Comparative analysis on the effects of the Asian and global financial crises on precious metal markets

Research in International Business and Finance 25 (2011) 203–227

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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Review

Comparative analysis on the effects of the Asian and global financial crises on precious metal markets Lucía Morales b,∗, Bernadette Andreosso-O’Callaghan a a

Jean Monnet Chair of Economics, Department of Economics and Euro-Asia Centre, Kemmy Business School, University of Limerick, Ireland b Department of Accounting and Finance, Business School, Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland

a r t i c l e

i n f o

Article history: Received 5 October 2010 Received in revised form 6 January 2011 Accepted 8 January 2011 Available online 18 January 2011 JEL classification: F G Keywords: Precious metal returns GARCH and EGARCH modeling Volatility persistence Volatility spillovers and asymmetric spillovers

a b s t r a c t The global financial crisis has vigorously struck major financial markets around the world, in particular in the developed economies since they have suffered the most. However, some commodity markets, and in particular the precious metal markets, seem to be unscathed by this financial downturn. This paper investigates therefore the nature of volatility spillovers between precious metal returns over fifteen years (1995–2010 period) with the attention being focused on these markets’ behavior during the Asian and the global financial crises. Daily closing values for precious metals are analyzed. In particular, the variables under study are the US$/Troy ounce for gold, the London Free Market Platinum price in US$/Troy ounce, the London Free Market Palladium price in US$/Troy once, and the Zurich silver price in US$/kg. The main sample is divided into a number of sub periods, prior to, during and after the Asian crisis. The aim of this division is to provide a wide and deep analysis of the behavior of precious metal markets during this financial event and of how these markets have reacted during times of market instability. In addition, this paper also looks at the effects of the global financial crisis from August 2007 to November 2010 using GARCH and EGARCH modeling. The main results show that there is clear evidence of volatility persistence between precious metal returns, a characteristic that is shared with financial market behavior as it has been demonstrated extensively by the existing literature in the area. In terms of volatility spillover effects, the main findings evidence volatility spillovers running in a bidirectional way

∗ Corresponding author. Tel.: +353 1 402 3230. E-mail addresses: [email protected] (L. Morales), [email protected] (B. Andreosso-O’Callaghan). 0275-5319/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ribaf.2011.01.004

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during the periods; markets are not affected by the crises, with the exception of gold, that tends to generate effects in all other metal markets. However, there is little evidence in the case of the other precious metals generating any kind of influence on the gold market. On the other hand, there is little evidence of spillover effects during the two crisis episodes. Finally, the results from asymmetric spillover effects show that negative news/information have a stronger impact in these markets than positive news, again a characteristic that has been also exhibited by financial markets. © 2011 Elsevier B.V. All rights reserved.

Contents 1. 2. 3. 4.

5.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data and methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Unit roots and likelihood tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Volatility persistence (EGARCH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Volatility spillovers (EGARCH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. Asymmetric spillovers (EGARCH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. GARCH results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Standardized residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

204 205 208 213 213 214 218 218 224 224 225 226 226

1. Introduction The accurate representation and empirical modeling of metal market volatility is a very important matter, as volatility causes uncertainty to producers, consumers and stockholders with regard to revenues, costs and margins. The main interest in commodity markets lies in their characteristic as an outlet for speculative activities and therefore for the implementation and evaluation of trading and hedging strategies, and the conduct of risk management (McMillan and Speight, 2001). This paper employs GARCH and EGARCH techniques to investigate the crisis effects on precious metal returns. It uses daily closing values of precious metal data (the US$/Troy ounce for gold, the London Free Market Platinum price in US$/Troy ounce, the London Free Market Palladium price in US$/Troy ounce and the Zurich silver price in US$/kg), over the period 1995–2010, with a special attention devoted to the periods of the Asian crisis (1997–1998), and of the global financial crisis (2007–2010). The objective is to analyze the reaction of precious metal returns during a long period and how they have evolved under circumstances of market stress. For this reason, the authors’ major interest focuses on analyzing precious metal interaction and performance during times of turmoil and uncertainty in the world economy, where investors and governments’ decisions are driven by serious economic doubts and hesitation. The main motivation of conducting this analysis is supported by the current economic situation, where financial markets are facing increasing depreciation in their assets and where investors seem to be altering their investment decisions in their quest for better returns. Precious metals have generally been ignored by investors in the construction of their portfolios where uncertainty or risk is of major importance in financial analysis. The volatility of financial asset returns changes over time, with periods of large movements in prices alternating with periods during which prices hardly change. The variability of commodities, exchange rates and stock prices has been widely investigated for many years due to its implications

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for the participants involved in these markets. Investors and hedgers attempt to offset their exposure and risk from these markets, and must adjust their hedge ratios in accordance with the movement of these main financial markets; on the other hand, speculators rely on price volatility in order to generate business opportunities that allow them to extract profits and at the same time provide liquidity to the markets. While there is a substantial literature on the analysis of volatility spillovers between stock returns and domestic exchange rates, startlingly, little empirical research has examined volatility spillovers between precious metal returns. This might appear as surprising given that these markets are of particular interest to investors as they are important stores of value and monetary assets. The authors of this study strongly believe that precious metals could be presenting stability properties, especially during times of crises, that could help investors to design optimal portfolio management strategies. Consequently, our main expectations are to find some sign of stability behavior in precious metal returns, a characteristic that will be of major importance for designing financial strategies that allow investors to manage and hedge their risk in a more efficient manner. Furthermore, the aim of this paper is to extend the research in this area, and also to provide practical conclusions on the implications of precious metal return volatility spillovers for risk management and hedging strategies in financial markets, by using GARCH and EGARCH analyses as the core modeling technique. The remaining of the paper is set out of as follow: Section 2 presents the literature review; Section 3 describes the data and methodology that is used to assess the nature of volatility spillovers between precious metal markets; Section 4 presents our empirical results, and Section 5 concludes the analysis. 2. Literature review There is an extensive literature analyzing volatility spillovers in the case of stock markets; however, the interaction between stock markets and precious metal markets, and more importantly the link between precious metals themselves, has received far less attention. This is rather puzzling as it is well known that the price of natural resource products and commodities are of high importance in both policy and business circles (Bernard et al., 2008). For that reason, the main purpose of this piece of writing is to provide a comparative analysis of volatility spillovers between precious metal markets (gold, platinum, palladium and silver) based on GARCH and EGARCH techniques during a time period the length of which allows us to analyze market behavior during times of stability, but significantly during times of financial distress. Therefore, we will be analyzing fifteen years of data that span from 1995 to November 2010. The motivation for this research is that precious metal markets could represent an important option for investors in order to diversify their investment strategies and portfolios, as the value of precious metals is perceived as being more stable than that of other commodities on average, and also more so than that of stock prices. An early study by McMillan and Speight (2001) examined the conditional volatility of daily nonferrous LME settlement prices (aluminium, copper, nickel, lead, tin and zinc) over the period of 1972–1995. Their analysis provided a decomposition of volatility into its long-run and short-run components. Their main findings are that the half-life of shocks to market-driven short-run volatility typically extends over periods of no more than 8 days, while the half-life of shock to fundamentaldriven long-run volatility extends over periods of up to 190 days, such that metal price volatility is only very slowly mean-reverting. Also, their findings shown superior results of their model in comparison with the standard model of conditional volatility widely applied in modeling financial market volatility. Their results confirmed the relevance and significance of the decomposition of metal price volatility and the presence of three separate principal components driving underlying metal volatility. Later on, Mills (2003) investigated the statistical behavior of daily gold price data from 1971 to 2002. He found that the phenomenon of volatility prices scaling with long-run correlations is important. Furthermore, gold returns are characterized by short-run persistence and scaling with a break point of 15 days. Daily returns are highly leptokurtic with multi-period returns only recovering gaussianity after 235 days.

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Research done by Aggarwal and Lucey (2005) studied the existence of psychological barriers in a variety of daily and intraday gold price series. The authors analyzed three data sets: daily gold prices from the official London AM fix over the period 2/11/1980 to 31/12/2000, daily data from COMEX for cash and futures gold for the period 2/11/1982 to 28/11/2002, high frequency data set supplied by UBS London over the period 28/08/2001 to 09/01/2003. The authors found evidence demonstrating that psychological barriers at the 100s digits (price levels such as $200, $300, etc.) do exist in daily gold prices, while the evidence is weaker for high frequency data for gold. They also found significant evidence of changes in conditional means around psychological barriers. A study developed by Bernard et al. (2008) analyzed aluminium price series with daily, weekly and monthly frequencies. They used three econometric specifications that cover: (i) random-walk models with ARCH or GARCH effects, (ii) Poisson-based jump-diffusion models with ARCH or GARCH effects and (iii) mean reverting models that allow for uncertainty in equilibrium price. Their results showed that in the case of high frequency (daily and weekly) data, the mean-reverting model with stochastic convenience yield outperforms to a large extent. All other competing models for all forecast horizons, within the class of non-mean reverting GARCH processes analyzed for the same frequency models with jumps or asymmetries fare best, yet the latter remain dominated by the mean reverting models. With monthly data, the mean-reverting model still fares well in comparison with the random-walk GARCH class. Precious metal future contracts are analyzed by Xu and Fung (2005). The authors’ examined patterns of across-market information flows for gold, platinum, and silver future contracts traded in both the U.S. and Japanese markets. They analyzed daily data for gold, platinum and silver future contracts traded in U.S. and Japan over the period from November 1994 to March 2001. Their results indicate that pricing transmissions for precious metal contracts are strong across the two markets, but information flows appear to lead from the U.S. market to the Japanese market in terms of returns. There are strong volatility spillover feedback effects across both markets and their impact appears to be comparable and similar. They also found evidence that intraday pricing information transmission across the two precious metal future markets is rapid, as offshore trading information can be absorbed in the domestic market within a trading day. The underpricing of gold initial pricing offerings is studied by Dimovski and Brooks (2006). The authors analyzed 114 Australian gold mining IPOs from 1994 to 2004 using closing prices for the first day trading and an OLS methodology. The main findings showed a significantly lower 13.3% average first day returns. Options offered to underwriters can in part explain these returns as can the change in either the Gold Index or the All Ordinaries Index from the date of the prospectus to the date of listing. It appears that underwriters openly display a positive sentiment towards the company and its future if underwriters are willing to take underwriter options. Another study looking at commodity markets was done by Watkins and McAleer (2006). The authors analyzed data on 3-month future contracts for aluminium, aluminium alloy, copper, lead, nickel, tin and zinc. They estimated various long-run models using daily London Metal Exchange price data for the period 1 February 1986 to 30 September 1998. They found that in most of the samples considered for the seven metal markets, the test for cointegration determined the existence of one statistically significant long-run relationship among the future price, spot price, stock level and interest rate. They also found that the risk premium and carry models are usefully applied to each of the LME metal markets over different time periods. In addition, Tully and Lucey (2007) investigated the macroeconomic influences on gold using the asymmetric power GARCH model (APGARCH). They examined cash and future prices of gold and significant economic variables over the 1983–2003 period, paying special attention to two periods, around 1987 and in 2001, the year of the equity market crashes. Their results suggest that the APGARCH model provides the most adequate description for the data, with the inclusion of a GARCH term, free power terms and unrestricted leverage effect terms. They also found that the gold cash and future data over a long period confirmed the US dollar is the main macroeconomic variable which influences gold. A more general analysis looking at commodities behavior was carried out by Wolfle (2006). He used a dataset of 19 commodities and two stock indices (S&P 500 and Dow Jones) daily data covering the period from 31 December 1999 through 31 May 2006. He applied GARCH procedures to analyze

