How has volatility in metals markets changed?

Available online at www.sciencedirect.com

Mathematics and Computers in Simulation 78 (2008) 237–249

How has volatility in metals markets changed?

Clinton Watkins a,∗, Michael McAleer b

a Reserve Bank of New Zealand, 2 The Terrace, Wellington, New Zealandb School of Economics and Commerce, University of Western Australia, Australia

Available online 18 January 2008

Abstract

Within the industrial metals industry, there has been a great deal of interest surrounding trends in metals market volatility overtime. This paper uses a rolling AR(1)-GARCH(1,1) model to estimate and forecast the volatility processes for daily returns on thefutures prices of two important non-ferrous metals, namely aluminium and copper. The rolling models are used to examine howthe processes driving aluminium and copper returns volatility have evolved over a long sample. The variation over time seen in thevolatility processes, as modelled by GARCH, suggest that, while volatility in returns has not necessarily increased, the conditionalvolatility process in metals markets is itself time-varying when analysed over a long horizon.© 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Keywords: Volatility forecasting; GARCH; Rolling models; Futures contract; Industrial metals

1. Introduction

The London Metal Exchange (LME) is the major international market for the main industrially used non-ferrousmetals, namely aluminium, aluminium alloy, copper, lead, nickel, tin, and zinc. Aluminium and copper have generallyhad the highest volume of spot and futures trade on the exchange. The two metals are also among the most importantmetals in an industrial sense. Within the industry, there has been a great deal of interest surrounding trends in non-ferrous metals market volatility over time. These have been examined in a number of studies which have examined thevariability in prices and market structure (for a recent survey of econometric modelling in non-ferrous metals markets,see [21]).

Metals market participants suggest that volatility in non-ferrous metals prices has increased over time. Furthermore,this increase in volatility is thought to be associated with a change in market organization, from pricing on a producerlist basis to exchange-based pricing. With the move to exchange-based pricing, the metals industry has noted theincreased activity in metals of other types of market participants, such as investment funds and speculators. Thisbroader participation in the metals trade has also been thought to be behind the increase in market volatility. Althoughexchange-based pricing allows access to hedging products, such as exchange traded futures and options, some haveargued that the associated hedging costs and increased volatility has led to higher cost structures for metal producesthan those connected with producer list pricing. See [22] for a recent analysis of futures pricing for seven metals tradedon the LME.

∗ Corresponding author.E-mail address: [email protected] (C. Watkins).

0378-4754/$32.00 © 2008 IMACS. Published by Elsevier B.V. All rights reserved.doi:10.1016/j.matcom.2008.01.015

mailto:[email protected]

dx.doi.org/10.1016/j.matcom.2008.01.015

238 C. Watkins, M. McAleer / Mathematics and Computers in Simulation 78 (2008) 237–249

In the early 1990s, [20] provided empirical evidence to support the proposition that metals price volatility is higherduring the 1980s relative to the 1970s, and that this increase in volatility was associated with the transition fromproducer list to exchange determined prices. However, [6] show that, by extending the sample in [20] to include morerecent data, there is no significant difference in the variability of exchange-based prices and producer list prices. In themid-1990s, [4] and [5] argued that, while the volatility of non-ferrous metals prices is itself highly volatile, volatilitydoes not trend stochastically over a sample covering 1972–1995. Periods of high volatility in metals markets are dueto tighter metals balances (essentially inventory levels taking into account demand and supply), rather than speculativeactivities. Speculative and informational pressures are not precluded from influencing volatility. However, the effectsare short lived, and fundamentals regarding the availability of metal generate persistence in volatility.

Changes in the prices of aluminium and copper are often closely aligned with changes in global industrial produc-tion, but also reflect market specific events, compliment and substitute relationships between the physical metals inproduction, and financial market-type influences. Ref. [4] characterise two sources of volatility in non-ferrous metalsmarkets, namely those related to financial market considerations and those related to market fundamentals. Financialconsiderations include information effects, speculative pressures and hedging activity, which typically lead to shortrun volatility effects. Market fundamentals refer to the underlying availability, namely the supply and demand of thephysical metal. Fundamentals are a source of long term volatility in metals markets, primarily due to the lags involvedin demand and supply side changes.

