Three essays on exchange traded funds

... international and country funds, and bond funds, I contribute to the literature by demonstrating momentum/contrarianism in a changing asset allocation setting which includes U.S stocks, U.S bonds,... & Lakonishok (1996), Hong & Stein (1999)), expectation extrapolation, conservatism in expectation updating (Barberis, Shleifer, Vishny (1998)), biased self attribution or investor overconfidence... MOMENTUM/CONTRARIAN ABNORMAL RETURNS AND EXCHANGE TRADED FUNDS Abstract: Investing in portfolios of exchange traded funds (ETFs) provides risk adjusted abnormal returns that exceed transactions costs

A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HA WAIT IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY

ININTERNATIONAL MANAGEMENT

August 2007

ByJack C De Jong Jr

Dissertation Committee:

S Ghon Rhee, Chairperson Rosita P Chang (Victor) Wei Huang Qianqiu Liu Sang Hyop Lee

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Essay #1 shows that investing in portfolios o f U.S exchange traded funds (ETFs) provides risk adjusted abnormal returns that exceed transactions costs Short formation and holding periods of one day to one week provide abnormal contrarian returns as past losers become winners and past winners become losers Medium formation and holding periods of four weeks to thirty nine weeks provide abnormal momentum returns as past winners keep winning and past losers keep losing Abnormal returns result for portfolios

o f ETFs when returns are adjusted for risk using the Capital Asset Pricing Model and Fama & French’s three factor model

Essay #2 shows that investing in portfolios of international ETFs provides risk adjusted abnormal returns using either Lo & MacKinlay’s or Jegadeesh & Titman’s weighting methodologies A short formation and holding period o f one week provides abnormal contrarian returns, while medium formation and holding periods of four weeks

to twenty six weeks provide abnormal momentum returns Abnormal returns result for portfolios o f international ETFs when returns are adjusted for risk using the Capital Asset Pricing Model and Fama & French’s three factor model High trading volume increases the momentum abnormal returns for formation and holding periods o f 4 weeks and 26 weeks; low trading volume increases the contrarian abnormal returns for a formation and holding period o f 1 week

Essay #3 shows that investing in portfolios o f non-U.S ETFs from Australia, Canada, France, Germany, Hong Kong, Japan, and the U.K provides risk adjusted abnormal returns Short formation and holding periods o f 1 day to 8 weeks provide

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52 weeks provide abnormal momentum returns Abnormal contrarian returns result for portfolios o f non-U.S ETFs when returns are adjusted for risk using international versions of both the Capital Asset Pricing Model and Fama & French’s three factor model; however, abnormal momentum returns result only when returns are adjusted for risk using an international version o f CAPM.

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Table Page

1.5 Abnormal Returns Using Fama & French’s Three Factor Model 391.6 Annualized Abnormal Returns with Extra Time between

1.7 Annualized Abnormal Returns Net o f Transactions Costs for WML

1.8 Abnormal Returns Divided Into Two Periods:

1.9 Abnormal Returns Using CAPM and Fama & French’s

1.10 Abnormal Returns Using 26 week Formation and Holding Periods 49

2.2 Annualized Abnormal Returns: All International ETFs 912.3 Abnormal Returns Using CAPM: All International ETFs 932.4 Abnormal Returns Using Fama & French’s Three Factor Model:

2.5 Annualized Raw Returns: All International ETFs by

2.6 Annualized Abnormal Returns Using CAPM: All International ETFs

2.7 Annualized Abnormal Returns Using Fama & French’s Three Factor

Model: All International ETFs by High and Low Trading Volume 1012.8 Annualized Abnormal Returns with Extra Time between Formation

2.9 Abnormal Returns Using Different Betas in Up and Down Markets 1052.10 Abnormal Returns Divided Into Two Periods:

2.11 Annualized Raw Returns: Chan, Hameed, & Tong’s Country ETFs 1102.12 Annualized Abnormal Returns: Chan, Hameed, & Tong’s Country ETFs 1112.13 Abnormal Returns Using CAPM: Chan, Hameed, & Tong’s

2.14 Abnormal Returns Using Fama & French’s Three Factor Model:

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LIST OF TABLES

3.4 Abnormal Returns Using International Version of CAPM 1583.5 Abnormal Returns Using International Version of Fama & French’s

3.6 Annualized Abnormal Returns with Extra Time between Formation

3.7 Abnormal Returns Divided Into Two Periods:

3.8 Abnormal Returns Using International Versions of CAPM and Fama &

French’s Three Factor Model and Annual Dummy Variables 1663.9 Abnormal Returns Using International Version o f CAPM and

3.10 Abnormal Returns Using International Version o f Fama & French’s

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MOMENTUM/CONTRARIAN ABNORMAL RETURNS

AND EXCHANGE TRADED FUNDS Abstract:

Investing in portfolios o f exchange traded funds (ETFs) provides risk adjusted abnormal returns that exceed transactions costs Short formation and holding periods o f one day to one week provide abnormal contrarian returns as past losers become winners and past winners become losers Medium formation and holding periods o f four weeks to thirty nine weeks provide abnormal momentum returns as past winners keep winning and past losers keep losing Abnormal returns result for portfolios of ETFs when returns are adjusted for risk using the Capital Asset Pricing Model and Fama & French’s three factor model

1 Introduction:

Previous studies show stock prices exhibit medium term momentum, as buying portfolios o f recent winners and shorting portfolios o f recent losers results in abnormal returns that may or may not exceed transactions costs One strand of the literature investigates whether the momentum anomaly exists in various markets; various studies find a momentum strategy generates abnormal returns in U.S equities (Jegadeesh & Titman (1993,2001), Hong, Lim, & Stein (2000)), in U.S mutual funds (Grinblatt, Titman, & Wermers (1995), Carhart (1997), Wermers (2003), Sapp & Tiwari (2004)), in U.S industries (Moskowitz & Grinblatt (1999)), in international equity markets

