Навигация
Популярное

Главная » Периодические издания » Multifactor explanations 1 2 3 multifactor explanations Rf is the onemonth Treasury bill rate observed at the beginning of the month (from CRSP). The explanatory returns RM, SMB, and HML are formed as follows. At the end of June of each year t (19631993), NYSE, AMEX, and Nasdaq stocks are allocated to two groups (small or big, S or B) based on whether their June market equity (ME, stock price times shares outstanding) is below or above the median ME for NYSE stocks. NYSE, AMEX, and Nasdaq stocks are allocated in an independent sort to three booktomarket equity (BE/ME) groups (low, medium, or high; L, M, or H) based on the breakpoints for the bottom 30 percent, middle 40 percent, and top 30 percent of the values of BE/ME for NYSE stocks. Six sizeBE/ME portfolios (S/L, S/M, S/H, B/L, B/M, B/H) are defined as the intersections of the two ME and the three BE/ME groups. Valueweight monthly returns on the portfolios are calculated from July to the following June. SMB is the difference, each month, between the average of the returns on the three smallstock portfolios (S/L, S/M, and S/H) and the average of the returns on the three bigstock portfolios (B/L, B/M, and B/H). HML is the difference between the average of the returns on the two highBE/ME portfolios (S/H and B/H) and the average of the returns on the two lowBE/ME portfolios (S/L and B/L). The 25 sizeBE/ME portfolios are formed like the six sizeBE/ME portfolios used to construct SMB and HML, except that quintile breakpoints for ME and BE/ME for NYSE stocks are used to allocate NYSE, AMEX, and Nasdaq stocks to the portfolios. BE is the COMPUSTAT book value of stockholders equity, plus balance sheet deferred taxes and investment tax credit (if available), minus the book value of preferred stock. Depending on availability, we use redemption, liquidation, or par value (in that order) to estimate the book value of preferred stock. The BE/ME ratio used to form portfolios in June of year t is then book common equity for the fiscal year ending in calendar year t  1, divided by market equity at the end of December of t  1. We do not use negative BE firms, which are rare prior to 1980, when calculating the breakpoints for BE/ME or when forming the sizeBE/ME portfolios. Also, only firms with ordinary common equity (as classified by CRSP) are included in the tests. This means that ADRs, REITs, and units of beneficial interest are excluded. The market return RM is the valueweight return on all stocks in the sizeBE/ME portfolios, plus the negative BE stocks excluded from the portfolios. BooktoMarket Equity (BE/ME) Quintiles Size Low 2 3 4 High Low 2 3 4 High Panel A: Summary Statistics Means Standard Deviations
BooktoMarket Equity (BE/ME) Quintiles
periodically on size, BE/ME, E/P, C/P, sales growth, and past returns results in loadings on the three factors that are roughly constant. Variation through time in the slopes is, however, important in other applications. For example, FF (1994) show that because industries wander between growth and distress, it is Table IContinued critical to allow for variation in SMB and HML slopes when applying (1) and (2) to industries. II. LSV Deciles Lakonishok, Shleifer, and Vishny (LSV 1994) examine the returns on sets of deciles formed from sorts on BE/ME, E/P, C/P, and fiveyear sales rank. Table II summarizes the excess returns on our versions of these portfolios. The portfolios are formed each year as in LSV using COMPUSTAT accounting data for the fiscal year ending in the current calendar year (see table footnote). We then calculate returns beginning in July of the following year. (LSV start their returns in April.) To reduce the influence of small stocks in these (equalweight) portfolios, we use only NYSE stocks. (LSV use NYSE and AMEX.) To be included in the tests for a given year, a stock must have data on all the LSV variables. Thus, firms must have COMPUSTAT data on sales for six years before they are included in the return tests. As in LSV, this reduces biases that might arise because COMPUSTAT includes historical data when it adds firms (Banz and Breen (1986), Kothari, Shanken, and Sloan (1995)). Our sorts of NYSE stocks in Table II produce strong positive relations between average return and BE/ME, E/P, or C/P, much like those reported by LSV for NYSE and AMEX firms. Like LSV, we find that past sales growth is negatively related to future return. The estimates of the threefactor regression (2) in Table III show, however, that the threefactor model (1) captures these patterns in average returns. The regression intercepts are consistently