Yu+Chen-Reexamination of the EP Anomaly by the Conditional Trading Strategy

8/6/2019 Yu+Chen-Reexamination of the EP Anomaly by the Conditional Trading Strategy

1/47Electronic copy available at: http://ssrn.com/abstract=1818642

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Reexamination of the E/P Anomaly by the Conditional Trading Strategy

Hsin-Yi Yu

Assistant Professor, Department of Finance, National University of Kaohsiung

700, Kaohsiung University Rd., Nanzih District 81148, Kaohsiung, Taiwan

Tel: +886-7-5919709; Fax: +886-7-5919329; Email: [email protected]

Li-Wen Chen

Assistant Professor, Department of Finance, National Chung Cheng University

168 University Road, Minhsiung Township, Chiayi County 62102, Taiwan,

Tel: +886-5-2720411 ext. 24213; Fax: +886-5-2720818; Email: [email protected]


2/47Electronic copy available at: http://ssrn.com/abstract=1818642

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Re-examination of the E/P Anomaly by the Conditional Trading Strategy

Abstract

This paper delivers a conditional trading strategy to re-examine the E/P anomaly, which has

been subsumed by the three-factor model for a long time. Under the conditional trading

strategy, we purchase undervalued stocks whose current E/P ratios are relatively high

compared to their own E/P ratios over the past decade and sell the owned stocks when their E/P

ratios are relatively low. The holding period for each stock is not fixed or exogenously

predetermined. The returns earned by the conditional trading strategy cannot be rationalized

with either Fama-French three-factor model or Carharts four-factor model. Moreover, the

significant risk-adjusted returns are not attributed to timing ability. Overall, this paper revises

the traditional trading strategy used in academic studies and confirms the E/P anomaly.

Keywords: Conditional trading strategy; Earnings-price ratio; Undervaluation; Anomaly;

Holding period


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Introduction

One of the fundamental conditions for efficient financial markets is the unbiased pricing of

assets. However, a large body of literature reveals a host of anomalies based on bias in pricing.

Analyzing the cross-section of expected stock returns becomes one of the central lines of

financial research. Although various models and rationales have been put forward to explain

anomalies, little attention is paid to the trading strategy, i.e. the method of constructing

portfolios. Is it possible that the trading strategy plays a determinant role in identifying

anomalies? Once we push the trading strategy closer to real investment behavior and

disentangle some trading limits, some anomalies subsumed by factor models may be

revitalized. This paper develops a conditional trading strategy to construct portfolios and

revises the way of sorting the E/P ratios. The finding indicates that the newly designed trading

strategy revitalizes the E/P anomaly, which has long been subsumed by the Fama-French

three-factor model.

Recently, more and more return patterns cannot be fully explained by asset pricing models. A

large number of studies reporting market anomalies in the top journals have mushroomed over

the years (Subrahmanyam, 2010). Recent research shows that capital investment, accruals,

sales growth rates, idiosyncratic volatility, and capital raising are found to be negatively


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equally-weighted or value-weighted portfolios are constructed at the beginning of time t. The

stocks in the same portfolio are all held until time t+n; that is, the holding period for each stock

in the portfolio is identical. While n is more than 1, the monthly return is computed by

averaging the overlapping portfolio returns using the buy and hold method or the rebalance

method (e.g., Jegadeesh and Titman, 1993)2.

Our major concern of the traditional trading strategy is that the holding period of a portfolio is

exogenously predetermined, i.e. the holding period is decided upon before stocks are

purchased, e.g. one month or one year. There is no theoretical explanation offered as to why the

portfolio should be held for a fixed time period, not to mention that such a constraint is not

consistent with real investment behavior. In practice, the holding period is usually set to be one

(e.g. one day in Diether, Lee, and Werner (2009), one month in Fang and Peress (2009), one

year in Cooper et al. (2008)). Portfolios are constructed at the beginning of time tbased on a

predictive variable of the immediately preceding time t-1 and then held until the end of time t.

This line of thinking implicitly assumes that the predictive variable of time t-1 will present its

2 In the buy and hold method, stocks are allowed to have different weights at the beginning of each time. In the

rebalanced method, stocks are rebalanced monthly to maintain equal weights. Some studies further long oneportfolio and short another portfolio to deliver a zero-investment strategy. The zero investment strategy implicitlyassumes that an investor shorts some assets (the short portfolio) to finance the purchase of others (the longportfolio). One of the famous zero investment examples is the phenomenon of momentum in Jegadeesh andTitman (1993). However, most individual investors only sell stocks that they have already owned. They seldomshort-sell stocks (Barber and Odean, 2008). Moreover, in practice, the zero-investment strategy is not reallyzero-cost. If the market begins to move against investors short position, money will be removed from their cash

balance and moved to their margin balance. If short shares continue to rise in price and the investor does not havesufficient funds in the cash account to cover the position, the investor will begin to borrow on margin for thispurpose, thereby accruing margin interest charges.


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predictive power exactly at time t, otherwise there is no anomaly caused by this variable. This

assumption is questionable. It is possible for us to underestimate the predictive power of the

variable if it requires a longer time to present its predictive power.

