The study of an adjusted CCAPM model through the Bayesian estimation of trading costs

The capital asset pricing model (CAPM), developed by Markowitz (1952), Sharpe (1964) and Lintner (1965), explains stock returns based on the mean-variance framework. However, many researchers and practitioners have found that stock returns cannot be fully explained by the CAPM. This has led to further attempts to incorporate other aspects of stock into the CAPM. One of the most successful findings is the role of liquidity in asset pricing. Amihud and Mendelson (1986) were among the first to examine how the level of liquidity affects asset prices. Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) also examined the role of the second moments of liquidity in asset prices. Other research works have been done in this area. In our study, we seek to make a liquidity adjustment to the consumption-based capital asset pricing model (CCAPM) and show that the liquidity-adjusted CCAPM is a generalized model of Acharya and Pedersen (2005). This aspect of CAPM has not been investigated in my country. So, the research is of novelty here. The study aims to show that the expected stock return is determined by both consumption risk (CR) and liquidity risk (LR). The latter (i.e., LR) has been defined as the covariance between transaction costs and consumption growth. In this study, the effective trading cost index of Hasbrouck (2009) was estimated using Gibbs Bayesian method and roll’s model with the daily data of the stock closing price in Tehran Stock Exchange during 2009-2010. Then, by including the two types of Hasbrouck trading cost and the bid-ask spread as well as the liquidity risk in the traditional consumption-based capital asset pricing models, adjustments are made in these models. The purpose is to show that the liquidity-adjusted CCAPM provides a better fit for the cross-sectional expected returns across various liquidity-based portfolios, while the traditional CCAPM fails to capture the liquidity effect. This study also seeks to show that the liquidity adjusted CCAPM is robust enough to include industry portfolios The model considered in this study is a generalized version of Acharya and Pedersen (2005) and suggests a novel source of liquidity risk which is the covariance between transaction costs and consumption growth. The question to arise is ‘Can the three channels of liquidity risk of Acharya and Pedersen (2005) be captured by the covariance between transaction costs and consumption growth?’ We try to enrich the literature that highlights the pricing of various systematic risks associated with consumption by showing the positive relation between stock returns and the sensitivity of transaction costs to consumption growth. Reviewing the literature, it seems this area has worked in advanced countries (Lettau and Ludvigson, 2001; Bansal and Yaron, 2004; Parker and Julliard, 2005; Yogo, 2006; Jagannathan and Wang, 2007; Savov, 2011; Boguth and Kuehn, 2013), while, in some country such as Iran, it has not been tried yet. The focus of this research is on the liquidity adjustment to the consumption-based pricing models, as an area that has attracted little attention in the literature. The research will add to the literature on asset pricing models in Iran by answering the following questions: -  Is there a significant and positive relationship between the expected stock returns and the expected transaction costs? -  Does liquidity-adjusted CCAPM have the power to explain the expected stock returns of Tehran stock exchange? -  Compared to the traditional CCAPM, can liquidity-adjusted CCAPM better explain the cross-sectional expected returns across various liquidity-based portfolios? - Does the increase in stock liquidity lead to lower stock returns (and vice versa)?   Also, the main research purposes are as follows: -  Investigating the impact of companies' expected returns through a factor called the liquidity systematic risk - Presentation of liquidity-adjusted CCAPM which is consistent with Tehran Stock Exchange, as a practical model to determine risk and return - Considering the liquidity risk as a covariance between transaction costs and the total consumption growth -  Testing the explanatory power of the theory in determining the rate of the expected return in Tehran Stock Exchange and examining the existence of a significant relationship between risk and return

