Corporate Income Tax and Stock Returns

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1 Corporate Income Tax and Stock Returns [Preliminary Draft] Alexander Schiller September 9, 2015 Abstract This paper examines the implications of corporate income taxes for the crosssection of stock returns. I show that firms that pay high e ective tax rates earn a return premium over firms that pay low e ective tax rates. This novel finding is a robust feature of the data that is not explained by firm characteristics or industry e ects. I propose a simple explanation: Di erences in e ective corporate tax rates are almost exclusively driven by the size of tax credits and deductions. Such tax shields reduce the e ective operating leverage of a firm. As a result, high-tax firms are more exposed to aggregate cash flow shocks and hence command a risk premium. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15209, USA

2 1 Introduction The e ects of taxation are an area of keen interest for a broad range of questions in finance. For instance, one of the major areas of study in corporate finance tries to understand the e ects of taxation on firm decisions such as capital structure, capital investment, payout policies, executive compensation, as well as organizational form. 1 Other strands of the literature highlight the importance of taxation for the value of corporate equity and risk premia. 2 Surprisingly, the e ects of taxation - and in particular of corporate income taxation - on the cross-section of stock returns has received much less attention. 3 The contribution of this paper is to show that corporate income taxes present a source of risk that is priced in the cross-section of stock returns. I focus my inquiry on di erences in the e ective corporate income tax rate (ETR), which I measure as the ratio of current tax expense to operating cash flows. While all corporations face the same marginal federal tax rate schedule, numerous tax shields consisting of tax deductions, credits, as well as provisions for net operating loss carry-forwards cause the ETR to vary widely in the cross-section of firms. I begin my empirical analysis by running cross-sectional regressions of stock returns on lagged firm characteristics, as in Fama and Macbeth (1973). This procedure allows me to measure the relation between the ETR and stock returns while controlling for other firm attributes that are know predictors of returns. The regression analysis shows that the ETR is a robust and statistically significant predictor of the cross section of stock returns that is not driven by other firm characteristics or industry e ects. The magnitude of the coe cients suggests that this relation is economically important: The predicted return di erential between a firm with a zero ETR and one whose ETR equals the current statutory tax rate of 35% is 2.31% per year. In order to investigate the properties of the return premium, I sort firms into decile portfolios based on their lagged ETR. The hedge portfolio that is long the high ETR stocks and short the low ETR stocks earns an excess return of over 5.7% per year. Furthermore, the return premium is poorly priced by common factor models. Specifically, the zero-cost portfolio earns an abnormal return of 7.8% per year with respect to the Fama and French 1 See e.g. Graham (2007) for a review of the literature. 2 Examples inclue McGrattan and Prescott (2005), Sialm (2006a), Sialm (2006b), Sialm (2009), Croce et al. (2012), Pastor and Veronesi (2012), Croce et al. (2013), Gomes et al. (2013), and Schulz (2015). 3 Exceptions incluce Hanlon et al. (2005), who study the e ects of di erences in taxable and book income, and Thomas and Zhang (2011), who focus on surprises in tax expense. 1

3 (1993) model which includes factors for the market return, size, and value. When the threefactor model is augmented with factors for profitability and investment as in Fama and French (2014), the abnormal return remains large at 4.7%, with most of the reduction due to the inclusion of the profitability factor. In addition to being economically large, the return premium as well as the abnormal returns with respect to the three and five- factor models are highly statistically significant. I perform a host of robustness checks. For instance, since the ETR is moderately correlated with measures of profitability in the data, I perform double-sorts to construct profitability-neutral ETR portfolios, which yields similar results. The conclusions also hold when the sample is restricted to after the Tax Reform Act of 1986, which was one of the most significant reforms of corporate taxation in the last century and reduced the marginal tax rate for the highest income bracket from 46% to 34%. To interpret the empirical findings, I propose a simple stylized model of the cross-section of firms. Pre-tax cash flows are driven by an aggregate as well as idiosyncratic cash flow shocks. As is common in this kind of model, firms face a fixed cost which introduces operating leverage. 4 I abstract from investment and adopt a reduced-form specification of the tax system. Firms are born with a tax shield that stays fixed throughout their lifetime and allows them to reduce their taxable income. The statutory tax rate is fixed and common across firms. The model replicates the positive relation between the ETR and stock returns that I document in the data. Tax shields reduce the e ective level of operating leverage of a firm. Hence, the after-tax cash flows of high-etr firms - i.e. firms with low tax shields - are more sensitive to shocks in pretax cash flows. High-ETR stocks hence command a risk premium to compensate for the increased exposure to aggregate risk. 2 Empirical Results In this section, I document that stocks that pay a high e ective tax rate earn a return premium over stocks that pay a low e ective tax rate. I show that the return premium is a robust feature of the data that is not explained by other firm or industry characteristics. Furthermore, I demonstrate that an investment strategy that is long high-etr stocks and short low-etr stocks generates an abnormal return with respect to standard factor models. 4 See Kogan and Papanikolaou (2012) for an overview of recent models that link firm fundamentals to stock returns and the use of fixed cost to generate operating leverage. 2

