IIIS Discussion Paper
No.460/November 2014
Which precious metals spill over on which, when and why? – Some
evidence.
Jonathan A. Batten
Department of Banking and Finance
Monash University, Caulfield Campus
PO Box 197, Caulfield East, Victoria 3145, Australia
Email: [email protected]
Cetin Ciner
Cameron School of Business
University of North Carolina- Wilmington
Wilmington, NC, USA
E-mail: [email protected]
Brian M Lucey
School of Business and Institute for International
Integration Studies (IIIS), The Sutherland Centre,
Level 6, Arts Building, Trinity College Dublin 2
Ireland Glasgow, Lanarkshire G4 0BA, United
Kingdom Faculty of Economics University of
Ljubljana Kardeljeva ploscad 17 Ljubljana, 1000 ,
Slovenia
Tel: +353 1 608 1552 Fax: +353 1 679 9503
Email: [email protected]
IIIS Discussion Paper No. 460
Which precious metals spill over on which, when and why? – Some
evidence.
Jonathan A. Batten
Department of Banking and FinanceMonash University,
Caulfield CampusPO Box 197, Caulfield East, Victoria 3145,
AustraliaEmail: [email protected]
Cetin Ciner
Cameron School of BusinessUniversity of North CarolinaWilmington Wilmington, NC, USA E-mail: [email protected]
Brian M Lucey
School of Business and Institute for International Integration
Studies (IIIS), The Sutherland Centre, Level 6, Arts Building,
Trinity College Dublin 2 Ireland Glasgow, Lanarkshire G4 0BA,
United Kingdom Faculty of Economics University of Ljubljana
Kardeljeva ploscad 17 Ljubljana, 1000 , Slovenia
Tel: +353 1 608 1552 Fax: +353 1 679 9503Email: [email protected]
Disclaimer
Papers may only be downloaded for personal use only.
Any opinions expressed here are those of the author(s) and not those of the IIIS.
All works posted here are owned and copyrighted by the author(s).
Which precious metals spill over on which, when and why? – Some
evidence.
Jonathan A. Batten
Department of Banking and Finance
Monash University, Caulfield Campus
PO Box 197, Caulfield East, Victoria 3145, Australia
Email: [email protected]
Cetin Ciner
Cameron School of Business
University of North Carolina- Wilmington
Wilmington, NC, USA
E-mail: [email protected]
Brian M Lucey
School of Business and Institute for International Integration Studies (IIIS), The
Sutherland Centre, Level 6, Arts Building, Trinity College Dublin 2 Ireland
Glasgow, Lanarkshire G4 0BA, United Kingdom
Faculty of Economics University of Ljubljana Kardeljeva ploscad 17 Ljubljana, 1000
, Slovenia
Tel: +353 1 608 1552 Fax: +353 1 679 9503
Email: [email protected]
Abstract
Much academic and investor analysis and commentary sees the four main
precious metals as a single market, integrated and to some degree with each
metal a substitute for the other. This proposition, which can be explicit or
implicit can be challenged on economic grounds and on statistical grounds. Using
the Diebold and Yilmaz (2009) methodology we show that the market is only
weakly integrated, that this degree of integration is time varying and that it
differs as between returns and volatility.
Keywords: Gold, Silver, Platinum, Palladium, integration
JEL Code C01, F49, G12, G15,
Forthcoming: Applied Economics Letters
Introduction
Commodity markets, in particular those for precious metals, are large and
important. Obtaining an accurate size of these markets is not simple – the
largest part of them are typically settled over the counter. One estimated size (in
gross traded volume per day) of the gold markets ranges, for 2012, between
$150b-350b, for silver $28-54, for platinum $2-4b and for palladium $0.5-1 (see
Lubber (2013). Compare these figures for 2012 US daily trade in treasuries of
just over $500b and for US corporate debt of $16b and we see that these markets
are not trivial. OTC derivatives outstanding in Gold (as of mid 2013, via the BIS
database) amount to a gross figure of some $461b; this is about 1/5 of all
commodity derivatives. London Bullion Market Association clearing data suggest
an approx. daily turnover for physical gold and silver of $30b and $2-$4b.
Regardless of which figure one uses these markets are not small.
Our goal in this note is to investigate the extent to which these metals can
be considered an asset class. An asset class should, it is generally agreed,
amongst other features show a high degree of integration, arising from common
shocks and common economic fundamentals, an alignment of forces that work
on all the assets (see Greer (1997))
Commodities matter to investors, both for their size as markets and also
for their diversification potential in portfolio management. For commodities in
general there is a wide literature on the diversification benefits. For financial
researchers, commodities are also of interest for their potential role in asset
allocation decisions. In this regard, recent papers by Abanomey and Mathur
(2001), Georgiev (2001), and Chan and Young (2006) argue that commodities
provide risk reduction in portfolios along with stocks and bonds. Both Caglayan
and Edwards (2001), Chow et al. (1999) suggest that commodities are in fact
more attractive when the general financial climate is negative. These findings are
confirmed in more recent work by Boido (2013), Cumming, Haß, and Schweizer
(2013), Nijman and Swinkels (2011) and Skiadopoulos (2012).
