What Drives the Low-Nominal-Price Return Premium in China s Stock Markets?

Transcription

1 What Drives the Low-Nominal-Price Return Premium in China s Stock Markets? Bing Zhang and Chung-Ying Yeh This version: Octorber 15, 2017 Abstract We examine whether nominal stock prices matter in cross section of stock returns and offer evidence of a positive low-nominal-price return premium in China s stock markets, which is in sharp contrast to that of US stock markets with a negative one. We explain the return premium by using Campbell and Vuolteenaho s (2004) two-beta theory in which market beta is decomposed by cash-flow beta and discount-rate beta, respectively. We employ Chen, Da, and Zhao s (2013) approach and estimate firms cash-flow and discount-rate betas in accordance with their nominal prices. Results show that cash-flow and discount-rate betas, respectively, earn a high and low premium. Low-priced stocks in China s (US) stock markets tend to have relatively high (low) cash-flow and low (high) discount-rate betas and, in turn, deliver high (low) expected returns. The low-nominal-price return turns out to be positive (negative). The high sensitive cash-flow risk to low-priced stocks in China s stock markets is associated with a low number of analyst forecasts and a low degree of price informativeness. Yeh is with Department of Finance, National Chung Hsing University. 145, Xingda Road, Taichung, Taiwan. cyyeh1@dragon.nchu.edu.tw. Zhang is with Department of Finance and insurance, Business School, Nanjing University, China ; Telephone: zhangbing@nju.edu.cn. We thank Yu-Lai Huang, Weimin Liu, Yanzhi Wang and participants in the IFABS Asia 2017 Ningbo Conference, National Central University and National Chung Hsing University for their helpful suggestions and comments.

2 What Drives the Low-Nominal-Price Return Premium in China s Stock Markets? Abstract We examine whether nominal stock prices matter in cross section of stock returns and offer evidence of a positive low-nominal-price return premium in China s stock markets, which is in sharp contrast to that of US stock markets with a negative one. We explain the return premium by using Campbell and Vuolteenaho s (2004) two-beta theory in which market beta is decomposed by cash-flow beta and discount-rate beta, respectively. We employ Chen, Da, and Zhao s (2013) approach and estimate firms cash-flow and discount-rate betas in accordance with their nominal prices. Results show that cash-flow and discount-rate betas, respectively, earn a high and low premium. Low-priced stocks in China s (US) stock markets tend to have relatively high (low) cash-flow and low (high) discount-rate betas and, in turn, deliver high (low) expected returns. The low-nominal-price return turns out to be positive (negative). The high sensitive cash-flow risk to low-priced stocks in China s stock markets is associated with a low number of analyst forecasts and a low degree of price informativeness. Keywords: China s stock markets; low-nominal-price return premium; cash-flow beta; discount-rate beta; analyst forecasts; price informativeness. JEL classification code: G12, G14.

3 1 Introduction Recent research has suggested that investors tend to have a perception about low-nominalprice firms (i.e. low-priced stocks) that will have greater upside potential and lottery-like characteristics. Individual investors have a preference for low-priced stocks (Schultz, 2000; Barberis and Huang, 2008; Kumar, 2009; Boyer, Mitton, and Vorkink, 2010; Boyer and Vorkink, 2014; Bali and Murray, 2014) and perform a nominal price illusion (Birru and Wang, 2016). Low-priced stocks can be overvalued and that may result in underperformance in subsequent months (Baker, Greenwood, and Wurgler, 2009; Singal and Tayal, 2015; Birru and Wang, 2015). Kumar (2009) advocates that investors tend to look for free or cheap bets as with lotteries and, as a result, overprice the lottery-like stocks. Baker, Greenwood, and Wurgler (2009) provide a catering theory of nominal stock price- that managers prefer to lower stock prices by splits since investors tend to overvalue low-nominal-price firms. Birru and Wang (2015 and 2016) find that investors overestimate the realized skewness of lowpriced stocks, especially for stock splits, and that results in an overvaluation. Stock prices will be corrected when the overpricing is dissipated. It turns out that nominal prices may have predictive power for future stock returns. It is evident that there is a negative lownominal-price return premium, defined by the return difference between the average return of low-nominal-price firms and that of high-nominal-price firms. 1 Interestingly, this casts doubt on the traditional finance theory that the nominal stock price should not matter in a frictionless and efficient market. We examine the low-nominal-price return premium in China stock markets in this study. China s stock markets that consist of Shanghai Stock Exchange (SHSE) and Shengzhen Stock Exchange (SZSE) have become one of most important stock exchanges in past decades. 2 1 In contrast, Baker, Greenwood, and Wurgler (2009) focus on valuation and, thus, define the low-nominalprice premium by the log difference between the average market-to-book ratio of low-nominal-price firms and that of high-nominal-price firms. 2 Since 1990, China s stock markets have experienced rapid growth. There are two major exchanges: Shanghai and Shenzhen stock exchanges in China. Starting with only eight stocks listed on Shanghai and six listed on Shenzhen, the total number of listed stocks on the two exchanges had increased to 311 by the end of 1995, to 1,060 by 2000 and to 2,349 by In 2004, the Shenzhen stock exchange additionally included the Small and Medium Enterprise (SME) board. Of late, the Growth Enterprise Market (SEM, 1

