Are Momentum Strategies Feasible in Intraday-Trading ...€¦ · Are Momentum Strategies Feasible...

Are Momentum Strategies Feasible in Intraday-Trading? Empirical Results from the German Stock Market

Tim A. Herbergera*, Matthias Horna and Andreas Oehlerb

Abstract Momentum trading strategies have been proved to be profitable in different asset classes and on various national capital markets in the past. However, there are some indications for eroding momentum profits. Based on the theory of gradual information distribution on capital markets and the technological progress of the last years, we suppose that the momentum effect transformed from a monthly basis to shorter time horizons. With regard to stocks that were listed in the German blue chip index DAX 30 between November 2013 and June 2014, this study is the first to examine, whether such strategies generate market adjusted excess returns on an intraday-trading basis. We analyze 16 momentum strategies, inspired by Jegadeesh/Titman´s (1993, 2001) original momentum strategy design (4x4), with ranking and holding periods of 15, 30, 45 or 60 minutes. For each stock, we analyze 15.131 price observations on a five minutes frequency. From the empirical results we conclude that the momentum strategy does not provide positive excess returns. However, we find indications for price reversals in intraday stock market returns for past loser stocks. Our results are robust on portfolio size (winning as well as loser portfolio) and the duration of a lag between the end of ranking period and beginning the holding period.

JEL Classification: G10, G11, G14

Key Words: Behavioral Finance, Intraday-Trading, Momentum Strategies

a Department of Finance, Bamberg University, Bamberg, Germany. b Full Professor and Chair of Finance, Bamberg University, Bamberg, Germany. * Address correspondence to Tim A. Herberger, Bamberg University, Department of Finance, Kaerntenstrasse 7, D-96045 Bamberg, Germany, e-mail: [email protected].

Are Momentum Strategies Feasible in Intraday-Trading? Empirical Results from the German Stock Market

Abstract Momentum trading strategies have been proved to be profitable in different asset classes and on various national capital markets in the past. However, there are some indications for eroding momentum profits. Based on the theory of gradual information distribution on capital markets and the technological progress of the last years, we suppose that the momentum effect transformed from a monthly basis to shorter time horizons. With regard to stocks that were listed in the German blue chip index DAX 30 between November 2013 and June 2014, this study is the first to examine, whether such strategies generate market adjusted excess returns on an intraday-trading basis. We analyze 16 momentum strategies, inspired by Jegadeesh/Titman´s (1993, 2001) original momentum strategy design (4x4), with ranking and holding periods of 15, 30, 45 or 60 minutes. For each stock, we analyze 15.131 price observations on a five minutes frequency. From the empirical results we conclude that the momentum strategy does not provide positive excess returns. However, we find indications for price reversals in intraday stock market returns for past loser stocks. Our results are robust on portfolio size (winning as well as loser portfolio) and the duration of a lag between the end of ranking period and beginning the holding period.

JEL Classification: G10, G11, G14

Key Words: Behavioral Finance, Intraday-Trading, Momentum Strategies

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1 Introduction

The momentum effect has been well documented and confirmed by numerous

empirical studies that are based on various asset classes like different international

equity markets1, bonds2, currencies3, commodities4 and real estate5 or use different

indicators for the buying and selling signals6. In 1993 Jegadeesh/Titman show for the

US stock market that significantly positive excess returns can be generated by applying

momentum strategies (16 strategies with respective formation periods of 3, 6, 9 or 12

months and with a subsequent holding period of 3, 6, 9, 12 months). Based on the

‘relative strength’-concept (Levy (1967)), those stocks are bought that generate the

highest return during the ranking period (winner portfolio). At the same time, stocks

showing the lowest return during the respective ranking period are sold short (loser

portfolio). The total return of the strategy consists of the return of the winner portfolio

plus the return of the looser portfolio (momentum portfolio). Consequently, a

momentum strategy is a gross zero cost portfolio strategy. The authors conclude that

stock prices are auto-correlated, contradicting to the neoclassic efficient market

hypotheses (Fama/Fisher/Jensen/Roll (1969)), and that significant excess returns can

be generated through exploitation of this existing auto-correlation.

