The Predictability of Aggregate Stock Market Returns:
Evidence based on Glamour Stocks
Venkat R. Eleswarapu
Assistant Professor of Finance
Southern Methodist University
Edwin L. Cox School of Business
Dallas, TX – 75275.
Marc R. Reinganum
Mary Jo Vaughn Rauscher Chair in Financial Investments
Southern Methodist University
Edwin L. Cox School of Business
Dallas, TX – 75275.
The Predictability of Aggregate Stock Market Returns:
Evidence based on Glamour Stocks1
Abstract
We find that annual excess returns on the stock market index are
negatively related to the returns of glamour stocks in the previous 36-month
period. In contrast, neither returns of value stocks nor aggregate stock market
returns, purged of glamour stock effects, have any predictive power. In addition,
the excess returns on the aggregate market are negatively skewed when the prior
returns of glamour stocks are high. Finally, the inclusion of term premium,
default premium, aggregate dividend yield, and the consumption-to-wealth ratio
(CAY) as control variables do not materially alter the predictive power of prior
glamour stock returns.
1
We gratefully acknowledge the comments and suggestions by Michael Brandt, J.B. Chay, Alison
Fox, Harrison Hong, Rex Thompson, Kumar Venkataraman as well as an anonymous referee. This
paper was presented in the 2001 American Finance Association meetings, New Orleans. Naturally,
all remaining errors are ours.
2
Introduction
The predictability of aggregate stock market returns, particularly over
longer investment horizons, is now well documented.2 The interpretations of this
evidence have divided into two views. The first, typified in Fama and French
(1989), is that conditional expected returns (discount rates) vary with the business
cycles as rational agents smooth consumption over time. In this framework,
predictability of stock returns is consistent with time-varying inter-temporal
marginal rates of substitution. The alternate view explains the existing empirical
evidence in terms of excessive stock price variability. Expected stock market
returns vary too much to be rationally explained (Shiller (1981), Campbell and
Shiller (1988), Poterba and Summers (1988)). In the second framework, a
possible implication is that the stock market is periodically prone to “animal
spirits” or an irrational investor sentiment3, which causes “speculative bubbles”
that get reversed over time.
We add to this debate by presenting empirical evidence that aggregate
stock market returns can be predicted using the prior returns on the “glamour”
stocks. Specifically, we find that the annual excess returns (over risk-free rate) on
the stock market are negatively related to the returns on the glamour stocks in the
prior 36-month period. Furthermore, past glamour portfolio returns,
orthogonalized by the corresponding market returns, continue to predict future
2
One set of papers find stock market index returns are negatively auto-correlated at long horizons
(Fama and French (1988a), Poterba and Summers (1988) Summers (1986)). Another set of papers
use other price-based variables such as dividend yields (Keim and Stambaugh (1986), Fama and
French (1988b)) and aggregate book-to-market ratio (Kothari and Shanken (1997), Pontiff and
Schall (1998)) to predict the market returns.
3
There are some papers (Neal and Wheatley (1998), Siegel (1992), Solt and Statman (1988)) that
study the relation between various measures of investor sentiment such as discounts on closed-end
funds, ratio of odd-lot sales, etc., and the returns on the stock market.
3
market excess returns. In contrast, past stock market returns, which are
orthogonalized by the corresponding glamour stock returns, do not have any
predictive power to explain future market excess returns. Also, the past returns of
value stocks do not have any explanatory power in predicting aggregate stock
market excess returns. One might expect that shocks to the market-wide discount
rate (risk-premium), that induce negative autocorrelation in aggregate returns,
would be reflected in all groups of stocks. Our evidence of the unique predictive
ability of glamour stocks is at odds with this simple view, refining our
understanding of the nature of the negative autocorrelation in market returns.
We also find that conditional excess returns on the aggregate market are
negatively skewed when prior returns of glamour stocks are high. Specifically,
the monthly excess returns on the market portfolio are negatively skewed when
the prior 36-month return on the glamour stocks is in the top quartile of the
overall sample distribution. That is, the probability of a large decline in the stock
market increases following periods in which glamour stocks have performed
particularly well. Perhaps, the evidence suggests that the aggregate market, and
glamour stocks in particular, experience a “correction” following periods of rapid
price appreciation among glamour stocks.
While our evidence does not rule out a rational model, it appears
consistent with some implications of “behavioral” models (Barberis, Sheifer and
Vishny (1998), Daniel, Hirshleifer and Subrahmanyam (1998), Hong and Stein
(1999)) in which overconfident investors and trend-chasing noise traders4 affect
4
There are psychology-based explanations of how certain traders extrapolate a positive trend by
over-weighting recent news or attention-grabbing irrelevant news (Kahneman and Tversky (1973),
Tversky and Kahneman (1974), and Debondt (1993)).
4
equilibrium prices. The noise traders can affect equilibrium prices, since the
existence of fundamental risk and the chance that the mis-pricing can persist and
increase over time deters rational speculators from betting too aggressively
(Campbell and Kyle (1993), DeLong, Shleifer, Summers, and Waldmann
(1990a)). Also, as Shleifer and Vishny (1997) point out, the arbitrageurs,5 who
are usually in an agency relationship, may be constrained to have a short-term
horizon in their speculative positions. The arbitrageurs may find it difficult and
costly to maintain a short position for a sustained period of time, with the result
that the excessive buying pressure of the noise traders on glamour stocks may be
hard to counter. As a result, the entire stock market, and in particular glamour
stocks, can be overpriced for a while before experiencing a correction. This may
explain our finding of the conditional negative skewness of the market returns
following a large price run-up of the glamour stocks. This is in the spirit of the
theoretical predictions of negative skewness by Hong and Stein (1999b).
Our evidence, that the expected returns of the aggregate stock market are
negatively related to the prior performance of the glamour stocks, may also be
consistent with the theoretical model in Barberis and Huang (2001). Relying on
the idea of “loss aversion” in prospect theory, their model predicts a decrease in
investors’ degree of risk aversion when the prior returns of the stocks are high –
because the investors feel they are “gambling with the house money” (Benartzi
and Thaler (1995) and Thaler and Johnson (1990)). This causes the discount rates
of these stocks to go down after a price run-up. In their model, the investors are
prone to a phenomenon called “individual stock accounting,” where prior
5
Of course, true risk-less arbitrage will not be possible when the price levels of the entire market
5
outcomes of individual stocks (such as glamour stocks) can affect the riskaversion of the investors. Our evidence perhaps suggests that such changes in the
degree of risk aversion caused by prior outcomes of glamour stocks also affect the
expected returns of the aggregate stock market.
The rest of the paper is structured as follows: Section I describes the data,
while our methodology and empirical design are elaborated in section II. Section
III discusses our results. Our conclusions and a summary of our findings are
contained in section IV.
I.
