1
Momentum investment performance and evaluation, gap, and
holding period
Riccardo ParrelloUniversity of Groningen
Abstract
In this paper, we examine the influence of the evaluation, gap, and holding period on the performance of momentum investment strategies. All combinations of strategies with an evaluation period between 1 and 12 months, a gap period between 0 and 12 months, and a holding period between 1 and 12 months, in steps of 1 month each, are examined. Their performance is evaluated during the period 2000-2010 on all stocks traded on the NYSE and NASDAQ. Contrary to our expectations, we find none of the momentum strategies to provide a positive risk adjusted return. However, many strategies with a statistically significant negative risk adjusted return are found. Therefore, we argue that it is better to utilize a contrarian investment strategy in the current period. We examine the returns of two strategies in more detail, one momentum strategy that performed poorly because of short-term reversals and one that performed poorly because of long-term reversals. We see that the negative returns of the first strategy are likely related to the financial crises in the examined period, while the second strategy performed poorly consistently. We simulate investing using these two strategies from 2011 to 2016 and find that both eventually provide a negative return. Thus, if contrarian versions of these strategies would have been used a positive return, especially for the strategy based on long-term reversals, would have been obtained. Furthermore, we argue that both strategies would have performed significantly better if no short position would be acquired.
Key words: Momentum investing, Contrarian investing, Evaluation period, Gap period,
Holding period, USA
JEL Classification: G11
MSc Finance Thesis
Riccardo Parrello (s2244640)
Supervisor: Jochen Mierau
Number of words: 7089
2 1. Introduction
Momentum investment strategies aim to benefit from the possibility that stocks that have performed well in the past continue to perform well and stocks that have performed poorly in the past continue to perform poorly. The original momentum investment strategy proposed by Jegadeesh and Titman (1993) buys the best performing stocks and sells the worst performing stocks based on their performance in the so-called “evaluation period”, after which this position is held for a number of months known as the “holding period”, leading to a profit if momentum is present in stock prices. Many variations of this basic strategy can be thought of, including using different lengths for the evaluation period, holding period, and the period than can be added in between these two periods, which we will refer to as the “gap period”. The influence of the lengths of these three periods on the performance of momentum investing is the focus of this paper.
Ever since momentum investing was shown to generate abnormal returns (see e.g. Jegadeesh and Titman, 1993), it has been a widely used investment strategy. For instance, there are numerous exchange traded funds that specifically utilize momentum investment strategies (ETF Database, 2016). Furthermore, Edwards et al. (2006) find evidence that individual investors as well as professional analysts also engage in momentum investing. Since so many investors use momentum investment strategies it is important to study the performance of these kind of strategies along with potential ways to improve their performance. For instance, if ways to improve momentum investing performance would be found investors could implement these changes improving the performance of their own portfolios. On the other hand, momentum investing might be found to be less profitable than it used to be and therefore investors might be better off switching to other investment strategies.
3 In order to find the ideal combination of the evaluation, gap, and holding periods, this study will examine the performance of all momentum investment strategies with an evaluation period between 1 and 12 months, a gap period between 0 and 12 months, and a holding period between 1 and 12 months, all in steps of 1 month, leading to a total of 1872 different strategies being examined. Previous studies, such as Jegadeesh and Titman (1993), have studied the effect of different lengths for each of these three periods, however in much less detail. We will focus on the performance of these strategies on the equity market in the United States, during the period from 2000 to the end of 2010. Besides the raw performance of each strategy, we will also calculate the risk adjusted returns using the Carhart (1997) four-factor model. Furthermore, we will elaborate on the most interesting strategies by presenting their performance during each year of the examined period separately and will examine their out-of-sample performance by simulating investing using these strategies starting in 2011 and continuing until 2016.
The rest of this paper is organized as follows. Section 2 presents a review of the current literature on momentum investing relevant to our study. Section 3 explains the methodology we will use and Section 4 describes the collection of our data. Section 5 follows with our results and Section 6 provides our conclusion.
2. Literature review
The literature review is split into three sections. The first section discusses the profitability of momentum investment strategies. Section 2 presents a discussion on the ideal evaluation, gap, and holding period. Section 3 closes with a short conclusion and presents our hypothesis.
2.1. Performance of momentum investment strategies
4 and Titman’s strategy for 12 European countries and finds the strategy to perform similarly in these countries as it does in the United States. Secondly, Griffin et al. (2003) and Chui et al. (2010) find momentum investing to yield positive returns in most large markets, with some exceptions mainly in Asia. Both Griffin et al. and Chui et al. confirm the finding that momentum profits reverse after 1 year. Recent research by Groot et al. (2012) shows that momentum investment strategies also generate abnormal returns in frontier emerging markets, even when a conservative estimation of transaction costs is incorporated.
Many of the variations on the basic momentum investment strategy have also been found to be perform well, providing additional support to the previous evidence. Grinblatt and Moskowitz (1999) find that momentum investing based on industries yields returns similar to the returns of the standard momentum investing strategy based on individual equities. George and Hwang (2004) compare the returns of the basic momentum investment strategy, the industry momentum investment strategy, and their own week high momentum investment strategy and find the 52-week high momentum investment strategy to perform about twice as well as the other two strategies. Furthermore, they find that the returns obtained using this strategy do not reverse in the long run. However, Gupta et al. (2010) find that, although the 52-week high momentum strategy is profitable, it does not perform as well as the standard momentum strategy. Bird and Whitaker (2004) find that momentum investing and value investing complement each other and therefore a combination of these two strategies performs exceptionally well. The strategy they find to perform the best shorts expensive losers and longs cheap losers, instead of longing cheap winners as might have been expected.
It is important to note that the previously discussed studies, except for Groot et al. (2012), do not take into account the transaction costs associated with performing the strategies. Therefore, the actual performance of these strategies might not be as high as argued. However, in their examination of low-cost momentum strategies, Brooks et al. (2009), Ammann et al. (2011) and Foltice and Langer (2015) do take into account transaction costs and find these cost-saving momentum investment strategies still to be profitable when transaction costs are included.
5 than half of the momentum profits found by Jegadeesh and Titman (2001) in the late 1990s were driven by the high-tech and telecom bubble. Similarly, Hammami (2013) argues that momentum profits are only significant in periods of good business conditions and that the profitability of momentum investment strategies completely disappeared after the year 2000. These findings are consistent with momentum being caused by a market inefficiency which especially emerged in good times.
2.2. Ideal evaluation, gap, and holding period
The ideal combination of evaluation, gap, and holding period has not been studied in the same depth as we do in this study before. Most studies on momentum investing focus on only a couple of combinations of these three periods, as the main focus of these studies lies on another aspect of momentum investing. The most commonly examined strategy is one with a 6-month evaluation period and a 6-month holding period, with either a 1-month gap period or no gap period (see e.g., Chui et al., 2010; Griffin et al., 2003; Jegadeesh and Titman, 2011).
One of the more elaborate studies considering the effect of the evaluation and the holding period on the performance of momentum strategies is Jegadeesh and Titman (1993). In this study all strategies with an evaluation period between 3 and 12 months and a holding period between 3 and 12 months, both in steps of 3 months, and with or without a gap period of 1 week are examined, for a total of 32 different strategies. The reason given to include a 1-week gap period is that this way some of the bid-ask spread, price pressure, and lagged reaction effects are avoided. They find a strategy with a 12-month evaluation period, 1-week gap period, and 3-month holding period to perform the best. The same approach is followed by Rouwenhorst (1998), who finds a strategy with a 9-month evaluation period, 1-month gap period, and 3-month holding period to perform the best. From these studies we can see that generally a longer evaluation period and a shorter holding period lead to a higher return. Also, including a gap period seems to increase the return of the strategy.
6 2.3. Conclusion and hypothesis
There is a large amount of evidence confirming momentum investment strategies to be profitable. A longer evaluation period and a shorter holding period generally seem to increase the performance of momentum investing strategies. Furthermore, we see that a longer gap period also can improve performance. Therefore, we form the following hypothesis:
“The ideal momentum investment strategy has a long evaluation period, a long gap period, and a short holding period.”
It is difficult to exactly predict the ideal lengths for each period, however by examining all possible combinations we should be able to pinpoint these values. On the other hand, as it has been argued that momentum profits in the past were due to a market efficiency that especially occurred during good times, it is also very well possible that the momentum strategies turn out to perform not so well anymore in the examined period.
3. Methodology
We examine all possible momentum strategies with an evaluation period between 1 and 12 months, a gap period between 0 and 12 months, and a holding period between 1 and 12 months, each with steps of one month. This provides a total of 1872 strategies, in contrast to other studies which usually focus on only a couple of strategies.
7 this overlap increases the power of the tests. The total monthly strategy return is equal to the return on the bought portfolios minus the return on the sold portfolios. The reported raw average return of a strategy is equal to the simple average of all monthly returns of this strategy during the examined period.