Over the past 2 years, volatility has been a particular focus for market participants as the prices of many industriallyused metals have reached record high levels, and have moved to these levels at a rapid pace. Analyst commentary,such as [8–11], have focused on increased volatility in the LME markets. Analysts frequently point to low inventorylevels, macroeconomic uncertainty and strong demand in the face of uncertainties around supply as key market themesunderlying high levels of volatility. However, beyond these fundamental factors, reports of increasing participation inmetals futures markets by investment banks, hedge funds and mutual funds have heightened scrutiny on speculativebehaviour by traditional LME market participants, namely those which have an industrially related exposure to physicalmetals. Investment banks and funds have been drawn to commodities markets over the last 2 years as commodity priceshave increased rapidly, while institutional investors have also been drawn to the asset class (see [19] for a discussionon institutional investors).

While it can be hard to distinguish commercial and speculative trades, commercial trades in LME futures may beconsidered as trades that hedge a future exposure to physical metal, copper or aluminium for the data considered in thispaper. It is harder to analyse the impact of speculative trade on the LME as the LME does not release data on commercialversus non-commercial positioning on the exchange. This is in contrast to many North American derivatives exchanges,where data released by the Commodity Futures Trading Commission show the broad split between the two types ofmarket participation. Views or fears of traditional metals industry participants on the increase in speculative tradersin derivatives markets are noted in publications such as [1]. These concerns include such markets no longer existingto serve primarily the underlying physical players, the impression that speculative activity can distort prices, and thatinvestment funds somehow alter prices away from their fundamental values.

This paper examines the issue of how volatility has changed over time in metals markets by analysing prices andreturns over a long horizon, and using a volatility model to provide rolling estimates and forecasts of the conditionalvolatility process. Section 2 of the paper discusses the rolling volatility model used to estimate and forecast aluminiumand copper futures volatility. LME 3-month futures prices and returns are described in Section 3. Sections 4–6 explainthe empirical estimates, specifically the parameter estimates, robust t-ratios and moment conditions, respectively. One-step-ahead volatility forecasts from the model are presented in Section 7, while Section 8 concludes the paper byexplaining the empirical significance of the results.

2. Rolling volatility model

This paper uses a rolling univariate volatility model to examine how the processes driving aluminium and coppervolatility have evolved over a long sample. Bollerslev’s GARCH model [2] is used, specifically AR(1)-GARCH(1,1).This is one of the most widely used time-varying financial volatility models in practice. Despite the model’s relativesimplicity, academics and practitioners have found that it adequately describes the volatility processes of a wide varietyof financial time series. For a recent survey of the GARCH literature, see [12,16].

C. Watkins, M. McAleer / Mathematics and Computers in Simulation 78 (2008) 237–249 239

In the AR(1)-GARCH(1,1) model, the conditional mean of futures price returns is given by the AR(1) model:

rt = μ + ϕrt−1 + εt, |ϕ| < 1, (1)

and the conditional variance of the shock to returns (or news), εt, is given by:

εt = ηt

√ht, (2)

ht = ω + αε2t−1 + βht−1, (3)

where rt denotes the returns on the futures price from period t − 1 to t; εt is the unconditional shock; ηt is the standardisedshock, namely a sequence of normally, independently and identically distributed (iid) random variables, with zero meanand unit variance; and ht is the conditional variance of the shock to returns. For the GARCH process to exist, ω > 0,α ≥ 0 and β ≥ 0 are sufficient conditions for the conditional variance to be positive. The ARCH coefficient, α, measuresthe short run persistence of shocks, and the GARCH effect, β, measures the contribution to the long run persistence ofshocks, namely α + β.

