Problems in Measuring Portfolio Performance - An Application to Contrarian Investment Strategies.pdf

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ECONOMICS

ELSINER

Journal of Financial Econo mics 38 (1995) 79-107

Problems in measuring portfolio performance

An application to contrarian investment strategies

Ray Ball, S.P. Kothari”, Jay Shanken

W illiam E. Simon Graduate School of Busine ss Administration, University of Rochester,

Rochester, NY 14627, USA

(Received September 1992; final version received July 1994)

Abstract

We document problems in measuring raw and abnormal five-year contrarian port-

folio returns. ‘Loser’ stocks are low-priced and exhibit skewed return distributions.

Their 163% mean return is due largely to their lowest-price quartile position. A %ith

price increase reduces the mean by 25%, highlighting their sensit ivi ty to micro-

structure/liquidity effects. Long positions in low-priced loser stocks occur dispro-

portionately after bear markets and thus induce expected-return ef fects. A contrarian

portfolio formed at June-end earns negative abnormal returns, in contrast with the

December-end portfolio. This conclusion is not limited to a particular version of the

CAPM.

Key

words:

Contrarian strategy; Low-priced stocks; Portfolio performance; Market

efficiency; Asset pricing

JEL classilfcation: Gil; G12; G14

*Corresponding author.

We thank Sudipta Basu and Richard Sloan for excellent research assistance . We are grateful for

the comm ents of John Long, Jay Ritter, Bi ll Schwert (the editor), Jerry Zimmerm an, two anony-

mous referees, and semina r participants at Bosto n University, University of Illin ois , University

of Iowa,

University

of Roches ter, Vand erbilt University, the Stanford Summer Camp, the

Cornell-Rochester joint workshop, the 1992 Conference on Financial Econo mics and Account-

ing at New York University, and the City University Bu sine ss Schoo l in London. We acknowledge

fina ncia l support from the Bradley Polic y Research Center a t the Sim on Sc hool, University

of Rochester, from the John M. Olin Foundation, and from the Institute for Quantitative Research

in Finance.

0304-405X/95/ 09.50 G 1995 Elsevier Scienc e S.A. All rights reserved

SSDI 0304405X9400806 C


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80 R. Ball et al. /Journal of Financial E conom ics 38 (1995) 79-107

1. Introduction

We study problems in measuring the performance of contrarian portfolios,

similar to those examined by DeBondt and Thaler (1985, 1987), Chan (1988),

Ball and Kothari (1989), ‘Chopra, Lakonishok, and Ritter (1992), and Jones

(1993), among others. Measurement problems are apparent in both raw and

abnormal five-year buy-and-hold returns. The problems are unusually severe for

contrarian portfolios because they invest in extremely low-priced ‘loser’ stocks.

Still, many of the issues we raise should be relevant to performance measure-

ment in general.

The possibility that microstructure factors systematically bias measured raw

returns has received little attention in the context of portfolio performance

measurement (Conrad and Kaul, 1993, is an exception). By being short in

comparatively high-priced winner stocks and long in comparatively low-priced

loser stocks, contrarian portfolios have an unhedged position in price-related

microstructure-induced biases. Loser stocks are on average so low-priced that

just a i increase in their purchase price reduces their average five-year buy-

and-hold return by 25% (2500 basis points). The corresponding reduction for

the lowest-price quartile of loser stocks is an enormous 86%. The surprisingly

large effect of a price adjustment highlights the sensitivity of measured returns

on these portfolios to microstructure effects (spreads, liquidity, and brokerage

costs), or to even a small amount of security mispricing.

We report a variety of evidence that microstructure-induced biases can be

acute, even in five-year returns. For example, loser-stock return distributions

are highly right-skewed. The 163% mean loser-stock five-year return is due

largely to the lowest-price quartile of losers, whose mean return is 357%. The

average price of these stocks is only 1.04. To make things worse, the effects of

long positions in low-priced loser stocks occur disproportionately after bear

markets and thus are compounded by expected-return effects, as observed by

Jones (1993).

We also investigate June-end investment periods. A body of evidence (Roll,

1983a; Lakonishok and Smidt, 1984; Keim, 1989; Bhardwaj and Brooks, 1992)

suggests that microstructure-related biases in measured returns are most

pronounced at the calendar year-end, which is precisely when contrarian port-

folios typically are formed (see studies by DeBondt and Thaler, Chan, Ball and

Kothari, and Chopra et al. previously cited). In addition, Zarowin (1990) shows

that size, January, and contrarian effects are not independent. We report that

the average five-year loser-stock return is 3 1O/o ower for June-end than Decem-

ber-end periods, even though they share 53.5 of their 54 years in common. For

the lowest-priced quartile of loser stocks, the December-June difference aver-

ages 103%. Similar results are obtained for August-end periods. The sensitivity

of the DeBondt and Thaler portfolio’s average return to an arbitrary starting

point in calendar time suggests performance measurement problems and casts


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R. Ba ll et al. /Journal of Finan cial Eco nom ics 38 (1995) 79-107 81

doubt on the evidence that has been presented for the contrarian hypothesis. As

DeBondt and Thaler (1985, p. 799) themselves note, their choice of Decem-

ber-end as the portfolio formation date is ‘essentially arbitrary’.

The above problems relate to measuring contrarian portfolio ‘raw’ returns.

We also highlight problems in performing a risk-adjusted abnormal-return

analysis. We employ Kothari and Shanken’s (1992) version of the excess-return

time-series regression methodology (see Chan, 1988; Ball and Kothari, 1989) to

estimate Jensen alphas, while allowing conditional betas to vary over time.

Because the contrarian strategy by definition selects stocks that have behaved

and are expected to behave contrary to the index, it is appropriate to control for

the index effects in its evaluation. Therefore, unlike raw returns, Jensen alphas

are still expected to be zero in spite of the disproportionate incidence of

low-price loser stocks after bear markets. The June-end contrarian portfolio has

a negative 2.5% alpha over the five-year post-formation period, compared with

a positive 4.3% for the December-end portfolio. It earns negative abnormal

returns in four of its five post-formation years when constructed at the end of

June, but it appears profitable in all five years if constructed at the end of

December. We argue that the June-end (or August-end) results are more reliable.

Regardless of its source, the sensitivity of the abnormal return estimates to

choosing a seemingly-arbitrary interval end point casts doubt on the robustness

of the DeBondt and Thaler (1985, 1987) results.

Chopra et al. argue that the empirical relation between estimated betas and

average returns is flatter than implied by the Sharpe-Lintner model, and that

Jensen alphas underestimate the contrarian strategy’s profitability as a conse-

quence. This argument is made more pointed by the conclusion of Fama and

French (1992, p. 464) that ‘ . . the relation between j and average return for

1941-1990 is weak, perhaps nonexistent’ and thus the model ‘ . . . does not

describe the last 50 years of average stock returns’. While the risk-return

tradeoff may indeed be flatter than implied by the Sharpe-Lintner model, we

argue that beta still plays an important role in risk adjustment (see Kothari,

Shanken, and Sloan, 1994; Jagannathan and Wang, 1993). In any event, the

June-end contrarian portfolio is not profitable even if the risk-return slope is

considerably flatter than the risk premium implied by the Sharpe-Lintner

model. An annual risk premium of 9% and zero-beta rate 5% above T-bill rates

(i.e., the risk premium and zero-beta rate estimates of Chopra et al.) would lead

to an average abnormal return of only 1.4% for the June-end strategy, merely

0.35 standard errors from zero. We conclude that the lack of evidence of

contrarian profitability for the June-end strategy is not limited to a particular

version of the capital asset pricing model (CAPM).

