*4.8. Behavioral Models*

In this section, we discuss several behavioral models for Behavioral Finance that relate to market efficiency and anomalies in stock markets. So far, all the models discussed in Sections 4.1–4.7 are behavioral models. Thus, in this section, we discuss the behavioral models that are not discussed in Sections 4.1–4.7.

#### 4.8.1. Behavioral Models for Some Financial Anomalies

By applying the concept of both conservatism and representativeness heuristics, Barberis et al. (1998) and others developed the Bayesian models, which can be used to explain investors' behavioral biases. Lam et al. (2010) extended their work by introducing a pseudo-Bayesian approach to reflect the biases from investors' behavior on each of each dividend being assigned (Thompson and Wong 1991, 1996; Wong and Chan 2004). Their model can be used to explain excess volatility, long-run overreaction, short-run underreaction, and their magnitude e ffect. Lam et al. (2012) improved the theory by establishing some new properties by using the pseudo-Bayesian model to explain the market anomalies and the investors' behavioral biases.

Fung et al. (2011) further improved the theory by considering the impact of a financial crisis. Guo et al. (2017a) improved the theory by first relaxing the normality assumption to any exponential family distribution for the earning shock of an asset that follows a random-walk model, with and without drift. They established additional properties to explain excess volatility, long-term overreaction, short-term underreaction, and their magnitude e ffects during financial crises, as well as the period of recovery thereafter.

The theory developed by Guo et al. (2017a) and the references therein can only explain some market anomalies, like excess volatility, long-run overreaction, short-run underreaction, and their magnitude effect, but cannot be used to test it empirically. To circumvent the limitation, Fabozzi et al. (2013) developed several statistics that can be used to test whether there is any long-run overreaction and short-run underreaction, and their magnitude effect in the markets. They applied their statistics empirically and concluded that long-run overreaction, short-run underreaction, and their magnitude effect did exist in the markets they studied.

In addition to conducting statistical analysis to real data of stock prices to test whether there is any market anomaly, scholars could also use questionnaires to conduct surveys to examine investors' attitude on the market anomaly. For example, Wong et al. (2018b) distributed their questionnaires to small investors in Hong Kong, to conduct a survey to examine the behavior of investor behavior on long-term overreaction, short-term underreaction, and their magnitude effect. Their empirical findings support the theory developed by Guo et al. (2017a), and the references therein, that small investors in Hong Kong have both conservative and representative heuristics and they do use momentum and contrarian strategies in their investment.

#### 4.8.2. Other Behavioral Models

The regret-aversion model is an important model for Behavioral Finance; for example, it can be used for investors to make decision in their portfolio investment (Barberis et al. 2006; Muermann et al. 2006). It can be used in many other areas, as well, for example, options (Sarver 2008) and hedging (Egozcue et al. 2015; Guo et al. 2015; Guo and Wong 2019).

On the other hand, the disappointment-aversion model developed by Bell (1982) and Loomes and Sugden (1982) can also be used in Behavioral Finance. For example, it can be used to determine the weights investors should hold stock and bond. Readers may refer to Guo et al. (2020) and the reference therein for more information.

Wan and Wong (2001) developed a behavioral model with incomplete information that can be used in refinancing during finance crisis. They found out the conditions to make financial crisis happen from one country to another one. In addition, Fry et al. (2010) and Fry-McKibbin and Hsiao (2018) developed statistics to test for contagion effect.

Given the studies in Sections 3.1 and 3.2, Fama (1998) claims that EMH survives in the abnormal returns brought by the Winner–Loser Effect and Momentum Effect. In particular, Fama insists that anomalies are chance results, which is consistent with the EMH, as it is obvious that overreaction to information is as common as underreaction to information. Moreover, the duration of abnormal returns before and after events is similar to the frequency of reversal of past events. Most importantly, consistent with market efficiency forecasts, the obvious anomalies may be due to different methodologies, as most long-term earnings anomalies tend to disappear as technology changes reasonably.

Some of the other literature has attempted to explain the above anomalies through the Behavioral Finance perspective, and the authors developed models. The first one is BSV model. Barberis et al. (1998) consider that there are two wrong paradigms when people make investment decisions: representative bias and conservative bias. The former refers to investors paying too much attention to the change patterns of recent data, but not enough attention to the overall characteristics of these data. The latter describes how investors cannot modify the increased forecasting model in time according to the changed situation. These two biases lead to underreaction and overreaction, separately. The BSV model explains how investors' decision-making models lead to market price changes deviating from the EMH.

By importing investor overconfidence and biased self-attribution, another two well-known psychological biases, Daniel et al. (1998) set up the DHS model. In the DHS model, overconfident investors are believed to overestimate their own prediction ability, underestimate their own prediction errors, over-trust private information, and underestimate the value of public information, which makes the weight of private signals in the eyes of overconfident investors higher than previous information and causes overreaction. While noisy public information can partially correct price inefficiencies when it arrives, overreacting prices tend to reverse when additional public information is available.