Data
The basic data consist of stock returns, prices and shares outstanding of
the firms obtained from the Center for Research in Security Prices (CRSP) NYSE
/AMEX/ NASDAQ monthly file, over the period January 1948 to December
1997. Each month the market capitalization (size) of every stock is computed by
multiplying the month-end stock price and the shares outstanding. The valueweighted monthly market return for the NYSE/ AMEX/ NASDAQ index is
obtained from the CRSP files. The one-month T-bill returns from the CRSP
SBBI files are used as the risk-free rates. EXMKTt is the excess return on the
market over the one-month risk-free rate in the corresponding month.
The accounting data are obtained from the 1998 COMPUSTAT annual
tape.6 For each stock, we collect the net annual sales (item 12), annual operating
or a whole group of stocks (such as in an entire industry) deviate from the fundamental values.
6
Prior researchers have noted a possible look-ahead bias in the COMPUSTAT data for the 1950’s
and the early years of the Nasdaq data. That is, the COMPUSTAT information was added only
for the surviving firms. This would obviously bias the expected returns of these surviving firms.
We believe our analysis and results will not be affected by such a bias, since we are trying to
6
cash-flow defined as the Earnings before Interest, Depreciation and Taxes (item
13), and the fiscal year-end book value of equity (item 60). The information on
net sales and operating cash-flow start in 1950, while the book-value data are
from 1963 onwards. In many of the prior studies glamour and value stocks are
defined in terms of the ratio of the book to market value of equity. However, this
would constrain the study to the post-1963 time period because of the data
availability on the COMPUSTAT. We choose to characterize stocks as value or
glamour stocks using two other definitions as well: (i) the ratio of the Operating
Cash-flow to Market Capitalization, and (ii) the ratio of Net Sales to Market
Capitalization. This allows us to conduct our analysis over a longer sample
period and, use three different metrics to identify value and glamour stocks. For
each ratio, we are taking a ratio of the market value of equity and a proxy for
cash-flows. This ratio gives us a proxy for expected returns and may also indicate
the likely level of mis-pricing. The operating cash flow and sales are likely to be
more stable over time, and hence be a better proxy of expected cash-flows, than
say net income which may have a larger transitory component.
Each month the market capitalization data for all
NYSE/AMEX/NASDAQ stocks are combined with the most recently available
fiscal-year-end accounting data. However, to ensure that the financial
information has been released to the market, we require a minimum four-month
gap between the fiscal year-ends and the use of the accounting information in the
portfolio formation. In such cases, we use the relevant information from the
predict the excess returns on the market and not in general the portfolio returns of the value and
glamour stocks in the post portfolio formation period. Also, such a look-ahead bias affects the
7
previous fiscal year. Each month our sample contains all stocks for which the
relevant data are available on both the CRSP and the COMPUSTAT tapes.7 Every
month starting in January 1951, the stocks are ranked and assigned to five equal
groups based on their Cash-flow to Market Capitalization ratio (CMRATIO) and
independently using the Sales to Market Capitalization ratio (SMRATIO). Of
course, the portfolio formation using the Book-to-Market ratio (BMRATIO) starts
only in January 1963. In all the three cases, we use the data in the portfolio
assignment only when the relevant ratio has a positive value. For example, a firm
with a negative book-to-market ratio in a particular month is discarded from the
sample in that month. This is consistent with the prior studies such as
Lakonishok, Shleifer and Vishny (1994). Stocks in the lowest (highest) quintile
of CMRATIO, the SMRATIO, or the BMRATIO are called glamour (value) stocks.
Note that these portfolio assignments and the subsequent analyses are conducted
independently using the three different ratios. Thus we will have three sets of
results corresponding to the three different definitions of value and glamour
stocks.
After we assign the stocks to a portfolio in each month, we compute the
compounded return of the stock over the prior 36 months (including that month’s
return). We require the stock to exist over this prior 36-month period, even
though we do not require it to trade every month over this period. We compute
these 36-month returns for all stocks in the glamour and value portfolios each
month. Next, we compute an equal-weighted average of these returns each month
distressed value stocks. It should not be an issue for the glamour stocks, which is our main
variable of interest.
7
Of course, we discard ADRs and other special stocks such as preferred stock, etc.
8
for all the stocks in the glamour portfolio (GLARET-36) and in the value portfolio
(VALRET-36). We also compute the difference between the returns of the glamour
and value portfolios in the prior 36 months, GMVRET-36.
To conserve space, the descriptive statistics for just the portfolios formed
using the cash-flow to market variable is presented in Table 1.8 Panel A presents
the sample statistics describing the portfolios. The pair-wise correlations between
the variables, and the selected autocorrelations of the portfolio returns are
reported in panels B and C, respectively.
EXMKT1 is the excess return (over the risk-free rate) on the market in the
month following the portfolio formation. EXMKT12 compounds the one-month
excess returns over the following twelve months. The annual excess returns are
computed on an over-lapping basis each month. Over our sample-period of 19511997, the mean monthly and annual excess returns are 0.64% and 7.85%,
respectively. The corresponding averages over the 1963-97 time-period are
0.52% and 6.13%, respectively.
Panel A in Table 1 contains the univariate statistics for the glamour and
value portfolios formed using cash-flow to market value ratios. On average, there
are 436 firms in the glamour and value portfolios each month. The average cashflow to market value ratios (CMRATIO) for the glamour and value portfolios are
0.0790 and 0.5226, respectively. Not surprisingly, these two portfolios, formed
using cash-flow to market value ratios, also differ in terms of their sales to market
capitalization ratios (SMRATIO) and book-to market value ratios (BMRATIO).
The average SMRATIO is 1.1286 and 5.7236 for glamour and value portfolios,
9
respectively. Similarly, the average BMRATIO for these two portfolios is 0.4853
and 1.4654, respectively. Stated differently, glamour and value portfolios formed
using cash-flow to market value ratios look like glamour and value portfolios
based on SMRATIO and BMRATIO. The average of the market capitalizations of
stocks in the glamour (SIZEGL) and value (SIZEVA) portfolios systematically
differ. On average, the glamour stocks have a market capitalization of $687
million; the average capitalization of the value stocks is $275 million. Glamour
stocks experience a higher past sales growth rates as compared to value stocks on
average. For example in table 1, the sales growth rates in the year preceding the
portfolio formation (SLSGRO-1) for glamour and value stocks are 36% and 29%,
respectively. In the year following the portfolio formation, the sales growth rate
(SLSGRO+1) for glamour stocks far outpace those of value stocks on average.
The sales of glamour stocks grew by 32% whereas value stocks experienced a
sales growth of just 4%. Thus, the instrument that measures glamour and value is
highly correlated with both past and future sales growth rates. Finally, and
perhaps not surprisingly, glamour stocks have experienced much greater returns
over the previous 36 months relative to value stocks. In Table 1, the average 36month return of the glamour stocks is 114%, while it is 31% for value stocks. Of
course, part of the reason for this relationship is that glamour and value portfolios
are created using a price variable.