While there is a significant body of work on the macroeconomic
determinants of volatility in and between equity and commodity markets (e.g.
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Forthcoming: Applied Economics Letters
Fernandez (2008)), and groups of commodities (e.g. Kroner, Kneafsey, and
Claessens (1995) Gilbert and Brunetti (1995), Pindyck (2004) and Gilbert
(2006)) , there is limited evidence for relationships between precious metals. If
similar macroeconomic or behavioral or other factors are important for all of
these, it could be argued that they constitute a market.
As to whether commodities as a whole are an asset class, the evidence is
mixed. Two highly cited papers, Erb and Harvey (2006) and Gorton and
Rouwenhorst (2006) provide analyses of the risk-return tradeoff in commodity
markets. They differ as to whether commodities should be seen as a single asset
class. The conclusions of Gorton and Rouwenhorst (2006) imply that
commodities can be best viewed as a single asset class that have attractive risk-
return patterns and furthermore, are useful for portfolio diversification. Erb and
Harvey (2006), however, question whether commodity markets can actually be
considered as a single asset class since differences in the behavior of prices
between individual commodities seem significant. More recently, Adams, Füss,
and Kaiser (2011) and Batten, Ciner, and Lucey (2010) investigate the
macroeconomic determinants of returns and volatility respectively. They
conclude that in the main the commodities under investigation are exposed to
different macroeconomic impacts and so cannot be considered as an asset class.
Spillovers and integration in the precious metal market have also been
considered by Hammoudeh et al. (2010) in a GARCH framework, concluding that
gold and silver volatility both respond to monetary shocks, and that these are
quite persistent. This long memory property of gold is confirmatory to the
findings in Byers and Peel (2001).
Methodology
The model presented in this paper is drawn from Diebold and Yilmaz (2009),
Diebold and Yilmaz (2012). These authors look at return and volatility spillovers
using a Vector Autoregressive Models (VAR’s) following Engle, Ito, and Lin
(1990) but concentrate on variance decompositions. This gives one measure of
spillover based on spillovers from a number of markets. A recent application of
this approach in the precious metal market is Lucey, Larkin, and O’Connor
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Forthcoming: Applied Economics Letters
(2014) who note the still limited impact of markets other than London and New
York on gold price formation.
Consider a set of assets. For each asset i the shares of its forecast error variance
coming from shocks to asset j, for all j ≠ i, are summed. These are then added for
all i = 1,…, N. Considered as a covariance stationary first-order two variable VAR
it can be written as
(1)
𝑥𝑥𝑡𝑡 = ∅𝑥𝑥𝑡𝑡−1 + ε𝑡𝑡
where 𝑥𝑥𝑡𝑡 = (𝑥𝑥1𝑡𝑡 𝑥𝑥2𝑡𝑡 ) and ∅ is a 2 x 2 parameter matrix. In this paper 𝑥𝑥𝑡𝑡 with
represent either a vector of gold returns or gold returns volatilities. Diebold and
Yilmaz (2009) show that by covariance stationarity we can represent this VAR as
a moving average given by equation (2) below.
𝑥𝑥𝑡𝑡 = ʘ(L)ε𝑡𝑡
(2)
Where ʘ(L) = (𝐼𝐼 − ∅𝐿𝐿)−1 . This can be rewritten as below for ease.
𝑥𝑥𝑡𝑡 = 𝐴𝐴(𝐿𝐿)𝜇𝜇𝑡𝑡
(3)
Where A(L) = ʘ(L)𝑄𝑄𝑡𝑡−1 , 𝜇𝜇𝑡𝑡 = 𝑄𝑄𝑡𝑡 ε𝑡𝑡 , 𝐸𝐸�𝜇𝜇𝑡𝑡 𝜇𝜇 ′ 𝑡𝑡 � = 𝐼𝐼, and 𝑄𝑄𝑡𝑡−1 is a unique lower
triangular Cholesky factor of the covariance matrix of ε𝑡𝑡 .