Several statistical properties have been established for the GARCH(p,q) process in order to define the moments ofthe unconditional shock. For a comprehensive discussion of moment conditions for GARCH and asymmetric powerGARCH models, see [13], and for alternative moment conditions of a generalisation of univariate GARCH, see [14].The necessary and sufficient condition for the second moment to exist for the GARCH(1,1) model, guaranteeing thatthe process is strictly stationary and ergodic, is given by:

α + β < 1. (4)

If the conditional shocks, ηt, are iid random variables, the fourth moment of the unconditional shock will exist if thefollowing condition is satisfied:

3α2 + 2αβ + β2 < 1. (5)

The model is estimated using a rolling window of 1000 observations, or around 4 years of daily data, which iterates4929 times for aluminium, and 6706 times for copper. Each model is estimated by the maximum likelihood method.Non-normality in the residuals is likely in the presence of extreme returns observations. Robust t-ratios based onstandard errors that are designed to be robust to non-normality are used (see [3]). Estimates from the rolling samplesare treated as “data” in the descriptive discussion below.

An empirical measure of volatility is required against which to evaluate the rolling one-step-ahead forecasts generatedby the model. The measure defined in [17] is used at the “true” or actual empirical volatility:

vt = |rt − r| , (6)

where vt refers to the ‘true’ volatility at time t, and r is defined as the mean return over the estimation window for thesample used. The 1-day ahead forecast error, ut+1, is defined as:

ut+1 = ht+1 − vt+1. (7)

A positive forecast error implies that the estimated GARCH model has over-forecast the empirical volatility, while anegative forecast error means that the empirical volatility has been under-forecast by the estimated GARCH model.

3. Prices and returns

The sample consists of daily data for 3-month futures settlement prices in US dollars for aluminium over the period1 October 1982 to 24 July 2006, and for copper over the period 5 January 1976 to 24 July 2006. Each returns series iscalculated as:

rt−1,t = ft − ft−1

ft−1, (8)

where rt−1,t is the return over period t − 1 to t, and ft is the futures price at time t. This gives a sample of 5929 returnson aluminium futures and 7706 returns on copper futures, noting that 79 zero returns observations were eliminatedfrom the aluminium sample.


Fig. 1. Aluminium prices and returns.

Plots of the price and returns series for aluminium and copper are presented in Figs. 1 and 2. While copper andaluminium sometimes share periods of clustered volatility at similar times, each market also contains periods of volatilitythat do not occur in the other series. While being affected by macroeconomic shocks, industrial metals markets arealso strongly influenced by financial and physical market-specific events. The extent to which these permeate betweenmetals markets depends on a number of factors, including the complimentary and substitute relationships between theparticular metals.

The recent increase in aluminium and copper prices is evident, in particular, for copper, where prices have beenincreasing to unprecedented levels since early 2006. Returns for both metals show clusters of volatility as prices beginto rise during 2004. Interestingly, there are fewer outlying returns compared with previous periods in which prices haveincreased rapidly. While markets have been volatile, the lower incidence of extreme and outlying observations suggeststhat, over the last 2 years of the sample, the returns series are less leptokurtic than in previous years. Despite the trendupward in prices being rapid, and for copper, far greater in magnitude than in the past, the copper and aluminiumfutures markets appear noticeably more stable than during previous periods of substantial price changes.

4. Parameter estimates

Plots of the rolling α coefficient estimates and their corresponding t-ratios are provided in Figs. 3 and 4 for aluminiumand copper, respectively. Rolling β estimates and the associated t-ratios are shown in Figs. 5 and 6. Dates on the x-axisof these figures indicate the last trading day contained in the estimation window.

Fig. 2. Copper prices and returns.


Fig. 3. Aluminium α estimates and t-ratios.

Fig. 4. Copper α estimates and t-ratios.

The α estimates for both metals indicate that short-run persistence varies in magnitude throughout each sample. Anumber of the features apparent in the rolling α estimates coincide with extreme observations that occur as a result ofshocks to the returns series. There appears to be an upward bias in the α estimates when large extreme observations arewithin the estimation window. A high α implies that the GARCH process will allow the level of estimated conditionalvariance to increase quickly in response to periods of high volatility in returns. The majority of the rolling β estimates

Fig. 5. Aluminium β estimates and t-ratios.


