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Seasonality, risk and return in daily COMEX gold andsilver data 1982–2002Brian M. Lucey a & Edel Tully ba School of Business Studies and Institute for International Integration Studies , University ofDublin, Trinity College , Dublin 2, Irelandb School of Business Studies , University of Dublin , Trinity College, Dublin 2, IrelandPublished online: 21 Aug 2006.

To cite this article: Brian M. Lucey & Edel Tully (2006) Seasonality, risk and return in daily COMEX gold and silver data1982–2002, Applied Financial Economics, 16:4, 319-333, DOI: 10.1080/09603100500386586

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Applied Financial Economics, 2006, 16, 319–333

Seasonality, risk and return in

daily COMEX gold and silver

data 1982–2002

Brian M. Luceya,* and Edel Tullyb

aSchool of Business Studies and Institute for International Integration

Studies, University of Dublin, Trinity College, Dublin 2, IrelandbSchool of Business Studies, University of Dublin, Trinity College,

Dublin 2, Ireland

This study examines seasonality in the conditional and unconditional mean

and variance of daily gold and silver contracts over the 1982–2002 periods.

Using COMEX cash and futures data, we find that the evidence is weak

for the mean but strong for the variance. There appears to be a negative

Monday effect in both gold and silver, across cash and futures markets.

Within a GARCH framework we find that the Monday seasonal does not

disappear, indicating that it is not a risk-related artefact, the Monday

dummy in the variance equations being significant also. No evidence of an

ARCH-in-Mean effect is found.

I. Introduction and Motivation

Gold and silver have acted as multifaceted metals

down through the centuries, possessing similar

characteristics to money in that they act as a store

of wealth, medium of exchange and a unit of value

(Goodman, 1956; Solt and Swanson, 1981). Dooley

et al. (1995) all report that gold is a borderless asset.

Gold and silver have also played closely related roles

as precious metals and are considered as substitutes

in portfolio diversification (Ciner, 2001). According

to Liu and Chou (2003), a close relationship exists

between gold and silver, regardless of the issue that

their monetary roles have not been significant in

recent times and their industrial uses offer little

substitutability. There is evidence that these metals

can play a useful role in diversifying risk (see

Sherman, 1982; Kaufman and Winters, 1989; Chua

et al., 1990; Davidson et al., 2003), as well as being an

attractive investment in their own right. In addition,

the importance of gold in the economy has been

shown to persist, with Davidson et al. (2003) finding

that many world industrial indices still show sensi-

tivity to gold prices. However, there are also

economic fundamentals that may act to drive the

prices of gold and silver apart. While both are used

extensively in industrial processes, there are signifi-

cant differences between these uses. Silver is extre-

mely reflective, a good conductor of electricity and

has extensive use in optics and photography. Gold’s

industrial uses are fewer, with the majority of demand

coming from the jewellery and dental markets as well

as being driven by Central Bank reserve demand

(official sector gold). Extensive documentation on

gold and silver can be found from the World

Gold Council (www.gold.org), the Silver Institute

(www.silverinstitute.org) and the International

Precious Metal Institute (www.ipmi.org).With recent equity market volatility, research has

also begun to re-examine the relationship between

these metals and equities. Thus for example Aggarwal

and Soenen (1988), Johnson et al. (1997) and Egan

and Peters (2001) show the defensive properties of

gold in a portfolio, given its high negative correlation

*Corresponding author. E-mail: blucey@tcd.ie

Applied Financial Economics ISSN 0960-3107 print/ISSN 1466-4305 online � 2006 Taylor & Francis 319http://www.tandf.co.uk/journalsDOI: 10.1080/09603100500386586

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with equity indices. Brauer and Ravichandran (1986)perform a similar analysis for silver, and Draper et al.(2002) for platinum, gold and silver. As noted,Davidson et al. (2003) find sensitivity of industrialindices to gold prices. Given that much financialresearch in equity markets involves searchingfor anomalies, in particular daily seasonal effectsin equity markets,1 it is interesting, therefore,to examine the extent and nature of any such seasonalin the precious metal markets. Moreover, in additionto the evidence from the research noted above, therealso exists significant evidence of persistent dailyseasonality across a wide variety of assets other thanequities. For fixed income securities, Gibbons andHess (1981), Flannery and Protopapadakis (1988),Jordan and Jordan (1991), Singleton and Wingender(1994), Kohers and Patel (1996) and Adrangi andGhazanfari (1996) have all detected various degreesof daily seasonality. Gold has previously beenanalysed by Ball et al. (1982) and Ma (1986), whileChang and Kim (1988), Chamberlain et al. (1990)and Johnston and Kracaw (1991) all investigatefutures markets. Finally, Redman (1997), findsevidence of daily and monthly seasonality in realestate investment trusts.

Equally, there is evidence of daily variation inthe higher moments of equity markets. Aggarwal andSchatzberg (1997) calculate aggregate skewness andkurtosis firm size classes and weekdays, and examinethese directly using ANOVA and Kruskal–Wallismeasures. Further evidence is to be found in Cheunget al. (1994), Kramer (1996) and Tang (1997).Evidence in Choudhry (2000) on South-East Asianmarkets indicates a significant daily seasonal in theconditional variance of a number of equity indices.With the exception of Choudhry (2000) these havefocused on the unconditional distribution of thesemoments.

To broader the evidence of seasonality in otherassets, the existence of seasonal behaviour patternsin commodity markets is examined. A number ofauthors in the 1980s documented the existence ofthe negative Monday effect and a January effect incommodity futures prices; see for example Chiangand Tapley (1983), Keim (1983) and Gay and Kim(1987). Milonas and Thomadakis (1997) reported amonthly effect in raw material prices, where over theperiod 1966 to 1977 the author found that the averagedaily growth rate in the Dow Jones Spot CommodityIndex for the first nine trading days was in excess ofthe last nine trading days. Girma and Paulson (1998)also find support for the existence of seasonality inpetroleum futures spreads.

