Abstract
This chapter adds a random shock to the futures market to see if an informationally efficient equilibrium would still occur. In this chapter, the prices are modeled as continuous variables and traders can buy or sell with a single submission of their quotes. The conclusion is that,with probability one, if the volatility of the underlying spot market is sufficiently small, then the proportion of time that the futures price is sufficiently close to the fundamental value converges to one. However, the interval containing the fundamental value, where the futures price eventually lies, is influenced by the underlying volatility generated from the spot market. In other words, the accuracy of the information for which the market can eventually select, depends on the volatility generated from the random shock in the spot market. The more volatile the spot market, the more noisy is the information that gets selected for. As a result, the futures market moves further away from informational efficiency. Numerical examples are used to illustrate the cause of the convergence and how the wealth is redistributed among traders.
This chapter is based on my article published in the Journal of Futures Markets 21(6): 489–516, 2001.
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Notes
- 1.
This issue is also examined in an experimental context in Smith (1982).
- 2.
See Camerer (1987) for a list of arguments (and counterarguments) used to defend economic theories from the criticism that markets are not rational.
- 3.
Furthermore, even if traders have access to the same information, they may disagree on its correct interpretation and may have differing abilities in processing the same information. Of course, this would further add to differing abilities of traders in predicting the fundamental value of the spot price. This would also be consistent with views of bounded rationality [e.g., Simon (1959, 1986) and Vriend (1996)].
- 4.
A similar descriptive story behind the above selection process can be found in Cootner (1967). Another market selection process for producers in an industry is formulated in Luo (1995) where efficient firms are selected for and a perfectly competitive market arises in the long run.
- 5.
To be consistent with the evolutionary framework, producers are also assumed to be irrational in the sense that producers have no understanding of the implication of the past futures prices and have no knowledge of the present futures price.
- 6.
This decomposition of the spot price is consistent with many economic stories. One of such stories is as follows. The output level of each of a very large number of producers is determined (although unknown to other producers) at the beginning of the time period and the total output of all producers is delivered and sold in the spot market at the end of the time period. The intersection of a prespecified consumers’ demand curve (determined at the beginning of the time period) with the producers’ aggregate supply in the spot market determines the underlying spot price (or fundamental value, Z t ), although unknown to all participants, at the beginning of the time period. However, if a random shock is added to the consumers’ demand or the producers’ supply at the end of each time period, then this spot price (P t ) at the end of the time period becomes \({P}_{t} = {Z}_{t} + {\omega }_{t}\).
- 7.
In the following it is assumed that traders actively use all of their wealth for speculation. However, even if traders withdraw for consumption a constant fraction of their wealth each time period, the results of the chapter remain the same.
- 8.
Of course, traders with more sophisticated behavior could be added to the model, but this would make it more difficult in isolating the filtering role of the market.
- 9.
This modeling of predictions is the same as Grossman (1976, 1978), Figlewski (1978, 1982), and Hellwig (1980).
- 10.
No assumptions are made with respect to the type of distribution of the prediction error. This contrasts with most papers including Figlewski (1978, 1982), where normality is assumed.
- 11.
The truncation keeps the upper bound of the spot price P s from exceeding the highest bid 10.
- 12.
This corollary is the same as Theorem 1 in Luo (1998) except the prices in this chapter are continuous.
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Luo, G.Y. (2012). Natural Selection, Random Shocks, and Market Efficiency in a Futures Market. In: Evolutionary Foundations of Equilibria in Irrational Markets. Studies in Economic Theory, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0712-6_5
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