Panel B in Table 1 contains the simple correlations between future excess
market returns and the past returns of these glamour and value portfolios. The
past returns of the glamour stock portfolio (GLARET-36) are negatively correlated
8
The authors will gladly provide the descriptive statistics for the other two definitions of glamour
10
(-0.31) with the future excess market returns (EXMKT12). The correlation
between past returns of the value portfolio (VALRET-36) and the future excess
market return is also negative but much closer to zero (-0.12). The correlation of
the difference in the past returns of the glamour and value portfolios (GMVRET36)
with future excess market returns is also negative (-0.28). These correlations
also reveal that the past return of the glamour stock portfolio is highly correlated
(0.86) with the differential return between the glamour and value portfolios. On
the other hand, the past returns of value stocks are virtually uncorrelated with the
past differential returns between glamour and value stocks (-0.06). That is, the
differential return in the past 36 months between glamour and value portfolios is
essentially driven by the performance of the glamour stocks.
Panel C of Table 1 presents the autocorrelations of the portfolio returns at
lags up to 60 months. The tendency for the autocorrelation to be positive over
shorter horizons is not surprising since we are using monthly over-lapping
observations. At the 60-month lag, all the return variables are negatively
autocorrelated. In this table, the negative autocorrelation of glamour stocks at the
60-month lag is –0.345, whereas the negative autocorrelation of the value stocks
is just –0.036. This evidence clearly suggests that the time-series properties of
value and glamour stocks differ.
In short, glamour stocks are larger than value stocks as measured by
market capitalization. Glamour stocks possess higher past and future sales growth
rates relative to value stocks. During the prior 36 months, glamour stocks
experienced higher stock returns than did value stocks. Finally, the negative
upon request.
11
autocorrelation in returns over longer investment horizons is most pronounced for
the glamour portfolios. In the next section, we formally test whether past returns
of glamour and value stocks yield differential information about the future excess
market returns.
II.
Empirical Methodology
The main focus of this research is to study the information content of
different portfolios of stocks for predictions of aggregate excess stock market
returns. In particular, we examine the unique predictive ability of glamour stocks.
To test for the predictive ability of glamour stocks, we first estimate the following
regression:
EXMKT12 = αG + βG GLARET-36 + ε.
(1)
That is, the return on the glamour stocks over the past 36 months is used to
predict the excess return on the market portfolio over the following 12 months.
We also examine the predictive ability of the glamour portfolios that are
orthogonalized by the corresponding returns on the market portfolio. Specifically,
ORTHGLA-36 is the residual from the regression of the returns on the glamour
portfolio in the past 36 months on the corresponding excess returns on the stock
market, that is,
ORTHGLA−36 = GLARET−36 − ( αˆ + βˆ × EXMKT−36 )
(2)
ORTHGLA-36, is purged of any market-wide information and hence reflects
information exclusive to glamour stocks.
12
We also investigate the predictive ability of market returns that are
orthogonalized by the glamour portfolio returns. That is, we examine the
predictive ability of market returns purged of any information contained in
glamour stocks. MKTXGLA-36, is the residual from the regression of the excess
returns on the stock market in the past 36 months on the corresponding glamour
portfolio returns,
MKTXGLA−36 = EXMKT−36 − ( αˆ + βˆ × GLARET−36 )
(3)
We use both these orthogonalized returns from equations (2) and (3) as regressors
separately to explain the future excess market returns, EXMKT12. That is, we
examine whether past returns of glamour stocks have any unique predictive
ability.
We additionally contrast the predictive power of glamour stocks with that
of value stocks. Specifically, we estimate the following regression using the
returns on the value stocks, VALRET-36, as an independent variable.
EXMKT12 = αV + βV VALRET-36 + ε.
(4)
Under a simple discount rate story, we expect the slope coefficients in both these
regressions to be negative. Shocks to the market-wide discount rate that induce
negative autocorrelation in stock market returns should be reflected in all groups
of stocks simultaneously.
Finally, we examine the information content in the differential return
between glamour and value stocks in the prior period (GMVRET-36), using the
following regression,
13
EXMKT12 = αD + βD GMVRET-36 + ε.
(5)
There are a couple of econometric issues that arise in the empirical design
of the regressions described above. First, the portfolios are formed, and all the
variables are measured, on a monthly basis. So the dependent variable EXMKT12
will have over-lapping observations. This makes the use of the O.L.S. standard
errors for the coefficients inappropriate. Secondly, the coefficients will be
affected by the small-sample bias noted by Stambaugh (1986). The independent
variables (the 36-month portfolio returns) in these regressions will have high
persistence at the monthly lag as shown in panel C of Table 1. The innovations in
these variables every month will be contemporaneously related to the monthly
returns on the market. This induces a bias in the estimates of the coefficients in
the above regressions in small samples. To account for both these problems and
to make proper inferences, we use a bootstrap procedure, following Nelson and
Kim (1993) and Pontiff and Schall (1998), to get an empirical distribution of these
regression coefficients. The exact procedure is explained in the appendix of the
paper. The p-values from this bootstrapping procedure are used in making
inferences in the results that follow.
III.
Results
A. Predictions of Excess Market Returns
The results from the three sets of regressions predicting the excess market
returns under the three definitions of value/glamour stocks are reported in Tables
2, 3 and 4. The results using the portfolios formed over 1951-1997 using the
14
Cash-to-Market ratio and Sales-to-Market ratio are in Tables 2 and 3,
respectively, while those using the Book-to-Market ratio over the 1963-1997
period are in Table 4.
In Table 2, the prior 36-month return on glamour stocks is negatively
related to the future 12-month excess market return (see regression (i)).
Furthermore, this negative relationship is reliably different from zero as indicated
by a p-value of 0.035 computed from the bootstrapping procedure. The adjusted
R-squared is 9.66%. This means that prior returns on glamour stocks can predict
future excess market returns. The regression coefficient (-0.0659) implies that a
one standard deviation shock in the 36-month glamour stock returns would
translate into a 500 basis point change in the excess return of the market.
Regression (i) in Table 2 suggests that the relationship between the past returns of
glamour stocks and the future excess return on the market are both statistically
and economically significant.
We orthogonalize the glamour portfolio returns by the market returns (as
described in equation (2) in the previous section) to determine if glamour stocks
contain unique information not contained in other stocks. This orthogonalization
process purges the glamour stock returns of any market wide effects. Regression
(ii) shows the relationship between the prior 36-month orthogonalized glamour
portfolio return and the future 12-month market excess return. The coefficient in
this regression (-0.0616) is nearly the same as the coefficient in regression (i).
The adjusted R-squared is 7.65%. This evidence suggests that glamour stocks
contain unique information over and above that contained in the market. The
15
unique information contained in past glamour stocks returns can help predict
future excess market returns.
