External Financing, Misvaluation Timing, and Stock Returns*



Dissecting the Positive Relation between Cash Holdings and Stock Returns☆F.Y. Eric C. LamDepartment of Finance and Decision SciencesHong Kong Baptist University Kowloon Tong, Hong KongEmail: fyericcl@hkbu.edu.hkTel: (852)-3411-5218; Fax: (852)-3411-5585Tai MaDepartment of FinanceNational Sun Yat-sen UniversityKaohsiung, TaiwanEmail: matai@finance.nsysu.edu.twTel: (886)-7-525-2000 ext. 4810; Fax: (886)-7-525-1523Shujing WangDepartment of FinanceThe Hong Kong University of Science and TechnologyClear Water Bay, Kowloon, Hong KongEmail: shujingwang@ust.hkTel: (852)-2358-7666; Fax: (852)-2358-1749K.C. John Wei*Department of FinanceThe Hong Kong University of Science and TechnologyClear Water Bay, Kowloon, Hong KongEmail: johnwei@ust.hk; Tel: (852)-2358-7676Fax: (852)-2358-1749This version: January, 2015_______________________________☆We appreciate the helpful comments from Alex Barinov, Jay Cao (FMA Asian discussant), Charles Clarke, John Crosby (AFBC discussant), Gerald Garvey, Gianluca Marcato (EFMA discussant), Clinton Newman, Anna-Leigh Stone (Eastern FA discussant), and conference participants at the 2014 European Financial Management Association (EFMA) Annual Meeting in Rome, the 2014 Financial Management Association Asian (FMA Asian) Conference in Tokyo, the 2014 Eastern Finance Association (Eastern FA) Annual Meeting in Pittsburgh, and the 2013 Australasian Finance and Banking Conference (AFBC) in Sydney. The previous version of the paper carried the title “Cash Holdings and Stock Returns: Risk or Mispricing?” All errors are ours.*Corresponding author: K.C. John Wei, Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. Tel: (852)-2358-7676; Fax: (852)-2358-1749. Email: johnwei@ust.hk.Dissecting the Positive Relation between Cash Holdings and Stock ReturnAbstractWe dissect the positive relation between cash holdings and expected stock returns through a mispricing channel. Ex-ante misvaluation and limits to arbitrage are key drivers of the relation. The relation is strong when high (low) cash-holdings firms are ex-ante relatively undervalued (overvalued) or when arbitrage is limited. The relation vanishes when ex-ante misvaluation is controlled for or when arbitrage is easy. In addition, the relation is stronger among firms with low leverage or among unprofitable firms. While high cash-holdings firms do have higher default risk, our key findings cannot be explained by exposures to default risk or macroeconomic risks.JEL Classification: G12, G14, G32Keywords: Cash holdings; Cross-section of stock returns; Default risk; Limits to arbitrage; Macroeconomic risks; MisvaluationIntroductionHigh cash-holdings firms provide higher future average stock returns than low cash-holdings firms (e.g., Simutin, 2010; Archarya, Davydenko, and Strebulaev, 2012; Palazzo, 2012). This phenomenon is referred to as the cash holdings effect. Archarya, Davydenko, and Strebulaev (2012) and Palazzo (2012) study rational models based on precautionary savings to explain this positive relation. However, the effect still exists even after controlling for various risk factors, such as the Fama and French (1993) three factors or the Hou, Xue, and Zhang (2014) four factors motivated by the q-theory. As the literature has not yet examined any alternative explanations based on the mispricing channel, our paper fills this gap and provides new findings to understand the effect from a different angle.We hypothesize that investors overreact to the salient agency problem of high cash holdings but underreact to the implicit real illiquidity concern of low cash holdings. On one hand, the agency theory of Jensen and Meckling (1976) and Jensen (1986) argues that self-interested managers might overspend cash reserves for their own benefits at the expense of outside shareholders. For example, Harford (1999) find that cash rich firms are more likely to bid for bad targets in the takeover market. Titman, Wei, and Xue (2004) document that the negative relation between capital investment and future stock returns is stronger for firms with greater agency problems of free cash flow, suggesting that managers of high cash firms have a tendency to overinvest. Harford, Mansi, and Maxwell (2008) further show that poorly governed firms spend cash reserves quickly on value-destroying acquisitions and capital expenditures. If investors excessively discount high cash-holdings firms due to overly emphasizing the salient agency costs, firms with high cash holdings might be temporarily undervalued.On the other hand, low cash reserves could be detrimental to firms, especially for those lacking liquidity. Bolton, Chen, and Wang (2011) show that corporate liquidity endogenously arises in a model of dynamic investment for financially constrained firms. Bolton, Chen, and Wang (2013) further show that when financing conditions are stochastic, firms optimally save cash due to both market-timing and precautionary-savings motives. Harford, Klasa, and Maxwell (2014) provide evidence that cash holdings can help firms mitigate refinancing risk. If investors insufficiently discount low cash-holdings firms due to neglecting the implicit real illiquidity costs, firms with low cash holdings might be temporarily overvalued. Taken together, the misreactions would generate a positive relation between cash holdings and future stock returns.We measure misvaluation by combining a battery of widely documented cross-sectional stock return anomalies into an ex-ante signal to indicate the relative degree of overvaluation. Our argument predicts that cash holdings should be negatively correlated with relative overvaluation. High cash-holdings firms that are ex-ante identified as relatively undervalued should have higher future return than low cash-holdings firms that are overvalued. Conversely, high cash-holdings firms that are not undervalued should not subsequently outperform low cash-holdings firms that are not overvalued. In addition, we expect the positive relation to vanish once ex-ante misevaluation is properly controlled for. Another mispricing prediction is that the relation should be stronger when arbitrage is limited (e.g., Shleifer and Vishny, 1997) and should disappear when arbitrage is easy.If investors overreact to the salient agency problem of high cash holdings, then the undervaluation of high cash-holdings firms should be more severe for those with low leverage as these firms tend to have stronger agency conflicts (e.g., Jensen, 1986). Hence we expect the position relation to be stronger among firms with low leverage. Moreover, if investors underreact to the implicit real illiquidity concern of low cash holdings, then the overvaluation of low cash-holdings firms should be more severe for those that are unprofitable as these firms tend to have poorer liquidity. Consequently we expect the position relation to be stronger among unprofitable firms as well.Using a sample of stock returns on U.S. listed firms from July 1960 to December 2011, we find that future average size and book-to-market adjusted stock returns are significantly higher for high cash-holdings firms than for low cash-holdings firms by 0.51% per month. Cash holdings are negatively correlated with our measure of ex-ante relative overvaluation identified with 11 cross-sectional stock return anomalies well documented in the literature (Stambaugh, Yu, and Yuan, 2012; 2014). Such correlation indicates that higher (lower) cash holdings are associated with a higher degree of undervaluation (overvaluation). Consistent with our prediction, high cash-holdings firms that are ex-ante undervalued generate significantly higher future stock returns than low cash-holdings firms that are overvalued. By contrast, high cash-holdings firms that are not undervalued do not particularly outperform low cash-holdings firms that are not overvalued. Furthermore, the positive relation becomes insignificant when ex-ante misevaluation is controlled for in an interactive regression.We construct a measure of limits to arbitrage based on three common dimensions of arbitrage barriers. We do not find a relation between cash holdings and returns when arbitrage is easy, while a significant positive relation emerges and becomes stronger when limits to arbitrage are more serve. In addition, we find that the future stock returns of high cash-holdings firms with low leverage are higher than those with high leverage and the position relation is also stronger among firms with low leverage than among firms with high leverage. Moreover, we find that the future stock returns of low cash-holdings firms that are unprofitable, indicated by non-positive return on assets, are lower than those that are profitable and the position relation is also stronger among unprofitable firms.Palazzo (2012) argues that systematically riskier firms optimally hold more cash to hedge against future cash flow shortfall to avoid costly external financing. In a related precautionary savings study, Archarya, Davydenko, and Strebulaev (2012) predict that firms subject to higher default risk optimally hold more cash to buffer against cash flow shortfall in the future. As such, these riskier firms should be priced with higher expected stock returns. We examine the exposures of firms with different levels of cash holdings to the five macroeconomic risks put forth by Chen, Roll, and Ross (1986). We find that high cash-holdings firms indeed have significantly higher exposure to the default risk factor than low cash-holdings firms. However, high cash-holdings firms still deliver significantly higher risk-adjusted returns than low cash-holding firms even after controlling for exposures to the five macroeconomic risks. Furthermore, our findings based on relative overvaluation, limits to arbitrage, and leverage or profitability classification hold with the returns adjusted for exposures to the macroeconomic risks.We document that the positive relation drops substantially over time. Even with the substantial increase in cash holdings for high cash-holdings firms, these firms no longer provide significantly higher future returns than low cash-holdings firms in the most recent subperiod. It seems that investors’ pricing of cash holdings has become much less systematically erroneous.There is also a clustering of cash holdings across some industries. For example, Bates, Kahle, and Stulz (2009) report that the average cash ratio of high-tech firms is greater than that of manufacturing firms. We do find that many more firms in medical equipment, pharmaceutical products, business services, computer hardware, and computer software industries are among the high cash holders. In contrast, many more firms in utilities, petroleum and natural gas, communication, and wholesale industries are among low cash holders. After controlling for the industry effect, we still find a positive relation between cash holdings and stock returns. We also find that around half of the positive relation is due to the industry effect and another half is due to the stock-level effect.We provide the following major contribution to the literature. Previous studies have provided rational explanations through the precautionary savings channel for the positive relation between cash holdings and future stock returns. In this paper, we are the first to behaviorally dissect the positive relation through the mispricing with limits to arbitrage channel. Specifically, we argue that investors overreact to the salient agency problem of high cash holdings but underreact to the implicit real illiquidity concern of low cash holdings. We find that the positive relation is subsumed by ex-ante misvaluation identified from 11 well documented stock return anomalies. The positive relation also disappears when limits to arbitrage are easy. The position relation is also stronger among firms with low leverage or among unprofitable firms.The paper proceeds as follows. Section 2 reviews the literature and develops our hypotheses. Section 3 describes the variables and our sample. Section 4 presents the positive relation between cash holdings and stock returns. Section 5 tests the role of ex-ante misvaluation on the cash holdings effect. Section 6 tests the role of limits to arbitrage on the effect. Section 7 examines the effect across leverage and profitability. Section 8 tests the role of macroeconomic risks on the effect. Section 9 conducts the robustness checks by examining the effect over time and by controlling for the industry effect. Finally, Section 10 concludes the paper.Literature Review and Hypothesis DevelopmentSimutin (2010) and Palazzo (2012) find that high cash-holdings firms earn higher average future stock returns than low cash-holdings ones. The positive relation cannot be explained by the CAPM or the Fama and French (1993) three-factor model consisted of the market, size, and value factors. Furthermore, the relation cannot be explained by the Hou, Xue, and Zhang (2014) four-factor model motivated by the q-theory consisted of the market, size, investment, and profitability factors either.As we mention at the outset, we test whether investors’ misreactions to the implications of cash holdings generate the positive relation between cash holdings and stock returns. Specifically, investors might excessively discount high cash-holding firms