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his time series, and in general he found strong evidence of interdependence among commodities. His results showed that the Dow Jones and S&P 500 Index do not spillover to commodities; however the Dow Jones Index reacts on innovations for coffee and soybeans. Information transmissions between stock and commodity markets are rejected which means that commodity and stock markets are not interdependent, which supports the use of commodities to diversify risk in stock portfolios. This finding allows us to hypothesize that a similar pattern could be found in relation to precious metals; thus, these markets need to be analyzed carefully in order to provide evidence of independent behavior between precious metals themselves, bearing in mind that these markets can represent an interesting option for capital allocation. The role of precious metals in financial markets has been analyzed by Draper et al. (2006) who used daily data for gold, platinum and silver from 1976 to 2004. They include the S&P 500 Index as a proxy for stock market returns from the US investors’ perspective. They found that all three precious metals have low correlations with stock index returns which suggest that these metals may provide diversification within broad investment portfolios. They found that normally, financial portfolios that contain precious metals perform significantly better than standard equity portfolios. They also found that precious metals exhibit some hedging capability during periods of abnormal market volatility, a characteristic of great relevance during times of financial crises, where investors could use precious metals to minimize their risk exposure. The linkages between prices of oil futures traded on the New York Mercantile Exchange and the Intercontinental Exchange of London is studied by Spargoli and Zagaglia (2007). They estimated a structural BEKK-GARCH model on daily data from the 26th of April 1998 to the 26th of April 2007 data series on prices of futures. The main conclusion from their analysis is that in normal periods, NYMEX and ICE futures are used by investors for hedging purposes. However, in turbulent periods when there are peaks in the structural conditional variance of both innovations, the structural correlation between them is positive and hedging is no more feasible. Finally, a more recent study done by Batten and Lucey (2010) analyzed the volatility structure of gold, trading as a future contract on the Chicago Board of Trade using intraday (high frequency) data from January 1999 to December 2005. They used GARCH modeling and the Garman Klass estimator. They found significant variations across the trading days consistent with microstructure theories, although volatility is only slightly positively correlated with volume when measured by tick-count. Another relevant study conducted by Fernandez and Lucey (2006) analyzed the implications for portfolio management of accounting for conditional heteroskedasticity and structural breaks in long-term volatility. They based their analysis in PGARCH models fitted to the return series. They used weekly data of the Dow Jones Country Titans CBT municipal bond, spot and future prices of commodities for the period 1992–2005. They also applied their procedure to artificial data generated from distribution functions. They conclude that neglecting GARCH effects and volatility shifts may lead to overestimating financial risk at different time horizons. From the literature review it becomes evident that most of the research that has been done until now has been mainly focused on the analysis of the gold market; a main area of interest has been the role of this precious metal as a hedger against inflation; some studies have also analyzed variables that could be affecting the behavior of gold prices, but little has been done with regard to other precious metals such as silver, platinum and palladium. Nonetheless, it seems that this trend is changing and researchers are starting to pay more attention to the other precious metal markets and their behavior, as they are becoming more aware of the importance of these markets in terms of portfolio risk management. However, there is still an important lack of studies analyzing both the reaction of precious metal markets to the different financial crises that had impacted financial markets in the past, and indeed what has happened in the markets since the unfolding of the U.S. subprime crisis that has translated itself into a global financial downturn. This new breed of studies are of key importance as they could provide important information to investors in order to help them diversify their portfolio and design their hedging strategies with the aim of minimizing losses, or finding alternative options that allow materializing profits during times of market instability. As a result, this paper’s main contribution to the existing literature in this area is that it provides new evidence on volatility spillover analysis by using a comparative analysis of volatility spillovers

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between the four precious metal returns (gold, palladium, platinum and silver) over the time period 1995 to November 2010, through GARCH and EGARCH modeling. 3. Data and methodology Our analysis focuses on the period 1 January 1995 to 4 November 2010. Initially, we analyze the long period that spans from January 1995 to July 2007, and we decided then to split this first time period into three sub samples in order to provide greater details that will help us gain a better understanding of volatility spillovers between precious metal returns. Besides, the sample division allows us to filter our analysis so as to avoid misleading results derived from the existence of structural breaks. Thus, our first sub-sample spans over the years 1995 to June 1997, the period prior to the Asian crisis. Since we are interested in examining whether the Asian crisis could generate volatility spillovers between these financial markets, the second sub-sample will cover the July 1997–1998 period (the ICSS algorithm has been used to verify that there is a breakpoint during this time1 ) when the crisis hit the markets, and when precious metal markets were prone to great economic uncertainty. Finally our last sample period covers the years 1999 to July 2007, where we intend to analyze the behavior of these markets after the major shock emanating from Asia, and how they have behaved afterwards. The second part of this study looks at the global financial crisis that is affecting the world economy since late 2007; hence, we consider of relevance to analyze precious metal behavior during August 2007 to November 2010 (again the ICSS algorithm and alternative tests for structural breaks were used)2 , as this time period will allow us to compare and identify patterns of behavior in these markets during times of crises. The data set consists of daily closing values for precious metal data. We took the US$/Troy ounce for gold, the London Free Market Platinum price in US$/Troy ounce, the London Free Market Palladium price in US$/Troy ounce and the Zurich silver price in US$/kg. All our data series are from DataStream International, giving a total of 5220 observations for each series. Following Kanas (2000) we use continuously compounded precious metal returns that are calculated as the first difference of the natural log. By letting PM be the series of precious metal prices, we can write: PM ) (Figs. 1 and 2). PMt = ln(PtPM ) − ln(Pt−1 The research main analysis and findings are organized as follows: as an initial step we provide descriptive statistics for precious metal returns, in order to summarize the statistical characteristics of our sample. We then proceed and perform a stationarity test on each of the relevant variables that are included in our study to ensure that the results from the analysis are not spurious. We apply the Dickey–Fuller (DF) test or Augmented Dickey–Fuller test (ADF) procedure if serial correlation is present. We also apply the Lagrange Multiplier (LMF) test, to ensure that a sufficient number of lags have been added in the ADF test to ensure that there is no serial correlation present, and that the results of the ADF test are valid. The LMF test is applied given that it is valid in the presence of lagged dependent variables as well as having the advantage of testing for first and higher orders of serial correlation. We estimate the lag selection tests up 20 lags. In terms of choosing between the various lag length selection criteria, we follow Johansen et al. (2000) who suggest that when different information criteria suggest different lag lengths, it is a common practice to select the Hannan–Quinn (HQ) criteria. We ensure that the lag length selected for the VAR model is free from serial correlation by applying the LMF test to test for serial correlation up to the number of lags previously obtained in the VAR model. We then proceed with our volatility analysis and apply a bivariate extension of the EGARCH (p,q) model in order to examine whether the volatility of precious market returns affects and is affected by the volatility of the other precious metal returns within each market. Taking into account that there are several methods that analyze the volatility issue, it is important that we justify our choice for this paper. In this study, we implement the analysis using the generalized

1 See Figs. 1 and 2 for more details on this issue. All the information and results regarding structural breaks are available upon request, and further details on the ICSS algorithm can be found in the Inclan and Tiao (1994) paper. 2 See Figs. 1 and 2 for more details (as above).