Although the success of momentum trading strategies is well documented for the

past, there are indications for eroding momentum profits at least for the US-stock

market since the early 90s of the last century (Hwang/Rubesam (2013)). Based on a

gradual distribution model for new information on the market (Hong/Stein (1999);

Hong/Stein (2000); Chan/Jegadeesh/Lakonishok (1996)), we suppose that the

technological progress, combined with a more efficient information distribution among

market participants, led to a transformation of the momentum effect from a monthly

basis to shorter time-horizons. In this sense, our paper contributes the extant literature

with an adaption of the original 4x4 framework of Jegadeesh/Titman (1993) based on

1 See Jegadeesh/Titman (1993) for the US stock market and Rouwenhorst (1998) for further national stock markets in Europe; Chan/Hameed/Tong (2000) for different national stock market indices; Andreu/Swinkels/Tjong-A-Tjoe (2013) for various country and industry exchange traded funds. 2 See Jostova/Nikolova/Philipov/Stahel (2013). 3 See Menkhoff/Sarno/Schmeling/Schrimpf (2012). 4 See Miffre/Rallis (2007). 5 See Ro/Gallimore (2014) for real estate mutual funds; Beracha/Skiba (2011) for residential real estate. 6 See Bootra/Hur (2013) for 52week-high and 52week-low.

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monthly stock returns, to an intraday momentum strategy scheme based on 5-minute

stock returns. We analyse 16 momentum strategies with ranking and holding periods

of 15, 30, 45 or 60 minutes. We provide robustness checks by applying different

portfolio sizes for winner and loser portfolios and various skipping periods between the

ends of the ranking periods and the beginnings of the holding periods in order to

rebalance the portfolios and to avoid bid-ask-biases.

Based on 15.131 test runs, the empirical results show that the momentum strategy

does not provide excess returns in intraday-trading. However, we find indications for

reversals in intraday stock market returns for past loser stocks. Our results are robust

on portfolio size and the duration of the lag between the ends of the formation periods

and the beginnings of the holding periods.

The remainder of the paper is structured as follows: Section 2 gives a literature

review, a description of our contribution and the derivation of our hypotheses. Section

3 explains the data and methodology of our analysis. The results of our analysis are

presented and discussed in section 4. Section 5 provides a summary.

2 Literature Review and Contribution

The success of momentum strategies has hardly been questioned in recent years, but

there are still controversial opinions on the cause of the excess returns that contradict

neoclassic finance. Based on the neoclassic theory, Lesmond/Schill/Zhou (2004)

argue that the momentum effect is a result of risk or liquidity premiums as well as

market frictions. They state that no significant excess returns can be generated through

momentum strategies after transaction costs have been taken into account. In contrast,

Korajczyk/Sadka (2004) conclude that the profits realized in former studies result only

partly on the negligence of transaction costs and thus, this does not constitute a

complete explanation for the amount of the drawn excess returns. Conrad/Kaul (1993)

explain the profitability of the momentum strategies by a cross-sectional variation of

the mean returns. In contrast to that, Moskowitz/Grinblatt (1999) point out that the

momentum effect can only be found in few industries. Thus, significant excess returns

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can hardly be attested if the data is adjusted for industry effects. According to Wu

(2002) as well as Wang (2003) the differences in expected returns over a specific

period of time are the reason for the profitability of the momentum strategy. However,

Grundy/Martin (2001) as well as Karolyi/Kho (2004) show that industrial influences and

differences in time can only partly account for the success of momentum strategies

with regard to expected returns. Chordia/Shivaumar (2002) conclude that

macroeconomic variables can predict the momentum effect and the resulting excess

returns.

Based on a Behavioral Finance approach, the momentum effect is a consequence of

investor biases. The investor-sentiment-model by Barberis/Shleifer/Vishny (1998)

identifies errors made by investors when forecasting expected profits as cause for the

momentum effect. The overconfidence-model by Daniel/Hirshleifer/Subrahmanyam

(1998) shows that investors overestimate their own capabilities with respect to the

valuation of assets. When interpreting public and private information, investors make

errors, which are responsible for the momentum effect. Chan/Jegadeesh/Lakonishok

(1996) as well as Hong/Stein (1999) explain the trading success of momentum

strategies based on an underreaction of market participants in their trading behavior.