4 2.1 Financial Data I obtain stock market data from CRSP and financial statement data from Standard and Poor s Compustat database. The sample period covers 1963 to Financial market variables are at monthly frequency and accounting variables at annual frequency. Using this data, I construct measures for a series of common characteristics that have been shown to predict stock returns in the cross section. I compute the 12 months rolling CAPM Beta (Beta), market capitalization (ME), the book-to-market ration (BM), momentum based on the prior 12 moths stock return (Mom), asset growth (AG), profitability as in Fama and French (2014) (Prof), cash flows (CF), financial leverage (LevF), and operating leverage (LevO). Appendix A explains in detail how these variables are constructed. 2.2 Measuring the E ective Tax Rate I measure the e ective tax rate (ETR) as the ratio of current taxes to operating cash flows, 5 ETR = Current Taxes Operating Cash Flows. The numerator is a proxy for the firms income tax liability for the year and includes U.S. federal, state, and local income taxes as well as foreign income taxes. The denominator uses a measure of operating cash flows, as opposed to earnings, in order to compensate for the e ects of accrual accounting procedures that can vary between firms, in particular with firm size (see Hagerman and Zmijewski (1979)). Furthermore, operating cash flows measure the before-tax cash payo to capital, which is the pretax cash flow variable relevant to capital budgeting decisions. Operating cash flows are measured as revenues (REV) minus the sum of cost of goods sold (COGS), selling, general and administrative expenses (SGA), and the change in working capital (4WCAP), Operating Cash Flows = REV COGS {z SGA } EBITDA 4WCAP, which is equivalent to EBITDA (earnings before interest, tax, depreciation, and amortization) adjusted for the change in working capital. For negative values of operating cash flows, the ETR is ill defined. For instance, if a firm with negative operating cash flows has positive tax expenditure (which can happen due to 5 Other studies that use ETR measures based on operating cash flows include Fama (1981) and Gonedes (1981). See Plesko (2003) for an overview of di erent ETR measures. 3

5 di erences in book and tax income), the resulting ETR measure would be negative. In the data, operating cash flows are quite frequently negative, for about 30% of observations, with the vast majority due to small firms. In order to not have to discard this significant number of observations, I set the ETR to zero for observations with negative operating negative cash flows. This amounts to simply applying the tax law, assuming that taxable income is zero and the firm cannot carry back the current net operating loss to reduce a prior year s positive tax expense. Note that this treatment biases my results against finding a return premium for high-etr firms, as it mostly applies to small firms which have historically earned higher returns (e.g. French and Fama (1992)). Nevertheless, I will conduct robustness checks with respect to this choice. Figure 1 shows a time-series plot of the average ETR, separately for all firms as well as for the subset of firms with a strictly positive ETR. The shaded areas indicate NBER recessions. The plot shows a large decrease for both measures of the ETR preceding the the Tax Reform Act of 1986, when the top marginal corporate tax rate was reduced from 46% to 34%. While the ETR further tends to fall during recessions, both time series exhibit substantial variation that is not related to business cycles. Table 1 shows summary statistics of the ETR by industry, this time including all observations. The average ETR di ers considerably between industries. It is highest in the consumer sector (which includes durable and non-durable consumption goods), on average 17%, and lowest in the utilities and financial sectors, where it averages 12% and 8%, respectively. 2.3 Sources of Tax Shields While all corporations face the same marginal federal tax rate schedule, numerous tax shields consisting of deductions, tax credits, as well as provisions for net operating loss (NOL) carryforwards cause the ETR to vary widely in the cross-section of firms. 6 In this section, I analyze the relative importance of the di erent sources of tax shields. Since about 75% of corporate income taxes are paid to the U.S. federal government, I proceed by analyzing the sources of tax shields at that level. To this end, I use the Statistics of Income published by the IRS. I rely on IRS data instead of financial reporting data from 6 Currently, all firms with pretax income greater than $75,000 face a statutory marginal tax rate of 34% or higher, with the marginal tax rate reaching 35% for all income above $18,000,000. In the CRSP/Compustat universe, which contains only publicly listed firms, over 99% of firms with positive pretax income face a marginal tax rate that is at most 1 percentage point below the marginal tax rate for the highest income during all years of the sample. As the firms in the sample have relatively large pretax income relative to the breakpoints on the marginal tax schedule, the e ect of progressivity in the tax code on the ETR is negligible. 4