The Wiener-Kolmogorov linear least-squares forecast is an optimal 1 step ahead
forecast from the above can be shown as:
𝑥𝑥𝑡𝑡+1,𝑡𝑡 = ∅𝑥𝑥𝑡𝑡
with a 1 step ahead error vector:
𝑎𝑎0,11
𝑒𝑒𝑡𝑡+1,𝑡𝑡 = 𝑥𝑥𝑡𝑡+1 − 𝑥𝑥𝑡𝑡+1,𝑡𝑡 = 𝐴𝐴0 𝜇𝜇𝑡𝑡+1 = �𝑎𝑎
0,21
which has a covariance matrix of:
(4)
𝑎𝑎0,12 𝜇𝜇1,𝑡𝑡+1
𝑎𝑎0,22 � �𝜇𝜇2,𝑡𝑡+1 �
𝐸𝐸�𝑒𝑒𝑡𝑡+1,𝑡𝑡 𝑒𝑒 ′ 𝑡𝑡+1,𝑡𝑡 � = 𝐴𝐴0 𝐴𝐴′0 .
(5)
(6)
Using this approach allows us to say what proportion of the error variance in
forecasting any particular x (a specific gold market e.g. London) is due to shocks
to itself, or spillover from shocks to another market e.g. New York. Diebold and
Yilmaz (2009)define own variance shares as “to be the fractions of the 1-step-
ahead error variances in forecasting xi due to shocks to xi” for all i and cross
variance shares, or spillovers, to be “the fractions of the 1-step-ahead error
variances in forecasting xi due to shocks to xj” for all j, where i = j.
In this 2 variable illustration the variance of the one step ahead error in
2
2
2
forecasting x1 at time t is then 𝑎𝑎0,11
+ 𝑎𝑎0,12
from equation (5) above. 𝑎𝑎0,12
can
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Forthcoming: Applied Economics Letters
then be thought of as a x1,t’s spillover that effects the forecast error variance of
2
x2,t and 𝑎𝑎0,21
can then be thought of as a x2,t’s spillover that effects the forecast
2
2
error variance of x1,t. Total spillover is then 𝑎𝑎0,12
+ 𝑎𝑎0,21
. Using these we can
calculate a spillover index measure as total spillover divided by the total forecast
2
2
2
2
+ 𝑎𝑎0,12
+ 𝑎𝑎0,21
+ 𝑎𝑎0,22
= 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝐴𝐴0 𝐴𝐴′0 ) as in (7).
error variation (𝑎𝑎0,11
𝑎𝑎2
+𝑎𝑎2
0,12
0,21
𝑆𝑆 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝐴𝐴
𝑋𝑋 100
𝐴𝐴′ )
0
0
(7)
This first-order two variable case can be generalised into a pth-order N-variable
case using 1 step ahead forecasts giving:
2
∑𝑁𝑁
𝑖𝑖,𝑗𝑗=1 𝑎𝑎0,𝑖𝑖𝑖𝑖
𝑖𝑖≠𝑗𝑗
𝑆𝑆 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝐴𝐴
𝑋𝑋 100
0 𝐴𝐴′0 )
For a H-step ahead forecasts:
𝑁𝑁
2
∑𝐻𝐻−1
ℎ=0 ∑𝑖𝑖,𝑗𝑗=1 𝑎𝑎ℎ,𝑖𝑖𝑖𝑖
𝑖𝑖≠𝑗𝑗
𝑆𝑆 = ∑𝐻𝐻−1 𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐𝑐𝑐(𝐴𝐴
ℎ=0
0 𝐴𝐴′0 )
𝑋𝑋 100
(8)
(9)
While it is commonplace to measure asset volatility based on the standard
deviation of the log difference across a regular time interval, we also utilise a
more complex measure, the GKe measure, which incorporates information about
the open, close, high and low prices within a particular time interval. As
discussed in Molnár (2012) the GK Range based estimator is amongst the most
efficient estimators for volatility estimation. From Garman and Klass (1980) the
GKe is:
(10)
GKe =
where H = log of interval high
L = log of interval low
O = log of interval open
C = log of interval close
Data
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Forthcoming: Applied Economics Letters
We examine the four main precious metals – gold, silver, platinum and
palladium. Data are drawn from Thomson Reuters Ecowin, and consist of the
nearest month futures closing price for each commodity, on NYMEX. Data are
initially collected on a daily basis and converted to weekly to facilitate both a
smoother data series and to allow the calculation of the Garman and Klass (1980)
volatiliy. Shown in Figure 1 is the evolution of the series.
Figure 1 : Precious metal prices 1982-2003
Results
Show in Table 1 are the results of the Diebold-Yilmaz spillover analyses for the
four assets. We note that gold and silver share the closest relationship. Gold
accounts for 27.7% of silvers return and only a small percentage of that of
platinum and less again of palladium. Silver contributes 27.5% of the gold return
and similar percentages to that of gold in terms of return to platinum and
palladium. In volatility terms the situation is starker – we can see significant
spillovers from gold and silver to each other while platinum and palladium are
almost insulated from each other. Overall there is a reasonable level of spillover
in returns, 42% while for volatility this is much lower at 18%. We can interpret
this as 43% of return being determined by the movements of the four assets,
while only 18% of volatility is so determined.