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Precious Metals 1990-2010

2,400 2,000 1,600 1,200 800 400 0

90

92

94

96

98

00

GOLD PLATINUM

02

04

06

08

PALLADIUM SILVER

Fig. 1. Precious metal prices behavior. This diagram shows how precious metal prices have evolved over 1990–2010. Through the graph analysis it is possible to appreciate how these series have been affected by different economic shocks during the time period under observation. Considering that the authors of this paper are focusing their attention on two main crisis periods (i.e.: the Asian crisis and the latest global financial turmoil), it has been deemed appropriate to split the sample according to these two financial crises. As a result, three different structural break tests have been performed in order to verify that the series have changed their regime around the mentioned events. Consequently, the Inclan and Tiao (1994) ICSS algorithm is used to identify how many breaks are affecting the series. This algorithm allows the detection of multiple break points in the variance in the case of time series. In addition the Chow test and Andrew Quandt test have been used to verify the results (see Fig. 2 for more details).

autoregressive conditional heteroscedasticity or GARCH model (Bollerslev, 1986) that has been proven successful at modeling stock return volatility by allowing the mean of stock returns to depend on its time-varying variance and other causes for the mean or the changing variance. We will apply two methodologies in order to analyze the behavior of precious metal market returns, and in order to

Precious Metals 1990-2010 - Structural Breaks Global Financial Crisis 2007/2009

2,400 2,000 1,600

Asian Crisis 1997/1998

1,200 800 400 0

90

92

94

96

98 GOLD PLATINUM

00

02

04

06

08

PALLADIUM SILVER

Fig. 2. Precious metal structural breaks. After performing the ICSS algorithm (see Inclan and Tiao, 1994 for more details on this methodology) it has been found that each series is affected by multiple break points. However, none of the series seem to be affected by the Asian crisis (i.e.: 2nd of July, 1997). While all of them have been affected by the global financial crisis (around observation 4370 that is the 1st of August 2007 each series is affected by a change of regime). The results obtained from the ICSS algorithm are confirmed by the Chow test. Therefore, the authors considered that the results are strong enough. Since the main interest of this paper is to look at comparative precious metal behavior during two crises, we have conducted the whole analysis as initially established with the aim of verifying that the volatility analysis will show stability patterns in these markets. All the results from these tests have been omitted for the sake of brevity, but they are available from the authors upon request.

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capture the impact of precious metal return depreciation on each market and its volatility. The form of the GARCH and EGARCH specifications are explained below. The generalized autoregressive conditional heteroscedasticity (GARCH) models were introduced by Engle (1982) and Bollerslev (1986). With regard to the precious metal markets, the EGARCH specification can be written as: PMyt = aPMy,0 +

r 

aPMy,i PMyt−i +

i=1

PMxt = aPMx,0 +

r 

r 

aPMx,i PMxt−i + ePMy,t

(1)

aPMy,i PMyt−i + ePMx,t

(2)

i=1

aPMx,i PMxt−i +

i=1

r  i=1

2 ePMy,t /˝t−1 ≈ N(0, PMy,t ),

2 ePMx,t /˝t−1 ≈ N(0, PMx,t )

The conditional variances of precious metal returns are specified as follows:

2 log PMy,t = exp

⎧ ⎨



pPMy

cPMy,0 +

⎩

2 bPMy,j log(PMy,t−j ) + ıPMy,PMy [(|zPMy | − E|zPMy,t−1 |

j=1

+ PMy,PMyzs,PMy−1 ) + ıPMy,PMx [(|zPMx,t−1 | − E|zPMx,t−1 | + PMy,PMxzPMx,t−1 )]]

2 log PMx,t

= exp

⎧ ⎨

pPMy

cPMx,0 +

⎩



(3)

2 bPMx,j log(PMx,t−j ) + ıPMx,PMx [(|zPMx,t−1 | − E|zPMx,t−1 |

j=1

+ PMx,PMzy ) + ıPMx,PMy [(|zS,t−1PMy | − E|zPMy,t−1 | + PMXPMyzPMx,t−1 )]]

(4)

 PMy,PMx,T = PMx  PMy,T  PMx,T . Each of the relevant terms in Eqs. (1)–(4) is explained in detail in Table 1. We specify the number of lags for the conditional mean Eqs. (1) and (2) using the Hannan–Quinn (HQ) criterion; the test was conducted up to 20 lags, selecting the number of lags where the HQ criteria was minimum. Griffin et al. (2001), note that the HQ criterion is preferable to the more commonly used Akaike’s Information Criteria (AIC), as the latter tends to over-parameterize the models. Next we apply the likelihood ratio (LR) test to determine the lag truncation length (p). We perform separate LR tests on the precious metal returns variance Eqs. (3) and (4) to determine the optimal lag length for the EGARCH ˆ − L()] ˜ ≈ 2 (m), specification of each equation. Hamilton (1994) defines the LR test as follows: 2[L() ˆ denotes the value of the log likelihood function of the unrestricted estimate and L() ˜ where L() denotes the value of the log likelihood functions of the restricted estimate. Bollerslev–Woolridge robust t-statistics are derived to take into account the possible non-normality of the residuals. In the second part of our methodology we perform a GARCH analysis, where the GARCH specification is presented in Eqs. (5) and (6). In Eq. (7) we present the error term that will be included in Eqs. (5) and (6) in order to improve the original model. PMy = c0 +

m 

˛i PMxt−i + εyt

(5)

i=1

PMx = a0 +

n 

ıi PMyt−i + εxt

(6)

i=1

εyt = yt − yt−1 ;

εxt = xt − xt−1

(7)

Stochastic error terms Information set at time t−1 Conditional (time varying) variances Standardized residuals assumed to be normally distributed with 0 mean and variances of 2 2 PMy,t ,PMx,t

Precious metal returns y

Precious metal returns x

ePMy,t ˝t−1 2 PMy,t zPMy,t = ePMy,t / PMy,t

ePMx,t ˝t−1 2 PMx,t zPMx,t = ePMx,t / PMx,t

2 ePMy,t /˝t−1 ∼N(0, PMy,t )

pPMy 

2 ePMy,t /˝t−1 ∼N(0, PMx,t )

pmx 

bPMy

Persistence of volatility j=1

bPMx,j j=1

ARCH effect where the parameters  PMy,PMy ,  PMx,PMx allow this effect to be asymmetric

[|zPMy,t | − E|zPMy,t | + PMy,PMy,PMx,t ]

Volatility spillover

ıPMy,PMx

Measures of spillovers Asymmetry of spillovers Correlation coefficient for standardized residuals

ıPMy,PMx  PMy,PMx PMy,PMx

     zPMx,t−1  − E zPMx,t−1  + PMy,PMxz,PMx,t−1

[|zPMx,t | − E|zPMx,t | +  PMx,PMx,PMx,t ]

ıPMx,PMy ıPMx,PMy  PMx,PMy PMx,PMy

     zPPMy  − E zPMy,t−1  + PMx,PMyz,PMy,PMyt−1

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Table 1 Description of parameter Eqs. (1)–(4).

211

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Eqs. (8) and (9) represent our model after the error term is included in each original equation: p 

PMy = c0 +

˛i PMxt−i +

q 

PMx = a0 +

r 

ıi PMyt−i +

i=1

yt |

yt−1 + yt

(8)

xt−1 + xt

(9)

i=1

i=1

s  i=1

yt−1 ∼N(0, hyt );

xt |

xt−1 ∼N(0, hxt )

(10)

Eq. (11) presents the variance of the error terms for Eqs. (8) and (12) shows the variance of the error term for Eq. (9). hyt = ˇ0 +

a 

ˇ1 hyt−1 +

c 

1 2yt−1

(11)

c1 2xt−1

(12)

i=1

i=1

hxt = b0 +

b 

b1 hxt−1 +

d 

i=1

i=1

We consider that it is important to take into account the effect of the depreciation of the alternative precious market in each model. Therefore, Eqs. (11) and (12) are modified as follows: hyt = ˇ0 +

f 

ˇ1 hyt−1 +

i=1

hxt = b0 +

l  i=1

b1 hxt−1 +

g 

1 2yt−1 +

j 

i=1

i=1

v 

w 

i=1

c1 2xt−1 +

1 (PMxt−1 )2

1 (PMyt−1 )2

(13)

(14)

i=1

where PMy is one precious metal return (e.g. gold) and PMx is the other precious metal return (e.g. platinum) on day t; the serially correlated errors εyt and εxt follow an MA(1) process. The variance hyt of the error term yt is obtained on the information set y available at time t − 1 ( yt−1 ). In the model yt−1 consists of past conditional variances and past squared error terms, PMx is the precious metal returns of the alternative market, and the conditions ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0 (ˇ1 + 1 ≤ 1) are the customary constraints applied to the parameters to enforce stationarity and a positive conditional variance. The variance hxt of the error term xt is obtained on the information set x available at time t − 1 ( xt−1 ); conversely, xt−1 consists of past conditional variances and past squared error terms, PMy is the precious metal returns of the alternative market, and the conditions b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0 (b1 + c1 ≤ 1) are as before. The parameters of the models: (a0 , ı, , b0 , b1 , c1 , 1 ) and (c0 , ˛, , ˇ0 , ˇ1 , 1 , 1 ) are estimated using the maximum likelihood method by the BHHH algorithm (Berndt et al., 1974). The GARCH (1,1) model will examine the depreciation effects of precious metal returns in each respective market through the mean return equation (Eq. (5)). The other is through the variance equation (Eq. (8)) that depends on the depreciation of the alternative market. The square is used to guarantee a positive value of the variance. Bollerslev–Woolridge robust t-statistics are derived to take into account possible non-normality of the residuals. The diagnostic tests on the standardized residuals are performed for the GARCH and EGARCH models; these include the Jarque–Bera test for normality; the Bollerslev–Woolridge robust t-statistics; the Ljung–Box (LB) statistics that will detect that there are no residual linear or non linear dependencies in the errors; and the LB statistics for the cross products of the standardized residuals for the two equations are calculated as these statistics indicate if the assumption of constant correlation over time can be accepted. Finally, the ARCH–LM residual test will be performed, to test whether the standardized residuals exhibit additional ARCH effects. If the variance equation is correctly specified, there should not be an ARCH effect left in the standardized residuals.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

