Noise trading induces a particular risk that, in addition to transaction costs or imperfect sub- stitutes, deters arbitrage. The literature offers several definitions for noise or noise traders. In one of the fundamental work on noise, Black and Scholes (1972) interpret noise traders as investors who falsely trade on information which they believe is correct. Shleifer (2000), on the other hand, states that noise traders conduct transactions based on their erroneous beliefs on future distributions of returns on risky assets. Yet, most definitions have in common that noise traders are considered irrational and objectively uninformed.
In one of the first theoretical studies on formal models of informed and uninformed trading, Grossman (1976) developed a pricing model which first included noise. In this model noise ultimately prevents informed traders to observe the true fundamental value of an asset. He concludes that a market equilibrium, where prices reflect all aggregated and available infor- mation, might break down in the presence of noise. In another study, Black (1986) offers eco- nomic reasonings for noise traders and their role in financial markets. In his argumentation, noise does exist in different dimensions. Noise provides substantial liquidity to a financial mar- ket, but in interaction with arbitrageurs, prices would ultimately be pushed back to their fun- damental value. Noise trading is in this perspective a complementary element in efficient mar- kets and a foundation for liquidity in financial markets.
Another view on noise is the risk perspective of noise. Mispricing resulting from noise trading might occur in the short-term but diminishes in the long run as long as informed traders exploit
the arbitrage opportunities. However, there is a risk for arbitrageurs that a noise trader’s mis- perception persists or even increases before prices return to the mean. For example, if the noise trader’s optimism drives up prices, arbitrageurs should (short-)sell this asset, assuming that prices reverse in the future. Yet, there is a risk that noise traders become even more optimistic and push prices further away from its fundamentals. Fearing additional losses or receiving pressure from their investors, arbitrageurs liquidate their positions and realize losses. The fear of loss, hence, limits the original amount invested by risk-averse arbitrageurs. This risk of ad- ditional losses is subsumed under the noise trading risk (De Long et al., 1990).
In a constitutional work on noise trader risk, De Long et al. (1990) developed a theoretical model on asset prices as a function of exogenous variables, which in its purest form is stated as follows: 𝑝𝑡= 1 + 𝜇(𝜌𝑡− 𝜌 ∗) 1 + 𝑟 + 𝜇𝜌∗ 𝑟 − (2𝛾)𝜇2𝜎 𝑝2 𝑟(1 + 𝑟)2 (5)
where pt is the asset price at time t, μ is the share of noise traders present in the model, r is the dividend of the asset, ρt is a random variable reflecting the misperceived expected price of the risky asset, ρ* is the measure of the average bullishness of the noise traders, γ is a coefficient describing the absolute risk-aversion of investors, and 𝜎𝑝2 denotes the variance of the noise trader’s misperception of expected returns per unit of the risky asset.8 The model in its simplest
form provides three main implications of noise trading for financial markets. First, a shift of noise trader’s opinions induces fluctuations of prices and hence volatility. Second, the average misperception of noise traders is unequal to zero. Deviations of beliefs by noise traders, there- fore, cause a mispricing of assets. Lastly and the probably most important implication, noise trading creates risks. The uncertainty over the noise trader’s belief in the next period makes an otherwise riskless asset risky, drives prices down and increases future expected returns. In this connection, a total risk-aversion of zero would imply that investors do not sell their assets in case of overpricing. As a result, prices remain high and expected future returns are low (De Long et al., 1990).
Based on this model, noise trading creates risks. Hence, if the noise trader’s belief follows a random walk, then prices revert to the mean in the long run. An instationary process of noise trader’s beliefs, however, results in a persistent deviation of the asset price with continuous risk premiums for noise trading.
Noise trading is commonly associated with transactions based on non-information. The be- havioral perspective, therefore, argues that noise traders base their decisions on false or inac- curate information (Black, 1986). Bloomfield et al. (2009) distinguish in their study between two types of noise traders. The first group are “liquidity traders” who’s trades are triggered by random liquidity shocks (for example, a fund’s investor requires liquidity for some unknown reasons and recalls funds without no economic reason). The second group consists of “unin- formed traders” who trade despite having any advantageous information. We do not differen- tiate between both groups and refer all non-informative trades to noise traders forth on.
In summary, noise trading and its associated risk have several implications for financial mar- kets. With the presence of noise traders, prices of assets are excessively volatile and not corre- lated to the variance of its fundamentals. If asset prices react to noise temporarily, then asset prices should revert to the mean in the long run. Yet, a persistence in noise trader risk might force capital constrained investors to withdraw from the market. The expected mean reversion of asset prices additionally changes the logic to traditional investment strategies that propagate the buy-and-hold-strategy. The noise trading theory creates room for the so-called contrarian investment strategy, where the timing of investment decisions is essential. With this strategy, arbitrageurs invest in times when noise traders are bearish and reduce their exposure when noise traders are bullish (De Long et al., 1990). One can infer that bullishness is one essential element in the concept of noise trading and in behavioral finance. Bullishness is highly con- nected to the concept of “investor sentiment”. Consequently, we discuss the theory and impli- cations of investor sentiment for financial markets in the next section.