The work on daily variation in the moments ofgold and silver is extremely thin. We have been ableto find no study that has investigated seasonality inthe silver market, and few indeed that have examinedgold. Ball et al. (1982) investigate the morning andafternoon fixings of gold in the London metalexchange over the 1975–79 period. They find littleevidence of either a daily seasonal or a negativeMonday. This is independent of whether Mondayreturns are measured as Friday am – Monday am orFriday pm – Monday pm. If anything, there appearsto be a negative Tuesday return. Ma (1986) providescontradictory results. Ma analyses the afternoonfixings from January 1975. He finds that while bothpre- and post-1981 (when significant changes insettlement procedures and institutional arrangementswere instituted) there existed daily seasonality, thenature of this seasonality changes. Pre-1981 therewas a negative Tuesday (as found by Ball et al. 1982)and a highly significant positive Wednesday. Post1981, the negative Tuesday disappears and theaverage return on Monday switches from positive tosignificantly negative.

Tschoegl (1987) investigates monthly Londonafternoon fixing mean returns of gold during theperiod 1975 to December 1984. The author reportsthat the data does not give support to the nullhypothesis of no monthly seasonality. The authorexamined seasonality under 3 definitions: cyclicalpatterns; particular months displaying returns thatare significantly different; and lastly where no onemonth is significantly different from the average,taking all months together add explanatory value.Under these conditions the author states that a stablecyclical pattern does not exist and nor does aJanuary effect. However the author did find weakevidence to support ‘a pattern of below-averagereturns in the second half, particularly September’Tschoegl (1987).

Herbst and Maberly (1988) issued a reply toMa (1986) where the authors reported on the validityof the results. Herbst and Maberly (1988) questionedthe synchronization of observations for spot andfuture gold prices. In addition, Wednesday’s spotmean returns was �4.31% compared to Wednesday’sfutures mean return of þ9.86% for the period, whileduring this period futures prices declined from$434.20 to $323.90 per troy ounce. Herbst andMaberly (1988) postulate that the conflicting resultsare due to 4 significant dates in 1982: 8 September;15 September; 13 October and 20 October, when spotand future gold prices moved in opposite paths.The authors report that if these outliers were deleted

1 See, for example, the research quoted in Keim (1983).

320 B. M. Lucey and E. Tully

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the reported mean returns for spot and future gold

prices on Wednesday over this period would be

þ2.72% and þ4.77% respectively.In a reply towards Ball et al. (1982) and Ma

(1986), Ma et al. (1989) replicate the tests of Herbst

and Maberly (1988), where the authors did not report

statistics of significant for their results. Ma et al.

(1989) report that Wednesday and non Wednesday

mean return on both spot and future markets are not

significantly different from zero, while the Kruskal–

Wallis Chi-squared reports that a significant differ-

ence between Wednesday and non Wednesday

returns does not exist regardless of the inclusion of

the four observations. Therefore, the authors confirm

the results of Ma (1986) and conclude that the high

Wednesday returns that existed before October 1981

may indeed be due to the next day settlement

procedure in foreign exchange.Coutts and Sheikh (2002) examined the All Gold

Index of the Johannesburg Stock Exchange for the

existence of weekend, January and pre-holiday effects

in gold equity stocks. Over the period 5 January 1987

to 15 May 1999, the authors report that no evidence

exists of a weekend, January or holiday effect in this

index.Since these works, the examination of gold and

related asset seasonality has lagged. This study thus

attempts to fill that gap, using a variety of robust

estimators that take account of the dynamics of the

series. In particular, we investigate the daily seasonal

in the conditional and unconditional first and second

moments (mean and variance) of four assets: gold

cash prices, silver cash prices, gold futures prices

and silver future prices. This study uses an extended

dataset of 20 years to investigate seasonality in the

cash and future markets of these metals. We thus

allow for comparisons between the gold market

dynamics as found in earlier studies such as

Ma (1986) and now. In addition, this is the first

study of its kind to examine seasonality in the silver

market. Using sophisticated econometric modelling,

with parametric and non-parametric analysis, we

provide an appropriate investigation of the cash and

futures market of gold and silver.The importance of daily seasonality lies in the

challenge that it may give to standard notions of

market efficiency. While there are many definitions of

an informational efficient market, the basic element

required is that there is no possibility of making

persistent trading profits over and above a ‘buy-

and-hold’ strategy from previous information. If

there was a discernable pattern evident then prices

would adjust to incorporate this and over time, the

pattern would disappear.

II. Gold and Silver Markets:An Introduction

Gold and silver prices float freely in accordance withsupply and demand, responding quickly to politicaland economic events. A large range of companiesfrom mining companies to fabricators of finishedproducts, users of silver and gold content industrialmaterials and investors, draw on COMEX futuresand options and the London Bullion Marketprimarily. LBM trades essentially physical gold andsilver while COMEX trades in the derivatives of thesemetals. Gold is quoted in dollars and cents per troyounce, while silver is quoted in cents per troy ounce.

Gold and to a lesser extent silver are highlyliquid. Gold can be readily bought or sold 24 hoursa day, in large denominations and at narrow spreads.This cannot necessarily be said of most otherinvestments. This is highlighted by Draper et al.(2002) who state that total annual production of gold(2300 tons) is cleared by the LBMA every 2.5 days.According to Ong and Izan (1999) gold is ahomogenous commodity, traded continuouslyacross the globe. Silver is traded in London, HongKong, Chicago, Zurich and New York. In London,silver is traded on a physical basis for spot andfutures prices. According to the Silver Institute,London remains the true centre of the physicalsilver trade for most of the world; however,significant study contracts trading market for silveroccurs in COMEX. Clearly, looking at the above, nomore than in equity markets, we see neither systemicforce that act at the daily frequency to alter thedynamics of these markets nor would we expect to seesuch daily seasonality persist in these markets giventhe high degree of liquidity.

