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1 Simposio de Análisis Económico 2008 Modelling and Measuring Price Discovery in Precious Metals Markets Isabel Figuerola-Ferretti Jesús Gonzalo Universidad Carlos III de Madrid Business Department and Economic Department December 2008
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2 The problem of price discovery Process by which financial markets reveal an asset´s permanent value The permanent value reflects fundamental market conditions In a framework in which an asset is traded in various markets, we want to determine which price is the major contributor to the revelation of the common permanent value
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3 Contributions There are two standard ways of measuring the contribution of financial markets to the price discovery process: (i) Hasbrouck (1995) Information Shares (ii) Gonzalo and Granger (1995) P-T decomposition, suggested by Harris et al. (1997) We adapt the model of Figuerola-Gonzalo (2007) to look at price discovery in the precious metals market With the idea of extending price discovery to a non linear framework.
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4 Outline Introduction and Literature Review Price Discovery in Crude Oil Markets Equilibrium Model and Implementation Data Results and Conclusions
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5 Literature Review 1: two Metrics Hasbrouck, J. (1995). One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175- 1199. Gonzalo, J. Granger C. W. J (1995). Estimation of common long-memory components in cointegrated systems. Journal of Business and Economic Statistics 13, 27-36.
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6 Literature Review 2: The Relevance Journal of Financial Markets (2002) Baillie R., Goffrey G., Tse Y., Zabobina T. (2002). Price discovery and common factor models. Harris F. H., McInish T. H., Wood R. A. (2002). Security price adjustment across exchanges: an investigation of common factor components for Dow stocks. Hasbrouck, J. (2002). Stalking the “efficient price” in market microstructure specifications: an overview. Leathan Bruce N. (2002). Some desiredata for the measurement of price discovery across markets. De Jong, Frank (2002). Measures and contributions to price discovery: a comparison.
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7 Literature Review 3: The Relevance Figuerola I., and J. Gonzalo (2007). “Modelling and measuring price discovery in commodity markets.” Working Paper 07-45-11, Business Department, U. Carlos III de Madrid
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8 Other studies on precious metals Escribano A. and W. J. Granger (1988). Investigating the relationship between Gold and Silver Prices. Journal of Forecasting, 17, 81-107 Adrangi B.; Chatrath A.; David R.C. (2000).Price discovery in strategically-linked markets: the case of the gold-silver spread. Applied Financial Economics, 10, 227-234 Applied Financial Economics J Cai, YL Cheung, MCS Wong (2001). What moves the gold market?- Journal of Futures Markets
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9 Other studies on precious metals MP Dooley, P Isard, MP Taylor (1995). Exchange rates, country-specific shocks, and gold. Applied Financial Economics Angela Ng (2000). Volatility spillover effects from Japan and the US to the Pacific-Basin. Journal of International Money and Finance, 19, pp 207-233
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10 Price Discovery and Precious Metals 1 We measure price discovery in precious metal markets Their price reflects the state of the economy –serve as hedging value Prices are linked to fundamentals They have highly developed futures markets Prices have increased by 250% in the last 6 years
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11 Price Discovery and Precious Metals 2 We measure price discovery in precious metals markets -Investmet and Industrial Assets - Plentiful Inventories Low (exogenous) Convenience Yields
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12 Table 1: Estimated annual storage costs and conveniente yields for DBCL commodities 1989-2004Storage cost Conv yield Crude Oil22.05%35.88% Heating Oil22.05%30.48% Aluminium6.31%9.19% Gold0.01%-0.84% Wheat11.91%15.72% Corn9.97%8.97% Source: DB Global Markets Research Price Discovery and Precious Metals
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13 Equilibrium Model and Implementation Equilibrium with infinitely elastic supply of arbitrage St = Log of the spot market price at time “t” Ft = Log of the contemporaneous price on a futures contract for a commodity for settlement after a time interval T 1 = T-t (e.g. 2 months) r t interest rate applicable to the interval from t to T.
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14 Equilibrium Model and Implementation Standard Assumptions: 1) No taxes or transaction cost 2) No limitations on borrowing 3) No costs other than interest and storage 4) No limitations on short sale of the commodity in the spot market 5) Interest rate and storage cost given by r t = + I(0), with the mean of r t 6) The difference between S t and S t-1 is I(0).