They argue that the gradual spread of new information in the market among market

participants constitutes the reason for the momentum effect, whereby the stock price

only gradually reflects the fair value based on the actual news status. Figure I shows

the gradual distribution of new information in the market with the consequent lagged

reaction on the stock price. On the left side, a positive company message is published

in T1 and the stock price reacts delayed in time until T2 when the price fully reflects all

available information about the company. On the right side of the figure, the same

phenomenon is shown for the occurrence of bad news.

[Insert Figure I about here]

In addition, Hong/Lim/Stein (2000) show that the momentum effect is stronger, when

less analysts cover a company and its stocks, because this aspect promotes the

gradual spread of new information in the market.

4

However, recent studies show that profits of technical trading strategies in general

(for an overview see Park/Irwin (2004 and 2007)) and momentum strategies in

particular (Hwang/Rubesam (2013)) have decreased over time. By combining Fama’s

“Efficient Market Hypothesis” with the field of behavioral finance, Lo’s Adaptive Market

Hypothesis (AMH) (Lo (2004)) delivers a theoretical framework that helps to explain

dynamic processes in financial markets and therefore might explain the absence of

momentum profits. One implication of this framework is the wax and wane of profit

opportunities and their disappearance when exploited by too many market participants.

Since classical momentum strategies (those using monthly stock price observations

as in Jegadeesh/Titman 1993) have been well documented for decades, they might

have become too popular and as a consequence the profit opportunities have

vanished.

Another implication of the AMH is the necessity of innovations to survive in the

markets. Market participants have intuitively known that already. With the help of

communication and information technologies, they have built a highly automated

market microstructure whose proportion of computer-initiated trades lies over 50%

(Viebig 2013). Today, these technologies enable market participants to screen and

process information and news much faster than several years ago. Combining the

accelerated information processing with the Hong-Stein-Model (1999) as well as

Chan/Jegadeesh/Lakonishok (1996), it seems possible that recent studies might not

have been able to identify momentum profits due to the low frequent data they use.

By focusing on new technologies, the question arises if these quantitative rule-

based systems have eliminated human-caused market anomalies like the momentum

effect. Yet, findings on trading strategies of automated systems show the opposite. A

considerable proportion of the strategies’ underlying algorithms are designed to initiate

(Lopez de Prado 2012) and exploit short term momentum (Gomber et al 2011). The

consequent hypothesis is that the momentum profits have drifted from daily/monthly to

hourly price movements. This hypothesis is supported by Schulmeister (2007, 2008)

who explains the phenomenon of vanishing technical trading strategies’ profits with the

underlying daily data of most studies. He states that the profits of technical trading

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rules have moved from daily to intraday strategies. With respect to both, Schulmeister’s

findings and Lo’s AMH, it seems essential to analyze intraday price movements when

trying to find momentum profits.

Based on the considerations of the gradual distribution model for new information

on the market, combined with the technological developments within the last decades,

we suppose that the original monthly framework of the momentum strategies is hardly

able to cover the momentum effect in the presence, because the effect should have

transformed to shorter time horizons.

3 Data and Methodology

Our analysis is based on 5-minutes candle quotations (containing open, close,

highest and lowest quotation of each 5-minutes candle) of all 30 DAX 30-stocks being

traded via XETRA from 11/01/2013 to 06/09/2014. We focus on a blue chip stock index

in order to provide adequate market liquidity. Stock prices are adjusted for increase in

capital and dividends. As market proxy, we use an equally weighted stock index

consisting of all stocks listed in the DAX 30 during the period under observation

(DeBondt/Thaler (1985)). Based on the original framework of Jegadeesh/Titman

(1993) we formulate 16 momentum trading strategies, however adopted for intraday-

trading. The duration of the ranking periods (J) and the holding periods (K) are either

15, 30, 45 or 60 minutes. To increase the validity of the results, overlapping analysis

runs are used as proposed in Fuertes/Miffre/Tan (2009), Jegadeesh/Titman (1993) and

Jegadeesh/Titman (2001). By skipping a 5-minutes candle between the end of the

ranking period and the beginning of the holding period, we avoid effects documented

by Jegadeesh (1990) and Lehmann (1990), e.g. price pressure and lagged effects,

which could skew our results. Table I presents the number of 5-minutes-candle

observations, which lies between 15.113 for the setup with the longest ranking and

holding periods (60 minutes per period) and 15.131 for the setup with the shortest

periods (15 minutes per period).