London and New York are two of the mostimportant markets for trading gold and silver. TheLondon Bullion Market (LBM) trades essentiallyphysical metals while COMEX trades in the deriva-tives of the metals. The COMEX Exchange or theLBM do not set prices of commodities. Rather, theexchange provides a platform where buyers andsellers can come together and publishes the pricesthat result from those transactions. There are fivemembers of the twice daily London Gold fixing, whilethree members of the LBMA meet each working dayat 12 noon for the daily silver fixing. Clients placeorders with the dealing rooms of the fixing members.The price is adjusted to reflect whether there are morebuyers or sellers at a given price. The price thatemerges from trading is determined by supply anddemand. It is important to note that the fixing priceemerging from the meetings is not the only price atwhich bullion trades daily – it should be considered as

Daily COMEX gold and silver data 1982–2002 321

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akin to a snapshot price to indicate market dynamicsat that time than to a ‘fixed’ or ‘maintained’ price.

The main factors of demand for gold areindustrial use, Central Bank demand and jewellerydemand. A sale of official gold reserves has a largeinfluence on the price of gold. A large component ofjewellery demand emanates from India and China.In addition, private demand includes the physicalhoarding of gold bars and investment in options andfutures. Therefore, a change in the attitudes of privateinvestors can have significant altercations for theprice of gold. Gold supply is composed of mineproduction with Indonesia having the largest pro-ducing mine; official sector sale, gold scrap withdiscarded jewellery the biggest component of scrapand net disinvestment (see Radetski, 1989).Investment holdings account for 16 percent of thetotal stock of gold. Gold’s status as an investmentasset has been examined by a number of authorsincluding Aggarwal and Soenen (1988), Johnson andSoenen (1997), Ciner (2001) and Egan and Peters(2001). Sherman (1982) recommended holding10–20% of portfolios in gold. Jaffe (1989) reportsthat gold has a low correlation with most assets overthe period of 1971–1987, suggesting that gold mayreduce portfolio risk. He finds that gold has virtuallyno relationship with stocks and bonds. Davidsonet al. (2003) commented that gold has renewed itsdiversification status in the aftermath of the Asiancrisis as it is once again being used as a hedging deviceby investors. According to Draper et al. (2002)portfolios that contain gold, silver or platinumperform significantly better than standard equityportfolios. Therefore, the astute investor, using thisfinancial shelter, can minimize risk while maximizingreturns.

The price of silver is determined by the interac-tion of the supply and demand components of themarket, the global economy, consumer tastes andimages, inflation, fluctuations in deficits, perfor-mance of the electronics industry, etc. Silver isproduced as a by-product of gold primarily andto a lesser extent lead, zinc and other metals.It is common practise for silver to follow themarket movements of gold. The demand for silveras a private investment is not as strong as for gold asindustry consumes silver while silver use in industry ismuch greater. Supply of silver is dominated bymine production, scrap recycling, disinvestment,government sales and producer hedging.

Gold and silver share a lot of similar propertiesas both are used as industrial components and

investment assets. The quantity of gold and silverrequired is determined by the quantity demanded forindustrial, investment and jewellery use. Therefore anincrease in the quantity demanded by the industrywill lead to an increase in the price of these metals(Radetski, 1989; Draper et al., 2002). Price changescan also be the result of a change in the CentralBank’s holding of these precious metals. In addition,changes in the rate of inflation, currency markets,political harmony, equity markets, producer andsupplier hedging all affect the price equilibrium ofthese metals.

Traditionally gold has played a significant roleduring times of political and economic crises andduring equity market crashes; whereby gold hasresponded with higher prices. According to Smith,in times of economic uncertainty attention turns toinvesting in gold as a safe haven (2002, p. 1).Similarly, Faff and Chan (1998) report that goldstocks play an important role as a hedge against otherstocks. The authors report that and investment ingold provides an effective hedge against inflation andpolitical instability (1998, p. 22). Taylor (1998) statesthat both gold and silver along with platinum haveprovided a short and long run hedge against inflation.

III. Methodology

We test both the conditional and unconditionalmeans and variances of the series. Testing theunconditional means is achieved by a series ofregressions of the form

Rt ¼X5

i¼1

�i þ "t ð1Þ

a simple dummy variable regression. The two setsof statistics that emerge are of course the regressiont-statistics, which test the difference from zero of eachcoefficient, and the regression F-statistic, which is ajoint test of the equality of each coefficient to zero,simultaneously. To ensure robustness of the resultsfrom outliers we also apply a robust method, atrimmed least squares regression model. This uses theiterative re-sampling model of Rousseeuw and Leroy(2003).2 We also report results with Whites correctionfor disturbances in the error terms to control forhetroskedasticity and autocorrelation. Testingfor seasonality in the unconditional variance isby means of Levene’s test, an alternative to the

2 Previous versions of this study used a simple trim of the top and bottom 2.5% of data. The results are not significantlydifferent.

322 B. M. Lucey and E. Tully

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well-known Bartlett test for equality of variance thatis robust to non-normality.

The Levene test tests H0: �i ¼ �j 8 i,j, Ha:. Let

W ¼N� kð Þ

Pki¼1 Ni Zi � Z...

� �2

k� 1ð ÞPk

i¼1

PNj¼i Zij � Zi

� �2 ð2Þ

The Levene test rejects the hypothesis that thevariances are homogeneous if W > Fð1��,k�1,N�1Þ

where Fð1��,k�1,N�1Þis the upper critical value of theF distribution with k� 1 and N� 1 degrees offreedom at a significance level of ~�.