4 Research on China s stock markets also gets more attention in the recent finance literature (see for example, Allen, Qian, Shan, and Zhu, 2017; Brunnermeier, Sockin, and Xiong, 2017; Carpenter, Lu, and Whitelaw, 2017). Moreover, China s stock markets have some special features that are very different from major stock markets, including price limits, short-sale constraints, and the absence of futures and options contracts on stocks. These features substantially increase the arbitrage risk. As a result, it is expected that overvaluation in low-priced stocks could be more severe and the negative low-nominal-price return premium might be more pronounced in China s stock markets. We use the data sample of stocks traded in Shanghai and Shenzhen stock exchanges (Chinese A shares) during the period from January 1996 to December Surprisingly, the empirical results sharply contrast with our predictions and show that low-priced stocks deliver high realized average returns and, in turn, earn a positive low-nominal-price return premium in China s stock markets. We further tackle the potential discount-rate effect advocated by Birru and Wang (2015) from raw nominal stock prices and find that the major results remain unchanged. Our findings are robust even after considering various cross-sectional variations (such as firm size, book-to-market ratio, illiquidity, idiosyncratic volatility, downside beta, coskewness, momentum, and lottery demand), different sample periods, and the January effect. To examine the low-nominal-price return premium, we first sort all stocks based on their nominal price levels and allocate them into ten groups. Both equal and value-weighted portfolio returns are calculated and the portfolios are annually rebalanced. 3 We then compute the returns on the long-short portfolio that take a long position in the portfolio of the lowest (nominal price) decile and a short position in the portfolio of highest (nominal price) decile. We compute the mean return in excess of the risk-free rate, the CAPM alpha, and the Fama-French alpha to assess the performance. We find that low-priced stocks can deliver high realized average returns and earn a positive low-nominal-price return premium in China s Nasdaq) was added in In sum, the number of stocks have substantially increased in China s stock markets in recent years (Chen et al., 2015). 3 We also calculate the portfolio returns that are quarterly rebalanced. The main findings remain unchanged. The empirical results based on quarterly rebalance are reported in the internet appendix. 2

5 China s stock markets. Moreover, we eliminate the discount-rate effect advocated by Birru and Wang (2015) by using a regressions approach and, in turn, sort all stocks based on the fitted stock prices. The main findings continue to hold under this univariate (one-pass) sort. Moreover, since stocks perform cross-sectional variations, like firm size, illiquidity, idiosyncratic volatility and etc., in nominal prices, we need to ease the concern that the positive low-nominal-price return premium may be associated with these firm characteristics and risk variables. We further conduct the bivariate (two-pass) sorts to examine the low-nominalprice return premium. Results show that our major findings remain unchanged. Finally, we perform the time series regression analysis that regresses the long-short portfolio returns that takes a long position in the cheapest stocks and a short position in the most expensive stocks on firm characteristics and risk variables in conjunction with the Fama-French three factors. Results continue to show that the low-nominal-price return premium is significantly positive. For robustness checks, we consider the subsample period when the China s security law was officially enacted (from January 2000 to December 2015) and the data sample without observations of January. Our findings remain unchanged. We employ the two-beta theory proposed by Campbell and Vuolteenaho (2004) to explain the low-nominal-price return premium. This theory, based on the traditional intertemporal CAPM model, has been used to explain several asset pricing anomalies in recent literaturesee for example Campbell and Vuolteenaho, 2004; Campbell, Polk, and Vuolteenaho, 2010; Miao, The Campbell and Vuolteenaho s (2004) two-beta theory decomposes the market beta of a firm into two components associated with cash-flow risk and discount-rate risk, respectively. The cash-flow beta reflects the price movement caused by the changes in market expectation about corporate cash flows. In effect, the cash-flow beta gauges the change in the permanent component of the stock price. The discount-rate beta corresponds to the change in the temporary component of the stock price caused by the movements in market expected returns. Changes in market expected returns might be caused by different driving forces, such as the variation in macroeconomic conditions or the change in investors views. Importantly, Campbell and Vuolteenaho (2004) demonstrate that the required return on a firm is determined primarily by its cash-flow beta rather than by its market beta due to 3

6 the fact that the cash-flow shocks earn a high premium whereas the discount-rate shocks earn an insignificant or low premium. As a result, we can hypothesize that low-priced stocks in China s (US) stock markets may have high (low) cash-flow and low (high) discount-rate betas. Therefore, low-priced stocks may deliver high (low) cross-sectional returns. Specifically, a firm s cash-flow and discount-rate betas are the covariances of its stock returns with the market-level cash-flow and discount-rate news divided by the variance of market returns. In this study, we utilize the implied cost of capital (ICC) approach devised by Chen, Da, and Zhao (2013) to calculate cash-flow and discount-rate news. We can take advantage of the direct cash-flow forecasts implied by this approach to obtain forward news measures. We start by calculating firm-specific cash-flow and discount-rate news. We back out the firm-specific ICC for each firm and at each time point under a given stock price and use it to calculate news. The firm s cash-flow news is defined by the price change when ICC is fixed and the discount-rate news is defined by the price change when the cash-flow forecast is fixed. We firm-by-firm calculate monthly cash-flow and discount-rate betas based on a three-year rolling window. We then aggregate the firm-specific cash-flow and discount-rate news across firms to obtain their corresponding market-level cash-flow and discount-rate news, respectively. Results show that the cross-sectional variation in nominal stock prices will be mostly reflected in the variations in cash-flow and discount-rate betas, and that low-priced stocks have higher cash-flow betas (lower discount-rate betas) than high-priced stocks in China s stock markets. This finding is robust even after controlling for firm characteristics and risk measures and under various forward horizons in calculating cash-flow and discountrate betas. We then access the risk prices implied by cash-flow and discount-rate betas. We perform cross-sectional regressions for the portfolios based on one- and two-pass sorts and the corresponding two betas and find that cash-flow beta earns a high premium and dominates discount-rate beta that earns a low premium. As a result, the two-beta model can provide a partial explanation to higher average returns for low-priced stocks in China s stock markets and explain at least 50% cross-sectional variation in expected returns. We proceed to compare the low-nominal-price return premium between US and Chinese 4

