Document Type : Research Paper
Authors
1 Associate Professor, Department of Economics, Allameh Tabataba'i University, Tehran, Iran
2 Ph.D. in Financial Economics, Allameh Tabataba'i University, Tehran, Iran
Abstract
Abstract
The current study examined the influence of sentiment as a key risk factor in capital markets, which contributes to behavioral deviations in the pricing of financial assets. The stochastic discount factor (SDF) framework was used to propose an estimation of the asset pricing model, incorporating both traditional and behavioral approaches. An attempt was made to extend the consumption-based capital asset pricing model (CCAPM) and incorporate sentiment into the utility function through Euler equations and the generalized method of moments (GMM). To measure sentiment, the analysis utilized the market turnover sentiment index as a reliable indicator. The data covered 18 stock exchange groups, including 63 companies listed on the Tehran Stock Exchange, over the years 2011 to 2020. The results showed that the behavioral SDF model demonstrates higher consistency and efficiency than the traditional model, aligning more closely with observed market dynamics in the Tehran Stock Exchange. Furthermore, the sentiment coefficient was found to be statistically significant. In terms of risk, the behavioral model demonstrated higher coefficients than the traditional model. Notably, both models indicated that market participants exhibit a high time preference factor and display patience in their investment behavior.
Introduction
One of the most important approaches to asset pricing is the asset pricing model based on the stochastic discount factor (SDF), from which most asset pricing models can be derived within a general framework combining macroeconomics, finance, and mathematics. The model is based on the concept of a random discount factor (Cochrane, 2000; Foldes, 2000). Shefrin (2008) derived the behavioral SDF model by introducing market sentiment as a random discount factor. A key premise of the behavioral SDF model is that, despite investor sentiment, mistakes are made. As long as sentiment remains in the market, stock prices will not reflect their true value; they may be either inflated or deflated. This has a significant impact on asset pricing and leads to fluctuations in the SDF, as investors exhibit mass behavior, such as excessive optimism or pessimism toward the market (Shefrin, 2008). The primary objective of this study was to address the following questions: Is the experimental SDF in the Tehran Stock Exchange traditional or behavioral? Does sentiment influence asset pricing? Which model better explains investor behavior, asset market fluctuations, market bubbles, and inflated or deflated stock values?
Materials and Methods
In general, the pricing patterns of capital assets can be analyzed using two approaches: Behavioral and traditional. In recent years, economists have introduced new traditional asset pricing models based on the SDF framework. However, these models often fail to align with real-world outcomes, primarily due to their reliance on rational assumptions and the lack of consideration for behavioral factors. Using Shefrin’s Log-SDF theorem and incorporating sentiment into the utility function, the present study estimated the empirical SDF through moment equations and the GMM with both traditional and behavioral approaches.
Shefrin’s approach involves estimating the log-SDF as the sum of fundamental components and emotions (Λ). The fundamental variables included in the SDF are total consumption growth (g), the market’s relative risk aversion coefficient and the market’s time discount factor ). The formal equation relating to the Log-SDF and market behavior is as follows:
In the framework of the traditional classical model, market sentiment is assumed to be zero and Ln(m) is equal to (Shefrin, 2008). In the present article, both the traditional and Shefrin’s behavioral models are estimated and compared. Shefrin presents the following figure, comparing the behavioral SDF with the traditional SDF:
Figure 1. Comparison of Behavioral SDF and Traditional SDF
Source: Shefrin (2008)
The analysis relied on the seasonal data from 2011 to 2020. The macroeconomic data included private sector consumption, money supply, exchange rates in the free market, the volume of demand deposits in banks and credit institutions, and the gold price per ounce. Initially, the capital market data sample consisted of 18 stock groups, totaling 130 shares. However, due to missing data for some stocks during the timeframe, the final sample was reduced to 63 stocks, as shown in the table below. An attempt was made to include a diverse selection of stocks, representing both high and low volatility, as well as winner and loser stocks from each group. The stock prices were obtained from the TSE website based on the daily closing prices, and the average quarterly returns were calculated for all the stocks in the sample. For the sentiment data across the 18 stock groups, the market turnover sentiment index was calculated for each group. Finally, the average sentiment index of stock market turnover and the average sentiment index of stock price fluctuations across the groups in the sample were estimated.