[Insert Table I about here]

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During the ranking period, stocks are graded according to their generated returns at

the end of the ranking period according to Jegadeesh/Titman (1993),

Jegadeesh/Titman (2001) and Rouwenhorst 1998. The stock with the lowest return

represents the loser extreme portfolio that is sold short at the beginning of the holding

period. The stock with the highest return represents the winner extreme portfolio and

is bought at the beginning of the holding period. The gross return of an test run

(cumulative return in a ranking or holding period of T 5-minutes candles in test run i,

TiCR , ) is defined as:

T

t

tLtWTi RRCR0

,,,

tWR , constitutes the 5-minutes return of the winner-portfolio and tLR , that of the loser-

portfolio.

The market-adjusted return of an analysis run (abnormal cumulative return in a

formation or holding period of T 5-minutes candles in test run i, TiCAR , ) is defined as:

T

t

tMtLtWTi RRRCAR0

,,,,

tWR , is the 5-minutes return of the winner-portfolio, tLR , the 5-minutes return of the loser-

portfolio. tMR , is defined as the 5-minutes return of the equally weighted stock index.

We provide robustness checks by testing our results with different portfolio sizes (3

and 6 stocks in the portfolios whereas the respective portfolios are equally weighted)

and different durations (10 and 15 minutes) of the lag between the ends of the ranking

periods and the beginnings of the holding periods.

4 Results

We analyze the profitability of momentum strategies by calculating the average

returns of winner- and loser-portfolios and the momentum-portfolios as a combination

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of both. In our calculations, we vary the length of ranking and holding periods, numbers

of stock included in the portfolios, and the number of five-minutes-periods between the

calculation of the returns in the ranking period and the composition of the portfolios.

We compare the momentum-portfolios’ gross returns with the consequent market-

portfolio to get the excess returns of the momentum strategies. The market return had

been positive at the observed period of time.

Table II shows the average five-minutes returns for loser- and winner-portfolios that

consist of one stock. The first column contains the ranking periods in minutes and the

third, fourth, fifth and sixth column contain the returns for holding periods of 15, 30, 45,

and 60 minutes, respectively. The average five-minutes return of a strategy that, for

example, short sells the worst performing stock of the last 15 minutes for the next 30

minutes would be about -0.00030 percent; meaning that the stock, on average, rises

0.00030% percent every 5 minutes of the 30 minutes of the holding period.

Except for one, returns of all winner-portfolios are positive. But most of them are not

able to outperform the market (except some of the winner-portfolios with either 15

minutes ranking or holding period). Furthermore, most of the winners-portfolios’

average returns are not different from zero at statistical significant levels according to

the results of the t-test. Consequently, we conclude that the former winners do not, on

average, outperform the market in the following periods.

[Insert Table II about here]

In contrast, the negative returns of the loser-portfolios are different from zero at least

at the 5 percent level. Moreover, the absolute value of the loser-portfolios’ negative

average returns is higher than the respective market returns for all parameter

combinations covered in Table II. Returns are most negative for ranking periods of 30

and 45 minutes. With respect to the holding periods, the returns are getting more

negative when the length of the holding periods decreases. We can conclude that the

former loser stocks outperform the market in the following periods at statistical

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significant levels; buying the worst performing stocks instead of selling them, therefore,

would lead to significant positive returns before transaction costs.

Since we follow the traditional approach of short selling former losers and buying

former winners, the momentum portfolios, which consist of the winner- and loser-

portfolios, show negative returns at statistical significant levels. As market returns are

positive in the observed period of time, the momentum portfolios underperform the

market. As gross returns are already negative, we do not adjust them for transaction

costs.

After calculating returns for the best and worst performing stock of the holding

period, we increase the number of stocks in the winner- and loser-portfolios to three

and six, respectively. Results are presented in Table III and support our findings from

above. Again, the winner-portfolios’ returns are not different from zero at statistical

significant levels, except, for a ranking and holding period of 15 minutes. The average

returns for this parameter-combination is more than twice as high as the market return.

[Insert Table III about here]

In contrast, the loser-portfolios show significant negative returns. Furthermore, the

pattern that the winner-portfolios’ returns are most negative for ranking periods of 30

and 45 minutes and are becoming less negative with longer holding periods is

supported for portfolio sizes of three and six stocks. By comparing the loser-portfolios’

negative returns with respect to the stocks included, we can see that the returns move

closer to the market portfolio with the number of stocks included. This leads us to

conclude that the negative returns are mainly caused by maximal three stocks with the

former greatest losses, which outperform the market in the holding period. Due to the

negative returns of the loser-portfolio, the momentum-portfolios’ returns are negative.