(Rouwenhorst (1998), Chan, Hameed, & Tong (2000), Balvers & Wu (2006)), and in foreign exchange markets (Okunev & White (2001)) Gebhardt, Hvidkjaer, &

Swaminathan (2002) find no evidence o f momentum among investment grade corporate bonds, but find contrarian returns as the bonds experienced significant reversals as well as

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a momentum spillover from stocks to bonds o f the same firm as past equity returns are good predictors of future bond rating changes Momentum/contrarianism is an anomaly

in the sense that it violates market efficiency in its weak form as investors can use technical analysis o f past prices and returns to form portfolios of winners and losers and

so earn arbitrage profits on a zero investment portfolio that buys the winners and shorts the losers or buys the losers and shorts the winners, respectively Momentum is also an anomaly in the sense that the standard empirical asset pricing model using Fama & French’s three factor model cannot explain the medium term return continuation of momentum

Another strand of the literature accepts the momentum anomaly as a stylized fact and seeks to explain what causes momentum using behavioral finance theory as rational, market efficiency has difficulty explaining its existence Behavioral finance posits various explanations o f momentum, including investor overreaction or underreaction (Chan, Jegadeesh, & Lakonishok (1996), Hong & Stein (1999)), expectation

extrapolation, conservatism in expectation updating (Barberis, Shleifer, Vishny (1998)), biased self attribution or investor overconfidence (Daniel, Hirshleifer, & Subrahmanyam (1998)), disposition effects (Grinblatt & Moskowitz (2004)), selective information conditioning, and herding behavior by investors (Jordan (2004)) and mutual fund managers Clearly, as anomalies, momentum and contrarianism require further research,

as current studies agree that a momentum/contrarian investment strategy generates abnormal returns, but disagree as to what causes a momentum/contrarian strategy to be successful and disagree as to whether the abnormal profits are realistically attainable by

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ask spreads, brokerage commissions, the price impact of large trades, and the higher capital gains taxes associated with increased trading.

Other studies focus on the persistence of performance by mutual funds and how mutual funds’ performance relates to their use of momentum strategies This strand of the literature is especially important in my study of ETFs, since ETFs are similar in some aspects to mutual funds as well as having many of the trading characteristics of individual stocks Grinblatt, Titman, and Wermers (1995) find that 77% of the mutual funds are momentum investors, buying stocks that are past winners, but most do not systematically sell past losers; they find a positive relationship between mutual fund positive

performance and the use of a momentum trading strategy Carhart (1997) finds that a momentum strategy of buying last year’s winner decile mutual funds and shorting last year’s loser decile mutual funds generates an abnormal return of 8% per year, where differences in market value and momentum o f stocks held explain 4.6%, differences in expense ratios explain 0.7%, and differences in transactions costs explain 1% Sapp & Tiwari (2004) use Carhart’s four factor model to determine that mutual fund investors are not “smart money” even though the mutual funds that receive positive cash inflows tend

to be the best performing funds When Sapp & Tiwari use Fama & French’s three factor model, a strategy of buying the positive cash inflow funds and shorting the negative cash

outflow funds generates positive a ' s indicating a “smart money” effect, but when they use Carhart’s four factor model, the same strategy generates a ' s that are insignificantly

different from zero indicating no “smart money” effect Sapp & Tiwari conclude that

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mutual fund investors are “naively chasing past returns, not identifying skilled fund managers” (Sapp & Tiwari p 14) who follow momentum style strategies Wermers (2003) studies mutual fund performance persistence and finds that part o f the abnormally positive performance o f the winner funds is due to their holding of winner stocks

providing momentum returns like Carhart found, but mutual fund investors strongly invest cash into last year’s top returning funds and only weakly disinvest in last year’s poorest returning funds and winner fund managers use their large cash inflows to implement momentum strategies more strongly than loser fund managers who tend to hold their loser stocks which continue to be losers Wermers found that investor cash inflows to winner funds continue for two to four years, which is longer than the one year period attributed to momentum effects, and thus the high cash inflow funds continue to perform well due to the manager’s flow related trades chasing stocks with high past returns

Chan, Hameed, & Tong (2000) find momentum returns in 23 country index returns during 1980 to 1995 of at least 1% per month for formation and holding periods

o f 1 week, 2 weeks, or 4 weeks They use Lo & MacKinlay’s (1990) weighting scheme where portfolio weights reflect the country’s past performance relative to the average past performance o f all 23 countries; above average performers are purchased and below average performers are shorted, but all countries may have a non-zero weight in the winner minus loser portfolio This weighting scheme differs from Jegadeesh & Titman’s usual methodology of buying long the top decile o f winners and shorting the bottom decile of losers Chan, Hameed, & Tong find that 80 to 90% of the momentum profits are

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predictability, and they find that momentum profits are larger for country indices following an increase in trading volume Their momentum profits would be difficult to obtain after transactions costs as country indices are not directly investable and some of their markets restrict short selling Balvers & Wu (2006) jointly consider momentum and mean reversion for 18 developed country index returns from 1970 to 1999 Their model generates a signal that identifies the winner and loser countries by its indicator score incorporating both momentum and mean reversion information, resulting in excess returns o f 1.1 - 1.7% per month, which outperforms both pure momentum and pure mean reversion strategies Balvers & Wu find a strong negative correlation of - 35% between momentum and mean reversion effects, which explains why controlling for mean reversion effects can improve momentum returns The studies of both Chan, Hameed, & Tong (2000) and Balvers & Wu (2006) can be improved by using ETFs rather than country indices since ETFs indexing various country stock indices are readily investable and shortable which are necessary conditions to realistically implement a momentum or contrarian strategy.

