Price Discovery and Hedging Properties of Gold and Silver Markets

Transcription

1 Price Discovery and Hedging Properties of Gold and Silver Markets Isabel Figuerola-Ferretti Business Department, Universidad Carlos III de Madrid Jesus Gonzalo Economics Department, Universidad Carlos III de Madrid January 19, 2010 Abstract In this paper we introduce a non linear price discovery equilibrium model that captures the long term heding properties of gold and silver markets. Price discovery is regime dependent and is determined by the relative number of participants in the gold and silver markets. Using COME gold and silver prices, the VI implied volatility index and the dollar-euro exchange rate, we show that gold and silver are cointegrated only under weak dollar and high volatility conditions. In this state, gold dominates silver indicating that is most e cient in re ecting their common hedging characteristics. Under low volatility and strong dollar conditions gold and silver can not be regarded as substitutes for hedging similar types of risks. 1 Introduction For centuries gold and silver were perceived to be important hedging devices in times of economic turmoil. Following the collapse of Bretton Woods, both prices were deregulated and the markets changed signi cantly. In this paper we use recently developed time series techniques to analyze the long term relationship and price discovery between gold and silver COME future prices. The main objective is to see whether there is a stable or semistable relationship between both markets, and to determine whether and under which circumstances gold and silver prices share a common stochastic trend that allows us to determine price discovery. Documenting the long term relations and leadership among nancial markets can help trading strategies. Silver and gold prices are usually considered as substitutes to reduce similar types of risk in portfolios. They are also tied 1

2 via a popular intercommodity spread strategy known as the gold silver spread (formally de ned as the di erence in the gold and silver prices). The strategy involves simultaneously taking a long position on one and a short position on the other. The rationale of this type of trading lies on the belief that the long run di erence between the two contracts is stable. One explanation for this is that there are many commonalities in the underlying economic, nancial and political factors that drive the prices of the two commodities and that makes them appropriate investment devices for diversi cation purposes However, gold and silver have distinct important uses for which they are no substitutes. For instance, silver has been extensively used as metal for electronics, rays and photography because of its unique physical and chemical properties. On the other hand demand for gold is largely determined by the actions of Central Banks, as industrial nations maintain a steady proportion of gold in their foreign exchange reserves. On the private side, the demand for gold consumption is dominated by jewelry applications. It can therefore be argued that separate fundamentals determine the prices of gold and silver and therefore they do not share a common stochastic trend. Price discovery is one of the social bene ts provided by future markets. It refers to the use of future prices for pricing cash market transactions (Working (1948), Wiese (1978)). In general, price discovery is the process of uncovering an asset s full information or permanent value. The unobservable permanent component re ects the underlying fundamentals. It di ers from the observable price which measures the permanent or e cient price with some transitory error. The contribution of markets to price discovery has been a relevant subject of research for some time. Several studies investigate the informational advantages of markets for single underlying assets (Garbade and Silver 1983, Harris et al. 1998, Hasbrouck 1995). Generally the price discovery literature applies two methodologies (see Lehman 2002, special issue on the Journal of Financial Markets) the information shares of Hasbrouck (1995) (IS thereafter) and the Gonzalo Granger (1995) Permanent-Transitory decomposition (PT thereafter). The use of the PT measure has been justi ed by Figuerola-Gonzalo (2007) (FG thereafter) who develop a general equilibrium model to measure price discovery that leads to the PT decomposition. Their theoretical nding states that price discovery depends on the relative number of players in each market. This nding is consistent with the literature, where the consensus has generally been that price discovery takes place in the most liquid markets where trading volume is concentrated. Price discovery in the gold and silver market has been studied by Bahram et al. (2000) who use intraday data and an Error Correction Model (ECM) to conclude that the silver contract bears the majority of the burden of convergence to the gold-silver spread. Prior work on the gold silver relationship focuses on cointegration analysis. Wahab Chon and Lashgri (1994) use daily cash and future prices and nd that there is cointegration between the gold and silver in both the spot and futures markets. Escribano and Granger (1998) analyze monthly prices of gold and silver using a sample ranging from 1971 to mid 1990s. They split their sample and nd evidence of cointegration between 1971 and 2