Some studies try to revise this weakness by including the information of the predictive variable

from t-n to t-1, where n is more than 1. For example, Anderson and Brooks (2006) argue that it

is not reasonable to postulate that only earnings from the previous year are relevant in valuing

companies. Moreover, the phenomenon of momentum also reveals that the information at an

earlier time period also provides predictive power. Jegadeesh and Titman (1993) select stocks

based on stock returns over the past 12 months. They regard the past 12-month return as awhole, which implies that the information at month t-12 can still possess predictive power for

the returns at month t. Based on Jegadeesh and Titmans work, Yu (2010) further analyzes the

trend of past 12-month returns and then creates a hybrid strategy to generate higher

risk-adjusted returns which cannot be fully explained by Carharts four-factor model (Carhart,

1997). But, is it possible to revise this weakness along the trading strategy avenue?

This paper develops a conditional trading strategy to construct portfolios. Like the traditional

trading strategy, the conditional trading strategy decides which to buy based on a predictive

variable. However, unlike the traditional trading strategy, the conditional trading strategy does


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not predetermine a fixed holding period in advance. A stock will be held until it does not

deserve to be owned. To be specific, in the conditional trading strategy we need to determine

not only when to buy a stock but also when to sell it.

In this vein, the most important question is how to decide when to buy and when to sell.

Turning to the unified theoretical models, it is less controversial that investors may overreact or

underreact to news about the fundamentals, for example, Daniel, Hirshleifer, and

Subrahmanyam (1998), Barberis, Shleifer, and Vishny (1998) and Hong and Stein (1999).

Taking all these studies together, most theories emphasize the fact that investors cannot

perform rational and homogeneous reactions to information. The conditional trading strategy is

developed based on the irrational side of investors. Once investors overreact or underreact to

news, stock prices deviate from the fundamentals. This misinterpretation of information

creates an opportunity to buy stocks which are more likely to be undervalued and sell them

when they are more likely to be overvalued.

The conditional trading strategy creates another question: How to know whether a stock is

more likely to be undervalued or overvalued? The prior-detected predictive variable the

earnings to price (E/P) ratio is employed to measure the level of under- or overvaluation

because the E/P ratio plays a critical role in asset pricing. The earliest described asset pricing


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anomaly, even before the capital asset pricing model (CAPM), was based on the E/P ratio

(Sharpe, 1964), so called the E/P effect. It is well subsumed by the three-factor model in Fama

and French (1993, 1996). However, the traditional way of employing the E/P ratio leads to a

problem. Previous studies cross-sectionally sort the E/P ratios at a given time. In other words,

they compare a stocks E/P ratio with the E/P ratios of other stocks in the market. This kind of

cross-sectional E/P sorting ignores the fact that there is heterogeneity across the industry

average E/P ratios. Furthermore, cross-sectional sorting also assumes that only earnings from

the previous year are relevant in valuing companies. Anderson and Brooks (2006) and

Campbell and Shiller (1988) argue that the E/P ratio over several years is a more powerful

predictor of the return on stock.

Therefore, this paper does not adopt such cross-sectional sorting but employs time-series

sorting. To identify whether a stock is undervalued, it is more natural to compare a stocks

current E/P ratio with its own historical E/P ratios. Under time-series sorting, the stocks in the

highest decile are those whose current E/P ratios are situated in the top 10% over the past ten

years. Conversely, the stocks in the lowest decile are those whose current E/P ratios are situated

in the bottom 10% over the past ten years. Intuitively, the stocks which are located in the higher

(lower) deciles are more likely to be undervalued (overvalued). Taking the conditional trading

strategy and time-series E/P sorting together, we purchase stocks in the higher deciles and hold


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these owned stocks until they drop to the lower deciles.

Using all common stocks listed in NYSE, AMEX, and NASDAQ from January 1962 to

December 2010, the conditional trading strategy creates significant risk-adjusted returns under

both the three-factor and four-factor models. If we purchase stocks whose time-series E/P

sortings are in the 9th and 10th deciles in the beginning of each month and hold these owned

stocks until they drop to the 1st deciles, the risk-adjusted return is the most significant 16.63

basis points (p-value=0.01), approximately 2.01% annually. The peak is 16.94 basis points per

month when we purchase stocks whose time-series E/P sortings are in the 9th and 10th deciles

and sell them as they drop to the 3rd, 2nd, and 1st deciles. Furthermore, we also find that holding

an undervalued stock without selling cannot generate significant risk-adjusted returns, which

suggests that selling behavior is a determinant of abnormal returns.

We next attempt to dissect the risk-adjusted returns earned by the conditional trading strategy.

Once a stock is considered as undervalued (overvalued) at time t, we postpone the buying

(selling) activity to observe whether the trading time points significantly affect the

risk-adjusted returns. Since the ideology behind the conditional trading strategy is to identify

and purchase undervalued stocks, which is in the spirit of stock selection ability rather than

timing ability, we expect that the risk-adjusted returns remain significant even though the


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trading activities are postponed. The finding confirms our expectation. In other words, the

risk-adjusted returns are not attributed to timing ability.

The remainder of this paper is organized as follows. Section I describes the data and the

methodology. Section II presents the empirical results of the conditional trading strategy. This

section also tests whether the profit of the strategy is conditional on time, along with a

discussion about the robustness checks. Section III dissects the risk-adjusted returns earned by

the conditional trading strategy. Section IV concludes.