GARCH models by now are well known asrepresentations simultaneously of the conditionalmean and variance of a series. Thus, we do notpropose here to give a detailed recapitulation.In general we can write the GARCH-M modelswith exogenous variables in both the mean andvariance equations (here daily dummies) as

Rt ¼ �0 þ �1ffiffiffiffiht

pþXr

i¼1

�iRt�i þXn

j¼1

�jXj þXm

k¼0

�k�t�k

þ �t; �t ¼ffiffiffiffiffiffiffiffiht"t

p; "t � ð0,1Þð1:Þ

ht ¼ �0 þXn

d¼i

�i Xi þXp

j¼1

jht�j þXq

i¼1

!i�2t�i ð3Þ

We can also account for potential asymmetricresponses in the conditional variance by adding aleverage term to the variance itself, as proposed inGlosten et al. (1993), giving the variance as

ht ¼ �0 þXn

d¼i

�i Xi þXp

j¼1

jht�j þXq

i¼1

!i�2t�i

þ It�1�2t�1;

�t < 0 ! I ¼ 1

�t < 0 ! I ¼ 0

ð4Þ

and providing the Leveraged GARCH (LGARCH)model.

In a GARCH framework, the ARCH-in-Meanelement represents the payoff for taking on risk whilethe constant in the mean equation represents theelement not related to risk, or the risk free return. Thepresence of dummy variables in the mean equationchanges this somewhat. Then, the coefficients on thedummy variables are the conditional returns toholding the asset on that day, the intercept beingthe returns expected on days other than that and theAIM term remaining unchanged.

The inclusion of daily dummies allows us notonly to model the conditional dependence betweenthe mean and the variance but also potentially toexamine the effect that daily seasonality has on theseconditional estimates. Recall that the examinationsearlier are of the unconditional mean and variance.

By including dummy variables for days of the week,we are in a position to examine the effect that thesehave both on the mean and the variance.

There is no agreement in the literature as towhich dummy variables should be included. Clareet al. (1998) and Lucey (2000) include daily dummiesin the mean and variance for those days that havebeen shown, from a standard OLS regression, to havesignificant coefficients in mean returns. Glosten et al.(1993) include dummies for January and October,on similar justification. Beller and Nofsinger (1998)test all calendar variables. Another issue is the modeof propagation of calendar effects. As Beller andNofsinger (1998) points out, there are of course threeplaces where such dummies can go. The equationsabove make the implicit assumption that the effect onthe conditional variance of calendar effects is throughthe intercept terms, in effect assuming that there isa different form of conditional variance for each dayof the week, etc. Alternatively, it could be the casethat the relationship is propagated through thevariance itself or through the unexpected returns(residuals).

As there have been very few if any studiespublished of the conditional variance of these metalcontracts, we confine ourselves here with the simplestinterpretation. Where there is evidence that there aredaily mean seasonals, we include relevant dummies.We also are interested in the potential effect that eachday may have on the variance. Thus, we includefour dummy variables in the conditional varianceequations. We exclude Friday in each of the fourcontracts studied. The constant term in the varianceequation can then be taken as either themean variance and/or the effect on the variance ofthe excluded day. The daily dummies for the varianceare then properly the differential effects on thevariance of the relevant day.

We can interpret the dummy variables as follows:If any daily dummies included in the mean equationremain significant then we may conclude thatseasonality is not due to daily variation in risk.If the dummies become insignificant in the meanequation but are significant in the variance equation,we can conclude that there is seasonality in marketrisk, whether this is priced or not. The extent, if any,of the degree of a relationship from risk to returncan also be seen from the magnitude and significanceof the ARCH-in-Mean term. In all cases aGARCH(1,1) model is applied in Leveraged form.

Data

We examine four series: daily prices for gold andsilver cash and futures traded on COMEX, denoted

Daily COMEX gold and silver data 1982–2002 323

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as Cash Gold, Cash Silver, Future Gold and FutureSilver. We analyse, as normal, percentage changes.The futures contract data are linked to form acontinual series using the methodology proposed bySpurgin (1999). The method used is described in moredetail therein, but in essence, it involves a continualroll strategy. Each day a percentage of the frontcontract is sold and rolled into the next-out contract.The roll strategy is linear, with the percentage Pt

held in the near contract being

# days until first day of nearby contract expiry month

# days from last expiration to nearby expiration

ð5Þ

Each day (Pt�1�Pt) is rolled. If NB is the nearbycontract and NX the next-out then the spot indexof any day is given by St¼NB*PtþNX* (1�Pt).The total data set extends over the period January1982 – November 2002. In total, we have 5256 datapoints available. Given the fact that the above rollmechanism will lose data at the end, the totaladjusted future index gives us 5225 data points.3

Shown in Table 1 are the average daily volumesof trade on the four contracts over the period – in allcases the markets have shown growth, on thismeasure, over the period of analysis. Although goldhas been freely traded since 1974, we have concen-trated on the post 1982 period for a number ofreasons including the attempted cornering of thesilver market by the Hunt brothers, and the change insettlement procedures in London in late 1981.Shown in Figs 1 and 2 are the price levels over thisperiod. All data are analysed in log-percentage returnterms. Table 2 shows detail of the first four momentsof gold and silver, by days of the week over the entiredataset.

As cited earlier, there is significant evidence fromthe equity markets of the tendency of stock marketsto decline on a Monday and peak on a Friday.Evidence from Fields (1931), Kelly (1930), French(1980), Lakonishok and Levi (1982), Kohers and

Kohers (1995) and Maberly (1995) all document a

peak in returns on a Friday and a trough on

Mondays.Shown in Table 2 are some basic statistics. The

above results correlate to the findings of this study,

that Monday returns are consistently negative and

the lowest for all days of the week. As evidenced inthe equity markets, Monday’s standard deviation in

both cash and futures gold and future silver is also the

highest of all days of the week. Lakonishok and

Levi (1982), Lakonishok and Smidt (1988) and

Kohers and Kohers (1995) have reinforced the

pattern of Monday having the lowest often negative

return of the week despite having the highest, or at

least the higher than average, risk as proxied by thestandard deviation. Thus, the pattern found stereo-

typically in equity markets follows here. This reflects

evidence from previous studies on seasonality in

equity markets and is in line with the results of

Ma (1986).