Furthermore, we will calculate the risk adjusted returns for each strategy using the Carhart (1997) four-factor model. This model is specified as follows:
− = + − + + ℎ + + (1)
is the return of the momentum strategy at the beginning of month t and is equal to the one-month Treasury bill rate at the beginning of month t. stands for the market return at time t, and , , stand for the size, value and momentum premium at time t, respectively. The coefficients b, s, h and m show the exposure of the strategy to their respective risk factors, while a equals the average risk adjusted return of the strategy. As this model incorporates the momentum premium, the average risk adjusted return shows the performance of our momentum strategies relative to the standard momentum strategy used to calculate the momentum premium.
8 Finally, we can calculate the values for the size and value premium using these returns. The size premium at time t is defined as the difference between the simple average of the returns of the three small-stock portfolios at time t and the simple average of the returns of the three big-stock portfolios at time t. The value premium at time t is the difference between the simple average of the returns on the two high-book-to-market equity portfolios at time t and the simple average of the returns on the two low-book-to-market equity portfolios at time t. We follow the methodology from Carhart (1997) in calculating the momentum premium. The momentum premium at time t is equal to the return of a 11-month evaluation period, 1-month gap period, and 1-month holding period momentum strategy that invests in the top 30% performing stocks and shorts the 30% worst performing stocks, using an equal weighting, at time t.
All our return calculations are based on the return index available from Datastream instead of the actual price, as this index takes into account the dividends that have been paid out and therefore better reflects the real return. As the holding periods overlap, possibly causing serial correlation, we use Newey-West standard errors (also used in e.g., Bird and Whitaker, 2004; Chui et al., 2010; Groot et al., 2012) with a maximum lag length equal to the number of previous returns that might be correlated with the current one, which equals the holding period minus 1, in order to calculate the statistical significance of the average risk adjusted returns.
Furthermore, we will present the performance of the most interesting strategies on a yearly basis. The raw yearly return for a strategy is equal to the simple average of the monthly returns of the strategy in that year. The risk adjusted return in each year is calculated by estimating the Carhart four-factor model specifically for that year. Lastly, we will simulate investing using these strategies starting at 1-1-2011 and continuing until 1-1-2016. For strategies with overlapping holding periods, the initial investment is equally split between the multiple positions. Additionally, we simulate investing in a risk-free asset, in our case 1-month Treasury bills, and investing in the market portfolio, equal to the market portfolio used in our Carhart four-factor model calculations. Our simulation assumes that all profits are reinvested directly.
4. Data
9 sample naturally comprises less stocks. The performance of the strategies is examined over the 11-year period from 2000 to the end of 2010. As we only want to investigate their performance when the maximum amount of overlapping holding periods is achieved, data is collected from 1997 onwards to make sure each strategy has achieved the maximum amount of overlap at the beginning of 2000. Furthermore, data is collected up to 2016 in order to be able to perform our out-of-sample simulations.
For each stock, both the price and the return index are collected from Datastream. The price is used for the value weighting necessary for some of the portfolios in the Carhart four-factor model. Furthermore, the size and book value of common stock are collected for all stocks. Size (ME) is defined as the market value of equity, which is equal to the share price multiplied by the number of ordinary shares issued. The book value of common stock (BE) is defined as the common shareholders' investment in a company, which not only includes the common stock value, but also other important items such as the retained earnings and the capital surplus. We also collect the risk-free rate for each month which is defined as the first available 1-month constant maturity Treasury bill rate of that month, available from the Federal Reserve (2016). For the period before august 2001, for which the 1-month rate is not available, the 3-month rate is collected instead.
Table 1 presents descriptive statistics of all stocks in our sample at the first available date.
Table 1. Descriptive statistics
Variable Observations Mean deviation Standard Median Minimum Maximum
Price ($) 1975 168.02 3,027.33 11.75 0.07 93,088.19
ME (million $) 1975 2,957.00 10,914.34 302.65 0.01 162,789.80
BE (million $) 1643 1,391.76 4,526.94 198.49 -2,734.84 60,152.02
Descriptive statistics of all stocks in our sample at 1/1/1997. ME stands for size, BE stands for book value of common stock.
5. Results
As the results are very extensive, we will summarize them in this section. The full results can be found in the appendices.
10 period, together with a short evaluation and holding period. The best performing strategy, with a 1-month evaluation period, 6-1-month gap period, and 1-1-month holding period, yields a return of 0.92% per month. It is unclear why these strategies yield a positive return. One possible reason is that a seasonality exists in stock prices, causing stocks to perform well every half year and not so well in between. Interestingly, many strategies generate a quite substantial negative return, often losing more than 3% per month. The worst performing strategy has an evaluation period of 11 months, a gap period of 11 months, and a holding period of 2 months, and loses 5.60% per month. Therefore, it currently might be better to use a contrarian investment strategy, selling stocks that have performed well in the past and buying stocks that have performed poorly in the past, as this leads to the opposite payoff of momentum investing and therefore should lead to a positive return. Table 2 presents the average of the average raw returns for all strategies with the specified evaluation, gap, or holding periods, to indicate the general effect of the lengths of each of these periods on the performance of momentum investing. We can see that generally a longer evaluation period, a longer gap period, and a shorter holding period lead to a worse performing momentum strategy, contrary to our hypothesis. However, this implies that contrarian strategies benefit from having a longer evaluation period, a longer gap period, and a shorter holding period.
Table 2. Average of average raw returns per specified period length
Length
Period 0 1 2 3 4 5 6 7 8 9 10 11 12
Evaluation - -0.79 -1.21 -1.47 -1.60 -1.90 -2.19 -2.37 -2.54 -2.70 -2.94 -3.17 -3.47
Gap -1.86 -1.69 -1.70 -1.66 -1.70 -1.74 -1.77 -2.21 -2.60 -2.81 -2.86 -2.99 -2.94
Holding - -2.53 -2.56 -2.53 -2.41 -2.23 -2.16 -2.05 -1.98 -1.96 -1.98 -1.98 -1.98
Average (in %) of all average raw returns for all strategies with the specified evaluation, gap or holding period length.
11 by bad economic conditions leading to a bad performance of the market overall. Therefore, we will analyze the risk adjusted returns which better measure the performance of the strategies.
The risk adjusted returns show a pattern similar to the unadjusted returns. Most of the risk adjusted returns are negative, and many of these negative returns are statistically significant. From table 3 we can see that generally a longer evaluation period and a longer gap period again lead to worse performing strategies. There does not seem to be a clear pattern in the influence of the holding period on the performance, however the worst performing strategies do have a shorter holding period ranging between 2 to 4 months. Although we see a bigger number of strategies with positive risk adjusted returns, 63 in total, none of these returns are statistically significant. Furthermore, we find that the average momentum premium, corrected for the other factors, is equal to -1.01%. Therefore, we conclude that in the examined period momentum investing is not a profitable strategy, no matter which combination of evaluation, gap, and holding period is chosen.
Table 3. Average of average risk adjusted returns per specified period length
Length
Period 0 1 2 3 4 5 6 7 8 9 10 11 12
Evaluation - -0.59 -0.84 -0.96 -1.04 -1.18 -1.42 -1.59 -1.73 -1.85 -2.07 -2.31 -2.61
Gap -0.96 -0.78 -0.78 -0.73 -0.83 -0.99 -1.20 -1.57 -1.94 -2.31 -2.41 -2.59 -2.62
Holding - -1.37 -1.49 -1.53 -1.53 -1.46 -1.47 -1.47 -1.47 -1.50 -1.58 -1.64 -1.66
Average (in %) of all average risk adjusted returns for all strategies with the specified evaluation, gap or holding period length.
12 strategy generates a large negative average risk adjusted return of -1.86% per month, significant at the 5% significance level. Furthermore, it is also the simplest strategy, and therefore easy to implement. Secondly, we find that momentum strategies with longer evaluation and gap periods and a holding period between 2 and 4 months perform very poorly. We find the worst performing momentum strategy to have an 11-month evaluation period, 11-month gap period, and 2-month holding period, leading to an average risk adjusted return of -4.85% per month, statistically significant at the 1% significance level. Therefore, we also find evidence of long term reversals, and argue that a contrarian strategy with a 11-month evaluation period, 11-month gap period, and 2-month holding period is ideal to take advantage of these reversals.
Many causes for the reversals we have found can be thought of. For instance, they are consistent with an overreaction in the market to firm-specific information. Overreaction to positive information causes stocks to be priced above their fundamental value. Eventually, this will lead to negative returns when the prices return to their true underlying value. Similarly, overreaction to negative information causes stocks prices to drop below their fundamental value, and this will eventually lead to positive returns when corrected. However, trying to find the exact reason behind these reversals is outside of the scope of this paper.
