مدل قیمت گذاری موقعیت پویای دارایی

Conventional wisdom suggests that the equilibrium stock price is not affected by investor sentiment, and the equilibrium price at an early time is higher than the one at a later time. In contrast to this wisdom, we present a dynamic asset pricing model with investor sentiment and we find that investor sentiment has a significant impact on the equilibrium stock price. The equilibrium stock price, which is affected by pessimistic sentiment at time 0, may be lower than the one at time 1. Moreover, consistent with the reality stock market, our model shows that time varying sentiments can lead to various price changes. Finally, the model could offer a partial explanation for the financial anomaly of high volatility.

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, investor sentiment and the arbitrage is limited. At first 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 canceled 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, 2013 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), Yang and Zhang (2013). 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) constructed a sentiment capital asset pricing model, and showed that investor sentiment is a nonlinear systematic factor for asset pricing. Yang and Zhang (2013) constructed 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, the static models usually assumed that the investor sentiment is a constant. In fact, the 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. Based on the framework of a consumption-based model, we construct a dynamic asset pricing model with sentimental investors. Similar to the static model of Yang and Zhang (2013), the dynamic sentiment asset pricing model shows that investor sentiment has a significant impact on the equilibrium stock price. The equilibrium price is amplified by optimistic sentiment, and reduced by pessimistic sentiment. Conventional wisdom suggests that the equilibrium stock price at an early time is generally higher than the one at a later time. In contrast to this wisdom, our model shows that the stock price, which is affected by pessimistic sentiment at an early time, may be lower than the stock price at a later time. Our model could offer a partial explanation for the financial anomaly of high volatility. One notable feature of Yan's model is that investors' beliefs do not change over time. This assumption is made for simplicity. In order to study the dynamic effect of time varying sentiment, this assumption is relaxed in our model. Our model shows that the equilibrium stock price at time 0 is impacted by time varying sentiments. First, if the representative investor updates his sentiment upon receiving more information, then the magnitude of the investor's error decreases over time. Second, if the representative investor is pessimistic (or optimistic) at time 0 but optimistic (or pessimistic) at time 1, then the impact of pessimistic sentiment can be partly offset by the impact of optimistic sentiment. Finally, time varying sentiment can lead to a more significant price change. The rest of this paper is organized as follows. Section 2 presents a dynamic model with investor sentiment. Section 3 presents the equilibrium stock price. Section 4 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 investor sentiment in a dynamic model asset pricing model. Our model shows that investor sentiment has a significant impact on the equilibrium stock price, which is amplified by optimistic sentiment, and reduced by pessimistic sentiment. Conventional wisdom suggests that the equilibrium stock price at an early time is generally higher than the one at later time. In contrast to the conventional wisdom, the equilibrium stock price at time 0 may be lower than the equilibrium stock price at time 1 because of the impact of the investor sentiment. Moreover, relaxing the traditional assumption that investor sentiment does not change over time, our model shows that the different time varying sentiments lead to various price changes. For example, if the representative investor is pessimistic at time 0 but optimistic at time 1, then the equilibrium price at time 1 is high and the one at time 0 is low. Our model could offer a partial explanation for the financial anomaly of high volatility. Our findings could raise a number of interesting issues for future research. For instance, in order to study the impact of heterogeneous sentiment investors, it would be interested in the dynamic asset pricing model with heterogeneous sentiment investors. The other issue is that in order to study the survival of sentiment investors, it would be interested in the continuous asset pricing model with sentiment investors.