My motivation in this study is to extend the domain of momentum/eontrarianism

to a relatively new investment vehicle, namely, exchange traded funds or ETFs ETFs are powerful and flexible investment vehicles that combine the diversified portfolio features

o f mutual funds with the trading possibilities of individual securities Currently, ETFs function similarly to passively managed index mutual funds, as they are composed o f a portfolio of stocks or bonds that track a particular index, thus providing diversification

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within the portion o f the market tracked by that index Four general categories o f ETFs include: (1) broad based domestic indices like the S&P 500, the NASDAQ 100, the Dow Jones U.S Total Market, the Russell 3000, the Wilshire 5000, some style specific indices

in both a “value” and a “growth” version, and size based indices including large cap, mid cap, small cap, and micro cap, (2) sector indices including consumer, energy, financial, health, natural resources, real estate, utilities, and technology, (3) international indices including global stock indices, regional indices, and country specific indices, and (4) bond indices including three of the Lehman Treasury bond indices, two different corporate bond indices, and the Lehman TIPS index What differentiates an ETF from a mutual fund is an ETF trades on an exchange (most on the AMEX) like a stock, enabling

an ETF to be: purchased or sold at intraday market prices, purchased on margin, sold short, and traded via stop orders and limit orders Ordinary mutual funds can only be purchased and sold by market orders for end o f day prices, and cannot be purchased on margin or sold short, which prevents the usual zero investment momentum and contrarian portfolios o f buying the winners and shorting the losers or of buying the losers and

shorting the winners Also, many mutual funds have redemption fees and other constraints to discourage or prevent the short term trading necessary to implement a momentum or contrarian strategy For implementing a momentum or contrarian strategy, purchasing or shorting an ETF gives the arbitrageur or investor a diversified portfolio of stocks while incurring only one bid ask spread and one round trip commission, clearly a cost advantage over assembling a portfolio o f individual winner and loser stocks, which entails many bid ask spreads and many commissions

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winners and shorting losers generates abnormal returns in the ETF market, (2) whether a contrarian investing strategy o f buying losers and shorting winners generates abnormal returns in the ETF market, and (3) which formation period, holding period is optimal for momentum investing and for contrarian investing My results contribute to the literature

an affirmative answer to the first research question about momentum, as buying the winner decile o f ETFs and shorting the loser decile o f ETFs provide statistically significant abnormal returns for formation and holding periods of 4 weeks, 8 weeks, 12 weeks, 16 weeks, 20 weeks, 26 weeks, and 39 weeks with risk adjustment by either CAPM or Fama & French’s three factor model The annualized momentum abnormal returns range from 8.2% to 22.1% under the Capital Asset Pricing Model and range from 8.4% to 13.5% under Fama & French’s three factor model My results contribute to the literature an affirmative answer to the second research question about contrarianism, as buying the loser decile o f ETFs and shorting the winner decile of ETFs provide

statistically significant contrarian abnormal returns for formation and holding periods of 1 day and 1 week The annualized contrarian abnormal returns range from 17.0% to 86.9% and hold true for risk adjustment by the Capital Asset Pricing Model and Fama &

French’s three factor model Following the classic approach of Jegadeesh & Titman (1993), I find for question (3) that a 26 week formation and holding period provides the highest annualized abnormal returns of 22.1% to an ETF momentum strategy using CAPM to adjust for risk, while a 20 week formation and holding period provides the highest annualized abnormal returns of 13.5% to an ETF momentum strategy using Fama

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& French’s three factor model to adjust for risk Also, a 1 day formation period and a 1 day holding period provide the highest abnormal returns to an ETF contrarian strategy, with annualized abnormal returns of 85.2% using CAPM and 86.9% using Fama & French’s three factor model These research questions are important, because momentum and contrarianism are both wide spread anomalies identified by researchers as well as investment strategies used by practitioners like mutual funds and individual investors to attempt to earn abnormal returns With the growth in ETFs from their introduction in

1993 with the SPDR Trust Series tracking the S&P 500 Index to 2005’s assortment of

217 ETFs consisting of 80 broad based domestic, 82 domestic sector, 49 global/international equity, and 6 bond ETFs, ETFs are on a growth path which should soon surpass the dollar amount invested in equity index mutual funds From the Investment Company Institute’s (a mutual fund trade organization) December 2005 statistics, ETFs (excluding Merrill Lynch’s HOLDRS) represent a market value of

$296.02 billion, which represents over 5% o f the $5,504.50 billion invested in stock and hybrid mutual funds Considering that about 10% o f stock mutual fund investments are

in indexed investments as opposed to actively managed funds, ETFs represent a significant portion (almost 35%) o f the U.S wealth invested in passively managed, index type investment vehicles With the growing popularity o f ETFs by traders and investors such an innovative financial product merits further study, especially when it can generate abnormal returns via a momentum or contrarian strategy

Most momentum/contrarian studies to date look at U.S stocks, U.S bonds, U.S domestic mutual funds, and international stocks or country indices separately By finding

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funds, sector or industry funds, international and country funds, and bond funds, I contribute to the literature by demonstrating momentum/contrarianism in a changing asset allocation setting which includes U.S stocks, U.S bonds, foreign stocks, as well as sector

or industry funds To my knowledge, this study is the first to identify momentum/contrarianism in such an asset allocation setting Also, I contribute to the literature by finding that ETFs are an ideally suited investment with which to implement a momentum or contrarian trading strategy, since ETFs permit the purchase or sale of a diversified portfolio of securities for one commission and one bid ask spread, resulting in abnormal returns that exceed transactions costs These results contradict Lesmond,Schill, & Zhou’s (2004) characterization o f momentum profits as illusory and further contribute to the existence o f momentum/contrarian profits that are realistically attainable

by investors and arbitrageurs utilizing ETFs, which provides further evidence against the theory o f market efficiency