213

Table 2 Descriptive statistics precious metal returns. Mean

SD

Skewness

Kurtosis

0.000168 0.000258 0.000345 0.00029

0.0086 0.0215 0.0134 0.0173

0.1096 0.0967 −0.6478 −0.6922

10.2094 9.6825 19.2013 12.8068

7112 6110 36,113 13,410

1995 to June 1997 Gold Palladium Platinum Silver

−0.00021 0.000312 4.91E−05 −7.95E−05

0.0044 0.0164 0.0101 0.0143

0.3319 1.0173 2.3290 0.6299

6.4210 11.9374 33.2392 10.4756

329 2275 25,353 1557

July 1997–1998 Gold Palladium Platinum Silver

−0.00038 0.001321 −0.00048 0.000173

0.0072 0.0275 0.0149 0.0183

−0.0111 0.2410 −0.1976 0.2691

3.9738 6.2832 4.4165 6.1449

15 180 35 166

0.000374 4.64E−05 0.000569 0.000419

0.0097 0.0217 0.0139 0.0179

0.0639 −0.0873 −1.0661 −1.0660

9.0372 9.8476 20.4116 13.9877

3399 4373 28,681 11,677

0.015057 0.026528 0.020022 0.025568

−0.167040 −0.067198 −0.690689 −1.013469

5.958253 7.793531 5.958206 10.35618

1995 to July 2007 Gold Palladium Platinum Silver

1999 to July 2007 Gold Palladium Platinum Silver

August 2007 to November 2010 Gold 0.000764 Palladium 0.000821 Platinum 0.000289 Silver 0.000786

JB

298 835 359 1962

The descriptive statistics for all precious metals under analysis provide valuable information confirming that these series tend to follow normal time series properties. As showed by the Jarque–Bera test the series returns are non-normal, a characteristic that tends to be shared by stock returns. In addition precious metals tend to be negatively skewed with the exception of the second sub-sample looking at 1995 to June 1997 where the results are positive. The coefficients looking at kurtosis tend to be quite high especially in the cases of Platinum and Silver for the 5 sub-samples, indicating that this series is showing leptokurtic behavior where the values of the series tend to be concentrated towards the mean. With regard to the mean, the results are positive for all the sub-samples under analysis, with the exception of 1995 to June 1997, where Gold and Silver present negative returns. Finally, the results from the standard deviation (SD) showed that during the Global Financial Crisis, precious metals where affected by more uncertainty than during previous sub-samples. Only Palladium showed a higher percentage (2.75%) during the Asian Crisis than during the latest financial turmoil.

4. Empirical results Our empirical results are presented through Sections 4.1–4.7. First we start presenting the basic descriptive statistics of our dataset which provide us with the details and characteristics of our series; second we will present the results of the unit root analysis, the likelihood ratio tests performed and the basic tests that will provide the necessary information to identify which EGARCH (p,q) specification will be the most appropriate to model our two financial variables. Finally, we present the results of the EGARCH analysis, results that will provide information of volatility persistence, volatility spillovers and asymmetric spillover effects. 4.1. Descriptive statistics The analysis of the descriptive statistics of precious metal returns is presented in Table 2. During the four periods of analysis, almost all markets present positive and small values, the exceptions being gold and silver for the period before to the Asian crisis (1995 to June 1997) where the means are negative. During the Asian crisis (July 1997–1998) the results show negative means in the case of gold and platinum. After the financial crisis all the means for the four precious metals are positive. The analysis of the returns volatility for all our samples shows that overall palladium is the most volatile

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Table 3 Augmented Dickey–Fuller test. Precious metals

1995 to July 2007

1995 to June 1997

July 1997–1998

1999 to July 2007

August 2007 to November 2010

Gold Palladium Platinum Silver

−14.11a −25.69a −18.08a −18.37a

−12.34a −4.97a −5.03a −14.62a

−44.47a −10.44a −16.26a −36.78a

−63.55a −8.16a −19.18a −53.698

−28.39a −27.15a −26.37a −31.24a

a The results from the ADF test show that all the series (precious metal returns) are stationary in levels at the 1% significance level. These results are needed in order to obtain robust results from the GARCH and EGARCH estimations.

Table 4 Likelihood ratio precious metals. Precious metals

1995 to July 2007

1995 to June 1997

July 1997–1998

1999 to July 2007

August 2007 to November 2010

Gold–palladium Palladium–gold Gold–platinum Platinum–gold Gold–silver Silver–gold Palladium–platinum Platinum–palladium Palladium–silver Silver–palladium Platinum–silver Silver–platinum

29.68b 1.83a 28.16b 4.00a 32.1b 116.15b 6.14b 1.01a 2.13a 99.39b 3.16a 104.84b

0.77a 13.64b 0.39a 2.22a 1.99a 20.43b 0.01a 3.48a 15.74b 23.22b 0.10a 20.63b

0.31a 34.95b 0.34a 0.84a 1.04a 2.10a 16.35b 1.02a 45.33b 1.92a 0.01a 2.2a

96.43b 0.00a 75.14b 5.28a 79.41b 28.29b 1.43a 0.17a 1.19a 10.82b 1.57a 25.01b

13.80b 4.106a 1.488a 1.94a 7.29b 13.81b 8.022b 20.35b 12.436b 7.87b 8.28b 10.36b

The 5% critical value for the LR test distributed as 2 with 2 degrees of freedom is 5.99. Overall, the results show that in half of the occasions (thirty times) the EGARCH (2,1) seems to be a better fit to explain precious metal behavior. While the EGARCH (1,1) is a better model for the other half. These results are not very conclusive and it seems that there is no possibility to generalize in order to identify which model is a better fit for this case. Therefore, the analysis needs to consider both models in order to identify which one is the best option for each sub-sample. a H0 : EGARCH (1,1). b H1 : EGARCH (2,1).

of the four precious metals, moving in a range of 1.64% prior to the crisis to 2.75% during the crisis time. Gold is the less volatile with a 0.44% standard deviation prior to the crisis as the minimum value and with a 0.97% as the highest value after the financial crisis. Platinum and palladium standard deviations move around 1.01–1.83% during the four periods. The skewness and kurtosis coefficients indicate that precious metal returns are leptokurtic relative to the normal distribution. The Jarque–Bera test also rejects the hypothesis that precious metal returns are normally distributed in all the cases. 4.2. Unit roots and likelihood tests The results from the ADF tests are given in Table 3. The values of the test statistics indicate that we can reject the null hypothesis of the existence of a unit root in levels for all variables during all periods indicating that all series are I(0).3 Given that all variables are integrated of the same order, (i.e. I(0), we proceed directly to perform our volatility analysis using EGARCH (p,q) modeling. In order to establish the correct lag length for the EGARCH model, we apply the likelihood ratio test. The results from this test for each of ours series are set out in Table 4. One asterisk refers to the selection of an EGARCH (1,1), and two asterisks to an EGARCH (2,1) model. There is a mix of (1,1) and (2,1) models chosen for the different bivariate models, with none of the models appearing as the dominant one. The estimated parameters from the EGARCH estimation are set out in Tables 5–74 for the four periods of analysis (1995 to July 2007, 1995 to June 1997, July 1997–1998, 1999 to July 2007 and 3 4

The LMF test results (not reported here) indicated that the ADF tests were free from serial correlation. The diagnostic tests results are omitted for the sake of brevity but they are available from the authors upon request.

1995 to July 2007 1995 to June 1997 July 1997–1998 1999 to July 2007 August 2007 to November 2010 Platinum–silver 0.2026 (0.000)* 0.2515 (0.000)* 0.1045 (0.420) 0.2092 (0.000)* 0.367 (0.002)**

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

0.2324 (0.006)* 0.1877 (0.149) 0.1041 (0.376) 0.2391 (0.011)** −0.1690 (0.069)***

0.2312 (0.006)* 0.2548 (0.001)* 0.1134 (0.322) 0.2412 (0.010)** 0.1240 (0.000)*

0.2354 (0.003)* 0.2048 (0.005)* −0.0037 (0.963) 0.2602 (0.001)* 0.3184 (0.000)*

0.1934 (0.000)* 0.1527 (0.069)*** 0.2008 (0.141) 0.2908 (0.000)* 0.3706 (0.000)*

0.2451 (0.000)* 0.3993 (0.000)* 0.3660 (0.034)** 0.2569 (0.000)* 0.0623 (0.6264)

Palladium–gold 0.2517 (0.006)* 0.2518 (0.000)* 0.2312 (0.115) 0.2631 (0.000)* (0.2733) (0.002)*

Platinum–gold 0.2864 (0.000)* 0.2310 (0.000)* 0.0762 (0.569) 0.2351 (0.000)* 0.1760 (0.000)*

Silver–gold 0.4561 (0.000)* 0.4698 (0.000)* 0.3632 (0.001)* 0.5220 (0.000)* 0.4859 (0.000)*

Platinum–palladium 0.2870 (0.000)* 0.2318 (0.000)* 0.0716 (0.571) 0.2341 (0.000)* 0.4073 (0.001)*

This table presents the coefficients looking at the EGARCH results for the volatility persistence coefficients as discussed in Table 1:

pPMy j=1

Silver–palladium 0.4638 (0.000)* 0.6009 (0.000)* 0.3388 (0.004)* 0.5271 (0.000)* 0.3532 (0.026)** bPMy ,

pmx j=1

Silver–platinum 0.4607 (0.000)* 0.4693 (0.000)* 0.3551 (0.000)* 0.5193 (0.000)* 0.397 (0.008)**

bPMx,j . Overall, precious metals tend

to exhibit volatility persistence. The only exception in our analysis is related to the results obtained for the Asian crisis sub-sample where in most of the cases the coefficients appear to be insignificant. This can be interpreted as a sign of certain stability reflected by precious metals during this time period. * 1% significance level. ** 5% significance level. ***

10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 5 EGARCH results volatility persistence.