13
Table 4. Yearly returns for worst performing strategies
Table 5 presents our simulation of investing in the two previously discussed momentum strategies, split into their buy and sell portfolios, starting at 1-1-2011 and ending at 1-1-2016. The initial investment is $1,000,000 in both the buy and the sell portfolio for both strategies. The payoff for the discussed contrarian strategies are equal to the opposite of the momentum strategy payoffs with the same evaluation, gap, and holding periods. We see that both momentum strategies end up losing money, and therefore the contrarian versions of these strategies would indeed have been profitable, as expected. However, we see that the contrarian strategy with a 1-month evaluation period, no gap period, and 1-month holding period, is quite a risky strategy, with the total payoff being negative for a long time before it finally becomes positive. Furthermore, the total payoff of $62,262 is not very high for the amounts invested. Interestingly, we see that both the buy and the sell portfolio perform very well independently. Therefore, it seems that buying one or both of these portfolios without acquiring any short position is a significantly better strategy. If money would be needed to invest, borrowing would be the best option, assuming the interest rate would not be much higher than the risk-free rate. We can see that the 11-month evaluation period, 11-month gap, and 2-month holding period momentum strategy indeed performed poorly and therefore the contrarian version of this strategy would have been quite profitable, earning a profit of $549,281 in 5 years. It is clear that the portfolio with past winners underperforms the market and the portfolio with the past losers outperforms the market. However, the past winners still gain in value and therefore it would
Strategy 1-0-1 Strategy 11-11-2
Year Raw Adjusted Raw Adjusted
2000 0.61 4.90 -4.64 -3.77 2001 -6.79 0.17 -14.15 -16.31 2002 -3.21 -9.41 -1.32 -2.10 2003 -1.24 -2.06 -6.43 -0.24 2004 -1.83 -2.43 -3.35 -3.54 2005 -0.59 -0.14 -9.53 -9.66 2006 -0.73 -0.62 -0.23 -0.42 2007 2.56 1.94 -0.58 -0.90 2008 -4.52 -6.12 -0.66 -1.47 2009 -5.59 -7.58 -18.18 3.55 2010 -1.13 -0.59 -2.52 -2.70
14 have been even better not to short this portfolio. Again, if money would be required to invest, borrowing would have been a better option.
Table 5. Out-of-sample simulation of investment strategies
Date Risk-free Market 1-0-1 Buy 1-0-1 Sell 1-0-1 11-11-2 Buy 11-11-2 Sell 11-11-2
1-1-2011 1,000,000 1,000,000 1,000,000 1,000,000 0 1,000,000 1,000,000 0 1-1-2012 1,000,525 926,982 1,374,114 943,988 430,127 871,046 969,506 -98,461 1-1-2013 1,001,151 1,060,668 1,538,830 1,368,855 169,975 1,041,558 1,338,906 -297,348 1-1-2014 1,001,559 1,382,174 2,377,131 2,181,068 196,064 1,460,582 2,421,971 -961,389 1-1-2015 1,001,793 1,465,439 2,416,342 2,078,555 337,787 1,518,454 2,376,599 -858,145 1-1-2016 1,002,077 1,418,195 1,948,626 2,010,889 -62,262 1,352,514 1,901,795 -549,281
Simulation of investing in a risk-free asset (1-month Treasury bills), the market portfolio, a momentum strategy with a 1-month evaluation period, no gap period, and 1-month holding period (1-0-1), and a momentum strategy with an 11-month evaluation period, 11-month gap period, and 2-month holding period (11-11-2). The payoffs for both momentum strategies are split into their buy and sell portfolios. The payoffs for contrarian strategies using the same evaluation, gap, and holding periods as the momentum strategies are the opposite of those from the momentum strategies.
Our simulation provides interesting insights on momentum and contrarian investing. We find that on the short term, both losers and winners will end up performing very well, which might be caused by the fact that big winners and losers receive more attention. Furthermore, we find that on the long term losers will end up performing very well, which might be caused by an overreaction only to negative firm-specific information. Thus, the strategies that we find to be ideal based on our simulation do not acquire any short position, in contrast to the standard momentum investing strategies. It would be interesting to investigate this further to see if these results are consistent throughout time.
6. Conclusion
15 performance of the most interesting strategies on a yearly basis and performed an out-of-sample simulation to see how well they performed during 2011 to 2016.
Unexpectedly, we found none of the examined momentum strategies to yield a positive risk adjusted return. However, many strategies generated a statistically significant negative risk adjusted return. We find that generally a longer evaluation period, a longer gap period, and a shorter holding period lead to worse performing momentum strategies, contrary to our hypothesis. Based on our findings, we argue that it might be better to use a contrarian investment strategy instead of a momentum investment strategy. We find two types of contrarian strategies that should provide a positive return, one based on short-term reversals and one on long-term reversals. We argue that the ideal contrarian strategy to take advantage of the short-term reversals is one with a 1-month evaluation period, no gap period, and 1-month holding period, as the momentum version of this strategy generates a large negative average risk adjusted return of -1.86% per month, significant at the 5% significance level, and it also is a very simple strategy. Furthermore, we argue that the best contrarian strategy to take advantage of the long term reversals has a 11-month evaluation period, 11-month gap period, and 2-month holding period, because the momentum version of this strategy is the worst performing strategy we have found with an average risk adjusted return of -4.85% per month, statistically significant at the 1% significance level.
When investigating the performance of the previously mentioned momentum strategies on a yearly basis, we find that the performance of the strategy with a 1-month evaluation period, no gap period, and 1-month holding period seems to be related to the economic circumstances, and therefore the poor performance is likely to be driven by the economic crises that happened during the examined period. Therefore, we expected this strategy to perform less poorly out-of-sample. On the other hand, the strategy with a 11-month evaluation period, 11-month gap period, and 2-month holding period seems to perform poorly consistently, and therefore we expected it also to perform poorly in our out-of-sample simulation.
16 both winners and losers will end up generating positive returns. Therefore, a strategy that only buys winners or losers without going short in one of these portfolios should lead to a substantial positive return.
For future research, it would be interesting to investigate the performance of both the buy and the sell portfolios of momentum investing strategies independently in more depth, as we have found evidence that these portfolios might perform better individually than together. Another interesting possibility would be to investigate the effect of the percentiles of stocks chosen to buy and sell. For example, instead of the top and bottom decile the second highest and lowest decile might be chosen. As the performance of the stocks in these percentiles might not be as noticeable compared to the stocks in the top and bottom deciles, perhaps reversals happen less often or not as quickly, and therefore momentum strategies based on these deciles might be profitable in contrast to the momentum strategies examined in this study.
This study has a number of limitations. First, we have only examined momentum strategies using all the stocks available on the market. However, certain types of stocks might experience more or less momentum than others. Second, we do not take into account transaction costs, which means that the real performance of the strategies we have examined is lower than argued. Lastly, we have only examined the basic strategy outlined by Jegadeesh and Titman (1993), although different momentum investment strategies exist that might have performed better.