Although the mean-variance framework has been the main approach to

performance evaluation in the literature, we point to several features of the

data that suggest this framework may not be completely satisfactory. First,

it is important to appreciate that incorporating the well-known size, price,


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82 R. Ball et al./Journal of Financial Econo mics 38 (1995) 79-107

book-to-market, and liquidity-related deviations from the security market line

(e.g., Banz, 1981; Fama and French, 1992; Amihud and Mendelson, 1986) would

only serve to increase the (normal) required return for the losers relative to that

for the winners. In this sense, abnormal contrarian returns based on the

mean-variance framework may well be biased upward.

Second, we also briefly examine the contrarian portfolio’s beta behavior

in up and down markets. DeBondt and Thaler (1987) and Chopra et al. observe

that the contrarian portfolio has a considerably higher up-market than down-

market beta. We show that this beta behavior is accompanied by a large

negative alpha, which diminishes the appeal of the relatively high up-market

beta.

Third, the distribution of loser-stock returns is highly right-skewed, such that

the difference between median returns on winner and loser stocks is less than

one-sixth of the difference between their means. This suggests caution when

focusing solely on mean returns of contrarian portfolios, and perhaps also when

using beta-adjusted returns.

We caution that our initial sample includes both New York and American

Stock Exchange (NYSE-AMEX) stocks. Hence, as a robustness check and to

provide better comparability with prior research, we briefly summarize results

for an NYSE-only sample. We are able to report that all the results are

essentially unchanged by the exclusion of AMEX stocks.

Section 2 describes the data and procedures for constructing contrarian

portfolios. Section 3 examines the effects on contrarian raw returns of price and

choice of year-end. Section 4 examines abnormal returns for both December-

and June-end contrarian portfolios, by estimating excess-return time-series

regressions. Section 5 contains concluding remarks.

2. Data and procedures for constructing contrarian portfolios

Each year we rank all NYSE-AMEX stocks on the Center for Research in

Security Prices (CRSP) monthly tapes on the basis of their buy-and-hold returns

over the preceding five years, denoted as the ranking period. The fifty stocks

ranked lowest and highest each year are labeled ‘losers’ and ‘winners’. These

loser and winner stocks’ performances are monitored over a five-year post-

ranking period. Ranking periods ending in both December and June are

considered. Data are available from December 31, 1925 for NYSE stocks and

from June 30, 1962 for AMEX stocks. The first post-ranking period begins in

1931 and the last in 1984. Thus, there are 54 overlapping ranking and post-

ranking periods, denoted as event years

- 4 through + 5. We examine both

five-year and annual buy-and-hold post-ranking returns.

To provide a more powerful test of the contrarian hypothesis, the contrarian

portfolios we simulate differ in two ways from those in previous studies. First, we


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R. Ball et al. JJournal of Financial Econo mics 38 11995) 79-107 83

study both NYSE and AMEX stocks, whereas DeBondt and Thaler, Ball

and Kothari, and Chopra et al. study only NYSE stocks. NYSE stocks

have higher average capitalization and price, and are followed by more

analysts. Evidence in Chopra et al. suggests that small-capitalization stocks

are more likely to experience overreaction. Thus, including AMEX stocks

would make both contrarian and microstructure effects more pronounced

and thus more observable. As a robustness check, and for better comparability

with prior research, Section 4.3 summarizes results for a NYSE-only sample,

which are similar. Second, the winner and loser portfolios consist of 50 stocks,

as in some of the DeBondt and Thaler (1985, 1987) analysis and in Ball and

Kothari, but different from the vitile portfolios in much of the Chopra et al.

analysis.

As in DeBondt and Thaler (1985, 1987) and Chopra et al., firms delisted

during the post-ranking period are included. Fifteen percent of the loser stocks

are delisted for financial-distress-related reasons, compared to less than 2% of

the winner stocks. The delisting frequency due to mergers and takeovers is about

7% for both winner and loser stocks. Inclusion of returns up to the delisting

date, as in Chopra et al., mitigates the bias in favor of the contrarian hypothesis,

but ignores the considerable losses on some of these stocks between the delisting

date and their liquidating dividend payment date. For the subset for which data

are available on the CRSP tape (about 30% of all the delisted stocks),

the liquidating dividend represents an additional 15% average loss. If the

final return or liquidating dividend is not reported on the CRSP tape, unlike

DeBondt and Thaler (1985, 1987), we do not assume a negative 100% return.

We only include returns available on the CRSP tapes. Because of the greater

delisting frequency of losers, this procedure imparts a slight upward bias to the

contrarian portfolio return. An informal analysis finds the earnings performance

over the post-ranking period of the delisted stocks, whose liquidating dividend is

unavailable, to be overwhelmingly poor. Note that CRSP generally correctly

reports the final return on stocks delisted due to takeovers and mergers. We

investigate two alternatives: 1) Include the liquidating dividend (i.e., include

a post-delisting return that on average is negative) and assume the market

return was earned on that dividend from the delisting month to the end of the

post-ranking period; or 2) ignore both. The results are similar, and we report the

latter.

3. Contrarian portfolio raw returns

This section reports the effect on raw returns of choosing June versus Decem-

ber ending periods and of the level of stock price (as a proxy for microstructure

effects such as spreads, liquidity, and other transaction costs). Analysis of

abnormal returns appears in Section 4.


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R. Ball et al. /Journal of Financial Econo mics 38 (1995) 79-107

Table 1

Loser and winner stocks’ market capitalization and stock prices: December- and June-end samples

Descriptive statistics for market capitalization and stock prices at the end of the five-year ranking

period ending on December 31 and June 30. Samples consist of 50 worst-performance and

best-performance stocks each year from among all the NYSE and AMEX stocks that have returns

available continuously over the preceding five years (the ranking period). The worst- and best-

performance stocks are identified by ranking all available stocks on buy-and-hold raw returns over

the five-year ranking period. There are 54 overlapping five-year ranking periods ending in December

1930 to December 1983 or June 1931 to June 1984, resulting in a total of 2700 firm-period

observations in each sample. The f irs t and second periods split the entire period in the middle.

Price Market capitalization

Period Mean S.D.” Min. Med.

Max. Mean SD.

Min. Med. Max.

Panel A: December/losers

Entire 10.49 28.25 0.06 5.00

1100 67.1 599.9 0.0 8.8 26708

First 11.07 20.48 0.06 5.00 247.5 21.1 140.8 0.0 4.6 3530

Second 9.90 34.28 0.19 4.89 1100 109.3 845.6 0.3 15.5 26708

Panel B: June/losers

Entire 10.30 16.61 0.13 5.38 215.5 44.9 178.1 0.0 8.0 4944

First 11.77 21.19 0.13 5.25 215.5 25.0 136.2 0.0 3.9 3530

Second 8.83 9.98 0.25 5.50 131.4 65.2 211.6 0.3 14.5 4944

Panel C: December/winners

Entire 43.47 43.37 0.50 34.19

650.0 295.3 821.3 0.1 74.7 15958

First 41.97 45.51 0.50 32.25 650.0 105.7 297.8 0.1 27.3 6498

Second 44.98 41.08 2.63 36.19 593.0 488.9 1095.7 4.0 177.3 15958

Panel D: June/winners

Entire 44.61 43.10 0.88 35.88 737.5 289.8 803.1 0.5 73.2 15958

First 43.32 45.02 0.88 33.53 737.5 87.0 189.0 0.5 26.9 3611

Second 45.89 41.05 2.13 37.50 545.0 496.1 1086.6 4.0 177.5 15958

Price is in dollars; market capitalization is in millions of dollars at the end of the ranking period.