215

216

Gold–palladium 1995 to July 2007 1995 to June 1997 July 1997–1998 1999 to July 2007 August 2007 to November 2010 Palladium–gold 0.0127 (0.703) 0.0815 (0.008)* 0.0343 (0.717) −0.0041 (0.919) −0.0569 (0.3967)

*

0.0608 (0.000) 0.0383 (0.411) 0.0357 (0.528) −0.1824 (0.047)** 0.0419 (0.1020) Platinum–gold 0.0713 (0.000)* 0.1406 (0.033)** 0.2313 (0.007)* 0.0642 (0.028)** −0.0069 (0.8190)

Gold–platinum

Gold–silver *

0.0627 (0.000) −0.0183 (0.776) 0.0324 (0.574) −0.1844 (0.042)** 0.0480 (0.066)*** Silver–gold 0.0405 (0.205) −0.2097 (0.002)* 0.3976 (0.000)* −0.2361 (0.039)** −0.0872 (0.1794)

Palladium-platinum *

0.0708 (0.000) 0.0528 (0.321) 0.0702 (0.367) 0.0347 (0.641) 0.0637 (0.000)*

*

0.7386 (0.000) 0.1067 (0.022)** 0.0836 (0.644) −0.0072 (0.863) 0.0088 (0.6028)

Platinum–palladium 0.0693 (0.000)* 0.1565 (0.001)* 0.2180 (0.009)* 0.0645 (0.027)** 0.0024 (0.927)

Palladium–silver

Platinum–silver

0.0085 (0.806) 0.1272 (0.041)** 0.0243 (0.936) −0.0113 (0.789) −1.626 (0.103)

0.0646 (0.003)* 0.1549 (0.003)* 0.2289 (0.004)* 0.0596 (0.030)** −0.002 (0.921)

Silver–palladium 0.0385 (0.269) −0.0037 (0.933) 0.2938 (0.001)* −0.2012 (0.132) −0.007 (0.877)

Silver–platinum 0.0401 (0.233) −0.2110 (0.002)* 0.3471 (0.000)* −0.2270 (0.045)** −0.006 (0.8948)

This table presents the coefficients looking at the EGARCH results for the Spillovers Effects. The coefficients measuring spillovers effects are: ıPMy,PMx , ıPMx,PMy as properly explained in Table 1. Looking at the results it seems that precious metals exhibit stability properties during the crises subsamples, as the coefficients tend to be insignificant in most of the cases. * 1% significance level. ** 5% significance level. ***

10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 6 EGARCH results volatility spillovers.

1995 to July 2007 1995 to June 1997 July 1997–1998 1999 to July 2007 August 2007 to November 2010 Palladium–gold 0.9334 (0.000)* 0.9768 (0.000)* 0.7328 (0.003)* 0.9218 (0.000)* 0.8318 (0.000)*

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

0.9864 (0.000)* 0.9444 (0.000)* −0.7072 (0.116) 0.9844 (0.000)* 0.9894 (0.000)*

0.9859 (0.000)* 0.9463 (0.000)* −0.7230 (0.054)*** 0.9844 (0.000)* 0.9913 (0.000)*

0.9784 (0.000)* 0.9465 (0.000)* 0.6558 (0.363) 0.8219 (0.000)* 0.9956 (0.000)*

0.1679 (0.000)* 0.9592 (0.000)* 0.8855 (0.000)* 0.8770 (0.000)* 0.9791 (0.000)*

0.9364 (0.000)* 0.7920 (0.000)* 0.5863 (0.130) 0.9206 (0.000)* 8.173 (0.000)*

0.9778 (0.000)* 0.9392 (0.000)* −0.2353 (0.516) 0.9723 (0.000)* 0.988 (0.000)*

Platinum–gold 0.9701 (0.000)* 0.9521 (0.000)* −0.1952 (0.612) 0.9613 (0.000)* 0.9798 (0.000)*

Silver–gold 0.9590 (0.000)* −0.3552 (0.251) 0.3174 (0.099)*** 0.8547 (0.000)* 0.9458 (0.000)*

Platinum–palladium 0.9720 (0.000)* 0.9445 (0.000)* −0.3392 (0.362) 0.9593 (0.000)* 0.996 (0.000)*

Silver–palladium 0.9466 (0.000)* 0.9936 (0.000)* 0.2849 (0.309) 0.8115 (0.000)* 0.979 (0.000)*

Silver–platinum 0.9522 (0.000)* −0.3534 (0.255) 0.3002 (0.205) 0.8499 (0.000)* 0.970 (0.000)*

This table shows the results obtained from the EGARCH model regarding asymmetric spillover effects. The coefficients under analysis are:  PMy,PMx ,  PMx,PMy (see Table 1) are significant in most of the cases. The results are quite consistent across all sub-samples showing that negative information tends to have a greater impact in these markets than positive. Another interesting result is the one obtained during the Asian crisis. During this time, the coefficients are quite mixed, a circumstance that it is not repeated during the Global financial crisis when all the coefficients are significant. Again, this divergence in results can be explained by the origins, characteristics and length of this financial event. It is necessary to consider that the Asian crisis has stronger effects in emerging economies located in the Asian region with limited spillover effects to the rest of the world. On the other hand, the 2007/08 financial event has a bigger impact around the world, with stronger effects in developed economies that are believed to be more resilient to economic downturns. * 1% significance level. ** 5% significance level. *** 10% significance level.

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Table 7 EGARCH results asymmetric spillovers.

217

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August 2007 to November 2010). Finally, the results for the GARCH (1,1) are in Tables 8–12. The p-values are given in parentheses beneath each coefficient estimate. 4.3. Volatility persistence (EGARCH) With regard to the coefficients pertaining to the volatility persistence term (Table 5), the results vary depending on the type of precious metal and on the equation under analysis, but we find that in the majority of the cases the coefficients are significant. This result is not surprising given that persistence is a feature of many financial market data; therefore we expected to find evidence of significant coefficients in most of the cases. For the first sub-period (1995 to July 2007), the coefficients are significant in all the cases. The coefficients are all significant for the period preceding the Asian crisis (1995 to June 1997); the exception is palladium–gold for which the coefficient appears to be insignificant. An interesting feature of our results is the insignificant coefficients obtained for the period of the Asian financial crisis; we expected to find significant coefficients during this particular time as the effect of the Asian crisis could be dragging all the markets into recession, an expectation that was not supported by our findings. Almost all the coefficients appear to be insignificant with the exception of the results for the equations analyzing palladium–silver, silver–gold, silver–palladium and silver–platinum. The results for the coefficients of the 1999 to July 2007 period are all significant. Finally, for the August 2007 to November 2010 period, volatility persistence appears to be generally significant, with only one exception in the case of palladium–silver. It is interesting to notice that the results obtained for the Asian crisis are quite different when compared to those obtained for the global financial crisis; in this latter case, the markets strongly react to the global financial crisis, with instability tending to last. However, the conditions during the Asian crisis were very different, as precious metals did not reflect any evidence of lasting effects; this means that precious metals seem to be more sensitive to the current financial turmoil than to what happened in the markets during the Asian crisis. Volatility persistence is a common finding in financial market returns, a situation that is reflected by the findings of significant coefficients. If the following coefficients are significant and greater than zero Pmx Pmy (i.e. b > 0), this implies that a deviation of the price from its expected value b and j=1 Pmx,j j=1 PMY ,j will cause the variance of the price to be larger than otherwise; this means that the amplitude of return fluctuations represents the amount of variation of the returns during a short-time. In the presence of a long memory process affecting volatility, this implies that the fluctuations will remain in the markets for a while with the uncertainty that this situation will bring to the markets. This is a situation that has important consequences in terms of risk management. Since investors base their decisions on expectations, the diversity of expectations causes a variability of stock returns. The insignificance of the volatility persistence coefficients found in this analysis in the precious metal returns could reflect the fact that, as a general rule, the Asian crisis did not generate a great impact on these markets, as investors expected stability in the precious metal prices. Therefore, their expectations tend to be constant and stable over a long time, a situation that will be translated in the precious metal markets returns as a lower fluctuation in their prices. The appreciation of precious metals as a store of value directly implies the expectation of price stability; this means that prices are expected to be moving gradually in an upward trend. Therefore, our volatility persistence analysis shows that overall there are significant coefficients on precious metal returns; however, they tend to be modified according to market fluctuations and investors’ decisions. This result indicates that precious metal return fluctuations do generate a mutual impact on these markets, indicating that when any of the precious metal markets faces fluctuations, these movements will be transmitted to the others. What is important in our findings is that the two crises have been perceived in a different manner by the markets, and therefore volatility persistence has adjusted accordingly. 4.4. Volatility spillovers (EGARCH) The analysis of the coefficients for the volatility spillovers are presented in Table 6, where it can be seen that results are quite mixed across time periods. The main results are showing evidence

Parameters

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

c0 ˛  ˇ0 ˇ1 1

1 ˇ1 + 1

0.0000 (0.710) 0.0733 (0.000)* 0.0000 (0.968) 0.0000 (0.030)** 0.0583 (0.000)* 0.9390 (0.000)* 0.0007 (0.060)** 0.9973

−0.0001 (0.528) 0.2006 (0.000)* −0.0002 (0.055)** 0.0000 (0.179) 0.0571 (0.000)* 0.9398 (0.000)* 0.0026 (0.044)** 0.9969

0.0000 (0.878) 0.2150 (0.000)* −0.0004 (0.001)* 0.0000 (0.002)* 0.2078 (0.000)* 0.6751 (0.000)* 0.0236 (0.000)* 0.8829

−0.0003 (0.115) 0.7476 (0.000)* 0.0014 (0.000)* 0.0000 (0.044)** 0.1934 (0.000)* 0.7386 (0.000)* 0.1679 (0.000)* 0.9320

0.0000 (0.949) 0.0456 (0.000)* 0.1756 (0.359) 0.0000 (0.000)** −0.0407 (0.017)** 0.0594 (0.003)* 0.8324 (0.000)* 0.0187

