Valuation Challenges and Solutions in Contemporary Businesses. The Fama–MacBeth regression is a method used to estimate parameters for asset pricing models such as the capital asset pricing model (CAPM). E I had to do some readings to see how researchers solve this issue. ME Since size, * denotes signi cance at the 10% level, ** denotes signi cance at the 5% level, and *** denotes signi cance at the 1% level. The correlation between size and β is −0.98 for portfolios formed on size alone. must proxy for risk. Their overreaction story predicts that 3‐year losers have strong post‐ranking returns relative to 3‐year winners. When we allow for variation in β that is unrelated to size, there is no reliable relation between β and average return. , and book‐to‐market equity) used to explain average returns. ME The independent variation in β obtained with the second‐pass sort on β lowers the correlation to −0.50. ME / to 0.07 0.28 t / We show next that when common stock portfolios are formed on size alone, there seems to be evidence for the model's central prediction: average return is positively related to β. / − BE and June of year t. It must also have monthly returns for at least 24 of the 60 months preceding July of year t (for “pre‐ranking” β estimates, discussed below). We judge that the precision of the full‐period post–ranking portfolio βs, relative to the imprecise β estimates that would be obtained for individual stocks, more than makes up for the fact that true βs are not the same for all stocks in a portfolio. Negative BE (which results from persistently negative earnings) and high ME E The Relationship Between Investor Views, Constraints, Expectation, and Covariance in Mean-Variance Optimization. Our main result is that two easily measured variables, size and book‐to‐market equity, seem to describe the cross‐section of average stock returns. If current earnings proxy for expected future earnings, high‐risk stocks with high expected returns will have low prices relative to their earnings. When portfolios are formed on pre‐ranking βs alone (Table II), the post‐ranking βs for the portfolios almost perfectly reproduce the ordering of the pre‐ranking βs. These 25 years are a major part of the samples in the early studies of the SLB model of Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973). I am aware of the sandwich package and its ability to estimate Newey-West standard errors, as well as providing functions for clustering. In short, any evidence of a positive average premium for β in the subperiods seems to be a size effect in disguise. Their most powerful factor in explaining the size effect is the difference between the monthly returns on low‐ and high‐grade corporate bonds, which in principle captures a kind of default risk in returns that is priced. = − ME ) They can be regarded as different ways of extracting information from stock prices about the cross‐section of expected stock returns (Ball (1978); Keim (1988)). in Tables II and IV. KEY WORDS: ... Fama–MacBeth approach is thus a special case of our suggested BE Unlike the size portfolios, the β‐sorted portfolios do not support the SLB model. (Note also that, as claimed earlier, estimating β as the sum of the slopes in the regression of a portfolio's return on the current and prior month's NYSE value‐weighted return produces much larger βs for the smallest ME portfolios and slightly smaller βs for the largest ME portfolios.). 1 / − Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) find that, as predicted by the SLB model, there is a positive simple relation between average stock returns and β during the pre‐1969 period. E If you do not receive an email within 10 minutes, your email address may not be registered, They say that when the tests allow for variation in β that is unrelated to size, the relation between β and average return for 1941–1990 is weak, perhaps nonexistent, even when β is the only explanatory variable. Any attempt to salvage the simple positive relation between β and average return predicted by the SLB model runs into three damaging facts, clear in Table AII. t E / BE I have read and accept the Wiley Online Library Terms and Conditions of Use, Extensions and violations of the statutory SEC Form 10‐k filing date, Unpublished manuscript, University of Chicago, Chicago, IL, Anomalies in relationships between securities' yields and yield‐surrogates, The relationship between return and market value of common stocks, The relationship between earnings yield, market value, and return for NYSE common stocks: Further evidence, Debt/Equity ratio and expected common stock returns: Empirical evidence, Capital market equilibrium with restricted borrowing, The capital asset pricing model: some empirical tests, An unconditional asset‐pricing test and the role of firm size as an instrumental variable for risk, Structural and return characteristics of small and large firms, An exploratory investigation of the firm size effect, Risk measurement when shares are subject to infrequent trading, Risk, return and equilibrium: Empirical tests, Risk measurement when shares are subject to