2 Methodology:

Since Jegadeesh & Titman (1993) establish the generally accepted methodology for researching the momentum anomaly, I follow their methodology with appropriate adjustments to accommodate my study o f ETFs Since ETFs represent diversified portfolios designed and passively managed to track various domestic, sector, international, and bond indices, forming portfolios o f ETFs is less necessary than Jegadeesh & Titman’s method o f forming decile portfolios of individual stocks based on

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formation period performance However, when Moskowitz & Grinblatt (1999) study industry momentum they define the winner and loser portfolios as the top or bottom 3 out

o f 20 industries, respectively, when ranked by formation periods of 1, 6, or 12 months, and measured holding period returns for periods of 1, 6, 12,24, or 36 months Most momentum studies of mutual funds also group winner and loser funds into portfolios; at least with ETFs it is possible to short the losers while shorting mutual funds is not possible With the relative newness o f ETFs such long periods as 24 or 36 months would restrict the sample sizes to be rather small, as the end of 1999 found only 32 ETFs in existence, 4 broad based domestic ETFs, 11 sector ETFs, 17 foreign or country ETFs, and

0 bond ETFs The year 2000 brought the largest number of new ETFs as 57 ETFs were introduced during 2000, resulting in 89 ETFs in existence by year end, consisting o f 29 broad based domestic ETFs, 35 sector ETFs, 25 foreign or country ETFs, and 0 bond ETFs Table 1.1 shows the annual growth in ETF offerings from 1993 to the present Following Jegadeesh & Titman’s methodology, I define the winner ETFs as the top performing decile over various formation periods and the loser ETFs as the poorest performing decile over various formation periods, and then form the momentum portfolio that buys the winner ETFs and shorts the loser ETFs over various holding periods Also, adapting Jegadeesh & Titman’s methodology, I form the winner minus loser portfolio each week to increase the power of my tests; I equally weight the appropriate winner and loser ETFs in the portfolios formed each week during the sample period and held for the indicated amount o f time Also, with ETFs tracking four different types o f indices, broad based domestic, sector or industry, foreign or country, and bond, I measure momentum

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performance may favor one of the four types over the other three, which can determine whether a momentum-based asset allocation strategy exists, as well as to maximize my sample size My sample period runs from March 20,1996 to December 31,2005, a period of 483 weeks, with 19 ETFs available in 1996, so that the top and bottom deciles begin with 2 ETFs each as winners and losers, respectively In 2005,217 ETFs are available so that the deciles o f winners and losers both include 21 ETFs I consider formation periods o f 1 day, 1 week, 2 weeks, 4 weeks, 8 weeks, 12 weeks, 16 weeks, 20 weeks, 26 weeks, 39 weeks, and 52 weeks coupled with holding periods o f the same length as the formation period for a total of 11 different momentum strategies Following Jegadeesh & Titman’s methodology, I also consider the above 10 weekly momentum strategies with a one week lag between portfolio formation and holding period to allow a more realistic time for an investor to determine the winner and loser ETFs and form the appropriate portfolios while avoiding some price pressure and perhaps minimizing the transactions costs compared to a hurriedly assembled portfolio For the 1 day, 1 day momentum/contrarian strategy, I use an extra one day lag rather than an extra week lag For each combination o f formation and holding period, I compute annualized abnormal returns for the winner ETFs, the loser ETFs, and the zero investment momentum portfolio

of buying the winner ETFs and shorting the loser ETFs using CAPM and Fama &

French’s three factor model to adjust for risk Clearly, the zero investment contrarian portfolio of buying the loser ETFs and shorting the winner ETFs simply reverses the sign

of the zero investment momentum portfolio

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3 Description of Data:

Since most ETFs are listed on the AMEX and others are listed on the NYSE and NASDAQ, the daily return data is available on the Center for Research in Securities Prices (CRSP) database Most of the previous studies use CRSP data which is of excellent quality when defining returns using close to close security prices

Momentum/contrarian portfolio risk characteristics like factor loadings on various risk

measures like the market risk premium, RM - R F, small firm size minus big firm size,

SMB, and high book to market value minus low book to market value, HML are calculated to confirm that abnormal momentum/contrarian returns are not due to different risk levels, or to different firm characteristics, like size or book-to-market ratios, or to different industry compositions, or to different value or growth measures Daily data on the factor mimicking portfolios for the three zero investment factor mimicking portfolios,

i.e., R m - R f , SMB, and HML are available on Kenneth R French’s website at:

http://mba.tuck.dartmouth.edu/pages/facultv/ken.french/data library.html

4 Outline of Model:

To evaluate the various ETFs in terms o f risk levels, I use CAPM and Fama & French’s three factor model Thus, the factor models used are:

CAPM: Rit - Rfl = or, + b: • RMRFt + e„

Fama & French’s three factor model:

Rit - R Fi = or, + b, ■ RMRF, + s, ■ SMB, + h, ■ HML, + e„

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RMRF is the excess return on a value-weighted market proxy, and SMB and HML are the returns on zero investment, value-weighted, factor-mimicking portfolios for firm size and book-to-market, respectively Thus, using both models, I calculate the cross-

sectional a ’s for the excess return on the winner ETFs, the excess return on the loser

ETFs, as well as the winner minus loser momentum portfolio to measure abnormal positive or negative returns Although the three risk factors, RMRF, SMB, and HML are all calculated relative to U.S equities, no adjustments need be made to use the above factor risk premiums for the foreign ETFs since all the ETFs are traded in dollars, traded during U.S market hours, and function as perfect substitutes for the other three categories

o f ETFs Also, Zhong & Yang (2005) find that the prices of international ETFs are greatly influenced by U.S risk factors