small. Despite the strong explanatory power of the regressions (most R2 values are greater than 0.92), the GRS tests never come close to rejecting the hypothesis that the threefactor model describes average returns. In terms of both the magnitudes of the intercepts and the GRS tests, the threefactor model does a better job on the LSV deciles than it does on the 25 FF sizeBE/ME portfolios. (Compare Tables I and III.) For perspective on why the threefactor model works so well on the LSV portfolios, Table III shows the regression slopes for the C/P deciles. HigherC/P portfolios produce larger slopes on SMB and especially HML. This pattern in the slopes is also observed for the BE/ME and E/P deciles (not shown). It seems that dividing an accounting variable by stock price produces a characterization of stocks that is related to their loadings on HML. Given the evidence in FF (1995) that loadings on HML proxy for relative distress, we can infer that low BE/ME, E/P, and C/P are typical of strong stocks, while high BE/ME, E/P, and C/P are typical of stocks that are relatively distressed. The patterns in the loadings of the BE/ME, E/P, and C/P deciles on HML, and the high average value of HML (0.46 percent per month, 6.33 percent per year) largely explain how the threefactor regressions transform the strong positive relations between average return and these ratios (Table II) into intercepts that are close to 0.0. Among the sorts in Table III, the threefactor model has the hardest time with the returns on the salesrank portfolios. Recall that high salesrank firms Table ii Summary Statistics for Simple Monthly Excess Returns (in Percent) on the LSV EqualWeight Deciles: 7/6312/93, 366 Months At the end of June of each year t (19631993), the NYSE stocks on COMPUSTAT are allocated to ten portfolios, based on the decile breakpoints for BE/ME (booktomarket equity), E/P (earnings/price), C/P (cashflow/price), and past fiveyear sales rank (5Yr SR). Equalweight returns on the portfolios are calculated from July to the following June, resulting in a time series of 366 monthly returns for July 1963 to December 1993. To be included in the tests for a given year, a stock must have data on all of the portfolioformation variables of this table. Thus, the sample of firms is the same for all variables. For portfolios formed in June of year t, the denominator of BE/ME, E/P, and C/P is market equity (ME, stock price times shares outstanding) for the end of December of year t  1, and BE, E, and С are for the fiscal year ending in calendar year t  1. Book equity BE is defined in Table I. E is earnings before extraordinary items but after interest, depreciation, taxes, and preferred dividends. Cash flow, C, is E plus depreciation. The fiveyear sales rank for June of year t, 5Yr SR(£), is the weighted average of the annual sales growth ranks for the prior five years, that is, 5Yr SR(*) = X (6 j) X Rank(* j) 7 = 1 The sales growth for year t  j is the percentage change in sales from t  j  1 to t  j, ln[Sales(£ j)/Sa\es(t  j  1)]. Only firms with data for all five prior years are used to determine the annual sales growth ranks for years t  5 to t  1. For each portfolio, the table shows the mean monthly return in excess ofthe onemonth Treasury bill rate (Mean), the standard deviation of the monthly excess returns (Std. Dev.), and the ratio of the mean excess return to its standard error [£(mean) = Mean/(Std. Dev./3651/2)]. Ave ME is the average size (ME, in $millions) of the firms in a portfolio, averaged across the 366 sample months. Deciles
Table III ThreeFactor TimeSeries Regressions for Monthly Excess Returns (in Percent) on the LSV EqualWeight Deciles: 7/6312/93, 366 Months Ri  Rf= at + bt(RM  Rf) + sSMB + ЛДШЬ + et The formation of the BE/ME, E/P, C/P, and fiveyearsalesrank (5Yr SR) deciles is described in Table II. The explanatory returns, RM  Rf, SMB, and HML are described in Table I. t{ ) is a regression coefficient divided by its standard error. The regression R2s are adjusted for degrees of freedom. GRS is the Fstatistic of Gibbons, Ross, and Shanken (1989), testing the hypothesis that the regression intercepts for a set of ten portfolios are all 0.0. p(GRS) is the pvalue of GRS, that is, the probability of a GRS value as large or larger than the observed value if the zerointercepts hypothesis is true. Deciles 123456789 10 GRS p(GRS)
High