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19 Appendices
Appendix A: Raw momentum strategy returns
Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -2.04 -1.90 -1.50 -1.39 -1.25 -1.07 -0.78 -0.77 -0.61 -0.62 -0.57 -0.56 2 -1.84 -2.23 -1.97 -2.02 -1.78 -1.37 -1.16 -1.03 -0.87 -0.80 -0.74 -0.81 3 -2.59 -2.48 -2.62 -2.51 -1.99 -1.58 -1.20 -1.03 -0.88 -0.84 -0.86 -0.94 4 -2.79 -2.98 -2.87 -2.51 -2.00 -1.51 -1.22 -1.06 -0.98 -0.99 -1.03 -1.07 5 -3.10 -3.14 -2.87 -2.51 -1.84 -1.51 -1.24 -1.08 -1.01 -1.08 -1.11 -1.15 6 -3.24 -3.11 -2.96 -2.50 -1.95 -1.61 -1.37 -1.28 -1.24 -1.28 -1.29 -1.32 7 -3.06 -3.00 -2.59 -2.32 -1.80 -1.54 -1.43 -1.34 -1.30 -1.34 -1.38 -1.50 8 -3.09 -2.78 -2.60 -2.38 -1.87 -1.67 -1.55 -1.45 -1.37 -1.43 -1.45 -1.57 9 -2.50 -2.66 -2.47 -2.33 -1.94 -1.77 -1.61 -1.50 -1.49 -1.56 -1.56 -1.69 10 -2.94 -2.85 -2.60 -2.53 -2.11 -1.89 -1.71 -1.65 -1.64 -1.68 -1.80 -1.98 11 -3.01 -2.98 -2.90 -2.78 -2.29 -2.06 -1.92 -1.83 -1.79 -1.96 -2.14 -2.24 12 -3.09 -3.24 -3.19 -3.04 -2.55 -2.33 -2.14 -2.10 -2.12 -2.34 -2.43 -2.52
Average monthly returns (in %) for momentum investment strategies with a 0-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -0.82 -0.78 -0.88 -0.96 -0.82 -0.37 -0.42 -0.28 -0.30 -0.28 -0.26 -0.34 2 -1.83 -2.09 -2.13 -1.96 -1.39 -1.02 -0.85 -0.66 -0.59 -0.56 -0.61 -0.70 3 -1.71 -2.53 -2.60 -2.16 -1.54 -1.07 -0.94 -0.76 -0.72 -0.76 -0.84 -0.88 4 -2.26 -2.79 -2.61 -2.17 -1.46 -1.07 -0.98 -0.79 -0.86 -0.90 -0.98 -1.00 5 -2.29 -2.67 -2.53 -1.92 -1.42 -1.13 -1.02 -0.93 -1.01 -1.07 -1.12 -1.15 6 -2.28 -2.64 -2.44 -2.00 -1.51 -1.25 -1.16 -1.13 -1.19 -1.21 -1.27 -1.37 7 -2.33 -2.42 -2.36 -1.94 -1.49 -1.35 -1.30 -1.21 -1.25 -1.31 -1.46 -1.49 8 -1.92 -2.49 -2.45 -2.01 -1.63 -1.49 -1.45 -1.32 -1.38 -1.44 -1.58 -1.73 9 -2.39 -2.71 -2.63 -2.36 -1.94 -1.75 -1.63 -1.56 -1.61 -1.63 -1.77 -1.95 10 -2.40 -2.71 -2.77 -2.45 -1.99 -1.79 -1.74 -1.67 -1.69 -1.86 -2.05 -2.14 11 -2.46 -3.06 -3.09 -2.70 -2.20 -2.04 -1.95 -1.84 -1.95 -2.16 -2.28 -2.35 12 -2.94 -3.38 -3.36 -2.96 -2.50 -2.33 -2.28 -2.24 -2.39 -2.50 -2.61 -2.62
20 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -0.88 -1.38 -1.39 -1.16 -0.48 -0.43 -0.25 -0.22 -0.20 -0.21 -0.29 -0.41 2 -1.29 -1.96 -2.04 -1.58 -0.97 -0.81 -0.64 -0.53 -0.51 -0.60 -0.71 -0.78 3 -2.02 -2.71 -2.33 -1.81 -1.07 -1.00 -0.82 -0.74 -0.77 -0.88 -0.94 -0.94 4 -2.09 -2.54 -2.25 -1.59 -1.06 -1.00 -0.82 -0.82 -0.89 -0.99 -1.01 -1.13 5 -2.02 -2.48 -1.93 -1.59 -1.11 -1.03 -0.98 -1.01 -1.06 -1.14 -1.19 -1.21 6 -2.03 -2.31 -2.06 -1.77 -1.25 -1.23 -1.22 -1.22 -1.25 -1.33 -1.47 -1.48 7 -1.58 -2.39 -2.04 -1.72 -1.37 -1.40 -1.35 -1.32 -1.37 -1.57 -1.72 -1.85 8 -2.16 -2.69 -2.21 -2.01 -1.63 -1.60 -1.49 -1.48 -1.51 -1.70 -1.86 -2.00 9 -2.21 -2.78 -2.56 -2.28 -1.83 -1.74 -1.69 -1.67 -1.68 -1.87 -2.05 -2.13 10 -2.23 -3.01 -2.72 -2.43 -1.94 -1.97 -1.89 -1.83 -1.93 -2.16 -2.26 -2.32 11 -2.79 -3.36 -3.01 -2.66 -2.21 -2.19 -2.07 -2.10 -2.24 -2.39 -2.48 -2.49 12 -3.05 -3.63 -3.25 -2.96 -2.50 -2.53 -2.49 -2.56 -2.58 -2.73 -2.74 -2.75
Average monthly returns (in %) for momentum investment strategies with a 2-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -0.67 -0.87 -0.88 -0.35 -0.33 -0.25 -0.30 -0.33 -0.33 -0.42 -0.58 -0.55 2 -1.28 -1.70 -1.40 -0.98 -0.78 -0.69 -0.64 -0.61 -0.66 -0.80 -0.90 -0.85 3 -2.20 -1.89 -1.60 -1.04 -0.97 -0.89 -0.84 -0.84 -0.94 -1.03 -1.05 -1.04 4 -2.03 -1.84 -1.40 -0.95 -0.86 -0.85 -0.95 -0.91 -1.00 -1.04 -1.17 -1.12 5 -1.98 -1.44 -1.36 -1.14 -1.00 -1.02 -1.11 -1.10 -1.17 -1.25 -1.30 -1.26 6 -1.98 -1.72 -1.61 -1.30 -1.30 -1.31 -1.36 -1.35 -1.38 -1.59 -1.62 -1.70 7 -2.30 -1.83 -1.58 -1.49 -1.46 -1.50 -1.50 -1.50 -1.62 -1.81 -1.96 -2.03 8 -2.35 -1.87 -1.88 -1.76 -1.66 -1.62 -1.65 -1.61 -1.73 -1.93 -2.11 -2.13 9 -2.40 -2.33 -2.22 -2.01 -1.80 -1.85 -1.86 -1.79 -1.94 -2.15 -2.26 -2.29 10 -2.88 -2.57 -2.42 -2.17 -2.12 -2.11 -2.06 -2.11 -2.27 -2.39 -2.47 -2.45 11 -3.10 -2.80 -2.61 -2.42 -2.31 -2.26 -2.32 -2.39 -2.47 -2.59 -2.63 -2.61 12 -3.37 -3.03 -2.92 -2.72 -2.67 -2.71 -2.79 -2.75 -2.81 -2.84 -2.87 -2.84
21 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.00 -1.06 -0.21 -0.23 -0.15 -0.23 -0.27 -0.26 -0.36 -0.57 -0.53 -0.50 2 -2.12 -1.66 -0.92 -0.72 -0.65 -0.63 -0.60 -0.64 -0.79 -0.94 -0.88 -0.88 3 -1.93 -1.50 -0.63 -0.78 -0.70 -0.75 -0.83 -0.87 -0.99 -1.05 -1.06 -1.06 4 -2.01 -1.34 -0.60 -0.72 -0.74 -0.81 -0.92 -0.96 -1.02 -1.23 -1.16 -1.14 5 -1.35 -1.37 -1.06 -1.01 -0.99 -1.17 -1.23 -1.23 -1.32 -1.41 -1.37 -1.48 6 -1.89 -1.59 -1.13 -1.36 -1.32 -1.51 -1.50 -1.49 -1.63 -1.67 -1.76 -1.87 7 -1.90 -1.58 -1.43 -1.61 -1.59 -1.63 -1.66 -1.70 -1.77 -2.01 -2.03 -2.10 8 -1.90 -2.06 -1.82 -1.86 -1.75 -1.86 -1.84 -1.89 -2.04 -2.25 -2.29 -2.28 9 -2.71 -2.43 -2.09 -1.99 -1.96 -2.06 -2.01 -2.07 -2.24 -2.37 -2.42 -2.40 10 -2.90 -2.63 -2.21 -2.32 -2.23 -2.27 -2.34 -2.42 -2.48 -2.58 -2.58 -2.55 11 -3.12 -2.77 -2.46 -2.48 -2.35 -2.51 -2.60 -2.59 -2.65 -2.71 -2.71 -2.69 12 -3.26 -3.09 -2.90 -2.99 -2.94 -3.12 -3.03 -3.01 -2.95 -2.97 -2.96 -2.91