due to overly emphasizing the salient agency conflict associated with high cash holdings. Harford (1999), Titman, Wei, and Xue (2004), and Harford, Mansi, and Maxwell (2008) show that, due to agency problem, firms with high cash holdings spend cash reserves quickly on value-destroying acquisitions and capital expenditures. Investors might be overly concerned that a substantial part of the cash reserves of high cash-holding firms might be wasted one way or the other by self-interested managers. Therefore investors undervalue firms with high cash holdings. In addition, investors might insufficiently discount low cash-holding firms due to neglecting the implicit real illiquidity concern of these firms. Bolton, Chen, and Wang (2011), Bolton, Chen, and Wang (2013), and Harford, Klasa, and Maxwell (2014) argue that financially constrained firms are subject to corporate liquidity hence cash holdings help mitigate refinancing risk and satisfy market-timing and precautionary-savings motives. Investors might overlook the implicit potential detriments to real liquidity associated with low cash holdings, therefore overvalue low cash-holdings firms.We measure ex-ante misvaluation by combining multiple cross-sectional stock return anomaly variables into a measure of relative overvaluation. According to our misvaluation argument, cash holdings should be negatively correlated with the measure. In particular, high cash-holding firms have high future stock returns only if they are undervalued and low cash-holding firms have low returns only if they are overvalued. The above discussion leads to our first hypothesis.H1a: The positive relation between cash holdings and expected stock returns should be strong when high cash-holding firms are undervalued and low cash-holding firms are overvalued and the relation should be weak otherwise.H1b: The positive relation should disappear after controlling for ex-ante misvaluation.If extreme cash holders are misvalued, the resulting profit opportunities would attract arbitrage activities that correct the mispricing. When such opportunities are riskless and costless to exploit, arbitrageurs should correct the mispricing quickly. However, when arbitrage is risky and costly, the correction might slow down. De Long, Shleifer, Summers, and Waldmann (1990) suggest that noise trading would cause prices to diverge from fundamental values, causing arbitrage to be risky. Shleifer and Vishny (1997) argue that arbitrageurs are typically capital constrained and might have to prematurely close arbitrage positions due to margin calls and suffer significant losses. Liu and Longstaff (2004) show that even optimized trades can still experience loss before prices converge when arbitrage is risky.Pontiff (1996, 2006) shows that arbitrageurs prefer to hold fewer stocks with higher idiosyncratic volatility. Arbitrageurs are typically under-diversified and hence the idiosyncratic risk adds substantially to the total risk of their overall positions. The added risk should be of great concern to arbitrageurs as there is still a debate whether they would be compensated with higher expected returns. Transaction costs would be another barrier to arbitrage. Trading expenses obviously reduce the profitability of arbitrage trades, which reduces their attractiveness to arbitrageurs. Finally, a lack of liquidity might further make arbitrage opportunities technically harder to exploit.When arbitrage is riskier, transaction costs are higher, and/or liquidity is lower, arbitrage opportunities provided by the misvaluation of extreme cash holders become more difficult and hence less attractive to exploit. It follows that arbitrageurs would only sparingly correct the mispricing. Hence our second hypothesis is as follows.H2: The positive relation between cash holdings and stock returns should be stronger when limits to arbitrage are more severe while the relation should be weaker when arbitrage is easier.As we discussed at the outset, we hypothesize that investors overreact to the salient agency problem due to high cash holdings. It follows that the undervaluation of high cash-holdings firms should be more severe for those with low leverage as these firms tend to have stronger agency conflicts. Thus our third hypothesis is as follows.H3: The positive relation between cash holdings and stock returns should be stronger among firms with low leverage.Furthermore we hypothesize that investors underreact to the implicit real illiquidity concern of low cash holdings. It follows that the overvaluation of low cash-holdings firms should be more severe for those that are unprofitable as these firms tend to have poorer liquidity. Hence our fourth hypothesis is as follows.H4: The positive relation between cash holdings and stock returns should be stronger among firms that are unprofitable.Palazzo (2012) models the optimal corporate cash holdings policy when a firm’s cash flow is correlated with a source of priced aggregate risk and faces costly external financing. As cash savings allow the firm to avoid costly financing to fund the exercise of valuable growth options in the future when the firm experiences a shortfall in cash flow, there is a hedging need of precautionary savings. On one hand, riskier firms save more cash. On the other hand, riskier firms are priced to provide higher expected returns. As cash holdings are positively correlated with this systematic risk, it is positively correlated with expected returns.In a related study, Archarya, Davydenko, and Strebulaev (2012) argue that a firm’s asset composition, especially cash, depends on the liability structure. When the financially-constrained firm faces higher default likelihood and expects lower future cash flow but higher returns, it holds more cash to raise the liquidity of its assets to buffer the potential shortfall in cash flow in the future. As the higher liquidity does not completely overcome the higher default risk, the distressed firm remains more risky. This hedging need of precautionary savings predicts that cash holdings are positively correlated with the default risk and therefore expected returns. The above discussion leads to our final hypothesis.H5: If the positive relation between cash holdings and stock returns is consistent with the risk-based rational explanation, it should be explained by macroeconomic risks, especially the default risk.Variables and Sample SelectionThis section summarizes the variables in our analysis and describes the sample data. Appendix 1 provides the detailed definitions of the variables. We measure a firm’s cash holdings (CHt) by its cash-to-assets ratio, i.e., cash and short-term investments scaled by total assets at the end of fiscal year t. It measures the proportion of total assets that the firm holds as cash and cash equivalents. The higher the ratio, the more intensive the firm hoards cash but less of the asset base is productive.3.1. The measure of ex-ante misvaluationOur measure of relative overvaluation (RO) is as follow. Like Stambaugh, Yu, and Yuan (2012, 2014), we identify the dispersion of abnormal valuations in the cross section by combining the following 11 stock return anomalies. (1) Total asset growth (TAG): Cooper, Gulen, and Schill (2008) find that firms that increase their total assets have lower future abnormal stock returns. They suggest that it is due to investors’ overreaction to total asset expansions or contractions. (2) Accruals (Acc): Sloan (1996) documents that firms with higher accruals have lower abnormal returns. He suggests that it is due to investors’ overestimation of the persistence of the accruals component of earnings. (3) Net operating assets (NOA): Hirshleifer, Hou, Teoh, and Zhang (2004) show that firms with higher net operating assets have lower abnormal returns. They suggest that it is due to limited attention to accounting profitability and to the neglecting of cash profitability. (4) Capital investment (I/A): Titman, Wei, and Xie (2004) report that firms with higher capital investment have lower future abnormal returns. They suggest that it is due to underreaction to the overinvestment by empire-building managers. (5) External financing (XF): Bradshaw, Richardson, Sloan (2006) document that firms that increase their overall external funding earn lower abnormal returns. They suggest that managers time the market by opportunistically issuing overvalued securities and retiring undervalued securities.(6) Net share issuance (NSI): Daniel and Titman (2006) find that firms that issue more shares have lower abnormal returns. They suggest that managers tend to issue (retire) shares in response to favorable (unfavorable) intangible information, which might reflect overvaluation (undervaluation). (7) Financial distress (O): Dichev (1998) documents that firms with higher bankruptcy risk earn lower abnormal returns. We use Ohlson’s (1980) bankruptcy risk score (O) to measure financial distress. (8) Gross profitability (GP): Novy-Marx (2013) shows that firms with higher gross profitability earn higher abnormal returns. (9) Earnings on assets (ROA): Fama and French (2006) document that firms with higher earnings earn higher abnormal returns. (10) Piotroski and So’s (2012) misvaluation score (MSCORE): The MSCORE is based on comparing the market-to-book equity ratio (M/B) to Piotroski’s (2000) financial strength score (F). Piotroski and So (2012) document that firms with higher book-to-market equity ratios but stronger fundamentals have higher abnormal returns, while firms with higher book-to-market equity ratios but weaker fundamentals do not. They suggest that it is due to biased expectations. (11) Momentum (PRet): PRet is measured as the previous year’s cumulative stock return. Jegadeesh and Titman (1993, 2001) show that firms with higher cumulative stock returns in the previous one year have higher abnormal returns. They suggest that it is due to misreaction to firm information.While each anomaly serves as a proxy for abnormal valuation itself, we combine them in order to diversify away the measurement error in each individual effect and produce a more precise measure. The combination also provides a comprehensive measure that summarizes abnormal valuation due to the various behavioral reasons described. We independently sort stocks into terciles based on each of the above 11 variables reflecting the anomalies. The first 10 variables are measured at the end of fiscal year t and the last one is measured at the end of June of calendar year t+1. For each of the sorts we assign a tercile rank to each stock such that the highest rank is associated with the lowest future abnormal stock return, i.e., the highest degree of relative overvaluation according to the given anomaly. Relative overvaluation (RO) is then the simple average of these 11 rankings on each stock. Stocks with higher (lower) RO are associated with higher (lower) relative overvaluation in the cross section and would earn lower (higher) future abnormal stock returns.3.2. The measure of limits to arbitrageLike Pontiff (1996) and others, we use idiosyncratic stock return volatility (IVol) to measure arbitrage risk. Our measure of transaction costs is the inverse of stock price (1/Price), which is related to the bid-ask spread and brokerage commission (Bhardwaj and Brooks, 1992). Ball, Kothari, and Shanken (1995) also use stock price as an inverse proxy for the bid-ask spread. Furthermore, Stoll (2000) shows that recent stock prices are inversely related to the relative bid-ask spread. Our measure of liquidity is the dollar trading volume (DVol), which is inversely related to price pressure and time required to fill an order or to trade a large block of shares (Bhushan, 1994). We consider stocks with higher arbitrage risk, higher transaction costs, and lower liquidity to have more severe limits to arbitrage. We compute these variables at the end of June of calendar year t+1. Again, we combine these three variables in order to diversify away the measurement errors and produce a more precise measure as well as a cleaner presentation of the results. We independently sort stocks into terciles based on each of these three variables. We then take the simple average of these three rankings on each stock to measure limits to arbitrage (LTA).3.3. Measure of leverage and identification of unprofitable and profitable firmsWe measure leverage by the debt-to-asset ratio (D/A), which is long term debt scaled by the book value of total assets. We identify firms with low (high) leverage as those with leverage below (above) the cross-sectional median at the end of fiscal year t. We classify firms into unprofitable ones versus profitable ones with return on assets (ROA). Specifically, we identify unprofitable (profitable) firms as those that have non-positive (positive) ROA at the end of fiscal year t.3.4. Macroeconomic risksWe measure the exposures to macroeconomic risks in Chen, Roll, and Ross (1986) (hereafter CRR) with the following time-series regression:Retp,t-Retft=αp+βp,MPRetMP,t+βp,UIRetUI,t+βp,UTSRetUTS,t +βp,DEIRetDEI,t+βp,UPRRetURP,t+?p,t,(1)where Retp,t is the monthly return on a cash holdings portfolio p and Retft is the risk-free rate in month t. RetMP, RetUI, RetUTS, RetDEI, and RetURP are the macroeconomic risk factors proposed by CRR and are related to the growth rate of industrial production (MP), unexpected inflation (UI), the term structure of interest rate (UTS), changes in expected inflation (DEI), and default risk (URP), respectively. The slope coefficient (β) measures the exposure of a cash holdings portfolio to a particular risk factor. The intercept (α) measures the average excess return on a cash holdings portfolio after controlling for the macroeconomic risks.The original factors are constructed as follows. MP is the growth rate of industrial production and is defined as MPt = log(IPt/IPt–1), where IPt is the index of industrial production in month t. MPt is led by a month to synchronize with the timing of the stock return. UI is unexpected inflation and is the change in expected inflation (DEI) as calculated in CRR and is derived from the total seasonally-adjusted consumer price index (CPI). UTS is the term premium and is the yield spread between the long-term (10-year) and the one-year Treasury bonds. Finally, URP is the default premium and is the yield spread between Moody’s Baa and Aaa bonds. All the variables are from the Federal Reserve Bank of St. Louis. As the explanatory variables in equation (1) are returns while the factors MP, UI, and DEI are not traded assets, we follow the standard asset pricing literature to employ mimicking portfolios to track these factors. Although the factors UTS and URP are traded assets, as in Chan, Karceski, and Lakonishok (1998) and Cooper and Priestley (2011), we also employ mimicking portfolios to track them for consistency. In order words, we construct mimicking portfolios for all the five CRR macroeconomic risks and use the returns on the mimicking portfolios to estimate equation (1). The basis assets of the mimicking portfolios consists of 10 equal-weighted book-to-market portfolios, 10 equal-weighted size portfolios, 10 equal-weighted momentum portfolios, and 10 equal-weighted cash-holdings portfolios. The book-to-market, size, and momentum portfolios are from French’s data library and we form our own cash holdings portfolios based on the cash-to-assets ratio.Following Lehmann and Modest (1988) and Cooper and Priestley (2011), we construct the pure factor mimicking portfolios as follows. Firstly, we project the monthly returns (in the excess of the risk-free rate) on each of the 40 basis assets on the five CRR factors. That is, we perform 40 time-series regressions to estimate a 40×5 matrix B of the slope coefficients on the five factors. Let V be the 40×40 covariance matrix of error terms for these regressions, which are imposed to be orthogonal. It follows that the portfolio weights to track the five factors are given by the 5×40 matrix w = (B’V-1B)-1B’V-1 and the mimicking portfolios are given by wR’, where R is a T×40 matrix with each column containing the time-series returns on a basis asset over the sample period. The product wR’ gives a 5×T matrix, in which each row represents the returns on a mimicking portfolio for a CRR factor over the sample period. The mimicking portfolio constructed this way for a specific factor has a sensitivity of one with respect to that factor and zero sensitivity with respect to other factors. (Why do we need to use Laura’s data? This reduces our sample period.)3.5.Industry classificationEach year we classify firms into industries according to the 49 industry groupings in Fama and French (1997). We obtain the updated groupings from Kenneth French’s data library. As described later we exclude financial firms from our sample, and therefore groups 45 to 48 are excluded. Our sample includes a total of 45 industries.3.6.Sample selectionOur data contain firms traded on the NYSE, Amex, and Nasdaq exchanges. Their annual financial statements and monthly stock data are from the Compustat and the Center for Research in Security Prices (CRSP), respectively. Like Fama and French (1992, 1993), certificates, American depositary receipts (ADRs), shares of beneficial interest (SBIs), unit trusts, closed-end funds, real estate investment trusts (REITs), and financial firms are excluded. We delete firms on which we do not have the information to compute the necessary variables in a year. Following the literature, delisting returns are further used to mitigate the survivorship bias. The baseline sample and the sample involving limits to arbitrage (LTA) covers annual firm characteristics from fiscal year 1959 to year 2011, and monthly stock returns from the end of July of 1960 to the end of December of 2012. The return data of the sample involving relative overvaluation (RO) begins at the end of July 1973, when the data needed to calculate the Piotroski and So (2012) misvaluation score (MSCORE) and external financing (XF) becomes more widely available. As return on assets (ROA) does not have sufficient variation around zero until the fiscal year 1962, the sample used to examine the cash holdings effect across profitable versus non-profitable firms starts at the end of July 1963. As the factors are available till the end of November 2011, the sample used to examine the macroeconomic risks also ends there.The Baseline Results on the Positive Relation between Cash Holdings and Stock ReturnsPanel A of Table 1 reports summary statistics of cash holdings (CH) in our baseline sample. The average firm holds around 15% of its total assets as cash. The standard deviation is about 17% and hence there is a meaningful variation in cash holdings in the cross section. While the 10th percentile of cash holdings is only 2%, the 90th percentile of cash holdings is 39%. Consistent with the previous literature (e.g., Simutin, 2010; Palazzo, 2012), Panel B of Table 1 shows that cash holdings are negatively correlated with market capitalization (Size) at the end of June of calendar year t+1 and the book-to-market equity ratio (B/M) at the end of fiscal year t. Therefore, when we characterize the relation between cash holdings and future stock returns, we control for these variables as previous studies (e.g., Fama and French, 1992) find that they are associated with future stock returns.We first identify the relation between cash holdings and stock returns by forming decile portfolios at the end of June every calendar year t+1 using cash holdings at the end of fiscal year t. We measure risk-adjusted returns as follows. We first sort all available stocks into quintiles based on their market capitalization (Size) and book-to-market equity (B/M) at the end of year t independently. The intersection of these 55 portfolios forms our benchmark portfolios. We measure the monthly risk-adjusted returns on a stock (aRet) between July of calendar year t+1 and June of calendar year t+2 as the monthly raw stock returns minus the monthly returns on the benchmark portfolio matched to the stock with the same ranks in Size and B/M. We then compute the monthly risk-adjusted returns for each cash holdings decile and rebalance the portfolios annually.Panel C of Table 1 presents summary statistics for cash holdings deciles. There are about 328 firms in each decile per year in the baseline sample. Firms in decile 1 (low) hold around 1% of its total assets in cash and those in decile 10 (high) hold around 52% of its total assets in cash. The difference in cash holdings between these two extreme groups amounts to a substantial 51%. The average risk-adjusted return on the lowest cash-holdings decile is –0.20% per month and is significant at the 5% level. The return monotonically increases as cash holdings increase. The average risk-adjusted return on the highest cash-holdings decile is 0.31% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.51% and the difference is significant at the 1% level.Second, we identify the relation between cash holdings and stock returns using the slope of lagged cash holdings (b1) estimated from the following Fama and MacBeth (1973) cross-sectional regression:Reti,t+1=a+b1CHi,t+b2Ln(Sizei.t)+b3B/Mi.t+εi,t+1,(2)where Rett+1 is the monthly raw stock return from July of calendar year t+1 and June of calendar year t+2 and Ln(Size) is the natural logarithm of market capitalization. Panel D of Table 1 presents the estimated slope coefficients. The slope of cash holdings (b1) is 0.692 and is significant at the 5% level. Consistent with the previous studies, we identify a significantly positive relation between cash holdings and subsequent stock returns.Ex-ante Misvaluation and the Relation between Cash Holdings and Stock Returns5.1. Summary statistics for the relative overvaluation measurePanel A of Table 2 presents the descriptive statistics of relative overvaluation (RO) and the constituent variables. The mean and median are similar at about 3.00 (it should be 2.00 since you use tercile ranking?), suggesting that the measure is not specifically skewed. Panel B of Table 2 reports the correlations between cash holdings (CH) and RO as well as the constituent variables. Cash holdings are negatively correlated with RO (correlation = –0.12), suggesting that firms with higher cash holdings tend to have a higher degree of undervaluation. In addition, cash holdings are negatively correlated with net operating assets (NOA) with a correlation of –0.38, suggesting that high (low) cash-holdings firms are more operationally inactive (active).5.2.The role of ex-ante misvaluation in the cash holding effectFor reference, Panel A of Table 3 reproduces Panel A of Table 2 using the sample excluding firms with missing RO. Although the number of firms in each decile per year drops to 128 from 328 (it drops too much. Can we allow some of them missing? For example, firms with at least 7 anomalies available to compute the RO score will be included in the sample), cash holdings and stock returns on the portfolios remain similar. Firms in decile 1 (low) hold almost none of its total assets in cash and those in decile 10 (high) hold around 46% of its total assets in cash. The difference in cash holdings between these two extreme groups amounts to a substantial 46%. The average risk-adjusted return on the low cash-holdings decile is –0.24% per month and is significant at the 5% level. The return almost monotonically increases as cash holdings increase. The risk-adjusted return on the high cash-holdings decile is 0.47% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.71% and the difference is significant at the 5% level. We again observe a significant positive relation between cash holdings and subsequent stock returns in this subsample.Panel B of Table 3 presents portfolios independently sorted by terciles of relative overvaluation and deciles of cash holdings. By construction, the distribution of cash holdings across cash holding deciles is very similar across RO. When RO is high, the average risk-adjusted return on the highest cash-holdings decile is only 0.15% (t-stat = 1.09) per month and is insignificant, suggesting that high cash-holdings firms do not necessarily earn higher returns. When RO is medium, the risk-adjusted return on the highest cash-holdings decile increases to 0.48% per month and is significant at the 1% level (please check the significance levels for the whole paper. In the paper, we use three levels, 1%, 5%, and 10%). Furthermore, when RO is low, the risk-adjusted return on the highest cash-holdings decile further rises to 0.51% and is significant at the 1% level (t-stat = 4.20). High cash-holding firms have high future stock returns only if they are not overvalued. Although the risk-adjusted return for the lowest cash-holding decile is significantly negative at –0.47% (t-stat = –3.78) when RO is high, it turns positive albeit insignificant at 0.06% when RO is low. These suggest that low cash-holdings firms do not necessarily earn lower returns. Low cash-holding firms have low future stock returns only if they are overvalued.The strategy of longing high cash-holdings firms with low RO and shorting low cash-holdings firms with high RO ([low,10]–[high,1]) produces risk-adjusted return of 0.98% (t-stat = 4.50). By contrast, the strategy of longing high cash-holdings firms with high RO and shorting low cash-holdings firms with low RO produces a nearly zero risk-adjusted return of 0.09% (t-stat = 0.50). The findings indicate that the cash holdings effect strongly depends on ex-ante misvaluation. Consistent with our hypothesis H1a, the positive relation between cash holdings and stock returns is strong when high cash-holding firms are undervalued and low cash-holding firms are overvalued but weak when high cash-holding firms are overvalued and low cash-holding firms are undervalued.We employ the Fama and MacBeth (1973) regression to further examine the dependence of the cash holdings effect on relative overvaluation. Panel C of Table 3 reports the estimated slope coefficients of the following cross-sectional regression:Reti,t+1=a+b1CH_hii,t+b2CH_loi,t+b3RO_hii,t+b4RO_loi,t + b5CH_hii,t×RO_loi,t+b6CH_loi,t×RO_hii,t +b7Ln(Size)+b8B/Mi,t+?i,t,(3)where CH_hi (CH_lo) is a dummy variable that equals one if the firm’s cash holdings are in the top (bottom) tercile of cash holdings and zero otherwise. RO_hi (RO_lo) is a dummy variable that equals one if the firm is in the top (bottom) tercile of relative overvaluation and zero otherwise. Compared to Equation (2), the dummies in this specification set the cash holdings and relative overvaluation variables in similar footings.Model 1 of Panel C in Table 3 reports that the