1. 1 PRICE DISCOVERY IN SPOT and FUTURE HARD COMMODITY MARKETS Isabel Figuerola-Ferretti Jesus Gonzalo Universidad Carlos III de Madrid Business Department and Economic Department Preliminary October 2006

2. 2 Trading Places Movie

3. 3 We are going to talk about … Introduction Theoretical Model Econometric Implementation (GG P-T decomposition) Data Results Conclusions

4. 4 Price Discovery The process by which future and cash markets attempt to identify permanent changes in transaction prices. The essence of the price discovery function of future markets hinges on whether new information is reflected first in changed future prices or changed cash prices (Hoffman 1932).

5. 5 Contribution We separately quantify the relative contribution of future and spot prices to the revelation of the underlying fundamentals. We demonstrate that for those metals with a liquid futures market the future price is more important in the price discovery process. The Gonzalo-Granger decomposition allows us to do this more robustly than in Habroucks alternative way.

6. 6 Why these commodity markets? Commodities are traded in highly developed future markets. In the metals sector 90% of the transactions take place in the forward/future markets. The LME quoted price is the world wide reference price and the common. It is important to quantify the price discovery role of metals futures.

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8. 8 Literature Review 1 Literature on price discovery Garbade, K. D. & Silver W. L. (1983). Price movements and price discovery in futures and cash markets. Review of Economics and Statistics. 65, 289-297. Hasbrouck, J. 1995. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175-1199. Harris F., McInish T. H. Shoeshmith G. L. Wood R. A. (1995) Cointegration, Error Correction, and Price Discovery on Informationally Linked Security Markets. Journal of Financial and Quantitative Analysis. 30, 563-579

9. 9 Literature Review 2: Price discovery metrics 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. Hasbrouck, J. 1995. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175-1199

10. 10 Literature Review 3 Comparing the two metrics of price discovery Special Issue 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.

11. 11 Theoretical Model: Garbade and Silber 1983 Equilibrium with infinitely elastic supply of arbitrage Assumptions: No taxes or transaction cost No limitations on borrowing No cost other than financing to storing a long cash market position No limitations on short sale of the commodity in the spot market The interest rate is flat and stationary at continuously compounded rate of r per unit time.

12. 12 Return of investing S 0 € in the spot market Alternatively investing S 0 in a risk free asset and at the same time taking a long position in the future market (delivery in one year) produces the return Theoretical Model: Garbade and Silver 1983

13. 13 Under the previous assumptions so Taking logs, at time t the equilibrium with infinitely elastic supply of arbitrage is Theoretical Model: Garbade and Silver 1983

14. 14 where St and Ft are in logs, and t t is the number of days to the first delivery date of the underlying commodity (in our case, 15 months). The previous assumptions imply that the supply of arbitrage services will be infinitely elastic whenever eq (1) is violated (1) Theoretical Model: Garbade and Silver 1983

15. 15 Equilibrium with finitely elastic supply of arbitrage services Lets define a cash-equivalent future price To describe the interaction between cash and future prices we must first specify the behavior 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. Theoretical Model: Garbade and Silver 1983

16. 16 Equilibrium with finitely elastic supply of arbitrage services Demand schedule of i th participant in spot market where A is the elasticity of demand Aggregate cash market demand schedule of arbitrageurs in period t where H is the elasticity of cash market demand by arbitrageurs. It is finite when the arbitrage transactions of buying in the cash market and selling the futures contract or vice-versa are not riskless Theoretical Model: Garbade and Silver 1983

17. 17 The cash market will clear at the value of S t that solves The future market will clear at the value of F t such that Theoretical Model: Garbade and Silver 1983

18. 18 Equilibrium with finitely elastic supply of arbitrage services Solving the clearing market conditions we get If there is no arbitrage H=0 If H=∞ Theoretical Model: Garbade and Silver 1983

19. 19 Dynamic price relationships To derive dynamic price relationships, we need a description of the evolution of reservation prices. Theoretical Model: Garbade and Silver 1983

20. 20 And the mean reservation price Theoretical Model: Garbade and Silver 1983

21. 21 Dynamic price relationships: VAR model When H=0, prices are independent random walks When H=∞ prices, will follow a common random walk ( e t s =e t f ) When 0<H<∞: –If Futures market dominate –If Cash markets dominate Mensures the importance of future markets relative to cash markets Theoretical Model: Garbade and Silver 1983

22. 22 VECM Representation The ratio is used to measure the importance of future market relative to the cash market in the price discovery process Theoretical Model: Garbade and Silver 1983

23. 23 Alternatively substituting Theoretical Model: Garbade and Silver 1983 with k =r t

24. 24 Incorporating Mean Backwardation/Contango Theoretical Model: Garbade and Silver 1983