3 1990. In their out of sample analysis they argue that the relationship between gold and silver is diminishing after This is con rmed by Ciner (2004) who uses gold and silver prices traded on the Tokyo Commodity Exchange (TOCOM) for the period and nd no evidence of cointegration between gold and silver. Cointegration based techniques were also applied to the spreads by Shi- Miin and Chih-Hsie (2003) who use a fractional ECM analysis to forecast spot and future spot and silver spreads. They claim that signi cant riskless pro ts can be earned based on ECM forecasting of the changes of spot and future spreads. Another popular area of research has focused on the casual relationship between gold and silver. Of particular relevance are the papers of Chan and Montain (1988) and Frank and Stengos (1989), who provided a an analysis of the pricing relationship between gold and other precious metals. Frak and Stengos revealed some non linear dependence between silver and gold prices, whereas Chan and Montain found a "simultaneous relationship" between the price of gold, the price of silver and the treasury bill rate. The literature on the role of gold and other precious metals in nancial markets also looks at the diversi cation properties of precious metals when combined with stock market investments in nancial portfolios (see Hiller et al. (2006) and references therein). The consensus is that there is a generally observed diversifying e ect for gold. Baur and Lucey (2007) considered the role of gold as a save heaven. This paper contributes to the price discovery literature of gold and silver taking account of their hedging statistical properties and the presence of non linearities in their spread. In particular we extend the model proposed by Figuerola- Gonzalo (2007) to the two regime case to capture the hedging properties of gold and silver in times of adverse market conditions. This allows us to establish which metal is most reliable as a hedging investment in the two di erent regimes. Our theoretical model suggests that discovery or reliability as hedging asset will be determined by the relative number of participants in each market for the di erent regimes. Precious metals are classi ed as investment as well as consumption assets. Non commercial positions in these metals are generally taken as means of portfolio diversi cation. The relevance of precious metals as hedging instruments increased signi cantly over the last 7 years and accelerated with the consequences subprime crises such as general fear, high volatility and weak dollar. Gold prices increased by 30% over the last year and reached a maximum of $ in December. Silver prices rose by 109% mainly due to increased investor demand re ected in higher non commercial positions. Investors increase their exposure to gold and silver for similar fundamental reasons such as weakening of the dollar or an increased market liquidity. Given that silver is cheaper than gold, market participants can substitute into the less expensive alternative. In this paper we use the VI volatility index and the euro dollar exchange rate as threshold variables in a non linear price discovery model to address the following two questions: are gold and silver substitute assets under times of economic turmoil? if this is the case, which market is more e cient as a hedg- 3