Consequently, the momentum strategy underperforms the market.

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We analyze whether the delay between the calculation of the stock returns and the

composition of the portfolio restricts the generality of our results. Table IV presents the

results for the loser-, winner-, and momentum-portfolios where two and three five-

minutes-candles are skipped between the end of the ranking and beginning of the

holding period. Loser- and winner-portfolios contain only one stock.

[Insert Table IV about here]

The results of the former calculations are basically supported. Results for the

winner-portfolios are barely significant according to the t-tests. In contrast, most of the

results of the loser-portfolios are different from zero at the one percent level. The

former described pattern of decreasing negative returns for longer holding periods can

be observed, again. For the most significant ranking periods of 15 and 30 minutes,

returns are more negative when only two instead of three candles are skipped. In all

cases, momentum-portfolios fail to outperform the market.

We interpret the results of Tables II to IV as follows. The winner-portfolios show

returns that are neither different from zero at statistical significant levels nor higher than

the returns of the market-portfolio. A possible explanation for these results can be

found with the positive market sentiment in the analyzed period of time. Since possibly

appearing good news are already considered in stock prices, underpriced stocks are

barely existent (even after the announcement of good news), making it impossible to

gain possible excess returns by buying past winners. This explanation is in line with

the findings of Antoniou/Doukas/Subrahmanyam (2011). They show that momentum

profits in optimistic periods are primarily driven by returns of the loser-portfolios. Due

to the composition of our dataset, we are not able to analyze the momentum strategies

within an opposite (negative) market sentiment. It would be interesting to see, if

additional support for a transformation of the findings of Antoniou/Doukas/

Subrahmanyam (2011) to an intraday-basis could be found.

Our results for the loser stocks are more clearly. In all samples, the former worst

performing stocks reverse with an average return that exceeds the respective market

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return in the holding period. In most cases, returns are different from zero at the one

percent level according to the t-tests. We explain these findings with an overreaction

of stocks in the ranking period, which reversals in the following holding period. Veronesi

(1999) explains such overreactions with the occurrence of bad news in times of

optimistic sentiment. By picking out the loser-portfolios with the most negative returns,

we can quantify the length of such an overreaction period. We state that the

overreaction lasts 30 to 45 minutes. The following reversal of the stock price is most

sharply in the first 15 to 30 minutes after the portfolio composition. Although this

overreaction leads to negative returns for our momentum strategies, it does not

necessarily contradict the idea of momentum in general. It seems possible that, due to

technical innovations, the momentum-period of the Hong/Stein-model became shorter

than 35 minutes, which was the shortest period we analyzed (ranking period of 15

minutes + skip of one five-minutes-candle + holding period of 15 minutes). Therefore,

our dataset is possibly not high-frequent enough to identify these short term

momentum possibilities. Nevertheless, some market participants who use shorter

ranking periods or are able to identify bad news very fast, could be able to ride the

stocks’ overreactions we identified and earn significant momentum profits. We leave

this question to further research.

Since our momentum-portfolios earned negative returns, we did not adjust for

transaction costs. It would be interesting to see, if fast acting market participants like

high frequency traders could earn positive net returns by exploiting the described

overreactions. As the bid-ask spread should account for the largest part of the

transaction costs, it furthermore could be interesting for market makers (who do not

pay spreads) to not hedge their inventory when they identify such an overreaction.

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5 Conclusion

Based on the theory of gradual information distribution on capital markets and the

technological progress, we analyzed the success of intraday momentum strategies

based on the original framework by Jegadeesh/Titman´s (1993, 2001). We suppose a

transformation of the momentum effect from a monthly basis to shorter time horizons

in intraday-trading. We analyzed 16 momentum strategies with ranking periods as well

as holding periods with 15, 30, 45 or 60 minutes. The empirical results show that the

momentum effect, as well as the underreaction phenomenon among market

participants, cannot be observed in intraday-trading. Following that, the validity of the

gradual information model of Chan/Jegadeesh/Lakonishok (1996) and Hong/Stein

(1999) for explaining the success of momentum strategies on a monthly base is

questioned based on our results as well. However, we find indications for reversals in

intraday stock market returns for loser stocks in the past. Our results are robust on

portfolio size and the duration of a lag between the end of ranking period and beginning

the holding period.