7 stock markets and further examine whether the two-beta model can explain the return premium for US stocks. We follow Birru and Wang (2015) and Singal and Tayal (2015) and use the data sample of stocks listed in NYSE, Amex, and NASDAQ. Results show that low-priced stocks deliver low realized average returns and, in turn, earn a negative low-nominal-price return premium. Furthermore, low-priced stocks have lower cash-flow betas (higher discount-rate betas) than high-priced stocks. As a result, the two-beta model continues to provide the explanation for the low-nominal-price return premium in US stock markets. Finally, we offer two possible explanations for the high sensitive cash-flow risk in lowpriced stocks in China s stock markets. We find that low-priced stocks have a low number of analyst earning forecasts and a low level of price informativeness proposed by Bai, Philippon, and Savov (2016). When a firm is given less attention by financial analysts, the exposure to its cash-flow risk might be high to the investors. Da and Warachak (2009) link a firm s analyst earning forecasts with its cash-flow beta and use this to explain cross section of stock returns. In addition, When a firm has a low degree of price efficiency, this increases the exposure to its cash-flow risk. Bai, Philippon, and Savov (2016) suggest that price could be a stronger predictor to cash flows. This study contributes to the literature in several ways. First, we demonstrate that nominal stock prices indeed matter in cross section of stock returns in China s stock markets. We find that low-priced stocks deliver high realized average returns and, in turn, earn a positive low-nominal-price return premium. This finding extends the asset pricing studies based on China s stock markets. Hilliard and Zhang (2015) find the size and price-to-book effects in China s stock market. Chen et al. (2015) investigate the size and value factors in the cross section of stock returns in China s stock markets. They show a substantial size effect but an insignificant value effect. Second, we compare the low-nominal-price return premium between the US and Chinese stock markets and employ the two-beta model to explain the difference in return premium. We find that the variation in cash-flow betas can mainly explain the the cross-sectional variation in nominal stock prices and the difference between US and Chinese stock markets. 5

8 Since cash-flow and discount-rate betas, respectively, earn a high and low risk premium, low-priced stocks in China s (US) stock markets have relatively high (low) cash-flow and low (high) discount-rate betas and, in turn, deliver high (low) expected returns. The lownominal-price return premium turns out to be positive (negative). Third, we show that the cross-sectional variation in nominal prices may hinge on the analyst attention and price informativeness. It is evident that, in contrast to common perception, stock prices in China are strongly associated with firm fundamentals. As a matter of fact, this finding is strongly consistent with that of Carpenter, Lu, and Whitelaw (2017). Furthermore, our findings complement to the current research pertaining to China s stock markets in finance literature (i.e. Allen, Qian, Shan, and Zhu, 2017; Brunnermeier, Sockin, and Xiong, 2017) that although Chinese firms may not have sufficient investment efficiency and information efficiency, stock prices in China s stock markets are still able to reveal some fundamental information about firms. The remainder of this study is organized as follows. Section 2 describes the data sample and examines the low-nominal-price return premium in China s stock markets. Section 3 conducts robustness checks. Section 4 introduces the two-beta model and the empirical approaches for the estimation of cash-flow and discount-rate betas, and the cross-sectional regressions. Section 5 reports the empirical results. Section 6 has further discussions. Finally, section 7 summarizes the findings and concludes the paper. 2 Low-priced stock premia and portfolio analysis 2.1 Data and variables The stocks traded on the Shanghai and Shenzhen Stock Exchanges are obtained from Wind Info financial database, which is a data analytics platform for stocks traded on China s markets. In China, Wind Info serves more than 90% of financial institutions, including hedge funds, asset management firms, securities and insurance companies, banks, research institutions, and government regulatory bodies, and 70% of Qualified Foreign Institutional Investors (QFII) overseas. We acquire stock prices, trading volumes, shares outstanding, 6

9 financial statement information of Chinese companies from this database. The data sample period is from January 1996 to December Following the standard convention, financial and utility firms are excluded. We also delete ST stocks. 4 In sum, we include 2651 stocks that cover approximately 95% of the listing companies in Chinese A share market in our data sample. 5 In addition, we obtained Fama-French factors MKT, SMB, and HML from RESSET financial research database, which is a data analytics platform specializing in financial databases and related software development investment research. Several firm characteristics and risk measures are calculated on a monthly basis, such as firm size (SIZE), book-to-market ratio (BM), illiquidity (ILLIQ ), idiosyncratic volatility (IV OL), coskewness (COSKEW ), downside risk (DRISK), and momentum (M OM). SIZE is the log market capitalization of a stock at the month t. BM is the log of the firm s book-to-market ratio. We use the proxy devised by Amihud (2002) to gauge ILLIQ, which is calculated by the absolute daily return divided by the daily dollar trading volume and averaged across trading days in month t. We regard IV OL as the standard deviation of the residuals from the time series regression of the Fama-French three-factor model by using daily returns of all trading days in month t. COSKEW is computed by the regression coefficient estimate associated with the squared excess market return from a regression of daily excess returns on the excess market returns and the excess market returns squared. DRISK is calculated as the beta coefficient of a market model by using only the trading days for which the market return was below the average daily market return during the past year. MOM in month t is defined as a stock s past 11-month return from months t 11 to t 1. The details of the risk measure construction are summarized in Table A1 of the Appendix. Panel A of Table 1 reports the summary statistics of these variables. 6 Results show that the monthly average of log market capitalization is approximately The stocks that have been labelled Special Treatment are called ST shares or stocks. The special treatment includes (i) the price limit of ST share quotation is 5%; (ii) the firm s interim report shall be audited; (iii) ST is added before the original stock name. Exchanges have the privilege to give special treatment to the listed stocks with abnormal financial conditions, such as negative net profits in two consecutive fiscal years, no auditing report and etc. 5 We also don t include an observation with a stock price whose stock prices are less than one dollar. 6 We winsorize each variable by using the 1st and 99th percentiles of the distribution to reduce the impact of outliers. 7