4 ing instrument? Once we are able to determine which price is most e cient in processing information, investors can evaluate the risk of holding the precious metal and make appropriate decisions. The paper is organized as follows. In section 2 we describe the threshold equilibrium model with nite elasticity of supply of arbitrage services for gold and silver COME prices. We demonstrate that price discovery is determined by the relative number of participants in each of the regimes. Section 3 presents empirical estimates of the model developed in section 2, and its linear counterpart. This requires i) testing for cointegration ii) Estimating a non linear VECM and iii) obtaining the price discovery parameters. Section 4 concludes. Graphs are collected in the appendix. 2 Theoretical Framework: A threshold equilibrium model for Price Discovery in Gold and Silver Markets The goal of this section is to capture the hedging properties and characterize price discovery of silver and gold prices by re-examining the equilibrium non arbitrage framework developed by FG and its extension to the non linear case. We develop a non linear VECM to test whether price discovery changes according to the magnitude of some threshold variable re ecting the existence of di erent market conditions. The main objective is to establish the extent to which gold and silver provide hedging capabilities in times of "abnormal" market behavior. A growing body of research in recent time series literature has incorporated non linear behavior into conventional linear reduced form speci cations such as autoregresive and moving average models. The motivation from moving away from the traditional linear model with constant parameters arises from the observation that many economic and nancial time series are often characterized by regime-speci c behavior and asymmetric responses to shocks. For such series the linearity and parameter constancy restrictions are typically inappropriate and may lead to misleading inferences about their dynamics. Within this setting, a general class of models that has been particularly popular are the family of the threshold models, characterized by piecewise linear processes separated according to the magnitude of a threshold variable that triggers regime changes. When each linear regime follows an autoregresive process, we have well known threshold autoregresive models the properties of which have been extensively investigated (see for example Gonzalo and Montesinos 2000 and Gonzalo and Pitarakis 2002). The concept of threshold cointegration has attracted considerable attention from practitioners interested in uncovering non linear adjustment patterns in relative prices and other variables. The goal of this section is to link non linear cointegration behavior to the hedging properties of gold and silver prices in order to determine price discovery. 4

5 Let g t be the natural logarithm of the one month futures price of a gold in period t and let s t be the natural log of the one month futures silver price. Let r t be the arbitrage cost applicable to the gold and silver markets. In order to nd the non-arbitrage equilibrium condition the following set of standard assumptions apply in this section: (a.1) No taxes or transaction costs (a.2) No limitations on borrowing (a.3) No cost other than arbitrage risk cost (a.4) No limitations on short sale of the commodity of the spot market (a.5) Arbitrage risk costs are given by the process r t = r + I(0) Where _ ris the mean of r t and I(0) is an stationary process with mean zero and nite positive variance. (a.6) g t and s t are I(1). If r t, is the continuously compounded arbitrage risk cost applicable to gold silver spread, by the above assumptions a1-a4, non-arbitrage equilibrium conditions imply s t = g t + r t (1). For simplicity and without loss of generality for the rest of the paper it will be assumed T1=1From (a.5) and (a.6), equation (1) implies that g t and s t are cointegrated. The following Econometric relationship will be used to represent the constant long run spread g t = 2 s t + 3 (2) Gold and silver prices are therefore closely linked via low risk spread arbitraging, where 3 = r t and 2 s t + 3 represents the silver price free of arbitrage risk cost. 2.1 Equilibrium prices with nitely elastic supply of arbitrage services under the presence of two regimes Consider two regimes in the economy speci ed by the threshold variable q t d the indicator function I(:)and the threshold parameter. We de ne two regimes in the economy so that when I(q t 1 > ) we are in regime 1 and when I(q t 1 ) and we are in regime 2, where d is the known lag lenh. To describe the interaction between gold and silver prices we must rst specify the behavior of agents in the marketplace. There are N 1;G participants 5

6 in gold market in regime 1 and N 2;G participants in the gold market in regime 2. Accordingly there are N 1;S participants in the silver market in regime 1 and N 2;S participants in silver market in regime 2. Let the demand for arbitrage services be H 1 in regime 1 and H 2 in regime 2. Let E i;t be the endowment of the ith participant immediately prior to period t and R it the reservation price at which the that participant is willing to hold the endowment E i;t:, under regime 1 and 2. Then the demand schedule of the i th participant in the gold market in period t in regime 1 will be given by E i;t A(g t R i;t ) A > 0; i = 1; :::N 1;G under regime 1 (3) E i;t A(g t R i;t ) A > 0; i = 1; :::N 2;G under regime 2 (4) The aggregate gold market demand for arbitrageurs is H 1 (( 2 s t + 3 ) g t ) ; H 1 > 0 under regime 1 (5) H 2 (( 2 s t + 3 ) g t ) ; H 2 > 0 under regime 2 (6) Equivalent relationships apply to the silver market. Accordingly the gold market will clear at the value of g t that solves N 1;G E i;t = N 1;G fe i;t A(g t R i;t )g+h 1 (( 2 s t + 3 ) g t ) when 1(q t 1 > ) and we are in regime 1 (7a) N 2;G E i;t = N 2;G fe i;t A(g t R i;t )g+h 2 (( 2 s t + 3 ) g t ) when 1(q t 1 ) and we are in regime 2 (7b) The silver market will clear at the value of s t such that 6