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Wu, X. (2002), A Conditional Multifactor Analysis of Return Momentum, in: Journal of Banking

and Finance, Vol. 26, No. 8, pp. 1675-1696.

15

Figure I: Gradual information distribution among market participants in case of good and bad company news

This figure presents the underreation effect of market participants during a new company message is published and the subsequent momentumperiod. On the left side a positive company message is published in T1 and

the stock price (P1) reacts delayed in time until T2 when the price fully reflects all information about the company (P2). On the right side a negative company message spreads lagged on the market.

P

T

Momentumperiod

Underreaction

Effect

T1

P1

P2

T2

P

T

Momentumperiod

T1

P2

P1

T2

Underreaction

Effect

16

Table I: Number of 5-minutes-candle test runs respectively observations

The lines represents the different durations (15, 30, 45 and 60 minutes) of ranking period (J) whereas the rows represents the different durations (15, 30, 45 and 60 minutes) of holding period (K). Following that we analyze

16 momentum strategies. Taking into account that between the ranking period and the holding period a 5 minute lag for rebalancing the portfolios is considered we have the maximum of test runs in the 15/15

momentum strategy with 15.131 observations.

Ranking Period in minutes

Holding Period in minutes (K)

(J) 15 30 45 60

15 15.131 15.128 15.125 15.122

30 15.128 15.125 15.122 15.119

45 15.125 15.122 15.119 15.116

60 15.122 15.119 15.116 15.113

17

Table II: Average 5-minutes- returns for the previous winner and loser stocks in the period

from November 2013 to June 2014

This table presents average 5-minutes-returns in percentages of price momentum portfolio strategies involving DAX 30 stocks from November 2013 to June 2014. At the end of each 5-minute-period, all stocks are ranked in ascending order based on their cumulative returns in the respective ranking period. The length of the ranking period in minutes (J) is 15, 30, 45 or 60 minutes. One 5-minutes-period after the ranking took place, the stock with the highest return in the ranking period is bought for the winner portfolio and the stock with the lowest return in the ranking period is short sold in the loser portfolio. Overlapping portfolios are constructed to increase the power of the tests. K represents the length of the different holding periods for the stocks in the portfolio in minutes. Returns of the winner and loser portfolios are computed for different holding periods of 15, 30, 45 and 60 minutes. The momentum-portfolio is the zero-cost, winner plus loser portfolio. The market returns are computed with the help of an equal weighted portfolio of all DAX 30 stocks. Market returns are subtracted from the gross returns of the momentum-portfolio to compute the momentum-portfolios’ excess returns. T-statistics for 5-minutes-period returns are shown by the symbols ***, ** and *. The symbols denote statistical significance at the one, five and ten percent level, respectively. The loser-portfolio with a ranking period of 15 minutes and a holding period of 30 minutes, for example, contains a short-position in the stock with the worst return in the ranking period. The average 5-minutes-return of the short-position is -0.0003 percent, which means that the stock-price increased 0.0003 percent per five minutes on average. The average 5-minutes-return is different from zero with a statistical significance at the one percent level.

Ranking Period

in minutes (J)

Holding Period (K) in minutes

Portfolio 15 30 45 60

15 Loser-P. -0,00046* -0,00030*** -0,00018*** -0,00009***

Winner-P. 0,00044* 0,00006 0,00007 0,00007**

Gross Momentum-P. -0,00003 -0,00024** -0,00011* -0,00002

Market Return 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00019 -0,00033*** -0,00018*** -0,00008*

30 Loser-P. -0,00107*** -0,00053*** -0,00025*** -0,00019***

Winner-P. 0,00037 -0,00001 0,00001 0,00004

Gross Momentum-P. -0,00071*** -0,00054*** -0,00024*** -0,00015***

Market Return 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00087** -0,00064*** -0,00031*** -0,00020***

45 Loser-P. -0,00104*** -0,00051*** -0,00031*** -0,00023***

Winner-P. 0,00025 0,00008 0,00006 0,00004

Gross Momentum-P. -0,00079** -0,00044*** -0,00025*** -0,00019***

Market Return 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00095** -0,00054*** -0,00032*** -0,00024***

