Traditional asset pricing theory suggests that economists can safely ignore individual irrational behavior at the aggregate level (Friedman, 1953). But this argument is not adopted by behavioral finance, which argues that the investment strategy may be impacted by investor noise, investor psychology, or investor sentiment. Some noise trader models are proposed to illustrate the influence of noise on the stock price (De Long et al., 1990 and Yan, 2010). For example, Yan (2010) presented a noise model, where individual biases often cannot be cancelled out by aggregation. The shortcoming of noise models is that the noise information is difficult to be identified and cannot be measured, consequently can't be empirically testified. Yang and Yan (2011) suggested that investor sentiment is easy to be measured by variant methods and the related result is supported by some financial experiments (Statman et al., 2008).
Nowadays, the systematic role of investor sentiment has been supported by some empirical and theoretical studies. A number of empirical studies have shown that investor sentiment has a systematic impact on stock return (Baker and Wurgler, 2006, Baker and Wurgler, 2007, Baker et al., 2012, Brown and Cliff, 2004, Kumar and Lee, 2006, Kurov, 2010, Lee et al., 1991, Liao et al., 2011, Schmeling, 2009, Verma and Soydemir, 2009, Yang and Zhang, 2013a, Yang and Zhang, 2013b and Yu and Yuan, 2011).
Some static asset pricing models have been developed to support the role of investor sentiment, such as Yang et al. (2012), Yang and Yan (2011), and Yang and Zhang (2013a). Yang and Yan (2011) showed that the excess return is negatively related to a high sentiment bigger than a critical point, but positively related to a high sentiment smaller than this point. Yang et al. (2012) presented a sentiment capital asset pricing model, and showed that investor sentiment is a nonlinear systematic factor for asset pricing. Yang and Zhang (2013a) presented a sentiment asset pricing model with consumption, and showed that the stock price has a wealth-weighted average structure and the investor's wealth proportion could amplify the sentiment shock on the asset price.
These static asset pricing models have showed the systematic impact of the investor sentiment on the stock price. However, compared with only one transaction, investors frequently trade stocks in capital market. Moreover, static models usually assumed that investor sentiment is a constant. In fact, investors usually update their sentiment upon receiving more data. For example, the magnitude of investor sentiment decreases over time when investors are learning over time. Hence, the dynamic characteristic of stock price model is closer to the reality capital market and the setting of dynamic sentiment asset pricing model could explain the complex of the stock price changing form.
Yang and Zhang (2013b) presented a dynamic sentiment asset pricing model with one representative investor, and showed that investor sentiment has a significant impact on the equilibrium stock price. Moreover, time varying sentiments can lead to a complex road of the price change. There is only one representative investor in the model, but there are many types of investors in the reality stock market, such as rational investors, optimistic investors and pessimistic investors etc. To our knowledge, the dynamic asset pricing models with heterogeneous sentiments have not been developed.
Based on the framework of consumption-based model, we present a dynamic asset pricing model with heterogeneous sentiments. The dynamic sentiment asset pricing model shows that heterogeneous sentiments have a significant impact on the equilibrium stock price.
First, to examine Friedman's (1953) argument that rational investors can cancel irrational investors out, let us consider an economy with one rational investor and one sentiment investor. The model shows that the wealth share of the sentiment investor is more than the one of the rational investor when investor sentiment is close to the stock's performance. This result is not consistent with the conventional argument.
Second, in an economy with one optimistic investor and one pessimistic investor, the impact of optimistic sentiment on stock price could be partly offset by pessimistic sentiment. The net impact of heterogeneous sentiments depends on the fraction of investor wealth and the sentiment level, and is not equal to zero in general. Hence, investor sentiment still has an effect on the equilibrium.
Finally, in an economy with many investors, the equilibrium stock price is the wealth-share-weighted average of the stock prices that would prevail in an economy with one sentiment investor only. Moreover, heterogeneous sentiments induce fluctuations in the wealth distribution, which increases the stock return volatility and induces mean reversion in stock returns. The model offers a partial explanation for the financial anomalies of mean reversion.
The rest of this paper is organized as follows. Section 2 presents a dynamic model with heterogeneous sentiments. Section 3 presents the equilibrium stock price. Section 4 is the discussion of the model. Section 5 concludes.
The recent behavioral finance literatures have made a great effort to document that the risky asset price tends to be impacted by investor sentiment. Our paper complements this literature by examining this argument with heterogeneous sentiments in a dynamic asset pricing model. Our model shows that heterogeneous sentiments have a significant impact on the equilibrium stock price.
First, in contrast to Friedman's (1953) argument, the model shows that the wealth share of sentiment investor is more than the one of rational investor when investor sentiment is close to the stock's performance. Moreover, the impact of optimistic sentiment on stock price could be partly offset by pessimistic sentiment. The net impact of heterogeneous sentiments depends on the fraction of investor wealth and the sentiment level. Finally, in an economy with heterogeneous investors, the equilibrium stock price is the wealth-share-weighted average of the stock prices that would prevail in an economy with one sentiment investor only. Heterogeneous sentiments induce fluctuations in the wealth distribution, which increases the stock return volatility and induces mean reversion in stock returns. The model offers a partial explanation for the financial anomaly of mean reversion.
Our findings could raise a number of interesting issues for future research. For instance, in order to study the survival of sentiment investors, it would be interested in the continuous asset pricing model with sentiment investors.