SILV CAS SILVER F

800 1600 2400 3200 4000 4800250

500

750

1000

1250

1500

Fig. 2. Silver prices 1982–2002

GOLD CAS GOLD FRO

800 1600 2400 3200 4000 4800

550

500

450

400

350

300

250

Fig. 1. Gold prices 1982–2002

Table 1. Average daily volume/open interest, 2002

$m terms

Cash silver Cash gold Future silver Future gold

1982 $6.05 $25.83 $15.26 $70.501987 $12.90 $26.11 $57.49 $95.811992 $9.51 $18.95 $67.04 $84.181997 $17.69 $34.52 $85.01 $171.812002 $12.69 $35.93 $81.53 $158.32

3We also analysed a continual series constructed by simply rolling to the nearest month when the contract expired. The resultsfrom this were qualitatively similar to the results presented here.

324 B. M. Lucey and E. Tully

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In examination of higher moments in the equitymarkets, Scott and Horvath (1980) show thatinvestors have a preference for kurtosis and areadverse to skewness. Aggarwal and Schatzberg(1997) find a negative Monday return. Skewnesspatterns follow those of the first two moments forthe first period they examine, but ‘flip’ in thesecond, with the Monday skewness going fromlowest to highest. This result contrasts with theresults here where Monday’s skewness statistics,with the exception of silver cash, are consistently thehighest and negative. Kurtosis does not follow meanreturns as reported in Aggarwal and Schatzberg(1997), Monday’s kurtosis are positive and thelargest in gold cash and silver futures. These resultson higher moments of the precious metals showgreater similarity with evidence from Asian equitymarkets as reported in Ho and Cheung (1994) andTang (1997), both of whom reported that highermoments do not follow a pattern similar to that oflower moments.

From the above results, it appears that season-ality in the first moment may exist. Monday returnsare low with no obvious explanation from risk.Similarly, the maximum returns, which occur not onFriday as in equity markets except for Cash gold, theremainder occurring on Thursday, have low standarddeviations. However, risk premia in futures and cashmarkets differ in their derivation, with both howeverultimately being a reward for the potential for lossarising from the tails of the distribution. What isinteresting here is that the cash and futures markets

are in broad agreement, indicating perhaps thatthe lack of payoff to potential risk is generalized.Table 3 displays the results of the KolmogorovSmirnov Z test and the Jarque–Bera statistics for theequality of distributions. The results for all variablesreject the equality of the distribution at the 5% level,thus confirming that the data is non-normal. Alsoshown as in Figs 3, 4 and 5 are histograms of the datain terms of log percentage change, with a normalcurve superimposed. All data sets are very peaked dueto the high kurtosis factor. The distributions do notdisplay any obvious degree of skewness. Accordingly,we do not carry out tests for seasonality in the highermoments.

IV. Results

Unconditional mean and variance results

Beginning the formal analysis, Table 4 shows theresults of a regression analysis of the first moments.

Table 2. Moments of the distribution by day of the week 1982–2002

MeanStandarddeviation Kurtosis Skewness

Cash gold Monday �0.0007 0.0121 17.1249 �1.0202Tuesday 0.0002 0.0097 7.6338 0.4657Wednesday �0.0002 0.0095 6.7646 0.0263Thursday 0.0002 0.0085 6.0197 �0.2455Friday 0.0003 0.0102 16.3361 1.7727

Cash silver Monday �0.0011 0.0173 4.1924 �0.3995Tuesday 0.0001 0.0180 32.3975 �2.5566Wednesday �0.0002 0.0153 4.4904 0.0806Thursday 0.0004 0.0159 4.1718 �0.0643Friday 0.0001 0.0157 7.4818 0.3670

Futures gold Monday �0.0002 0.0101 6.5391 �0.2923Tuesday �0.0001 0.0089 12.4844 0.8314Wednesday 0.0000 0.0079 4.3973 0.0618Thursday 0.0001 0.0087 11.2163 0.1556Friday �0.0000 0.0098 8.6970 0.4981

Futures silver Monday �0.0007 0.0171 11.0493 �1.3391Tuesday �0.0002 0.0152 9.6115 0.0542Wednesday 0.0001 0.0140 3.9647 �0.0679Thursday 0.0006 0.0148 4.5205 0.2695Friday �0.0006 0.0144 3.1528 �0.1670

Table 3. Normality tests of data

N Z P JB P

Cash gold 5256 6.379 0.00 70.99 0.00Cash silver 5256 6.164 0.00 8575.04 0.00Futures gold 5225 6.862 0.00 19450.95 0.00Futures silver 5225 5.713 0.00 10271.61 0.00

Daily COMEX gold and silver data 1982–2002 325

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Changes PlotsGold Cash

800 1600 2400 3200 4000 4800

800 1600 2400 3200 4000 4800

800 1600 2400 3200 4000 4800

800 1600 2400 3200 4000 4800

−0.05

−0.10

−0.15

−0.20

−0.00

0.05

0.10

0.15

0.20

−0.05

−0.10

−0.15

−0.20

−0.00

0.05

0.10

0.15

0.20

−0.05

−0.10

−0.15

−0.20

−0.00

0.05

0.10

0.15

0.20

−0.05

−0.10

−0.15

−0.20

−0.00

0.05

0.10

0.15

0.20Silver Cash

Gold Future

Silver Future

Fig. 3. Data in percentage change

Evolution over 4/1/82 - 28/11/02

Gold Cash

800 1600 2400 3200 4000 4800 800 1600 2400 3200 4000 4800

800 1600 2400 3200 4000 4800800 1600 2400 3200 4000 4800

−0.50

−0.25

0.00

0.25

−0.50

−0.25

0.00

0.25Silver Cash

Gold Future

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6Silver Future

Fig. 4. Data relative changes

326 B. M. Lucey and E. Tully

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There does not appear to be an issue of daily

seasonality in the first moment as none of the

regressions show a significant F-statistic, indicating

that overall seasonality is not evident. However,

Monday has significant t-statistics for Cash Gold and

Cash Silver, while there are no significant coefficients

for the futures series. The results for the robust

regression, where the t-statistics are calculated

according to whites procedure, are qualitatively the

same as for the trimmed OLS, with the evidence being

if anything weaker again. The trimmed least squares

approach, TLS, shows no days as being significantly

different from zero.We have, however, evidence that the data are

non-normally distributed, which would warn against

an over-reliance on parametric evidence alone.