10 with a median value of The monthly average of idiosyncratic volatility is 2% per month. All variables are positively skewed. Negative coskewness represents a higher probability of extreme negative returns in the stock over market returns. Positive downside beta poses a significant downside risk. The large dispersion between maximum and minimum in each variable suggests a wide range of cross-sectional variation. We examine the characteristics and risk measures for stocks with different nominal stock price levels. We sort all stocks into ten groups based on their nominal stock prices at the end of fiscal year t 1. Sample averages of firm characteristics and risk measures of stocks are calculated for each group. Decile portfolios are annually rebalanced. 7 Panel B of Table 1 reports the results. 1(Low) ( 10(High) ) represents the lowest (highest) decile. prices. Results show that stocks perform a substantial cross-sectional variation in nominal stock For example, low-priced stocks, on average, tend to have smaller firm size than that of high-priced stocks. Moreover, in comparison with high-priced stocks, low-priced stocks are less liquid, have smaller idiosyncratic volatility, have higher book-to-market ratios, downside risk and coskewness, and have poor past performance (smaller momentum). Most of our findings are consistent with those of Birru and Wang (2016) except for the patterns pertaining to idiosyncratic volatility and book-to-market ratios. In accordance with the US stock data sample, Birru and Wang (2016) find low-priced stocks have larger volatility and lower book-to-market ratios. 8 One possible explanation about the difference is that some large state-owned enterprises tend to have low stock prices and, thus, have been allocated to the group with low nominal stock prices in our data sample. 2.2 Univariate portfolio sorts We first examine the return premium between low-priced and high-priced stocks by conducting the one-pass portfolio sort. At the end of December in year t, we sort all stocks 7 For robustness checks, we also monthly rebalance all portfolios based on stock prices at the end of month t 1. The main findings based on annually rebalanced portfolios continue to hold. The results are reported in internet appendix. 8 For robustness of the cross-sectional variation, we also sorted all stocks by using the fitted stock pricesthat eased the concern advocated by Birru and Wang (2015). Results show that the main findings remain unchanged. 8

11 traded on the Shanghai Stock Exchange (SSE) and Shenzhen Stock Exchange (SZSE) based on nominal prices levels, and then allocate them into ten groups. Monthly portfolio returns are then calculated from January of year t + 1 through December of year t + 1. The decile portfolios are both valued and equal-weighted. We compute the mean return in excess of the three-month Treasury-bill rate and the intercepts (alphas) of the CAPM and the Fama-French three-factor model for each portfolio formed on the nominal price level. The estimated intercepts (alphas), in effect, capture the average monthly abnormal returns for each portfolio. Table 2 reports the results. 1(Low) ( 10(High) ) represents the lowest (highest) decile portfolio and L H corresponds to the long-short portfolio between the lowest and highest deciles. Exclude 5% denotes the long-short portfolio between the lowest and highest deciles where the 5% most extreme data in both tails have been eliminated. T statistics based on Newey-West heteroskedasticity-consistent standard errors are calculated and reported in the parentheses. Results show that stocks with low nominal prices earn high average realized returns. For the equal-weighted portfolios, the monthly mean excess return for the low-priced stocks (the lowest decile portfolio 1(Low) ) reaches 1.30% and that for the high-priced stocks (the highest decile portfolio 10(High) ) reduces to the value of 0.22%, exhibiting a negative relation with the level of nominal stock prices. The low-minus-high ( L H ) long-short portfolio earns an average return of 1.09% per month (13.08% per annum) and that reaches 1.13% (13.56% per annum) even after excluding the 5% most extreme data in both tails. The average returns for the long-short portfolios are all economically and statistically significant at the five-percent level. Moreover, the alphas of the CAPM and the Fama-French threefactor model for the long-short portfolios remain positively significant. Our findings suggest a negative relationship between the level of nominal stock prices and average realized returns. Low-priced stocks earn higher average realized returns than high-priced stocks. We additionally conduct tests by using value-weighted portfolios. Results show that the average returns, and the alphas of the CAPM and the Fama-French three-factor model for long-short portfolios, are all positively significant. Although large firms may affect value- 9