Results and Discussion
The results of the behavioral SDF model with the assumption of the market turnover sentiment index by different stock market groups are as follows:
Table 1. The Results of the Estimation of the Behavioral SDF Model of the Stock Groups in the Tehran Stock Exchange
Stock group
The results of the estimation
The statistic J
The probability of test statistic J
β
P-Value
Metallic minerals
0.99 0.039 0.020
4.02
0.67
Sugar
0.99 0.034 0.018
3.6
0.73
Ceramic Tile
0.99 0.055 0.011
6.04
0.41
Rubber and plastic
0.99 0.083 0.005
5.23
0.51
Financial intermediation
0.99 0.047 0.031
4.04
0.54
Investment
0.99 0.031 0.013
5.52
0.35
Metals
0.99 0.030 0.019
5.75
0.33
Bank
0.99 0.091 0.049
5.64
0.22
Transportation
0.99 0.059 0.021
1.5
0.90
Car
0.99 0.063 0.030
5.39
0.36
Metal products
0.99 0.079 0.011
4.35
0.49
Equipment and machinery
0.99 0.031 0.003
5.06
0.53
Non-metallic minerals
0.99 0.021 0.003
6.49
0.37
Electrical devices
0.99 0.055 0.020
5.48
0.48
Oil products
0.99 0.061 0.006
8.01
0.23
Paper
0.99 0.031 0.001
4.63
0.59
Cement
0.99 0.035 0.006
5.69
0.45
Chemical products
0.99 0.061 0.004
6.99
0.32
Source: Shefrin (2008)
The general tools used in the behavioral SDF test for all groups are as follows: GSKS (-1), Gexch (-1), Gm (-1), Ghesab (-1), Ggold (-1)
The results and estimations indicated several key points. First, the time preference factor (β) is close to one in three cases, indicating that people in the society are patient and have a strong desire to save. Second, the risk tolerance coefficient (γ) in both behavioral SDF models is higher than in the traditional SDF model. This difference arises from the inclusion of the emotion variable in the behavioral model, which aligns with the theoretical expectations that investors do not always behave rationally and are often risk-seeking. Third, the ϵ coefficient, which represents the share of sentiment in the utility function (indicating optimism and pessimism), varies between 0.04 and 0.001 for different stock market groups in the sample when the turnover sentiment index is considered. Fourth, the results showed that the risk-reward ratio of the behavioral SDF model is higher than that of the traditional SDF model in the TSE. Fifth, when considering the average quarterly returns of the stock sample as a proxy for risky assets, the risk premium compared to short-term and one-year deposits is 0.039. The behavioral SDF model, assuming the turnover sentiment index, yields a risk premium of 0.035, suggesting that the behavioral SDF model’s risk-reward results are close to real-world observations. Sixth, the Hansen-Jonathan (HJ) distance criterion, used to compare the performance of non-linear models based on the GMM method, indicated that the SDF model performs better and more efficiently. Moreover, the coefficients of the model were calculated and placed into the LOG-SDF equation, and the two models were compared graphically.
Conclusion
According to the results, the behavioral SDF model aligns more closely with the realities of the TSE than the traditional model, with the sentiment coefficient being statistically significant. The risk tolerance factor in the behavioral model is higher than the traditional model, and in both models, individuals exhibit a high time preference and a degree of patience. When the charts of the behavioral and traditional SDF models intersect, it signifies a market where sentiment is zero, and stock prices are efficient. However, when the behavioral SDF exceeds the traditional SDF, it suggests that investors are overly optimistic, pushing prices above their true value. This scenario can lead to market overvaluation, potentially resulting in sales queues or a shift to negative sentiment after a large volume of transactions. For instance, in 2019 and early 2020, the market was inefficient, with prices falling below their intrinsic value. During this period, the behavioral SDF was lower than the traditional SDF, reflecting pessimism in the market. The two charts converged, signaling that prices were undervalued. As we approached the end of 2020, the gap between the behavioral and traditional SDF charts widened, indicating that investors became overly optimistic, thus driving prices beyond their intrinsic value. This reinforces the importance of considering emotional factors, which are absent in traditional models, and demonstrates how the behavioral model can help in asset pricing. Similar to Barbaris (2018), the findings of the present study suggest that by incorporating transaction volume as a sentiment indicator, we can better understand market fluctuations and identify market bubbles, in line with deviations from the inherent value of shares. Furthermore, like the results of Lu et al. (2000), this research showed that the experimental SDF in the TSE is behavioral and volatile.
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