“Standard deviation.

3.1. Winner and loser stocks prices and returns

3.1.1. Prices and capitalization of contrarian stocks

Table 1 provides descriptive statistics on stock price and market capitaliza-

tion at the end of the ranking period. Each sample is 2700 firm-period observa-

tions (50 firms x 54 periods of five years each). Statistics also are reported for

the first 27 and last 27 five-year subperiods. We focus initially on panels A and

C, which assume December-end periods, for comparison with prior studies.


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R. Ball et al. JJournal of Financial Econom ics 38 (1995) 79-107 85

The loser-stock price distribution is right-skewed. The 10.49 mean price is

more than double the 5 median. The 0.06 minimum price is for six stocks that

bunch in two adjacent year ends, 1939 and 1940. In contrast, winner-stock mean

(median) prices are approximately four (seven) times loser-prices.’ We empha-

size three implications.

First, the typically low prices and small market capitalizations of loser stocks

question the implementability of the DeBondt and Thaler (1985, 1987) research

design, which assumes that positions can be established at CRSP closing prices

and thus ignores bid-ask spreads, illiquidity, and other transaction costs.

Expressed in percentage terms (for comparison with rates of return), bid-ask

spreads and transactions costs are large for these stocks. It could be difficult to

invest any substantial amount in most of these stocks without influencing the

price. (Although we expect greater liquidity in the higher-priced winner stocks,

whether an economically meaningful number of their shares can be sold short to

implement the DeBondt and Thaler strategy is also unclear.)

Second, the price difference between winners and losers implies that price is

not controlled for in simulated contrarian portfolios, which are short on winners

and long on losers. These portfolios are thus unhedged with respect to price-

related microstructure effects (spreads, illiquidity, and other transaction costs).

Third, the low market capitalization of the loser stocks suggests that prior

research on contrarian strategies is unlikely to be of great interest to the

investment community in any event.

3.1.2. December-end mean and median returns

In Table 2, panels A and C report December-end raw returns over the

five-year post-ranking period. The mean returns on the loser and winner

portfolios differ by 91% (163% and 72%, respectively). The result holds in both

subperiods (rows 2 and 3), even though the first subperiod has higher volatility

and higher average return (196% versus 130% for losers). (The higher average

returns of both loser and winner stocks over the first subperiod is due, in part, to

market-wide factors. The average annual return on the CRSP equal-weighted

market portfolio is 18.9%, as compared to 15.6% over the second subperiod.)

Taken uncritically, the difference in mean returns between loser and winner

stocks supports the contrarian theory.

The distributions of five-year buy-and-hold returns are right-skewed, with

minimum - 99% and maximum + 5936% among losers. In a sample of size

2700, the maximum observation alone adds 2.2% to the mean. Median returns for

both winners and losers are substantially lower than their means. Moreover, the

‘The median capitalization of the losers is only 8.8 million. (The average of 67 million is influenced

by a 26 billi on outlier.) Ta ble 1 sugg ests the price distribu tion is more stationary than market

capitalization, presumably due to stock splitting, so in time-series or pooled research designs price is

les s likely to proxy for time. It nevertheless has a cyc lica l compo nent.


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R. Ball et al. /Journal of Financial Econo mics 38 (1995) 79-107

Table 2

Loser and winner stocks’ post-ranking period returns: December- and June-end samples

Descriptive statistics for five-year buy-and-hold post-ranking period returns and returns adjusted

for a i transaction cost. Ranking periods ending on December 31 and June 30. Samples consist o f

50 worst-performance and best-performance stocks each year from among all the NYSE and AMEX

stocks that have returns available continuously over the preceding five years (the ranking period).

The worst- and best-performance stocks are identified by ranking all available stocks on buy-and-

hold raw returns over the five-year ranking period. There are 54 overlapping five-year ranking

periods ending in December 1930 to December 1983 or June 1931 to June 1984, resulting in a total of

2700 firm-period observations in each sample. The first and second periods split the entire period in

the middle.

5-year return 5-year adj. return

Period Mean S.D. Min. Med. Max. Mean S.D. Min. Med. Max.

Panel A: December/losers

Entire 1.63 4.27 -0.99 0.49 59.36 1.38 3.51 - 1.00 0.44 55.91

First 1.96 4.85 -0.99 0.61 55.32 1.59 3.75 -1.00 0.54 45.08

Second 1.30 3.56 -0.98 0.40 59.36 1.17 3.25 -0.98 0.35 55.91

Panel B: JuneJlosers

Entire 1.32 3.17

First 1.64 3.88

Second 1.01 2.18

-0.97 0.41 46.26 1.16 2.75 - 1.00 0.36 38.38

-0.97 0.46 46.26 1.39 3.28 -1.00 0.42 38.38

-0.96 0.35 29.37 0.93 2.07 - 1.00 0.30 26.00

Panel C: December/winners

Entire 0.72 1.60 -0.98 0.35 27.90 0.70 1.59 -1.00 0.34 27.57

First 0.89 1.45 -0.92 0.56 17.86 0.87 1.44 - 1.00 0.55 16.60

Second 0.55 1.72 -0.98 0.15 27.90 0.54 1.71 -1.00 0.14 27.57

Panel D: JuneJwinners

Entire 0.75 1.53 -0.99 0.36 18.57 0.73 1.53 - 1.00 0.34 18.36

First 0.91 1.49 -0.96 0.57 15.81 0.89 1.48 -1.00 0.56 15.66

Second 0.59 1.56 -0.99 0.19 18.57 0.57 1.55 - 1.00 0.18 18.36

If a firm is delisted during the five-year post-ranking period, then returns up to the delisting date and

the liquidating dividend, if available, are included in calculating the firm’s return over the post-

ranking period. Adjusted returns are calculated by adding 4 to the price of each stock at the end of

the ranking period.

median five-year returns on winners and losers are 49% and 35%, respectively,

thus differing by only 14% (this is nut an annualized rate). Medians therefore tell

a noticeably different story about contrarian stock selection than means.

Low-priced stocks contribute to the right-skewedness of returns. Equitable

Office Building Corporation, one of the six lowest-priced six-cent loser stocks,

earned a + 3500% return. This motivates us to investigate below the effect of

the low-priced loser stocks on mean returns.


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R. Ball et d/Journal of Financial Econo mics 38 (1995) 79-107 81

3.1.3. December-end adjusted returns

Table 2 also reports the effect on returns of adjusting upward, by , the

purchase prices of all stocks at the end of the ranking period. This adjustment

fulfills two objectives. First, it calibrates the sensitivity of average rate of return

estimates to a small dollar amount of either mispricing or microstructure

factors. Second, i is a conservative estimate of the combined bid-ask spread,

brokerage commissions, and liquidity costs that might be considered part of the

cost of trading in stocks.

There is a dramatic 25% reduction in the average return on the loser portfolio

with the 4 price adjustment, from 163% to 138%. In contrast, the average for

winners falls by only 2%, from 72% to 70%, and the median return on losers

declines only from 49% to 44%. The loser stocks’ low prices, together with the

sensitivity of their returns to even small increases in opening prices, highlights

the potential importance of microstructure effects in this context.