I. Data and Methodology

A. Data

The sample covers all common stocks listed in the New York, American Stock Exchanges, and

NASDAQ from the Compustat monthly file. Throughout, we include stocks that have a stock

exchange code of 11, 12, or 14 that is, ADRs, REITs, closed-end funds, and primes and

scores are excluded. The sample period is from January 1962 to December 2010.

B. Earnings-Price Ratio


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We employ the earnings-price ratio (E/P ratio) to measure the level of undervaluation and

overvaluation. Many previous studies discuss the E/P anomaly, which is applied in many

countries, for example the UK (Levis, 1989; Gregory, Harris, and Michou, 2001; Levis and

Liodakis, 2001; Anderson and Brook, 2006); the UK and several European countries together

(Brouwer, Put, and Veld, 1997; and Bird and Whitaker, 2003); Japan (Aggarwal, Rao, and

Hiraki, 1990; Chan, Hamao, and Lakonishok, 1991; Cai, 1997; and Park and Lee, 2003); New

Zealand (Chin, Prevost, and Gottesman, 2002).

Institutively, a relatively high E/P ratio indicates that under such profitability, investors intend

to buy the stock at a lower price. Given this, the stock is more likely to be undervalued.

Conversely, a relatively low E/P ratio indicates that investors are willing to buy the stock at a

higher price given such profitability, which means that this stock is more likely to be

overvalued. Previous studies, however, usually sort stocks into several groups by comparing

the stocks E/P ratio with the E/P ratios of other stocks in the market. It is not natural to identify

undervalued stocks through this kind of cross-sectional sorting, because the heterogeneity of

the E/P ratio across industries would influence the sorting results. For example, the average E/P

ratio of the agriculture industry is higher and more stable than that of the technology industry3.

3

During the sample period, the mean and standard deviation of E/P ratios in the agriculture industry, i.e. SIC code0100~0999, are 3.73% (7.31%) respectively. In the wholesale trade (SIC code 5000~5199), the mean and standarddeviation of E/P ratios are 2.42% (26.36%).


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Given this, sorting all stocks in the market based on individual E/P ratios may ignore the E/P

ratio characteristics of industry and thereby drives plausible results when picking undervalued

stocks. Therefore, we replace cross-sectional sorting with time-series sorting. In time-series

sorting, the benchmark is the E/P ratios of a stock over the past ten years rather than the

contemporary E/P ratios of other stocks in the market.

In time-series E/P sorting, a stock whose E/P ratio at the time of portfolio formation is located

in the top 10% over the past 10 years would be classified into the highest decile.4 Conversely,

when the E/P ratio of a stock at the time of portfolio formation is situated in the bottom 10% of

its own E/P ratio distribution over the past ten years, the stock would be grouped into the lowest

decile. Thus, undervalued stocks can be defined as being located in the higher deciles, whereas

overvalued stocks are those in the lower deciles.

C. Trading Strategy

This paper employs two trading strategies the traditional trading strategy and the conditional

trading strategy. This section first presents the traditional trading strategy and discusses the

weakness of it. The conditional trading strategy is introduced subsequently to complement the

4In Fama and French (1993), portfolios are formed only in June of year t, and the E/P ratio used is computed as the

equity income for the fiscal year ending in calendar year t-1 divided by the market equity of calendar year t-1.Inother words, Fama and French (1993) update the E/P ratio annually. The calculation of E/P ratio in this study issimilar to that of Fama and French (1993). However, we update the E/P ratio quarterly.


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insufficiency of the traditional trading strategy.

We first introduce the traditional trading strategy. Similar to Fama and French (1993), at the

beginning of each month t, stocks are ranked to several groups based on the sorting of E/P ratios

at the end of month t-1.5 The monthly return of each group is the value-weighted average of the

selected stock returns in that group. These portfolios are held for one month, and then

re-constructed according to the same criteria at the beginning of the next month. If one can

obtain significant risk-adjusted returns by purchasing (short-selling) the stocks in the highest

(lowest) group, the E/P anomaly is identified. We also compute the long-short profit. The

long-short profit is obtained by purchasing the highest group portfolio and short selling the

lowest group portfolio. Evidently, the traditional trading strategy only pays attention to the

buying time point. There is no need to decide the selling time point because all positions are

sold at the end of each month. That is, the holding period for each stock is fixed to one month.

This implicitly assumes that an anomaly can only be observed in a fixed and predetermined

time period (e.g. one month). However, there is no underlying theory to decide how long the

holding period should be. The holding period is mainly decided under personal subjective

preference. This subjective decision may cause two problems. First, some predictive variables

5 As was discussed in Section I.B, the E/P sorting can be cross-sectional or time-series. One can also rank stocksinto terciles, quintiles, or deciles.


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are unable to reflect predictive power exactly within the predetermined holding period. The

traditional trading strategy would neglect the importance of these variables. Secondly, the

traditional trading strategy does not consider the speed of information diffusion. If the speed of

information diffusion is homogeneous across firms, previous literature should be unable to

demonstrate that some anomalies are more significant in firms with specific characteristics.

However, they do find such phenomena (e.g. media coverage in Fang and Peress (2009)).