Fig. 6. Copper β estimates and t-ratios.

for both metals series are greater than 0.8 and less than 1, as expected. However, the β estimates also display varyingcharacteristics over time.

Periods in which the α estimates appear biased upward often coincide with periods of apparent downward bias inthe corresponding β estimates. A low β estimate allows for the rapid decay of volatility, as might be expected followingan extreme observation. However, the presumption under the GARCH model is that observations from high volatilityperiods and low volatility periods follow the same parametric volatility process. If extreme observations generate alower degree of persistence, and that cannot be captured in the GARCH(1,1) parameterisation, it would be expectedthat biases will occur in the estimates. In this case, the β estimate may be biased downward following an extremeobservation.

Examining the estimates generated as the rolling window covers the last few years of the sample, opposite trendsare evident in the two metals. For aluminium, the α estimates become small (and are also frequently insignificant),particularly as aluminium prices appear to have peaked. Despite being notably variable, the copper α estimates trendupward as prices increase. The importance of short term volatility persistence in the aluminium market appears to havesubsided, while in the copper market, the short run persistence of volatility seems to have become more important.The opposite is true for the estimated β contribution to long run volatility persistence. The β estimate increases toalmost one toward the end of the sample for aluminium, but decreases for copper (while also being variable). Themodels seem to suggest the presence of different volatility dynamics that are underlying the returns structure in eachmarket.

5. Robust rolling t-ratios

For the empirical results prior to December 1998, all of the aluminium α estimates are significant at the 5% level.However, toward the end of the sample, the t-ratios generally lie just above the 5% significance level. Althoughthe majority of the estimates appear significant, the null hypothesis is not rejected for some estimates. Copper t-ratios for the estimated α parameters exceed 2 for much of the sample. However, there are some periods in whichthe t-ratio varies around the 5% critical value. There is an extended period over which the null hypothesis is notrejected, namely from March 2003 to May 2004. Interestingly, a level shift in the α estimate around September1987 coincides with noticeably higher significance levels. Toward the end of the sample, the α estimates for alu-minium are frequently insignificant, while the null hypothesis is rejected for the copper estimates from early 2004onward.

Typically, the estimated β t-ratios for both series are large, particularly so when the coefficient estimates liebetween 0.8 and 1. The copper β estimates are significant over the entire sample, despite both the estimates andt-ratios being noticeably variable from late 2004 onward. Between July 2000 and December 2001, when the alu-minium β estimate becomes extremely variable, its t-ratio becomes low and most estimates do not appear to besignificant. As the aluminium β estimate approaches one during 2005, its t-ratio becomes large but also highlyvariable.


Table 1Moment conditions satisfied (in %)

Moment Aluminium Copper

Second 84.32 89.82Fourth 82.35 87.25

Fig. 7. Aluminium second and fourth moment.

6. Rolling moment conditions

The percentage of the rolling estimation windows for which the second and fourth moment conditions are satisfiedis shown in Table 1. Both the second and fourth moment conditions are satisfied more frequently in models for copperthan for the aluminium returns data, by around 5%. Overall, the moment conditions are satisfied in more than 80%of the rolling models. For both metals, the more stringent fourth moment condition is satisfied in around 2% fewermodels than is the second moment. Overall, the moment conditions are satisfied for the majority of rolling models,which indicates that valid inferences can be made for the empirical results.

Plots of the moment conditions are given in Fig. 7 for aluminium and in Fig. 8 for copper. The aluminium momentsexceed one for several periods over the sample, including for over 2 years of trading days from November 1987 toDecember 1990, and for many rolling models from February 2006 onward. Similarly for copper, there is an extendedperiod where the moment conditions are violated, namely between October 1987 and October 1990. However, it isinteresting that the moment conditions are not violated for any copper models during the period of substantial and

Fig. 8. Copper second and fourth moment.