estimated slope on CH_hi (b1) is 0.193 and is significant at the 10% level (t-stat = 1.66). The positive sign shows that firms with high cash holdings provide higher average stock returns than the average firm. The estimated slope on CH_lo (b2) is –0.157 and is significant at the 5% level (t-stat = –2.62). The negative sign indicates that firms with low cash holdings provide lower average stock returns than the average firm. These results are consistent with a positive relation between cash holdings and stock returns. In Model 2 the estimated slope on RO_hi (b3) is –0.554 and is significant at the 1% level (t-stat = –7.08). The negative sign shows that firms with high relative overvaluation provide lower average stock returns than the average firms. The estimated slope on RO_lo (b4) is 0.225 and is significant at the 1% level (t-stat =4.21). The positive sign indicates firms with low relative overvaluation provide higher average stock returns than the average firms.Model 3 partially studies the interaction terms and the cash holding dummies. The estimated slopes on CH_hi (b1) and CH_lo (b2) are 0.032 (t-stat = 0.19) and 0.088 (t-stat = 1.26), respectively, and both are insignificant. The estimated slopes on CH_hi×RO_lo (b5) and CH_lo×RO_hi (b6) are 0.395 (t-stat = 3.28) and -0.587 (t-stat = –7.47), respectively, and both are significant at the 5% level. When relative overvaluation is low (RO_lo = 1), the slope on CH_hi increases to 0.427 ( = 0.032+0.395), suggesting that high cash-holdings firms (CH_hi) with low relative overvaluation earn a significantly higher return of 0.427% per month than the average firm. However, when relative overvaluation is not low (RO_lo = 0), the slope on CH_hi reduces to 0.032, suggesting that high cash-holdings firms (CH_hi = 1) without low relative overvaluation do not earn a significantly higher return than the average firm. When relative overvaluation is high (RO_hi = 1), the slope on CH_lo decreases to –0.499 ( = 0.088–0.587), suggesting that low cash-holdings firms (CH_lo = 1) with high relative overvaluation earn a significantly lower return of –0.499% per month than the average firm. However, when relative overvaluation is not high (RO_hi = 0), the slope on CH_lo is 0.088, indicating that low cash-holdings firms (CH_lo = 1) without high relative overvaluation do not earn a significantly lower return than the average firm. The results suggest that the cash holding effect is strongly influenced by ex-ante misvaluation as expected.Model 4 partially examines the interaction terms and the relative overvaluation dummies. The estimated slopes on RO_hi (b3) and RO_lo (b4) are –0.490 and 0.159, respectively, and both are significant at the 5% level. The estimated slopes on CH_hi×RO_lo (b5) and CH_lo×RO_hi (b6) are 0.123 and –0.136, respectively, and both are insignificant. When cash holdings are low (CH_lo = 1), the slope on RO_hi decreases to –0.626 ( = –0.490–0.136), indicating that high overvaluation firms (RO_hi = 1) with low cash holdings earn a significantly lower return of –0.626% per month than average firms. Even when cash holdings are not low (CH_lo = 0), the slope on RO_hi is –0.490, suggesting that high RO firms (RO_hi = 1) still earn a significantly lower return than the average firm. When cash holdings are high (CH_hi = 1), the slope on RO_lo increases to 0.282 ( = 0.159+0.123), indicating that low overvaluation firms (RO_lo = 1) with high cash holdings earn a significantly higher return of 0.282% per month than the average firm. Even when cash holdings are not high (CH_hi = 0), the slope on RO_lo is 0.159, indicating that low relative overvaluation firms (RO_lo = 1) without high cash holdings still generates a significantly higher return than the average firm.In the full interactive model (Model 5), the estimated slopes on CH_hi (b1) and CH_lo (b2) are 0.125 and –0.091, respectively, and both are insignificant. The estimated slopes on two interaction terms CH_hi×RO_lo (b5) and CH_lo×RO_hi (b6) are –0.008 and 0.004, respectively, and both are insignificant. The estimated slopes on RO_hi (b3) and RO_lo (b4) are –0.526 and 0.203, respectively, and both are significant at the 5% level. These results suggest that once ex-ante misvaluation is controlled for, the cash holdings effect vanishes. Overall our findings are consistent with our hypothesis H1b.Limits to Arbitrage and the Relation between Cash Holdings and Stock Returns6.1. Summary statistics for the limits to arbitrage measurePanel A of Table 4 presents the descriptive statistics of limits to arbitrage (LTA) and the constituent variables. The mean and median of LTA are similar at 2.00, suggesting that the measure is not particularly skewed. Panel B of Table 4 reports the correlations between cash holdings (CH) and limits to arbitrage as well as the LTA constituent variables. Cash holdings are positively correlated with limits to arbitrage (correlation = 0.11) and the correlation seems to be mainly driven by higher idiosyncratic volatility (IVol) and lower stock price (Price) of firms with higher cash holdings.6.2. The role of limits of arbitrage in the cash holding effectFor reference, Panel A of Table 5 reproduces Panel C of Table 1 using the sample excluding firms with missing limits to arbitrage. Although the number of firms in each decile per year drops to 219 from 328, cash holdings and risk-adjusted returns on the portfolios remain similar. In particular, the average risk-adjusted return on the lowest cash-holdings decile is –0.12% per month and is significant at the 10% level. The return is almost monotonically increasing as cash holdings increases. The average risk-adjusted return on the highest cash-holdings decile is 0.44% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.57% and the difference is significant at the 5% level. Panel B of Table 5 shows that the slope of cash holdings (b1) in Equation (2) is 0.713 and is significant at the 5% level. We also observe a significant positive relation between cash holdings and subsequent stock returns in this subsample.Panel C of Table 5 presents portfolios independently sorted by tercile of limits to arbitrage and decile of cash holdings. By construction, the spread in cash holdings across limits to arbitrage remains very similar. The results indicate that the cash holding effect is substantially affected by limits to arbitrage. When limits to arbitrage are low, cash holdings is no longer related to future stock returns. The average risk-adjusted returns on the lowest and highest cash-holdings deciles are 0.03% and 0.11% per month, respectively, and both are insignificant. The difference in the risk-adjusted return between the highest cash-holdings decile and the lowest cash-holdings decile is merely 0.08% and is insignificant. When limits to arbitrage is medium, the risk-adjusted return on the lowest cash-holdings decile is –0.20% and is insignificant while the risk-adjusted return on the highest cash-holdings decile is 0.21% and is significant at the 10% level. The difference in risk-adjusted return between the highest cash-holdings decile and the lowest cash-holdings decile rises to 0.41% but it is still insignificant. When limits to arbitrage are high, the risk-adjusted return on the lowest cash-holdings decile is –0.27% and is significant at the 5% level while the risk-adjusted return on the highest cash-holdings decile is 0.88% and is also significant at the 5% level. High cash-holdings firms now outperform low cash-holdings firms by 1.15% and the difference is significant at the 5% level. The difference in the return spread between the highest and the lowest cash-holdings firms across high and low limits to arbitrage deciles ([high–low] of [10–1]) is 1.07% and is significant at the 5% level as well.Panel D of Table 5 presents the estimated slope coefficients of Equation (2) across subgroups sorted by the limits-to-arbitrage measure. When limits to arbitrage are low, the slope of cash holdings (b1) is 0.537 and is insignificant. When limits to arbitrage are medium, the slope decreases slightly to 0.495 and remains insignificant. When limits to arbitrage are high, the slope increases substantially to 1.452 and is significant at the 5% level. The increase in the magnitude of the slope ([high–low]) is 0.795 and is also significant at the 5% level. Both the portfolio and regression approaches show that a relation between cash holdings and future stock returns does not appear in the low limits-to-arbitrage environment. The magnitude of the positive relation gets larger in the medium limits-to-arbitrage environment and becomes significant in the high limits-to-arbitrage scenario. Overall, these findings are consistent with our second hypothesis H2.The Cash Holding Effect: The Roles of Leverage and Profitability7.1. The role of leverageFor reference, Panel A of Table 6 replicates Panel C of Table 1 using the sample having non-missing debt-to-asset ratio. The average risk-adjusted return on the lowest cash-holdings decile is –0.20% per month and is significant at the 1% level. The return is monotonically increasing as cash holdings increases. The average risk-adjusted return on the highest cash-holdings decile is 0.31% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.51% per month and the difference is significant at the 1% level. Panel B of Table 6 shows that the slope of cash holdings (b1) in Equation (2) is 1.199 and is significant at the 1% level. We again observe a significant positive relation between cash holdings and subsequent stock returns in this subsample.Panel C of Table 6 presents portfolios constructed by first sorting firms into low leverage versus high leverage ones and then by decile of cash holdings. The spread in cash holdings is much higher among low leverage firms (0.60) than that among high leverage firms (0.27). Consistent with our agency cost argument, high cash-holdings firms having low leverage hold substantially more cash (0.62) than high cash-holdings firms having high leverage (0.28). As a result, the cash holdings effect is stronger among low leverage firms than among high leverage firms as predicted. Among low leverage firms, the average risk-adjusted returns on the lowest and the highest cash-holdings deciles are –0.19% and 0.36% per month, respectively, and both are significant at the 5% level. The difference in risk-adjusted returns between the highest cash-holdings decile and the lowest cash-holdings decile is 0.55% and is significant at the 1% level. Among high leverage firms, the risk-adjusted return on the highest cash-holdings decile is only 0.07% and is insignificant while the risk-adjusted return on the lowest cash-holdings decile is –0.19% and is significant at the 5% level. The return spread between high cash-holdings firms and low cash-holdings firms drops to 0.26% and is significant at the 10% level.The difference in the return spread between high and low cash-holdings firms across low leverage and high leverage firms ([low–high] of [10–1]) is 0.29% and is significant at the 5% level. In addition, the difference in the return between low cash-holdings firms having low leverage and those having high leverage ([low,1]–[high–1]) is 0.29% and is significant at the 5% level. The difference in the return between high cash-holdings firms having low leverage and those having high leverage ([low,10]–[high–10]) is 0.00% and is insignificant. This is consistent with investors overreacting to the salient agency costs associated high cash holdings and the undervaluation of high cash-holdings firms is more severe for those with low leverage as these firms are perceived to have stronger agency conflicts.Panel D of Table 6 presents the estimated slope coefficients of Equation (2) across low leverage and high leverage firms. Among low leverage firms, the slope on cash holdings (b1) is 0.672 and is significant at the 5% level. Among high leverage firms, the slope is 0.640 but is no longer significant while the difference in the magnitude of the slope ([low–high]) is 0.032 and is insignificant. This echoes that the weaker cash holding effect among high leverage firms is due to weaker agency conflict and lower cash holding. Overall, these findings are consistent with our third hypothesis H3.7.2. The role of profitabilityFor reference, Panel A of Table 7 replicates Panel C of Table 1 using the sample starting from the end of July 1963 with firms having non-missing return on asset. The average risk-adjusted return on the lowest cash-holdings decile is –0.21% per month and is significant at the 5% level. The return is almost monotonically increasing as cash holdings increases. The average risk-adjusted return on the highest cash-holdings decile is 0.32% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.53% per month and the difference is significant at the 5% level. Panel B of Table 7 shows that the slope on cash holdings (b1) in Equation (2) is 1.209 and is significant at the 1% level. We also observe a significant positive relation between cash holdings and subsequent stock returns in this subsample.Panel C of Table 7 presents portfolios constructed by first sorting firms into unprofitable versus profitable ones then by decile of cash holdings. The spread in cash holdings is higher among unprofitable firms (0.62) than that among profitable firms (0.43). The findings indicate that the