Therefore, t is reasonable to conjecture that the speed of information diffusion is heterogeneous

across firms. Collectively, an overly-long holding period may dilute the predictive power of

information; an overly-short holding period may underestimate the predictive power of

information. Therefore, we release this constraint and develop a conditional trading strategy,

which is based on the concept that information at time t may not reflect predictive power

exactly at time t+1.

In the conditional trading strategy, we invest money in stock which satisfy the buying criterion

at the beginning of each month and sell the owned stocks which meet the selling criterion. The

portfolio is value-weighted. Here is a brief example when the buying (selling) criterion is

whether a stock is undervalued (overvalued). There are three stocks, X, Y, and Z, in the market.

At month t, if stock X is undervalued and stocks Y and Z are not, we buy stock X in proportion

to its size (usually a millionth of the size). At the beginning of time t+1, if stocks X and Y are


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undervalued, we increase the positions in stocks X and Y with money in proportion to their

sizes. At the beginning of time t+2, if stock X is overvalued and stocks Y and Z are

undervalued, we sell the whole position of stock X and invest in stocks Y and Z in a

value-weighted way.

This study uses the E/P ratios to define the buying and selling criteria. According to the sorting

on E/P ratios6, stocks are classified into several groups. If stocks are sorted into deciles, the

lowest decile of E/P sorting is 1 and the highest decile is 10. We use the form (Buy, Sell) to

describe the buying and selling criteria in the conditional trading strategy. For example, if the

buying criterion is to purchase stocks whose E/P sorting is more than or equal to 8 (>=8) and

the selling criterion is to sell the owned stocks whose E/P sorting is less than 5 (=8,


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wheretpr , is the monthly return on a portfolio in excess of the one-month T-bill return; p is

the risk-adjusted return of portfolio i; andtRMRF is the return on the market portfolio in excess

of the risk-free rate.tSMB and tHML are value-weighted, zero-investment, factor-mimicking

portfolios for size and book-to-market equity in stock returns respectively. These factor data

are collected from the website of Kenneth R. French.

We also employ Carharts four-factor model to examine whether the risk-adjusted returns

earned by the conditional trading strategy are overlapped with the phenomenon of momentum.

The momentum factor (UMD) is computed as the equally weighted average of firms with the

highest 30 percent eleven-month returns lagged one month minus the equal-weight average of

firms with the lowest 30 percent eleven-month returns lagged one month.

tpt

UMD

pt

HML

pt

SMB

pt

RMRF

pptp eUMDHMLSMBRMRFr ,, +++++= (2)

II. Empirical Results of the Buy-Sell Strategy

In this section, two trading strategies the traditional trading strategy and the conditional

trading strategy are used to construct portfolios. Two E/P sorting methods cross-sectional


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sorting and time-series sorting are also adopted to sort stocks into several groups. Therefore,

there are in total four combinations with different trading strategies and sorting methods. All

combinations are examined and reported.

A. Traditional Trading Strategy and Conditional Trading Strategy

As a base case, we first mirror the methodology in Fama and French (1993), which uses

cross-sectional E/P sorting to rank stocks into quintiles and construct portfolios by the

traditional trading strategy. The lowest quintile of E/P sorting is 1 and the highest quintile is 5.

The portfolio is value-weighted and constructed at the beginning of each month. Table 1

reports the raw returns and risk-adjusted returns.

[INSERT TABLE 1 HERE]

The central results in this table are consistent with those in Fama and French (1993). First, the

three-factor model leaves no residual E/P effect. Although there are significant risk-adjusted

returns for P4 and P5 under CAPM, the three-factor intercepts for the five E/P portfolios are

insignificant between -8.87 and 8.32 basis points per month. Even if we long the highest E/P

portfolio and short sell the lowest E/P portfolio (P5-P1), the risk-adjusted return is not


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significant. To sum up, there is no E/P effect under the three-factor model. Second, both raw

returns and risk-adjusted returns increase from the lowest to the highest E/P quintile. Moreover,

the untabulated results indicate that the increasing pattern in the risk-adjusted returns on the

E/P portfolios is due to their loadings on the book-to-market factor HML. The lowest E/P

quintile has an HML slope of -0.14, and the highest E/P quintile has an HML slope of 0.41. In

brief, the results in Table 1 can be interpreted as suggestive evidence in favor of the argument

that the three risk factors in Fama and French (1993) explain the E/P effect.

Next we turn to time-series sorting, whose sorting benchmark is the stocks own E/P ratios over

the past decade rather than the E/P ratios of other stocks in the market. Table 2 illustrates that

under the traditional trading strategy there is no significant three-factor risk-adjusted return in

every portfolio, including the long-short portfolio, P5-P1. To sum up, the three risk factors

fully explain the portfolio returns when the traditional trading strategy is employed.


However, the traditional trading strategy gives no consideration to the fact that the holding

period of each stock should not be fixed. Therefore, we disentangle the constraint on the

holding period through the conditional trading strategy. Table 3 presents the three-factor


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risk-adjusted returns under the conditional trading strategy. The stocks are ranked into deciles

through cross-sectional E/P sorting7. We can observe that there are 55 combinations of (Buy,

Sell) in Table 3. For example, we can purchase undervalued stocks whose E/P sortings are

located in the 9th and 10th deciles and hold them until they fall to the lowest decile. The

risk-adjusted return earned under such a trading criteria is shown in cell (>=9,


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not consider the E/P ratios from the previous years in valuing companies. Therefore, it may not

suit the ideology behind the conditional trading strategy. Time-series E/P sorting is developed

to eschew these weaknesses.