Average monthly returns (in %) for momentum investment strategies with a 4-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.34 -0.05 0.00 -0.02 -0.17 -0.27 -0.25 -0.35 -0.58 -0.57 -0.53 -0.63 2 -1.57 -0.38 -0.13 -0.33 -0.35 -0.44 -0.59 -0.69 -0.88 -0.86 -0.89 -0.93 3 -1.51 -0.18 -0.49 -0.57 -0.63 -0.81 -0.92 -1.00 -1.09 -1.11 -1.13 -1.12 4 -0.91 -0.15 -0.42 -0.50 -0.70 -0.92 -0.99 -1.03 -1.26 -1.25 -1.23 -1.35 5 -1.78 -1.03 -0.85 -1.03 -1.20 -1.38 -1.39 -1.42 -1.52 -1.48 -1.60 -1.73 6 -1.75 -0.99 -1.46 -1.54 -1.70 -1.72 -1.71 -1.78 -1.80 -1.89 -2.02 -2.04 7 -1.65 -1.39 -1.76 -1.86 -1.80 -1.92 -1.96 -2.01 -2.07 -2.20 -2.20 -2.20 8 -2.62 -1.94 -1.89 -1.91 -1.96 -2.03 -2.09 -2.17 -2.34 -2.39 -2.42 -2.37 9 -2.74 -2.11 -1.96 -2.10 -2.15 -2.18 -2.28 -2.36 -2.44 -2.51 -2.52 -2.48 10 -2.88 -2.16 -2.44 -2.45 -2.41 -2.57 -2.64 -2.62 -2.66 -2.64 -2.64 -2.61 11 -3.00 -2.44 -2.62 -2.58 -2.68 -2.89 -2.85 -2.84 -2.83 -2.81 -2.81 -2.74 12 -3.51 -3.12 -3.29 -3.34 -3.45 -3.41 -3.34 -3.18 -3.10 -3.08 -3.04 -3.00
22 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 0.92 0.87 0.44 0.09 -0.08 -0.14 -0.33 -0.58 -0.55 -0.49 -0.63 -0.60 2 0.60 0.71 0.09 -0.13 -0.23 -0.50 -0.68 -0.89 -0.87 -0.88 -0.95 -0.91 3 0.76 -0.06 -0.40 -0.54 -0.77 -0.99 -1.12 -1.22 -1.25 -1.24 -1.24 -1.34 4 0.25 -0.18 -0.42 -0.81 -1.03 -1.20 -1.26 -1.48 -1.45 -1.39 -1.52 -1.63 5 -0.64 -0.51 -0.96 -1.32 -1.47 -1.55 -1.58 -1.65 -1.59 -1.71 -1.85 -1.87 6 -0.54 -1.45 -1.68 -1.95 -1.90 -1.95 -2.04 -1.99 -2.00 -2.12 -2.16 -2.13 7 -1.52 -1.97 -2.11 -2.13 -2.17 -2.27 -2.24 -2.30 -2.35 -2.36 -2.38 -2.29 8 -1.76 -1.76 -1.98 -2.16 -2.17 -2.35 -2.42 -2.56 -2.52 -2.52 -2.50 -2.45 9 -1.93 -1.80 -2.15 -2.33 -2.30 -2.50 -2.60 -2.63 -2.62 -2.59 -2.57 -2.55 10 -1.92 -2.49 -2.61 -2.67 -2.77 -2.93 -2.89 -2.87 -2.74 -2.72 -2.71 -2.67 11 -2.38 -2.72 -2.75 -2.99 -3.15 -3.15 -3.13 -3.05 -2.91 -2.91 -2.84 -2.88 12 -3.25 -3.47 -3.61 -3.85 -3.67 -3.68 -3.44 -3.28 -3.16 -3.10 -3.06 -3.05
Average monthly returns (in %) for momentum investment strategies with a 6-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 0.86 -0.02 -0.26 -0.35 -0.42 -0.60 -0.73 -0.76 -0.66 -0.81 -0.73 -0.70 2 0.79 -0.50 -0.78 -0.69 -0.99 -1.10 -1.16 -1.16 -1.11 -1.16 -1.07 -1.16 3 -0.91 -1.24 -1.30 -1.44 -1.63 -1.65 -1.52 -1.53 -1.46 -1.44 -1.49 -1.55 4 -0.74 -1.08 -1.54 -1.66 -1.82 -1.68 -1.72 -1.64 -1.52 -1.65 -1.71 -1.74 5 -0.57 -1.38 -1.84 -1.98 -1.98 -2.03 -1.98 -1.88 -1.91 -2.03 -2.03 -2.02 6 -2.58 -2.47 -2.68 -2.51 -2.47 -2.56 -2.36 -2.33 -2.34 -2.35 -2.32 -2.21 7 -2.84 -2.72 -2.57 -2.62 -2.66 -2.65 -2.60 -2.53 -2.54 -2.51 -2.48 -2.43 8 -2.05 -2.32 -2.62 -2.62 -2.74 -2.83 -2.85 -2.78 -2.67 -2.61 -2.57 -2.54 9 -1.95 -2.52 -2.81 -2.74 -2.90 -3.00 -2.91 -2.87 -2.73 -2.69 -2.66 -2.62 10 -3.43 -3.25 -3.28 -3.35 -3.42 -3.39 -3.21 -3.03 -2.90 -2.87 -2.82 -2.79 11 -3.37 -3.17 -3.53 -3.67 -3.59 -3.59 -3.33 -3.17 -3.05 -2.96 -2.98 -2.93 12 -4.14 -4.08 -4.42 -4.18 -4.06 -3.87 -3.61 -3.41 -3.26 -3.21 -3.19 -3.36
23 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.04 -1.12 -1.15 -0.97 -1.18 -1.26 -1.11 -0.98 -1.07 -0.94 -0.87 -0.94 2 -1.95 -1.85 -1.55 -1.71 -1.77 -1.71 -1.50 -1.39 -1.37 -1.24 -1.29 -1.37 3 -1.83 -1.77 -1.96 -2.11 -2.07 -1.82 -1.75 -1.60 -1.54 -1.59 -1.62 -1.64 4 -1.69 -2.21 -2.30 -2.39 -2.14 -2.14 -1.94 -1.75 -1.80 -1.84 -1.85 -1.85 5 -2.51 -2.69 -2.71 -2.58 -2.55 -2.48 -2.23 -2.21 -2.23 -2.20 -2.18 -2.10 6 -2.84 -3.00 -2.70 -2.79 -2.80 -2.69 -2.64 -2.56 -2.49 -2.44 -2.34 -2.34 7 -3.02 -2.63 -2.85 -2.99 -3.00 -2.94 -2.82 -2.77 -2.69 -2.57 -2.51 -2.44 8 -2.92 -3.19 -3.19 -3.29 -3.32 -3.35 -3.11 -2.95 -2.76 -2.68 -2.65 -2.59 9 -3.42 -3.51 -3.36 -3.49 -3.52 -3.42 -3.23 -3.04 -2.87 -2.83 -2.76 -2.76 10 -3.45 -3.43 -3.66 -3.83 -3.68 -3.59 -3.33 -3.13 -3.00 -2.92 -2.90 -2.87 11 -3.44 -3.90 -4.15 -4.04 -3.93 -3.74 -3.50 -3.29 -3.10 -3.12 -3.07 -3.26 12 -4.29 -4.72 -4.56 -4.62 -4.26 -4.04 -3.68 -3.45 -3.32 -3.31 -3.50 -3.73
Average monthly returns (in %) for momentum investment strategies with a 8-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.39 -1.17 -1.06 -1.43 -1.46 -1.24 -1.14 -1.15 -0.98 -0.90 -0.96 -0.95 2 -2.04 -1.48 -1.88 -2.05 -1.86 -1.62 -1.53 -1.41 -1.25 -1.31 -1.40 -1.30 3 -2.01 -2.20 -2.49 -2.45 -2.04 -2.00 -1.84 -1.67 -1.65 -1.67 -1.73 -1.64 4 -3.12 -2.79 -2.90 -2.56 -2.44 -2.28 -2.05 -2.02 -1.97 -1.96 -2.00 -1.82 5 -3.37 -3.07 -2.81 -2.87 -2.69 -2.53 -2.49 -2.42 -2.31 -2.28 -2.23 -2.06 6 -3.61 -2.84 -3.08 -3.15 -2.93 -2.98 -2.85 -2.69 -2.57 -2.43 -2.45 -2.28 7 -2.57 -2.96 -3.30 -3.36 -3.35 -3.27 -3.00 -2.93 -2.65 -2.60 -2.58 -2.42 8 -3.90 -3.59 -3.76 -3.82 -3.74 -3.54 -3.30 -3.02 -2.83 -2.78 -2.73 -2.61 9 -3.98 -3.57 -3.84 -3.95 -3.71 -3.60 -3.32 -3.07 -2.93 -2.84 -2.86 -2.70 10 -3.83 -4.06 -4.36 -4.15 -3.94 -3.72 -3.43 -3.22 -3.05 -3.02 -2.99 -3.07 11 -4.77 -4.74 -4.61 -4.63 -4.22 -4.00 -3.62 -3.34 -3.28 -3.21 -3.43 -3.52 12 -5.48 -4.84 -5.09 -4.82 -4.42 -4.09 -3.70 -3.50 -3.41 -3.62 -3.88 -3.76
24 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.10 -1.02 -1.69 -1.67 -1.40 -1.20 -1.18 -0.97 -0.86 -0.94 -0.91 -0.84 2 -1.21 -1.97 -2.31 -2.13 -1.78 -1.70 -1.59 -1.34 -1.35 -1.42 -1.33 -1.24 3 -2.60 -2.77 -2.61 -2.18 -2.08 -2.00 -1.84 -1.75 -1.72 -1.78 -1.71 -1.51 4 -2.76 -2.93 -2.39 -2.41 -2.17 -2.07 -2.09 -1.96 -1.92 -2.00 -1.82 -1.65 5 -3.03 -2.58 -2.97 -2.83 -2.61 -2.72 -2.61 -2.44 -2.34 -2.26 -2.12 -1.96 6 -2.23 -2.87 -3.26 -3.08 -3.12 -3.10 -2.91 -2.75 -2.51 -2.51 -2.35 -2.15 7 -3.51 -3.81 -3.99 -3.66 -3.69 -3.49 -3.13 -2.92 -2.72 -2.69 -2.45 -2.29 8 -3.45 -3.76 -4.06 -4.00 -3.71 -3.55 -3.22 -2.97 -2.84 -2.77 -2.66 -2.43 9 -3.41 -3.91 -4.28 -4.00 -3.80 -3.59 -3.28 -3.07 -2.91 -2.92 -2.78 -2.80 10 -4.54 -4.77 -4.62 -4.52 -4.12 -3.86 -3.50 -3.25 -3.15 -3.11 -3.20 -3.27 11 -4.87 -4.63 -4.97 -4.69 -4.33 -3.97 -3.56 -3.44 -3.30 -3.53 -3.65 -3.51 12 -4.58 -5.51 -5.40 -5.00 -4.38 -4.07 -3.73 -3.58 -3.75 -3.99 -3.78 -3.42