Fig. 9. Aluminium forecast volatility.

rapid price increases from 2004 onward. Despite the variability in the copper models estimates over the last year ofestimation, the empirical copper moments are less variable during this period than at some earlier times.

Clearly, market conditions surrounding the fall-out of the equity market meltdown at that time have influencedvolatility in both aluminium and copper prices. It is interesting to note that, at the time when market participants mighthave been expected to be most concerned with accurate estimates of returns volatility, inferences from the simplerolling GARCH model may not always have been relied upon. This is also the case for aluminium toward the end ofthe sample, when the May 2006 price peak is within the estimation window. For copper, there are also instances whenthe fourth moment condition is violated, in particular between December 1991 and June 1993. While prices movedsubstantially toward the end of the sample, the copper moments remained at typical levels, unlike those for aluminium.

Despite these moment condition violations, the long run persistence in volatility is generally closer to unity forcopper than it is for aluminium. Long run persistence for aluminium is low in the early 1990s and from September2000 to December 2001, while for copper it is low in the mid-1980s. Long run persistence in volatility has becomemore important in the aluminium market following the increase in prices since 2004. In the copper market, long runvolatility is variable after 2004, but it has not increased in importance.

7. Volatility forecasts

Forecasts of volatility that are generated by the models, and the actual of ‘true’ volatility, are shown in Figs. 9 and 10.Table 2 compares the forecasts using mean error (ME), mean absolute error (MAE), root mean squared error (RMSE),smoothed mean absolute percentage error (SMAPE), smoothed weighted median absolute percentage error (SMed-WAPE), and smoothed weighted mean absolute percentage error (SWMAPE). The forecast errors are shown inFigs. 11 and 12.

Fig. 10. Copper forecast volatility.


Table 2Forecast evaluation criteria

Criteria Aluminium Copper

ME 0.00311 0.00357MAE 0.00688 0.00789MedAE 0.00597 0.00685RMSE 0.00909 0.01033RMSE(−) 0.01150 0.01271RMSE(+) 0.00810 0.00934RMedSE 0.00597 0.00685SMAPE 74.08 74.40SMedAPE 63.08 62.76SMWAPE 52.12 51.00SMedWAPE 32.70 32.93R2 0.14 0.13R2

e 0.71 0.74Forecasts under 25.62 26.39Forecasts over 74.38 73.61

Fig. 11. Aluminium forecast error.

Fig. 12. Copper forecast error.


ME is defined as:

ME = 1

N

N∑t=1

(√

ht − vt), (9)

where N represents the sample size, ht is the forecast conditional variance, and vt is the actual volatility, as defined bythe observed first difference in absolute returns.

MAE is the mean of the absolute values of the forecast errors:

MAE = 1

N

N∑t=1

∣∣∣√ht − vt

∣∣∣ . (10)

Similarly, the MedAE is defined as the median of the absolute values of the forecast errors.RMSE is defined as the square root of the mean of the squared forecast errors:

RMSE =√√√√ 1

N

N∑t=1

(√

ht − vt)2. (11)

RMedSE is the square root of the median of the squared forecast errors.Smoothed forecast evaluation measures, such as the SMAPE, normalise the forecast error on the mean of the forecast

and actual volatilities. Several smoothed percentage measures of forecast performance are used.SMAPE is defined as:

SMAPE = 100

N

N∑t=1

( ∣∣√ht − vt

∣∣(1/2)(vt + √

ht)

). (12)

The SMedAPE normalises the median of the absolute forecast errors, and presents this as a percentage forecast error.The SMWAPE weights the forecast error criteria by the size of actual volatility relative to its mean over the full

sample. SMWAPE is defined as:

SMWAPE = 100

N

N∑t=1

(vt

v

∣∣√ht − vt

∣∣(1/2)(vt + √

ht)

), (13)

where v represents the mean of actual volatility over the entire sample. Thus, if volatility in the forecast period ishigher than the mean level of actual volatility, the forecast error for that period is relatively more important than aforecast error during a period in which actual volatility is lower than the mean for the entire sample. The SMedWAPEis weighted in the same way, but it is the median forecast error that is weighted rather than the mean.