7 N 1;S E i;t = N 1;S fe i;t A(s t R i;t )g+h 1 (( 2 s t + 3 ) s t ) when 1(q t 1 > ) and we are in regime 1 (7c) N 2;S E i;t = N 2;S fe i;t A(s t R i;t )g+h 2 (( 2 s t + 3 ) s t ) when 1(q t 1 ) and we are in regime 2 (7d) Solving system 7 as afunction of the mean reservation price for gold market participants in regime 1 Rt G = 1 P NG N 1;G R i;t and the mean reservation price for silver market participants in regime 1 Rt S = 1 P N1;s N 1;S R i;t we obtain (AN1;s + H 1 g 1;t = 2 ) N G Rt G + H 1 N 1;s 2 Rt S + H 1 N s 3 (8) (H 1 + AN 1;G ) N 1;S + H 1 N 1;G 2 AN1;G Rt G + (H 1 + AN 1;G )N 1;S R S t + H 1 N 1;G s 1;t = 3 (H 1 + AN 1;G ) N 1;S + H 1 N 1;G 2 (9) Equilibrium prices in regime 2 will therefore be given by (ANs + H2 g 2;t = 2 ) N G Rt G + H 2 N 2;S 2 Rt S + H 2 N S 3 (H 2 + AN G ) N 2;S + H 2 N 2;G 2 (10) AN2;s Rt G + (H 2 + AN 2;G )N 2;s R s t + H 2 N 2;G s 2;t = 3 (H 2 + AN 2;G ) N 2;s + H 2 N 2;G 2 (11) To derive the dynamic price relationships, the model in equation must be characterized with a description of the evolution of reservation prices. Following FG It is assumed that in regime 1, immediately after market clearing in period t 1 the ith gold market participant was willing to hold an amount E it at a price g 1;t 1. Accordingly the mean reservation price in each market in period t will be 7

8 R G t = g 1;t 1 + v t + w G t (12) Rt S = s 1;t 1 + v t + wt S with N G N 1;S w 1;G t = N 1 1;G w i;t, w 1;S t = N 1 1;S Equivalent dynamics apply to regime 2. Substituting equation 12 into the equations (8-11) the following VAR model is obtained under regime 1 w i;t s t u G t u S t = H 1 3 d 1 where N1;S N 1;G v G = M t + wt G 1 vt S + wt S + (M 1 ) 1 u G + t u S t M 1 = 1 N1;G (H 1 2 ) H 1 2 N 1;G d 1 H 1 N 1;G (H 1 + AN 1;s )N 1;G (13) Taking rst di erences of eq 13 and taking account of equilibrium prices in both regimes, we may write the non linear threshold model within the general equilibrium model as s t = H1 N1;S + d 1 N 1;G H2 N2;s d 2 N 2;G g t 1 (q t d > ) + (14) g 1 1 t 1 3 (q s t d ) + u t t 1 Applying the PT decomposition, our non linear price discovery metric will be de ned in terms of the relative number of participants in each of the observed regimes. N 1;G N 1;S g t + s t when (q t d > ) (15) N 1;G + N 1;S N 1;G + N 1;S N 2;G N 2;S g t + s t when (q t d ) (16) N 2;G + N 2;S N 2;G + N 2;S This implies that price discovery will depend only on the relative number of players in each of the regimes and it is not dependent on the spread s long term parameters or the elasticities of arbitrage services. 8