Interestingly, when one removes the information of glamour stocks from
past market excess returns, past excess market returns do not help to predict future
excess market returns. As regression (iii) shows, when orthogonalized market
returns are used as the explanatory variable, the adjusted R-square is virtually
zero and the p-value of the regression is 0.513. Without glamour stocks, past
stock market excess returns cannot predict its future values even in part.
Regression (iv) includes both GLARET-36 and MKTXGLA-36 so that one can test
directly whether the orthogonalized market returns can have any predictive power
after controlling for past glamour returns. The evidence shows that the past
returns on the glamour portfolio have an exclusive predictive ability and past
glamour returns subsume the information content of lagged market returns
documented in other studies such as Fama and French (1988a). Not surprisingly,
there is no improvement in adjusted R-square in regression (iv) compared to
regression (i).
Regression (v) in Table 2 defines the independent variable as the 36month prior return on value stocks. Unlike the evidence from regression (i), the
prior 36-month return on value stocks is not reliably related to the subsequent
market excess return. The p-value of the regression is 0.277 and the adjusted Rsquared is merely 1.23%. The evidence suggests that the value stocks do not have
predictive ability.
We also model future excess market returns as a function of the
differential returns between glamour and value stocks in the prior 36-month
16
period (GMVRET-36). This result is contained in regression (vi) in Table 2.
Regression (vi) suggests that subtracting the value portfolio return from the
glamour portfolio return isolates the unique information content of glamour
stocks. The adjusted R-square of this regression, 7.85%, is similar to that
obtained when modeling future excess market returns as a function of the
orthogonalized glamour returns as in regression (ii). The glamour stocks seem to
contain unique information that is not contained in value stocks. This can be seen
directly in regression (vii) that includes the past returns of both glamour and value
stocks.
In Table 3, the glamour and value portfolios are formed using sales to
market value ratios. The regression results, however, are qualitatively and
quantitatively similar to those reported in Table 2 where portfolios are formed
using cash-flow to market value ratios. The evidence in Table 3 once again
shows that glamour stocks have a unique ability to predict future excess market
returns. Further, past stock market returns, purged of glamour stock effects,
cannot predict future excess market returns.
The results in Table 4 are based upon portfolios formed with book-tomarket ratios. The results in Table 4 are generally consistent with those in Tables
2 and 3 – future excess market returns are negatively correlated with the past
returns of glamour stocks. The coefficients on the glamour stock portfolio returns
are negative. But the results are weaker. None of the coefficients are statistically
significant at the 0.05 level. The tests in Table 4 have less statistical power than
those Tables 2 and 3, which contain 12 additional years of data.
17
While this research finds that past glamour returns predict future excess
market returns, previous research of Fama and French (1989) and Lettau and
Ludvigson (2001) suggests that other variables, reflecting macroeconomic
conditions, may also predict future excess returns. Table 5 explores the question
of whether past glamour returns continues to predict future excess market returns
after controlling for these macroeconomic influences. In particular, we test
whether the relationship between past glamour returns and future excess market
returns remains stable in the presence of regressions that include the term
premium (TRMPREM), default premium (DFLTPREM), aggregate market
dividend yield (ADIVYLD) and the aggregate consumption to wealth ratio (CAY).
In Table 5, the first nine columns present regressions that include past
glamour returns (using the three definitions of glamour) along with each of the
Fama-French macro variables (TRMPREM, DFLTPREM, ADIVYLD). In general,
the results from Tables 2, 3 and 4 are not materially altered by the inclusion of the
macro variables. Past glamour returns and future excess market returns are still
negatively related. The p-values on the glamour return variables in Table 5 are
slightly higher than those reported in Tables 2, 3 and 4 but they still suggest a
reliable relation. Furthermore, the p-values associated with the past glamour
return variables are typically lower than the p-values associated with the control
variables, TRMPREM, DFLTPREM, and ADIVYLD. In columns x, xi and xii, the
regressions include both past glamour returns and the CAY variable. The glamour
returns remain statistically significant with the anticipated sign; the CAY variable
is also significant.
18
The last six columns of Table 5 present regressions with the final
combination of variables specified in Fama and French (1989) and past glamour
returns. Again, the past glamour return variables hold up well. The magnitudes
of the coefficients on the past glamour return variables and their statistical
significance are not materially altered in the presence of the Fama-French
specifications. In short, the macroeconomic variables do not destroy the
explanatory power of past glamour returns.
The fact that past glamour returns predict future excess market returns
raises an intriguing question. Are past glamour-stock returns really only
forecasting future glamour stock returns or do past glamour stock returns also
forecast the future returns of other stocks such as value stocks? That is, is the
negative correlation between past glamour returns and future stock market returns
primarily a reflection of a reversal effect that exists exclusively among glamour
stocks? To answer this question, the predictive ability of the past glamour stock
returns for the future twelve-month excess (over risk-free returns) returns on both
glamour (EXGLA12) and value portfolios (EXVAL12) is investigated. The relevant
regression results are presented in Table 6. The evidence does suggest a negative
relationship between past glamour returns and future excess returns of glamour
stocks. Depending on the classifying variable for glamour, the bootstrapped pvalues of the slope coefficients range between 0.05 and 0.11. Thus, the evidence
seems persuasive that past glamour returns predict future excess glamour returns.
The adjusted R-squares are smaller in Table 6 than in Tables 2, 3 and 4 in large
part because the dependent variables in Table 6 have a standard deviation about
1.7 times as great as the standard deviation of the excess market return.
19
The relationship between the past returns of glamour stocks and future
value stock excess returns is harder to ascertain from our tests. The coefficient
values are all negative and nearly the same magnitude as those for the glamour
stock regressions, but the p-values only range from about 0.10 to 0.26. To a large
extent, the predictability of the market is driven by the reversals among glamour
stocks. But the evidence is not so strong as to support the hypothesis that the
predictability of market returns is driven exclusively by the reversals among
glamour stocks.
B. Skewness of Stock Market Excess Returns and Prior Glamour Returns
The regression evidence in Tables 2, 3 and 4 suggests that when glamour
stocks have experienced high returns in the prior 36-months, the conditional
expected excess returns on the market are lower over the next twelve months.
That is, a “boom” period for glamour stocks implies a future weakness in the
overall market. Tables 2, 3 and 4 document this future weakness in terms of
conditional means.