The criteria suggest a broadly similar forecast performance in each market. Median errors are always smaller thanthe comparable mean errors, and the errors are generally slightly greater for copper volatility than for aluminium.When RMSE are calculated separately for positive and negative forecast errors, RMSE(−) is substantially larger thanRMSE(+) for both markets. Volatility forecast errors from the GARCH(1,1) model are negatively biased. The weightedforecast performance measures are considerably lower than their non-weighted counterparts. This suggests that a largeproportion of forecast errors occur when the actual volatility of the forecast period is lower than the average volatilityin the entire sample.

R2 is obtained by regressing ex post volatility on forecast volatility and, being relatively low for both metals,suggests a poor overall predictive performance. Similarly, R2

e is obtained by regressing the forecast errors on the expost volatility, and shows that the actual volatilities have a high degree of explanatory power over the forecast errors.The final two criteria show that the GARCH model tends to over-predict volatility for both metals.

Examining Figs. 9 and 10, the forecasts from the GARCH models capture the major features of the actual volatilityin aluminium and copper returns over the sample. A clear period of heightened volatility is evident between October1987 and early 1990, coinciding with the October 1987 equity market meltdown, and flow on volatility in globalfinancial markets and the major macroeconomies. However, during this period, the forecast errors suggest that themodel tends to over-predict the persistence of volatility in both markets.


While for aluminium, the October 1987 crash corresponds with the highest volatility forecasts, the largest copperforecasts occur in early 1996. The LME copper market was systematically manipulated by a trader in the SumitomoCorporation of Japan during the early and mid-1990s (see [7]). Substantial volatility can be observed in returns aroundearly to mid-1996, when conditions in the copper market made Sumitomo’s position untenable. At that time, hedgefunds saw an opportunity to attack the inflated copper price, which fell by USD700 per tonnes over a 4-week period.Forecast volatility reflects the increased aluminium and copper actual volatility apparent during 2006, over the periodduring which prices for the metals peaked and then fell back to some extent.

In general, large negative forecast errors tend to be associated with the model under-predicting when a substantialshock to returns hits the market, while any large positive forecast errors tend to be associated with the model over-predicting the persistence of these shocks. In general, the majority of forecast errors are small and positive, whilenegative forecast errors tend to be relatively large in absolute magnitude, but occur less frequently. In periods ofrelatively low volatility, the model is prone to over-predict actual volatility, but not significantly. Extreme observationsassociated with a period of relatively higher volatility appear to be the most important source of adverse effects on thepredictive ability of the GARCH model in subsequent periods.

8. Empirical significance

The α and β estimates for both aluminium and copper indicate that both short and long run volatility persistence canvary over a relatively wide range as the models change over time. At various times the estimates exhibit a high degreeof stability. However, shocks in returns can move the process dramatically. At some points throughout the sample, theα estimates are close to zero, suggesting the absence of short run persistence. Generally, the β contribution to the longrun persistence becomes relatively more important than to short run persistence, towards the end of the sample foraluminium, but not for copper.

Tail events have a clear effect on the likelihood function, and thus on the estimation of volatility models using max-imum likelihood methods. Biased GARCH model estimates occur because the (quasi) maximum likelihood estimatorseeks a model in which the estimated conditional variance may increase quickly, while also allowing for rapid volatilitydecay. The means by which a GARCH(1,1) model achieves this is with a high α parameter value, which allows a quickincrease in conditional variance, and a low β parameter which provides for rapid decay.

The rolling GARCH models produce a number of results that have interesting economic implications, particularlywith regard to the perception within the non-ferrous metals industry that metals prices and returns have become morevolatile over time. However, inspection of the aluminium and copper returns plots does not support this proposition.On the contrary, it would appear that returns are less volatile in both the aluminium and copper markets in the laterportion of the sample, particularly in terms of the prevalence of tail or extreme events.