5 Results:

A Raw Returns:

Table 1.2 shows the annualized mean raw returns and t-statistics for the 11 momentum strategies with information for the winner minus loser portfolio as well as the winner and loser portfolios separately reported The momentum returns for the formation and holding periods of 2 weeks to 39 weeks are economically significant, ranging from annualized winner minus loser returns of 5.8% to 18.6% Also, the winner portfolios keep winning and some of the losers keep losing while others reverse with winner annualized returns ranging from 8.2% to 16.4% and with loser annualized returns ranging

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from - 2.8% to 2.3% Momentum returns are maximized at 18.6% with a 20 week formation period and a 20 week holding period Contrarian returns are evident in the short formation and holding periods of 1 day and 1 week as well as in the long formation and holding periods o f 52 weeks with mean annualized winner minus loser returns ranging from - 2.8% to - 86.4% Thus, by reversing our momentum strategy to a contrarian strategy of buying the past losers and shorting the past winners, economically significant returns are possible with annualized loser returns ranging from 7.6% to 55.9% and annualized winner returns ranging from - 30.5% and 4.8% for the 1 day, 1 week, and

52 week formation and holding periods The long formation and holding periods of 39 weeks and 52 weeks are not clearly momentum or contrarian strategies as both winners and losers continue to win but with less economic significance than the short formation and holding periods

However, all the raw returns are statistically insignificant as the largest t-statistic

is only 0.49 These results are consistent with Balvers & Wu (2006) who find economically significant but statistically insignificant returns for their model which combines momentum and mean reversion for 16 international ETFs from April 1996 to December 2003 Balvers & Wu attribute the statistical insignificance to the shortness of the available sample period which may also be the problem in my study Henker,

Martens, & Huynh (2006) find statistically insignificant momentum returns for U.S stocks in the 1993 - 2004 period due to the poor performance o f momentum strategies during the 2001 - 2004 subperiod The statistical insignificance could also be a sample specific result from the added volatility in stock returns during the late 1990s and early

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my momentum strategies for risk and identify statistically significant abnormal returns.

5 Results:

B Risk Adjusted Momentum Returns:

Table 1.3 shows that the annualized momentum abnormal returns for winner minus loser portfolios are very statistically significant at the 1% level of significance for strategies of formation and holding periods from 4 weeks to 39 weeks with risk adjusted

by both CAPM and Fama & French’s three factor model The winner minus loser annualized momentum abnormal returns range from 8.2% to 22.1% over the strategies of formation and holding periods from 4 weeks to 39 weeks with risk adjusted by CAPM and Fama & French’s three factor model In general, the annualized momentum abnormal returns are larger for CAPM than for Fama & French’s three factor model, which is the expected result, as CAPM makes less complete risk adjustments In general, the annualized momentum abnormal returns are maximized for the 20 week or 26 week formation and holding period strategy with momentum returns o f 22.1% under CAPM for

26 weeks and 13.5% under Fama & French’s three factor model for 20 weeks

From the results for the excess returns above the appropriate periodic Treasury bill rate for the momentum winner and loser ETF portfolios, I find that the losers drive the winner minus loser results under both CAPM and Fama & French’s three factor model The loser annualized momentum abnormal returns are very significant at the 1% level for all formation and holding periods from 4 weeks to 39 weeks with magnitudes

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ranging from - 8.2% to - 14.4%, while the winner annualized momentum abnormal returns are statistically insignificant for the formation and holding periods o f 4 weeks, 8 weeks, 12 weeks, and 39 weeks with statistically significant magnitudes ranging from 3.5% to 6.3% for the formation and holding periods o f 16 weeks, 20 weeks, and 26 weeks.

Annualized contrarian abnormal returns are very statistically significant at the 1% level of significance for the short formation and holding periods o f 1 day and at the 5% level o f significance for the formation and holding periods of 1 week with risk adjusted

by both CAPM and Fama & French’s three factor model The winner minus loser returns range from - 17.0% to -86.9% Thus, by reversing our momentum strategy to a

contrarian strategy o f buying the past losers and shorting the past winners, statistically significant returns are possible with abnormal annualized loser returns for the 1 day formation and holding period of 45.2% under CAPM and 45.4% under Fama & French’s three factor model, and abnormal annualized winner returns for the 1 day formation and holding period o f — 40.1% under CAPM and - 41.6% under Fama & French’s three factor model The long formation and holding periods of 39 weeks and 52 weeks under CAPM and Fama & French’s three factor model are not clearly momentum or contrarian

strategies as both winners and losers continue to lose with negative abnormal annualized returns Thus, a formation and holding period o f 1 day maximizes our contrarian

abnormal returns, while a formation and holding period of 20 weeks or 26 weeks maximizes our momentum abnormal returns

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C Risk Adjustment under CAPM:

Table 1.4 shows the winner minus loser portfolio has a negative beta or systematic risk measure with significantly negative coefficients on the market risk premium term for all formation and holding periods except 20 weeks Excess returns on all winner and loser portfolios have very significant positive betas with positive coefficients on the market risk premium and p-values o f less than 0001 for all formation and holding periods The losers have higher betas than the winners across all formation and holding periods, indicating that the loser portfolios have a higher level of systematic risk than the winners Clearly, the resulting momentum abnormal returns to the winner minus loser ETFs for formation and holding periods from 2 weeks to 39 weeks are not due to a higher level o f risk in the winner ETFs than the loser ETFs Also, the higher level of systematic risk in the loser portfolios explains some but not all o f the contrarian abnormal returns as

a beta difference of 0.19 to 0.28 is too small to generate the magnitude of the contrarian returns With risk adjustment under CAPM, momentum strategies of buying the winner ETFs and shorting the loser ETFs with formation and holding periods from 2 weeks to 39 weeks generate significant positive abnormal returns and contrarian strategies of buying the loser ETFs and shorting the winner ETFs with formation and holding periods from 1 day to 1 week generate significant positive abnormal returns