9 3 Empirical Price Discovery in gold and silver markets The data include daily observations of gold and silver 1 month future COME prices. Prices are available from January 1990 to October Threshold variable data include daily observations for the S&P 500 VI implied volatility index quoted in the Chicago Board Options Exchange, and the dollar-euro exchange rate. The data source is Ecowin for all series. Figures in the appendix depict gold and silver COME prices together with the VI index (Figure 1) and the dollar-euro exchange rate (Figure 2). Gold and silver COME prices seem to be a ected by the VI index and dollar-euro exchange rate data. As a preliminary Analysis we report linear cointegration and price discovery results. Table 1A in the appendix presents a linear Augmented Dickey Fuller cointegration analysis. Results suggest that gold and silver are I(1) series and are cointegrated, suggesting that they can be regarded as substitutes investment assets. Table 2A in the appendix shows results from estimating a linear VECM. Estimation output shows that whereas gold does not react signi catively to changes in the equilibrium error while silver does, suggesting that gold leads silver in the linear case, implying that is more e cient as a hedging instrument. 3.1 Non Linear Price Discovery with the VI index as a threshold variable The second purpose of this analysis is to use the non linear framework to determine whether gold and silver hedging role is regime dependent. Particularly we want to establish whether theirs substitutability is greater during periods of "abnormal" market conditions. The investment and diversi cation properties of precious metals has been widely discussed in the literature. Hillier et al (2004) provide a review of this literature. Other authors have concentrated in gold and have analyzed its role as a potential hedging variable (see Davidson et al. 2003) and a as a save heaven (see Baur and Lucey 2007). The consensus of these studies is that there is a diversifying e ect in gold. In this section we consider the price discovery properties of precious metals taking a proxy for market volatility as the threshold variable. Hillier et al. (2004) look at the hedging properties of precious metals considering GARCH(1,1) errors of S&P 500 market index returns. We follow Hillier et al. (2004) in using volatility to promote understanding of the investment properties of precious metals. To accommodate conditional diversifying properties of gold and silver markets, we consider general market volatility indicator, the S&P 500 implied volatility VI index, which reports implied volatilities of CBOT traded options on market index. This is constructed as a weighted average from the implied volatilities obtained from out of the money options whose underlying asset are included in the S&P 500. The level of the VI implied volatility index is taken as threshold variable. The ptimal threshold level is chosen using the AIC and BIC criteria. We divide the data on the threshold variable into deciles and nd 9

10 that the optimal threshold level is at the 80% decile for which the VI index takes a value of The threshold variable q takes the value of 1 when the volatility index is greater than and zero otherwise. The optimal threshold lag lenght is 2. And the optimal number of lags in the system, according to the BIC criteria is 2. Results from estimating the non linear VECM for the VI index are reported in Table 1. We take those periods where the VI index reaches a value greater than as times of "abnormal" volatility conditions. Estimation output reported in table 1 suggest that gold and silver COME prices are only cointegrated under times of "abnormal volatility" conditions. Under this regime the silver price reacts signi catively to changes in the equilibrium error but gold prices do not react, to euquilibrium error changes, indicating that the gold market is dominant in terms of price discovery. Gold futures are more liquid that silver COME futures. If we take volumes traded as a proxy for the number of participants we can state that the results on price discovery are consistent with with the theoretical prediction. Table 1. Estimation of the non linear VECM with VI as threshold variable (t stats in brackets) Sample June October 2009 N1;S = s H1 d t 1 (q N t d )z 1 t 1 + 1;G + + s t 0 N2;S N 2;F = 0:0003 ( 0:247) 0:002 (0:782) (q t d < )z 1 t :0004 B 0:004 (1:730) 1 C A (V I t 2 25:24)z 1 t 1 + C A (V I t 2 < 25:24)z 1 t 1 z t = g t 1:22 0:74s t k(aic) = 2; 3.2 The exchange rate as a threshold variable In this section we focus on the relationship between gold and silver prices and the exchange rate. It is commonly believed that since the dissolution of the Bretton Woods International monetary system, oating exchange rates among the major currencies have been a major source of price instability in the gold market. Before the euro was formally introduced, Sjaastad and Scacchiavillani (1996) argued that the European countries heavily dominate the international market for gold and hence movements in the European exchange rates against the US dollar impact heavily on the dollar price of gold. 1 1 While a 10% appreciation of the Deutche Mark (against all other currencies) increases the dollar price of gold by 6.5% (and viceversa) a 10% appreciation of the dollar against the 10