Moreover, [5] contend that volatility itself has become more volatile. Several of the results presented in thispaper support their conclusion to the extent that the volatility process, as parameterised by the GARCH(1,1)model, is time-varying. Variation in the GARCH(1,1) estimates can be relatively large, and movements in theestimates can be sharp, particularly when periods of substantial market volatility enter or leave an estimationwindow. While the volatility of returns does not appear to display an upward trend, relative to the 1980s thereare periods during the following years where the process driving time-varying conditional volatility appears tohave become more variable. Consequently, to some degree this may be more difficult to model using a simpleGARCH specification. However, the GARCH(1,1) model does not necessarily perform worse during periods inwhich market participants see the markets as turbulent, volatile, and facing unprecedented change in the underly-ing economic fundamentals, such as post-2004. However, the forecasting performance is adversely affected whenthere are large or prevalent outlying returns observations, such as during the October 1987 stock market melt-down.

The modelling results also suggest that different dynamics underlie the conditional volatility processes of aluminiumand copper. This is despite the forecast evaluation criteria suggesting a broadly similar predictive performance of theGARCH(1,1) model across both markets. Fundamental factors related directly to each metals market could wellmotivate a rationale for different market behaviour following general shocks to both markets, and provide soundreason for expecting metal-specific shocks from time to time. For instance, over the last 2 years of the sample, thesereasons include tighter metals balances for copper relative to aluminium, a proportionally larger increase in investmentin production capacity for aluminium, at times severe disruption to very large copper mines but relatively smooth


extraction of alumina, and a particular pocket of potentially disruptive (unauthorised) speculative behaviour in thecopper market.

Notably, despite the substantial movement in both aluminium and copper prices post-2004, there appear to berelatively few outlying or extreme observations during this period relative to what has been seen during previousperiods of large or rapid price movements. This is despite commentary by analysts focusing on high levels of recentvolatility, in which analysts typically look back in time over a very short horizon (see [8–10]). While the distributionsof metals prices remain both symmetric and leptokurtic, recent history suggests that distributions are less fat-tailedthan they once were. This apparent trend to more stable markets is not purely a phenomenon of metals futures. Manypractitioners and academics have noted the prolonged low level of price volatility in recent years simultaneously overa wide range of financial market prices. Bank for International Settlements researchers (see [18]) have proposed anumber of factors that may potentially be behind this. Macroeconomic factors include the current on-going phaseof economic expansion, the “Great Moderation” in output growth volatility since the mid-1980s, and the conduct ofmonetary policy playing a key role in reducing the volatility in some interest rates. Metals futures long been seen ashaving a close relationship with global macroeconomic trends, particularly industrial production levels.

The authors of [18] have noted the rise in prominence of firm-specific components of volatility. Volatility is negativelyrelated to profitability, and corporate profits in the major economies have been strong over recent years, with largemetals industry firms generally following this trend. Financial market developments also appear to have contributed tothe lower volatility environment through the improvement in market liquidity, growth in transactions volumes, growthof markets for risk transfer instruments, and growth in the fraction of assets held by “well-informed” investors. Themacroeconomic, firm-specific and financial market factors mentioned are all highly pertinent to the aluminium andcopper futures markets. Increased investment bank and fund participation in metals markets has seen greater two-waytrading interest in futures, deeper and more liquid markets (see [1]), greater development of products for offsetting,and more market participants that are willing to take on the risks that hedgers wish to eliminate.

Of course, the instability in the rolling GARCH model over some parts of the sample raises the question of whethera more complex rolling volatility model could better reflect the changing volatility process within the long horizondata set. Multivariate analysis of a portfolio of metals may be a useful extension to this work. Such an approach wouldimplicitly incorporate correlation structures between several industrially used metals. For a discussion of suitablemultivariate GARCH models, see [15]. More generally, the analysis could be extended by using a variety of univariateand multivariate, conditional and stochastic volatility models (see [16]).