0.0000 (0.794) 0.1627 (0.000)* −0.0006 (0.013)** 0.0000 (0.073)*** 0.1137 (0.000)* 0.8724 (0.000)* 0.0088 (0.002)* 0.9861

Parameters

Palladium–gold

Platinum–gold

Silver–gold

Platinum–palladium

a0 ı  b0 b1 c1 1 b1 + c1

0.0001 (0.194) 0.5425 (0.000)* 0.0008 (0.044)** 0.0000 (0.014)** 0.1307 (0.000)* 0.8341 (0.000)* 0.1188 (0.017)* 0.9649

0.0000 (0.800) 0.4971 (0.000)* −0.0007 (0.001)* 0.0000 (0.005)* 0.1020 (0.000)* 0.8846 (0.000)* 0.0320 (0.000)* 0.9866

0.0003 (0.165) 0.9334 (0.000)* −0.0030 (0.000)* 0.0000 (0.000)* 0.1733 (0.000)* 0.5800 (0.000)* 0.4010 (0.000)* 0.7533

0.0002 (0.147) 0.3093 (0.000)* −0.0001 (0.588) 0.0000 (0.000)* 0.1863 (0.000)* 0.6891 (0.000)* 0.0266 (0.000)* 0.8754

Silver–palladium **

0.0002 (0.084) 0.0640 (0.000)* −0.0014 (0.000)* 0.0000 (0.000)* −0.0865 (0.000)* 0.4012 (0.000)* 0.2838 (0.000)* 0.3147

Silver–platinum 0.0001 (0.656) 0.3395 (0.000)* −0.0025 (0.000)* 0.0001 (0.000)* 0.2826 (0.000)* 0.3354 (0.000)* 0.2212 (0.000)* 0.6180

The parameter conditions constraints are as follows: b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0, (b1 + c1 ≤ 1) and ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0, (ˇ1 + 1 ≤ 1). These constraints are applied to the parameters to enforce stationarity and a positive conditional variance as properly explained in the methodology section of this paper. The volatility persistence of each GARCH estimation is measured by the sum of the following coefficients for each equation (ˇ1 + 1 ≤ 1) and (b1 + c1 ≤ 1). Taking into account that the depreciation of each precious metals return could be a cause of market volatility squared rate of changes in each series returns is used to introduce precious metal depreciation in each one of the equation looking at the bidirectional relationship between the series. In order to guarantee a positive value of the variance the squared rate of returns is used in the model(i.e. ␭>0 and ␥>0). The results show that the GARCH results are quite strong as the coefficients looking at volatility persistence tend to be quite high and stable in almost all the cases. The only exception can be seen in the case of the silver–palladium relationship where the results are quite low from the bidirectional analysis. In addition, the coefficient looking at market depreciation is significant in all the cases, confirming the authors initial expectations pointing out that this variable can be considered as a source of market instability. * 1% significance level. ** 5% significance level. ***

10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 8 Estimates of the GARCH (1,1): 1995 to July 2007.

219

220

Parameters

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

c0 ˛  ˇ0 ˇ1 1

1 ˇ1 + 1

−0.0001 (0.378) 0.0845 (0.000)* −0.0002 (0.283) 0.0000 (0.020)** 0.1022 (0.000)* 0.8309 (0.000)* 0.0019 (0.1758) 0.9331

−0.0001 (0.486) 0.2806 (0.000)* −0.0005 (0.002)* 0.0000 (0.009)* 0.1498 (0.001)* 0.6185 (0.000)* 0.0274 (0.000)* 0.7683

−0.0001 (0.257) 0.1389 (0.000)* −0.0003 (0.021)** 0.0000 (0.180) 0.1113 (0.011)** 0.8377 (0.000)* 0.0010 (0.181) 0.9490

−0.0003 (0.439) 0.8995 (0.000)* 0.0005 (0.294) 0.0000 (0.290) 0.2078 (0.000)* 0.5995 (0.000)* 0.2781 (0.020)** 0.8074

−0.0007 (0.083)** 0.2742 (0.000)* 0.0002 (0.692) 0.0000 (0.134) 0.1847 (0.000)* 0.7569 (0.000)* −0.0105 (0.314) 0.9416

−0.0005 (0.069)*** 0.2505 (0.000)* −0.0008 (0.002)* 0.0000 (0.064)*** 0.1857 (0.027)** 0.7154 (0.000)* 0.0138 (0.022)** 0.9012

Parameters

Palladium–gold

Platinum–gold

Silver–gold

Platinum–palladium

Silver–palladium

Silver–platinum

a0 ı  b0 b1 c1 1 b1 + c1

−0.0004 (0.328) 0.8245 (0.000)* −0.0003 (0.595) 0.0000 (0.371) 0.1006 (0.021)** 0.8259 (0.000)* 0.2215 (0.353) 0.9264

−0.0003 (0.325) 0.8977 (0.000)* −0.0010 (0.001)* 0.0000 (0.045)** 0.2315 (0.001)* 0.6787 (0.000)* 0.0973 (0.101) 0.9102

−0.0003 (0.439) 0.8995 (0.000)* 0.0005 (0.294) 0.0000 (0.290) 0.2078 (0.000)* 0.5995 (0.000)* 0.2781 (0.020)** 0.8074

−0.0002 (0.368) 0.3705 (0.000)* 0.0000 (0.957) 0.0000 (0.017)** 0.0925 (0.004)* 0.6343 (0.000)* 0.0442 (0.000)* 0.7268

−0.0001 (0.849) 0.2761 (0.000)* −0.0009 (0.013)** 0.0001 (0.000)* 0.5521 (0.000)* 0.0278 (0.397) 0.0347 (0.074)*** 0.5799

0.0001 (0.849) 0.7744 (0.000)* −0.0027 (0.000)* 0.0001 (0.000)* 0.2527 (0.003)* −0.0043 (0.944) 0.5253 (0.000)* 0.2484

The parameter conditions constraints are as follows: b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0, (b1 + c1 ≤ 1) and ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0, (ˇ1 + 1 ≤ 1). The volatility persistence of each GARCH estimation is measured by the sum of the following coefficients for each equation (ˇ1 + 1 ≤ 1) and (b1 + c1 ≤ 1). Taking into account that the depreciation of each precious metal return could be a cause of market volatility the squared rate of changes in each series returns is used to introduce precious metal depreciation in each one of the equations looking at the bidirectional relationship between the series. In order to guarantee a positive value of the variance the square of returns is used in the model (i.e. ␭>0 and ␥>0). The results obtained show that the GARCH model is stable as the coefficients measuring volatility persistence are lower than one. In addition these markets tend to be strongly affected by uncertainty as the coefficients are significant and quite high in most of the cases. The results from the depreciation coefficient are quite mixed and not significant in every case. Taking into account that this sub-sample can be considered as a tranquil period, it is possible to conclude that market uncertainty was not a major characteristic of this market during the studied period. * 1% significance level. ** ***

5% significance level. 10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 9 Estimates of the GARCH (1,1): 1995 to June 1997.

Parameters

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

c0 ˛  ˇ0 ˇ1 1

1 ˇ1 + 1

−0.0004 (0.230) 0.0347 (0.004)* 0.0005 (0.185) 0.0000 (0.210) 0.0278 (0.390) 0.7166 (0.000)* −0.0008 (0.453) 0.7444

−0.0003 (0.348) 0.1386 (0.000)* 0.0002 (0.048)** 0.0000 (0.228) −0.0194 (0.498) 0.6825 (0.006)* 0.0128 (0.140) 0.6631

−0.0006 (0.066)*** 0.1482 (0.000)* 0.0001 (0.690) 0.0000 (0.039)** 0.0503 (0.166) 0.6446 (0.000)* 0.0187 (0.001)* 0.6949

0.0014 (0.171) 0.7310 (0.000)* 0.0027 (0.023)** 0.0000 (0.643) 0.1240 (0.014)** 0.8335 (0.000)* 0.1049 (0.162) 0.9575

0.0007 (0.486) 0.0997 (0.117) 0.0036 (0.008)* 0.0000 (0.192) 0.1037 (0.004)* 0.8771 (0.000)* −0.0058 (0.740) 0.9809

−0.0003 (0.622) 0.2243 (0.000)* −0.0014 (0.069)*** 0.0001 (0.206) 0.0971 (0.193) 0.5983 (0.015)** 0.0255 (0.174) 0.6954

Parameters

Palladium–gold

Platinum–gold

Silver–gold

Platinum–palladium

Silver–palladium

Silver–platinum

a0 ı  b0 b1 c1 1 b 1 + c1

0.0007 (0.507) 0.2155 (0.140) 0.0023 (0.096)*** 0.0000 (0.038)** 0.0887 (0.002)* 0.9011 (0.000)* −0.4434 (0.000)* 0.9898

0.0000 (0.968) 0.5953 (0.000)* −0.0020 (0.011)** 0.0001 (0.044)** 0.1058 (0.015)** 0.5081 (0.011)** 0.0859 (0.565) 0.6139

−0.0007 (0.342) 0.8391 (0.000)* −0.0013 (0.205) 0.0002 (0.000)* 0.4846 (0.000)* 0.0579 (0.553) −0.3310 (0.000)* 0.5424

−0.0005 (0.441) 0.2857 (0.000)* −0.0017 (0.019)** 0.0001 (0.068)*** 0.1129 (0.198) 0.4597 (0.051)*** 0.0204 (0.007)* 0.5726

−0.0006 (0.450) 0.1017 (0.002)* −0.0008 (0.452) 0.0003 (0.000)* 0.1972 (0.001)* −0.3174 (0.000)* 0.0454 (0.010)** −0.1202

−0.0008 (0.318) 0.2939 (0.000)* −0.0011 (0.283) 0.0001 (0.000)* 0.2617 (0.014)** 0.3134 (0.028)** −0.0164 (0.763) 0.5752

The parameter conditions constraints are as above. The volatility persistence of each GARCH estimation is measured by the sum of the following coefficients for each equation (ˇ1 + 1 ≤ 1) and (b1 + c1 ≤ 1). Taking into account that the depreciation of each precious metal return could be a cause of market volatility, the square of changes in each series returns is used to introduce precious metal depreciation in each one of the equation looking at the bidirectional relationship between the series. In order to guarantee a positive value of the variance, the squared returns is used in the model (i.e.  > 0 and > 0). The results for the Asian crisis are in line with the authors’ expectations. The GARCH model exhibit volatility persistence in almost all the cases with coefficients that are lower than one but showing a high magnitude. With regard to market depreciation the results are insignificant in the majority of the cases, supporting the authors’ belief that this market reacts differently during times of equity markets distress. * 1% significance level. ** ***

5% significance level. 10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 10 Estimates of the GARCH (1,1): July 1997–1998.