In Table 4, we adopt the conditional trading strategy with time-series E/P sorting, whose

sorting benchmark is the stocks own E/P ratios over the past decade. The three-factor

risk-adjusted returns are reported. Three features stand out.


First and foremost, the three-factor risk-adjusted returns become significant. We can observe

that when the buying criteria are between >=6and >=10 and the selling criteria are between


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Secondly, once we tighten the buying criteria, the risk-adjusted returns increase. In other words,

purchasing stocks in the higher two deciles would obtain higher risk-adjusted returns than

purchasing stocks in the higher three deciles. This increasing pattern of returns is not

influenced by the selling criteria. Theoretically, undervalued stocks should be found in the

higher deciles rather than in the lower deciles. Purchasing stocks in the higher deciles should be

more consistent with the spirit of the conditional trading strategy. The results confirm this

inference. In a similar vein, once we hold the stocks whose E/P sortings are positioned in the

higher deciles, the risk-adjusted returns should be reduced because these stocks are less likely

to be overvalued. The results show that the returns decrease when we sell the owned stocks

whose E/P sortings are positioned in the higher deciles. This decreasing pattern of returns is not

influenced by the buying criteria. Taken together, we can conclude that purchasing stocks in the

higher deciles and selling stocks in the lower deciles can achieve higher returns. In other words,

it is profitable to purchase stocks which are highly undervalued and hold them until they are

very likely to be overvalued.

Thirdly, it is interesting to note that if the selling criterion is


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risk-adjusted returns, the holding period should be neither fixed nor unlimited. It should be

varied with the characteristics of every individual stock. Collectively, these results are

supportive of the notion that both the buying behavior and the selling behavior independently

contribute to the enhancement of risk-adjusted returns.

To summarize, the conditional trading strategy revitalizes the E/P anomaly, which was no

longer considered as an anomaly under the three-factor model. This finding suggests that the

conditional trading strategy can enhance the possibility of identifying anomalies.

B. The Holding Period

It is reasonable to expect that the average holding period for a stock under the conditional

trading strategy is longer than that in the traditional trading strategy. But how much longer?

Table 5 describes the statistics of the holding period under the two strategies. For brevity, here

the conditional trading strategy is to purchase stocks whose time-series E/P sortings are in the

9th and the 10th deciles and hold them until they drop to the 1st deciles, i.e (>=9,


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sample and then dividing by the number of stocks. If there are time gaps in the holding period

for the same stock, the stock in different holding zones would be viewed as different objectives.

Note that under the traditional trading strategy, if a stock is chosen to be held at the beginning

of month t, t+1, and t+2 based on the sorting result, the holding period for the stock is 3. In this

way, the average holding period of the traditional trading strategy is not always one month.


Panel A of Table 5 shows that the average holding period is a striking 68.9 months under the

conditional trading strategy, whereas it is only 1.7 months under the traditional trading strategy.

In other words, once we purchase a stock, we will on average hold it for 5.7 years under the

conditional trading strategy. However, on average we would not continuously choose to buy a

stock into the portfolio over two months under the traditional trading strategy. Panel B reports

the average holding period for different industries. We can first observe that the average

holding period under the conditional trading strategy is still much longer than that under the

traditional trading strategy for all industries. Among various industries, public administration

has the shortest holding period under both trading strategies.

Furthermore, we also compute the average holding period along size partition. However, it is


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whose market capitalizations are in the smallest NYSE/AMEX/NASDAQ decile to repeat

previous analysis. All major findings remain unchanged under these tests.

C.1 Carharts Four-Factor Model

Some may raise a concern that the E/P anomaly overlaps with the momentum effect. Carharts

four-factor model is employed to test this argument. Carharts four-factor model is based on the

three-factor model and further includes the momentum factor (UMD). This momentum factor

is computed as the equally weighted average of firms with the highest 30 percent eleven-month

returns lagged one month minus the equal-weight average of firms with the lowest 30 percent

eleven-month returns lagged one month.

As anticipated, there remain significant risk-adjusted returns in Carharts four-factor model.

The momentum factor cannot completely explain the significant risk-adjusted returns when the

conditional trading strategy is employed. For example, when (Buy, Sell) is (>=9,


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C.2 Time Partition

We also test whether the above findings are sensitive to time. Fama and French (1992, 1993,

1996, and 1998) claim in their work that the three-factor model can fully explain the anomalies

derived from the E/P ratios. The sample periods are generally from 1962 to 1989 in Fama and

French (1992, 1993, and 1996) for the US domestic market, and from 1975 to 1995 in Fama

and French (1998) for international markets. In Panel A of Table 6, we first follow the sample

period in Fama and French (1992), which ranges from January 1962 to December 1989 and

sorts stocks into quintiles by using time-series E/P sorting. The second sub-period from

January 1990 to December 2010 is used to examine the E/P anomaly in the time period which is

not covered by the work of Fama and French. Here (Buy, Sell) is set to be (>=9,


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However, when we use the conditional trading strategy to construct portfolios from January

1990 to December 2010, the E/P anomaly cannot be rationalized with the three risk factors. The

significant intercept demonstrates the effectiveness of the conditional trading strategy.