25. 25 The ‘Theory’ of Normal Backwardation Normal backwardation is the most commonly accepted “driver” of commodity future returns “Normal backwardation” is a long-only risk premium “explanation” for futures returns –Keynes coined the term in 1923 –It provides the justification for long-only commodity futures indices Keynes on Normal Backwardation “If supply and demand are balanced, the spot price must exceed the forward price by the amount which the producer is ready to sacrifice in order to “hedge” himself, i.e., to avoid the risk of price fluctuations during his production period. Thus in normal conditions the spot price exceeds the forward price, i.e., there is a backwardation. In other words, the normal supply price on the spot includes remuneration for the risk of price fluctuations during the period of production, whilst the forward price excludes this.” A Treatise on Money: Volume II, page 143

26. 26 Backwardation Contango Note: commodity price term structure as of May 30 th, 2004 Backwardation refers to futures prices that decline with time to maturity Contango refers to futures prices that rise with time to maturity Nearby Futures Contract

27. 27 VECM with Mean Backwardation/Contango Theoretical Model: Garbade and Silver 1983

28. 28 Econometric Implementation We use the Gonzalo-Granger (GG) methodology as opposed to Hasbrouck´s because it is robust to the presence of correlations in the error terms (e t ). This is important for commodity price data with daily frequency. Both techniques impose a minimum structure in the dynamics of the price series.

29. 29 Metodology: the GG Permanent-Transitory

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31. 31 Metodology: the GG Permanent-Transitory P-T decomposition where

32. 32 Easy Estimation and Testing

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34. 34 The steps are… 1) Perform unit root test on price levels 2) Estimate the VECM model 3) Test the rank of cointegration r 4) Estimate  by finding the first r eigenvectors of the following eigenvalue problem 5) Estimate the α  vector by finding the last n-r eigenvectors of the following eigenvalue problem

35. 35 The steps are… 6) Test the H 0 : 7) Test the H 0 α  = (1,0) and α  = (0,1) 8) Set up the PT decomposition

36. 36 Data Daily spot and future (15 months) for Al, Cu, Ni, Pb, Sn, Zi, quoted in the LME. Sample January 1990- July 2006. Source Ecowin. Copper: historically most important contract traded in LME. Aluminium took over in terms of volume in 1997. Aluminium and Nickel trading introduced in 1979.

37. 37 Descriptive Statistics al cu ni Pb Zi (1-L) SpotAverage ret0.00000.00020.00000.0001 Robust SE(0.0002) (0.0003) (0.0002) (1-L) F15- monthAverage ret0.00000.00020.0001 Robust SE(0.0001)(0.0002)(0.0003)(0.0002) Spot- F15monthAverage ret-0.02520.04110.0312-0.0202-0.0095 Robust SE(0.0009)(0.0015) (0.0014)

38. 38 Table 1: Cointegration test, common factor weights and hypothesis testing Al CuNiPbZi r ≤10.061.220.00 0.02 r = 019.7315.7223.3719.3315.20 11 1.00 22 H0:  =(1,-1) 0.14350.35530.15020.46380.8320 -0.02520.04110.0312-0.0202-0.0095 Robust Sd (0.0009)(0.0015)(0.0048)(0.0044)(0.0043) This table presents results on the Trace test of r= 0 against r>0. and r ≤against r>1for the whole sample. The 95% critical values for rejecting the null are 19.99 and 9.13 respectively. The 90% critical levels are 17.79 and 7.50. We also present p values from testing the null hypothesis of unit cointegrating vector and average constant terms of cointegrating relations with corresponding and Wewey West Stadanrd errors

39. 39 Table 2: Proportion of price discovery for spot and future markets AlCuNiPbZi 11 -0.29340.88640.00530.7886-0.3081  2  0.95600.46301.00000.61500.9514 H0:   =(0,1) (0.1473)(0.0991)(0.1294)(0.0822)(0.2753) H0:   =(1,0) (0.0002)(0.4847)(0.0039)(0.2453)(0.0035) H0:   =(1,1) (0.7092)(0.8516) We present the common-long memory factor weights for five LME spot and future markets,. Since we have two series and one cointegrating vector r=1 there is only one common factor orthogonal to the adjustment vector. We test the elements of this last eigen vector of the common factor matrix for significance using the methodology of Gonzalo and Granger (1995). In each the null hypothesis is that the factor weight for the indicated market is 0. We have also tested the null hypothesis that the common factor weight is 1 in both markets for copper and lead.The test statistic is distributed with a chi-squared with one degree of freedom. We report P values which are given in parenthesis and calculated from the likelihood ratio test statistics reported in table A2 estimated following the PT methodology.

40. 40 Conclusions and implications For those metals with most liquid future markets the future price is the major contributor to the revelation of the common factor. Producers and consumers should rely on the LME future price to make their production and consumption decisions. The LME future price changes lead price changes in cash markets more often than the reverse. Future and spot prices are cointegrated implying that it is not possible to make profits in the long run trading futures and taking positions in the underlying commodity

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