However, the variation over time seen in the volatility process, as modelled by GARCH, suggests that, whilevolatility in returns has not necessarily increased, the conditional volatility process in metals futures markets is itselftime-varying, and at some points volatile, when analysed over a long horizon.

Acknowledgements

The first author would like to acknowledge the Australian Research Council (ARC) for an Ad Hoc PhD Scholarshipand the University of Western Australia for a C.A. Vargovic Memorial Fund Award. The second author wishes toacknowledge the financial support of the ARC. Both authors would like to thank participants at the 2005 BiennialCongress of the Modelling and Simulation Society of Australia and New Zealand for helpful comments and suggestions.

References

[1] J. Banks, Friend or foe? in: The Ringsider: Metals 2005, London Metal Exchange, 2005, pp. 131–133.[2] T. Bollerslev, Generalised autoregressive conditional heteroskedasticity J. Econom. 31 (1986) 307–327.[3] T. Bollerslev, J.M. Wooldridge, Quasi-maximum likelihood estimation and inference in dynamic models with time varying covariances, Econom.

Rev. 11 (1992) 143–172.[4] C. Brunetti, C.L. Gilbert, Metals price volatility, 1972–95, Resour. Policy 21 (1995) 237–254.[5] C. Brunetti, C.L. Gilbert, Are metals’ prices becoming more volatile? Proc. Miner. Econ. Manage. Soc. (1996) 58–72.[6] I. Figuerola-Ferretti, C.L. Gilbert, Price variability and marketing method in non-ferrous metals: Slade’s analysis revisited, Resour. Policy 27

(2001) 169–177.[7] C.L. Gilbert, Manipulation of metals futures: lessons learned from Sumitomo, Discussion Paper No. 1537, Centre for Economic Policy Research,

1996.[8] Goldman Sachs, Metals Watch, January 12, 2005.[9] Goldman Sachs, Metals Watch, May 25, 2006.


[10] Goldman Sachs, Metals Watch, July 5, 2006.[11] Goldman Sachs, Commodities Watch, August 17, 2006.[12] W.K. Li, S. Ling, M. McAleer, Recent theoretical results for time series models with GARCH errors, J. Econ. Surv. 16 (2002) 245–269

(Reprinted in M. McAleer, L. Oxley (Eds.), Contributions to Financial Econometrics: Theoretical and Practical Issues, Blackwell, Oxford,2002, pp. 9–33).

[13] S. Ling, M. McAleer, Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models, Econom.Theory 18 (2002) 722–729.

[14] S. Ling, M. McAleer, Stationarity and the existence of moments of a family of GARCH processes, J. Econom. 106 (2002) 109–117.[15] S. Ling, M. McAleer, Asymptotic theory for a vector ARMA-GARCH model, Econom. Theory 19 (2003) 278–308.[16] M. McAleer, Automated inference and learning in modeling financial volatility, Econom. Theory 21 (2005) 232–261.[17] A.R. Pagan, G.W. Schwert, Alternative models for conditional stock volatility, J. Econom. 45 (1990) 267–290.[18] F. Panetta, P. Angelini, G. Grande, A. Levy, R. Perli, P. Yesin, S. Gerlach, S. Ramaswamy, M. Scatigna, The recent behaviour of financial

market volatility, BIS Paper No. 29, Bank for International Settlements, 2006.[19] E. Russel-Walling, Commodities as a new institutional asset class, in: The Ringsider: Metals 2005, London Metal Exchange, 2005, pp. 135–137.[20] M.E. Slade, Market structure, marketing method, and price instability, Quart. J. Econ. 106 (1991) 1309–1339.[21] C. Watkins, M. McAleer, Econometric modelling of non-ferrous metal prices, J. Econ. Surv. 18 (2004) 651–701.[22] C. Watkins, M. McAleer, Pricing of non-ferrous metals futures on the London Metal Exchange, Appl. Financ. Econ. 16 (2006) 853–880.

How has volatility in metals markets changed?

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