We also investigate the future weakness in the overall market using a
conditional skewness measure as in Hong and Stein (1999b). In particular, we
test whether the monthly excess returns on the market are conditionally skewed
when the prior returns on the glamour portfolio are high. We also examine the
conditional skewness of monthly glamour returns and the excess market returns
orthogonalized by corresponding glamour returns. In Table 7, the monthly
20
excess returns on the market portfolio are negatively skewed9 when prior 36month return on the glamour stocks is in the top quartile of the overall sample
distribution. In other words, we sort all of the 36-month returns of glamour
portfolios from high to low. Next, we select those time periods that are in the top
quartile of this distribution. We then examine the excess market return in the
month following each of these periods. We find that the distribution of excess
market returns from these months is negatively skewed. That is, the probability
of a large decline in the stock market increases following periods in which
glamour stocks have performed particularly well. In contrast, when prior glamour
returns have been low (in the bottom quartile), the skewness in excess market
returns is slightly positive. This may suggest that the stock market is likely to
have a “correction” following large price run-ups in glamour stocks. Is this
“correction” driven solely by the behavior of glamour stocks within the market?
Using the cash flow to market value definition of glamour (Panel A, Table 7), one
might be tempted to conclude that this is the case because the negative skewness
for the market returns purged of glamour return effects (-0.23) cannot be reliably
differentiated from zero (p-value = 0.13). In contrast, the skewness coefficients
for the market with glamour and glamour by itself are both negative when the
prior returns on glamour stocks are high and have highly significant p-values of
0.01. However, using the other definitions of glamour, the answer is not so clearcut. Clearly, the behavior of glamour stocks is an important component of our
finding of conditional negative skewness in the market.
9
The p-value is for the null hypothesis that the skewness is zero (that is, the underlying
distribution is a normal distribution). The test statistic for skewness is based on equation 12.91 of
Stuart and Ord (1994).
21
IV.
Summary and Conclusions
We investigate the predictability of aggregate stock market returns using
the past returns of glamour stocks, value stocks, and the overall market. We find
the relationship of glamour stocks with future stock market returns is unique. In
particular, we find that annual excess returns on the stock market index are
negatively related to the returns of glamour stocks in the previous 36-month
period. Past returns on the stock market, purged of the effects of the glamour
stocks, do not have any reliable predictive power in explaining future stock
market returns. On the other hand, the glamour portfolio returns, even
orthogonalized by the corresponding market returns, have predictive power. In
contrast, the past returns of value stocks do not have any explanatory power in
predicting aggregate stock market excess returns. We also find that the
explanatory power of past glamour returns is in general robust to the inclusion of
term premium, default premium, aggregate dividend yield, and the consumptionto-wealth ratio (CAY) as control variables. This unique predictive ability of
glamour stocks extends our understanding of the previously documented negative
autocorrelation in stock market returns. Our evidence suggests the predictability
of the aggregate stock market returns arises from some information that is
exclusive to glamour stocks.
We also find that the probability of a large decline in the stock market
value increases in the periods following large price run-ups in glamour stocks.
Specifically, the monthly excess returns on the aggregate market are negatively
skewed when the returns on the glamour stocks in the prior 36-months are high.
22
This evidence may be consistent with an investor sentiment explanation of
predictability, in which the stock market in general and the glamour stocks in
particular become over-priced periodically. A subsequent correction causes a
decline in the stock market in general, and among glamour stocks in particular.
One may be reluctant to embrace an investor sentiment explanation of the
predictability of aggregate stock market returns. Any theory, however, will need
to explain why future stock market returns are negatively correlated with past
glamour stock returns and why the probability of a large decline in the stock
market increases following periods in which glamour stocks have performed
particularly well.
23
Appendix
Bootstrap Procedure
We estimate the following auto-regressive model for all our independent variables
using the monthly observations in our sample:
Xi,t = a + b Xi,t-1 + ei,t
(1)
Since the small-sample bias arises from the correlation between the monthly
innovations in the independent variable (ei,t) and the corresponding excess market
returns, we retain the estimates of the residuals from the above regressions and the
contemporaneous monthly excess market returns. These pairs of excess market
returns and ei,t are then randomized by drawing with replacement from the
original data. Next, using these randomized series we create pseudo independent
variables and excess market returns that have time-series properties just as in the
original data, but yet satisfy the null hypothesis of no predictability. Each pseudo
independent variable is created by using the randomized series of residuals along
with the parameters from regression equation (1). The starting values for Xi,t-1 are
randomly chosen from the actual data. The corresponding pseudo series of
monthly excess market returns are used to compute a pseudo dependent variable
EXMKT12. We then estimate all the regressions just as in Tables 2, 3 and 4 using
these pseudo data and save the coefficients. This process is repeated 1000 times,
to obtain an empirical distribution for each of the coefficients. The p-values are
based on the proportion of times the bootstrapped coefficient is lower than the
coefficient from the actual data series.
24
References
Barberis, N., and Huang, M. 2001. Mental Accounting, Loss Aversion, and
Individual Stock Returns. Journal of Finance 56 (August): 1247-1295.
Barberis, N., Shleifer, A., and Vishny, R. 1998. A model of investor sentiment.
Journal of Financial Economics 49 (September): 307-343.
Benartzi, S., and Thaler, R. 1995. Myopic loss aversion and the equity premium
puzzle. Quarterly Journal of Economics 110: 73-92.
Black, F. 1986. Noise. Journal of Finance 41 (July): 529-543.
Campbell, J.Y., and Shiller, R. 1988. The dividend price ratio and expectations of
future dividends and discount factors. Review of Financial Studies 1
(Fall): 195-228.
Campbell, J.Y., and Kyle, A. S. 1993. Smart Money, Noise trading, and stock
price behaviour. Review of Economic Studies 60 (January): 1-34.
Daniel, K., Hirshleifer, D., and Subrahmanyam A. 1998. Investor Psychology and
investor security market under- and overreactions. Journal of Finance
53 (December): 1839-1886.
Daniel, K. D., and Titman, S. 1999. Market Efficiency in an irrational world.
Financial Analysts Journal 55 (November/December): 28-40.
Debondt, W. 1993. Betting on trends: Intuitive forecasts of financial risk and
return. International Journal of Forecasting 9: 355-371.
DeLong, J.B., Shleifer, A., Summers L.H., and Waldmann, R. J. 1990a. Noise
trader risk in financial markets. Journal of Political Economy 98: 703-738.
25
DeLong, J.B., Shleifer, A., Summers L.H., and Waldmann, R. J. 1990b. Positive
feedback investment strategies and destabilizing rational speculation.
Journal of Finance 45 (June): 379-395.
Fama, E. F., and French, K. R. 1988a. Permanent and temporary components of
stock prices. Journal of Political Economy 96 (April): 246-273.
Fama, E. F., and French, K. R. 1988b. Dividend yields and expected stock returns.
Journal of Financial Economics 22 (October): 3-25.
Fama, E. F., and French, K. R. 1989. Business Conditions and expected returns on
stocks and bonds. Journal of Financial Economics 25 (November): 23-49.
Fama, E. F., and French, K. R. 1993. Common risk factors in the returns on bonds
and stocks. Journal of Financial Economics 33: 3-56.
Hong, H., and Stein, J. 1999a. A unified theory of under-reaction, momentum
trading and overreaction in asset markets. Journal of Finance 54
(December): 2143-2184.
