samples but there is no clear trend. Finally,

the coefficient estimates for the asymmetric parameter increase for all three return series. From

-0.0274 to -0.0562 for gold in US Dollar form the first sub-sample to the third and from -0.0333

to -0.0557 and -0.0354 to -0.0595 for gold in British Pounds and Australian Dollar (Perth

Mint), respectively. These results indicate that the volatility asymmetry strengthened through

time implying a stronger safe haven effect of gold on volatility.

In the next stage of the specification tests, we extend the sub-sample analysis and focus on the

global financial crisis of 2007 and 2008. We use three different periods to analyze the volatility

of gold in the crisis episode. The first period commences July 2, 2007 and ends December 31,

2008. The second and third periods commence January 1, 2008 and September 1, 2008,

respectively. Both periods finish at the end of December 2008. We use different periods due to

the difficulty to assign specific crisis starting or outbreak days.10

The results demonstrate that

the asymmetric effect strengthens (decreases toward minus infinity) for all return series. The

strongest decrease can be observed for gold in British Pounds and Euro currency which move

from -0.0054 in the first crisis sub-sample to -0.1895 and from 0.0210 to -0.3659, respectively.

Finally, we describe the estimation results for alternative gold coins based on daily returns. The

gold coins are Vreneli Konvent, Napoleon, Old Sovereign, New Sovereign, Double Eagle, and

Mexico Centenario. All coins are denominated in Swiss Franc except the Centenario which is a

50 (Mexican) pesos gold coin11

9 Results can be obtained from the authors upon request.

. The estimation results are similar to the results for gold

10 The contagion literature uses crisis windows to examine the effect of a crisis on the transmission mechanism or the comovement of markets. The location of the window in time and its length is generally defined by descriptive or anecdotal evidence (e.g. see Forbes and Rigobon, 2002 and Baur and Fry, 2009). 11 The Mexican 50 Pesos gold coin contains 37.5 grams (1.2057 oz) of gold in an alloy of 90% gold and 10% copper.

12

bullion. The strongest asymmetry exhibits New Sovereign with a coefficient of -0.1505 and the

weakest inverted asymmetry is estimated for Double Eagle (-0.0087). All asymmetric

coefficients with negative coefficients are highly significant (minimum t-statistic is -3.55).

There is only one gold coin which exhibits a positive coefficient. The Centenario gold coin

displays a coefficient estimate of 0.0029. However, the estimate is statistically insignificant.

< Insert figure 10 about here >

Finally, figure 10 displays the time-series of estimated volatility obtained with a symmetric and

an asymmetric GARCH(1,1) model. The graph demonstrates that the assumption of a

symmetric volatility structure can lead to substantial differences in the levels of volatility.

II. CONCLUSIONS

This paper demonstrated that the volatility of gold returns exhibit an asymmetric reaction to

positive and negative shocks which can be characterized as abnormal or inverted compared to

the findings reported for the volatility of equity returns. The usual explanations for asymmetric

volatility, i.e. financial leverage and volatility feedback, cannot be applied to commodities.

Moreover, the inverted asymmetric volatility pattern is not consistent with these explanations.

We argue that the finding is related to the safe haven property of gold. If financial volatility and

macroeconomic uncertainty is high gold generally acts as a safe haven and the price of gold

rises in response to the heightened level of volatility and uncertainty. If the price of gold rises in

times of financial or macroeconomic crisis and decreases in relatively normal or calm periods

gold reflects the volatility and uncertainty of the other assets or markets. Hence, investors

transmit the volatility and uncertainty to the gold market by purchasing gold in these times.

Investors establish a volatility spillover effect from the financial markets and the real economy

to the gold market. An analysis of this effect for equity portfolios including gold shows that the

increased volatility of gold complements the beneficial negative correlation of gold and equity

markets and enhances the safe haven property of gold.

Future research could investigate the volume of gold and its effect on the volatility of gold.