12 weighted returns and obscure the nominal price effect, the results remain quantitatively similar to those based on equal-weighted portfolios and do not change our conclusions. The cross-sectional relationship between nominal prices and expected returns can be confounded by the mechanical discount-rate effect (see Birru and Wang, 2015) and using the raw nominal price as a sorting variable will cause an underestimation of the nominal return premium. To circumvent this issue, we apply their approach and use the fitted prices from regressions on stock prices. Specifically, we first perform the following regression P rice i,t = β 0 + β 1 P rice i,t+1 + β 2 P rice i,t+2 + e i,t. (1) This regression can remove the influence from future price levels. We regard the sum of intercept ˆβ 0 and residual ê i,t as the adjusted nominal price P rice + it. We then perform the following regression P rice + i,t = γ 0 + γ 1 BP S i,t + γ 2 AP S i,t + u i,t (2) where BP S is the book value per share, and AP S is the total assets per share. The fitted price P rice it is the sum of intercept ˆγ 0 and the residual û i,t. The fitted value circumvents the mechanical issue between raw nominal price and future returns. As a result, we conduct the one-pass sort by using the fitted stock prices. Table 3 reports the results. It can be seen that our main findings continue to hold. In comparison with the values reported in Table 2, the values of the return premium for the low-priced stocks by using the adjusted prices are quantitatively larger than those based on raw nominal stock prices. Low-priced stocks earn higher average realized returns than high-priced stocks even after considering the mechanical discount-rate effect. In short, we find that stocks with low nominal prices can earn high average realized returns, revealing a negative relation with the level of nominal stock prices. This finding is robust even though we use the fitted stock prices. The long-short portfolio that takes a long position in low-priced stocks and a short position in high-priced stocks can earn positive returns. 10

13 2.3 Bivariate portfolio sorts Since stocks perform substantial cross-sectional variations, like firm size, illiquidity or idiosyncratic volatility, in nominal prices, we need to ease the concern that low-priced stocks delivering high average realized returns may be associated with these firm characteristics and risk variables. As a result, we conduct two-pass sorts to further control those firm characteristics and risk variables in examining the cross-sectional relationship between nominal prices and future returns. At the end of year t, we sort all stocks into five groups based on one of the control variables (i.e. firm characteristics and risk measures). For each group, we then sort all stocks within the group into ten decile portfolios based on the level of nominal stock prices. Monthly equal-weighted and value-weighted portfolio returns are calculated from January of year t + 1 through December of year t + 1; as a result, fifty (5 10) portfolio returns are obtained in this two-pass sort for each month of year t + 1. We compute the mean excess return and the alphas of the CAPM and the Fama-French three-factor model for each portfolio to assess the return premium from nominal prices. Controlling for size First, we control for firm size in a two-pass sort. Low-priced (high-priced) stocks tend to have a smaller (larger) firm size in accordance with the evidence from Table 1. Banz (1981) and Fama and French (1992, 1993) suggest that small-cap stocks deliver high average realized returns. We therefore control for firm size to ease the concern about the size effect in the low-nominal-price return premium. Table 4 reports the mean excess return and the alphas of the CAPM and the Fama- French three-factor model for the portfolios formed on firm size and nominal stock price. The portfolios can be summarized as a squared matrix with firm size from low to high (1:lowest to 5:highest) at the vertical axis and the level of nominal price from low to high (1:lowest to 10:highest) at the horizontal axis. L H represents the long-short portfolio that takes a long position in the lowest nominal price decile portfolio and a short position in the highest nominal price decile portfolio. We report the mean excess return and the alphas of 11

14 the CAPM and the Fama-French three-factor model on the portfolios of the squared matrix. Panels A, B, and C (D, E, and F) of Table 4 are based on equal-weighted (value-weighted) portfolios. T statistics based on Newey-West heteroskedasticity-consistent standard errors are reported in the parentheses. Results show that holding the cheapest stocks (the lowest decile) and shorting the most expensive stocks (the highest decile) delivers a positive return even after controlling for firm size. As shown in column L H, the mean excess returns and the alphas of the CAPM and the Fama-French model across firm size quintiles between the cheapest stocks and the most expensive stocks are all positive and statistically and economically significant for equaland value-weighted portfolios. The mean excess returns for long-short portfolios ranges from 1.00% to 1.62% per month (12.00% to 19.44% per annum) for equal-weighted portfolios. The alphas of the CAPM and the Fama-French model also have substantial temporal variations. In particular, the alpha of the Fama-French model has a high of 1.72% per month (20.64% per annum) and a low of 1.14% per month (13.68% per annum). The smallest-cap stocks tend to have the largest (mean excess and abnormal) returns for the long-short portfolios. Moreover, small-cap stocks have larger returns than large-cap stocks across nominal price and the corresponding size premiums (returns on small-cap over returns on large-cap) are all positively significant. Interestingly, the low-priced stocks tend to have the larger size premium. For example, the size premium in terms of the alpha of the Fama-French model in the lowest priced decile portfolio is 1.35%(= 1.97% 0.62%) per month (16.20% per annum) whereas that in the highest priced decile portfolio is 1.16%(= 0.24% %) per month (13.92% per annum). Chen et al. (2015) also suggest a size premium of 0.85% per month in China s stock market. The discrepancy in size premium may result from the difference in portfolio formations. The above findings continue to hold when we use value-weighted portfolios in the two-pass sort. The return from holding the cheapest stocks and shorting the most expensive stocks remains significantly positive but the magnitude of the low-nominal-price return premium is smaller than that based on equal-weighted portfolios. 12