Average monthly returns (in %) for momentum investment strategies with a 10-month gap period over the period 2000-2010. Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.17 -2.04 -2.06 -1.73 -1.41 -1.47 -1.26 -1.07 -1.09 -1.02 -0.96 -0.89 2 -2.83 -2.89 -2.43 -2.03 -1.86 -1.82 -1.58 -1.50 -1.52 -1.42 -1.34 -1.19 3 -3.13 -2.67 -1.99 -2.04 -1.90 -1.88 -1.84 -1.74 -1.78 -1.74 -1.56 -1.47 4 -3.30 -2.23 -2.39 -2.23 -2.05 -2.25 -2.13 -2.02 -2.06 -1.86 -1.70 -1.62 5 -2.23 -2.95 -2.97 -2.77 -2.90 -2.90 -2.70 -2.56 -2.37 -2.19 -2.05 -1.94 6 -3.61 -3.90 -3.71 -3.62 -3.54 -3.34 -3.03 -2.72 -2.62 -2.43 -2.22 -2.15 7 -4.27 -4.00 -4.00 -4.05 -3.74 -3.45 -3.12 -2.89 -2.82 -2.52 -2.35 -2.26 8 -4.27 -4.49 -4.51 -4.08 -3.81 -3.52 -3.22 -3.01 -2.86 -2.74 -2.51 -2.66 9 -4.61 -4.85 -4.53 -4.41 -4.02 -3.74 -3.39 -3.14 -3.08 -2.91 -2.95 -3.13 10 -5.10 -4.73 -4.89 -4.58 -4.17 -3.83 -3.48 -3.31 -3.19 -3.28 -3.37 -3.33 11 -4.70 -5.60 -5.38 -5.00 -4.31 -3.97 -3.73 -3.52 -3.70 -3.78 -3.55 -3.29 12 -5.09 -5.50 -5.33 -4.76 -4.20 -3.91 -3.77 -3.91 -4.09 -3.87 -3.49 -3.29
25 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -3.04 -2.43 -1.67 -1.35 -1.35 -1.23 -1.10 -1.06 -1.02 -0.98 -0.92 -0.79 2 -3.11 -2.23 -1.66 -1.62 -1.54 -1.45 -1.45 -1.45 -1.37 -1.32 -1.19 -1.09 3 -2.30 -1.31 -1.66 -1.64 -1.63 -1.77 -1.74 -1.78 -1.75 -1.56 -1.47 -1.40 4 -1.31 -1.83 -2.03 -1.90 -2.18 -2.20 -2.10 -2.17 -1.93 -1.73 -1.67 -1.59 5 -3.77 -3.37 -3.19 -3.24 -3.22 -3.02 -2.75 -2.53 -2.31 -2.14 -2.00 -1.91 6 -4.33 -3.73 -3.86 -3.75 -3.46 -3.25 -2.89 -2.75 -2.53 -2.28 -2.22 -2.11 7 -4.36 -3.81 -4.30 -3.77 -3.64 -3.37 -3.11 -2.82 -2.58 -2.40 -2.32 -2.49 8 -4.67 -4.61 -4.37 -4.21 -3.78 -3.53 -3.20 -2.99 -2.84 -2.58 -2.76 -2.97 9 -5.13 -4.49 -4.68 -4.38 -3.98 -3.66 -3.33 -3.21 -3.02 -3.05 -3.26 -3.22 10 -4.69 -5.35 -5.17 -4.71 -4.08 -3.82 -3.54 -3.36 -3.45 -3.50 -3.37 -3.09 11 -5.11 -5.39 -5.23 -4.59 -4.01 -3.86 -3.64 -3.82 -3.88 -3.63 -3.37 -3.16 12 -4.64 -5.23 -4.87 -4.42 -3.93 -3.89 -4.08 -4.23 -3.96 -3.55 -3.35 -3.14
26 Appendix B: Risk adjusted momentum strategy returns
Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 -1.86** (-2.42) (-1.81) -1.88* (-1.79) -1.28* (-1.78) -1.26* -1.17** (-2.14) (-1.91) -0.95* (-1.58) -0.67 -0.69** (-2.00) (-1.76) -0.48* -0.50** (-2.04) -0.47** (-2.08) -0.46** (-2.19) 2 -1.61** (-2.02) (-1.79) -1.83* (-1.51) -1.47 (-1.73) -1.62* (-1.82) -1.37* (-1.46) -0.98 (-1.48) -0.83 (-1.61) -0.69 (-1.47) -0.52 (-1.54) -0.50 (-1.60) -0.47 (-1.91) -0.54* 3 (-1.81) -1.65* (-1.66) -1.72* (-1.75) -1.85* (-1.78) -1.80* (-1.62) -1.34 (-1.38) -0.98 (-1.20) -0.65 (-1.19) -0.50 (-0.99) -0.37 (-1.13) -0.39 (-1.35) -0.44 (-1.76) -0.54* 4 -1.84** (-2.18) (-1.86) -2.13* (-1.71) -2.00* (-1.57) -1.72 (-1.44) -1.28 (-1.13) -0.80 (-1.05) -0.58 (-0.96) -0.45 (-0.94) -0.40 (-1.18) -0.47 (-1.52) -0.54 (-1.79) -0.60* 5 -1.92** (-2.44) (-1.79) -2.08* (-1.53) -1.82 (-1.44) -1.58 (-1.12) -0.93 (-0.95) -0.64 (-0.84) -0.47 (-0.71) -0.35 (-0.66) -0.32 (-1.03) -0.45 (-1.31) -0.51 (-1.54) -0.58 6 -1.85** (-2.36) (-1.60) -1.90 (-1.51) -1.79 (-1.32) -1.34 (-1.12) -0.86 (-0.92) -0.60 (-0.84) -0.47 (-0.79) -0.42 (-0.85) -0.43 (-1.16) -0.53 (-1.43) -0.59 (-1.66) -0.64 7 -1.61** (-2.07) (-1.50) -1.76 (-1.18) -1.28 (-1.12) -1.08 (-0.86) -0.66 (-0.72) -0.47 (-0.77) -0.47 (-0.76) -0.45 (-0.80) -0.46 (-1.07) -0.57 (-1.34) -0.64 -0.84** (-2.03) 8 -1.56** (-2.06) (-1.25) -1.27 (-1.10) -1.10 (-1.10) -1.03 (-0.83) -0.64 (-0.77) -0.53 (-0.80) -0.51 (-0.75) -0.48 (-0.71) -0.45 (-1.00) -0.58 (-1.23) -0.65 (-1.89) -0.84* 9 (-0.91) -0.59 (-0.90) -0.94 (-0.81) -0.86 (-0.88) -0.86 (-0.72) -0.60 (-0.73) -0.54 (-0.70) -0.50 (-0.63) -0.45 (-0.71) -0.49 (-1.00) -0.64 (-1.17) -0.68 (-1.84) -0.89* 10 (-1.58) -0.98 (-1.11) -1.13 (-0.93) -0.97 (-1.04) -1.04 (-0.91) -0.74 (-0.84) -0.63 (-0.78) -0.56 (-0.79) -0.56 (-0.85) -0.60 (-1.12) -0.72 (-1.83) -0.95* -1.19*** (-2.78) 11 (-1.76) -1.07* (-1.21) -1.21 (-1.16) -1.24 (-1.28) -1.26 (-1.08) -0.90 (-1.00) -0.77 (-1.02) -0.75 (-0.98) -0.72 (-1.02) -0.73 (-1.79) -1.04* -1.30*** (-2.83) -1.47*** (-3.36) 12 (-1.83) -1.05* (-1.38) -1.42 (-1.37) -1.46 (-1.45) -1.46 (-1.29) -1.10 (-1.26) -0.99 (-1.23) -0.93 (-1.42) -0.98 (-1.74) -1.08* -1.42*** (-2.79) -1.59*** (-3.49) -1.75*** (-3.67) Average monthly risk adjusted returns (in %), estimated using the Carhart four-factor model, for momentum investment strategies with a 0-month gap period over the period 2000-2010. *statistically significant at the 10% significance level **statistically significant at the 5% significance level ***statistically significant at the 1% significance level