221

222

Parameters

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

c0 ˛  ˇ0 ˇ1 1

1 ˇ1 + 1

0.0004 (0.020) 0.1133 (0.000)* −0.0001 (0.690) 0.0000 (0.000)* 0.1546 (0.000)* 0.5673 (0.000)* 0.0115 (0.001)* 0.7219

0.0003 (0.114) 0.2368 (0.000)* −0.0002 (0.323) 0.0000 (0.000)* 0.1407 (0.000)* 0.5817 (0.000)* 0.0340 (0.009)* 0.7224

0.0003 (0.055) 0.2647 (0.000)* −0.0008 (0.000)* 0.0000 (0.000)* 0.1777 (0.000)* 0.4558 (0.000)* 0.0535 (0.000)* 0.6335

−0.0005 (0.067) 0.7088 (0.000)* 0.0019 (0.000)* 0.0000 (0.016)** 0.2079 (0.000)* 0.7125 (0.000)* 0.1603 (0.000)* 0.9204

0.0003 (0.453) 0.2020 (0.000)* 0.0013 (0.009)* 0.0000 (0.082)*** 0.1713 (0.000)* 0.7248 (0.000)* 0.0461 (0.056)*** 0.8961

0.0007 (0.005)* 0.1089 (0.000)* −0.0005 (0.097)*** 0.0000 (0.000)* 0.1866 (0.000)* 0.7270 (0.000)* 0.0165 (0.018)** 0.9136

Parameters

Palladium–gold

Platinum–gold

Silver–gold

Platinum–palladium

Silver–palladium

Silver–platinum

a0 ı  b0 b1 c1 1 b1 + c1

0.0002 (0.608) 0.5128 (0.000)* 0.0012 (0.024)** 0.0000 (0.014)** 0.1667 (0.000)* 0.7610 (0.000)* 0.1394 (0.037)** 0.9277

0.0005 (0.042)** 0.4112 (0.000)* −0.0007 (0.009)* 0.0000 (0.005)* 0.1410 (0.000)* 0.8081 (0.000)* 0.0362 (0.013)** 0.9492

0.0005 (0.108) 0.8531 (0.000)* −0.0034 (0.000)* 0.0000 (0.002)* 0.1416 (0.000)* 0.6021 (0.000)* 0.3417 (0.000)* 0.7437

0.0006 (0.001)* 0.2993 (0.000)* −0.0001 (0.708) 0.0000 (0.000)* 0.2077 (0.000)* 0.6070 (0.000)* 0.0272 (0.000)* 0.8147

0.0008 (0.044)** 0.1350 (0.000)* −0.0008 (0.067)*** 0.0001 (0.000)* 0.2192 (0.002)* 0.4926 (0.000)* 0.0476 (0.004)* 0.7119

0.0005 (0.139) 0.2395 (0.000)* −0.0025 (0.000)* 0.0001 (0.000)* 0.2285 (0.000)* 0.5124 (0.000)* 0.1033 (0.025)** 0.7409

*

***

***

The parameter conditions constraints are as follows: b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0 (b1 + c1 ≤ 1) and ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0 (ˇ1 + 1 ≤ 1). The volatility persistence of each GARCH estimation is measured by the sum of the following coefficients for each equation (ˇ1 + 1 ≤ 1) and (b1 + c1 ≤ 1). The results from this table are in line with the ones obtained for Table 1. Again, our GARCH model volatility persistence coefficients are significant and stable with a rather high magnitude. In this case, the coefficient measuring market returns depreciation is also significant. Therefore, it seems that precious metals tend to be affected by uncertainty during times of financial stability, while these markets appear to be quite strong during times of financial downturn. * 1% significance level. ** 5% significance level. ***

10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 11 Estimates of the GARCH (1,1): 1999 to July 2007.

Parameters

Gold–palladium

Gold–platinum

Gold–silver

Palladium–platinum

Palladium–silver

Platinum–silver

c0 ˛  ˇ0 ˇ1 1

1 ˇ1 + 1

0.0011 (0.012)** 0.0108 (0.5986) −6.15E−05 (0.8917) 2.09E−06 (0.2356) 0.0601 (0.000)* 0.9157 (0.000)* 0.0052 (0.1998) 0.9759

0.0012 (0.005)* 0.0658 (0.023)** −0.0007 (0.079)*** 0.0000 (0.076)*** 0.0451 (0.019)** 0.8964 (0.000)* 0.0252 (0.0163)** 0.9415

0.0009 (0.011)** −0.0061 (0.699) −0.0022 (0.000)* 2.15E−05 (0.000)* 0.0335 (0.203) 0.4677 (0.000)* 0.1306 (0.000)* 0.5012

0.0005 (0.000)* 1.0534 (0.000)* 0.0149 (0.000)* 3.70E−06 (0.026)** 0.8811 (0.004)* 0.2419 (0.013)** 0.0141 (0.036)** 1.1231

0.0013 (0.088)*** 0.4304 (0.000)* −0.0018 (0.0382)** 1.25E−05 (0.322) 0.0591 (0.055)*** 0.8746 (0.000)* 0.0466 (0.0127)** 0.9337

0.0009 (0.0742)*** 0.3507 (0.000)* −0.0011 (0.0424)** 1.47E−06 (0.6517) 0.0794 (0.005)* 0.8109 (0.000)* 0.0605 (0.000)* 0.8904

Parameters

Palladium–gold

Platinum–gold

Silver–gold

Platinum–palladium

Silver–palladium

Silver–platinum

a0 ı  b0 b1 c1 1 b1 + c1

0.0018 (0.013)** −0.1598 (0.471) 0.0051 (0.078)*** 3.92E−06 (0.58) 0.0661 (0.008)* 0.9049 (0.000)* 0.0866 (0.044)** 0.9710

0.0010 (0.041)** 0.2029 (0.000)* −8.21E−05 (0.8916) 1.56E−05 (0.0570)*** 0.1216 (0.001)* 0.6071 (0.000)* 0.4224 (0.000)* 0.7287

0.0012 (0.1083) 0.0100 (0.88) −0.0018 (0.046)** 9.23E−05 (0.0447)** 0.1482 (0.0445)** 0.3635 (0.0087)* 1.0217 (0.000)* 0.5118

5.97E−05 (0.3922) 0.5354 (0.000)* 0.0085 (0.000)* 1.72E−07 (0.000)* 0.7126 (0.000)* 0.4684 (0.000)* 0.0010 (0.0828)** 1.1811

0.0019 (0.0146)** 0.0529 (0.1152) −0.0012 (0.1869) 2.25E−05 (0.0278)** 0.0768 (0.0456)** 0.8906 (0.000)* −0.0009 (0.3084) 0.9675

0.0017 (0.0160)** 0.0716 (0.133) −0.0015 (0.107) 1.73E−05 (0.051)*** 0.0509 (0.244) 0.8599 (0.000)* 0.1023 (0.004)* 0.9108

The parameter conditions constraints are as follows: b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0, (b1 + c1 ≤ 1) and ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0, (ˇ1 + 1 ≤ 1). The volatility persistence of each GARCH estimation is measured by the sum of the following coefficients for each equation (ˇ1 + 1 ≤ 1) and (b1 + c1 ≤ 1). The analysis looking at the Global Financial Crisis shows that the GARCH coefficients measuring volatility persistence are significant and stable. Only in one case (palladium–platinum, and platinum–palladium), the model exhibits explosive behavior. In this case, the coefficients measuring market depreciation are significant in the majority of the cases. This time the pattern has changed and precious metals are exhibiting a behavior quite different from the one showed during the Asian crisis. This can be explained by the characteristics of the financial shock, as this time, market instability started in the U.S (the main economic power in the world) and the effects of the crisis are lasting longer than in the Asian case. * 1% significance level. ** ***

5% significance level. 10% significance level.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

Table 12 Estimates of the GARCH (1,1): August 2007 to November 2010.