15 Controlling for illiquidity Stocks with low nominal prices tend to be less liquid than those with high nominal prices. In fact, illiquidity can deliver a risk premium for risky assets (see for example, Amihud, 2002; Pastor and Stambaugh, 2003; Lin, Wang, and Wu, 2011; Hu, Pan, and Wang, 2013; Amihud et al, 2015). In order to ease the concern about illiquidity, we control for it in the two-pass sort. Table 5 reports the mean excess return and alphas of the CAPM and the Fama-French three-factor model for the portfolios formed on illiquidity and nominal stock price. The portfolios can be summarized as a squared matrix with illiquidity from low to high (1:lowest to 5:highest) at the vertical axis and the level of nominal price from low to high (1:lowest to 10:highest) at the horizontal axis. The definitions of columns and test statistics are the same as those of Table 4. Results show that the long-short portfolios that take a long position in the cheapest stocks and a short position in the most expensive stocks earn positive returns even after controlling for illiquidity. The column L H suggest that the mean excess returns and alphas of the CAPM and the Fama-French model across illiquidity quintiles between the cheapest stocks and the most expensive stocks are positive and statistically significant for both equal- and value-weighted portfolios. For example, the alpha of the Fama-French model has a high of 1.73% per month (20.76% per annum) and a low of 1.31% per month (15.72% per annum) for the equal-weighted portfolios. They are economically significant as well. Moreover, the mean excess returns and alphas of the CAPM and the Fama-French model for the long-short portfolios tend to increase with illiquidity. In addition, stocks with high illiquidity have higher returns than those with low illiquidity. For example, the liquidity premium calculated by the alpha of the Fama-French model has a high of 1.12%(= 1.81% 0.69%) per month in the cheapest stocks and a low of 0.84%(= 0.16% %) per month in the most expensive stocks. All liquidity premiums across nominal prices are all economically and statistically significant. These results continue to hold in accordance with mean excess returns and the CAPM alphas. 13

16 Amihud et al. (2015) examine the illiquidity premium in stock markets across 45 countries. They find that stock illiquidity is priced in major international equity markets. The most illiquid stocks have a significantly higher risk-adjusted return than that of the most liquid stocks. The risk-adjusted monthly illiquidity premium ranges from 0.45% to 0.82% per month. As shown, China s stock markets have a higher illiquidity premium. In Table 5, the return in the most illiquid portfolio is significantly higher than that in the most liquid portfolio in all deciles. Moreover, in comparison with the results reported in Amihud et al. (2015), China stock markets tend to have a greater liquidity premium. The above findings continue to hold in accordance with value-weighted portfolios. The return from holding the cheapest stocks and shorting the most expensive stocks remains significantly positive but the corresponding magnitude is smaller than that based on equalweighted portfolios. Controlling for idiosyncratic volatility In comparison with high-priced stocks, low-priced stocks have smaller idiosyncratic volatility. Ang, Hodrick, Xing, and Zhang (2006, 2009) find that stocks with low idiosyncratic volatility have high average returns. Moreover, Drew, Naughton, and Veeraraghavan (2004) find that the small-cap and low idiosyncratic volatility stocks have higher returns than largecap and high idiosyncratic-volatility firms on the Shanghai Stock Exchange. It turns out to be that the effect on nominal stock prices and idiosyncratic volatility can be confounded. In order to ease the concern about idiosyncratic volatility, we control for it in the two-pass sort. Table 6 reports the mean excess returns and the alphas of the CAPM and the Fama- French three-factor model for the portfolios formed on idiosyncratic volatility and nominal stock price. The portfolios can be summarized as a squared matrix with the level of idiosyncratic volatility from low to high (1:lowest to 5:highest) at the vertical axis and the level of nominal price from low to high (1:lowest to 10:highest) at the horizontal axis. Results show that the long-short portfolios that take a long position in the cheapest stocks and a short position in the most expensive stocks earn positive returns even after controlling for idiosyncratic volatility. Moreover, the mean excess returns and alphas of the CAPM 14

17 and the Fama-French model for the long-short portfolios tend to decrease with idiosyncratic volatility. Stocks with low idiosyncratic volatility outperform those with high idiosyncratic volatility portfolios. For example, the premium pertaining to idiosyncratic volatility calculated by the alpha of the Fama-French model has a high of 0.32%(= 1.12% 0.80%) per month in the cheapest stocks and a low of 0.12%(= 0.72% %) per month in the most expensive stocks. All premiums across nominal prices are all economically and statistically significant. Controlling for downside risk, coskewness, and momentum Stocks with low nominal prices tend to have higher downside risks and coskewness than those with high nominal prices. In the asset pricing literature, downside risk and coskewness are able to substantially affect the cross section of stock returns. For example, Roy (1952) and Markowitz (1959), and Bawa and Lindenberg (1977) have shown that the effect of downside risk are material in stock returns. Ang et al. (2002) find that the downside risk can explain cross-sectional stock returns in the US market and stock returns increase with greater downside beta. In addition, Kraus and Litzenberger (1976) find that stocks with high skewness risk can earn higher returns. Harvey and Siddique (2000) find that stocks with greater negative coskewness deliver a higher expected return. In order to ease these concerns, we control for them when we conduct the two-pass sorts. Tables 7 and 8 report the results pertaining to downside risk and coskewness. Results show that the long-short portfolios that take a long position in the cheapest stocks and a short position in the most expensive stocks earn positive returns after controlling for downside risk and coskewness, respectively. Moreover, the mean excess returns and alphas of the CAPM and the Fama-French model for the long-short portfolios are statistically significant in most cases. For example, according to the equal-weighted portfolio, the Fama- French alphas range from 1.55% to 1.99% per month when controlling for downside risk and from 1.28% to 2.16% when controlling for coskewness. The results remain unchanged when we use the value-weighted portfolio returns. Interestingly, stocks with a high downside risk cannot consistently outperform stocks with 15

