Noise Traders

The term used to describe an investor who makes decisions regarding buy and sell trades without the use of fundamental data. These investors generally have poor timing, follow trends, and over-react to good and bad news. Let us consider the noise traders’ decision making. They are assumed to base decisions on noise in the sense of a large number of small events. The behavior of a noise trader can be formalized as maximizing the quadratic utility function

W(x_tⁿ, y_tⁿ) = g(y_tⁿ + (p_t + ε_t)x_tⁿ) – k(x_tⁿ)² —– (1)

subject to the budget constraint

y_tⁿ + p_tx_tⁿ = 0 —– (2)

where x_tⁿ and y_tⁿ represent the noise trader’s excess demand for stock and for money at time t, respectively. The noise ε_t is assumed to be an IID random variable. In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent. The excess demand function for stock is given as

x_tⁿ = γε_t, γ = g/2k > 0 —– (3)

where γ denotes the strength of the reaction to noisy information. In short, noise traders try to buy stock if they believe the noise to be good news (ε_t > 0). Inversely, if they believe the noise to be bad news (ε_t < 0), they try to sell it.

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