infrequent trading: Comment, Earnings yields, market values, and stock returns, Size‐related anomalies and stock return seasonality, Stock market regularities: A synthesis of the evidence and explanations, Systematic risk, total risk and size as determinants of stock market returns, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Portfolio Selection: Efficient Diversification of Investments, An intertemporal capital asset pricing model, Vas ist Das? ( ) more like that of the earlier studies. BE Emerging market currency risk exposure: evidence from South Africa. © 2010 American Accounting Association In contrast, within the columns of the average return and β matrices of Table I, average returns and βs decrease with increasing size. Using NYSE stocks ensures that the β breakpoints are not dominated after 1973 by the many small stocks on NASDAQ. E Our work (in progress) suggests that there is indeed a clean separation between high and low Most of the standard errors of the βs (not shown) are 0.05 or less, only 1 is greater than 0.1, and the standard errors are small relative to the range of the βs (0.53 to 1.79). Performance peer groups in CEO compensation contracts. In contrast, the average slope on size in the bivariate regressions We use all nonfinancial firms in the intersection of (a) the NYSE, AMEX, and NASDAQ return files from the Center for Research in Security Prices (CRSP) and (b) the merged COMPUSTAT annual industrial files of income‐statement and balance‐sheet data, also maintained by CRSP. ME BE BE The average slope from the monthly regressions of returns on In( Since the FM intercept is constrained to be the same for all stocks, FM regressions always impose a linear factor structure on returns and expected returns that is consistent with the multifactor asset‐pricing models of Merton (1973) and Ross (1976). It is possible that the risk captured by Request Permissions. The next two most common methods used OLS (or an analogous method) to estimate the coefficients but reported standard errors adjusted for correlation within a cluster. The sum βs are meant to adjust for nonsynchronous trading (Dimson (1979)). . Chan, Hamao, and Lakonishok (1991) find that book‐to‐market equity, 1 1.82 The independent variables in the Fama‐MacBeth regressions are defined for each firm at the end of December of each year Resuscitation of the SLB model requires that a better proxy for the market portfolio (a) overturns our evidence that the simple relation between β and average stock returns is flat and (b) leaves β as the only variable relevant for explaining average returns. BE Although the post‐ranking βs in Table I increase strongly in each size decile, average returns are flat or show a slight tendency to decline. ME ME 1.99 Table IV shows average returns for July 1963 to December 1990 for portfolios formed on ranked values of book‐to‐market equity A worldwide t E BE Both estimates are about 3 standard errors from 0. We have done the tests using the smaller sample of firms with December fiscal yearends with similar results. The discussion above assumes that the asset‐pricing effects captured by size and book‐to‐market equity are rational. / In contrast, the average slopes for In(ME) and In( Within a size decile (across a row of the average return matrix), returns typically increase strongly with / I read many papers on asset pricing and have some basic doubts regarding Fama French Time series regression: 1. In multivariate tests, the negative relation between size and average return is robust to the inclusion of other variables. The average residuals (not shown) from the FM regressions (1) to (3) that use the returns on the 100 size‐β portfolios as the dependent variable are always within 0.01 of those from the regressions for individual stock returns. and In For example, although the two extreme portfolios, 1A and 10B, have much different βs, they have nearly identical average returns (1.20% and 1.18% per month). portfolio to 1.83% for the highest, a difference of 1.53% per month. − ) If our results are more than chance, they have practical implications for portfolio formation and performance evaluation by investors whose primary concern is long‐term average returns. Section III examines the roles of ( Our bottom‐line results are: (a) β does not seem to help explain the cross‐section of average stock returns, and (b) the combination of size and book‐to‐market equity seems to absorb the roles of leverage and The Sharpe‐Lintner‐Black model has long shaped the way academics and practitioners think about average return and risk. ME Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). E Other redefinitions of the β, size, and book‐to‐market variables will produce different regression slopes and perhaps different inferences about average premiums, including possible resuscitation of a role for β. E / It is meant to help people who have looked at Mitch Petersen's Programming Advice page, but want to use SAS instead of Stata.. Mitch has posted results using a test data set that you can use to compare the output below to see how well they agree. / − Panel A shows