(strong past performers) have low future returns, and low salesrank firms (weak past performers) have high future returns (Table II). The threefactor model of (1) captures most of this pattern in average returns, largely because low salesrank stocks behave like distressed stocks (they have stronger load ings on HML). But a hint of the pattern is left in the regression intercepts. Except for the highest salesrank decile, however, the intercepts are close to 0.0. Moreover, although the intercepts for the salesrank deciles produce the largest GRS Fstatistic (0.87), it is close to the median of its distribution when the true intercepts are all 0.0 (its pvalue is 0.563). This evidence that the threefactor model describes the returns on the salesrank deciles is important since sales rank is the only portfolioformation variable (here and in LSV) that is not a transformed version of stock price. (See also the industry tests in FF (1994).) III. LSV DoubleSort Portfolios LSV argue that sorting stocks on two accounting variables more accurately distinguishes between strong and distressed stocks, and produces larger spreads in average returns. Because accounting ratios with stock price in the denominator tend to be correlated, LSV suggest combining sorts on sales rank with sorts on BE/ME, E/P, or C/P. We follow their procedure and separately sort firms each year into three groups (low 30 percent, medium 40 percent, and high 30 percent) on each variable. We then form sets of nine portfolios as the intersections of the salesrank sort and the sorts on BE/ME, E/P, or C/P. Confirming their results, Table IV shows that the salesrank sort increases the spread of average returns provided by the sorts on BE/ME, E/P, or C/P. In fact, the two doublewhammy portfolios, combining low BE/ME, E/P, or C/P with high sales growth (portfolio 11), and high BE/ME, E/P, or C/P with low sales growth (portfolio 33), always have the lowest and highest postformation average returns. Table V shows that the threefactor model has little trouble describing the returns on the LSV doublesort portfolios. Strong negative loadings on HML (which has a high average premium) bring the low returns on the 11 portfolios comfortably within the predictions of the threefactor model; the most extreme intercept for the 11 portfolios is 6 basis points (0.06 percent) per month and less than one standard error from 0.0. Conversely, because the 33 portfolios have strong positive loadings on SMB and HML (they behave like smaller distressed stocks), their high average returns are also predicted by the threefactor model. The intercepts for these portfolios are positive, but again quite close to (less than 8 basis points and 0.7 standard errors from) 0.0. The GRS tests in Table V support the inference that the intercepts in the threefactor regression (2) are 0.0; the smallestpvalue is 0.284. Thus, whether the spreads in average returns on the LSV doublesort portfolios are caused by risk or overreaction, the threefactor model in equation (1) describes them parsimoniously. IV. Portfolios Formed on Past Returns DeBondt and Thaler (1985) find that when portfolios are formed on longterm (three to fiveyear) past returns, losers (low past returns) have high Table IV Summary Statistics for Excess Returns (in Percent) on the LSV EqualWeight DoubleSort Portfolios: 7/6312/93, 366 Months At the end of June of each year t (19631993), the NYSE stocks on COMPUSTAT are allocated to three equal groups (low, medium, and high: 1, 2, and 3) based on their sorted BE/ME, E/P, or C/P ratios for year t  1. The NYSE stocks on COMPUSTAT are also allocated to three equal groups (high, medium, and low: 1, 2, and 3) based on their fiveyear sales rank. The intersections of the salesrank sort with the BE/ME, E/P, or E/P sorts are then used to create three sets of nine portfolios (BE/ME & Sales Rank, E/P & Sales Rank, C/P & Sales Rank). Equalweight returns on the portfolios are calculated from July to the following June. To be included in the tests for a given year, a stock must have data on all of the portfolioformation variables. The sample of firms is thus the same for all variables. BE/ME (booktomarket equity), E/P (earnings/price), C/P (cashflow/ price), and fiveyear sales rank are defined in Table II. The 11 portfolios contain strong firms (high sales growth and low BE/ME, E/P, or C/P), while the 33 portfolios contain weak firms (low sales growth and high BE/ME, E/P, or C/P). For each portfolio, the table shows the mean monthly return in excess of the onemonth Treasury bill rate (Mean), the standard deviation of the monthly excess returns (Std. Dev.), and the ratio of the mean excess return to its standard error Y(mean) = Mean/(Std. Dev./3651/2)]. Ave. ME is the average size (ME, in $millions) of the firms in a portfolio, averaged across the 366 sample months. Count is the average across months of the number of firms in a portfolio.