60 Loser-P. -0,00062** -0,00044*** -0,00028*** -0,00020***

Winner-P. 0,00007 0,00009 0,00007 0,00004

Gross Momentum-P. -0,00056 -0,00035*** -0,00021*** -0,00016***

Market Return 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00072* -0,00045*** -0,00028*** -0,00021***

18

Table III: Average 5-minutes-returns of momentum portfolios with three and six winner and loser stocks in the period from November 2013 to June 2014

This table presents average 5-minutes-returns in percentages of price momentum portfolio strategies involving DAX 30 stocks from November 2013 to June 2014. At the end of each 5-minute-period, all stocks are ranked in ascending order based on their cumulative returns in the respective ranking period. The length of the ranking period in minutes (J) is 15, 30, 45 or 60 minutes. One 5-minute-period after the ranking took place, the three (six) stocks with the highest return in the ranking period are bought for the winner portfolio and the three (six) stocks with the lowest return in the ranking period are short sold in the loser portfolio. Overlapping portfolios are constructed to increase the power of the tests. K represents the length of the different holding periods for the stocks in the portfolio in minutes. Returns of the winner and loser portfolios are computed for different holding periods of 15, 30, 45 and 60 minutes. The momentum-portfolio is the zero-cost, winner plus loser portfolio. The market returns are computed with the help of an equal weighted portfolio of all DAX 30 stocks. Market returns are subtracted from the gross returns of the momentum-portfolio to compute the momentum-portfolios’ excess returns. T-statistics for 5-minutes-period returns are shown by the symbols ***, ** and *. The symbols denote statistical significance at the one, five and ten percent level, respectively. The loser-portfolio with six short sold stocks, a ranking period of 15 minutes and a holding period of 30 minutes, for example, contains a short-position in the six stocks with the worst return in the ranking period. The average 5-minutes-return of the short-positions is -0.00019 percent, which means that the price of the six stocks increased 0.00019 percent per five minutes on average. The average 5-minutes-return is different from zero with a statistical significance at the one percent level.

Ranking Period (J) in

minutes

Holding Period (K) for three winner and loser stocks in

minutes

Holding Period (K) for six winner and loser stocks in

minutes

Portfolio 15 30 45 60 15 30 45 60

15 Loser-P. -0,00011 -0,00022*** -0,00015*** -0,00010*** -0,00013 -0,00019*** -0,00013*** -0,00010***

Winner-P. 0,00047*** 0,00007 0,00004 0,00004* 0,00039*** 0,00007 0,00003 0,00003*

Gross Momentum-P. 0,00035** -0,00015** -0,00011*** -0,00006*** 0,00026** -0,00013*** -0,00010*** -0,00006***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. 0,00019 -0,00025*** -0,00018*** -0,00012*** 0,00010 -0,00022*** -0,00017*** -0,00012***

30 Loser-P. -0,00056*** -0,00036*** -0,00020*** -0,00015*** -0,00040*** -0,00029*** -0,00017*** -0,00014***

Winner-P. 0,00004 -0,00003 0,00001 0,00001 0,00007 -0,00002 0,00001 0,00001

Gross Momentum-P. -0,00052*** -0,00039*** -0,00019*** -0,00014*** -0,00034*** -0,00030*** -0,00017*** -0,00012***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00069*** -0,00049*** -0,00026*** -0,00020*** -0,00050*** -0,00040*** -0,00023*** -0,00018***

45 Loser-P. -0,00067*** -0,00035*** -0,00023*** -0,00017*** -0,00054*** -0,00030*** -0,00019*** -0,00014***

Winner-P. 0,00006 -0,00000 0,00002 0,00002 -0,00007 -0,00001 -0,00000 0,00000

Gross Momentum-P. -0,00061*** -0,00035*** -0,00021*** -0,00016*** -0,00060*** -0,00031*** -0,00019*** -0,00014***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005


60 Loser-P. -0,00058*** -0,00037*** -0,00023*** -0,00016*** -0,00052*** -0,00030*** -0,00020*** -0,00015***

Winner-P. 0,00002 -0,00001 0,00000 0,00000 -0,00002 0,00000 -0,00000 0,00001

Gross Momentum-P. -0,00056 -0,00038*** -0,00022*** -0,00016*** -0,00053*** -0,00030*** -0,00020*** -0,00015***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00010