6 Compustat for two reasons. First, corporate tax returns are confidential, and not all sources of tax shields can be inferred from financial statements. Second, tax and GAAP accounting standards serve di erent purposes, leading to di erences in the timing and types of income recognized under the two standards. The quantitatively most important example of such tax-book di erences is the accelerated depreciation of capital assets allowed for tax purposes compared to the straight-line depreciation generally required by GAAP. 7 The IRS data provides the sum for all firms of various income statement items. In Table 2, I present this information as a common-sized income statement with each position normalized by EBITDA. The sample includes all non-financial firms that report positive net income in Deductions for interest, amortization, and depreciation total 44% of EBITDA. Provisions that allow companies to o set current income with past net operating losses (NOL carry-forwards) amount to a further 7% of EBITDA, leaving 49% subject to tax. Income tax before credits is 17% of EBITDA and is reduced by the foreign tax credit, which serves to avoid double-taxation, and several general business tax credits which are used to incentivize certain behavior (like investment in clean energy). Total credits are 11% of EBITDA, leaving a tax-burden of 11% of EBITDA. Note that the tax rate implied by the income subject to tax and the income before credits is 35%, exactly equal to the current statutory rate in the highest income bracket. In 2012, tax shields lowered the tax burden from the statutory 35% to a much lower e ective tax rate of 11% (Total Income Tax divided by EBITDA). The second column shows the percent contribution of each type of tax shield to this reduction. The most important tax shields arise from depreciation and the conceptually similar amortization with 28% and 8%, respectively. Interest expense is responsible for about one quarter of total tax shields. Provisions for NOL carry-forwards make up 10% of total tax shields and the foreign and general business credits make up 21% and 4%, respectively. 2.4 Fama-MacBeth Regressions As in Fama and Macbeth (1973), I run monthly cross-sectional regressions of excess returns Rt+1 i on lagged regressors, including the ETR and a vector of controls Xi t,i.e. R i t+1 = 0,t+1 + 1,t+1 ETR i t + 0 2,t+1X i t + i t+1. 7 For a detailed treatment of di erences between financial and tax reporting, see e.g. Plesko (2003). 8 The sample further excludes firms that report income on forms 1120S, 1120-REIT, 1120-RIC, which apply to small business that do not pay corporate income taxes as well as certain types of real-estate and investment companies. 5

7 The characteristics Xt i are the 12 months rolling CAPM Beta (Beta), the log of market capitalization (ME), the log of the book-to-market ration (BM), momentum based on the prior 12 moths stock return (Mom), asset growth (AG), profitability as in Fama and French (2014) (Prof), cash flows (CF), financial leverage (LevF), and operating leverage (LevO). Accounting data for a given fiscal year are updated in June of the following year and financial data are updated monthly. The sample excludes financial firms. To control for industry e ects, I de-mean the ETR regressor for each of the Fama-French 49 industries, each period. Table 3 shows summary statistics for the firm characteristics, including averages of crosssectional Pearson correlation coe cients. The ETR is most closely correlated with cash flows and profitability, with an average Pearson correlation of 0.5 and 0.61, respectively. The ETR is moderately negatively related to financial leverage, as expected, and moderately positively related to firm size, consistent with prior research (e.g. Zimmerman (1983)). The ETR is essentially unrelated to market beta, the book-to-market ratio, momentum, and operating leverage. Table 4 shows the results of the Fama-MacBeth regressions and reports time-series averages of the monthly cross-sectional regression coe cients. The reported t-statistics use Newey and West (1987) standard errors and are robust to autocorrelation in the cross-section and time-series. For most specifications, the monthly coe cient of ETR is close to This implies that the predicted return di erential between a firm with a zero ETR and one whose ETR equals the current statutory tax rate of 35% is 2.31% per year ( ). The ETR coe cient is also highly statistically significant in all specifications, with t-statistics mostly around 3 and never below The only control variable that meaningfully reduces the ETR coe cient is profitability in specification (5), which produces an ETR coe cient of In specification (10), which includes all control variables, the ETR coe cient is 0.38 and virtually the same as in specification (5) with profitability as the only control. 2.5 Portfolio Sorts and Factor Pricing I proceed by analyzing the return premium for high-tax stocks using portfolio sorts. Each year, at the end of June, I sort stocks into ten portfolios based on their ETR. Similar to the previous section, I de-mean the sorting variable each year by industry, using the Fama-French 49 industries. Table 5 shows average firm characteristics across the ERT decile portfolios. H- L shows the di erence in the average characteristic between the high and low tax portfolios. To set this number into perspective, I compare the H-L spread for each characteristic to the spread that would result from a direct double-sort on that characteristic instead of on ETR and express it as a percentage (%sprd). The portfolio sorts paint a similar picture of the relationship between ETR and the other firm characteristics as the Pearson correlations in 6