However, even when the conditional trading strategy is adopted, the E/P anomaly does not

prevail in the market from January 1965 to December 1989, which means that the E/P anomaly

can only be found in the past two decades. It would be interesting to uncover the reasons which

lead to the above finding in the future.

In Panel B of Table 6, we further divide the whole period into five non-overlapping sub-periods.

The results show that the traditional trading strategy generates no significant risk-adjusted

returns. However, the conditional trading strategy can create significant risk-adjusted returns

during some sub-periods. The return reaches a peak during the 1990s, which is 33.56 basis

points per month, approximately 4.10% per year. All combinations of (Buy, Sell) are examined,

although not always reported, and the major conclusions remain unchanged. In brief, as long as

we use the traditional trading strategy to construct portfolios, the E/P anomaly is always

subsumed by the three-factor model.

C.3 Robustness Check


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A test is conducted to ensure that the findings are not driven by small and illiquid stocks. Hence,

we filter out all stocks priced under $5 at the beginning of the holding period, and all stocks

with market capitalizations that would place them in the smallest NYSE/AMEX/NASDAQ

decile and repeat the previous analyses. The test results indicate that the deletion of low-priced

and illiquid stocks has little effect on the results. The previous findings are not changed.

Moreover, some may ask why use the E/P ratios over the past ten years as the benchmark in

time-series E/P sorting. Therefore, we also compare a stocks current E/P ratio with its E/P

ratios over the past 5, 12, or 20 years to decide in which decile this stock is grouped and repeat

all the above analyses. We find that as long as the conditional trading strategy is adopted, the

significant risk-adjusted returns can be identified regardless of which time periods E/P ratio is

employed.

III. Dissecting the Risk-Adjusted Returns of the Buy-Sell Strategy

Fama (1972) proposes that the returns of mutual fund managers can be subdivided into two

parts: return from stock selection and return from timing activity. Stock selection is the ability

to forecast the price movements of individual investment targets relative to other targets in the

same market. Timing is the ability to forecast the price movements of one investment set

relative to another set, and is an investment strategy based on the outlook for an aggregate


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29

market rather than for a particular financial asset.

A methodology is designed to ascertain whether the risk-adjusted returns under the conditional

trading strategy are driven by timing ability. Theoretically, when the returns are mainly

attributed to timing ability, the time of purchasing and selling stocks would influence the

returns significantly. On the other hand, if a portfolio is always able to produce significant

risk-adjusted returns when the purchasing and selling time points are postponed, we can infer

that the reason is less associated with timing ability and more with stock selection ability. Since

the design of the conditional trading strategy is to purchase undervalued stocks and hold them

until the undervaluation disappears, the whole process is less related to the spirit of timing

activity. Hence, we expect that the portfolio constructed under the conditional trading strategy

can still generate significant risk-adjusted returns when the buying and selling time points are

postponed.

Following this line, we postpone the buying and selling activities to observe whether the

risk-adjusted returns are reduced or become insignificant. When a stock is regarded as

undervalued at month t, its purchasing time would be postponed to month t+1, t+2, t+3 or

t+6. Similarly, the selling time can also be postponed. When a stock is considered as

overvalued at month t, it would be sold at month t+1, t+2, t+3 or t+6respectively rather


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30

than at month t. Because the results look so similar for different combinations of (Buy, Sell), we

only present (>=9,


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31

IV. Conclusion

The traditional trading strategy usually fixes the length of the holding period and thereby

underestimates the potential of predictive information. To revise this weakness and be closer to

real investment behavior, this paper delivers a conditional trading strategy to revitalize the E/P

anomaly previously subsumed by Fama-French (1993) three-factor model. The conditional

trading strategy purchases stocks which are more likely to be undervalued and sells them when

the stocks are more likely to be overvalued. Apparently, unlike the traditional trading strategy,

there is no predetermined holding period for a stock. To measure the levels of undervaluation

and overvaluation, the current E/P ratio of a stock is compared with its E/P ratios over the past

decade. If the stock has a relatively high (low) E/P ratio it is considered to be undervalued

(overvalued).

The risk-adjusted returns of portfolios constructed under the conditional trading strategy

remain significant in Fama-French three-factor model. Moreover, the phenomenon of

momentum cannot fully explain the observed E/P anomaly. The results are robust to sample

division into sub-periods and removing outliers. Even when we postpone the buying and

selling activities, the risk-adjusted returns are still significant. In other words, the risk-adjusted

returns earned by implementing the conditional trading strategy are less likely to be attributed


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32

to timing ability.

Based on these findings, this paper addresses several fundamental concerns. First, the

traditional trading strategy merely focuses on the time of purchasing stocks. The selling time

point is seldom discussed in the asset-pricing field. Our findings indicate that the criterion and

time of selling behavior possesses significant influence on risk-adjusted returns. Secondly, the

findings in both this paper and Jegadeesh and Titman (1993) imply that information at time t

which can predict stock returns does not have to take effect exactly at time t+1. In other words,

information at time t-2, t-3, , t-n may still have predictive power on stock returns at time t.