27 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 (-0.22) -0.17 (-1.38) -1.15 (-1.90) -1.25* (-1.79) -0.94* (-0.85) -0.36 (-1.23) -0.40 (-0.65) -0.15 (-0.61) -0.13 (-0.72) -0.14 (-0.78) -0.14 (-1.32) -0.23 -0.36*** (-2.65) 2 (-0.69) -0.46 (-1.59) -1.51 (-1.83) -1.44* (-1.52) -0.99 (-1.09) -0.57 (-1.28) -0.48 (-1.02) -0.31 (-0.88) -0.24 (-1.14) -0.26 (-1.55) -0.36 -0.49** (-2.32) -0.57*** (-2.87) 3 (-1.38) -0.97 (-1.59) -1.72 (-1.49) -1.35 (-1.25) -0.92 (-0.68) -0.35 (-0.86) -0.36 (-0.65) -0.24 (-0.70) -0.23 (-1.03) -0.31 (-1.64) -0.46 -0.54** (-2.06) -0.56** (-2.14) 4 (-1.24) -0.85 (-1.32) -1.45 (-1.32) -1.20 (-0.88) -0.57 (-0.44) -0.22 (-0.57) -0.27 (-0.38) -0.16 (-0.60) -0.23 (-1.05) -0.36 (-1.60) -0.50 (-1.78) -0.55* -0.69** (-2.29) 5 (-1.00) -0.67 (-1.20) -1.29 (-0.84) -0.66 (-0.65) -0.39 (-0.19) -0.10 (-0.27) -0.14 (-0.32) -0.17 (-0.62) -0.28 (-0.97) -0.39 (-1.36) -0.52 (-1.65) -0.61 (-1.78) -0.66* 6 (-0.94) -0.62 (-0.93) -0.88 (-0.83) -0.62 (-0.73) -0.46 (-0.24) -0.14 (-0.35) -0.20 (-0.50) -0.29 (-0.73) -0.39 (-1.02) -0.50 (-1.41) -0.63 -0.85** (-2.33) -0.88** (-2.49) 7 (0.33) 0.21 (-0.73) -0.74 (-0.57) -0.49 (-0.46) -0.33 (-0.26) -0.18 (-0.48) -0.32 (-0.56) -0.38 (-0.73) -0.45 (-1.04) -0.58 -0.87** (-2.05) -1.10*** (-3.00) -1.30*** (-3.39) 8 (-0.53) -0.33 (-1.05) -1.05 (-0.76) -0.63 (-0.79) -0.58 (-0.57) -0.39 (-0.72) -0.50 (-0.70) -0.49 (-0.91) -0.58 (-1.18) -0.68 -0.97** (-2.20) -1.21*** (-3.24) -1.42*** (-3.71) 9 (-0.55) -0.34 (-1.09) -1.08 (-1.10) -0.93 (-1.09) -0.80 (-0.78) -0.55 (-0.84) -0.59 (-0.91) -0.64 (-1.11) -0.72 (-1.36) -0.80 -1.11** (-2.42) -1.36*** (-3.51) -1.51*** (-3.75) 10 (-0.54) -0.33 (-1.26) -1.27 (-1.24) -1.04 (-1.19) -0.89 (-0.85) -0.61 (-1.03) -0.74 (-1.07) -0.78 (-1.24) -0.82 (-1.88) -1.03* -1.36*** (-3.29) -1.54*** (-3.94) -1.66*** (-3.91) 11 (-1.40) -0.84 (-1.56) -1.58 (-1.51) -1.31 (-1.44) -1.10 (-1.15) -0.86 (-1.26) -0.94 (-1.25) -0.93 (-1.74) -1.10* -1.33*** (-2.64) -1.59*** (-3.73) -1.77*** (-4.10) -1.84*** (-3.93) 12 (-1.70) -1.06* (-1.80) -1.82* (-1.75) -1.53* (-1.77) -1.38* (-1.44) -1.08 (-1.90) -1.26* -1.37** (-2.29) -1.57*** (-3.12) -1.68*** (-3.81) -1.93*** (-4.38) -2.04*** (-4.28) -2.11*** (-4.02) Average monthly risk adjusted returns (in %), estimated using the Carhart four-factor model, for momentum investment strategies with a 2-month gap period over the period 2000-2010. *statistically significant at the 10% significance level **statistically significant at the 5% significance level ***statistically significant at the 1% significance level
28 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 (-1.94) -0.86* (-1.34) -0.53 (-0.06) -0.02 (-0.73) -0.19 (0.25) 0.05 (-0.25) -0.05 (-0.84) -0.14 (-0.92) -0.13 (-1.57) -0.24 -0.46*** (-3.68) -0.42*** (-3.79) -0.40*** (-3.24) 2 (-1.49) -0.97 (-0.96) -0.59 (-0.95) -0.39 (-0.94) -0.29 (-0.51) -0.17 (-0.71) -0.21 (-1.07) -0.25 (-1.38) -0.31 -0.50** (-2.39) -0.68*** (-3.72) -0.63*** (-3.30) -0.63*** (-3.04) 3 (-1.13) -0.70 (-0.55) -0.34 (0.41) 0.14 (-0.18) -0.08 (-0.01) -0.01 (-0.37) -0.14 (-0.92) -0.31 (-1.27) -0.40 (-1.92) -0.57* -0.67** (-2.46) -0.68** (-2.44) -0.70** (-2.47) 4 (-1.14) -0.72 (0.11) 0.05 (0.63) 0.32 (0.14) 0.09 (0.06) 0.04 (-0.23) -0.11 (-0.76) -0.33 (-1.06) -0.41 (-1.43) -0.53 -0.78** (-2.18) -0.73** (-2.11) -0.73** (-2.13) 5 (0.61) 0.40 (0.43) 0.29 (0.34) 0.25 (0.13) 0.10 (0.06) 0.05 (-0.44) -0.27 (-0.82) -0.44 (-1.04) -0.52 (-1.45) -0.67 (-1.85) -0.81* (-1.93) -0.81* -0.99*** (-2.79) 6 (-0.13) -0.09 (0.12) 0.08 (0.28) 0.20 (-0.18) -0.13 (-0.26) -0.19 (-0.82) -0.52 (-1.15) -0.64 (-1.41) -0.71 -0.94** (-2.23) -1.03*** (-2.64) -1.21*** (-3.48) -1.37*** (-3.86) 7 (-0.22) -0.15 (0.11) 0.08 (-0.11) -0.08 (-0.51) -0.37 (-0.61) -0.46 (-1.05) -0.68 (-1.43) -0.82 -0.97** (-2.05) -1.10** (-2.53) -1.46*** (-3.95) -1.52*** (-4.03) -1.65*** (-3.58) 8 (-0.12) -0.08 (-0.51) -0.34 (-0.59) -0.42 (-0.82) -0.63 (-0.79) -0.61 (-1.30) -0.86 (-1.61) -0.95 -1.10** (-2.27) -1.35*** (-3.30) -1.65*** (-4.56) -1.75*** (-4.39) -1.79*** (-3.92) 9 (-1.28) -0.84 (-0.98) -0.69 (-0.87) -0.66 (-0.93) -0.73 (-1.00) -0.79 (-1.49) -1.01 (-1.78) -1.09* -1.26** (-2.49) -1.51*** (-3.64) -1.74*** (-4.52) -1.85*** (-4.43) -1.89*** (-4.01) 10 (-1.44) -1.00 (-1.15) -0.84 (-0.98) -0.74 (-1.21) -0.95 (-1.22) -0.97 (-1.66) -1.15 -1.40** (-2.47) -1.58*** (-3.47) -1.73*** (-4.23) -1.92*** (-4.69) -2.00*** (-4.37) -2.03*** (-4.09) 11 (-1.68) -1.19* (-1.29) -0.96 (-1.21) -0.95 (-1.33) -1.09 (-1.30) -1.07 -1.42** (-2.19) -1.66*** (-3.24) -1.75*** (-3.89) -1.91*** (-4.40) -2.07*** (-4.58) -2.15*** (-4.35) -2.19*** (-4.11) 12 (-1.78) -1.31* (-1.62) -1.25 (-1.50) -1.18 -1.50** (-2.23) -1.63*** (-2.72) -2.00*** (-3.89) -2.07*** (-4.33) -2.16*** (-4.42) -2.20*** (-4.48) -2.33*** (-4.30) -2.39*** (-4.03) -2.41*** (-3.71) Average monthly risk adjusted returns (in %), estimated using the Carhart four-factor model, for momentum investment strategies with a 4-month gap period over the period 2000-2010. *statistically significant at the 10% significance level **statistically significant at the 5% significance level ***statistically significant at the 1% significance level