8 3. The sort on the ETR measure is most closely related with cash flows and profitability, picking up 19% and 31% of the univariate spread in those variables, respectively. Table 6 shows average value-weighted returns for the decile portfolios as well as results for regressions on the Fama-French 3-factor and 5-factor models. The 3-factor model includes factors for the market return (MKT), size (SMB) and book-to-market (HML) while the 5- factor model adds factors for profitability (RMW) and investment (CMA). T-statistics use Newey and West (1987) standard errors. The excess returns rise from 0.16% per month in the lowest tax portfolio to 0.64% per month in the highest tax portfolio, generating a return spread of 0.48% per month for the hedge portfolio that is highly statistically significant. The abnormal return (alpha) with respect to the 3-factor model is large at 0.65% per month and highly statistically significant with a t-statistic of 5.0. When measured against the 5-factor model, the abnormal return drops to 0.39% per month, but remains statistically significant with a t-statistic above 3. The reduction in the abnormal return is mostly due to a large and significant loading on the profitability factor. Consistent with the Fama-MacBeth regressions, these results highlight the importance of controlling for profitability. Since the ETR and profitability are correlated in the data and the inclusion of the profitability factor reduces the abnormal return of the H-L ETR strategy, I next examine how much of the excess return and abnormal return (alpha) remains after non-parametrically controlling for profitability. To this end, I perform double-sorts to construct ETR portfolios that exhibit only a minimal spread in average profitability. I first assign stocks into five portfolios based on profitability and then sort again into 5 portfolios based on the ETR measure within each profitability quintile, resulting in 25 total portfolios. I then combine portfolios across all profitability sorts, within each ETR quintile. Table 7 shows the characteristics of the double-sorted ETR portfolios. Most notably, the spread in the profitability characteristic is reduced to only 10% of the total univariate spread in that measure. Table 8 shows the average excess returns and results of factor model regressions for the double-sorted ETR portfolios. Both the average monthly return of the hedge portfolio as well as the abnormal return with respect to the 5-factor model remain economically and statistically significant. The average excess return and the abnormal return are now both around 0.3% per month with t-statistics around Robustness To further investigate the sources of the ETR return premium, I conduct a series of robustness checks using alternative measures of the ETR as well as various sub-samples of the data. Table 9 summarizes the results. Note that all robustness checks are performed as double-sorts, by first sorting on profitability, as described in the previous section. 7

9 I first investigate the importance of observations with zero or negative values for the ETR. Rows (2) and (3) of the table show that removing these observations from the sample does not significantly a ect the size and statistical significance of the return premium and abnormal return. To further explore the contribution of stocks with non-positive ETRs, I define a binary measure of the ETR that distinguishes only between two kinds of firms, those with ETRs that are zero or negative and those with ETRs that are strictly positive. Row (4) reports the H-L return for a strategy that is long the positive ETR stocks and short the portfolio of zero and negative ETR stocks. While a large portion of the return spread in the previous section (Table 8) appears to be driven by the return di erence in the lowest two ETR portfolios, the results here highlight the importance of di erentiating among the positive ETR stocks as well. While the excess return achieved by the binary ETR measure is almost as large as that of the benchmark measure, it is not statistically di erent from zero. Furthermore, the abnormal return of the binary measure is essentially zero. This results makes sense, given that in Table 8 the abnormal returns increase nearly monotonically across the ETR quintiles. Row (5) of the table shows that an alternative ETR measure that does not adjust for the change in working capital achieves a similar excess return spread as the benchmark measure while the abnormal return and its t-statistic fall by a bit less than a third. This result highlights the importance of using an ETR measure that is based on operating cash flows instead of earnings, as the former is less susceptible to di erences in accrual accounting procedures between firms. Row (6) shows that the results are not driven by micro-caps, which I define as firms with a market capitalization below the 5th percentile of all NYSE stocks. Finally, Row (7) that the conclusions also hold when the sample is restricted to after the Tax Reform Act of Model In this section, I develop a simple, stylized model in which tax shields reduce the e ective operating leverage of a firm. As a result, high-tax firms are more exposed to aggregate cash flow shocks and hence command a risk premium. 3.1 Setup There is a cross section of firms, indexed by i, whose revenues yt i are subject to an aggregate shock x t and an idiosyncratic shock zt. i Revenues are given by yt i =exp x t zt i,where x t+1 = x x t + x,t+1 8

10 z i t+1 = z z i t + i z,t+1 and the disturbances are independently normally distributed with x,t s N 0, 2 x and i z,t s N 0, 2 z. Firms incur a fixed operating cost f, so that pretax profits t i are given by t i = yt i f. The fixed cost serve two roles in the model: i) they introduce operating leverage and ii) they allow the model to match the frequency of negative pre-tax profits in the data. All firms face the same statutory tax rate but di er in their tax shield S i,whichthey can deduct from their taxable income to reduce their tax bill. The tax shield is fixed through time for each firm. I use it as reduced form that captures the e ects of tax deductions, credits, as well as NOL carry-forwards. 9 Firms dividends, after corporate taxes, are then given by D i t = i t max i t S i, 0. I assume a standard exogenous log-linear pricing kernel M t+1 with ln (M t+1 ) = ln x,t x, where is the time discount rate and controls the price of risk of the aggregate productivity shock. The last term in the pricing kernel corrects for Jensen s inequality and normalizes it to ensure that E t [M t+1 ]=. Note that the pricing kernel implies a constant risk-free rate since the distribution of the innovation x,t+1 does not depend on the current productivity state. Finally, at time zero, firm s tax shields are drawn from a normal distribution S i N µ S, 2 S with mean µ S and volatility S. Negative draws are set equal to zero. 9 Tax deductions and credits work in mechanically the same way. Hence, I do not model them separately. To see this, consider a company with taxable income X, tax deductions D, and tax credits C, that faces tax rate. Taxes due are determined as tax = max ( max (X D, 0) C, 0). Since C 0, this can be re-written as 0 1 tax = max X D C, 0C {z A. } S Hence, tax deductions and credits can be combined into a tax shield S that mechanically operates the same way as a tax deduction. 9