3.1.4. June-end vs. December-end holding periods

DeBondt and Thaler (1985, p. 799) note that the choice of December-end

portfolio formation dates is ‘essentially arbitrary’. The contrarian strategy

should be profitable when implemented in other months. On the other hand, the

evidence in Roll (1983a), Lakonishok and Smidt (1984), Keim (1989), and

Bhardwaj and Brooks (1992) suggests that microstructure-related effects on

measured returns are most pronounced at the calendar year-end, which is

precisely the point at which contrarian portfolios typically are assumed to be

formed (DeBondt and Thaler, 1985,1987; Chan; Ball and Kothari; and Chopra

et al.). In addition, Zarowin (1990) studies a June-end strategy in testing

for a January/size-related overreaction effect, and obtains different results.

(His strategy is based on quintiles, not extreme winners and losers, so his

contrarian portfolios are quite different from ours. For example, his June-

end contrarian portfolio beta estimated from monthly returns is 0.10, while

ours estimated from annual returns is 0.78. He also focuses on initial-

month returns, i.e., January and July.) We therefore test whether measured

contrarian portfolio returns are biased by some systematic or chance Decem-

ber-end effect.

The mean contrarian portfolio return is much lower for June-ends, even

though the December- and June-end periods are almost identical (they share

53; of the 54 years). The 132% loser-stock average return is 31% lower than the

163% equivalent for December-end peirods. For winner stocks, whether the

period ends in December or June does not make a material difference. This is

not surprising, since most winners are not low-priced. The average five-year

return on a June-end contrarian portfolio is 57% (132% - 75%, panels C and

D), compared to the 91% average on the December-end contrarian portfolio

(163% - 72%, panels A and B). This 34% decline in average return, due to the

seemingly innocuous difference of investing at the end of June rather than


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88 R. Ball et al. jJourna1 of Financial Econo mics 38 (1995) 79-107

December, shows that, whether or not there is overreaction, at least one other

factor affects the December-end prices of extreme loser stocks.

To be sure that the difference in results is not due to our accidentally

discovering a June-end anomaly, we also analyze an August-end sample. The

performance of the August-end sample (not reported) is virtually indistinguish-

able from that of the June-end sample.

One explanation is that small stocks trade at bid prices more frequently at the

end of December (Roll, 1983a; Lakonishok and Smidt, 1984; Keim, 1989). Loser

stocks have low average prices at the purchase date, but trade at higher average

prices at the end of the five-year period. [The mean return over the five years is

163% (see Table 2).] Measured post-ranking returns on December-end lower

stocks therefore could contain a decrease in the probability of trading at a bid

price over the period. The presence of very low-priced stocks in the loser

portfolio, with high proportionate bid-ask spreads, could make this effect

material, even in five-year returns. This is distinct from the spread-induced bias

in cumulating average returns (Blume and Stambaugh, 1983; Roll, 1983b), which

is largely avoided by using buy-and-hold returns. The remaining bias equals

s2/4, where s is proportionate spread, and thus is relatively small.

Alternatively, there could be some other systematic or chance December-

effect in the DeBondt and Thaler research design. One possible explanation is

that the December loser returns are related to tax-loss selling (see, for example,

Ritter and Chopra, 1989). However, we see later that the risk-adjusted perfor-

mance of the contrarian strategy does not lend support for the tax-loss-selling

hypothesis.

The June-December difference seems due largely to microstructure rather

than chance factors because: (1) It is confined to loser stocks, which are

low-priced; (2) it is essentially confined to the 25% lowest-price loser stocks (see

below); (3) the 34% difference is comparable to the 25% effect of an adjust-

ment reported earlier, and thus is in the order of microstructure effects; (4) the

difference occurs in both 27-year subperiods; (5) the June- and August-end

results are similar; and (6) the data overlap in 53; of the 54 years, which makes

chance unlikely. [Keim (1989) documents the tendency of low-priced stocks to

be recorded at their bid prices at the end of December since the early 1970s. Our

evidence indirectly suggests the same phenomenon might have been occurring

since the thirties.] Whatever the explanation, the result casts doubt on the

contrarian evidence.

3.2. The relation between price and return

Because the above results show that price is related to losers’ post-ranking

period returns, we now explore ‘the relation between price and return more

formally. Initially, we do this by reporting returns by price-quartile analysis and

then by regression analysis.


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R. Ball et al. /Journal of Financial Econom ics 38 (1995) 79-107 89

3.2.1. Returns by price quartiles

Table 3 summarizes the post-ranking period returns of December- and

June-end winner and loser portfolios by their price quartiles. Initially, the 2700

pooled firm-period observations in each winner and loser portfolio are ranked

on their stock prices at the end of the 54 ranking periods and assigned to

price-quartile portfolios. The stocks tied for the 25th, 50th, or 75th percentile are

ranked chronologically before assigning to quartiles. The first price-quartile

portfolio consists of the 25% lowest-priced stocks. The price distributon is

pooled over both firms and years because prior research (DeBondt and Thaler,

1985, 1987; Chan; Ball and Kothari; Chopra et al.) pools the data, and our

objective is to investigate the role of low-price loser stocks in their results. We

subsequently analyze individual-year data.

For December-end loser stocks, the 357% mean post-ranking return for

price-quartile portfolio 1 is strikingly greater than the means for portfolios

2 through 4 (113%, 96%, and 85%). The average price in this portfolio is only

1.04. The average market capitalization is only 8 million. Comparison of the

June- and December-end results in Table 3 demonstrates that the sensitivity of

the contrarian portfolio return to the assumed end point is due almost entirely

to its very low-priced loser stocks. The lowest price quartile of the June-end loser

stocks earns 254%, on average, over the five-year post-ranking period, far less

than the 357% December-end return. This is consistent with a bias in measured

December-end contrarian returns, due to the turn-of-the-year seasonality in

bid-ask prices for low-priced loser stocks.

The effect of a i adjustment to the opening price is dramatic for the lowest

price quartile of loser stocks. The average return on the lowest price quartile of

loser stocks declines by 86% (357% - 271%). Since most of the contrarian

portfolio return comes from the lowest price quartile, the large effect of the

price adjustment and an illiquid market for the loser stocks together cast

doubt on its alleged profitability. The reduction in average return due to

the 4 price adjustment is 55% for the lowest-price June-end loser portfolio,

much less than the December reduction, but still substantial. In contrast, all

winner-stock quartiles are relatively high-priced and their returns are essentially

unaffected by the adjustment.

An alternative to reporting contrarian portfolio performance by price quartiles

is to exclude stocks priced 1 or less. This reduces the influence of the very-low-

priced stocks whose post-ranking returns are more likely to be biased due to

microstructure factors. It also gives insight into the economic significance of

published evidence of contrarian profitability. Virtually all of the stocks priced

1 or less are losers. The December-end loser portfolio has 359 such stocks, or

13.3% of all 2700 loser stocks. The corresponding frequency in the June-end

portfolio is 10.6%. Excluding stocks priced 1 or less has a dramatic effect on the

average return for the loser portfolio, which declines from 163% to 116%.

The corresponding numbers for the June-end portfolio are 132% and 105%.


12/29

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92

R. Ball et al. JJournal of Financial Econo mics 38 (1995) 79-107

In the above analysis, the effects of price and time are related. While the price

distribution is comparatively stationary over long periods of time, price also has

an obvious positive relation with the market index.2 Low-priced stocks cluster

in years after large market declines. We therefore recalculate the loser portfolio’s

returns after omitting the three years (1930, 1940, and 1973) with the lowest

average loser-stock price. Omitting these years reduces the average loser-port-

folio return from 163% to 125%. This raises further doubts that the evidence

reported in the literature reflects a general behavioral tendency for investors to

overreact in the case of extreme winner and loser stocks (the DeBondt and

Thaler, 1985, 1987, hypothesis).