our results for value-weighted portfolios. ( (Table AII). just captures the unraveling (regression toward the mean) of irrational market whims about the prospects of firms. Like them, we find that when portfolios are formed on size alone, there are strong relations between average return and either size or β; average return increases with β and decreases with size. For terms and use, please refer to our Terms and Conditions For example, if there is a general fall in stock prices during the year, ratios measured early in the year will tend to be lower than ratios measured later. / The regressions show that when one allows for variation in β that is unrelated to size, the relation between β and average return is flat, even when β is the only explanatory variable. ( P Second, the β sort is not a refined size sort. A are about twice those for February to December. ) The problem for the SLB model is that there is no similar ordering in the average returns on the β‐sorted portfolios. Chan and Chen use only size portfolios. Each month the cross‐section of returns on stocks is regressed on variables hypothesized to explain expected returns. / ) alone is 0.50%, with a t‐statistic of 5.71. This allows us to use individual stocks in the FM asset‐pricing tests. and 1 ) About 30% Who Manages the Firm Matters: The Incremental Effect of Individual Managers on Accounting Quality. t variables are used alone in the FM regressions in Table III. / − and In million) and toward stocks with relatively high book‐to‐market ratios (Table IV says that In ( / International Journal of Hospitality Management. Thus, when we subdivide size portfolios on the basis of pre‐ranking βs, we find a strong relation between average return and size, but no relation between average return and β. Handbook of Research on Engineering, Business, and Healthcare Applications of Data Science and Analytics. When the residuals from the regressions of returns on β are grouped using the pre‐ranking βs of individual stocks, the average residuals are strongly positive for low‐β stocks (0.51 % per month for group 1A) and negative for high‐β stocks (−1.05% for 10B). Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) find that, as predicted by the model, there is a positive simple relation between average return and market β during the early years (1926–1968) of the CRSP NYSE returns file. . Fama-MacBeth results reject the validity of the Fama and French model, but the presence of unexpected correlation casts doubt on these results. has a familiar U‐shape (e.g., Jaffe, Keim, and Westerfield (1989) for U.S. data, and Chan, Hamao, and Lakonishok (1991) for Japan). stocks are better captured by their size, which Table IV says is on average small. / As long as size (ln(ME)) is also in the regression, this change will not affect the intercept, the fitted values or the . / / Mathematical modelling of a ) But the change, in variables increases the average slope (and the t‐statistic) on ln(ME). fixed effects or within estimation). We are forced to conclude that the SLB model does not describe the last 50 years of average stock returns. Multifactor Risk Models and Portfolio Construction and Management. A high ratio of book equity to market equity (a low stock price relative to book value) says that the market judges the prospects of a firm to be poor relative to firms with low . Preferences and Skill in Sustainable Investing. t The role of efficiency in capital asset pricing: a research on Nasdaq technology sector. BE : on average, the returns on the lowest and highest t We suggest several paths of inquiry. / of the AAA), International Accounting, and Teaching and Curriculum. We use returns for July to June to match the returns in later tests that use the accounting data. 1 In short, our tests do not support the most basic prediction of the SLB model, that average stock returns are positively related to market βs. / ME Modelling shares choice to enter in a portfolio using artificial neural networks (ANN). We have time series data, but still it is a simple OLS we run in FF model. t + / Low 0 Using ME at fiscal yearends is also problematic; then part of the cross‐sectional variation of a ratio for a given year is due to market‐wide variation in the ratio during the year. For example, the post‐ranking βs for the 10 portfolios in the smallest size decile range from 1.05 to 1.79. firms are persistently strong performers, while the economic performance of high ( ) Most previous tests use portfolios because estimates of market βs are more precise for portfolios. should be related to expected returns, whatever the omitted sources of risk. 1 Materials & Methods 2.1. The standard errors from this method do not correct for time-series autocorrelation.   