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REFERENCES Batten, J.A. and B.M. Lucey (2007), “Volatility in the Gold Futures Market”, IIIS Discussion

Paper, Trinity College Dublin

Baur, D.G. and R. A. Fry (2009), “Multivariate contagion and interdependence," Journal

of Asian Economics, 20 (4), 353-366

Baur, D.G. and T.K. McDermott (2009), “Is Gold a Safe Haven? International Evidence”, IIIS

Discussion Paper No. 310, Trinity College Dublin

Bekaert, G. and G. Wu (2000), “Asymmetric Volatility and Risk in Equity Markets”, The

Review of Financial Studies, 13, 1, 1-42

Black, F. (1976), ”Studies of Stock Price Volatility Changes”, Proceedings of the 1976

Meetings of the American Statistical Association, Business and Economic Statistics

Campbell, J.Y. and L. Hentschel (1992), “No News is Good News: An Asymmetric Model of

Changing Volatility in Stock Returns”, Journal of Financial Economics, 31, 281-318

Christie, A.A. (1982), ”The Stochastic Behavior of Common Stock Variances - Value,

Leverage and Interest Rate Effects,” Journal of Financial Economics, 3, 145-166

Forbes, K. And R. Rigobon (2002), “No Contagion, Only Interdependence: Measuring Stock

Market Comovements" Journal of Finance, 57 (5), 2223-2261

Giamouridis, D.G. and M.N. Tamvakis (2001), “The Relation Between Return and Volatility in

the Commodity Markets”, Journal of Alternative Investments, 4, 1, 54-62

Glosten, L.R., Jagannathan, R. And D.E. Runkle (1993), “On the Relation between the

Expected Value and the Volatility of the Nominal Excess Return on Stocks", Journal of

Finance, 48(5), 1779-1801

Roache, S.K. and M. Rossi (2009), “The Effects of Economic News on Commodity Prices: Is

Gold Just Another Commodity?”, IMF Working Paper WP 09/140

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Table 1: Descriptive Statistics This table presents descriptive statistics of gold bullion returns (per troy ounce) in US$, in British Pounds and in Euro denoted as GOLDBLN, GOLDBN£ and GOLDBNE respectively. SFGOLDB, GOLDPMT and SFKRUGR denote gold returns in Swiss Franc (995kg), Perth Mint gold in Australian Dollar and Kruger gold in Swiss Franc. The sample period is November 1979 to November 2009 for daily, weekly, monthly and quarterly data. The sample period for the Euro-denominated gold returns commences January 1999 and is thus shorter.

mean std. dev. min max skewness kurtosis

Daily GOLDBLN 0.0001 0.0122 -0.1787 0.1221 -0.3567 19.5651 GOLDBN£ 0.0002 0.0123 -0.1567 0.1194 0.1709 18.4744 GOLDBNE 0.0004 0.0128 -0.2563 0.2609 0.3407 135.3169 SFGOLDB 0.0000 0.0105 -0.1157 0.0997 -0.1927 12.2291 GOLDPMT 0.0002 0.0123 -0.2002 0.1271 -0.0174 24.7200 SFKRUGR 0.0000 0.0116 -0.1550 0.1582 -0.2696 22.9513

weekly GOLDBLN 0.0007 0.0263 -0.1563 0.2356 0.7496 13.6465 GOLDBN£ 0.0008 0.0257 -0.1340 0.2075 1.0095 11.9041 GOLDBNE 0.0020 0.0219 -0.0921 0.1155 0.1404 5.2796 SFGOLDB 0.0002 0.0220 -0.1197 0.1076 -0.0894 5.5894 GOLDPMT 0.0008 0.0262 -0.1448 0.1955 0.9705 11.7047 SFKRUGR 0.0002 0.0230 -0.1206 0.1509 0.0090 6.8179

monthly GOLDBLN 0.0030 0.0600 -0.2528 0.5351 1.8766 21.7346 GOLDBN£ 0.0037 0.0585 -0.2244 0.4784 1.6244 16.5257 GOLDBNE 0.0083 0.0455 -0.1652 0.1906 -0.0698 5.9204 SFGOLDB 0.0005 0.0434 -0.1438 0.1981 0.2892 4.9915 GOLDPMT 0.0035 0.0607 -0.2924 0.5159 1.8176 19.0873 SFKRUGR 0.0005 0.0431 -0.1406 0.1986 0.3688 5.1336

quarterly GOLDBLN 0.0089 0.0936 -0.2315 0.5072 1.4400 9.1359 GOLDBN£ 0.0112 0.0967 -0.2479 0.4841 1.3318 7.6205 GOLDBNE 0.0234 0.0831 -0.1274 0.2731 0.6166 3.5724 SFGOLDB 0.0014 0.0726 -0.1776 0.2457 0.4862 3.4841 GOLDPMT 0.0105 0.0964 -0.2598 0.5260 1.3315 9.7334 SFKRUGR 0.0013 0.0722 -0.1754 0.2458 0.4420 3.4703