The third model to fix momentum anomalies is the HS model. The HS model, also known as the unified theoretical model, di ffers from the BSV model and DHS model in that it focuses on the mechanism of di fferent actors rather than the cognitive bias of the actors (Hong and Stein 1999). The model divides participants into two categories: observers and momentum traders. Observers are assumed to make predictions based on future value information, while momentum traders rely entirely on past price changes.

Under the above assumptions, the model unifies the underreaction and overreaction as the basis. The model argues that the tendency of observers to underreact to private information first leads momentum traders to try to exploit this by hedging strategies, which in turn leads to overreaction at the other extreme.

#### *4.9. Unit Root, Cointegration, Causality, and Nonlinearity*

Unit root test, cointegration, and causality are important areas in Behavioral Finance because they can measure many di fferent behaviors in Behavioral Finance. For example, Lam et al. (2006) developed three test statistics that can be used to test whether a series follows a random-walk or a stationary general-mean-reversed (GMR) model. It is investors' behavior to make stock prices follow a stationary general-mean-reversed (GMR) model. If the market is e fficient, the stock price should follow a random-walk model. It is also because of investors' behavior that some stocks are moving together (cointegration) or not moving together, or one stock price could cause (causality) another one.

The authors have developed some unit root (Tiku and Wong 1998), cointegration (Penm et al. 2003; Wong et al. 2007), causality (Bai et al. 2010, 2011a, 2018), and nonlinearity (Hui et al. 2017) tests that related to Behavioral Finance.

There are many applications of unit root, cointegration, causality, and nonlinearity tests in many di fferent areas of Behavioral Finance, including Manzur et al. (1999), Wong et al. (2004a, 2004b, 2007), Lam et al. (2006), Qiao et al. (2008a, 2008b, 2008c, 2009, 2011), Zheng et al. (2009), Chiang et al. (2009), Liew et al. (2010), Owyong et al. (2015), Vieito et al. (2015), Chow et al. (2018a, 2018b, 2019a), Batmunkh et al. (2018), Demirer et al. (2019), Gupta et al. (2019b), Zhu et al. (2019), Cheng et al. (2019), Lv et al. (2019), and many others.

## *4.10. Covariance and Copulas*

Covariance and copulas are important areas in Behavioral Finance because they can measure the time-varying covariances that are caused by investors' di fferent behavior over time; for example, Lam et al. (2010, 2012), Fung et al. (2011), Guo et al. (2017a), and many others showed that investor conservatism and representativeness heuristics cause excess volatility in financial markets.

We have developed some theories in covariance and copulas (see, for example, Egozcue et al. (2009, 2010, 2011a, 2011b, 2011c, 2012, 2013), Bai et al. (2009a, 2009b, 2011c), and Ly et al. (2019a, 2019b)). We have also conducted some analysis by using covariance and copulas (Tang et al. 2014).

#### *4.11. Robust Estimation and Other Econometric Models*/*Tests*

Robust estimation and other econometric models/tests are an important area in Behavioral Finance because they can measure the models in Behavioral Finance better. For example, Wong and Bian (2000) found that the robust Bayesian estimation introduced by Bian and Dickey (1996) could lead to mean square error (MSE) being greater than one thousand times smaller than that of the traditional least squares (LS) estimates when the error terms follow very heavy tails that are common in Behavioral Finance.

We have developed some theories in robust estimation and other econometric models/tests (see, for example, Wong and Miller (1990); Matsumura et al. (1990); Tiku et al. (1999a, 1999b, 2000); Wong and Bian (2005); Wong et al. (2001); Leung and Wong (2008b); Bian et al. (2011); and many others).

We have also used robust estimation to conduct many applications (see, for example, Wong and Bian (2000); Phang et al. (1996); Phang and Wong (1997); Wong et al. (2001); Fong and Wong (2006);

#### Qiao et al. (2008c); Bian et al. (2011); Raza et al. (2016); Xu et al. (2017); Chan et al. (2018); Guo et al. (2018b); Tsendsuren et al. (2018); Gupta et al. (2019a); Pham et al. (2020); and many others).

Fong and Wong (2007) applied the volatility–volume regressions to the daily realized volatility of common stocks to study sources of volatility predictability. They found that unexpected volume can explain half of the variations in realized volatility and find that the ARCH e ffect is robust in the presence of volume.

#### *4.12. Anchoring and Adjustment*

In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insu fficient. That is, di fferent starting points yield di fferent estimates, which are biased toward the initial values. We call this phenomenon anchoring (Tversky and Kahneman 1974).

Thus, anchoring refers to the decision-making process where quantitative assessments are required and where these assessments may be influenced by suggestions. People have in their minds some reference points (anchors), for example, in the study of Momentum E ffect, anchors are previous stock prices. When they ge<sup>t</sup> new information, they adjust this past reference insu fficiently (under-reaction) to new information acquired. Anchoring describes how individuals tend to focus on recent behavior and give less weight to longer time trends.

Anchoring can cause investors to underreact to new information (Fuller 1998). Values in speculative markets, like the stock market, are inherently ambiguous. It is hard to tell what the value of the Hang Seng Index should be. There is no agreed-upon economic theory that would provide an answer to this question. In the absence of any better information, past prices are likely to be important determinants of prices today. Therefore, the anchor, being the most recently remembered prices, causes the Momentum E ffect.