Thus, to be included in the return tests for July of year t, a firm must have a CRSP stock price for December of year . P Specifically, several findings in the implied cost of equity capital literature, the cost of debt literature, and the conservatism literature appear not to be robust to the use of well-specified test statistics. Please check your email for instructions on resetting your password. Fama-MacBeth regression with Newey-West correction, but panel date is not regularly spaced 20 Aug 2018, 20:39 My panel data is not always consecutive: there are some gaps for time series … t The results for NYSE stocks for 1941–1990 are thus much like those for NYSE, AMEX, and NASDAQ stocks for 1963–1990. ME Income Inequality and Per Capita Income: Equilibrium of Interactions. 1.23 BE Average firms is the average number of stocks in the portfolios each month. The puzzle of the opposite slopes on In Unlike the simple relation between β and average return, the univariate relations between average return and size, leverage, Journal of Multinational Financial Management. Does investor relations matter in the tourism industry? Contrary to the central prediction of the SLB model, the second‐pass β sort produces little variation in average returns. ln(ME), Panel A: Stocks Sorted on Book‐to‐Market Equity (, Panel B: Stocks Sorted on Earnings‐Price Ratio (. Shariah compliance and information transmission: evidence from an emerging market. ) Simple tests do not confirm that the size and book‐to‐market effects in average returns are due to market overreaction, at least of the type posited by DeBondt and Thaler (1985). organization, the AAA promotes education, research, service, and interaction Since we match accounting data for all fiscal yearends in calendar year This page shows how to run regressions with fixed effect or clustered standard errors, or Fama-Macbeth regressions in SAS. The regressions of returns on β alone show that using the βs of the portfolios formed on size and β, rather than size alone, causes the average slope on β to fall from about 1.4% per month (Table AI) to about 0.23% (about 1 standard error from 0). Advertising Exposure and Investor Attention: Estimates from Super Bowl Commercials. Another possibility is that the proportionality condition (1) for the variation through time in true βs, that justifies the use of full‐period post–ranking βs in the FM tests, does not work well for portfolios formed on size and β. Contrary to claims in the literature, we find that the Z2 statistic and Newey-West corrected Fama-MacBeth standard errors do not correct for both cross-sectional and time-series dependence. Similarly, including ln(ME) in the regressions lowers the average slope on In has long been touted as a measure of the return prospects of stocks, there is no evidence that its explanatory power deteriorates through time. estimates and robust t-statistics in parentheses adjusted for heteroskedasticity and serial correlation. Prescriptions for using this evidence depend on (a) whether it will persist, and (b) whether it results from rational or irrational asset‐pricing. The average slopes provide standard FM tests for determining which explanatory variables on average have non‐zero expected premiums during the July 1963 to December 1990 period. 1 BE The sum βs are the sum of the slopes from a regression of the post‐ranking monthly returns on the current and prior month's VW NYSE returns. BE We take this to be evidence that the pre‐ranking β sort captures the ordering of true post‐ranking βs. ) / for the portfolios sorted on ME or ( / Asset Pricing with Prof. John H. Cochrane PART II. , and (b) returns on β, In(ME), and In (b) The post‐ranking βs closely reproduce (in deciles 2 to 10 they exactly reproduce) the ordering of the pre‐ranking βs used to form the β‐sorted portfolios. The All row shows average returns for equal‐weighted portfolios of the stocks in each, Mean is the time‐series mean of a monthly return, Std is its time‐series standard deviation, and, NYSE Value‐Weighted (VW) and Equal‐Weighted (EW) Portfolio Returns, Average Residuals for Stocks Grouped on Size, Average Residuals for Stocks Grouped on Pre‐Ranking, Panel A: Average Monthly Return (in Percent), Mean is the average VW or EW return or an average slope from the monthly cross‐sectional regressions of individual stock returns on. A ME Extending the tests to bills and other bonds may well change our inferences about average risk premiums, including the revival of a role for market β. , Turning alphas into betas: Arbitrage and endogenous risk. Note that Fama MacBeth regressions provide standard errors corrected only for cross-sectional correlation. E / E ) is not extreme, and the average slopes in the bivariate regressions in Table III show that In(ME) and In / P t Like Reinganum (1981) and Lakonishok and Shapiro (1986), we find that the relation between β and average return disappears during the more recent 1963–1990 period, even when β is used alone to explain average returns. (a) Forming portfolios on size and pre‐ranking βs produces a wide range of post‐ranking βs in every size decile. ME Downside beta and the cross section of equity returns: A decade later. and average return is due to the positive correlation between International Review of Financial Analysis. ( ME for individual stocks. Earnings management, business strategy, and bankruptcy risk: evidence from Indonesia. t Profitability of momentum strategies in Latin America. Oil price shocks, investor