future returns and winners (high past returns) have low future returns. In contrast, Jegadeesh and Titman (1993) and Asness (1994) find that when portfolios are formed on shortterm (up to a year of) past returns, past losers tend to be future losers and past winners are future winners. Table VI shows average returns on sets of ten equalweight portfolios formed monthly on shortterm (11 months) and longterm (up to five years of) past returns. The results for July 1963 to December 1993 confirm the strong continuation of shortterm returns. The average excess return for the month Table V ThreeFactor Regressions for Monthly Excess Returns (in Percent) on the LSV EqualWeight DoubleSort Portfolios: 7/6312/93, 366 Months Rt  Rf = at + bt(RM ~ Rf) + stSMB + HML + et The formation of the doublesort portfolios is described in Table IV. BE/ME (booktomarket equity), E/P (earnings/price), C/P (cashflow/price), and fiveyear sales rank are described in Table II. The 11 portfolios contain strong firms (high sales growth and low BE/ME, E/P, or C/P), while the 33 portfolios contain weak firms (low sales growth and high BE/ME, E/P, or C/P). tO is a regression coefficient divided by its standard error. The regression R2 are adjusted for degrees of freedom. GRS is the Fstatistic of Gibbons, Ross, and Shanken (1989), testing the hypothesis that the nine regression intercepts for a set of doublesort portfolios are all 0.0. p(GRS) is the pvalue of GRS. 11 12 13 21 22 23 31 32 33 GRS p (GRS) BE/ME & Sales Rank
1.22 0.284 1.06 0.394 1.04 0.405 after portfolio formation ranges from 0.00 percent for the decile of stocks with the worst shortterm past returns (measured from 12 to 2 months before portfolio formation) to 1.31 percent for the decile with the best shortterm past Table VI Average Monthly Excess Returns (in Percent) on EqualWeight NYSE Deciles Formed Monthly Based on Continuously Compounded Past Returns At the beginning of each month t, all NYSE firms on CRSP with returns for months t  x to t  у are allocated to deciles based on their continuously compounded returns between t  x and t  y. For example, firms are allocated to the 122 portfolios for January 1931 based on their continuously compounded returns for January 1930 through November 1930. Decile 1 contains the NYSE stocks with the lowest continuously compounded past returns. The portfolios are reformed monthly, and equalweight simple returns in excess of the onemonth bill rate are calculated for January 1931 (3101) to December 1993 (9312). The table shows the averages of these excess returns for 6307 to 9312 (366 months) and 3101 to 6306 (390 months). Portfolio Average Excess Returns Formation 
returns. (Skipping the portfolio formation month in ranking stocks reduces bias from bidask bounce.) Table VI also confirms that average returns tend to reverse when portfolios are formed using returns for the four years from 60 to 13 months prior to portfolio formation. For these portfolios, the average return in the month after portfolio formation ranges from 1.16 percent for the decile of stocks with the worst longterm past returns to 0.42 percent for stocks with the best past returns. In the 19631993 results, however, longterm return reversal is observed only when the year prior to portfolio formation is skipped in ranking stocks. When the preceding year is included, shortterm continuation offsets longterm reversal, and past losers have lower future returns than past winners for portfolios formed with up to four years of past returns. Can our threefactor model explain the patterns in the future returns for 19631993 on portfolios formed on past returns? Table VTI shows that the answer is yes for the reversal of longterm returns observed when portfolios are formed using returns from 60 to 13 months prior to portfolio formation. The regressions ofthe postformation returns on these portfolios on RM  Rf, SMB, and HML produce intercepts that are close to 0.0 both in absolute terms and on the GRS test. The threefactor model works because longterm past losers Table VII ThreeFactor Regressions for Monthly Excess Returns (in Percent) on EqualWeight NYSE Portfolios Formed on Past Returns: 7/6312/93, 366 Months Rt Rf= at + bt(RM  Rf) + sSMB + ЛДШЬ + et The formation of the pastreturn deciles is described in Table VI. Decile 1 contains the NYSE stocks with the lowest continuously compounded returns during the portfolioformation period (122, 482, or 6013 months before the return month). t() is a regression coefficient divided by its standard error. The regression R2s are adjusted for degrees of freedom. GRS is the Fstatistic of Gibbons, Ross, and Shanken (1989), testing the hypothesis that the regression intercepts for a set of ten portfolios are all 0.0. p(GRS) is the pvalue of GRS. 123456789 10 GRS p(GRS)
4.45 0.000 2.02 0.031 1.29 0.235 load more on SMB and HML. Since they behave more like small distressed stocks, the model predicts that the longterm past losers will have higher average returns. Thus, the reversal of longterm returns, which has produced so much controversy (DeBondt and Thaler (1985, 1987), Chan (1988), Ball and 1 2 3 
© 2003 GARUN.RU.
Копирование материалов запрещено. 