11 3.2 Calibration I calibrate the model targeting aggregate and firm-level moments of bond and stock returns as well as cash flows. Importantly, I do not choose any parameters to improve the model s fit of the ETR return premium. Table 11 summarizes the calibration which is done at monthly frequency. I calibrate the two parameters that govern the SDF to match the risk-free rate and the Sharpe ratio of the market return. This yields a time discount rate of = and a price of risk of = 10. The persistence of the aggregate shock z =0.983 is set to a value commonly used for TFP. The volatility of the aggregate shock z =0.012 is chosen to match the volatility of the equity premium. The persistence of the idiosyncratic shock, z =0.95, its volatility z =0.05, and the fixed cost f =0.915 are chosen to match the average crosssectional volatility of stock returns, the ratio of operating cash flows to assets, as well as the percentage of firms with negative operating cash flows. The statutory tax rate is = 0.35, representing the current tax code. Finally, the mean of the tax shield distribution µ S =0.03 and its volatility S =0.15 are chosen to match the mean and volatility of the ETR in the data. 3.3 Results I compute model-implied moments by simulating a panel of 500 firms for 10,000 periods. Table 11 summarizes the firm-level and asset pricing moments and shows that they match their empirical counterparts well. Firms virtually never default in the model simulations, with the probability of a firm defaulting in a given year being %. Table 12 shows average returns for quintile portfolios sorted on the ETR in the model and compares them to the data. The return spread is 0.32% per month in the model and closely matches that in the data. The average ETR for each of the portfolios in the simulation also closely matches the data. To illustrate the model mechanism driving the ETR premium, Figure 2 plots the expected excess return of a firm as a function of the idiosyncratic productivity state exp (z t ) for di erent values of the tax shield S. The aggregate shock is held constant at its mean, x i t = 0. The figure shows that expected returns and productivity are inversely related. For low productivity shocks, the di erence between cash flows and fixed cost shrinks and the firm is riskier. This relation also emerges from other models (that typically are more complex and usually also incorporate capital investment with costly adjustment) that study the e ect of fixed operating 10

12 cost on asset returns. 10 This is also the mechanism underlying the value premium in Zhang (2005): Firms with low productivity shocks have low market values (relative to their book value), i.e. high book-to-market ratios, and high expected future returns. 11 In this setting, tax shields reduce the e ects of operating leverage, leading to lower expected returns. 4 Conclusion This paper examines the implications of corporate income taxes for the cross-section of stock returns. I show that firms that pay high e ective tax rates earn a return premium over firms that pay low e ective tax rates. This novel finding is a robust feature of the data that is not explained by firm characteristics or industry e ects. I propose a simple explanation: Di erences in e ective corporate tax rates are almost exclusively driven by the size of tax credits and deductions. Such tax shields reduce the e ective operating leverage of a firm. As a result, high-tax firms are more exposed to aggregate cash flow shocks and hence command ariskpremium. 10 See e.g. Kogan and Papanikolaou (2012) for an overview of that literature. 11 In this type of model, the value premium is essentially a profitability discount. I.e these models are not consistent with the profitability premium that we observe in the data. The model presented here su ers the same shortcoming. 11

13 References Croce, M., T. Nguyen, and L. Schmid (2012): The market price of fiscal uncertainty, Journal of Monetary Economics, 59, Croce, M. M., H. Kung, L. Schmid, and T. T. Nguyen (2013): Fiscal Policies and Asset Prices, Review of Financial Studies. Fama, E. F. (1981): Stock Returns, Real Activity, Inflation, and Money, American Economic Review, 71, Fama, E. F. and K. R. French (1993): Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33, (2014): A five-factor asset pricing model, Journal of Financial Economics, 116, Fama, E. F. and J. D. Macbeth (1973): Risk, Return, and Equilibrium: Empirical Tests, Journal of Political Economy, 81, French, K. R. and E. F. Fama (1992): The Cross-Section of Expected Stock Returns, The Journal of FinanceJournal of Finance, 47, Gomes, F., A. Michaelides, and V. Polkovnichenko (2013): Fiscal policy and asset prices with incomplete markets, Review of Financial Studies. Gonedes, N. J. (1981): Evidence on the Tax E ects of Inflation Under Historical Cost Accounting Methods, The Journal of Business, 54, 227. Graham, J. R. (2007): Taxes and Corporate Finance, Handbook of Empirical Corporate Finance SET, 1, Hagerman, R. L. and M. E. Zmijewski (1979): Some economic determinants of accounting policy choice, Journal of Accounting and Economics, 1, Hanlon, M., S. K. Laplante, and T. Shevlin (2005): Evidence for the Possible Information Loss of Conforming Book Income and Taxable Income, Journal of Law and Economics, 48, Kogan, L. and D. Papanikolaou (2012): Economic Activity of Firms and Asset Prices, Annual Review of Financial Economics, 4,