Finally, in the past, most predictive variables are sorted cross-sectionally. Time-series sorting is

seldom adopted. The revitalized E/P anomaly suggests that identifying other anomalies

through time-series sorting is possible, such as the dividend/price (D/P) ratio in Fama and

French (1993). It is interesting to examine whether the other anomalies which have been

subsumed by the three-factor model would reappear under the conditional trading strategy and

time-series sorting in the future.


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33

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Table 1

Raw and Risk-Adjusted Returns under the Traditional Trading Strategy: Cross-Sectional

Sorting

This table reports the raw returns, excess returns and monthly risk-adjusted returns of the portfolios under the

traditional trading strategy. The unit is basis points. The sample includes all common stocks listed in NYSE,

AMEX, and NASDAQ from January 1962 to December 2010. At the beginning of each month, stocks are ranked

into quintiles based on the earnings-price (E/P) ratios. The E/P ratio used in this study is similar to that of Fama

and French (1993), but we update the E/P ratio quarterly rather than annually. All portfolios are value-weighted

and held for one month. The t-statistics are in parentheses and the p values are in brackets.

Quintile Raw Ret Excess Ret CAPM Fama-French

P1 (lowest)92.36

(2.938)

[0.003]

47.64(1.511)

[0.131]

-9.19(-0.511)

[0.610]

-8.87(-0.506)

[0.613]

P2

86.95

(3.714)

[0.000]

42.32

(1.805)

[0.072]

-3.21

(-0.387)

[0.699]

6.83

(0.878)

[0.381]

P3

93.97

(4.835)

[0.000]

49.69

(2.553)

[0.011]

10.15

(1.257)

[0.209]

7.78

(0.952)

[0.342]

P4106.79(5.642)

[0.000]

62.83(3.315)

[0.001]

20.77(2.551)

[0.011]

5.46(0.741)

[0.459]

P5 (highest)

117.13

(5.871)

[0.000]

73.18

(3.657)

[0.000]

29.69

(3.086)

[0.002]

8.32

(0.983)

[0.326]

P5-P1

23.76

(0.986)

[0.325]

68.48

(2.831)

[0.005]

40.79

(1.779)

[0.076]

19.78

(0.916)

[0.360]


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Table 2

Raw and Risk-Adjusted Returns under the Traditional Trading Strategy: Time-Series Sorting

Four kinds of monthly returns of the portfolios for the traditional trading strategy are reported in this table. The

unit is basis point. The sample includes all common stocks listed in NYSE, AMEX, and NASDAQ from January

1962 to December 2010. At the beginning of each month, stocks are grouped into quintiles by using time-series

E/P sorting. The benchmark is their own past 10-year E/P ratios. A stock whose E/P ratio at the time of portfolio

formation is located in the top 20% over the past 10 years would be ranked in the highest quintile. All portfolios

are value-weighted and held for one month. The t-statistics are in parentheses and the p values are in brackets.

Quintile Raw Ret Excess Ret CAPM Fama-French

P1 (lowest)

95.23

(3.839)[0.000]

50.16

(2.018)[0.044]

6.88

(0.569)[0.570]

6.55

(0.532)[0.595]

P2

98.04

(4.358)

[0.000]

53.39

(2.368)

[0.018]

9.60

(1.047)

[0.296]

7.38

(0.792)

[0.429]

P3

112.27

(4.472)

[0.000]

67.77

(2.697)

[0.007]

22.12

(1.506)

[0.133]

20.63

(1.376)

[0.169]

P4

95.98

(4.679)

[0.000]

51.47

(2.505)

[0.013]

9.32

(1.234)

[0.218]

9.54

(1.237)

[0.216]

P5 (highest)

94.46

(4.755)

[0.000]

50.05

(2.515)

[0.012]

9.46

(1.295)

[0.196]

7.65

(1.034)

[0.301]

P5-P1

0.81

(0.051)

[0.959]

-44.29

(-2.781)

[0.006]

-3.83

(-0.243)

[0.808]

-1.77

(-0.111)

[0.912]


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Table 3

The Risk-Adjusted Returns under the Conditional Trading Strategy: Cross-Sectional Sorting

This table presents the monthly risk-adjusted returns of the portfolios under the Fama-French three-factor model for the conditiona

common stocks listed in NYSE, AMEX, and NASDAQ from January 1962 to December 2010. At the beginning of each month, we c

ratios of other stocks in the market and group stocks into deciles. One is the lowest E/P group and ten is the highest E/P group. In

satisfies the buying criterion at time t, we invest in stock X in proportion to its size. At the beginning of time t+1, if stock X satisfie

criteria, it will be held without investing new money. This stock will only be sold when it satisfies the selling criterion. Rows (>=

columns (


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41

>=4

6.36

(1.156)

[0.248]

6.86

(1.219)

[0.223]

9.52

(1.609)

[0.108]

11.00

(1.770)

[0.077]

>=5

6.54

(1.136)

[0.256]

7.01

(1.190)

[0.234]

9.53

(1.547)

[0.123]

10.95

(1.709)

[0.088]

8.50

(1.332)

[0.184]

>=6

5.88

(0.990)

[0.323]

6.34

(1.043)

[0.297]

9.01

(1.419)

[0.156]

10.44

(1.600)

[0.110]

8.03

(1.232)

[0.218]

5.92

(0.828)

[0.408]