This evidence implies it is unlikely that the high returns to the lowest price

quartile could be obtained from an ex ante strategy of forming price-quartile

portfolios every year, rather than pooling observations from all years. One

consequence of forming price-quartile portfolios every year is that whether or

not there are many stocks with very low prices in a given year, they are assigned

equally to all four portfolios. Thus, the lowest price quartile’s performance is

contaminated by some not-so-low-priced stocks and vice versa for the high-

est-price-quartile stocks. As expected, the results in Table 4 indicate that

forming quartile portfolios every year does not yield much variation in average

returns across price-quartile portfolios. Results for winner stocks are similar to

the pooled sample results in Table 3. The smallest price quartile’s average price

increases, from 1.04 in Table 3 to 2;70 for the December-end loser stocks. The

average return on the lowest price-quartile stocks declines from 357% in

Table 3 to only 169% in Table 4. The adjustment continues to have a dra-

matic effect on the smallest-price-quartile portfolio’s return, however, reducing

its average return by 43%.

3.2.2. Regressionanalysis: Price vs. past return

To investigate the relation between price and post-ranking returns more

closely, we perform Fama-MacBeth cross-sectional regressions. Each year we

regress the 100 stocks’ (50 winners and 50 losers) post-ranking period returns on

their prices at the end of the ranking period, and their ranking period returns.

The coefficients’ standard errors are calculated from the time series of coefficient

estimates. We note that since the five-year post-ranking periods are overlapping,

the annual cross-sectional regression coefficient estimates are not independent

through time. The standard errors therefore are adjusted for this dependence

using the Newey and West (1987) correction. The average estimated coefficients

on past return and price using the December-end data are - 0.14 (standard

error = 0.06) and - 0.0094 (standard error = O.OOSl), which is consistent with

both past returns and stock price predicting post-ranking period returns.

‘We are grateful to a referee for pointing this out.


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16/29

94 R. Ball et al. /Journal

of

Financial Economics 38 (199.5) 79-107

Thus, risk considerations aside, the cross-sectional behavior of raw returns is

consistent with both low-price/microstructure and contrarian effects.

This result complements Conrad and Kaul (1993) and Bhardwaj

and

Brooks (1992), who find that price and the turn-of-the-year seasonal in

bid-ask prices are the primary determinants of January returns, and perhaps

of the contrarian strategies’ measured returns. Both employ a pooled sample

design.

Zarowin (1990) argues that contrarian strategy returns are another manifesta-

tion of the size effect. Therefore, we also estimate annual cross-sectional

regressions in which the natural log of market capitalization (size) is included.

The average estimated coefficient on size is not significant (p-value > 0.75)

but the average estimated coefficients on past return and stock price remain

significant. For the June-end sample, size again is insignificant, past return

is significant, and prick is marginally significant (t-statistic = 1.50). The insigni-

ficant coefficient on size is of interest because it brings into question the use

of size-adjusted returns by Chopra et al. as a control for expected returns in

this context. If price is a better proxy than size for risk or microstructure bias

in the post-ranking period returns, then it provides a superior control.

The conclusion that price dominates size in explaining contrarian raw

returns is consistent with Conrad and Kaul (1993). However, they conclude

that past performance has no predictive power for contrarian raw returns

once price is held constant. They use three-year, rather than five-year, returns.

They estimate pooled time-series and cross-sectional regressions, but do not

take into account the considerable cross-sectional correlation between returns

on losers or winners. Thus, it is difficult to interpret their reported

t-statistics.

4. Contrarian portfolio abnormal returns

The preceding analysis of the importance of past returns, size, and price in

explaining post-ranking returns is intended only to highlight the difficulties

of measuring returns and attributing them to overreaction. Since these

variables are correlated with beta, it is important to focus on risk-adjusted

returns. This section begins by briefly describing the use of intercepts

(‘Jensen alphas’) from excess-return time-series regressions as abnormal-

return estimates. We then report abnormal-return estimates for both the

December- and June-end contrarian strategies. Finally, we assess the sensitivity

of our results to the zero-beta rate exceeding the riskless rate and other

deviations from the Sharpe-Lintner CAPM, discuss subperiod analysis,

provide additional evidence on the behavior of beta as a function of up-

and down-market returns, and summarize our analysis of NYSE-only

stocks.


17/29


95

4.1. Excess-return time-series regressions

We report intercepts from time-series regressions of annual portfolio excess

returns on those of an equal-weighted market index. Assuming the

Sharpe-Lintner CAPM version is true and the index adequately proxies for the

market portfolio, market (informational) efficiency requires that the index be

mean variance efficient and the intercepts be zero. As Chopra et al. emphasize,

the empirical relation between estimated betas and average returns tends to be

flatter than that implied by the Sharpe-Lintner model. Fama and French (1992)

suggest that it may even be zero. If the market index is efficient, but with

a zero-beta rate higher than the riskless rate, then the excess-return time-series

methodology overestimates the contrarian strategy’s expected performance,

conditional on the market. This follows since the strategy is long in a relatively

high beta portfolio (losers) and short in a significantly lower beta portfolio

(winners). Hence, Chopra et al. argue, Jensen alphas understate the stock

market’s tendency to overreact and the zero-beta methodology is preferable.

We offer the following responses. First, zero-beta rate estimates are not very

precise and may be biased upward due to the well-known errors-in-variables

problem, so interpretation of the relatively low empirical slope is unclear. As

a practical matter, however, it is easy to adjust the Jensen alphas to accommod-

ate alternative zero-beta rates, and we do this in order to assess he robustness of

our conclusions. Second, estimates of the equal-weighted market risk premium

based on annual data, as reported by Kothari, Shanken, and Sloan (1994), are

substantial. They range from 9% to 12% per annum for the period 1927-90 and

about 6% to 9% for the 1941-90 period considered by Fama and French.

Related evidence also appears in Chan and Lakonishok (1993) and Jagannathan

and Wang (1993). Third, evidence in Fama and French (1992) suggests that

smaller size and higher book-to-market stocks’ expected returns exceed that

estimated using the CAPM. Their findings are relevant in evaluating contrarian

performance because of the relatively smaller size and higher book-to-market

values for losers, as compared to winners. While Kothari, Shanken, and Sloan

raise doubts about the importance of the book-to-market variable, the

Fama-French results predict that a CAPM-based benchmark will, if anything,

understate the contrarian expected return and therefore overstate the contrarian

abnormal return.

Before turning to the empirical results, we emphasize some additional norma-

tive considerations in interpreting excess-return time-series regression results.

As is well known, the finding of a positive Jensen alpha for a portfolio implies

that the efficiency of the market index can be improved upon (i.e., the Sharpe

ratio of expected excess retufn to standard deviation can be increased) by

a marginal shift out of the index and into the portfolio. While a symmetric result

holds for negative alphas, one can make the stronger statement that no amount

of tilting the investment in the direction of a negative or zero alpha portfolio


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96

R. Ball et al. /Journal

of

Financial Econo mics 38 (1995) 79-107

(i.e., placing positive weight on both the market index and the portfolio), will

improve upon the efficiency of the index. The improved position would have to

have a positive alpha (Dybvig and Ross, 1985a), which is impossible, since the

index has an alpha of zero. This perspective is relevant to the empirical analysis

below.