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5 Results:

D Risk Adjustment under Fama & French’s three factor model:

Table 1.5 shows the winner minus loser portfolio has a negative beta or systematic risk measure with significantly negative loadings on the market risk premium for all formation and holding periods except 1 week, 20 weeks, and 26 weeks All winner and loser portfolios have very significant positive betas with positive factor loadings on the market risk premium and p-values o f less than 0001 for all formation and holding periods The losers have higher factor loadings on the market risk premium than the winners across all formation and holding periods, indicating that the loser portfolios generally have a higher level of systematic risk than the winners

The winner minus loser portfolio has positive factor loadings on HML, the value minus growth risk premium, for all formation and holding periods except 39 weeks, with about half o f the formation and holding periods significant at the 5% level and the rest insignificant In general, the winner portfolios have positive factor loadings on HML suggesting the winner ETFs contain value stocks with higher book to market ratios; however, most formation and holding periods are insignificant at the 10% level In contrast, the loser portfolios have negative factor loadings on HML with most significant suggesting the loser ETFs contain growth stocks with lower book to market ratios Thus, book to market levels significantly distinguish winner and loser ETFs, as loser ETFs contain more growth stocks than winner ETFs

The winner minus loser portfolio has a positive factor loading on SMB, the small firm minus big firm risk premium for all formation and holding periods from 2 weeks to

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loadings suggest the winner ETFs contain smaller cap stocks than the loser ETFs for these time periods corresponding to momentum abnormal returns The winner minus loser portfolio has a negative factor loading on SMB, for the 1 day, 1 week, and 52 week formation and holding periods corresponding with contrarian abnormal returns, but only

52 weeks is significant, which again suggests that the loser ETFs contain larger cap stocks than the winner ETFs The winner ETFs load significantly positive on SMB for all formation and holding periods except the 1 week, 2 week, and 52 week winners which are positive but insignificant The loser ETFs’ factor loadings on SMB are all insignificantly different from zero except for the 1 day and 52 week formation and holding period which are very significantly positive with p-values less than 0001 and of larger magnitude than the corresponding winner ETFs, indicating that the loser ETFs for both the 1 day and 52 formation and holding periods have significantly smaller cap stocks on average than the corresponding winner stocks, which are also small cap but not as small on average as the loser ETFs Thus, small cap stocks in the ETFs account for both the positive momentum abnormal returns and the positive contrarian abnormal returns with the momentum returns driven by winners in the formation period and the contrarian returns driven by the losers in the formation period

Clearly, the resulting momentum returns to the winner minus loser ETFs are not due to a higher level of risk in the winner ETFs than the loser ETFs The losers have higher systematic risk than the winners, the winners have higher book to market ratios than the losers, suggesting winners include more value stocks while losers include more

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growth stocks, and the ETFs with positive abnormal returns during the holding period, i.e., contrarian losers and momentum winners, are generally smaller cap than the ETFs with negative abnormal returns during the holding period, i.e., contrarian winners and momentum losers With risk adjustment under Fama & French’s three factor model, momentum strategies o f buying the winner ETFs and shorting the loser ETFs with formation and holding periods from 4 weeks to 39 weeks generate significant positive abnormal returns and contrarian strategies o f buying the loser ETFs and shorting the winner ETFs with formation and holding periods from 1 day to 1 week generate significant positive abnormal returns.

6 Robustness of Results:

A Extra Time Between Formation and Holding Periods:

If ETF returns are autocorrelated, then a momentum strategy that benefits from continuation o f returns would appear to be profitable Two possible explanations are nonsynchronous trading as the underlying stocks in some of the international ETFs may trade over different time periods than the actual ETFs trade on the U.S markets and bid ask bounce from pricing pressure attempting to buy past winners or to short past losers Jegadeesh & Titman’s usual methodology is to allow an extra week between the portfolio formation period where the winners and losers are identified by past performance and the portfolio holding period where the winners are purchased and the losers are shorted I adapt Jegadeesh & Titman’s methodology to add an extra day between the formation and holding period for the 1 day 1 day strategy since an extra week seemed excessive; for all

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between the formation and holding periods Such an adjustment should reduce the ability

of a momentum strategy to take advantage o f the autocorrelation in ETF returns Since contrarian strategies benefit from reversals of returns rather than continuations, it is not clear apriori what impact the extra week between formation and holding periods should have on the contrarian abnormal returns

Table 1.6 shows adding extra time between the formation and holding period does not eliminate the momentum and contrarian returns identified earlier in Table 1.3

Momentum strategies o f buying past winner ETFs and shorting past loser ETFs continue

to generate significant abnormal returns for all formation and holding periods from 2 weeks to 39 weeks when adjusting for risk using both CAPM and Fama & French’s three factor model The extra time generally only slightly reduces the abnormal momentum returns for most holding periods from 4 weeks to 39 weeks However, the extra day removes about 72% of the contrarian abnormal returns for the formation and holding period o f 1 day, but a significant but smaller contrarian return still remains The extra week converts the formation and holding period o f 1 week from generating a significant contrarian abnormal return to generating an insignificant momentum return and it increases the magnitude and significance of the momentum abnormal returns for a formation and holding period o f 2 weeks under both risk adjustment models The 52 week contrarian returns remain insignificant under both CAPM and Fama & French’s three factor model

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6 Robustness of Results:

B Transactions Costs:

Another issue is whether the momentum and contrarian abnormal returns are real

or illusory after considering transactions costs, since both momentum and contrarian strategies require a significant amount o f trading to implement, potentially costing the investor or arbitrageur the bid ask spread, brokerage commissions, and price impact for large orders Lesmond, Schill, & Zhou (2004) characterize the momentum profits with individual stocks identified by Jegadeesh & Titman in 1993 and 2001 and Hong, Lim, & Stein in 2000 as illusory since the momentum profits net o f their transactions cost estimates are insignificantly different from zero However, ETFs are much less costly to trade than individual equities with smaller bid ask spreads and more liquidity to reduce the price impact of large trades

Table 1.7 shows the momentum returns net o f transactions costs for the formation and holding period o f 26 weeks, which is the usual recommended momentum strategy in most previous studies The actual transactions were tabulated by domestic and bond, sector, and international ETF over the 9.29 years studied On average, the winner ETFs consisted of 10.64% domestic and bond ETFs, 46.52% sector ETFs, and 42.84%

international ETFs, while the loser ETFs consisted o f 8.08% domestic and bond ETFs, 54.97% sector ETFs, and 36.95% international ETFs I estimated the quoted bid ask spreads as the higher o f those identified in Huang & Wei (2004) and Salomon Smith Barney (2002), resulting in estimates o f 0.33% for domestic and bond ETFs, 0.62% for sector ETFs, and 0.867% for international ETFs Brokerage commissions were estimated

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$125,000 invested long in the winner ETFs and $125,000 invested short in the loser ETFs Quoted bid ask spreads and brokerage commissions total 8.25% per year which reduced the net annualized abnormal returns to 13.81% under CAPM and 4.58% under Fama & French’s three factor model Huang and Wei estimated the effective bid ask spread to be about 30% less than the quoted bid ask spread as transactions often take place between the quoted bid and ask prices; using effective bid ask spreads reduces the transactions cost to 5.82% per year With effective spreads, the net annualized abnormal returns are 16.24% under CAPM and 7.01% under Fama & French’s three factor model Clearly, the momentum abnormal returns under CAPM and Fama & French’s three factor model are not illusory, but represent economically viable risk adjusted returns even when reduced by transactions costs.

6 Robustness of Results:

C Growth in Number of ETFs:

Another issue is the rapid growth in the number o f ETFs Were the momentum and contrarian returns determined by the early years when a smaller number o f ETFs existed? Table 1.8 considers this question by dividing the sample period into the early period from March 20,1996 to December 31,2000 with 19 to 89 ETFs in existence and the later period from January 1, 2001 to December 31, 2005 with 113 to 217 ETFs in

existence I distinguish these two sample periods for portfolios with a formation and

holding period o f 26 weeks with risk adjusted by CAPM and Fama & French’s three

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factor model Significant momentum abnormal returns occur under both risk adjustment models for the early period from 1996 to 2000 However, during the later period from

2001 to 2005, significant momentum abnormal returns occur under CAPM, but significant contrarian abnormal returns occur under Fama & French’s three factor model Most o f the factor loadings remain the same sign and significance in both periods as well

as similar to the sign and significance for the entire period from 1996 to 2005 as denoted

in Tables 1.4 and 1.5 previously For some portfolios the abnormal returns are larger in the earlier period and for others they are larger in the later period One clear difference between the two periods is that winner ETFs included growth stocks, with low book to market ratios, during the 1996 - 2000 period but winner ETFs included value stocks, with high book to market ratios, during the 2001 - 2005 period Dividing the sample period into two shorter periods illustrates some periodic differences between winner and loser ETFs in the two periods However, such differences do not indicate a problem with the number o f ETFs in existence, but more likely reflect the differing economic conditions in the different sub-periods as 1996 to early 2000 reflected a roaring bull market, followed

by the bear markets o f later 2000 through 2002, and the milder bull markets of 2003 to 2005

from today’s winners and losers and one sixth formed from each of the previous one, two, three, four, and five month’s winners and losers My methodology used equal weightings

of the top and bottom decile ETF performers to form the winner and loser portfolios like Jegadeesh and Titman, but formed a new portfolio each week during the sample period and held it for the indicated period of time without rebalancing Table 1.9 compares the abnormal returns for portfolios with a formation and holding period of 26 weeks, with risk adjustment by CAPM and Fama & French’s three factor model, using my

methodology and 4 week rebalancing similar to Jegadeesh and Titman Rebalancing six portfolios over 4 week periods necessitates using a 24 week formation and holding period rather than a 26 week formation and holding period The results are qualitatively the same for abnormal returns under both CAPM and Fama & French’s three factor model Annualized abnormal return magnitudes are 22.1% (no rebalancing) vs 22.2% (4 week rebalancing) under CAPM and 12.8% (no rebalancing) vs 16.1% (4 week rebalancing) under Fama & French’s three factor model, while 4 week rebalancing has slightly lower statistical significance than no rebalancing

6 Robustness of Results:

E Asset Allocation vs Type of ETF:

My results so far have not identified the source of the abnormal momentum or contrarian returns since I formed all winner and loser portfolios o f ETFs from the asset pool that included all four types o f ETFs, namely, domestic, sector, international, and

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bond My study purposefully chooses all four types of ETFs simultaneously to extend momentum/contrarian studies to the asset allocation domain as well as to maximize the length of the sample period studied, since ETFs are a relatively new investment vehicle

On average, about 51% of the ETFs in the winner and loser portfolios are sector ETFs and about 40% are international ETFs, with the remaining 9% from the domestic and bond ETFs To control for the effects of including sector and international ETFs, I augmented CAPM and Fama & French’s three factor model with dummy variables identifying whether or not the winner, loser, and WML portfolios included sector or international portfolios Specifically, the augmented models are:

CAPM: Rit - RFl = a t + bi ■ RMRFt + c, • Dum St + d t - Dum It + ejt

Fama & French’s three factor model:

Rlt - RFt = a , + bt ■ RMRFt + st ■ SM B, + ht ■ HML t + c, • Dum St + d t • Dum lt + eit

where: DumSt = 1 if the portfolio at time t includes at least one sector ETF, and 0 otherwise, DumIt = 1 if the portfolio at time t includes at least one international ETF, and

0 otherwise, and all the other variables are defined as before In the augmented model,

or, measures the abnormal momentum/contrarian returns in portfolios consisting ofdomestic and bond ETFs only, while c, measures the difference in abnormal momentum/contrarian returns in portfolios including sector ETFs relative to those

consisting o f domestic and bond ETFs, and dt measures the difference in abnormal

momentum/contrarian returns in portfolios including international ETFs relative to those consisting of domestic and bond ETFs

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for WML portfolios formed from domestic and bond ETFs only with annualized abnormal momentum returns ranging from 44.7% to 101.8% with larger magnitudes for risk adjustment by augmented CAPM than Fama & French’s augmented three factor model and larger magnitudes using 4 week rebalancing than no rebalancing These large abnormal momentum returns are driven by the loser portfolios of domestic and bond ETFs which continue to lose a very significant annualized abnormal momentum return of

- 33.2% to - 56.6% Clearly, the economic times when the top and bottom 26 week performance deciles are dominated by domestic and bond ETFs rather than the more volatile and focused sector and international ETFs are excellent times to implement a momentum strategy for the next 26 weeks At more typical economic times when the top and bottom 26 week performance deciles include either sector or international ETFs or both, the abnormal momentum returns over the next 26 weeks are reduced, with the result being driven by the sector and international ETF losers losing significantly less than their domestic and bond ETF counterparts

Table 1.10 frames the analysis of Asset Allocation vs Type of ETF differently, by comparing the 26 week formation and holding period WML, Winner, and Loser ETF performance over a shorter sample period from January 1, 1999 to December 31,2005 to allow a sufficient number o f ETFs in each category to meaningfully define winners and losers With risk adjustment by CAPM, the asset allocation pool including all four types

of ETFs generates very significant abnormal momentum returns as do all four ETF types separately as well Both the sector ETFs and domestic ETFs generate larger abnormal

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momentum returns than the asset allocation pool, but the bond ETFs and international ETFs both generate smaller abnormal returns than the asset allocation pool primarily because the bond loser abnormal returns are insignificantly different from zero and the international loser abnormal returns are positive rather than negative With risk adjustment by Fama & French’s three factor model, the asset allocation pool including all four types o f ETFs generates a somewhat significant abnormal contrarian return, but the bond ETFs generate a significant abnormal momentum return and the domestic,

international, and sector ETFs generate abnormal contrarian returns that are insignificantly different from zero Only the international winner ETFs generate a positive significant abnormal return The bond loser ETFs generate a negative very significant abnormal return, but the loser ETFs for the asset allocation pool and the domestic, international, and sector generate positive very significant abnormal returns Since losing 1996, 1997, and 1998 from the sample reduces the magnitude and

significance of the abnormal momentum/contrarian returns across all five ETF pools, some of the advantage of the asset allocation pool of all four types o f ETFs is due to the longer available sample period However, this analysis indicates some differences between the holding period performance o f the four different types o f ETFs which may lead to improvements over a naive momentum/contrarian strategy

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This study extends Jegadeesh & Titman’s momentum/contrarian anomaly to a new domain, portfolios of ETFs that either buy the winners and short the losers or buy the losers and short the winners, respectively Currently, all U.S ETFs are passively

managed to track an index, not actively managed to time the market or “beat the market”

by loading up on high momentum stocks Yet, in spite of this disadvantage to actively managed mutual funds, ETFs provided economically and statistically significant abnormal returns to contrarian strategies o f buying the loser ETFs and shorting the winner ETFs with formation and holding periods of 1 day and 1 week, and to momentum

strategies o f buying the winner ETFs and shorting the loser ETFs with formation and holding periods from 4 weeks to 39 weeks This study is also the first to demonstrate momentum in a changing asset allocation setting which includes U.S stocks, U.S bonds, foreign stocks, as well as sector or industry funds In contrast to Lesmond, Schill, & Zhou, I find that momentum/contrarian abnormal returns are not illusory, but are achievable by investors and arbitrageurs using realistic estimates of bid ask spreads and brokerage commissions ETFs are ideal instruments with which to implement a

contrarian and momentum strategy, since ETFs allow the purchase or short sale o f a diversified portfolio o f securities for one commission and one bid ask spread with minimal price impact Using CAPM and Fama & French’s three factor model to adjust for risk, I find that the contrarian and momentum abnormal returns available with ETFs can not be explained by rational differences in risk and so I provide further evidence of the momentum/contrarian anomaly’s attack on market efficiency Such findings

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contribute support to the behavioral explanation o f why momentum occurs as investors underreact to relevant information and so prices only gradually reflect relevant news and information.

In the future, as the sample period o f ETFs’ data is longer, I plan to check the longer term performance for 18, 24, and 36 months after portfolio formation, to determine the duration o f momentum/contrarian performance and anticipate the normal long-term reversals as documented by De Bondt & Thaler (1985, 1987), thus extending their results

to a new domain of ETFs Also, I anticipate that ETFs will continue to grow and expand their array o f offerings where eventually I anticipate actively managed ETFs to more directly compete with mutual funds and yet appeal to larger investors and investors that trade more actively than permitted by mutual funds With actively managed ETFs, I expect the usual hot performance chasing behavior by investors, resulting in ETF managers that utilize momentum strategies thus magnifying the momentum performance from the passively managed ETFs studied in this paper ETFs will continue to adapt and evolve to provide more flexible investment vehicles for investors and traders, as well as future questions to research and investigate relative to momentum/contrarian strategies as new ETFs and more years o f data become available

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