cash holdings effect is stronger among unprofitable firms than among profitable firms as expected. Among unprofitable firms, the average risk-adjusted returns on the lowest and the highest cash-holdings deciles are –0.49% and 0.42% per month, respectively, and both are significant at the 5% level. The difference in risk-adjusted return between the highest cash-holdings decile and the lowest cash-holdings decile is 0.91% and is significant at the 1% level. Among profitable firms, the risk-adjusted return on the lowest cash-holdings decile is –0.12% and is insignificant while the risk-adjusted return on the highest cash-holdings decile is 0.25% and is significant at the 1% level. Although the return spread between high cash-holdings and low cash-holdings firms remains significant at the 1% level, it drops to 0.37%. The difference in the return spread between high and low cash-holdings firms across unprofitable and profitable firms ([unprofitable–profitable] of [10–1]) is 0.54% and is significant at the 5% level. In addition, the difference in the return between low cash-holdings firms that are unprofitable and those that are profitable ([unprofitable,1]–[profitable–1]) is –0.37% and is significant at the 5% level. The difference in returns between high cash-holdings firms that are unprofitable and those that are profitable ([unprofitable,10]–[profitable–10]) is 0.17% and is insignificant. This is consistent with investors underreacting to the implicit real illiquidity concern associated low cash holdings and the overvaluation of low cash-holdings firms is more severe for those that are unprofitable as these firms have poorer liquidity.Panel D of Table 7 presents the estimated slope coefficients of Equation (2) across unprofitable and profitable firms. Among unprofitable firms, the slope of cash holdings (b1) is 1.750 and is significant at the 1% level. Among profitable firms, the slope is significant at the 5% level but drops to 0.629. The difference in the magnitude of the slope ([unprofitable–profitable]) is 1.122 and is significant at the 10% level. Both the portfolio and regression analyses show that the positive relation between cash holdings and stock returns is stronger among unprofitable firms than among profitable firms. Overall, these findings are consistent with our fourth hypothesis H4.Macroeconomic Risks and the Relation between Cash Holdings and Stock Returns8.1. Summary statistics for macroeconomic risksFor reference, Panel A of Table 8 reproduces Panel C of Table 1 using the sample with returns ending at the end of November 2011. The number of firms in each decile per year remains at around 328, cash holdings and risk-adjusted returns on the portfolios also remain similar. Firms in decile 1 (low) hold around 1% of its total assets in cash and those in decile 10 (high) hold 51% more of its total assets in cash. The average risk-adjusted return on the lowest cash-holdings decile is –0.20% per month and is significant at the 5% level. The return is monotonically increasing as cash holdings increase. The risk-adjusted return on the highest cash-holdings decile is 0.32% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings firms by 0.52% and the difference is also significant at the 5% level.Panel B of Table 8 reports the average premiums on the five CRR macroeconomic risks or essentially the average return on the mimicking portfolios tracking the five factors. Like Liu and Zhang (2008) and Cooper and Priestley (2011), we find a significantly positive premium on the industrial production factor (MP). Similar to Cooper and Priestley (2011), we also find insignificant premiums on the unexpected inflation (UI) and the change in expected inflation (DEI) factors, a significantly positive premium on the term structure (UTS) factor, and a significantly negative premium on the default risk (URP) factor. The average premiums on the MP, UTS, and URP factors are 1.22%, 1.10%, and –0.25% per month, respectively. The magnitudes of these premiums are very close to those reported in Cooper and Priestley (2011).8.2. Macroeconomic risk exposures and the cash holdings effectPanel C of Table 8 presents estimated parameters of Equation (1) across the cash holdings deciles. The exposures of the lowest and highest cash-holdings deciles to the MP factor (βMP) are –0.003 and 0.046, respectively. The difference in the exposure [10–1] is 0.049 and is insignificant. It seems that the macroeconomic risk in terms of the MP factor is not able to explain the relation between cash holdings and returns. For the UI factor, the exposures of the lowest and highest cash-holdings deciles (βUI) are 0.337 and -0.010, respectively. The difference in the exposure is –0.347 and is significant at the 10% level. For the UTS factor, the exposures of the lowest and highest cash-holdings firms (βUTS) are 0.000 and –0.062, respectively. The difference in the exposure is –0.062 and is significant at the 5% level. As high cash-holdings firms are indeed less risky in terms of the UI and UTS factors, these dimensions of macroeconomic risks do not seem to be able to explain the positive relation between cash holdings and stock returns. For the DEI factor, the exposures of the lowest and highest cash-holdings deciles (βDEI) are –1.304 and 1.061, respectively. The difference in the exposure is 2.365 and is significant at the 10% level. Although high cash-holdings firms are indeed riskier in terms of the DEI factor, the premium on this factor is insignificant and hence this dimension of macroeconomic risk does not seem to be able to explain the relation either.Finally, for the URP factor, the exposures of the lowest and highest cash-holdings deciles (βURP) are –0.335 and 0.454, respectively. The difference in the exposure is 0.789 and is significant at the 5% level. High cash-holdings firms are indeed riskier in terms of the covariance with the URP factor, which echoes the finding in Panel B of Table 2 that cash holdings and the Ohlson (1980) bankruptcy risk score (O) are positively correlated (correlation = 0.14). The hedging need of precautionary savings does seem to drive firms to hoard more cash to buffer future bad states. However, the premium on the default factor is significantly negative and hence neither this dimension of macroeconomic risk seems to be able to explain the relation. In fact, the significant difference in the exposure to the default risk between the highest and lowest cash-holdings deciles in fact worsens the cash holding effect. Furthermore, after controlling for all the CRR macroeconomic risks, the average stock return on the lowest cash-holdings decile remains negative at –0.28% per month and is significant at the 5% level. The return still monotonically increases as cash holdings increase. The return on the highest cash-holdings decile is again positive at 0.45% per month and is significant at the 5% level. The difference in the return between the two extreme cash-holdings deciles is 0.73% and is also significant at the 5% level. All these findings are inconsistent with our last hypothesis H5 and do not support the prediction that high cash holdings carries a higher expected return due to higher exposures to macroeconomic risks, especially the default risk.8.3. Further results on mispricing after controlling for macroeconomic riskWe examine whether the key results from Tables 3, 5, 6, and 7 survive after controlling for the exposures to the CRR macroeconomic risks. Panel A of Table 9 reproduces Panel B of Table 3 using the estimated intercept of equation (1). The dependence of the cash holdings effect on ex-ante misvaluation remains similar. The risk-adjusted return for the highest cash-holding decile is insignificant at 0.53% (t-stat = 0.74) per month when relative overvaluation is high and it rises to a significant 0.74% (t-stat = 4.63) when relative overvaluation is low. The risk-adjusted return for the lowest cash-holding decile is insignificant –0.02% (t-stat = –0.21) when relative overvaluation is low and drops to a significant –0.55% (t-stat = –5.16) when relative overvaluation is high. The strategy of longing high cash-holdings firms with low relative overvaluation and shorting low cash-holdings firms with high relative overvaluation ([low,10]–[high,1]) produces the high risk-adjusted return of 1.29% (t-stat = 5.40). Conversely, the strategy of longing high cash-holdings firms with high relative overvaluation and shorting low cash-holdings firms with low relative overvaluation produces an insignificant risk-adjusted return of 0.55% (t-stat = 0.77).Panel B of Table 9 reproduces Panel C of Table 5. Similar as before, when limits to arbitrage are low, cash holdings is no not related to future stock returns. The relation becomes stronger when arbitrage is limited. The risk-adjusted return on the lowest cash-holdings decile is 0.09% per month and is insignificant while the return on the highest cash-holdings deciles is 0.29% and is significant at the 5% level. The difference in the risk-adjusted return between the highest and the lowest cash-holdings deciles is 0.10% and is insignificant. When limits to arbitrage is medium, the risk-adjusted return on the lowest and highest cash-holdings deciles are –0.24% and is 0.27% and both are significant at the 5% level. The difference in risk-adjusted return between the two deciles rises to 0.51% and is significant at the 1% level. When limits to arbitrage are high, the risk-adjusted return on the lowest cash-holdings decile is –0.65% and is significant at the 1% level while the return on the highest cash-holdings decile is 0.77% and is significant at the 5% level. High cash-holdings firms now outperform low cash-holdings firms by 1.42% and the difference is significant at the 1% level. The difference in the return spread between high and low cash-holdings firms across high and low limits to arbitrage deciles ([high–low] of [10–1]) is 1.32% and is significant at the 1% level.Panel C of Table 9 reproduces Panel C of Table 6. The cash holdings effect across low leverage and high leverage firms remains similar. Among low leverage firms, the risk-adjusted returns on the lowest and highest cash-holdings deciles are –0.30% and 0.47% per month, respectively and are significant at the 1% level. The difference in the risk-adjusted return between the highest cash-holdings decile and the lowest cash-holdings decile is 0.78% and is significant at the 1% level. Among high leverage firms, the risk-adjusted return on the lowest cash-holdings decile is –0.23% and is significant at the 1% level while the return on the highest cash-holdings decile is 0.18% and is significant at the 5% level. The return spread between high cash-holdings and low cash-holdings firms remains significant at the 1% level but it drops to 0.41%. The difference in the return spread between high and low cash-holdings firms across low leverage and high leverage firms ([low–high] of [10–1]) is 0.37% and is significant at the 5% level. Moreover, the difference in the return between low cash-holdings firms having low leverage and those having high leverage ([low,1]–[high–1]) is –0.07% and is insignificant. The difference in the return between high cash-holdings firms having low leverage and those having high leverage ([low,10]–[high–10]) is 0.30% and is significant at the 5% level.Panel D of Table 9 reproduces Panel C of Table 7. The cash holdings effect across unprofitable and profitable firms remains similar. Among unprofitable firms, the risk-adjusted return on the lowest cash-holdings decile is –0.87% per month and is significant at the 1% level while the return on the highest cash-holdings decile is 0.25% and is insignificant. The difference in the risk-adjusted return between the highest cash-holdings decile and the lowest cash-holdings decile is 1.12% and is significant at the 1% level. Among profitable firms, the risk-adjusted return on the lowest cash-holdings decile is –0.10% and is insignificant while the return on the highest cash-holdings decile is 0.47% and is significant at the 1% level. The return spread between high cash-holdings and low cash-holdings firms remains significant at the 1% level but it drops to 0.57%. The difference in the return spread between high and low cash-holdings firms across unprofitable and profitable firms ([unprofitable–profitable] of [10–1]) is 0.54% and is significant at the 5% level. Furthermore, the difference in the return between low cash-holdings firms that are unprofitable and those that are profitable ([unprofitable,1]–[profitable–1]) is –0.76% and is significant at the 1% level. The difference in the return between high cash-holdings firms that are unprofitable and those that are profitable ([unprofitable,10]–[profitable–10]) is –0.22% and is insignificant. Overall these findings are again consistent with our mispricing hypotheses H1 to H5.Robustness Checks The relation between cash holdings and stock returns over timePanel A of Table 10 reports the estimated slopes of Equation (2) across three subperiods of our full sample. During the earlier fiscal years 1959 to 1976, the slope of cash holdings (b1) is 1.199 and is significant at the 5% level. During the fiscal years 1977 to 1994, the slope decreases by almost 42% ((1.199–0.699)/1.199) to 0.699 but remains significant at the 5% level. During the most recent fiscal years 1995 to 