Therefore, the Kruskal–Wallis test, a non-parametric

alternative to ANOVA, is used to supplement the

results above. The results are shown in Table 5. While

we cannot reject the null that the cash series are

drawn from a distribution where the daily returns are

the same this is not the case for the futures data. This

result is inconsistent with the regression results.

Testing for a day of the week effect in equity markets,

using both the regression F and Kruskal–Wallis test,

Elyasiani et al. (1996), Arsad and Coutts (1997) and

Steeley (2001) all found agreement between the two

sets of tests. Our finding here is thus perhaps evidence

that the seasonality in the mean, if present, is weak

and not statistically robust.Table 6 shows the results for the presence of

seasonality in the second moment. In all cases, we can

reject the null of homogeneity of variance across days

of the week, indicating that there may well exist, a

daily seasonality in the variances of these assets.4

Thus, we can conclude for the unconditional means

goldcash ret

.100.088

.075.063

.050.038

.025.013

.000−.012

−.025−.037

−.050−.062

−.075−.087

−.100−.112

−.125

Gold Cash % Changes4000

3000

2000

1000

0

Std. Dev = .01Mean = −.000N = 5256.00

silvcash ret

.087.062

.037.012

−.013−.038

−.063−.088

−.113−.138

−.163−.188

−.213−.238

Silver Cash % Changes3000

2000

1000

0

3000

2000

1000

0

3000

2000

1000

0

Std. Dev = .02Mean = −.000N = 5256.00

goldfront ret

.088.075

.063.050

.038.025

.013.000

−.012−.025

−.037−.050

−.062−.075

Gold Futures % Changes

Std. Dev = .01Mean = −.000N = 5256.00

silvfront ret

.138.113

.088.063

.038.013

−.012−.037

−.062−.087

−.112−.137

−.162−.187

Silver Futures % Changes

Std. Dev = .02Mean = −.000 N = 5256.00

Fig. 5. Histograms of data plus normal curve

4 The question remains open, given our dataset, as to whether this daily seasonal in variance is a weekend or Monday issue.According to Cross (1973) and French (1980) the Monday effect is Friday close to Monday close data. However, Rogalski(1984) and Harris (1986) state that a weekend effect if evident is returns examined from Friday close to Monday opening.The consensus evidence for equities is for a weekend effect.

Daily COMEX gold and silver data 1982–2002 327

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and variances that the evidence is stronger forseasonality, at the daily frequency, for the varianceof the data than for the means.

Conditional mean and variance results

Table 7 shows the results of GARCH models. Shownare the coefficients and beside them their P-values.Both specifications provide a good fit to the data: thediagnostic statistics (available on request) indicate no

significant residual serial correlation or significantresidual ARCH effects, the constant of variance ispositive and significant for gold series, and thevariance is non-explosive. The likelihood ratio testin Table 8 indicates that the Leveraged GARCHmodel does not fit the data any better than the simpleGARCH model, a typical finding. In generaltherefore we concentrate on the GARCH(1,1) results.

For cash gold the constant in the mean, thepayoff for non risk factors, is positive. However, it isnegative for all other series, but is in all casesinsignificant. Thus, in no case can we assert thatthere is a significant payoff to gold or silver forfactors related other than risk. Indeed, given that theARCH-in-Mean terms are also statistically insignif-icant, indicating no payoff for risk it appears that theprecious metals are being priced by states outside thestandard pricing model. This result is in line withthat found in Faff and Hillier (2004) in relation to therisk-return trade-off for gold industry stocks.

For cash gold and silver, we note that theMonday dummy in the mean remains significantand negative even with the addition of the dummyvariables in the variance equation. Overall, therefore,the Monday effect in the cash gold and silver pricesis not driven by variations in risk on Monday.We should note that the dummies in the variance

Table 4. Regression analysis of daily seasonality

OLS Robust OLS TLS

Variable Coefficient P P Coefficient P

Cash gold Monday �0.0007 0.03 0.08 �0.0002 0.30Tuesday 0.0002 0.59 0.58 0 0.96Wednesday �0.0002 0.45 0.43 �0.0002 0.42Thursday 0.0002 0.60 0.55 0.0003 0.23Friday 0.0003 0.28 0.29 0.0002 0.48F(5256) 1.3628 0.23 0.30 F(4828) 0.72

Cash silver Monday �0.0011 0.04 0.05 �0.0004 0.29Tuesday 0.0001 0.84 0.86 0.0003 0.37Wednesday �0.0002 0.75 0.73 0 0.93Thursday 0.0004 0.42 0.41 0.0005 0.17Friday 0.0001 0.86 0.85 0.0001 0.78F(5256) 1.024 0.40 0.43 F(4828) 0.79

Futures gold Monday �0.0002 0.51 0.55 0 0.82Tuesday �0.0001 0.83 0.83 �0.0002 0.37Wednesday 0 0.85 0/83 0 0.82Thursday 0.0001 0.70 0.68 0.0001 0.63Friday 0 0.87 0.88 �0.0001 0.72F(5256) 0.1678 0.95 0.98 F(4964) 0.94