19

Table IV: Average 5-minutes-period returns for the delayed in time winner and loser stocks in the period from November 2013 to June 2014

This table presents average 5-minutes-returns in percentages of price momentum portfolio strategies involving DAX 30 stocks from November 2013 to June 2014. At the end of each 5-minute-period, all stocks are ranked in ascending order based on their cumulative returns in the respective ranking period. The length of the ranking period in minutes (J) is 15, 30, 45 or 60 minutes. Two (three) 5-minute-periods after the ranking took place, the stock with the highest return in the ranking period is bought for the winner portfolio and the stock with the lowest return in the ranking period is short sold in the loser portfolio. Overlapping portfolios are constructed to increase the power of the tests. K represents the length of the different holding periods for the stocks in the portfolio in minutes. Returns of the winner and loser portfolios are computed for different holding periods of 15, 30, 45 and 60 minutes. The momentum-portfolio is the zero-cost, winner plus loser portfolio. The market returns are computed with the help of an equal weighted portfolio of all DAX 30

stocks. Market returns are subtracted from the gross returns of the momentum-portfolio to compute the momentum-portfolios’ excess returns. T-statistics for 5-minutes-period returns are shown by the symbols ***, ** and *. The symbols denote statistical significance at the one, five and ten percent level, respectively. The loser-portfolio, for example, with a ranking period of 15 minutes and a holding period of 30 minutes, which starts three 5-minutes-periods after the ranking period, contains a short-position in the stock with the worst return in the ranking period. The average 5-minutes-return of the short-position is -0.0003 percent, which means that the stock-price increased 0.0003 percent per five

minutes on average. The average 5-minutes-return is different from zero with a statistical significance at the one percent level.

Ranking Period (J) in

minutes

Holding Period (K) two periods after ranking

Holding Period (K) three periods after ranking

Portfolio 15 30 45 60 15 30 45 60

15 Loser-P. -0,00035 -0,00032*** -0,00015*** -0,00010*** -0,00052** -0,00030*** -0,00011** -0,00011***

Winner-P. 0,00047* 0,00012 0,00010** 0,00008** -0,00006 0,00006 0,00009* 0,00006*

Gross Momentum-P. 0,00012 -0,00020* -0,00005 -0,00002 -0,00059* -0,00024** -0,00002 -0,00005

Market Return 0,00016 0,00010 0,00007 0,00005 0,0001 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00005 -0,00030** -0,00012* -0,00007* -0,00075** -0,00034*** -0,00009 -0,00010**

30 Loser-P. -0,00103*** -0,00045*** -0,00022*** -0,00018*** -0,00094*** -0,00029*** -0,00019*** -0,00017***

Winner-P. 0,00013 -0,00002 0,00003 0,00004 -0,00019 -0,00011 0,00002 0,00003

Gross Momentum-P. -0,00090*** -0,00048*** -0,00020*** -0,00014*** -0,00114*** -0,00040*** -0,00017*** -0,00014***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005


45 Loser-P. -0,00085*** -0,00046*** -0,00028*** -0,00022*** -0,00084*** -0,00042*** -0,00027*** -0,00022***

Winner-P. 0,00015 0,00007 0,00007 0,00006* -0,00015 -0,00001 0,00004 0,00004

Gross Momentum-P. -0,00070** -0,00039*** -0,00021*** -0,00017*** -0,00099*** -0,00043*** -0,00024*** -0,00018***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00087** -0,00049*** -0,00028*** -0,00022*** -0,00116*** -0,00053*** -0,00030*** -0,00024***

60 Loser-P. -0,00072** -0,00041*** -0,00027*** -0,00021*** -0,00096*** -0,00041*** -0,00028*** -0,00021***

Winner-P. 0,00010 0,00011 0,00006 0,00005 0,00002 0,00009 0,00005 0,00005

Gross Momentum-P. -0,00062* -0,00030** -0,00021*** -0,00016*** -0,00094*** -0,00032*** -0,00023*** -0,00016***

Market Return 0,00016 0,00010 0,00007 0,00005 0,00016 0,00010 0,00007 0,00005

Excess Return Momentum-P. -0,00078** -0,00039*** -0,00027*** -0,00021*** -0,00110*** -0,00042*** -0,00030*** -0,00021***

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