2011, the slope further drops by about 85% ((0.699–0.130)/0.699) to 0.130 and is insignificant. The relation between cash holdings and future stock returns has declined substantially by around 89% ((1.199–0.130)/1.199) over the three subperiods and there seems to no longer have a relation between cash holdings and returns in the most recent subperiod.Panel B of Table 10 presents the cash-holdings decile portfolios across the three subperiods. During the earlier fiscal years 1959 to 1976, the number of firms in each decile per year is about 191. Firms in decile 1 (low) hold around 2% while firms in decile 10 (high) hold around 30% of its total assets in cash. The spread in cash holdings is 28% and is smaller than the spread of 51% in the full period reported in Panel C of Table 1. During the fiscal years 1977 to 1994, the number of firms in each decile per year rises to 408. Firms in decile 1 (low) hold almost none while firms in decile 10 (high) hold about 52% of its total assets in cash. The spread in cash holdings rises to 51%. During the recent fiscal years 1995 to 2011, the number of firms in each decile per year drops slightly to 388. Firms in decile 1 (low) hold around 1% while firms in decile 10 (high) hold about 76% of its total assets in cash. The spread in cash holdings further increases to 75%. The substantial rise in cash holdings of high cash-holdings stocks echoes the findings in Bates, Kahle, and Stulz (2009) that listed U.S. industrial firms’ average cash-to-assets ratio increase substantially from 10% in 1980 to 23% in 2006.Even with the massive rise in the spread of cash holdings, the strategy based on longing high cash-holdings stocks and shorting low cash-holdings stocks does not generate monotonically more reliable profits. During the early fiscal years 1959 to 1976, the average risk-adjusted return on the lowest cash-holdings decile is –0.06% per month and is insignificant. The risk-adjusted return on the highest cash-holdings decile is 0.24% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings ones by 0.30% and the difference is significant at the 5% level. During the fiscal years 1977 to 1994, the risk-adjusted return on the lowest cash-holdings decile is –0.21% and is significant at the 5% level. The risk-adjusted return on the highest cash-holdings decile is 0.47% and is significant at the 5% level. High cash-holdings firms outperform low cash-holdings ones by 0.68% and the difference is also significant at the 5% level. As Figure 1 shows, the higher average risk-adjusted return spread seems to be heavily influenced by the spike in the spread during October 1987. Finally, during the fiscal years 1995 to 2011, the risk-adjusted return on the lowest cash-holdings decile is –0.34% and is significant at the 10% level. The return on the highest cash-holdings decile is 0.23% and is insignificant. The difference in the average risk-adjusted return between the highest and lowest cash-holdings deciles is 0.56% but is insignificant due to a high standard error of the estimate. High cash-holdings firms do not outperform low cash-holdings ones unambiguously as in the past. Consistently Figure 1 shows that the monthly risk-adjusted return spread becomes much more volatile during this period. Despite a few very high return spreads between the end of 1999 and the beginning of 2000, the strategy suffers from numerous negative returns afterwards. It seems that investors overvalue low cash-holdings firms to a much lesser extent and no longer consistently undervalue high cash-holdings firms in the recent period. The strategy might arguably still be economically profitable but is undoubtedly much riskier. The relation between cash holdings and stock returns: The industry effectAs discussed at outset, we find that there is substantial clustering of cash holdings across some industries. As a result, our results may be driven by the industry effect. To exclude this possibility, we conduct a robust check by controlling for the industry effect. Table 11 reports the results of the industry effect on the relation between cash holdings and stock returns. Panel A of Table 11 presents the decile portfolios sorted by industry-adjusted cash holdings, which is a firm’s cash holdings minus the average cash holdings of the industry to which the firm belongs. Firms in decile 1 (low) hold about 3% of its total assets in cash and 17% less than its industry average holdings. Firms in decile 10 (high) hold around 51% of its total assets in cash and 30% more than its industry average holdings. The difference in industry-adjusted cash holdings or cash holdings between these two extreme groups is 48%.The average risk-adjusted return on the lowest industry-adjusted cash-holdings decile is –0.02% per month and is insignificant. This is 90% ( = (0.20–0.02)/0.20) less than the risk-adjusted return based on raw cash holdings reported in Panel C of Table 1. The return on the highest industry-adjusted cash-holdings decile is 0.24% and is significant at the 5% level. This is about 23% ( = (0.31–0.24)/0.31) less than the return based on raw cash holdings. The spread in the risk-adjusted return between the two extreme deciles is 0.26% and it is significant at the 5% level. This is about 49% (= (0.51–0.26)/0.51) less than the spread based on raw cash holdings. After controlling for the industry effect, we still observe a significant positive relation between cash holdings and subsequent stock returns. Each of the stock-level effect and the industry effect contributes around 50% to the positive relation between raw cash holdings and returns. For a robustness check, we replace cash holdings in Equation (2) with the industry-adjusted cash holdings. Panel B of Table 11 reports that the slope coefficient on industry-adjusted cash holdings is positive and significant at the 5% level. Panel C of Table 10 shows that the slope on cash holdings remains significantly positive when we add industry dummies to the set of control variables in Equation (2).ConclusionsWe dissect the positive relation between cash holdings and future stock returns through a mispricing with limits to arbitrage channel, which has not yet been explored in the literature. We find that the relation is tightly linked to ex-ante relative misvaluation, limits to arbitrage, as well as to leverage or profitability classification but is not captured by the exposures to macroeconomic risk factors. The relation weakens over time and high cash-holdings firms no longer precisely provide higher returns than do low cash-holdings ones in the recent period. The industry and stock-level effects are equally important in the relation.ReferencesAli, Ashiq, Lee-Seok Hwang, and Mark A. Trombley, 2003. Arbitrage risk and the book-to-market anomaly. Journal of Financial Economics 69, 355-373.Ang, Andrew, Robert J. 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Data source: CRSP.B/M: Book-to-market equity ratio, calculated as the book value of equity divided by the market value of equity (Size) at the end of fiscal year t. Book equity is total assets minus liabilities (item LT), plus balance sheet deferred taxes (item TXDB) and investment tax credits (item ITCI), minus preferred stock liquidation value (item PSTKL) if available, or redemption value (item PSTKRV) if available, or carrying value (item PSTK) if available. Data source: Compustat Annual and CRSP.TAG:Growth in book value of total assets, calculated as the change in total assets (item AT) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.Acc:Accounting accruals, calculated as the change in non-cash assets (item AT less item CHE) less the change in non-debt liabilities (item LT less item DLTT less item DLC) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.NOA:Net operating assets, calculated as the change in operating assets and operating liabilities over a fiscal year scaled by beginning total assets. Operating assets is total assets minus cash and short-term investments (item CHE). Operating liabilities is total assets less current liabilities (item DLC), long-term debt (item DLTT), minority interests (item MIB), preferred stocks (item PSTK), and common equity (item CEQ). Data source: Compustat Annual.I/A:Investment-to-assets ratio, calculated as the change in inventories (item INVT) and gross property, plant, and equipment (item PPEGT) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.XF:Net cash flow from external financing, calculated as the sum of ?E and ?D. ?E is net cash flow from equity financing, measured as the cash proceeds from sales of common and preferred stocks (COMPUSTAT item SCSTKC plus item SPSTKC) less the cash payments for purchases of common and preferred stocks (item PRSTKCC plus PRSTKPC) less cash payments for dividends (item CDVC) over a fiscal year scaled by beginning total assets. ?D is net cash flow from debt financing, measured as the cash proceeds from issuance of long-term debt (Compustat item DLTIS) less the cash payments for long-term debt reductions (item DLTR) plus changes in current debt (item DLCCH, set to zero if it is missing) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.NSI:Net share issuance, calculated as the natural logarithm of the ratio of split-adjusted shares (item CSHO multiplied by item ADJEX_C) outstanding at the end of a fiscal year to that at the beginning of the year. Data source: Compustat Annual.O:Bankruptcy risk score suggested by Ohlson (1980), which is calculated as–4.07×Ln(A) + 6.03×(L/A) – 1.43×(CA – CL)/TA + 0.0757×CL/CA – 2.37×NI/TA + 0.285×Loss – 1.72×NegBook – 0.521×ΔNI – 1.83×Op/TL,where Ln(A) is the natural logarithm of total assets, L is liabilities CA is current assets (item ACT), and CL is current liabilities (item LCT) at the end of a fiscal year. NI is net income (item NI) for the lagged fiscal year. Loss is equal to one if net income for both a fiscal year and the lagged fiscal year is negative and zero otherwise. NegBook is equal to one if L is greater than A and zero otherwise. ΔNI is the change in net income between a fiscal year and the lagged fiscal year scaled by the sum of the absolute values of the net income for the two years. Op, funds from operations, is defined as that in FSCORE. Data source: Compustat.GP:Gross profitability, calculated as the gross profit (item GP) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.ROA:Return on assets or earnings profitability, calculated as operating income before extraordinary items (item IB) over a fiscal year scaled by beginning total assets. Data source: Compustat Annual.F:A financial strength score of Piotroski (2000) and is calculated as the sum of nine dummies, each equals one if a given condition holds and zero otherwise. The conditions are: (1) income before extraordinary items (Compustat item IB) for a fiscal year is positive; (2) cash flow from operations for a fiscal year as defined below is positive; (3) the change in return on assets, defined as income before extraordinary items over a fiscal year divided by beginning total assets, is positive; (4) cash flow from operations exceeds income before extraordinary items for a fiscal year; (5) the change in leverage, defined as long-term debt (items DLTT and DD1) divided by assets at the end of a fiscal year, is negative; (6) the change in liquidity, defined as current assets (item ACT) divided by current liabilities (item LCT) at the end of a fiscal year, is positive; (7) the change in gross margin, defined as one minus the ratio of the cost of goods sold (item COGS) to sales (item REVT) for a fiscal year, is positive; (8) the change in asset turnover, defined as sales for a fiscal year divided by beginning total assets, is positive; and (9) the company has a positive cash flow from the sale of common and preferred stock (item SSTK) for a fiscal year. The changes above are measured between a fiscal year and the lagged fiscal year. If Compustat indicates that the company reports a statement of cash flows (format code 7), cash flow from operations is net cash from operating activities (OANCF). If the company reports a statement of working capital (format code 1), cash flow from operations equals funds from operations (Op), minus other changes in working capital (item WCAPC), if available. For other format codes, cash flow from operations is funds from operations plus other changes in working capital, if available. Op is income before extraordinary items (item IB) plus income statement deferred tax (item TXDI), if available, plus equity’s share of depreciation expenses for a fiscal year, which is depreciation expenses (item DP) multiplied by market value of equity and divided by total assets minus book value of equity plus market value of equity at the end of a fiscal year. Data source: Compustat.M/B: Market-to-book equity ratio, calculated as the market value of equity divided by the book value of equity at the end of a fiscal year. As in Fama and French (1993), book equity is total assets (Compustat item AT) minus liabilities (item LT), plus balance sheet deferred taxes (item TXDB) and investment tax credits (item ITCI), minus preferred stock liquidation value (item PSTKL) if available, or redemption value (item PSTKRV) if available, or carrying value (item PSTK) if available. Data source: Compustat and CRSP.MSCORE:A misevaluation score in Piotroski and So (2012) and is calculated by