Conjuncted: Noise Traders, Chartists and Fundamentalists

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Let us leave traders’ decision-making processes and turn to the adjustment of the stock-market price. We assume the existence of a market maker, such as a specialist in the New York stock exchange. The role of the market maker is to give an execution price to incoming orders and to execute transactions. The market maker announces a price at the beginning of each trading period. Traders then determine their excess demand, based on the announced price and on their expected prices. When the market maker observes either excess demand or excess supply, he applies the so-called short-side rule to the demands and supplies, taking aggregate transactions for the stock to be equal to the minimum of total supply and demand. Thus traders on the short side of the market will realize their desired transactions. At the beginning of the next trading period, he announces a new price. If the excess demand in period t is positive (negative), the market maker raises (reduces) the price for the following period t + 1. The process then is repeated. Let κ and ξ be the fractions of chartists and of noise traders in the total number of traders, respectively. Then the process of price adjustment can be written as

pt+1 − pt = θn[(1 − κ − ξ)xtf + κxtc + ξxtn]

where θ denotes the speed of the adjustment of the price, and n the total number of traders.

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