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Table 2: Estimation Results – Gold returns This table presents the estimation results of an asymmetric GARCH(1,1) model for gold returns in different currency-denominations, different types or quantities of gold and different return frequencies. Model: rGold,t = μ + et ht = π + γ1 (et-1) ² + γ2 (et-1)²I(et-1<0) + δ ht-1

constant ARCH GARCH Asymmetry

Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat.

daily GOLDBLN 0.0000 0.2604 0.0643 29.1071 0.9564 700.5838 -0.0414 -15.8452

GOLDBN£ 0.0000 0.4458 0.1022 28.1355 0.9117 326.5985 -0.0453 -10.9055

GOLDBNE 0.0005 1.9171 0.1631 6.0091 0.6783 19.0023 -0.1030 -3.7744

SFGOLDB 0.0001 0.6788 0.0584 18.0034 0.9313 318.9205 -0.0101 -2.8376

GOLDPMT 0.0000 0.3043 0.0684 27.1825 0.9497 701.8043 -0.0398 -13.3109

SFKRUGR 0.0003 2.5438 0.1502 17.4698 0.7775 79.9568 -0.0362 -4.4947

weekly GOLDBLN 0.0002 0.4814 0.1502 13.0761 0.8799 112.5393 -0.0685 -4.8649

GOLDBN£ 0.0005 0.9454 0.1463 10.3886 0.8432 62.4460 -0.0820 -5.0685

GOLDBNE 0.0020 2.3652 0.2178 3.3734 0.7651 13.2793 -0.1098 -1.9285

SFGOLDB 0.0001 0.2742 0.1300 5.4170 0.8152 25.6222 -0.0646 -2.5176

GOLDPMT 0.0005 0.9583 0.1411 12.1305 0.8826 96.7466 -0.0917 -7.0908

SFKRUGR 0.0004 0.7747 0.1053 6.7691 0.8769 63.0659 -0.0836 -4.3284

monthly GOLDBLN 0.0013 0.5888 0.4101 6.0905 0.6009 8.9732 -0.2145 -2.4104

GOLDBN£ 0.0030 1.3653 0.3286 5.3019 0.6189 8.4985 -0.1944 -2.2599

GOLDBNE 0.0092 2.5039 1.0707 3.0876 0.1128 0.7368 -1.0092 -2.8445

SFGOLDB 0.0004 0.1837 0.0432 1.5737 0.9200 16.6656 -0.0432 -1.2336

GOLDPMT 0.0027 1.0779 0.4415 6.2350 0.5735 10.5551 -0.1927 -1.9285

SFKRUGR 0.0004 0.1680 0.0413 1.4924 0.9170 15.1037 -0.0413 -1.1648

quarterly GOLDBLN 0.0096 1.4843 0.1310 1.7470 0.8573 10.8589 -0.1310 -1.1702

GOLDBN£ 0.0094 1.3393 1.0472 3.7476 0.2406 1.5128 -0.8064 -1.9180

GOLDBNE 0.0183 1.5509 1.4413 1.7697 0.0000 0.0000 -1.4413 -1.5900

SFGOLDB -0.0002 -0.0239 0.0357 0.3818 0.9821 3.5249 -0.0357 -0.2504

GOLDPMT 0.0121 1.9166 0.1732 2.4705 0.8339 17.0441 -0.1732 -1.4124

SFKRUGR 0.0000 -0.0018 0.0373 0.4007 0.9814 3.2469 -0.0373 -0.2960

16

Table 3: Estimation Results – Commodity indices This table presents the estimation results of an asymmetric GARCH(1,1) model for different commodity indices for daily returns. The indices are the S&P GSCI Industrial Metals (GSINSPT), Copper (GSICPT), Nickel (GSIKSPT), Zinc (GSIZSPT), Aluminium (GSIASPT) and the GSCI commodity spot index (CGSYSPT). Model: rGold,t = μ + et ht = π + γ1 (et-1) ² + γ2 (et-1)²I(et-1<0) + δ ht-1

S&P GSCI Index constant ARCH GARCH Asymmetry

Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat.