Futures silver Monday �0.0005 0.29 0.34 0.0001 0.78Tuesday �0.0001 0.88 0.88 �0.0004 0.27Wednesday 0.0002 0.65 0.63 0.0003 0.47Thursday 0.0007 0.11 0.10 0.0002 0.63Friday �0.0005 0.31 0.28 �0.0004 0.21F(5256) 1.2845 0.29 0.42 F(4965) 0.60

Table 5. Non-parametric analysis of daily seasonality

KW statistic P

Cash gold 4.029 0.40Cash silver 5.908 0.20Futures gold 0.750 0.00Futures silver 2.824 0.00

Table 6. Levene’s test for homogeneity of variance

Levene statistic P

Cash gold 7.879 0Cash silver 3.524 0.01Futures gold 4.865 0Futures silver 3.251 0.01

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term properly refer to the differential impact thatthese days have on the variance versus Friday, whichinfluence is subsumed in the constant of variance.

The daily dummies are significant in the varianceequations for cash and futures gold, whereas for cashsilver we note that only Monday appears to have asystemic effect, increasing variance. For futures silverwe find that only Wednesday is significant, with the

effect of decreasing variance. However, the magni-tude of these effects is extremely small.

Switching to the LGARCH model, we note thatthe leverage term is negative and significant in allcases, indicating that the effect of a negativeinnovation in the mean this period acts to reducethe variance next period. The leverage terms are also,in absolute terms, quite large. However, as noted,

Table 7. GARCH results for gold and silver. Table shows the results of a GARCH(1,1) model of the following type

Rt ¼ �0 þ �Rt�1 þ ��t�1 þ �ffiffiffiffiht

pþXn

j¼1

�jXj þ �t;

�t ¼ffiffiffiffiffiffiffiffiht"t

p; "t � ð0,1Þ; ht ¼ �0 þ ht�1 þ !i�

2t�1 þ

Xn

d¼i

�i Xi þ It�1�2t�1;

�t < 0 ! I ¼ 1�t < 0 ! I ¼ 0

Cash gold Cash silver

Coefficient P Coefficient P Coefficient P Coefficient P

� 0.00006 0.82 0.00019 0.52 �0.00035 0.53 �0.00043 0.46� �0.34945 0.10 �0.36208 0.07 �0.51740 0.05 �0.51385 0.05� 0.30308 0.16 0.31107 0.13 0.49386 0.07 0.48958 0.06� �0.00046 0.08 �0.00049 0.05 �0.00088 0.04 �0.00092 0.03� �0.00632 0.87 �0.03640 0.37 0.02368 0.59 0.01544 0.73� 0.00001 0 0.00001 0 0 0.80 0 0.64 0.08981 0 0.07333 0 0.07943 0.00 0.06098 0.00! 0.92914 0 0.92089 0 0.93469 0.00 0.93043 0.001 �0.00001 0 �0.00001 0 0.00001 0.01 0.00001 0.022 �0.00002 0 �0.00002 0 0 0.59 0 0.883 �0.00001 0 �0.00001 0 �0.00001 0.30 �0.00001 0.254 �0.00001 0 �0.00001 0 0 0.71 0 0.99 �0.05016 0 �0.04222 0Likelihood

ratio17 685.72 17 663.31 14 911.02 14 892.35

Future gold Future silver

Coefficient P Coefficient P Coefficient P Coefficient P

� 0.00005 0.85 0.00009 0.74 �0.00014 0.82 �0.00045 0.49� 0.01022 0.99 �0.52108 0.13 0.00732 0.99 �0.00826 0.99� �0.03520 0.95 0.50169 0.15 �0.03691 0.94 �0.02360 0.96� �0.01294 0.71 �0.03408 0.34 �0.00283 0.95 0.00512 0.91� 0.00001 0 0.00001 0 0 0.25 0 0.56 0.06360 0 0.04476 0 0.06378 0 0.04289 0! 0.95541 0 0.95401 0 0.95388 0 0.95246 01 �0.00001 0 �0.00001 0 0 0.54 0.00001 0.312 �0.00001 0 �0.00002 0 0 0.94 0.00001 0.313 �0.00001 0 �0.00001 0 �0.00002 0.02 �0.00002 0.014 �0.00001 0 �0.00001 0 0 0.78 0 0.88 �0.04067 0 �0.04200 0Likelihood

ratio17 483.81 17 453.40 14 535.00 14 510.31

Table 8. Likelihood ratio tests for GARCH model accuracy. LR statistic computed as 22 ln(LRGARCH(1,1)/LRLGARCH(1,1))

Gold cash Silver cash Gold future Silver future

LR statistic 0.00253585 0.00250576 0.00348168 0.00340021LR P-value 0.9598 0.9601 0.9529 0.953

Daily COMEX gold and silver data 1982–2002 329

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the LGARCH model is rejected as an improved fitfor the data.

The statistical significance notwithstanding, thesmall size of the variance coefficients is indicative oflow economic significance. In all cases, compared toeither the absolute value or the deviation betweenthe absolute value and Friday value of the uncondi-tional variance, the conditional variance coefficientsare between 20 and 200 times smaller than theunconditional. Thus, while statistically significant,there is little likelihood of economic significance.By comparison, the conditional mean dummy valuesfor Monday are greater than the unconditional,but again, small in absolute terms. At levels of0.05%, the Monday return is well below anyfeasible trading cost, and thus makes the possibilityof a trading mechanism based on exploitationof same unlikely to be successful. This finding isnot new in the literature on seasonality (see,for example, Cooper, 1982; Ho and Cheung, 1991;Alexakis and Xanthakis 1995; Athannasakos, 1997;Chow et al., 1997; Anon., 1998; Lucey, 2004 andSteeley, 2004), and thus the usual implication canbe drawn; while seasonality may exist, it perhapsprovides market timing rather than market tradingstrategies.