29 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 (0.52) 0.36 (0.50) 0.27 (1.15) 0.46 (0.40) 0.14 (-0.05) -0.01 (-0.15) -0.03 (-1.37) -0.24 -0.51*** (-2.84) -0.48*** (-3.02) -0.44*** (-2.85) -0.58*** (-3.66) -0.56*** (-4.26) 2 (0.20) 0.14 (0.55) 0.42 (0.47) 0.31 (0.20) 0.11 (0.03) 0.01 (-0.78) -0.23 (-1.73) -0.46* -0.70*** (-2.62) -0.68*** (-2.64) -0.70*** (-2.78) -0.79*** (-3.47) -0.77*** (-3.83) 3 (0.76) 0.84 (0.36) 0.34 (0.30) 0.26 (0.06) 0.04 (-0.45) -0.23 (-1.20) -0.48 (-1.87) -0.69* -0.84** (-2.31) -0.88** (-2.59) -0.90*** (-2.89) -0.93*** (-3.26) -1.10*** (-5.15) 4 (0.33) 0.36 (0.25) 0.24 (0.30) 0.28 (-0.27) -0.18 (-0.89) -0.46 (-1.53) -0.66 (-1.95) -0.80* -1.07** (-2.61) -1.04*** (-2.78) -1.02*** (-2.94) -1.22*** (-4.59) -1.39*** (-5.58) 5 (0.17) 0.13 (0.32) 0.27 (0.00) 0.00 (-0.78) -0.49 (-1.34) -0.71 (-1.84) -0.89* -1.02** (-2.27) -1.15*** (-2.65) -1.11*** (-2.83) -1.31*** (-4.09) -1.51*** (-4.85) -1.57*** (-4.18) 6 (0.30) 0.25 (-0.38) -0.29 (-0.62) -0.50 (-1.40) -0.91 (-1.81) -1.03* -1.17** (-2.31) -1.40*** (-3.17) -1.42*** (-3.49) -1.49*** (-4.12) -1.69*** (-4.77) -1.80*** (-4.34) -1.81*** (-3.78) 7 (-0.81) -0.65 (-1.00) -0.79 (-1.07) -0.89 (-1.71) -1.15* -1.30** (-2.21) -1.51*** (-3.18) -1.59*** (-3.51) -1.75*** (-4.23) -1.87*** (-4.70) -1.95*** (-4.33) -2.03*** (-3.98) -1.97*** (-3.74) 8 (-1.02) -0.86 (-0.96) -0.87 (-1.05) -0.93 (-1.77) -1.21* -1.31** (-2.23) -1.60*** (-3.33) -1.81*** (-4.29) -2.02*** (-5.02) -2.02*** (-5.16) -2.10*** (-4.79) -2.15*** (-4.40) -2.15*** (-4.05) 9 (-1.14) -0.99 (-0.95) -0.86 (-1.20) -1.05 (-1.93) -1.34* -1.40** (-2.34) -1.72*** (-3.49) -1.93*** (-4.56) -2.06*** (-4.93) -2.09*** (-5.11) -2.15*** (-4.72) -2.20*** (-4.48) -2.23*** (-4.16) 10 (-1.04) -0.92 (-1.39) -1.17 (-1.47) -1.27 -1.51** (-2.15) -1.80*** (-3.29) -2.07*** (-4.40) -2.19*** (-4.69) -2.25*** (-4.83) -2.18*** (-4.67) -2.25*** (-4.45) -2.31*** (-4.17) -2.33*** (-3.76) 11 (-1.54) -1.37 (-1.61) -1.38 (-1.59) -1.38 -1.88*** (-3.17) -2.17*** (-4.42) -2.31*** (-4.67) -2.43*** (-4.81) -2.44*** (-4.79) -2.37*** (-4.65) -2.46*** (-4.42) -2.47*** (-4.03) -2.56*** (-3.88) 12 (-1.81) -1.49* -1.92*** (-3.08) -2.22*** (-3.75) -2.67*** (-4.41) -2.66*** (-4.07) -2.81*** (-4.07) -2.73*** (-4.07) -2.66*** (-4.00) -2.62*** (-4.00) -2.66*** (-3.75) -2.70*** (-3.61) -2.73*** (-3.40) Average monthly risk adjusted returns (in %), estimated using the Carhart four-factor model, for momentum investment strategies with a 6-month gap period over the period 2000-2010. *statistically significant at the 10% significance level **statistically significant at the 5% significance level ***statistically significant at the 1% significance level
30 Holding period Evaluation period 1 2 3 4 5 6 7 8 9 10 11 12 1 (0.30) 0.23 (-0.85) -0.40 (-1.25) -0.52 (-1.27) -0.41 -0.67** (-2.39) -0.84*** (-2.95) -0.77*** (-3.15) -0.70*** (-2.82) -0.81*** (-3.80) -0.73*** (-3.42) -0.67*** (-3.15) -0.81*** (-3.18) 2 (-0.73) -0.60 (-1.40) -0.80 (-1.41) -0.65 -0.90** (-2.21) -1.10*** (-2.94) -1.19*** (-3.32) -1.08*** (-3.28) -1.02*** (-3.38) -1.04*** (-3.83) -0.95*** (-3.50) -1.07*** (-3.51) -1.19*** (-3.07) 3 (-0.59) -0.48 (-1.16) -0.67 -0.98** (-2.02) -1.26*** (-2.75) -1.37*** (-3.32) -1.33*** (-3.47) -1.33*** (-3.75) -1.22*** (-3.99) -1.20*** (-4.25) -1.34*** (-4.28) -1.42*** (-3.54) -1.49*** (-3.14) 4 (-0.38) -0.32 (-1.90) -1.06* -1.28** (-2.55) -1.47*** (-2.97) -1.46*** (-3.32) -1.59*** (-3.74) -1.48*** (-3.90) -1.33*** (-4.04) -1.45*** (-4.70) -1.56*** (-4.27) -1.64*** (-3.63) -1.67*** (-3.26) 5 (-1.29) -1.03 -1.48** (-2.60) -1.59*** (-2.97) -1.67*** (-3.23) -1.74*** (-3.63) -1.79*** (-3.92) -1.65*** (-3.97) -1.71*** (-4.45) -1.79*** (-4.83) -1.84*** (-4.09) -1.88*** (-3.56) -1.84*** (-3.12) 6 (-1.67) -1.38* -1.75*** (-2.97) -1.78*** (-3.55) -1.93*** (-3.78) -2.07*** (-4.24) -2.04*** (-4.40) -2.12*** (-4.66) -2.11*** (-4.72) -2.09*** (-4.45) -2.12*** (-3.91) -2.09*** (-3.39) -2.13*** (-3.22) 7 (-1.77) -1.49* -1.68*** (-2.98) -1.91*** (-3.67) -2.18*** (-4.10) -2.30*** (-4.02) -2.31*** (-4.37) -2.30*** (-4.53) -2.34*** (-3.92) -2.31*** (-3.94) -2.29*** (-3.48) -2.26*** (-3.45) -2.24*** (-3.26) 8 (-1.62) -1.39 -1.88*** (-3.02) -2.01*** (-3.50) -2.31*** (-3.84) -2.50*** (-3.99) -2.66*** (-4.14) -2.54*** (-4.04) -2.44*** (-3.90) -2.33*** (-3.80) -2.34*** (-3.53) -2.37*** (-3.32) -2.35*** (-3.07) 9 -1.83** (-2.12) -2.15*** (-3.36) -2.15*** (-3.65) -2.49*** (-4.13) -2.67*** (-4.26) -2.70*** (-4.14) -2.63*** (-4.13) -2.52*** (-3.97) -2.42*** (-4.00) -2.48*** (-3.76) -2.48*** (-3.43) -2.53*** (-3.31) 10 -1.84** (-2.07) -2.06*** (-3.13) -2.52*** (-3.98) -2.85*** (-3.97) -2.84*** (-3.79) -2.87*** (-3.85) -2.75*** (-3.85) -2.62*** (-3.76) -2.56*** (-3.82) -2.58*** (-3.49) -2.63*** (-3.36) -2.64*** (-3.19) 11 -1.82** (-2.02) -2.67*** (-4.06) -3.05*** (-3.78) -3.10*** (-3.52) -3.12*** (-3.59) -3.05*** (-3.65) -2.94*** (-3.73) -2.82*** (-3.68) -2.71*** (-3.64) -2.83*** (-3.58) -2.83*** (-3.39) -3.04*** (-3.56) 12 -2.93*** (-4.19) -3.55*** (-3.66) -3.52*** (-3.25) -3.72*** (-3.42) -3.51*** (-3.44) -3.40*** (-3.58) -3.18*** (-3.59) -3.03*** (-3.52) -2.98*** (-3.64) -3.05*** (-3.51) -3.28*** (-3.66) -3.54*** (-3.68) Average monthly risk adjusted returns (in %), estimated using the Carhart four-factor model, for momentum investment strategies with a 8-month gap period over the period 2000-2010. *statistically significant at the 10% significance level **statistically significant at the 5% significance level ***statistically significant at the 1% significance level