18 a low downside risk. Except for the cheapest firms, stocks with low coskewness tend to have higher returns than those with high coskewness. For example, according to equal-weighted portfolio, the Fama-French alphas for the most expensive stocks in the lowest coskewness quintile is 0.24% whereas those in the highest coskewness quintile is 0.56%, which is two times smaller than that in the lowest coskewness quintile. Jegadeesh and Titman (1993) and Carhart (1997) suggest that the momentum factor is an important pricing factor in addition to the Fama-French three factors. Inclusion of the momentum factor can successfully explain asset pricing anomalies in the literature. We control for the mid-term momentum in the two-pass sort. Table 9 reports the results. Results show that the long-short portfolios that take a long position in the cheapest stocks and a short position in the most expensive stocks earn positive returns after controlling for mid-term momentum. According to the equal-weighted portfolio, the Fama-French alphas for the long-short portfolios range from 0.38% to 1.90%. Interestingly, stocks in the lowest momentum quintile have higher returns than those in the highest momentum quintile. This highlights a reversal feature past losers become winners in the future. In fact, Wang and Zhao (2001) examine the momentum and contrarian strategies in China s stock market, and find that the former effect is relatively weak and, in contrast, the reversal effect is more pronounced in the market. Our finding is also consistent with Wang and Zhao (2001). In short, we find that stocks with a low nominal price earn high average realized returns and that the low-nominal-price return premium is material and robust after controlling for various cross-sectional variations. 2.4 Regression analysis We further examine the low-nominal-price return premium via regression analysis. We perform time series regressions by regressing the long-short portfolios returns that take a long position in the cheapest stocks (lowest price-level decile) and a short position in the most expensive stocks (highest price-level decile) on the Fama-French three factors (F t ) and aggregate risk measures pertaining to illiquidity (ILLIQ), idiosyncratic volatility (IV OL), downside beta (DRISK), coskewness (COSKEW ), mid-term momentum (M OM), and 16

19 lottery demand (M AX). Specifically, it can be expressed as R low,t R high,t = α + b F t + γ 1 ILLIQ t + γ 2 IV OL t + γ 3 DRISK t (3) + γ 4 COSKEW t + γ 5 MOM t + γ 6 MAX t + e t where R low,t R high,t is the long-short portfolio return in month t. Note that the aggregate risk measures are calculated by aggregating firm-specific risk measures across firms. The estimate of α is expected to be significantly positive if the low-nominal-price return premium is positive. Table 10 reports the regression results. T statistics are in the parentheses. Columns (1) to (6) report the regression results when a specific risk measure is included and column (7) corresponds to the model with six aggregate risk measures. 9 Results show that the estimates of α in regressions are all significantly positive. This is consistent with the finding of the positive low-nominal-price return premium. The size of low-nominal-price return premium ranges between 0.9% and 2.8% per month, which is also consistent with the magnitude of low-nominal-price return premium reported in tables 2 to 9. As shown in Table 10, the coefficient estimate of ILLIQ is 3.18 with a t-statistic of 2.36 and becomes 5.36 with a t-statistic of 3.23 when all risk measures are included. Liquidity risk serves as an important risk factor in China s stock markets. However, the coefficient estimates associated with other risk measures, such as IV OL, MOM, COSKEW and etc., are not significant in column (7) with all risk measures although they are statistically significant when they are individually considered in columns (1) to (6). In short, we find that stocks with low nominal prices earn high average realized returns and the low-nominal-price return premium is material and robust even after considering various cross-sectional variations. 9 For brevity, we do not report coefficient estimates of the Fama-French three factors. 17

20 3 Robustness checks 3.1 Robustness test for different time period As shown in Table 2, low-priced stocks have higher returns than high-priced stocks during the sample period from January 1996 to December 2015, suggesting a positive low-nominalprice return premium. For robustness checks, we examine the positive low-nominal-price return premium by using the sample period from January 2000 and December This is because the securities law of China was officially enacted in 1999 and it established a centralized monitor system and new phase in China s stock markets. It is predicted that the stock prices of low-priced stocks tend to be manipulated before If so, the low-priced stock returns may be affected by it. Table 11 reports the results of univariate portfolio sorts for both equal and value-weighted portfolios by using data sample since January We compute the mean return in excess of the three-month Treasury-bill rate and the intercepts (alphas) of the CAPM and the Fama- French three-factor model for each portfolio formed on the nominal price level. 1(Low) ( 10(High) ) represents the lowest (highest) decile portfolio and L H corresponds to the long-short portfolio between the lowest and highest deciles. Exclude 5% denotes the long-short portfolio between the lowest and highest deciles where the 5% most extreme data in both tails have been eliminated. T statistics based on Newey-West heteroskedasticityconsistent standard errors are calculated and reported in the parentheses. Results show that, for equal-weighted portfolios, the differences in returns between the cheapest stocks and the most expensive stocks reaches 0.86% with a Newey-West adjusted t-statistic of 1.73, which becomes 1.25% when the extreme 5% extreme values are dropped. Meanwhile, the CAPM and three-factor alphas are 1.40% and 1.12%, respectively. The main results continue to hold for the value-weighted portfolios. Thus, the low-nominal-price return premium is not affected by the early data sample. 18

