Modelling and Measuring Price Discovery in Commodity Markets. Isabel Figuerola-Ferretti Jesús Gonzalo Universidad Carlos III de Madrid Business Department and Economics Department December 2007. Trading Places Movie. Two Whys.
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Universidad Carlos III de Madrid
Business Department and Economics Department
(i) Hasbrouck (1995) Information Shares
(ii) Gonzalo and Granger (1995) P-T decomposition, suggested by Harris et al. (1997)
We want to find a THEORETICAL JUSTIFICATION for the USE of GGP-Tdecomposition for price discovery.
Markets have two important functions: Liquidity and Price Discovery, and these functions are important for asset pricing.
Commodities, in sharp contrast to more traditional financial assets, are more tied to current economic conditions.
The chief market place is the London Metal Exchange (LME).
(built on Garbade and Silver (1983))
Theoretical model and the GG P-T decomposition
Future markets contribute in three important ways to the organization of economic activity:
Price discovery is the process by which security or commodity markets attempt to identify permanent changes in equilibrium transaction prices.
For producers as well as consumers it is important to determine where the price information and price discovery are being produced.
More on Price Discovery:
(i) All the markets are in Backwardation but Copper
(ii) For those metals with highly liquid future markets, future prices are the dominant factor in the price discovery process.
Equilibrium with infinitely elastic supply of arbitrage
1) No taxes or transaction cost
2) No limitations on borrowing
3) No costs other than financing + storage a (short or long) future position
4) No limitations on short sale of the commodity in the spot market
5) Interest rate rt + storage cost ct = + I(0), with the mean of (rt + ct)
6) St is I(1).
In consumption commodities is very likely that
where is the convenience yield.
Convenience yield is the flow of services that accrues to an owner of the physical commodity but not to an owner of a contract for future delivery of the commodity (Brennan Schwartz (1985) ). The existence of convenience yields can produce two situations very common in commodity markets: BACKWARDATION and CONTANGO.
One more Assumption:
7) The convenience yield is modeled as
with and .
It is important to notice the different values that 2 can take
(“St<Ft” in the long-run)
1 = 1+rc/ β3 and 2 = 1- β2 (1- 1 ).
In realistic cases we expect the arbitrage transactions of buying in the cash market and selling the futures contracts or vice versa not to be riskless: unknown transaction costs, unknown convenience yields, constraints on warehouse space, basis risk, etc. These are the cases of finite elasticity of arbitrage services.
To describe the interaction between cash and future prices we must first specify the behaviour of agents in the marketplace.
where A is the elasticity of demand
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.
And the mean reservation prices time to maturity
Garbade and Silver (with b2=1, b3=0) stop their analysis at this point stating that
Measures the importance of future markets relative to cash markets
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.
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
In VAR (12) the matrix M has reduced rank
(1, -2)M =0 ,
and the errors are perfectly correlated. Therefore the long run equilibrium relationship (4), St= 2 Ft + 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.
with Y denoting the common row vector of Y(1) and l a column unit vector.
ut=Qet, with Var(ut)=W=QQ’
and Q a lower triangular matrix (Choleski decomposition of W )
where [YQ]j is the j-th element of the row matrix YQ.
Solution: To calculate all the Choleskys, and form upper and lower bounds of the IS.
Problem: Theses bounds can be very distant.
(2) It is not clear how to proceed when the cointegrating vector is different from (1, -1).
(4) Economic Theory behind it???
It exists if det(b’a) different from zero.
The LME data has the advantage that there are simultaneous spot and forward ask prices, for fixed maturities, every business day.
Six 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))
6) Set up the PT decomposition.
(2) Backwardation and contango jointly in the model. This will imply a non-linear ECM.
Figure 6: Range of annual Aluminum convenience yields in % time to maturity
Figure 7: Range of annual Copper convenience yields in % time to maturity
Figure 6: Range of annual Nickel convenience yields in % time to maturity
Figure 9: Range of annual Lead convenience yields in % time to maturity
Figure 10: Range of annual Zinc convenience yields in % time to maturity