>=7

5.87

(0.946)

[0.345]

6.50

(1.022)

[0.307]

9.47

(1.425)

[0.155]

10.69

(1.564)

[0.118]

7.55

(1.112)

[0.267]

6.45

(0.875)

[0.382]

4.99

(0.710)

[0.478]

>=86.55

(1.002)

[0.317]

7.26(1.081)

[0.280]

10.34(1.464)

[0.144]

11.09(1.535)

[0.125]

7.13(0.999)

[0.318]

6.61(0.868)

[0.386]

5.07(0.691)

[0.490]

>=9

5.50

(0.822)

[0.411]

6.39

(0.926)

[0.355]

9.52

(1.309)

[0.191]

10.69

(1.420)

[0.156]

5.60

(0.781)

[0.435]

4.69

(0.619)

[0.536]

4.80

(0.629)

[0.530]

>=103.01

(0.425)

[0.671]

4.44

(0.619)

[0.536]

7.02

(0.945)

[0.345]

9.27

(1.199)

[0.231]

5.95

(0.757)

[0.449]

6.72

(0.796)

[0.426]

8.26

(0.950)

[0.342]


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42

Table 4

The Risk-Adjusted Returns under the Conditional Trading Strategy: Time-Series Sorting

This table reports the monthly risk-adjusted returns of the portfolios under the Fama-French three-factor model for the conditiona

common stocks listed in NYSE, AMEX, and NASDAQ from January 1962 to December 2010. At the beginning of each month, sto

own past 10-year E/P ratios. When the E/P ratio of a stock at the time of portfolio formation is situated in the bottom 10% over the pas

decile. One is the lowest E/P group and ten is the highest E/P group. For the conditional trading strategy, if stock X satisfies the buy

in proportion to its size. At the beginning of time t+1, if stock X satisfies neither the buying criteria nor the selling criteria, it will b

stock will only be sold when it satisfies the selling criterion. Column (>=1 ~ >=10) describes the buying criteria and row (


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43

>=4 5.38

(1.027)

[0.305]

9.75

(1.729)

[0.084]

9.12

(1.644)

[0.101]

9.79

(1.638)

[0.102]

>=5 5.94

(1.120)

[0.263]

11.18

(1.912)

[0.056]

10.43

(1.816)

[0.070]

10.81

(1.769)

[0.077]

10.73

(1.620)

[0.106]

>=6 6.31

(1.199)

[0.231]

12.67

(2.130)

[0.034]

11.93

(2.027)

[0.043]

12.07

(1.918)

[0.056]

11.79

(1.744)

[0.082]

9.67

(1.359)

[0.175]

>=7 6.64

(1.258)

[0.209]

14.39

(2.346)

[0.019]

13.69

(2.216)

[0.027]

13.33

(2.039)

[0.042]

12.52

(1.798)

[0.073]

9.36

(1.278)

[0.202]

9.88

(1.290)

[0.198]

>=8 6.94(1.349)

[0.178]

15.87(2.578)

[0.010]

15.65(2.447)

[0.015]

15.42(2.287)

[0.023]

14.38(2.006)

[0.045]

10.79(1.435)

[0.152]

10.28(1.323)

[0.186]

>=9 7.68

(1.461)

[0.145]

16.63

(2.590)

[0.010]

16.52

(2.462)

[0.014]

16.94

(2.391)

[0.017]

16.05

(2.163)

[0.031]

13.37

(1.733)

[0.084]

11.43

(1.430)

[0.153]

>=10 7.29

(1.370)

[0.171]

16.43

(2.492)

[0.013]

15.79

(2.298)

[0.022]

16.50

(2.264)

[0.024]

16.13

(2.083)

[0.038]

14.41

(1.798)

[0.073]

12.59

(1.523)

[0.128]


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44

Table 5

The Average Holding Periods for the Traditional Trading Strategy and the Conditional Trading

Strategy: Time-Series Sorting

This table reports the average holding months for stocks in the portfolios constructed by the traditional trading

strategy and the conditional trading strategy respectively. The sample includes all common stocks listed in NYSE,

AMEX, and NASDAQ from January 1962 to December 2010. The traditional trading strategy here is to purchase

stocks in the highest quintile. The conditional trading strategy here is to purchase stocks whose time-series E/P

sortings are in the 9th and the highest deciles, and hold them until they drop to the lowest deciles, i.e. (Buy, Sell) is

(>=9, =9,


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45

Panel C: Size Partition

1 (smallest) 1.6 11.4 1 478 65.2 92.6 1 516

2 1.7 12.6 1 480 72.1 96.4 1 519

3 1.8 13.1 1 459 72.3 93.8 1 521

4 1.7 12.6 1 448 70.7 85.4 1 507

5 (largest) 1.5 9.5 1 452 62.4 69.2 1 495


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Table 7

The Risk-Adjusted Returns under the Conditional Trading Strategy with Postponed Buying

and Selling Time

This table shows the three-factor risk-adjusted returns of portfolios in basis point under the conditional trading

strategy with postponed buying and selling time. The sample includes all common stocks listed in NYSE, AMEX,

and NASDAQ from January 1962 to December 2010. The (Buy, Sell) is (>=9,

Documents

Yu+Chen-Reexamination of the EP Anomaly by the Conditional Trading Strategy