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Do Investors Care About Noise Trader Risk?

Journal 35: Zicklin-Capco Institute Paper Series in Applied Finance

Francisca Beer, Mohamad Watfa, Mohamed Zouaoui

The link between investor sentiment and asset valuation is at the center of a long-running debate in behavioral finance. Using a new composite sentiment indicator, we show that the conventional risk does not explain the abnormal returns of portfolios most sensitive to the sentiment factor. Our result supports the existence of a sentiment risk valued by financial markets. We also find that the firms more impacted by the sentiment risk correspond to difficult-to-arbitrage and hard-to-value stocks, e.g. small stocks, growth stocks, young stocks, unprofitable stocks, lower dividend-paying stocks, intangible stocks and high volatility stocks.

The standard risk-based asset pricing literature does not take into consideration the role of cognitive factors in financial markets. According to classical finance theory, investors are supposed to be Bayesian in forming fully rational expectations about future cash flows and investment risks. As a result the equilibrium asset price reflects the fundamental value, i.e. rationally-discounted value of expected cash flows. The classical theory further recognizes that some investors cannot be rational, arguing that their positions are offset by arbitrageurs bringing prices back to their fundamental value.

The succession of numerous stock market anomalies has led to an alternative theory stating that asset prices are established through the dynamic interplay between noise traders and rational investors. Several theoretical studies have modeled the role of investor sentiment in asset pricing [Black (1986), De Long et al. (1990), Barberis et al. (1998)]. In these models, there are two types of investors that interact: rational investors and noise traders (i.e. individuals). Rational investors have rational expectations about asset returns. In contrast, noise traders’ expectations about asset returns are subject to the influence of sentiment; they underestimate the expected returns (relative to the fundamental value) in some periods and overestimate them in others. Each period, rational investors and noise traders trade the assets based on their respective beliefs. The theoretical framework assumes that noise traders’ sentiment is stochastic and cannot be perfectly forecasted by rational investors. Because assets are risky and all investors are risk averse, the equilibrium price reflects the opinions of both the rational investors and the noise traders. It follows that noise traders’ sentiment influences asset prices. The theoretical studies point out that asset prices can significantly diverge from fundamental values. Moreover, because arbitrage has practical limits, rational investors fail to fully offset the effects of noise traders’ sentiment. Thus, the “noise trader risk”, also known as the “sentiment risk”, becomes a priced factor by stock markets. As noted by De Long et al., (1990), “Noise traders can earn higher relative expected returns solely by bearing more of the risk they themselves create.”

In financial markets, noise traders limit arbitrageurs’ ability to bring prices to their fundamental value. Not knowing what the reaction of noise traders will be, arbitrageurs understand risk is involved and limit the funds committed. For example, suppose that in a given period, the noise traders’ optimistic expectations result in asset prices inflation. Rational investors should theoretically react to this situation by using futures market to sell short these overvalued stocks. However, arbitrageurs could still experience a severe loss if prices increase instead of dropping because noise traders have continued to be too optimistic. Conversely, an investor who purchases these stocks thinking they are undervalued runs the risk that noise traders’ pessimistic expectations result in lower prices. In this case, the risk of holding stocks comes from two sources: the traditional risk and additional risk introduced by noise traders.

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