comparing the rank of the financial strength measure FSCORE with the rank of the market-to-book equity ratio M/B. When a firm’s financial performance is strong (high FSCORE) and its earnings expectation is weak (low M/B), expectation error is set to 1 and indicates a high potential for undervaluation. When financial performance is strong (high FSCORE) and earnings expectation is medium (medium M/B) or when financial performance is medium (medium FSCORE) and earnings expectation is weak (low M/B), MSCORE is set to 2 and indicates a mild potential for undervaluation. Likewise, with medium FSCORE and high M/B or low FSCORE and medium M/B, MSCORE is set to 4 and indicates a mild potential for overvaluation. With low FSCORE and high M/B, MSCORE is set to 5 and indicates a high potential for overvaluation. For the rest, MSCORE is set to 3 and indicates a low potential for misvaluation. Data source: Compustat and CRSP.PRet:Prior-one-year stock return at the end of June, calculated by compounding the 11 monthly raw stock return since the end of previous June. Data source: CRSP.IVol:Idiosyncratic stock return volatility, measured as the standard deviation of the residual values from the following time-series market model:,where Ri is the monthly stock return and RM is the monthly return on S&P 500 index. The model is estimated with 36 months of return ending in June and requires a full 36-month history. Data source: CRSP.Price:Share price, measured as the closing stock price (the average of bid and ask prices if the closing price is not available) at the end of June. Data source: CRSP.DVol:Dollar trading volume, defined as the time-series average of monthly share trading volume multiplied by the monthly closing price over the past one year ending in June. Data source: CRSP.D/A:Leverage or debt-to-asset ratio, calculated as long term debt (item DLTT) scaled by total assets at the end of a fiscal year. Data source: Compustat Annual.Table 1. Descriptive statistics, sample correlations, and the relation between cash holdings and stock returnsPanel A reports descriptive statistics of cash-to-assets ratio or cash holdings (CH) at the end of fiscal year t. Stdev is the standard deviation. 10%, 25%, 75%, and 90% refer to the 10th, 25th, 75th, and 90th percentiles, respectively. Panel B reports the time-series averages of the cross-sectional correlations between CH and Size or B/M. Size is the market value of equity at the end of June of calendar year t+1. B/M is the book-to-market equity ratio using Fama and French (1993) book value at the end of fiscal year t. Panel C reports time-series averages of firm characteristics at portfolio formation and adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on decile portfolios sorted and rebalanced annually by CH. N is the number of firms. CHm is the median cash holdings. Ret is the equal-weighted characteristic-adjusted return, which is the stock return minus the return on a 5-by-5 benchmark portfolio matched to the stocks by Size and B/M. [10–1] is the difference in CHm or Ret between the high (10) and the low (1) CH deciles. t is the t-statistic of the average return. Panel D reports the estimated slope coefficients (Coeff.) of the following Fama and MacBeth (1973) cross-sectional regression:Reti,t=a+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,t,where Rett is the unadjusted monthly stock return and Ln(Size) is the natural logarithm of Size. t is the t-statistic of the estimate. All the t-statistics are based on Newey and West (1986) standard error with autocorrelations up to 12 lags.Panel A. Descriptive statistics of cash holdingsMeanStdev10%25%Median75%90%0.150.170.020.030.080.210.39Panel B. Sample correlations with cash holdingsSizeB/M–0.03–0.17Panel C. Decile portfolios sorted by cash holdingsNCHmaRett-stat1 (low)3270.01–0.20(–2.70)23280.02–0.16(–2.86)33270.03–0.13(–2.22)43270.05–0.11(–1.92)53280.070.00(0.11)63280.100.02(0.46)73270.150.09(2.19)83280.210.13(2.62)93270.310.16(1.82)10 (high)3280.520.31(2.45)[10–1]0.510.51(2.82)Panel D. Slopes of returns against cash holdings and controlsCH (b1)Ln(Size) (b2)B/M (b3)Coeff0.692–0.1050.282t-stat(2.15)(–2.37)(4.65)Table 2. Summary statistics for the relative overvaluation measurePanel A reports descriptive statistics of relative overvaluation (RO) and its constituents. The constituents are total asset growth (TAG), accounting accruals (Acc), net operating assets (NOA), the capital-investment-to-assets ratio (I/A), external financing (XF), net share issuance (NSI), Ohlson’s (1980) bankruptcy risk score (O), gross profitability (GP), return on assets (ROA), market-to-book equity ratio (M/B), and Piotroski (2000) financial strength score (F) at the end of fiscal year t as well as prior year stock return ending at the end of May of calendar year t+1 (PRet). Panel B reports the time-series averages of the cross-sectional correlations between cash holdings (CH) and RO or its constituents. Panel C reproduces the decile portfolios sorted by CH using the sample containing non-missing RO observations. The detailed definitions of these variables are described in the Appendix.Panel A. Descriptive statistics of relative overvaluation and its constituentsMeanStdev10%25%Median75%90%RO3.000.542.332.612.993.373.74TAG0.161.02–0.12–0.020.070.190.42Acc–0.030.10–0.13–0.08–0.030.010.07NOA–0.710.660.370.540.690.820.97I/A0.090.43–0.050.010.060.130.25XF0.010.11–0.07–0.020.000.030.11NSI1.111.600.981.001.011.041.21O–73.769.55–84.12–78.91–73.66–68.45–63.85GP0.470.490.130.240.400.610.86ROA0.020.28–0.110.000.040.090.14F5.441.743.074.245.516.817.68M/B2.6412.550.590.881.402.414.34PRet0.070.32–0.28–0.090.070.240.43Panel B. Sample correlations with cash holdingsROTAGAccNOAI/AXFNSIOGPROAFM/BPRet–0.120.07–0.06–0.38–0.08–0.040.020.140.080.01–0.040.100.00Table 3. Relative overvaluation and the relation between cash holdings and stock returnsPanel A reproduces the median cash holdings (CHm) and average risk-adjusted returns (aRet) for decile portfolios sorted by cash holdings (CH) reported in Table 1 using the sample containing non-missing relative overvaluation (RO) observations. Panel B reports time-series averages of firm characteristics at portfolio formation and risk-adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on portfolios independently sorted and rebalanced annually by terciles of RO and deciles of CH. [low,10]–[high,1] is the difference in median cash holdings or returns between firms with low relative abnormal valuation (RO=low) and high cash holdings and firms with high relative overvaluation (RO=high) and low cash holdings. The other differences are defined analogously. Panel C reports the estimated slope coefficients of the following cross-sectional regression:Reti,t+1=a+b1CH_hii,t+b2CH_loi,t+b3RO_hii,t+b4RO_loi,t + b5CH_hii,t×RO_loi,t+b6CH_loi,t×RO_hii,t+b7Ln(Size)+b8B/Mi,t+?i,t,where Reti,t+1 is the raw return on stock i in moth t+1, CH_hi (CH_lo) is a dummy variable which equals one if the firm’s cash holdings are in the top (bottom) tercile of cash holdings and zero otherwise, while RO_hi (RO_lo) is a dummy variable which equals one if the firm is in the top (bottom) tercile of relative overvaluation and zero otherwise. Ln(Size) is the logarithm of firm market capitalization and B/M is book-to-market equity. The sample starts from July 1973.Panel A. Decile portfolios sorted by cash holdings (sample without missing RO or returns)NCHmaRett-stat1 (low)1280.00–0.24(–2.56)21280.01–0.10(–1.27)31280.02–0.11(–1.52)41280.04–0.11(–1.61)51280.050.02(0.33)61280.080.10(1.37)71280.120.17(2.77)81280.180.14(2.01)91280.280.24(2.82)10 (high)1280.460.47(4.69)[10–1]0.460.71(3.31)Table 3 - continuedPanel B. Relative overvaluation and the return spread on the decile portfolios sorted by cash holdingsRO=lowNCHmaRett-stat1 (low CH)300.000.06(0.42)2330.010.09(0.77)3380.020.09(0.91)4400.040.15(1.46)5420.050.25(2.57)6460.080.22(2.18)7480.120.42(4.32)8510.180.30(3.14)9520.280.29(2.94)10 (high CH)500.450.51(4.20)RO=medium1 (low CH)420.00–0.19(–1.54)2440.010.08(0.74)3420.020.00(–0.04)4420.040.14(1.27)5430.050.10(0.84)6410.080.28(2.40)7420.120.10(0.96)8440.180.37(3.21)9440.280.37(2.69)10 (high CH)440.470.48(3.51)RO=high1 (low CH)550.00–0.47(–3.78)2510.01–0.29(–2.45)3480.02–0.38(–3.33)4460.03–0.55(–4.49)5430.05–0.25(–2.13)6410.08–0.22(–1.72)7370.12–0.05(–0.29)8330.18–0.45(–2.96)9310.27–0.03(–0.16)10 (high CH)340.480.15(1.09)[low,10]–[high,1]0.440.98(4.50)[high,10]–[low,1]0.470.09(0.50)Panel C. Slopes of returns against cash holdings dummies, relative overvaluation dummies, and controlsModelCH_hiCH_loRO_hiRO_loCH_hi×RO_loCH_lo×RO_hiLn(Size)B/M(b1)(b2)(b3)(b4)(b5)(b6)(b7)(b8)1Coeff0.193–0.157–0.1230.200t-stat(1.66)(–2.62)(–2.67)(3.31)2Coeff–0.5540.225–0.1590.108t-stat(–7.08)(4.21)(–3.44)(1.75)3Coeff0.0320.0880.395–0.587–0.1350.166t-stat(0.19)(1.26)(3.28)(–7.47)(–2.97)(2.87)4Coeff–0.4900.1590.123–0.136–0.1550.115t-stat(–4.48)(1.97)(1.27)(–0.90)(–3.42)(1.97)5Coeff0.125–0.091–0.5260.203–0.0080.004–0.1510.125t-stat(0.77)(–1.36)(–5.11)(3.49)(–0.08)(0.04)(–3.38)(2.25)Table 4. Summary statistics for the limits to arbitrage measurePanel A reports descriptive statistics for the limits to arbitrage (LTA) measure and its constituents. The constituents are idiosyncratic volatility (IVol), stock price (Price), and dollar trading volume (DVol) at the end of June of calendar year t+1. Panel B reports the time-series averages of the cross-sectional correlations between CH and LTA or its constituents. Panel A. Descriptive statistics of limits to arbitrage and its constituentsMeanStdev10%25%Median75%90%LTA2.000.671.011.352.002.652.99IVol0.120.070.060.080.110.150.20Price21.2724.663.597.2715.6128.8944.17DVol1.69E+087.18E+083.90E+052.00E+061.56E+079.19E+073.56E+08Panel B. Sample correlations with cash holdingsLTAIVolPriceDVol0.110.14–0.030.00Table 5. Limits to arbitrage and the relation between cash holdings and stock returnsPanel A reproduces the median cash holdings (CHm) and average risk-adjusted returns for decile portfolios sorted by cash holdings (CH) reported in Table 1 using the sample containing non-missing LTA observations. Panel B reproduces the estimated slope coefficients of the following cross-sectional regression:Reti,t=a+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,tusing the sample containing non-missing LTA observations. Panel C reports time-series averages of firm characteristics at portfolio formation and risk-adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on portfolios independently sorted and rebalanced annually by tercile of LTA and decile of CH. “[High–Low] of [10–1]” is the difference in the [10–1] spread of median cash holdings or risk-adjusted return between firms with high limits to arbitrage (LTA=high) and firms with low limits to arbitrage (LTA=low). Panel D reports the estimated slope coefficients of the above cross-sectional regression across the three LTA terciles. [high–low] is the difference in the slope estimate between firms with high limits to arbitrage and firms with low limits to arbitrage.Panel A. Decile portfolios sorted by cash holdings (sample with non-missing LTA)NCHmaRett-stat1 (low)2190.01–0.12(–1.68)22190.02–0.11(–1.65)32190.03–0.10(–1.51)42190.04–0.06(–0.96)52190.060.04(0.74)62190.090.06(1.40)72190.130.14(3.01)82190.180.18(3.24)92190.270.15(1.83)10 (high)2190.450.44(2.95)[10–1]0.440.57(2.76)Panel B. Slopes of returns against cash holdings and controls (sample with non-missing LTA)CH (b1)Ln(Size) (b2)B/M (b3)Coeff0.736–0.1220.202t-stat(2.12)(–2.69)(3.43)Table 5 - continuedPanel C: Limits to arbitrage and the return spread on the decile portfolios sorted by cash holdingsLTA=lowNCHmaRett-stat1 (low CH)770.010.03(0.33)2780.02–0.03(–0.48)3770.030.01(0.20)4730.040.04(0.65)5690.060.12(1.89)6670.090.03(0.58)7620.130.13(1.80)8570.180.12(2.13)9510.270.26(2.99)10 (high CH)320.420.11(0.90)[10–1]0.410.08(1.28)LTA=medium1 (low CH)790.01–0.20(–1.62)2850.02–0.30(–3.18)3870.03–0.12(–1.56)4860.04–0.14(–1.64)5890.06–0.06(–0.84)6880.090.07(1.14)7940.130.06(0.69)8960.180.10(1.88)91010.270.09(1.02)10 (high CH)1000.450.21(1.73)[10–1]0.440.41(1.59)LTA=high1 (low CH)630.01–0.27(–1.96)2560.02–0.10(–0.76)3560.03–0.24(–2.10)4610.04–0.05(–0.47)5610.060.04(0.32)6640.090.07(0.62)7630.130.27(2.77)8660.180.31(2.37)9670.270.17(1.27)10 (high CH)870.480.88(2.80)[10–1]0.471.15(2.92)[high–low] of [10–1]0.061.07(2.49)Panel D. Limits to arbitrage and the slopes of returns against cash holdings and controlsLTACH (b1)Ln(Size) (b2)B/M (b3)lowCoeff0.537–0.0830.121t-stat(1.45)(–2.10)(1.37)mediumCoeff0.495–0.0310.286t-stat(1.37)(–0.77)(4.19)highCoeff1.452–0.4860.184t-stat(3.12)(–6.86)(2.59)[high–low]Coeff0.915–0.4030.063t-stat(2.06)(–4.88)(0.70)Table 6. The relation between cash holdings and stock returns across low and high leveragePanel A reproduces the median cash holdings (CHm) and average risk-adjusted returns for decile portfolios sorted by cash holdings (CH) reported in Table 1 using the sample containing non-missing debt-to-asset ratio (D/A) observations. Panel B reproduces the estimated slope coefficients of the following cross-sectional regression:Reti,t=a+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,tusing the sample containing non-missing ROA observations. Panel C reports time-series averages of firm characteristics at portfolio formation and risk-adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on