21 3.2 Robustness test considering the January effect The January effect, also known as the turn-of-the-year effect, refers to the phenomenon in which stocks, especially low-priced stocks, tend to have unusually higher returns in January than in other months. Givoly and Ovadia (1983), and Reinganum (1983) show that lowpriced stocks have abnormally higher volumes in December and abnormally higher returns in January. Bhardwaj and Brooks (1992) also suggest that the January effect comes primarily from the low-priced stocks rather than the small-cap ones. Moreover, Hwang and Lu (2008) show that the returns of penny stocks in excess of that of non-penny stocks are mainly attributable to the January effect. The return difference reaches 11% in January and becomes -0.4% returns in all other months of the year. Therefore, the January effect and the positive low-nominal-price return premium may be confounded. In order to ease this concern, we examine the positive low-nominal-price return premium by using the data sample for non- January observations. Table 12 reports the results of univariate portfolio sorts based on (i) only January observations and (ii) non-january observations, respectively. Both equal- and value-weighted portfolios are considered. We compute the mean excess returns and the intercepts (alphas) of the CAPM and the Fama-French three-factor model for each portfolio formed on the nominal price level. 1(Low) ( 10(High) ) represents the lowest (highest) decile portfolio and L H corresponds to the long-short portfolio between the lowest and highest deciles. Results show that, for the equal-weighted portfolios, the difference in mean excess return on the cheapest stocks and the most expensive stocks is 3.74% when we only use January observations and it becomes 0.95% when we use non-january observations. Moreover, in the lowest price level decile, we find that the excess return for the cheapest stocks is 3.37% per month when we only use January observations, whereas that declines to 1.31% when we use non-january observations. The finding remains unchanged when we use the CAPM and three-factor alphas. In short, the positive low-nominal-price return premium continues to hold even after considering the January effect. 19

22 4 Explaining the low-nominal-price return premium 4.1 Beta decomposition Since a stock price is the discounted sum of expected future cash flows, the unexpected price movements can be attributed to the fact that investors update expectations of cash flows and discount rates. Campbell and Shiller (1998) suggest a corresponding decomposition of stock returns r t+1 E t [r t+1 ] = N CF,t+1 N DR,t+1. (4) The first component represents the unexpected shocks to a firm s cash-flow growth N CF,t+1 = (E t+1 E t ) ρ j d t+j+1, (5) and the second component corresponds to the unexpected shocks to a firm s discount rates N DR,t+1 = (E t+1 E t ) ρ j r t+j+1, (6) where (E t+1 E t ) denotes the unexpected shock or news and ρ is a log-linearization constant. As shown, a positive shock to a firm s cash flows raises today s stock price and then increases the unexpected return. In contrast, a positive shock to future expected returns increases current firm s required return and reduces the unexpected return. With a given stream of cash flows, high future returns result from future price appreciation from a lower current price. Campbell and Vuolteenaho (2004) break the market return into the market-level cash-flow and (negative of) discount-rate shocks, N M,CF,t+1 and N M,DR,t+1, and measure covariances Cov(r i,t+1, N M,CF,t+1 ) and Cov(r i,t+1, N M,DR,t+1 ). They further use them to define cashflow and discount-rate betas, and j=0 j=1 β i,cf = Cov(r i,t+1, N M,CF,t+1 ), (7) V ar(r M,t+1 ) β i,dr = Cov(r i,t+1, N M,DR,t+1 ). (8) V ar(r M,t+1 ) Importantly, these two betas constitute the CAPM market beta β i,m = β i,cf + β i,dr. 20

23 4.2 Measuring cash-flow and discount-rate news We utilize the ICC approach devised by Chen, Da, and Zhao (2013) to calculate cash-flow and discount-rate news. The equity price of a firm is assumed to be evaluated by the present value of future cash flows and a terminal value. Specifically, it is expressed as follows: T F E t+k (1 b t+k ) P t = + F E t+t +1 (1 + q t ) k q t (1 + q t ) = T f(ct, q t ) (9) k=1 where P t is the stock price, F E t+k is the earnings forecast k years ahead, b t+k is the plowback rate, and q t is the ICC. T is a truncated year and set to 15 in the extant literature, such as in Pastor, Sinha, and Swaninathan (2008) and Chen, Da, and Zhao (2013). In effect, a stock price at time t can be regarded as a nonlinear function of a vector of predicted cash flows, c t, as well as an ICC, q t, at time t. A stock price variation between t and t + h is able to be decomposed by cash-flow news, which is defined by N CF,h = ( ) f(c t+h, q t+h ) f(c t, q t+h ) + f(ct+h, q t ) f(c t, q t ) /2, (10) P t P t and discount-rate news, which is defined by ( ) f(c t, q t+h ) f(c t, q t ) N DR,h = + f(ct+h, q t+h ) f(c t+h, q t ) /2. (11) P t P t h is the forward horizon (in terms of quarters). Specifically, cash-flow news, N CF,h (discountrate, N DR,h ), is driven by the change in cash flows (discount rates) forecasts between t and t + h. It is worth noting that these news is forward-looking and hinge on firm s fundamental. We firm-by-firm calculate cash-flow discount-rate news at each time point and aggregate them across firms to obtain the market-level cash-flow and discount-rate news, N M,CF,t and N M,DR,t. We then use them to compute the cash-flow and discount-rate betas by using equations (7) and (8). 4.3 Cross-sectional regressions We examine whether cash-flow beta has a substantially higher risk price than that of discount-rate beta. In equilibrium, the conditional two-beta model, the expected stock 21