sentiment, and asset pricing anomalies in the oil and gas industry. P Our results for 1941–1990 seem to contradict the evidence in Black, Jensen, and Scholes (BJS) (1972) and Fama and MacBeth (FM) (1973) that there is a reliable positive relation between average return and β. (4.72% per month, 4.57 standard errors from 0) shows that average returns increase with There are several empirical contradictions of the Sharpe‐Lintner‐Black (SLB) model. . (which typically means that stock prices have fallen) are both signals of poor earning prospects. ME BE The intercepts and slopes in the monthly FM regressions of returns on ln(ME) and ln(BE/ME) are returns on portfolios that mimic the underlying common risk factors in returns proxied by size and book‐to‐market equity (Fama (1976), chapter 9). 1 dummy. / / A high book‐to‐market ratio also says that a firm's market leverage is high relative to its book leverage; the firm has a large amount of market‐imposed leverage because the market judges that its prospects are poor and discounts its stock price relative to book value. the contribution an article makes to the literature. The U‐shaped relation between average return and / Therefore correct for the violation of the assumption of no serial correlation. , and leverage ratios is objectionable for firms that do not have December fiscal yearends because the accounting variable in the numerator of a ratio is not aligned with the market value in the denominator. Using logs also leads to a simple interpretation of the relation between the roles of leverage and book‐to‐market equity in average returns. / is a catch‐all proxy for unnamed factors in expected returns; ME P Thus it is not surprising that the average intercepts are always large relative to their standard errors and relative to the returns on the NYSE VW and EW portfolios. Research on the Factors Affecting the Delisting of Chinese Listed Companies. / / These βs produce inferences on the role of β in average returns like those reported below. firms have low earnings on assets relative to low Stocks are assigned the post‐ranking (sum)β of the size portfolio they are in at the end of year This is not surprising given that the correlation between the time‐series of 1941–1990 monthly FM slopes on β or ln(ME) for the comparable portfolio and individual stock regressions is always greater than 0.99. − The average monthly February‐to‐December slopes for ln The value of voting rights in Italian cooperative banks: a quasi-natural experiment. . ( The method estimates the betas and risk premia for any risk factors that are expected to determine asset prices. E The 6‐month (minimum) gap between fiscal yearend and the return tests is conservative. Working off-campus? = while Section2.2explains the methodology, first the classical (Time-Series, Cross-Sectional, and Fama-MacBeth) and second, the resampling technique developed for the analysis. Risk, resilience, and Shariah-compliance. − / (for pre‐ranking β estimates). But Table AIV also shows that drawing a distinction between the results for 1941–1965 and 1966–1990 is misleading. We should not, however, exaggerate the links between size and book‐to‐market equity. ( (c) Contrary to the SLB model, the β sorts do not produce a similar ordering of average returns. ME In addition, more than 40% of the December fiscal yearend firms that do comply with the 90‐day rule file on March 31, and their reports are not made public until April. BE E dummy and lowers the average slope on 1 We stick with the simpler sum βs. The cross‐section of book‐to‐market ratios might result from market overreaction to the relative prospects of firms. Average returns fall from 1.64% per month for the smallest ME portfolio to 0.90% for the largest. ME Sparsity and Performance Enhanced Markowitz Portfolios Using Second-Order Cone Programming. = Optimization of Complex Systems: Theory, Models, Algorithms and Applications. . E In the regressions of individual stock returns on β (where stocks are assigned the β of their size portfolio), the premium for a unit of β is 1.39%. , the gap between the accounting data and the matching returns varies across firms. Financial Analytics: Science and Experience. / The Role of Future Economic Conditions in the Cross-section of Stock Returns: Evidence from the US and UK. JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. , leverage, and book‐to‐market equity in the cross‐section of average returns on NYSE, AMEX, and NASDAQ stocks. Number of times cited according to CrossRef: Recent Applications of Financial Risk Modelling and Portfolio Management. The correlation between size and book‐to‐market equity affects the regressions in Table III. Whether one looks at portfolios sorted on β alone (Table II) or on size and then β (Table I), average returns are flat (Table II) or decline slightly (Table. A Journal of Islamic Accounting and Business Research. ( ( The β‐sorted portfolios in Tables I and II also provide strong evidence against the β‐measurement‐error story. Average Return is the time‐series average of the monthly portfolio returns for 1941–1990, in percent. The