14 McGrattan, E. and E. Prescott (2005): Taxes, Regulations, and the Value of US and UK Corporations, The Review of Economic Studies, 72, Newey, W. K. and K. D. West (1987): A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Metrix, Econometrica, 55, Pastor, L. and P. Veronesi (2012): Uncertainty about Government Policy and Stock Prices, Journal of Finance, LXVII, Plesko, G. a. (2003): An evaluation of alternative measures of corporate tax rates, Journal of Accounting and Economics, 35, Schulz, F. (2015): On the Timing and Pricing of Dividends : Revisiting the Term Structure of the Equity Risk Premium,. Sialm, C. (2006a): Investment Taxes and Equity Returns, WP. (2006b): Stochastic taxation and asset pricing in dynamic general equilibrium, Journal of Economic Dynamics and Control, 30, (2009): Tax changes and asset pricing, American Economic Review, 99, Thomas, J. and F. X. Zhang (2011): Tax Expense Momentum, Journal of Accounting Research, 49, Zhang, L. (2005): The value premium, The Journal of Finance, 60, Zimmerman, J. L. (1983): Taxes and firm size, Journal of Accounting and Economics, 5,

15 Figure 1: Average E ective Tax Rate This figure plots a time series of the equally-weighted cross-sectional average of the e ective tax rate (ETR) for non-financial firms. Shaded areas indicate NBER recessions NBER Recessions all firms ETR> ETR

16 Table 1: E ective Tax Rates by Industry This table reports summary statistics for the e ective tax rate (ETR) by industry. The table shows the mean, standard deviation, 5th percentile (P 5 ), 95th percentile (P 95 ), and the number of firms (N). Statistics are computed across firms and then averaged over time. Data are from Compustat. The sample excludes financial firms and covers 1963 to Consumer Manufacturing Utilities High Tech Health Finance Other Total Mean Std P P N 4,252 3, ,958 1,955 2,487 4,493 22,264 15

17 Table 2: Sources of Tax Shields This table reports parts of a common-sized income statement which is normalized by EBITDA as well as the importance of the various sources of tax shields in percent. Data are from the IRS 2012 Statistics of Income on Corporate Income Tax Returns. The sample includes only corporations that reported positive net income on forms other than 1120S, 1120-REIT, 1120-RIC. Value % of tax shields EBITDA (IRS rules) 100 Deductions 44 Interest 19 27% Amortization 6 8% Depreciation 19 28% Net income 56 NOL carry-forward 7 10% Income subject to tax 49 Income tax before credits 17 Credits 6 Foreign tax 5 21% General business 1 4% Total income tax % 16

18 Table 3: Summary Statistics for Characteristics and Return Predictors This table reports summary statistics for firm characteristics. The table shows the mean, standard deviation, 5th percentile (P 5 ), 95th percentile (P 95 ), and Spearman rank correlations. Statistics are computed across firms and then averaged over time. ETR is the e ective tax rate. Beta is the 12-months rolling CAPM beta. ME is market capitalization in billions of dollars. BM is the bookto-market ratio, Mom is the prior 12 months stock return, AG measures asset growth, Prof measures profitability as in Fama and French (2014), CF measures cash flows, LevF is financial leverage, and LevO measures operating leverage. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1963 to Characteristics ETR Beta ME BM Mom AG Prof CF LevF LevO Panel A: Means, Standard Deviations, and Percentiles Mean Std P P Panel B: Contemporaneous Correlations ETR Beta ME BM Mom AG Prof CF LevF LevO

19 Table 4: Fama-MacBeth Regressions This table reports the results of Fama-MacBeth regressions. Monthly stock returns are regressed on lagged firm characteristics. ETR is the e ective tax rate, demeaned by industry. Beta is the 12-months rolling CAPM beta. ME is the log of market capitalization. BM is the log of the book-to-market ratio, Mom is the prior 12 months stock return, AG measures asset growth, Prof measures profitability as in Fama and French (2014), CF measures cash flows, LevF is financial leverage, and LevO measures operating leverage. The reported average slope coe cients are computed following Fama and Macbeth (1973). T-statistics use Newey and West (1987) standard errors with 12 lags. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1963 to Reg ETR Beta ME BM Mom AG Prof CF LevF LevO [2.88] [-0.53] [-3.03] [2.96] [-0.07] [-2.29] [3.69] [2.95] [-0.21] [-2.78] [3.70] [2.26] [3.32] [-0.08] [-2.70] [3.09] [2.25] [-6.24] [2.45] [0.11] [-3.99] [3.66] [2.01] [3.76] [0.19] [-3.67] [3.62] [3.18] [4.69] [3.17] [-0.22] [-2.71] [3.52] [2.16] [-2.97] [2.67] [-0.15] [-2.98] [3.71] [2.14] [-1.80] [2.94] [0.00] [-2.76] [3.69] [2.10] [0.45] [2.67] [0.47] [-3.87] [2.93] [1.92] [-5.23] [4.35] [-1.62] [-1.79] [0.29] 18