In this study, the liquidity-adjusted model is examined by means of a portfolio constructed on the basis of liquidity criteria and market characteristics. Based on the previous studies and the structure of the capital market in Iran, 20 portfolios were observed in the present study, and Liu and Strong’s (2008) approach was used to calculate the portfolio return. This model shows that the expected return on stocks is determined by the risk of consumption and the risk of liquidity. According to the study by Liu et al. (2016), the following two regressions are used to estimate the beta consumption and the beta liquidity in the present study: (1)   (2)  where  is the ratio of the residual of the returns in portfolio i to risk-free returns, ΔC refers to the growth in the consumption of non-durable goods and services, and  is the residual of the following regression:  (3)   where  is the transaction cost of the asset i in season t. Using the change in the transaction costs, , is because of the durability and stability of liquidity. In addition, beta liquidity can be directly estimated using transaction costs as follows:                     (4)   It should be noted that, in this study, Pooled GLS and Generalized Method of Moments (GMM) were used to estimate the regressions. However, considering the similar results yielded by these two methods, only the results of Pooled GLS are analyzed in this section. Comparative assessments between the liquidity-adjusted CCAPM model (6) and the traditional CCAPM (5) are performed using the following cross-sectional regressions:(5)  (6) where  refers to excess of portfolio p to risk-free returns in season t,  is the beta consumption,  is the transaction costs of portfolio p and  is the beta liquidity. Beta consumption is estimated through a time series regression of the excess return on consumption growth as in Equation (1). Beta liquidity is also estimated through the time series regression of liquidity changes on consumption growth as in Equation (2). Similar to the procedure applied in studies by Acharya and Pedersen (2005) and Lettau and Ludvigson (2001), beta consumption and beta liquidity are estimated over the entire sample period in this study.

In recent studies, transaction costs have been cited as a key measure of performance and a central role in financial markets. Also, transaction costs have been discussed in a non-liquidity way in many studies. However, transaction costs are considered as a determining factor in market liquidity and assets return. Given the importance of the role of transaction cost in financial markets, this study proposed an adjusted consumption-based capital asset pricing model and examined how this model is adjusted by transaction costs and liquidity risk. In this study, like Hasbrouck (2009), the researchers aimed at estimating the dynamic model of Roll (1984) in order to estimate effective transaction costs using daily ultimate prices of Tehran Stock Exchange. In other words, using Gibbs cost-effectiveness estimation, the initial analysis of the liquidity changes has been carried out, which is a new approach in the literature related to the Iranian capital market. In other words, using different proxies for transaction costs such as Hasbrouck’s (2009) effective transaction costs and estimated bid-ask spread based on the highest and lowest prices, liquidity-adjusted CCAPM is shown to be more appropriate for the expected cross-sectional returns through portfolios formed on the basis of liquidity criteria. However, the traditional CCAPM is unable to account for liquidity effects. Comparing the results of the adjusted CCAPM model with the traditional CCAPM model in explaining the stock return in the Iranian capital market shows that the explanatory power of the model in liquidity-adjusted CCAPM is 67% (when the transaction cost is based on CSspread) and 50% (when the transaction cost is based on cGibbs). But in the traditional CCAPM model, this explanatory power is 28% and 21% respectively. It means that the adjusted CCAPM can better explain the expected stock return in the Iranian capital market as compared to the traditional CCAPM. In this study, liquidity risk is expressed as the covariance between transaction costs and consumption growth. This is because the high sensitivity of transaction costs to fluctuations in consumption highlights the difficulty of converting investment funds into cash. The model presented in this study shows that neglecting the transaction costs and liquidity risk can lead to inaccurate estimation of the expected returns.

The results of this study show that traditional CCAPM underestimates the expected risk and return. This is a reason for the poor performance of the traditional model. In fact, the results of the study are in line with the results of previous studies. The consumption risk proposed in the model of this study has limited power to explain the expected stock return. But liquidity risk has a significantly positive effect on the expected stock return, so that, with no increase in liquidity risk, the expected stock return can increase. Furthermore, the analysis of the proposed model shows that the transaction costs have a significant effect on the expected stock return. In other words, this study theoretically and empirically supports the effective role of liquidity and transaction costs in asset pricing. According to the results, the adjusted CCAPM model is suggested as a more desirable model to estimate the returns in Tehran Stock Exchange. It is also suggested to evaluate other pricing models using transaction cost and liquidity risk in future research. This is because neglecting these two factors can lead to inaccurate estimates of expected returns. Moreover, the effect of other variables such as stock interest and growth on stock returns should be investigated.