Hong, H, and Stein, J. 1999b. Differences of Opinion, Rational Arbitrage and
Market Crashes. Working Paper, Stanford University.
Jegadeesh, N., and Titman, S. 1993. Returns to buying winners and selling losers:
Implications for stock market efficiency. Journal of Finance 48 (March):
65-91.
Kahneman, D., and Tversky, A. 1973. On the psychology of prediction.
Psychological Review 80: 237-251.
Keim, D. B., and Stambaugh, R.F. 1986. Predicting returns in the stock and bond
markets. Journal of Financial Economics 17 (December): 357-390.
26
Kothari, S. P., and Shanken, J. 1997. Book-to-market, Dividend yield, and
expected market returns: A time-series analysis. Journal of Financial
Economics 44 (May): 169-203.
Lakonishok, J., Shleifer, A., and Vishny, R. 1994. Contrarian investment,
extrapolation, and risk. Journal of Finance 49 (December): 1541-1578.
Lee, C., Shleifer, A., and Thaler, R. 1991. Investor sentiment and closed-end fund
puzzle. Journal of Finance 46 (March): 75-109.
Lettau, M., and Ludvigson, S. 2001. Consumption, Aggregate Wealth, and
Expected Stock Returns. Journal of Finance 56 (June): 815-849.
Neal, R., and Wheatley, S. M. 1998. Do measures of investor sentiment predict
returns? Journal of Financial and Quantitative Analysis 33 (December):
523-547.
Nelson, C.R., and Kim, M. J. 1993. Predictable stock returns: the role of small
sample bias. Journal of Finance 48 (June): 641-661.
Pontiff J., and Schall, L. D. 1998. Book-to-market ratios as predictors of market
returns. Journal of Financial Economics 49 (August): 141-160.
Poterba, J.M., and Summers, L.H. 1988. Mean Reversion in stock prices:
Evidence and Implications. Journal of Financial Economics 22 (October):
27-59.
Shiller, R. 1981. Do stock prices move too much to be justified by subsequent
changes in dividends? American Economic Review 71 (June): 421-436.
Shleifer, A., and Vishny, R. 1997. The limits to Arbitrage. Journal of Finance 52
(March): 35-55.
27
Siegel, J.J. 1992. Equity risk premia, corporate profit forecasts, and investor
sentiment around the stock market crash of October 1987. Journal of
Business 65: 557-570.
Solt, M.E., and Statman, M. 1988. How useful is the sentiment index. Financial
Analysts Journal 44 (September): 45-55.
Stambaugh, R. 1986. Bias in regressions with lagged stochastic regressors. CRSP
Working paper 156, The University of Chicago.
Stuart, A., and Ord, K. 1994. Distribution Theory: Kendall’s Advanced Theory of
Statistics, Edward Arnold, 6th Edition.
Summers, L.H. 1986. Does the stock market rationally reflect fundamental
values? Journal of Finance 41 (July): 591-601.
Thaler, R., and Johnson, E. 1990. Gambling with the house money and trying to
break even: the prior outcomes on risky choice. Management Science 36:
643-660.
Tversky, A., and Kahneman, D. 1974. Judgement under uncertainty: heuristics
and biases. Science 185: 1124-1131.
28
Table 1
Descriptive Statistics for Glamour and Value portfolios formed using Cash-flow
to Market value ratio over the period 1951-1997.
EXMKT1 and EXMKT12 are the monthly and annual excess returns (in %), over the risk-free rate,
on the value weighted market portfolio, respectively. They are measured on a monthly basis.
Each month over the period 1951-1997, all the NYSE, AMEX and NASDAQ stocks are classified
into quintiles based on the ratio of Cash-flow to Market value (CMRATIO). Cash-flow is the
EBIDTA (item 13) in the preceding year. The stocks in the lowest and highest quintile each month
are called ‘glamour’ and ‘value’ stocks respectively. SMRATIO is the Sales to Market value ratio,
where Sales is the annual net sales (item 12) in the preceding year. BMRATIO is the ratio of Book
to Market value of equity, where Book value of equity (item 60) is in the preceding year. SIZE is
the average of the market capitalization (millions of dollars) of the stocks in each portfolio in a
particular month. SLSGRO-1 (SLSGR0+1) is the average growth (%) in sales in the year preceding
(following) the portfolio formation. N is the number of firms in the portfolios in a given month.
GLARETCM,-36 and VALRETCM,-36 are the average compounded returns (in %) of the glamour and
value stocks, respectively, in the 36 months preceding the portfolio formation. GMVRETCM,-36 is
the difference between GLARETCM,-36 and VALRETCM,-36 each month of the sample period. The
time-series statistics of the monthly portfolio observations are reported in Panel A below.
29
Table 1 (contd.)
Panel A: Sample Statistics
Mean
Variable
Glamour
Std. Dev
Value
Glamour
Q1
Value
Glamour
Median
Value
Glamour
Q3
Value
Glamour
Value
CMRATIO
0.0790
0.5226
0.0366
0.1810
0.0503
0.3778
0.0670
0.4973
0.1026
0.6243
SMRATIO
1.1286
5.7236
0.4609
2.3292
0.8173
4.1087
1.0085
4.9891
1.3051
6.9755
BMRATIO
0.4853
1.4654
0.1694
0.4720
0.3691
1.1776
0.4498
1.3227
0.5559
1.6992
SIZE (in $ mill.)
687
275
329
241
478
91
675
142
866
466
SLSGRO-1 (in %)
35.96
28.96
34.57
80.65
12.14
11.14
24.46
17.31
46.36
22.67
SLSGRO+1 (in %)
32.65
4.05
16.50
5.13
18.42
0.79
33.88
4.83
42.68
7.62
436
436
307
307
127
127
391
391
710
710
114.13
30.88
75.92
38.57
52.41
7.36
101.48
31.96
158.37
56.12
Number of firms in each
portfolio (N)
GLARETCM,-36 &
VALRETCM,-36 (in %)
EXMKT1 (in %)
0.6374
4.1297
-1.7860
0.9015
3.2660
EXMKT12 (in %)
7.8508
15.8447
-2.2100
8.8081
18.2199
Table 1 (contd.)