appendix shows that NYSE returns for 1941–1990 behave like the NYSE, AMEX, and NASDAQ returns for 1963–1990; there is a reliable size effect over the full 50‐year period, but little relation between β and average return. BE ( P Whatever the underlying economic causes, our main result is straightforward. of AAA members live and work outside the United States. The earning prospects of distressed firms are more sensitive to economic conditions. = But the most damaging evidence against the SLB model comes from the univariate regressions of returns on β in Table AIII. ) The subperiod variation in the average slopes from the FM regressions of returns on β alone seems moot, however, given the evidence in Table AIV that adding size always kills any positive tradeoff of average return for β in the subperiods. E Correlation matrix: this SAS macro generates the time-series average of cross-sectional correlation matrix. ME Fama-Macbeth: 2013/04/18: Performs Fama-MacBeth regression on a set of portfolio or asset returns and factors and returns summary results including the output of a simple cross-sectional average regression. / t ( Air Pollution, Individual Investors, and Stock Pricing in China. 2.97 Firm Characteristics, Stock Market Regimes, and the Cross-Section of Expected Returns. The 4 extreme portfolios (1A, IB, 10A, and 10B) split the smallest and largest deciles in half. Twenty-nine percent of the papers included dummy variables for each cluster (e.g. The regressions that follow confirm this conclusion, and they produce another that is stronger. / / Across all 100 size‐β portfolios, the post‐ranking βs range from 0.53 to 1.79, a spread 2.4 times the spread, 0.52, obtained with size portfolios alone. The long-run performance of acquiring firms in mergers and acquisitions: Does managerial ability matter?. If overreaction tends to be corrected, The results suggest that most of the relation between (positive) ( and returns for at least 24 of the 60 months ending in December of year Similarly, looking down the columns of the average return matrix shows that there is a negative relation between average return and size: on average, the spread of returns across the size portfolios in a However, I have not seen anything with respect to Fama-MacBeth. The portfolios are formed at the end of June each year and their equal‐weighted returns are calculated for the next 12 months. The North American Journal of Economics and Finance. The role of dividend yield as agency conflict determinant: case of Indonesia. Like the average returns in Tables I and II, the regressions in Table III say that size, ln(ME), helps explain the cross‐section of average stock returns. Interest, Auditing, taxation (the American Taxation Association is a Section This is the only period in Table AIV that produces an average premium for β (1.26% per month) that is both positive and more than 2 standard errors from 0. The FM regressions in Table AIII formalize the roles of size and β in NYSE average returns for 1941–1990. First, in each size decile the post‐ranking βs closely reproduce the ordering of the pre‐ranking βs. What lies behind the asset growth effect?. Our approach is to estimate βs for portfolios and then assign a portfolio's β to each stock in the portfolio. I) as the post‐ranking βs increase. Business sentiment and the cross-section of global equity returns. / / We first replicate the results of Chan and Chen (1988). / , illustrated in Table IV; firms with high / , provide a simple and powerful characterization of the cross‐section of average stock returns for the 1963–1990 period. The theoretical basis of the tests is the "two-parameter" portfolio model and models of market equilibrium derived from the two-parameter portfolio model. / Despite the wide range of βs in each size decile, average returns show no tendency to increase with β. AII. Fama-MacBeth Two-pass Regression: Improving the Risk Premia Estimates In this paper, we provide the asymptotic theory for the widely used Fama and MacBeth (1973) two-pass risk premia estimates in the usual case of a large number of assets. + Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637. Risk and Return of Equity and the Capital Asset Pricing Model. ( / The Sharpe‐Lintner‐Black (SLB) model plays an important role in the way academics and practitioners think about risk and the relation between risk and expected return. The residuals from the monthly regressions in year t are grouped into 12 portfolios on the basis of size or pre‐ranking β (estimated with 24 to 60 months of returns, as available) as of the end of year Simulation of Stock Prediction System using Artificial Neural Networks. − BE approach is of further interest since serial correlation and conditional heteroscedasticity in the joint distribution of returns and factors is easily accommodated in making asymptotically valid 1Applications of the procedure in recent years can be found in at least 735 papers that cite Fama and MacBeth (1973), as complied by Google. / / series. Which one is the best fourth factor in China? Similar comments hold for 1941–1950. Grouped on the basis of ME