11 Following this argument, we look at the relationship of precious metal prices taking the $/e exchange rate as the threshold variable in a non linear VECM framework. The consensus in the literature is that gold prices are negatively related to the exchange rate (measured in units of foreign currency), see Sherman (1983). Capie et al. (2005) nd negative signi cant correlations between the change in the log price and the change in the pound-dolar and yen-dolar exchange rate providing statistical con rmation of the hedging properties of gold. Capie et al. (2005) are concerned by the role of precious metals as a hedge against changes in the external purchasing power of the dollar. They argue that If gold were a perfect external hedge its dollar (i.e. nominal ) price would rise at the same rate and time as the number of units of foreign currency per dollar fell. In this paper we investigate the extent to which the exchange rate hedging properties of precious metals a ect price discovery. Figure 2 suggest that the rise of silver and gold prices over the past 7 years coincides with an increase in the price of both metals and an increase in the dollar-euro exchange rate, suggesting that both gold and silver act as a hedge against low dollar. As in the previous analysis, we choose the optimal threshold level using the AIC and BIC criteria. The optimal threshold is set at its 70% decile level which is The optimal threshold lag lenh is 1. We use the BIC criteria for choosing the optimal system lag lenh which is set at 2. Table 2 reports results from estimating a non linear VECM with the threshold variable q taking the value of 1 when the dollar-euro exchange rate is greater than 1.27 and zero otherwise. Note that the sample now starts in January 2000, so that it is consistent with the introduction of the euro. Table 2. Estimation of the non linear VECM with dollar-euro exchange as threshold variable Sample June October 2009 N1;S = s H1 d t 1 (q N t d )z 1 t 1 + 1;G + + s t 0 N2;S N 2;F = 0:001 (0:717) 0:004 (0:810) (q t d < )z 1 t :003 B 0:001 (3:541) 1 C A (exrate t 1 1:27)z 1 t 1 + C A (exrate t 1 < 1:27)z 1 t 1 z t = g t 0:377 0:869s t k(aic) = 2; Deutche Mark depresses the price of gold by about 8% 11

12 Results reported in table 2 are consistent with those in table 1. They show that gold and silver are cointegrated under "abnormal" exchange rate conditions, re ected in a weak dollar-euro exchange rate. In this state while gold does not react signi catively to changes in the long term equilibrium, silver does, suggesting that gold is information dominant when gold and silver are cointegrated. Again this is consistent with our theoretical predictions. 4 Conclusions In this paper we introduce a non linear price discovery equilibrium model that captures the long term hedging properties of gold and silver markets. In consensus with the literature, the theoretical predictions of the model show that price discovery takes place where volumes are concentrated. Using one month future COME gold and silver daily price data, we show that gold and silver future prices are only cointegrated under weak dollar and high volatility conditions. This nding should be of relevance to participants in gold and silver markets as it indicates that under normal (strong dollar and low volatility) conditions these two markets should be approached as separate markets, and changes in the gold to silver ratio should not be used to predict prices in the future. It also suggests that under normal conditions gold and silver should not be regarded as substitutes to hedge similar type of risks. Gold and silver act as substitutes in times of generalized fears of economic turmoil, and that, in this state, the gold market is most important in re ecting their hedging statistical properties. 5 Appendix Table 1A: Linear Dickey Fuller and Cointegration test results Aug DF test Levels Aug DF test ( rst di erences) g t 0:067 71:59 s t 0:544 72:23 z t 2:594 12

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