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Forthcoming: Applied Economics Letters
Table 1 Diebold – Yilmaz Spillover estimates
Returns
To Gold
Silver
Platinum
Palladium
Contribution to
others
Contribution
including own
Volatility
To Gold
Silver
Platinum
Palladium
Contribution to
others
Contribution
including own
From
Gold
51.1
27.7
17.8
6.9
52
Silver
27.5
51.5
14.9
9.9
52
Platinum
16.4
13.5
56
14.3
44
Palladium
5.1
7.3
11.3
69
24
From Others
49
49
44
31
173
103
104
100
93
From
Gold
70.4
27.6
1.4
4.9
34
Spillover
Index
43.10%
Silver
25.4
69.4
0.4
3.4
29
Platinum
0.8
0.3
97.3
0.9
2
Palladium
3.3
2.7
0.8
90.9
7
From Others
30
31
3
9
72
104
99
99
98
Spillover
Index
18.00%
We then proceed to a time varying analysis. Below we show the evolving
importance of spillovers to returns between the 4 markets through the spillover
index in Figure 2 for returns and Figure 3 for volatility. We use an initial window
of 100 weeks, and then update this by 10 observations (weeks) each iteration.
While the average result for the returns spillover index over the full sample
given in the last section was 43%, we can see that this varies very substantially
over time. In the 1998 – 2005 period return spillovers were low, suggesting a
market that was not very integrated. The markets degree of integration in
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Forthcoming: Applied Economics Letters
general fell throughout the 1980-1993 period, then reversed until 1996 when it
resumed its path towards a low point of integration in the early 2000s. Since
then the markets have returned to a high degree of integration in returns
Figure 2 : Rolling Return Spillover index.
Figure 3 : Rolling Volatility Spillover index.
In Figure 4 and 5 we show the net spillovers from and to each market for returns
and volatility, following Diebold and Yilmaz (2012). The interpretation is of a
positive figure indicating a source and a negative a recipient of spillovers. . Gold
shows four distinct period when it acts as a source of return spillovers: 1992-96,
2000-2002, 2003-4 and 2006-8. Silver is a source of return spillovers in the
2004-8 period, palladium in the 2008-10 period and platinum rarely. The effect
of the GFC is marked in Platinum, Silver and Palladium, the latter becoming a
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Forthcoming: Applied Economics Letters
source of spillovers (perhaps linked to the heavy industrial use of the metal) the
other two becoming (even more ) a recipient of spillovers. It is also clear in gold,
the metal moving from being a source of return spillover to a neutral position.
In volatility we see that while in general there is little net spillover in any of the
four metals when they do show such it tends to be large. While the largest
returns spillovers are in the range of 40% the range in volatility exceeds 100% at
times. Gold is a net positive volatility spillover in the 2001-3 period, matching a
return spillover period. Similarly for palladium volatility shows positive
spillovers in the 2008-9 period matching returns. Platinum spillovers in
volatility match those for returns in the 2008 period alone.
Figure 4 : Net Asset Spillover indices for Returns
Figure 5: Net Asset Spillover indices for volatility
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Forthcoming: Applied Economics Letters
Shown in Figure 6 and Figure 7 are bidirectional spillovers. These show the
influence of a particular asset on another. We concentrate here on gold and
silver. We see that in both cases there are distinct regimes. For both the pattern
is generally to decline from about 25% to almost zero by 2002, rising thereafter.
Gold-Silver and Silver-Gold show very similar bidirectional spillovers as we
might expect. The aftermath of the 9/11 attacks and the Iraq/Afghan wars, plus
the gradual increase in global money supply show clearly. In 2003/4, post the
second Iraq war, we see a major sustained increase in the influence of gold on
platinum and palladium and also of silver on the same metals. Interestingly the
influence of gold on silver and vice versa fell in that period.
In volatility spillovers we see the influence of gold disappearing on platinum and
palladium in the 2000-2003 period and diminishing significantly for silver in
that period. However, Silver shows its largest level of volatility spillover on gold
in that period.
Figure 6 : Bi-Directional Spillovers in Return - Gold and Silver
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Forthcoming: Applied Economics Letters
Figure 7 Bi-Directional Spillovers in Volatility - Gold and Silver
Conclusions
We apply a new method of spillover/integration, and surface timevarying
spillovers amongst the four main precious metals. The metals split into two
categories : gold and silver show consistent spillovers between them, while
platinum and palladium are much more disconnected. In terms of time variation,
we can attribute shifts and changes to geopolitical and economics events.
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Forthcoming: Applied Economics Letters
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Institute for International Integration Studies
The Sutherland Centre, Trinity College Dublin, Dublin 2, Ireland