4.2. Abnormal return and beta estimates

Abnormal returns and beta risks in event-years - 4 to + 5 are estimated

using annual return data. Previous research by Ball and Kothari (1989) and

Chopra et al. (1992) uses Ibbotson’s (1975) ‘returns across time and securities’

technique. We employ a modification of this technique based on Kothari and

Shanken’s (1992) argument that the contrarian portfolio’s beta should vary in

calendar time, conditional on the realized market risk premium over the ranking

period. The rationale is that if the realized premium in the ranking period is

positive, the loser portfolio is more likely to consist of low-beta stocks. Con-

versely, if the realized premium is negative, the loser portfolio will contain more

high-beta stocks.

We allow winner and loser portfolios’ betas to be a function of the market

return over the ranking-period, by estimating the following model in each

event-year r = - 4, . . . ,O, . . . , 5:3

R,,(z) = ~~(4 + P,@) * R,, + (4 * C d - 490) - Aw&I* Rn, + &,tW ,

(1)

where

R,,(z)

is the annual buy-and-hold excess return on portfolio p = (winner,

loser) in calendar year t and event-year z, R, is the buy-and-hold equal-

weighted annual excess eturn on NYSE-AMEX stocks in calendar year t, excess

returns are obtained by subtracting the annual return on Treasury bills

(Ibbotson and Sinquefield, 1989) up(z) is abnormal return in event-year z, /-I,(r)

is the 54-year average relative risk of portfolio p in event-year Z,

AvgR,

is

the time-series average of annual excess returns on the market index, while

R,,(

- 4,0) is the average excess return on the market index over event years

- 4 through 0 relative to calendar year t. The deviation of a portfolio’s beta in

a given calendar year from its 54-year average beta, &(r), is given by the

product of 6,(z) and the unexpected market excess return over the relevant

ranking period. This can be seen by substituting

AvgR,

for

R,,( - 4,0)

in

Eq. (1). The corresponding term then drops out, leaving &,(r) as the sole

coefficient on

R,,.

For further details, see Kothari and Shanken (1992, Sect. 4.2)

and Jones (1993).

‘See Shanken (1990) for a more general application of this methodology to tests of conditional asset

pricing models.


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R. Ball et aLlJournal of Financial Econo mics 38 (1995) 79-107 91

4.2.1. Abnormal return estimates

Table 5 reports abnormal return, beta, and delta estimates for the winner and

loser portfolios. In calculating the standard error of the average post-ranking

period abnormal return, beta and delta, we incorporate the dependence among

the time series of event-time regression residuals. The standard error of the

average abnormal return is only slightly smaller than that of the individual

years’ abnormal return estimates. This is due to strong positive correlations

among the estimates for different years. Thus, it is important not to attribute too

much significance to any consistency of results over different post-ranking years.

Details are available on request.

The December-end loser portfolio alpha averages 0.7% per year (standard

error 2.7%) over the five-year post-ranking period. In none of the five post-

ranking years is the loser portfolio’s estimated abnormal return reliably positive.

The winner portfolio’s alphas average - 3.6% per year (standard error 1.3%)

over the post-ranking period, and are reliably negative in years 2, 3, and 4. The

December-end contrarian portfolio thus averages 4.3% abnormal return (stan-

dard error 3.4%), ignoring transaction costs (notably, costs of short-selling

winner stocks) and microstructure-related biases. Since the contrarian port-

folio’s estimated abnormal return is due primarily to the winner portfolio, it is

not attributable to tax-loss selling.4

The average alpha of the June-end loser portfolio is noticeably lower than its

December-end equivalent, consistent with the June- and December-end differ-

ences observed in raw returns. Its estimated abnormal return averages - 5.3%

(standard error = 2.9%) per year over the post-ranking period and is negative in

each of the five post-ranking years. This is inconsistent with the overreaction

hypothesis. Consistent with the overreaction hypothesis, the winner portfolio

loses 2.8% (standard error = 1.7%) on average per year, which is comparable to

the December-end winner portfolio’s performance. Combining these, the June-

end contrarian portfolio loses in each of the five years, or 2.5% on average

(standard error = 4.0%). This is without giving any consideration to transaction

costs, a particular concern when assessing benefits from investing in the relative-

ly low-priced loser stocks. Comparison of the December- and June-end results

reveals that the loser portfolio’s average abnormal retun) declines noticeably

from 0.7% to - 5.3%, which is consistent with the security microstructure

biases affecting the low-priced loser stocks’ December-end returns. The Decem-

ber-end winner stocks’ abnormal return estimate is only marginally higher than

that of the June-end winner stocks’ ( - 3.6% versus - 2.8%).

4Previous evidence on the performance of portfolios formed on the basis of prior one-year returns

(e.g., DeBondt and Thaler, 1985, Table 1; Ball and Kothari, 1989, Table 5; Chopra et al., 1992,

Table 3; Jegadeesh and Titman, 1993) suggests ‘momentum’, which is also inconsistent with the

tax-loss-selling hypothesis.


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Table 5

Annual abnormal return and systematic risk estimates, allowing portfolio betas to var y with the market performance over the ranking period: December-

and June-end samples

Winner- and loser-portfolio average abnormal return, beta, and delta estimates over the five-year post-ranking periods. The ranking period ends in

December or June. The winner and loser portfolios consist of 50 best-performance and 50 worst-performance stocks each year from among all the NYSE

and AMEX stocks that have returns available continuously over the ranking period. The worst- and best-performance stocks are identified by ranking all

available stocks on buy-and-hold raw returns over the five-yea r ranking period. There are 54 overlapping five-yea r ranking periods ending in December

1930 (June 1931) to December 1983 (June 1984), resulting in a total of 54 portfolio-year observations in each event year . Beta o f the winner and loser

portfolio in a given calendar year is allowed to be a function of the return on the market portfolio over the ranking period corresponding to the calendar

period.

December-end ranking

Event

year Alpha S.E.” Beta

Panel A: Loser portfolio performance

1

4.1% 3.9

1.47

2 1.6

3.6 1.43

3 0.6

3.2 1.47

4 -1.5 3.2

1.42

5 - 1.5 3.4

1.45

SE. Delta S.E.

0.12 0.01 0.12

0.11 -0.26

0.14

0.11 -0.13

0.17

0.11 0.07 0.16

0.11 0.20 0.17

June-end ranking

Alpha S.E.

-0.6%

4.8

-8.9 4.2

-7.2 3.4

-5.2

4.1

-4.4

2.6

Beta SE. Delta S.E.

1.69 0.14 -0.15 0.09

1.95 0.13

- 1.02 0.17

1.72 0.11

-0.51 0.17

1.65 0.13 - 0.22 0.17

1.52 0.09 -0.30

0.16

1 to 5 0.7 2.7

1.45

0.09 -0.02

0.10

-5.3 2.9

1.71 0.08 -0.44 0.09


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Panel B: Winner portfolio performance

1 - 1.9 2.3 0.87

2 -4.6 1.9 0.92

3 -4.5 1.7 0.94

4 -4.0 1.7 0.98

5 -3.1 1.9 0.89

1 to 5 -3.6 1.3 0.92

0.07 0.26 0.07 1.1 2.8 0.84 0.08 0.28 0.06

0.06 0.37 0.07 -3.4 2.3 0.93 0.07 0.15 0.10

0.06 0.25 0.09 -5.9 2.2 0.97 0.07 -0.18 0.11

0.06 0.28 0.08 -4.2 2.1 1.00 0.07 0.30 0.09

0.06 0.10 0.10 -1.4 2.1 0.90 0.07 0.08 0.13

0.04 0.25 0.05 -2.8 1.7 0.93 0.05 0.13 0.05

Abnorma l return, b eta, and delta, averaged over the five-year ranking and five-year post-ranking periods are reported for the winner and loser portfolios.