20 Table 5: Characteristics of Tax Rate Portfolios This table reports average characteristics for 10 portfolios of stocks sorted by the e ective tax rate (ETR), which is demeaned by industry. Beta is the 12-months rolling CAPM beta. ME is the log of market capitalization. BM is the log of the book-to-market ratio, Mom is the prior 12 months stock return, AG measures asset growth, Prof measures profitability as in Fama and French (2014), CF measures cash flows, LevF is financial leverage, and LevO measures operating leverage. Statistics are computed across firms and then averaged over time. H-L refers the di erence of a particular characteristic between the high and low tax rate portfolios. As a frame of reference, %sprd expresses H-L as a percentage of the H-L spread that would be achieved by sorting directly on that characteristic. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1963 to Characteristics ETR Beta ME BM Mom AG Prof CF LevF LevO Low High H-L %sprd 100% -7% 8% -3% 9% 9% 19% 31% -14% -9% 19

21 Table 6: Excess Returns and Factor Model Regressions for Tax Portfolios This table reports average excess returns and abnormal returns ( ), in percent per month, and factor loadings for the 10 portfolios of stocks sorted by their e ective tax rates (ETR), which is demeaned by industry. The factors are the market return (MKT), size (SMB), book-to-market (HML), profitability (RMW), and investment (CMA). H-L refers to the zero-cost portfolio that is long in the high tax stocks and short in the low tax stocks. Newey and West (1987) t-statistics that use 12 lags are reported in brackets. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1963 to Panel A: Fama-French 3-Factor Model Excess Return MKT SMB HML Low High H-L t-stat [3.41] [5.00] [-2.74] [-3.88] [-0.16] Panel B: Fama-French 5-Factor Model Excess Return MKT SMB HML RMW CMA Low High H-L t-stat [3.41] [3.32] [-2.39] [-2.72] [-1.26] [6.18] [1.88] 20

22 Table 7: Characteristics of Profitability-Neutral Tax Rate Portfolios This table reports average characteristics for double-sorted portfolios. I first assign stocks into five portfolios based on profitability and then sort again on the ETR measure (which has been demeaned by industry) within each portfolio, resulting in 25 portfolios. I then combine portfolios across all profitability sorts, within each ETR quintile. This procedure yields 5 ETR portfolios with nearly identical profitability characteristics. Beta is the 12-months rolling CAPM beta. ME is the log of market capitalization. BM is the log of the book-to-market ratio, Mom is the prior 12 months stock return, AG measures asset growth, Prof measures profitability as in Fama and French (2014), CF measures cash flows, LevF is financial leverage, and LevO measures operating leverage. Statistics are computed across firms and then averaged over time. H-L refers the di erence of a particular characteristic between the high and low tax rate portfolios. As a frame of reference, %sprd expresses H-L as a percentage of the H-L spread that would be achieved by sorting directly on that characteristic. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1970 to Characteristics of Profitability-Neutral ETR Portfolios ETR Beta ME BM Mom AG Prof CF LevF LevO Low High H-L %sprd 100% -8% 11% -1% 7% 8% 10% 30% -21% -7% 21

23 Table 8: Excess Returns and Factor Model Regressions for Profitability- Neutral Tax Rate Portfolios This table reports average excess returns and abnormal returns ( ), in percent per month, and factor loadings for double-sorted portfolios. I first assign stocks into five portfolios based on profitability and then sort again on the ETR measure (which has been demeaned by industry) within each portfolio, resulting in 25 portfolios. I then combine portfolios across all profitability sorts, within each ETR quintile. This procedure yields 5 ETR portfolios with nearly identical profitability characteristics. The factors are the market return (MKT), size (SMB), book-to-market (HML), profitability (RMW), and investment (CMA). H-L refers to the zero-cost portfolio that is long in the high tax stocks and short in the low tax stocks. Newey and West (1987) t-statistics that use 12 lags are reported in brackets. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1970 to Panel A: Profitability-neutral ETR Portfolios Excess Return MKT SMB HML RMW CMA Low High H-L t-stat [2.94] [3.33] [-3.61] [-0.22] [-1.66] [2.70] [1.12] 22