223

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of volatility spillovers between precious metal markets at 1%, 5% and 10% significance levels. Some exceptions are found with regard to this evidence. For example, if we start analyzing the results per sample period, we find that for the long sample (1995 to July 2007), the coefficients are significant in the case of volatility running from gold to the other metals, but that there is weak evidence of the opposite trend; the only coefficient that is significant is volatility spillovers running form platinum to gold. In relation to the period prior to the Asian crisis (1995 to June 1997), the results show insignificant coefficients in the case of volatility spillovers from gold to any of the other metals, while we find that the opposite effect appears to be significant, meaning that the other metals are generating an impact on the gold market. Regarding the Asian crisis period (July 1997–1998) the coefficients are insignificant in the case of volatility from gold to the other precious metals; they are significant for volatility spillovers running from platinum to gold and from silver to gold. Regarding the rest of the metals, there are spillover effects running from platinum to silver, platinum to palladium, silver to palladium and silver to platinum. For the 1999 to July 2007 period, the results are quite mixed. The trend shows significant volatility spillovers from gold to palladium and platinum, silver to gold, platinum to palladium, silver to platinum and platinum to silver. Finally, the results for the global financial crisis (August 2007 to November 2010) tend to be insignificant in the majority of the cases. There are only two occasions where volatility spillovers are running from gold to platinum and from gold to silver. Significant coefficients are indicative of integration between precious metal markets; they also imply that the volatility of precious metal returns are a determinant of the volatility between these markets, meaning that information contained in precious metal markets impact on the other markets. These results show that these markets are initially influenced; this is especially the case for the gold market, which appears to generate effects in the rest of the metals, but there is no strong evidence for an effect in the opposite direction. Another important remark is in terms of market behavior during the two crisis events under analysis. The results confirmed that there is weak evidence of spillovers effects across these markets. This result is particularly important, as it is verifying our initial expectation of independent behavior among precious metal markets, which is translated by real possibilities of diversification. 4.4.1. Asymmetric spillovers (EGARCH) The results for the asymmetric spillover effects are presented in Table 7. We found that the coefficients are significant in almost all cases for all periods, with the following exceptions: during 1995 to June 1997 the coefficient is insignificant in the case of the equation for silver–platinum. During July 1997–1998, the coefficients are insignificant in the cases of gold–palladium, gold–silver, palladium–silver, platinum–silver, platinum–palladium, silver–palladium and silver–platinum. The existence of insignificant coefficients indicates that the spillover effects in these instances are symmetric, that is that positive and negative shocks have the same impact on volatility. Our results are showing that, in general, bad news will generate a greater impact on these markets than good news, a characteristic that is generally common to these markets and in line with existing research looking at financial market behavior. 4.4.2. GARCH results The analyses of the coefficients for volatility persistence are presented in Tables 8–12. The parameter conditions constraints are: b0 ≥ 0, 1 ≥ b1 ≥ 0, 1 ≥ c1 ≥ 0,  ≥ 0 (b1 + c1 ≤ 1) and ˇ0 ≥ 0, 1 ≥ ˇ1 ≥ 0, 1 ≥ 1 ≥ 0, ≥ 0 (ˇ1 + 1 ≤ 1). These constraints are applied to the parameters to enforce stationarity and a positive conditional variance. Volatility persistence will be measured through the sum of the following coefficients for each equation (b1 + c1 ≤ 1) and (ˇ1 + 1 ≤ 1). The depreciation of the precious metal returns could be a cause of market volatility (i.e.  > 0 and > 0). Regarding the return-generating process, we can draw the following conclusions. First there is a significantly positive relation between the precious metal returns, and overall there is a significant negative relation between precious metal returns and metal return depreciation, with most of the coefficients appearing to be negative. This situation reflects that, in general, when the precious metal markets are appreciating there is a trend of increasing returns for almost all the markets, but when the prices of any of these markets depreciates, the prices of the rest of the markets will tend to be dragged downwards.

L. Morales, B. Andreosso-O’Callaghan / Research in International Business and Finance 25 (2011) 203–227

225

Examining the estimates, we can appreciate that for all five periods of analysis all variance parameters are positive and statistically significant. During the long period 1995 to July 2007 (Table 8), and for the palladium–silver equations, the coefficients are negative, with GARCH parameter sums indicating high volatility shock persistence for all the cases, with the exception of palladium–silver, where the coefficients sum is 0.018 for the palladium–silver, and 0.31 for silver–palladium. During 1995 to June 1997 (Table 9) the estimates are positive and statistically significant in all the cases. The exception is the silver–platinum equation where the coefficient is negative. The GARCH parameter sum is quite high for all equations with the exception of silver–palladium (0.57) and silver–platinum (0.24). The results for the Asian crisis period (Table 10) show that gold–platinum and silver–platinum equation coefficients are the only ones that appear to be negative. The GARCH parameter sum is moving between 0.54 as the lowest value to 0.98 as the highest. The results for the final sample (1999–July 2007, Table 11) show that the coefficients are positive in all the cases, with a GARCH parameter sum moving between 0.63 and 0.94, which indicates high volatility shock persistence for all the cases. Finally, for the August 2007 to November 2010 period (Table 12) the coefficients fluctuate between 0.97 and 0.51 indicating high volatility persistence in almost all the cases, with the exception of platinum–palladium and palladium–platinum where the coefficient is higher than 1 showing explosive behavior, a behavior that can be corrected by adding an extra lag to the GARCH estimation. The coefficients that take into account precious metal returns depreciation ( > 0 and > 0) are positive and significant in almost all the cases with the exceptions of palladium–silver and silver–platinum during 1995 to June 1997. During the Asian crisis, the parameters are negative in the case of gold–palladium, palladium–silver, palladium–gold, silver–gold, and silver–palladium and silver–platinum. Overall, the results show that precious metal depreciation is a source of volatility and consequently, they need to be considered as an extra variable when analyzing precious metal market fluctuations. In general, these results are consistent with the findings of the EGARCH model where we also found evidence of volatility persistence between these markets; therefore we can consider that our results seem to be quite robust. 4.5. Standardized residuals The diagnostic tests on the standardized residuals for the EGARCH and GARCH models5 are discussed in this section. The Jarque–Bera test indicates that we reject the hypothesis that the residuals are normally distributed in all the cases, hence justifying the use of the Bollerslev–Woolridge robust t-statistics. In the case of the EGARCH model, the Ljung–Box statistics for all four periods for all precious metal equations indicate that there are no residual linear or non linear dependencies in most of the cases. There are some exceptions where the coefficient was not significant but the problem was corrected after introducing more lags into the test. A similar situation was found in the case of the GARCH results. Finally to check the validity of the assumption of constant correlation adopted in the estimation of the bivariate models (Kanas, 2000), the LB statistics for the cross products of the standardized residuals from the precious metal return equation are calculated and these statistics indicate that the assumption of constant correlation over time can be accepted in almost all the cases. The exceptions are: palladium–gold during 1995 to July 2007, palladium–platinum and palladium–silver during July 1997 to 1998, and finally palladium–gold and silver–palladium during 1999 to July 2007, all in the case of the EGARCH model. Regarding the GARCH results, the exceptions were found for the 1995 to July 2007 period in the cases of gold–palladium, palladium–silver and platinum–silver; during July 1997–1998 in the cases of gold–platinum and palladium–silver; and finally during the 1999 to July 2007 period, the exception was gold–palladium. These exceptions are normally corrected after increasing or decreasing the number of lags in the test.

5

The diagnostic tests are omitted due to space restrictions, but they are available from the authors upon request.

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The ARCH–LM residual test results show that overall the variance equation for the EGARCH model is correctly specified, as we reject the null hypothesis of remaining ARCH effects in the equation in almost all the cases. The exceptions are: during the crisis period (July 1997–1998) in the case of palladium–platinum, palladium–silver, palladium–gold, silver–gold, silver–palladium and silver–platinum. This problem is corrected after increasing or decreasing the number of lags using the estimation. The test results show that the variance equation is correctly specified for the GARCH model, as we reject the null hypothesis in almost all the cases, with the following exceptions: silver–palladium for the whole sample during the Asian crisis (1995 to July 2007, July 1997–1998), and gold–palladium, silver–palladium and silver–platinum during the global financial crisis. 5. Conclusions This paper investigates the existence of volatility effects in precious metal returns, using GARCH and EGARCH modeling. The empirical results indicate that the depreciation of precious metals under conditions of stable and unstable market situations tends to decrease the mean stock return and also to increase market volatility. The results show that there is clear evidence of volatility persistence between precious metal returns during the global financial crisis. However this effect was very weak during the Asian financial crisis. These contrasting results indicate that the two events have generated different effects in the financial markets and indeed they have been appreciated in a different manner by investors, in so far as the global financial downturn seems to be causing more uncertainty in the markets than during the case of the Asian crisis in the late 1990s. In terms of volatility spillover effects, the main findings are that there is evidence of volatility spillovers running in a bidirectional way in some cases. However, there is weak evidence suggesting strong interlinkages among these markets, and more precisely in the case of gold, where the general pattern reflects that gold tends to dominate the markets. There is nevertheless little evidence in the case of the other precious metals influencing the gold market. In the case of asymmetric spillover effects, the results show that negative news have a stronger impact on these markets than positive news, results that are common to financial markets in general. Consequently, and taking into account the fact that the investment demand for precious metals is rising, as institutional and high net worth investors in developed and developing economies are increasing their interest in precious metals, it is clear that financial markets continually evolve. One of the recent developments is the emergence of the Exchange Traded Funds (ETFs); this has had a major impact on precious metal markets. The ETFs will increase the volume of investment in precious metals, because investors who otherwise would not invest in precious metals are and will buy shares of ETFs. Thus the ETFs represent an upward shift in the investment demand curve. The ETFs provide the markets with greater transparency regarding an investor’s attitude towards these metals. Metals and energy markets seem to be markets that will attract investment for quite some time. This stems from the fact that these markets are characterized by scarcity, and since consumption in these markets from emerging countries such as China and India could raise the price of their commodities, precious metal markets are deemed an increasingly good option for investment. These results provide evidence of the need for further research in this area, since precious metal markets could have important implications in terms of risk management and hedging activities, and could represent new market options of where to locate capital in the future. We also consider that future research should be looking at alternative GARCH methodologies to model precious metal markets. In particular, we think that the GARCH–DCC model under a 100–200 day moving window will be a good starting point to find out whether alternative methodologies do validate the results presented in this paper. References Aggarwal, R., Lucey, B., 2005. Psychological barriers in gold prices? Rev. Finan. Econ. 16, 217–230. Batten, J., Lucey, B., 2010. Volatility in the gold futures market. Appl. Econ. Lett. 17, 187–190. Bernard, J.T., Khalaf, L., Kichian, M., McMahon, S., 2008. Forecasting aluminium prices: GARCH, jumps, and mean-reversion. J. Forecast. 27, 270–291.

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