Panel B: Correlations
Variable
EXMKT1
EXMKT1
EXMKT12
1.0000
EXMKT12
GLARETCM,-36
VALRETCM,-36
0.2836
-0.0876
-0.0472
-0.0709
1.0000
-0.3134
-0.1186
-0.2831
1.0000
0.4475
0.8620
1.0000
-0.0675
GLARETCM,-36
VALRETCM ,-36
GMVRETCM,-36
GMVRETCM,-36
1.0000
Panel C: Autocorrelations
Lag Structure
1-month
3-month
6-month
12-month
36-month
60-month
EXMKT1
0.0601
0.0053
-0.0501
0.0249
0.0079
-0.0376
EXMKT12
0.9230
0.7471
0.4353
-0.1896
0.0461
-0.0418
GLARETCM,-36
0.9570
0.8598
0.7238
0.5407
-0.0871
-0.3450
VALRETCM ,-36
0.9649
0.8932
0.7795
0.5906
0.0666
-0.0368
GMVRETCM,-36
0.9644
0.8888
0.7825
0.6303
-0.0704
-0.1869
Variable
Table 2
Coefficients (p values) from regressions of twelve-month excess market returns on lagged returns on Glamour and
Value portfolios formed using Cash-flow to Market value ratio over the period 1951-1997.
EXMKT12, the excess returns on the value weighted market portfolio over the risk-free rate, in the 12 months following the portfolio formation, is the dependent variable. These
annual returns are measured on a monthly basis. GLARETCM,-36 and VALRETCM,-36 are the average compounded returns of the Glamour and Value stocks, respectively, in the 36
months preceding (and including the month of) the portfolio formation. GMVRETCM,-36 is the difference between GLARETCM,-36 and VALRETCM,-36 each month of the sample period.
Orthogonalized Glamour Returns, ORTHGLA-36, are the residuals from the regression of the returns on the Glamour Portfolios over the prior 36 months, GLARET-36, on the excess
return on a value-weighted market portfolio, EXMKT-36, over the corresponding 36 months. Similarly, the Orthogonalized excess market return, MKTXGLA-36, are the residuals of
the regression of the excess return on the value-weighted market portfolio, EXMKT-36, on the returns of the Glamour portfolios over the corresponding 36 months, GLARET-36. The
p-values for the coefficients are obtained from a bootstrapping procedure as explained in the appendix.
Variable
(i)
Intercept
0.1524
(0.084)
GLARETCM,-36
-0.0659
(0.035)
ORTHGLACM,-36
(ii)
(iii)
0.0778
(0.562)
0.0784
(0.521)
(iv)
0.1504
(0.103)
(v)
0.0935
(0.366)
0.1328
(0.133)
-0.0645
(0.048)
(vii)
0.1519
(0.110)
-0.0690
(0.060)
-0.0616
(0.062)
MKTXGLACM,-36
-0.0242
(0.513)
-0.0309
(0.501)
VALRETCM,-36
-0.0483
(0.277)
GMVRETCM,-36
Adj. R2 (%)
(vi)
0.0130
(0.369)
-0.0669
(0.045)
9.66
7.65
-0.00
32
9.56
1.23
7.85
9.57
Table 3
Coefficients (p values) from regressions of twelve-month excess market returns on lagged returns on Glamour and
Value portfolios formed using Sales to Market Value ratio over the period 1951-1997.
EXMKT12, the excess returns on the value weighted market portfolio over the risk-free rate, in the 12 months following the portfolio formation, is the dependent variable. These
annual returns are measured on a monthly basis. GLARETSM,-36 and VALRETSM,-36 are the average compounded returns of the Glamour and Value stocks, respectively, in the 36
months preceding (and including the month of) the portfolio formation. GMVRETSM,-36 is the difference between GLARETSM,-36 and VALRETSM,-36 each month of the sample period.
Orthogonalized Glamour Returns, ORTHGLA-36, are the residuals from the regression of the returns on the Glamour Portfolios over the prior 36 months, GLARET-36, on the excess
return on a value-weighted market portfolio, EXMKT-36, over the corresponding 36 months. Similarly, the Orthogonalized excess market return, MKTXGLA-36, are the residuals of
the regression of the excess return on the value-weighted market portfolio, EXMKT-36, on the returns of the Glamour portfolios over the corresponding 36 months, GLARET-36. The
p-values for the coefficients are obtained from a bootstrapping procedure as explained in the appendix.
Variable
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Intercept
0.1502
(0.084)
0.0781
(0.545)
0.0783
(0.538)
0.1497
(0.086)
0.0885
(0.368)
0.1322
(0.145)
0.1508
(0.098)
GLARETSM,-36
-0.0722
(0.032)
ORTHGLASM,-36
-0.0713
(0.052)
-0.0742
(0.077)
-0.0673
(0.070)
MKTXGLASM,-36
-0.0290
(0.502)
-0.0347
(0.507)
VALRETSM,-36
-0.0502
(0.280)
GMVRETSM,-36
Adj. R2 (%)
0.0072
(0.419)
-0.0676
(0.072)
8.80
6.95
0.05
33
9.21
1.35
6.16
8.66
Table 4
Coefficients (p values) from regressions of twelve-month excess market returns on lagged returns on Glamour and
Value portfolios formed using Book to Market ratio over the period 1963-1997.
EXMKT12, the excess returns on the value weighted market portfolio over the risk-free rate, in the 12 months following the portfolio formation, is the dependent variable. These
annual returns are measured on a monthly basis. GLARETBM,-36 and VALRETBM,-36 are the average compounded returns of the Glamour and Value stocks, respectively, in the 36
months preceding (and including the month of) the portfolio formation. GMVRETBM,-36 is the difference between GLARETBM,-36 and VALRETBM,-36 each month of the sample period.
Orthogonalized Glamour Returns, ORTHGLA-36, are the residuals from the regression of the returns on the Glamour Portfolios over the prior 36 months, GLARET-36, on the excess
return on a value-weighted market portfolio, EXMKT-36, over the corresponding 36 months. Similarly, the Orthogonalized excess market return, MKTXGLA-36, are the residuals of
the regression of the excess return on the value-weighted market portfolio, EXMKT-36, on the returns of the Glamour portfolios over the corresponding 36 months, GLARET-36. The
p-values for the coefficients are obtained from a bootstrapping procedure as explained in the appendix.
Variable
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Intercept
0.1284
(0.180)
0.0617
(0.536)
0.0600
(0.572)
0.1286
(0.187)
0.0596
(0.586)
0.1374
(0.198)
0.1219
(0.305)
GLARETBM,-36
-0.0456
(0.108)
ORTHGLABM,-36
-0.0468
(0.114)
-0.0414
(0.226)
-0.0342
(0.238)
MKTXGLABM,-36
-0.1041
(0.337)
-0.1144
(0.298)
VALRETBM,-36
-0.0921
(0.239)
GMVRETBM,-36
Adj. R2 (%)
-0.0174
(0.496)
-0.0511
(0.137)
6.94
2.48
1.28
34
8.82
3.67
5.63
6.79
Table 5
Coefficients (p values) from regressions of twelve-month excess market returns on lagged returns on Glamour
portfolios and macro-economic variables over the period 1951-1997.