24 Table 9: Robustness of Tax Portfolio Performance This table reports average excess returns and abnormal returns ( ), in percent per month, and factor loadings for double-sorted portfolios. I first assign stocks into five portfolios based on profitability and then sort again on the ETR measure (which has been demeaned by industry) within each portfolio, resulting in 25 portfolios. I then combine portfolios across all profitability sorts, within each ETR quintile. This procedure yields 5 ETR portfolios with nearly identical profitability characteristics. The factors are the market return (MKT), size (SMB), book-to-market (HML), profitability (RMW), and investment (CMA). H-L refers to the zero-cost portfolio that is long in the high tax stocks and short in the low tax stocks. Row (1) reports results for the benchmark ETR measure. Row (2) excludes stocks with negative operating cash flows. Row (3) excludes stocks with negative tax expense. Row (4) analyzes the hedge portfolio that is long all stocks with strictly positive ETR and short all stocks with zero or negative ETR. Row (5) uses an alternative ETR measure that does not adjust for the change in working capital. Row (6) excludes micro-caps, defined by firms with a market value below the 5th percentile of NYSE stocks. Rows (7) restricts the sample period to after the Tax Reform Act of Newey and West (1987) t-statistics that use 12 lags are reported in brackets. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1970 to Excess Return MKT SMB HML RMW CMA 1 Benchmark ETR measure H-L t-stat [2.94] [3.33] [-3.61] [-0.22] [-1.66] [2.70] [1.12] 2 Excluding stocks with negative operating cash flows H-L t-stat [2.49] [3.27] [-4.39] [0.85] [-2.81] [1.31] [0.79] 3 Excluding stocks with negative tax expense H-L t-stat [3.69] [4.55] [-3.99] [-1.76] [-2.02] [3.80] [1.26] 4 Hedge portfolio that is long ETR> 0 and short ETRapple 0 H-L t-stat [1.49] [0.29] [-3.39] [-4.18] [0.87] [10.15] [1.73] 5 ETR measure without adjustment for change in working capital H-L t-stat [2.78] [2.27] [-2.56] [0.37] [-1.78] [3.59] [1.70] 6 Excluding micro-caps H-L t-stat [2.83] [3.13] [-3.63] [-0.47] [-1.51] [3.26] [1.33] 7 After Tax Reform Act of 1986 H-L t-stat [2.75] [2.90] [-3.19] [0.20] [-2.55] [3.80] [1.46] 23

25 Table 10: Calibration This table summarizes the model calibration. The model is calibrated at monthly frequency. Parameter Value SDF Time discount rate = Price of risk = 10 Fixed cost f = Productivity shocks Persistence of aggregate shock x =0.983 Volatility of aggregate shock x = Persistence of idiosyncratic shock z =0.95 Volatility of idiosyncratic shock z = 0.05 Taxes Tax rate = 0.35 Mean of tax shields µ S =0.03 Volatility of tax shields S =

26 Table 11: Firm-level Moments and Asset Prices in the Model This table reports average firm-level and asset pricing moments from the model and the data. Model results are obtained by simulating a panel of 500 firms for 10,000 periods. Moments are annualized. Moment Model Data Firm-level Frequency of negative operating cash flows Average e ective tax rate Average volatility of operating cash flows Asset prices Risk-free rate (%) Equity premium (%) Sharpe ratio Average volatility of returns (%)

27 Table 12: Tax Portfolios in the Model This table reports average characteristics for 5 portfolios of stocks sorted by their e ective tax rate (ETR) in the model and in the data. H-L refers the di erence between the high and low tax rate portfolios. Model results are obtained by simulating a panel of 500 firms for 10,000 periods. Excess returns are in percent per month. Data are from CRSP and Compustat. The sample excludes financial firms and covers 1963 to Model Data Excess Return ETR Excess Return ETR Low T T T High H-L

28 Figure 2: Risk Premia in the Model This figure plots the expected excess return of a firm in the model as a function of the idiosyncratic shock exp (z) for di erent values of the tax shield S S=0 S=µ S S=µ S + 1σ S= E[R - Rf] exp(z) 27

29 APPENDIX A Data Definitions I use the following definitions of variables: ETR is measured as the ratio of current taxes (TXC) to revenues (REVT) minus the sum of cost of goods sold (COGS), selling, general, and administrative expenses (XSGA), and the change in working capital (WCAPCH). Beta is the CAPM beta from rolling monthly regressions of the market return on the past 12 months of returns. ME is the market equity of the firm calculated as the product of the firms share price times the number of shares outstanding. BM is the ratio of book equity to market equity. Mom is the stock return over the prior 12 months period. As in Fama and French (2014), I construct asset growth AG as the percent change in total assets (AT) from two years ago to the prior year and measure profitability Prof as the ratio of their measure of operating cash flows (REVT - COGS - XSGA - XINT) to book equity (BE), where XINT is interest expense. CF is cash flows and is defined as the sum of depreciation and amortization (DP) plus income before extraordinary items (IB) divided by total assets (AT). Financial leverage LevF is defined as (DLC + DLTT) / (BE + DLC + DLTT), where DLC is debit in current liabilities, DLTT is long term debt total, and BE is book equity. Operating Leverage LevO is measured as the ratio of selling, general, and administrative expenses to total assets. 28

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