Abnorma l return and beta are estima ted from the following regression usin g 54 annu al p ortfolio-return observation s for each event-year T = 1, 2, . . ,5

and for both the winner and loser portfolios:

where R,,(r) is the annu al buy-and-hold exces s return on portfolio p = (winner, loser) in calenda r year t and event-year 5, R,, is the buy-and-hold

equal-weighted annual excess return on the NYSE-AMEX stocks in calendar year t, exce ss returns are obtained by subtrac ting the annua l return on

Treasury bills (Ibbotson and Sinqu efield, 1989), AuyR, is the time-series average of annua l e xces s returns on the market index, R,,( -4,0) is the average

exce ss return on the market index over the ranking-period event years - 4 through 0 relative to the calenda r year t, czp is the abnorma l return on the

winner portfolio, /I,, is the CAPM measure of relative risk, and 6 is the sens itivity of a portfolio’s beta to the market return over the ranking period.

Standard errors of the five-year average CI, p, and 6 are calc ulated by incorporating depend ence among the time series of event-time residu als from the

above CAPM regressions.

“Standard errors.


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Financial Econo mics 38 (1995) 79-107

In summary, the contrarian strategy’s estimated abnormal return is sensitive

to the choice of ranking-period end. [We also estimate, but do not report,

abnormal return and beta estimates without letting beta vary over time, i.e., the

technique in Ball and Kothari (1989). The December-end (June-end) contrarian

portfolio earns an average annual abnormal return of 4.6% ( - 1.4%), which is

greater than that reported in Table 5.1 The June-end portfolios exhibit no

evidence of economically significant profits from pursuing a contrarian portfolio

strategy. If anything, the ‘profits’ appear negative.

4.2.2. Systematic risk and delta estimates

The systematic risk estimates behave as documented in previous research. The

loser portfolio’s beta exceeds the winner portfolio’s beta, consistent with the

changes in leverage caused by their ranking-period performances (Chan, 1988;

Ball and Kothari, 1989). The deltas are generally consistent in sign with the

hypothesized relation between the riskiness of stocks assigned to the winner and

loser portfolios and the market performance over the ranking period. As

a result, the contrarian deltas are reliably negative (see Table 6), indicating that

relative risk is lower when the ranking period market return is high.

Table 6

Winner, loser, and contrarian portfolios’ abnormal return and beta estimates, allowing portfolio

betas to vary with the market performance over the ranking period: Entire period and subperiod

analysis of December- and June-end samples

Winner-, loser-, and contrarian-portfolio average abnormal return, beta, and delta estimates over

the five-year post-ranking periods. The ranking period ends in December or June. The winner and

loser portfolios consist of 50 best-perfomance and 50 worst-performance stocks each year from

among all the NYSE and AMEX stocks that have returns available continuously over the ranking

period. The worst- and best-performance stocks are identified by ranking all available stocks on

buy-and-hold raw returns over the five-year ranking period. There are 54 overlapping five-year

ranking periods ending in December 1930 (June 1931) to December 1983 (June 1984), resulting in

a total of 54 portfolio-year observations in each event year. The first and second periods split the

entire period in the middle. Beta of the winner and loser portfolio in a given calendar year is allowed

to be a function of the return on the market portfolio over the ranking period corresponding to the

calendar period.

Period

Event

years

December-end ranking June-end ranking

Alpha Beta Delta Alpha Beta Delta

S.E. S.E. SE.

S.E. S.E. S.E.

Pan el A: Loser portfolio performance

Entire 1 to 5 0.7%

2.7

First 1 to 5 -4.2

4.2

Second 1 to 5 3.1

1.9

1.45 -0.02 -5.3% 1.71 -0.44

0.09 0.10 2.9 0.08 0.09

0.72 0.08 -10.6 2.14 -0.49

0.11 0.12 4.1 0.11 0.10

1.19 -0.12 -1.1 1.29 -0.41

0.08 0.11 2.0 0.08 0.18


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101

Table 6 (continued)

December-end ranking June-end ranking

Period

Event Alpha Beta Delta Alpha Beta Delta

years S.E. S.E. SE. S.E. SE. SE.

Panel B: Winner portfolio performance

Entire 1 to 5 -3.6% 0.92

1.3 0.04

First 1 to 5 -0.7 0.85

1.2 0.04

Second 1 to 5 -6.1 0.98

2.0 0.08

Pane l C: Contrarian portfolio performance

Entire 1 to 5 4.3% 0.53

3.4 0.12

First 1 to 5 - 3.4 0.87

4.8 0.16

Second 1 to 5 9.3 0.20

3.0 0.12

0.25 -2.8% 0.93 0.13

0.05 1.7 0.05 0.05

0.24 1.7 0.70 0.09

0.04 1.8 0.05 0.05

0.25 -5.8 1.25 0.47

0.11 1.8 0.07 0.15

-0.28 -2.5% 0.78 -0.57

0.11 4.0 0.11 0.12

-0.16 -12.3 1.34

-0.58

0.14 5.4 0.14 0.13

-0.37 4.7 0.04 -0.88

0.18 2.4

0.10 0.21

Abnormal return, beta, and delta, averaged over the five-year ranking and five-year post-ranking

periods are reported for the winner, loser, and contrarian portfolio. Abnormal return, beta, and delta

are estimated from the following regression using 54 annual portfolio-return observations for each

event-year 7 = 1,2, . ,5 and for both the winner and loser portfolios:

R,tW = ~(4 + &(d*Rmt + ~pWIL(- 4>0)

- &&,,I *R,, + ~pt(+

where R,,(z) is the annual buy-and-hold excess return on portfolio p = (winner, loser) in calendar

year

t

and event-year r, R,, is the buy-and-hold equal-weighted annual excess return on the

NYSE-AMEX stocks in calendar year t, excess returns are obtained by subtracting the annual

return on Treasury bills (Ibbotson and Sinquefield, 1989),

AugR,

is the time-series average of annual

excess eturns on the market index,

R,,(

-4,0) is the average excess eturn on the market index over

the ranking-period event years - 4 through 0 relative to the calendar year

t,

Q is the abnormal

return on the winner portfolio, /I, is the CAPM measure of relative risk, and 6 is the sensitivity of

a portfolio’s beta to the market return over the ranking period.

Standard errors of the five-year average a, fi , and 6 are calculated by incorporating dependence

among the time series of event-time residuals from the above CAPM regressions.

4.3. Robustness ests

4.3.1. Zero-beta rate exceeding the riskless rate

The preceding analysis relies on the Sharpe-Lintner version of the CAPM to

interpret Jensen alphas as abnormal returns. We now examine whether the

June-end contrarian portfolio earns abnormal returns, assuming the market


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102

R. Ball et al.lJournal of Financial Economics 38 (1995) 79-107

index is on the stock-only efficient frontier with a zero-beta rate that exceeds the

riskless rate. It is easy to show that the estimated abnormal return of the

contrarian portfolio using the zero-beta CAPM then exceeds its Jensen alpha by

approximately fi,(R, - Rf), where PC s the contrarian portfolio’s average beta

and

R,

is the zero-beta rate. The June-end contrarian portfolio’s beta estimate is

0.78 (see Table 6, which summarizes results for the entire time period and two

subperiods of 27 calendar years). Therefore, even if the zero-beta rate exceeds the

(riskless) T-bill rate by 5% (the approximate estimate of Chopra et al.) then the

June-end contrarian portfolio’s estimated abnormal return increases from

- 2.5% (see Table 5) to + 1.4%, which is only 0.35 standard errors above zero.