V. Conclusion and Discussion

Ma (1986) et seq. found significant negative Mondayeffects in the gold market. We confirm this findingfor cash gold but not for the futures market, perhapsindicating a greater degree of efficiency in that series.In general, it is the case that futures markets arefound to be more efficient, being more liquid. TheMonday effect in cash gold appears to be weak andstatistically not robust. We also provide the firstevidence of daily seasonality in silver prices. These aresimilar to the gold findings. The evidence from aGARCH model, using a leveraged GARCH specifi-cation, is that the seasonality in the mean may notresult from seasonality in the variance. We also notethat there is no evidence of a return-risk relation-ship as indicated by the ARCH-in-Mean beinginsignificant and negative.

This set of results indicates a number of unusualfeatures. First, although the four assets are correlatedpositively and significantly with one another, thereappears to be a different set of dynamics across themarkets. The authors do not wish to imply that thecash and futures markets are not integrated. See,for example, Ciner (2001) where the author finds thatthe long run stable relationship between the futures

prices of gold and silver has broken down during the1990s. This is also supported by Escribano andGranger (1998) who found that since the 1990s theco-integration relationship between gold and silverhas died. However, this is inconsistent with theresults of Ma (1985), Ma and Sorensen (1988) andWahab et al. (1994). Second, in some ways goldin particular can be seen as the ultimate risk-lessasset, despite its having volatility. The finding thatthese markets appear to be driven almost entirely bytheir own lagged values, the autoregressive andmoving average terms being significant, with neitherrisk (ARCH-in-Mean) nor non-risk (constant in themean) variables having any significant impact indi-cates that returns to these assets are perhaps separatefrom other influences. Fuller investigation of theconditional mean responses of gold and silver to theequity market for example would require a multi-variate GARCH modelling. Third, the finding thatthe leverage term is in many ways the most importantelement of the variance indicates that while the dailyseasonal in the variance is important it is not assignificant, again, as the markets response to its owndynamics. Overall, the results indicate that there arefruitful questions of investigation in these markets,and that an understanding of them requires at theleast an understanding of the daily seasonaldynamics.

If we accept that there are daily seasonalinfluences, the question arises as to the source ofthese. As has been noted the equity markets aresignificant contributors to this literature. Drawingfrom this we find that there are three main theoriesregarding why markets would indicate a dailyseasonal. The most relevant can be broadly summedup as the market settlement system (e.g. Bell andLevin, 1998), arrivals of news to the market(e.g. Steeley, 2001) and dissemination of news in themarket (e.g. Pettengill and Buster, 1994) hypotheses.At first glance, none of these would seem clearcontenders for the causal mechanism. According toSteeley (2001), news announcements occur onTuesday, Wednesday and Thursday in the UK. Theauthor states that this allows investors to assimilateand consider information over the weekend, in theabsence of additional news, and this perhaps favoursMonday selling which could ‘depress prices andso produce a significantly negative return over theweekend’ (2001, p. 1942).

Much of the discussion on the causes of seasonalfactors in gold has concentrated on longer-termcycles. Thus, Ma (1986) postulated that asWednesday’s mean returns for the post October1981 period changed from being negative to positive,therefore the mean returns for Wednesday were

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affected by the existence of same-day foreignexchange market settlement. However, Herbst andMaberly (1988) comment that if the four outliers, thatare discussed previously, are deleted then the same-day settlement in foreign exchange does not affectWednesday’s spot mean returns. Tschoegl (1987)reports that gold should not be affected by tax yeareffects, which has been reported in Roll (1983) as apotential source of seasonal behaviour in stocks.Tschoegl argues that as (at that stage) gold has amarket capitalization greater than that of the largestcompany on the NYSE, and that in addition as goldis traded in many countries throughout the worldit is subjected to carrying tax regimes and tax years(1987: 251). The author also postulates thatproduction cycles should bear no influence on goldreturns as significant above ground stocks of themetal exist. The author cites interest rates seasonalbehaviour as grounds for seasonal behaviour in thegold market also. Milonas (1991) states that seasonalbehaviour in commodities may be due to the cyclicnature of their production. The author notes thatcrop cycle related seasonality’s have been unearthedby various authors including Roll (1983), Anderson(1985) and Fama and French (1988).

According to Coutts and Sheikh (2002), the nonexistence of seasonal effects in the All Gold Indexon the Johannesburg Stock Exchange may be due tothe market microstructure of the exchange or indeedthe composition of the index. The authors reportthat this is in contrast to the many studies, whichhave discovered international evidence of seasonalbehaviour in stock markets. Many practitionersin these markets believe that evidence of seasonalityis attributed to the tax payment and accountingcycles. In addition, seasonal buying behaviour inthe jewellery market, especially in Asia and theMiddle East where gold and silver are purchased asa form of savings, during wedding and festivalseasons can induce seasonal effects. As silver ismore of an industrial metal than gold, it mayshare some seasonality with base metals which isrelated to annual auto production and consumptioncycles.

In the case of the settlement system we havein gold a rolling settlement, and the prices of bothcash and future gold include the cost of carry(explicitly so in the case of the futures and via thegold lease rate in the case of cash gold) in the price.News generated internally in the market is difficult toextract from general news – the mechanism usedby Pettengill and Buster (1994) involves data, rise/fallratios, that have no analogy in the precious metalmarkets. Thus, we are left with the potential that it isas a consequence of news arriving to the market,

or an as yet unspecified mechanism, that inducesdaily seasonality, especially in the variance.

Acknowledgements

We wish to thank participants at the Eastern FinanceAssociation Annual Meeting, Orlando, FL, 2003for their helpful comments. Particular thanks go toRaj Aggarwal, Harald Henke, Gregory Bauerand Gerald Madden. We also wish to thank partici-pants at the Irish Economic Association AnnualConference, Limerick 2003, particularly PatrickHonohan.

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