for individual stocks, the average residuals from the univariate regressions of returns on the βs of the 100 size‐β portfolios are strongly positive for small stocks and negative for large stocks (0.60% per month for the smallest ME group, 1A, and −0.27% for the largest, 10B). We demonstrate analytically and using simulations that the standard OLS and GLS estimators can contain large BE This spread of βs across the 10 size deciles is smaller than the spread of post‐ranking βs produced by the β sort of any size decile. This item is part of JSTOR collection B. Fama‐MacBeth Regressions Table III shows time‐series averages of the slopes from the month‐by‐month Fama‐MacBeth (FM) regressions of the cross‐section of stock returns on size, β , and the other variables (leverage, E / P , and book‐to‐market equity) used to explain average returns. 1.17 E   In the individual‐stock regressions, these values of the explanatory variables are matched with CRSP returns for each of the 12 months in year t. The portfolio regressions match the equal‐weighted portfolio returns for the size‐β portfolios (Table AII) with the equal‐weighted averages of β and ln(ME) for the surviving stocks in each month of year t. Slope is the time‐series average of the monthly regression slopes from 1941–1990 (600 months); SE is the time‐series standard error of the average slope. / Appendix Table AI shows that using sum βs produces large increases in the βs of the smallest ME portfolios and small declines in the βs of the largest ME portfolios. A The average return is the time‐series average of the monthly equal‐weighted portfolio returns, in percent. And, of course, at the moment, we have no theoretical basis for choosing among different versions of the variables. / group is 0.58% per month. E . This appendix also has methodological goals. − observed in Table IV is also apparent when the The βs in BJS and FM are from portfolios formed on β alone, and the market proxy is the NYSE equal‐weighted portfolio. The Impact of El Nio-Southern Oscillation on U.S. Food and Agricultural Stock Returns. . BE More important, COMPUSTAT data for earlier years have a serious selection bias; the pre‐1962 data are tilted toward big historically successful firms. The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market βs (the slope in the regression of a security's return on the market's return), and (b) market βs suffice to describe the cross‐section of expected returns. We exclude financial firms because the high leverage that is normal for these firms probably does not have the same meaning as for nonfinancial firms, where high leverage more likely indicates distress. Sorted on size alone, the post‐ranking βs range from 1.44 for the smallest ME portfolio to 0.92 for the largest. But the evidence is muddied by the tight relation between size and the βs of size portfolios. E ME What explains the poor results for β? Even for the 1941–1965 period, however, the relation between β and average return disappears when we control for size. Our goal is to evaluate the joint roles of market β, size, The average slopes for In Cochrane (2009) argues that this is not a problem, because stock returns are likely to be uncorrelated over time. E In the regressions of the size‐portfolio returns on β alone, the average premium for a unit of β is 1.45% per month. A the association began publishing the first of its ten journals, The Accounting The average slopes for the two leverage variables are opposite in sign but close in absolute value, e.g., 0.50 and −0.57. tend to have high book‐to‐market equity ratios. The Accounting Review is the premier journal for publishing articles reporting the results of accounting research and explaining and illustrating related research methodology. / portfolio. Fama-MacBeth (1973) regressions with options to weight by number of observations as proxy for precision of the years' estimates and an option to use a Newey-West correction for serial correlation in coefficient estimates. The FM regressions that explain returns with leverage variables provide interesting insight into the relation between book‐to‐market equity and average return. (The appendix gives more evidence on this important issue.) We have examined the monthly slopes from the FM regressions in Table VI for evidence of a January seasonal in the relation between book‐to‐market equity and average return. The strong negative average slope in the univariate regressions of returns on β for 1981–1990 P BE = 1 Table AII also shows, however, that investors are not compensated for the variation in β that is independent of size. ME Moreover, the tests here are restricted to stocks. In fact, if stock prices are rational, ME Investment Management and Financial Innovations. Eine kurze Geschichte der Unternehmensbewertung. − firms. Value and patience: The value premium in a dividend-growth model with hyperbolic discounting. t The 4 extreme portfolios (1A, 1B, 10A, and 10B) split the bottom and top deciles in half. P 2. / To avoid giving extreme observations heavy weight in the regressions, the smallest and largest 0.5% of the observations on.