EXMKT12, the excess returns on the value weighted market portfolio over the risk-free rate, in the 12 months following the portfolio formation, is the dependent variable. These
annual returns are measured on a monthly basis. GLARETCM,-36, GLARETSM,-36 and GLARETBM,-36 are the average compounded returns of the Glamour stocks, respectively, in the
36 months preceding (and including the month of) the portfolio formation, with portfolios formed using the three different metrics. TRMPREM, Term Premium, is the difference
between the yields of AAA corporate bonds and the one-month T-bill. DFLTPREM, Default Premium, is the difference between the yields of BAA and AAA corporate bonds.
ADIVYLD is the dividend yield for the market portfolio based on the dividends of the preceding 12 months and the most recent price-level . CAY is the aggregate consumptionwealth ratio from Lettau and Ludvigson (2001). The data for the CAY variable were obtained from their website at the Federal Reserve Bank of New York The p-values for the
coefficients are obtained from a bootstrapping procedure as explained in the appendix.
Panel A:
Variable
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Intercept
0.0960
(0.454)
0.0951
(0.446)
0.0553
(0.645)
0.1166
(0.365)
0.1122
(0.365)
0.0683
(0.550)
-0.0330
(0.361)
-0.0436
(0.376)
-0.0279
(0.550)
GLARETCM,-36
-0.0567
(0.054)
GLARETSM,-36
-0.0667
(0.033)
-0.0620
(0.073)
GLARETBM,-36#
TRMPREM
-0.0562
(0.055)
-0.0757
(0.047)
-0.0382
(0.172)
0.0209
(0.085)
0.0208
(0.089)
-0.0678
(0.054)
-0.0501
(0.099)
0.0259
(0.036)
DFLTPREM
0.0387
(0.235)
0.0449
(0.204)
0.0640
(0.141)
ADIVYLD
Adj. R2 (%)
#
12.93
12.42
-0.0470
(0.087)
14.29
10.45
Regressions with GLARETBM,-36 are estimated over the period 1963-1997.
35
10.40
10.70
0.0477
(0.242)
0.0521
(0.218)
0.0458
(0.374)
16.86
18.02
12.76
Table 5 (Contd.)
Panel B:
Variable
(x)
(xi)
(xii)
Intercept
-3.9935
(0.006)
-3.9898
(0.003)
-4.0935
(0.006)
GLARETCM,-36
-0.0563
(0.062)
GLARETSM,-36
(xiii)
(xiv)
(xv)
(xvi)
(xvii)
(xviii)
0.0891
(0.535)
0.0857
(0.530)
0.0310
(0.742)
-0.1359
(0.200)
-0.1415
(0.196)
-0.1182
(0.366)
-0.0581
(0.071)
-0.0631
(0.056)
GLARETBM,-36#
-0.0451
(0.081)
-0.0651
(0.075)
-0.0464
(0.131)
-0.0557
(0.093)
-0.0418
(0.185)
TRMPREM
0.0193
(0.090)
0.0183
(0.098)
0.0222
(0.081)
DFLTPREM
0.0127
(0.390)
0.0192
(0.365)
0.0371
(0.291)
ADIVYLD
*
CAY*
6.8269
(0.004)
6.8205
(0.003)
6.9751
(0.005)
Adj. R2 (%)
25.89
25.62
25.78
12.87
The data for the regressions with CAY are measured on a quarterly basis.
36
12.49
15.18
-0.0392
(0.152)
0.0276
(0.043)
0.0272
(0.022)
0.0276
(0.042)
0.0559
(0.215)
0.0593
(0.179)
0.0495
(0.390)
22.80
23.80
20.81
Table 6
Coefficients (p values) from regressions of twelve-month excess return on
Glamour and Value portfolios, respectively, on lagged returns on Glamour
portfolios over the period 1951-1997.
EXGLA12 and EXVAL12 are the excess returns over the risk-free rate on the Glamour and Value portfolios, respectively, in
the 12 months following the portfolio formation. GLARET-36 is the average compounded returns of the Glamour stocks in
the 36 months preceding (and including the month of) the portfolio formation. Value and Glamour portfolios are formed
using three different metrics: Cash-flow to Market value ratio (CMRATIO); Sales to market value ratio (SMRATIO); Book
to Market value ratio (BMRATIO). The p-values for the coefficients are obtained from a bootstrapping procedure as
explained in the Appendix.
Dependent Variable
EXGLA12 EXVAL12
Panel A: Portfolios based on cash-flow to market value ratio
Intercept
0.1598
(0.144)
0.2261
(0.199)
GLARETCM,-36
-0.0707
(0.073)
-0.0647
(0.097)
Adj. R2 (%)
4.94
4.00
Panel B: Portfolios based on sales to market value ratio
Intercept
0.1349
(0.120)
0.2188
(0.246)
GLARETSM,-36
-0.0784
(0.053)
-0.0648
(0.154)
Adj. R2 (%)
6.13
2.51
Panel C: Portfolios based on book to market value ratioa
Intercept
0.1398
(0.168)
0.2080
(0.510)
GLARETBM,-36
-0.0682
(0.111)
-0.0435
(0.259)
Adj. R2 (%)
a
Over the period 1963-1997.
5.91
37
2.23
Table 7
Conditional Skewness (p-values) of the monthly excess market returns, EXMKT1,
returns on glamour portfolios, GLARET1, and the market returns orthogonalized
by glamour portfolios, MKTXGLA1, under different states of performance of the
glamour portfolios in the prior 36 months, GLARET-36, over the period 19511997.
GLARET-36 is the return on the Glamour portfolios over the prior 36 months of the portfolio formation. Glamour portfolios
are formed using three different metrics: Cash-flow to Market value ratio (CMRATIO); Sales to Market value ratio
(SMRATIO); Book to Market value ratio (BMRATIO). The skewness of EXMKT1, GLARET1 and MKTXGLA1 are measured
for the sub-samples where GLARET-36 is in lowest quartile (<Q1) or the highest quartile (Q>3) of the overall sample
distribution.
Variable
Skewness measures in
the sub-sample when
prior returns of the
glamour portfolio are in
bottom quartile
Skewness measures in
the sub-sample when
prior returns of the
glamour portfolio are in
top quartile
Panel A: Portfolios based on CMRATIO
EXMKT1
0.0810
(0.350)
-0.5165
(0.010)
GLARETCM,1
0.2730
(0.090)
-0.5171
(0.010)
MKTXGLA1
-0.0551
(0.390)
-0.2365
(0.130)
EXMKT1
0.1749
(0.200)
-0.3494
(0.050)
GLARETSM,1
0.2543
(0.110)
-0.2775
(0.090)
MKTXGLA1
0.0411
(0.420)
-0.2654
(0.100)
EXMKT1
0.2818
(0.120)
-0.3086
(0.100)
GLARETBM,1
0.2182
(0.180)
-0.2836
(0.120)
MKTXGLA1
0.3168
(0.090)
-0.3024
(0.100)
Panel B: Portfolios based on SMRATIO
Panel C: Portfolios based on BMRATIOa
a
Over the period 1963-1997.
38
39