(The r-statistic for the December-end strategy is about 2 in this case.) The

average June-end contrarian abnormal return does not produce a t-statistic

greater than 2 until the annual zero-beta rate is 13.3% above the T-bill rate. The

average return on the market index is then only about 1% greater than the

zero-beta rate. Thus, the lack of evidence of contrarian profitability for the

June-end strategy is not limited to a particular version of the CAPM.

4.3.2. Subperiod analysis

Table 6 reports that the December-end contrarian strategy is not profitable in

the first subperiod (average annual abnormal return of -3.4%), but it yields

a large average annual abnormal return of 9.3% in the second subperiod. The

profitability in the second period is driven largely by the significant -6.1%

(standard error 2.0%) abnormal return of the December-end winner portfolio.

Since we had no prior theoretical reason to focus on the second subperiod,

aggregating the abnormal-return t-statistics over the two periods is more appro-

priate than emphasizing the maximum. Assuming the statistics are approxi-

mately independent standard normal variates, the aggregated t-statistic is 1.69.

The June-end contrarian portfolio has - 12.3% average annual abnormal

return in the first subperiod, but earns 4.7% in the second. The contrarian

portfolio is very risky in the first subperiod (December-end and June-end be-

tas =0.87 and 1.34), but not in the second (December-end and June-end be-

tas = 0.20 and 0.04). The June-end portfolio deltas are nontrivial in both sub-

periods (-0.58 and -0.88), however, indicating that the beta varies considerably

over time. Allowing betas to vary reduces the estimated abnormal returns for the

June-end strategy by 3.8% in the first subperiod and 2.3% in the second.

The evidence that the contrarian strategy does not exhibit positive abnormal

performance in the first period is somewhat surprising, because Fama and French

(1988) and other previous research indicates that serial correlation in index

returns is observed predominantly in the pre-World War II period. We therefore

expect the contrarian strategy to be profitable, if at all, in the first subperiod, not

the second. The reversal of the contrarian strategy’s profitability over the sub-

periods is an additional reason to exercise caution in evaluating claims that

contrarian rules reliably ‘beat the market’.


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of

Financial Econo mics 38 (1995) 79-107 103

4.3.3. Up-and down-market betas

The preceding analysis assessesportfolio performance in the context of the

mean-variance framework of the CAPM and previously documented deviations

from that model. DeBondt and Thaler (1987) express reservations concerning

the use of beta as a risk measure since, as they report (Table 4) the contrarian

portfolio beta is 0.40 in up markets and -0.32 in down markets. Chopra et al.

(1992, Table 7) report corresponding betas of 1.05 and 0.27. Thus, there is a sense

in which contrarian returns exhibit a desirable form of risk that is not recognized

in the mean-variance framework. We find similar results (available on request)

even after allowing for variation in

ex ante

betas over time, as discussed earlier.

It is important to emphasize, however, that the appealing up- and down-market

behavior of beta is accompanied by an unappealing negative alpha, - 4.3% for

the December-end and - 17.6% for the June-end strategy. In addition, Jones

(1993) reports that the seemingly desirable up- and down-market beta behavior

largely disappears over the post-war period.

The evidence of different up- and down-market betas means that expected

contrarian returns, conditional on the ex post market return, are not linear in

the market return. This linearity condition is satisfied under joint normality and

certain other return distributions that are often used to motivate mean-variance

analysis (see Stapleton and Subrahmanyam, 1983). Therefore, it may be impor-

tant to explore other utility frameworks and associated equilibrium bench-

marks, for example, a skewness preference model (Kraus and Litzenberger, 1976;

Rubinstein, 1973). We leave for future research the task of evaluating the

tradeoff between the behavior of beta and the negative contrarian alpha in such

a framework.

4.3.4. Exclusion of low-priced stocks

When stocks priced less than 1 are excluded, the December-end loser

portfolio post-ranking period average abnormal return declines from 0.7% to

0.1%. The corresponding numbers for the June-end portfolio are - 5.3% and

- 4.6%. Thus, the basic conclusion that the June-enQ contrarian investment

strategy is not profitable is not altered when restricted to stocks priced greater

than 1 at the beginning of the post-ranking period.

4.3.5. NYSE firms only

Our sample consists of extreme-performance stocks selected from a universe

that includes AMEX stocks, beginning in July 1962. It therefore differs from

samples in previous research using only NYSE stocks. We include AMEX

stocks because they typically have lower market capitalization and are less

closely followed by analysts; thus they would seem to give the overreaction

hypothesis its ‘best shot’. Of course, the microstructure factors discussed earlier

are likely to be more influential as well. There are reasons to believe, however,

that excluding AMEX stocks would not alter the tenor of our results. First,


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Financial Economics 38 (1995) 79-107

notwithstanding some of the sample-selection differences, our evidence for the

December-end portfolios is similar to that reported in Ball and Kothari and

Chopra et al. for NYSE-only samples. The December-end contrarian portfolio

in Ball and Kothari earns an average Sharpe-Lintner abnormal return of 3.9%

compared to 2.5% in Chopra et al. and 4.3% in our examination. Second, the

June versus December differences are similar in both subperiods, even though

the first subperiod contains no AMEX stocks.

We replicate all results on a NYSE-only sample. The full results are available

on request. The raw as well as abnormal return results are virtually unchanged.

For example, in panel A of Table 3 we report (for the full sample of Decem-

ber-end loser-stock price quartiles) average prices of 1.04, 3.23, 7.78, and

29.80. For the NYSE-only sample, the equivalent figures are 1.27, 3.98, 8.94,

and 31.20. Similarly, the average post-ranking returns for the full sample

price-quartiles are 357%, 113%, 96%, and 85%; for the NYSE-only sample,

equivalent figures are 346%, llO%, 98%, and 82%.

The abnormal-return analysis reveals only small differences when NYSE-only

stocks are examined. For example, excluding AMEX stocks reduces the sec-

ond-period December-end contrarian abnormal return, from 9.3% to 6.8%,

whereas for the June-end portfolio it increases from 4.7% to 5.0%. Recall that

the first subperiod results are unaffected, because AMEX stocks came on line

only in mid-1962. For the entire period, the December-end contrarian port-

folio’s average alpha is 2.9% for the NYSE-only sample, compared to 4.3% for

the NYSE-AMEX sample. The corresponding figures for the June-end sample

are - 2.3% and - 2.5%.

5. Conclusions

We explore a variety of performance measurement problems, in the context of

a DeBondt and Thaler (1985, 1987) contrarian research design. The first set of

issues is concerned with the measurement of raw returns. We show that much of

the reported profitability of a contrarian strategy is driven by low-priced loser

stocks. The skewness in rates of return due to low-priced stocks is so pronounced

that, while winner and loser five-year means differ by 91% (the result that

stimulated the contrarian literature), their medians differ by only 14%. Loser-

stock prices are so low that their subsequent five-year returns are extremely

sensitive to even a i of either mispricing or microstructure-induced effect.

Worse, the low prices tend to bunch in a very few years following bear

markets, so price-related microstructure effects in the DeBondt and Thaler

(1985, 1987) research design are entangled with problems in specifying expected

returns for low-priced stocks in particular market settings. Surprisingly, ignoring

transaction costs and simply changing the month in which trading is initiated

(from June-end to December-end) drastically reduces the (raw and abnormal)


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R. Ball et al. /Journal of Financial Econo mics 38 (1995) 79-l 07

105

returns of the lower-priced ‘loser’ stocks. This is consistent w

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