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15 Equilibrium Model and Implementation Let T 1 =1 With infinite elasticity of arbitrage services Non-arbitrage equilibrium conditions imply
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16 Equilibrium Model and Implementation With finite elasticity of arbitrage services 7) Convenience yields are exogeneously determined so that
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17 Equilibrium Model and Implementation To describe the interaction between cash and future prices we must first specify the behaviour of agents in the marketplace. There are N s participants in spot market. There are N f participants in futures market. E i,t is the endowment of the i th participant immediately prior to period t. R it is the reservation price at which that participant is willing to hold the endowment E i,t. Elasticity of demand, the same for all participants.
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18 Equilibrium Model and Implementation
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19 Equilibrium Model and Implementation The cash market will clear at the value of St that solves The future market will clear at the value of Ft such that
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20 Equilibrium Model and Implementation Solving the clearing market conditions as a function of the mean reservartion prices and
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21 Equilibrium Model and Implementation To derive dynamic price relationships, we need a description of the evolution of reservation prices.
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22 And the mean reservation prices with Equilibrium Model and Implementation
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23 where and Garbade and Silver (1983) stop their analysis at this point stating that Measures the importance of future markets relative to cash markets Equilibrium Model and Implementation
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24 Equilibrium Model and Implementation
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25 Equilibrium Model and Implementation The G-G decomposition
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26 This is our price discovery metric, which coincides with the one proposed by GS. Our metric does not depend on the existence of backwardation or contango. Equilibrium Model and Implementation
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27 1.H = 0 No VECM, no cointegration. Spot and Future prices will follow independent randon walks. This eliminates both the risk transfer and the price discovery functions of future markets 2.H = ∞ In VAR (12) the matrix M has reduced rank (1, - 2 )M =0, and the error terms are perfectly correlated. Therefore the long run equilibrium relationship (4), S t = 2 F t + 3, becomes an exact relationship. Future contracts are in this situation perfect substitutes for spot market positions and prices will be “discovered” in both markets simultaneously. Equilibrium Model and Implementation
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28 Five Simple Steps : 1) Perform unit root test on price levels 2) Determine the rank of cointegration 3) Estimation of the VECM 4) Hypothesis testing on beta 5) Estimation of α and hypothesis testing on it (e.g. α ´=(0,1)) Equilibrium Model and Implementation
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29 Daily spot and future (2 months) for Ag, Au, Pd, Pt quoted in the LME Sample January 1986- December 2006 Source Ecowin. Data
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30 Data Table A1: Future volumes traded for precious metals and non-ferrous metals over the 2004-2007 period AgAuPdPtAlCuNiPbZn 22400653201475155213467775118146781653344346
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31 Data
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32 Data
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33 Data
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34 Data
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35 Results and Conclusions Table 1: Trace Cointegration rank test AgAuPdPt Trace test r ≤1 vs r=2 (95% c.v=9.14)0.971.122.191.84 r = 0 vs r=2 (95% c.v=20.16)150.5272.23105.39108.63
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36 Results and Conclusions AgAu PdPt
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37 Results and Conclusions Table 3: Hypothesis testing on the cointegrating vector and long run backwardation AgAuPdPt Cointegrating vector ( 1, - 2,- 3 ) 11 1.000 22 -0.996-1.001-0.990-1.010 SE ( 2 ) 0.0020.0010.0140.006 3 (constant term) 0.03-0.0060.03-0.060 SE ( 3 ) (0.015)(0.006)(0.05)(0.035) Hypothesis testing H 0 : 2 =1 vs H 1 : 2 >1 (p-value) (0.060)(0.427)(0.485)(0.08)
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38 Results and Conclusions Table 4: Proportion of spot and future prices in the price discovery function ( EstimationSiAuPdPt 11 0.1380.2730.9500.870 22 0.8620.7270.1000.130 Hypothesis testing (p-values) H 0 : ´=(0,1) (0.43)(0.50)(0.049)(0.7) H 0 : ´=(1,0) (0.03)(0.04)(0.50)(0.3) Note: is the vector orthogonal to the adjustment vector : ` =0. For estimation of and inference on it, see Gonzalo- Granger (1995).
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39 Results and Conclusions On the believe that precious metals have low convenience yields, we introduce a way of modelling them exogenously. Backwardation and Contango are captured in the constant of the cointegrating vector (1, - 1). This model fits well precious metal data With liquid futures markets price discovery takes place in the futures price This framework allows the construction of a non linear ECM to derive a “non linear price discovery mechanism”
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