INDUSTRIAL METALS 0.0000 0.2073 0.0454 15.3983 0.9547 418.9734 -0.0054 -1.3467

COPPER 0.0001 0.4687 0.0424 15.4968 0.9555 436.5941 -0.0043 -1.2813

NICKEL 0.0002 0.5565 0.0405 12.9596 0.9549 288.1156 -0.0073 -1.8295

ZINC 0.0001 0.6653 0.0393 21.6257 0.9756 889.6365 -0.0311 -13.316

ALUMINIUM 0.0000 -0.1483 0.0495 9.9539 0.9344 213.6729 0.0060 1.2647

COMMODITY 0.0001 1.0314 0.0633 19.764 0.9393 308.5651 -0.0098 -2.1008

17

Table 4: Portfolio effect of asymmetric volatility of gold This table shows how the portfolio variance changes for different weights, correlations and standard deviation assumptions for stocks and gold across four portfolios with stocks and gold only. The example demonstrates that the negative correlation of gold with stocks and an increased volatility of gold can reduce the total portfolio variance (portfolio 4) compared to a case of lower gold volatility (portfolio 3).

Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4

stocks gold stocks gold stocks gold stocks gold

weights 0.95 0.05 0.80 0.20 0.80 0.20 0.80 0.20

correlation 0.05 -0.20 -0.20 -0.20

std. dev. 0.20 0.10 0.20 0.10 0.40 0.10 0.40 0.20

Portfolio variance 0.0381 0.0180 0.0868 0.0720

components

stocks 0.0361 0.0256 0.1024 0.1024

gold 0.0000 0.0004 0.0004 0.0016

covariance 0.0020 -0.0080 -0.0160 -0.0320

18

Figure 1: Gold price through time This table presents the evolution of the price of gold (troy ounce) in US Dollar, British Pounds and Euro for a 30-year period from November 1979 to November 2009.

0

200

400

600

800

1000

1200

GOLDBLN

GOLDBN£

GOLDBNE

19

Figure 2: Gold price (different types of gold) through time This table presents the evolution of the price of 995kg gold in Swiss Franc, Gold Perth Mint in Australian Dollars and Kruger rand gold in Swiss Franc for a 30-year period from November 1979 to November 2009.

0

5000

10000

15000

20000

25000

30000

35000

40000

0

200

400

600

800

1000

1200

1400

1600

1800

GOLDPMT

SFKRUGR

SFGOLDB

20

Figure 3: Histogram daily gold returns (troy ounce) in US Dollar

21

Figure 4: Gold returns and volatility This figure illustrates the daily returns of gold (in US$) and the squared return as a proxy for volatility.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

GOLDBLN

GOLDBLN squared

22

Figure 5: Conditional Volatility – Asymmetric GARCH(1,1) estimates of Gold bullion in US$

0

0.01

0.02

0.03

0.04

0.05

0.06

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

23

Figure 6: News-impact curve Gold in US$ The graph displays the reaction of past return shocks of gold (t-1) on its current volatility (t). The return shocks are plotted on the horizontal axis and the volatility is plotted on the vertical axis (conditional volatility x 1000).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

24

Figure 7: News-impact curve Gold in British Pounds The graph displays the reaction of past return shocks of gold (t-1) on its current volatility (t). The return shocks are plotted on the horizontal axis and the volatility is plotted on the vertical axis (conditional volatility x 1000).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

25

Figure 8: News-impact curve Gold in EURO The graph displays the reaction of past return shocks of gold (t-1) on its current volatility (t). The return shocks are plotted on the horizontal axis and the volatility is plotted on the vertical axis (conditional volatility x 1000).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

26

Figure 9: News-impact curve Gold in US$ (monthly) The graph displays the reaction of past return shocks of gold (t-1) on its current volatility (t). The return shocks are plotted on the horizontal axis and the volatility is plotted on the vertical axis (conditional volatility x 1000).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

27

Figure 10

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

GARCH(1,1)

asymmetric GARCH

difference (GARCH - asymmetric GARCH)