portfolios first grouped into firms with low leverage (D/A below median) and firms with high leverage (D/A above median) at the end of fiscal year t then by decile of CH. “[low–high] of [10–1]” is the difference in the [10–1] spread of median cash holdings or risk-adjusted return between low leverage firms and high leverage firms. [low,1]–[high,1] is the difference in the median cash holdings or risk-adjusted return between low leverage firms with low cash holdings and high leverage firms with low cash holdings. [low,10]–[high,10] is the difference in the median cash holdings or risk-adjusted return between low leverage firms with high cash holdings and high leverage firms with high cash holdings. Panel D reports the estimated slope coefficients of the above cross-sectional regression across the low leverage firms and high leverage firms. [low–high] is the difference in the slope estimate between low leverage firms and high leverage firms.Panel A. Decile portfolios sorted by cash holdings (sample from fiscal year 1959 and non-missing D/A)NCHmaRett-stat1 (low)3270.01–0.20(–2.70)23280.02–0.16(–2.86)33270.03–0.13(–2.22)43270.05–0.11(–1.92)53280.070.00(0.11)63280.100.02(0.46)73270.150.09(2.19)83280.210.13(2.62)93270.310.16(1.82)10 (high)3280.520.31(2.45)[10–1]0.510.51(2.82)Panel B. Slopes of returns against cash holdings and controls (sample from fiscal year 1959 and non-missing D/A)CH (b1)Ln(Size) (b2)B/M (b3)Coeff1.199–0.1320.397t-stat(3.50)(–1.49)(3.05)Table 6 - continuedPanel C: The return spread on the decile portfolios sorted by cash holdings across low and high leverageLeverage = lowNCHmaRett-stat1 (low CH)1640.01–0.19(–2.43)21640.04–0.14(–2.75)31640.070.02(0.25)41640.100.07(1.14)51640.140.00(0.10)61640.190.15(2.39)71640.250.09(1.23)81640.320.27(2.71)91640.430.30(1.74)10 (high CH)1640.620.36(2.51)[10–1]0.600.55(2.96)Leverage = high1 (low CH)1640.01–0.19(–2.23)21640.02–0.13(–2.06)31630.02–0.21(–2.88)41640.03–0.21(–3.13)51640.04–0.08(–1.06)61640.05–0.11(–1.47)71640.070.04(0.52)81640.100.06(1.05)91640.150.05(0.73)10 (high CH)1640.280.07(0.81)[10–1]0.270.26(1.84)[low–high] of [10–1]0.29(2.25)[low,1]–[high,1]0.29(2.53)[low,10]–[high,10]0.00(0.03)Panel D. The slopes of returns against cash holdings and controls across low and high leverageLeverageCH (b1)Ln(Size) (b2)B/M (b3)lowCoeff0.672–0.1360.357t-stat(2.38)(–2.83)(5.00)highCoeff0.640–0.0680.252t-stat(1.43)(–1.53)4.30[low–high]Coeff0.032–0.0680.105t-stat(0.10)(–2.91)(2.45)Table 7. The relation between cash holdings and stock returns across unprofitable and profitable firmsPanel A reproduces the median cash holdings (CHm) and average risk-adjusted returns for decile portfolios sorted by cash holdings (CH) reported in Table 1 using the sample starts from fiscal year 1962 and containing non-missing return on assets (ROA) observations. Panel B reproduces the estimated slope coefficients of the following cross-sectional regression:Reti,t=a+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,tusing the sample starts from fiscal year 1962 and containing non-missing ROA observations. Panel C reports time-series averages of firm characteristics at portfolio formation and risk-adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on portfolios first grouped into firms with non-positive ROA (unprofitable) and firms with positive ROA (profitable) in fiscal year t then by decile of CH. “[unprofitable–profitable] of [10–1]” is the difference in the [10–1] spread of median cash holdings or risk-adjusted return between unprofitable firms (ROA≤0) and profitable firms (ROA>0). [unprofitable,1]–[profitable,1] is the difference in the median cash holdings or risk-adjusted return between unprofitable firms with low cash holdings and profitable firms with low cash holdings. [unprofitable,10]–[profitable,10] is the difference in the median cash holdings or risk-adjusted return between unprofitable firms with high cash holdings and profitable firms with high cash holdings. Panel D reports the estimated slope coefficients of the above cross-sectional regression across the unprofitable firms and profitable firms. [Unprofitable–Profitable] is the difference in the slope estimate between unprofitable firms and profitable firms.Panel A. Decile portfolios sorted by cash holdings (sample from fiscal year 1962 and non-missing ROA)NCHmaRett-stat1 (low)3440.01–0.21(–2.65)23450.02–0.16(–2.63)33440.03–0.13(–2.04)43440.05–0.13(–2.19)53450.07–0.01(–0.30)63450.100.01(0.32)73440.150.10(2.46)83450.210.13(2.62)93440.320.17(1.79)10 (high)3450.530.32(2.37)[10–1]0.520.53(2.74)Panel B. Slopes of returns against cash holdings and controls (sample from fiscal year 1962 and non-missing ROA)CH (b1)Ln(Size) (b2)B/M (b3)Coeff1.209–0.1590.343t-stat(3.12)(–1.54)(2.27)Table 7 - continuedPanel C: The return spread on the decile portfolios sorted by cash holdings across unprofitable and profitable firmsROA≤0 (unprofitable)NCHmaRett-stat1 (low CH)850.01–0.49(–2.84)2850.02–0.36(–2.07)3850.04–0.51(–3.30)4850.06–0.19(–1.37)5850.09–0.13(–0.79)6850.14–0.08(–0.51)7850.200.00(–0.03)8850.290.11(0.57)9850.430.21(0.68)10 (high CH)850.630.42(1.97)[10–1]0.620.91(3.43)ROA>0 (Profitable)1 (low CH)2600.01–0.12(–1.34)22590.02–0.08(–1.15)32610.03–0.07(–1.10)42600.04–0.09(–1.21)52590.060.00(0.00)62600.090.12(2.07)72600.120.06(1.07)82600.180.17(3.09)92600.260.11(2.09)10 (high CH)2600.440.25(3.09)[10–1]0.430.37(2.78)[unprofitable–profitable] of [10–1]0.190.54(2.26)[unprofitable,1]–[profitable,1]0.00–0.37(–1.97)[unprofitable,10]–[profitable,10]0.190.17(0.81)Panel D. The slopes of returns against cash holdings and controls across unprofitable and profitable firmsCH (b1)Ln(Size) (b2)B/M (b3)ROA≤0 (unprofitable)Coeff1.750–0.3350.259t-stat(2.73)(–5.44)(4.13)ROA>0 (profitable)Coeff0.629–0.0870.245t-stat(1.98)(–2.12)(3.62)[unprofitable–profitable]Coeff1.122–0.2480.014t-stat(1.83)(4.86)(–0.22)Table 8. Macroeconomic risks and the relation between cash holdings and stock returnsPanel A reproduces the decile portfolios sorted by cash holdings (CH) using the sample that ends on November 2011. Panel B reports the average monthly return in % on five traded portfolios mimicking the Chan, Roll, and Ross (1986) macroeconomic risk factors. RetMP is the return on the portfolio that tracks the growth rate of industrial production (MP). RetUI is the return on the portfolio that tracks the unexpected inflation (UI). RetUTS is the return on the portfolio that tracks the term premium (UTS). RetDEI is the return on the portfolio that tracks the change in expected inflation (DEI). RetURP is the return on the portfolio that tracks the default premium (URP). Panel C reports the estimated parameters of the following time series regressions:Retp,t-Retft=αp,CRR+βp,MPRetMP,t+βp,UIRetUI,t+βp,UTSRetUTS,t+βp,DEIRetDEI,t+βp,URPRetURP,t+?p,t,where Retp is the subsequent characteristics-adjusted monthly return on a cash-holdings decile portfolio or the return spread [high–low] between the highest and the lowest cash-holdings deciles while Retf is the risk-free rate. Bolded intercept estimates are significant at the 5% level.Panel A. Decile portfolios sorted by cash holdings (sample ending November 2011)NCHmaRett-stat1 (low)3280.01–0.20(–2.70)23290.02–0.16(–2.73)33280.03–0.13(–2.21)43280.05–0.12(–1.99)53290.070.00(–0.06)63290.100.01(0.31)73280.140.09(2.05)83290.210.14(2.82)93280.310.17(1.95)10 (high)3290.520.32(2.42)[10–1]0.510.52(2.80)Panel B. Average risk premiums on macroeconomic risk factorsRetMPRetUIRetUTSRetDEIRetURPAverage1.22–0.061.10–0.01–0.25t-stat(8.23)(–0.75)(2.44)(–0.41)(–2.21)Panel C. Time series regressions of cash holding portfolio returns on macroeconomic risk factorsβMPβUIβUTSβDEIβURPαCRR1 (low)–0.0030.3370.000–1.304–0.335–0.2820.0470.0690.019–0.789–0.146–0.2830.0240.0660.021–0.863–0.113–0.2240.0450.0310.023–0.518–0.141–0.2350.039–0.0120.031–0.410–0.088–0.116–0.024–0.0950.0130.346–0.0780.017–0.025–0.1050.0040.4640.0940.138–0.061–0.0820.0030.6570.0990.249–0.090–0.146–0.0261.4940.1830.3610 (high)0.046–0.010–0.0631.0610.4540.45[high–low]0.049–0.347–0.0622.3650.7890.73t-stat(0.73)(–1.75)(–2.30)(1.75)(5.89)(4.84)Table 9. The relation between cash holdings and macroeconomic risk-adjusted stock returns across relative overvaluation, limits to arbitrage, low versus high leverage, and unprofitable versus profitable firmsPanels A, B, C, and D reproduce key results of Panel B of Table 3, Panel C of Table 5, Panel C of Table 6, and Panel C of Table 7, respectively, using the estimated intercept of the following time series regressions described in Table 7:Retp,t-Retft=αp,CRR+βp,MPRetMP,t+βp,UIRetUI,t+βp,UTSRetUTS,t+βp,DEIRetDEI,t+βp,URPRetURP,t+?p,t.Panel A. Relative overvaluation and the return spread on decile portfolios sorted by cash holdingsRO=lowαCRRt-stat1 (low CH)–0.02(–0.21)10 (high CH)0.74(4.63)RO=medium1 (low CH)–0.14(–1.32)10 (high CH)0.63(3.76)RO=high1 (low CH)–0.55(–5.16)10 (high CH)0.53(0.74)[low,10]–[high,1]1.29(5.40)[high,10]–[low,1]0.55(0.77)Panel B. Limits to arbitrage and the return spread on decile portfolios sorted by cash holdingsLTA=low1 (low CH)0.09(1.51)10 (high CH)0.29(2.20)[10–1]0.10(1.28)LTA=medium1 (low CH)–0.24(–2.57)10 (high CH)0.27(2.50)[10–1]0.51(2.93)LTA=high1 (low CH)–0.65(–4.49)10 (high CH)0.77(2.57)[10–1]1.42(3.86)[high–low] of [10–1]1.32(3.27)Panel C. The return spread on decile portfolios sorted by cash holdings across low and high leverageLeverage = low1 (low CH)–0.30(–3.98)10 (high CH)0.47(3.58)[10–1]0.78(4.51)Leverage = high1 (low CH)–0.23(–3.35)10 (high CH)0.18(1.95)[10–1]0.41(3.20)[low–high] of [10–1]0.37(2.54)[low,1]–[high,1]–0.07(–0.74)[low,10]–[high,10]0.30(2.53)Table 9 - continuedPanel D. The return spread on decile portfolios sorted by cash holdings across unprofitable and profitable firmsROA≤0 (unprofitable)1 (low CH)–0.87(–5.27)10 (high CH)0.25(1.22)[10–1]1.12(4.54)ROA>0 (profitable)1 (low CH)–0.10(–1.52)10 (high CH)0.47(5.62)[10–1]0.57(4.62)[profitable–unprofitable] of [10–1]0.54(2.08)[unprofitable,1]–[profitable,1]–0.76(–4.16)[unprofitable,10]–[profitable,10]–0.22(–1.05)Table 10. The relation between cash holdings and stock returns over timePanel A reports the estimated slope coefficients of the following cross-sectional regression:Reti,t=a+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,tacross three subperiods: fiscal year 1959 to 1976, 1977 to 1994, and 1995 to 2011. Panel B reports the decile portfolios sorted by CH across the three subperiods.Panel A. Slopes of returns against cash holdings and controls across subperiods1959-1976CH (b1)Ln(Size) (b2)B/M (b3)Coeff1.199–0.1320.397t-stat(3.50)(–1.49)(3.05)1977-1994Coeff0.699–0.0950.299t-stat(2.10)(–1.46)(3.01)1995-2011Coeff0.130–0.0860.139t-stat(0.15)(–1.16)(2.44)Panel B. Decile portfolios sorted by cash holdings across subperiods1959-1976NCHmaRett-stat1 (low)1910.02–0.06(–0.87)21910.03–0.13(–2.28)31910.04–0.11(–2.41)41900.06–0.08(–0.93)51930.070.12(1.65)61920.090.06(0.73)71910.110.05(0.82)81920.140.08(1.38)91910.180.18(2.67)10 (high)1920.300.24(2.77)[10–1]0.280.30(2.67)1977-19941 (low)4080.00–0.21(–2.00)24080.01–0.28(–5.99)34080.02–0.21(–2.64)44080.03–0.11(–1.49)54080.05–0.10(–1.78)64080.080.01(0.26)74080.120.10(2.08)84080.180.26(3.60)94080.280.04(0.41)10 (high)4080.520.47(2.44)[10–1]0.510.68(2.85)1995-20111 (low)3880.01–0.34(–1.84)23880.02–0.07(–0.42)33880.03–0.06(–0.40)43880.05–0.15(–1.08)53880.09–0.01(–0.08)63880.14–0.02(–0.27)73880.210.13(1.29)83890.320.05(0.41)93880.480.27(1.12)10 (high)3880.760.23(0.68)[10–1]0.750.56(1.13)Table 11. Industry and the relation between cash holdings and stock returnsPanel A reports time-series averages of firm characteristics at portfolio formation and adjusted monthly stock returns in % from July of year t+1 to June of year t+2 on decile portfolios sorted and rebalanced annually by industry adjusted cash holdings (aCH) at the end of fiscal year t. Every year we compute the average cash holdings by Fama and French (1997) 49 industries as defined in French’s data library. Firm level industry adjusted cash holdings is the firm’s cash holdings minus the average cash holdings of the industry to which the firms belong. aCHm is the median industry-adjusted cash holdings in %. Panel B reports the estimated slope coefficients of the following cross-sectional regression:Reti,t=a+c1aCHi,t+c2Ln(Size)+c3B/Mi,t+?i,t.Panel C reports the estimated slope coefficients of the following cross-sectional regression:Reti,t=j=149ajIndDVi,j+b1CHi,t+b2Ln(Size)+b3B/Mi,t+?i,t,where IndDV is the set of 49 industry dummies with each equals to one if a firm belongs to industry j and zero otherwise.Panel A. Decile portfolios sorted by industry-adjusted cash holdingsNaCHmCHmaRett-stat1 (low)327-0.170.03-0.02(-0.41)2328-0.120.04-0.17(-3.17)3328-0.090.03-0.09(-1.48)4327-0.070.04-0.07(-1.02)5328-0.050.05-0.04(-0.71)6328-0.020.070.01(0.20)73270.000.110.04(1.02)83280.050.180.09(2.19)93270.130.300.13(1.78)10 (high)3280.300.510.24(2.19)[10–1]0.480.480.26(2.00)Panel B. Slopes of returns against industry-adjusted cash holdings and controlsaCH (c1)Ln(Size) (c2)B/M (c3)Coeff0.509-0.1100.269t-stat(2.06)(-2.45)(4.24)Panel C. Slopes of returns against cash holdings and controls with industry dummiesCH (b1)Ln(Size) (b2)B/M (b3)Coeff0.497-0.1150.260t-stat(1.98)(-2.85)(5.65)Figure 1Monthly return spread between high and low cash-holdings deciles ................
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