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Market volatility and momentum returns: Evidence from
the Frankfurt Stock Exchange
Master Thesis MSc Finance Julian Moser1
Supervisor: Dr. A. Plantinga
Abstract
The momentum strategy created by Jegadeesh and Titman (1993) appears to create consistent abnormal returns across markets and asset classes. However, the momentum strategy comes with high kurtosis and negative skewness in their distribution that implies potential crash risk. Consequently, it would be important to find determinants that explain and predict subsequent momentum returns so that investors have indications about potential momentum crashes in order to hedge their exposure. This paper investigates the impact of market volatility measures on momentum returns on the Frankfurt stock market from 1995 to 2015. The volatility measures are cross-sectional volatility and implied volatility, and both measures function as a proxy for the market state. The results show that cross-sectional volatility does contain information about the subsequent short-term momentum strategies, while implied volatility contains information about the subsequent mid- to long-term momentum strategies. Keywords: Momentum, momentum crashes, cross-sectional volatility, implied volatility, market states
JEL classification: G11, G14. G17
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1. Introduction
In recent decades researchers and investors have tried to come up with various investing strategies based on past returns in order to challenge the efficient market hypothesis. The market efficiency hypothesis implies that the existing share prices reflect all publicly available information (Fama, 1970). Some strategies aim to obtain abnormal returns by predicting future stock price movements. One approach that has met with success in predicting future stock prices is the momentum strategy. This strategy was developed by Jegadeesh and Titman (1993) and involves taking a long position on stocks that performed well in the past and short position on stocks that performed poorly in the past over a short to medium time period. Their paper applied the momentum strategy to stocks traded on the NYSE and AMEX from 1956-1989. The strategy resulted in a significant average annual excess return of 12.01%. Other researchers found similar significant results regarding the momentum factor across different asset classes and markets (for example, see: Rouwenhorst, 1998; Griffin, Ji and Martin, 2003; Chui, Titman and Wei, 2000).
The existence of these positive returns for momentum strategies is now accepted as a given, and is even included in the standard models of empirical asset pricing. Carhart (1997) extended the Fama-French three-factor model (1993) by adding the momentum factor. Among the various anomalies, the momentum factor is the most difficult to explain (Jegadeesh, 2011). Jegadeesh (2011) argues that the persistence and magnitude of the momentum returns are too strong to be explained by risk.
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Recent literature has tried to explain these momentum crashes. Grundy and Martin (2001), Cooper et al. (2004), Asem and Tian (2010), Stivers and Sun (2010) and Barroso and Santa-Clara (2014) argue that the momentum returns depend on the state of the market. These papers argue that momentum returns are procyclical, meaning that momentum returns are higher following good economic times. Barroso and Santa-Clara (2014) state that the largest momentum crashes, of -91.59% in 1932 and -73.42% in 2009, occurred following bear markets when volatility was still high and the stock market was starting to recover. Grundy and Martin (2001) explain momentum crashes through the systematic risk of momentum strategies. During bear markets, the winners tend to be low-beta stocks and the losers tend to be high-beta stocks, resulting in a negative beta for the winners-minus-losers strategy. Consequently, during market recoveries the momentum return becomes negative. Since volatility is high during turbulent bear markets (Barroso and Santa-Clara, 2014), recent volatility should provide some information about subsequent momentum returns and potential momentum crashes.
Although volatility has been accepted as a countercyclical proxy for the market state in recent literature (Gomes, Kogan, Zhang, 2003; Zhang, 2005; Stivers and Sun; 2010), its impact on momentum returns has not been adequately investigated. One paper that found significant predictive power was a study by Stivers and Sun (2010). This research found significant evidence that the recent cross-sectional volatility (CSV) does predict subsequent momentum returns on the US stock market. Motivated by these findings and the lack of literature about the impact of volatility on momentum returns outside of the US stock market, this paper investigates the following research question:
“Does recent market volatility contain information about the subsequent momentum returns on the Frankfurt Stock Exchange?”
To answer this question, this paper uses data from 1995 to 2015 on the Frankfurt Stock Exchange, one of the most important stock exchanges in Europe. It is constructed similarly to the study by Stivers and Sun (2010). However, in addition to the equally weighted CSV measure in Stivers and Sun (2010), this paper also includes a market-weighted CSV measure and an implied volatility measure (VDAX). For each measure a three-month moving average is used, because it can be argued that a period of three months shows changing market condition and eliminates noise in month-to-month variations.
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the implied volatility measure does contain information for mid- to long-term momentum strategies. The macroeconomic variables add explanatory power in some cases. The results indicate that a stressed market, when volatility is high, entails lower subsequent momentum returns on the Frankfurt Stock Exchange.
The paper is structured as follows: first, a literature review summarizes the research about momentum returns and their predictability. The data and methodology are then introduced, followed by the empirical results. Finally, a conclusion is drawn to answer the research question.
2. Literature Review
This section describes the origin of momentum strategies and summarizes the literature about the predictability of momentum returns.
2.1 Momentum returns
The underlying theory behind the momentum anomaly is that buying past winning stocks and selling past losing ones results in high average returns. Generating abnormal returns due to historic information stands in stark contrast to the market efficiency theory, which implies that existing share prices reflect all known information on the market. This information includes past and future data about the share. Thus, it should not be possible to obtain abnormal returns based on past information. However, If stock prices either underreact or overreact to new information, then it should be possible to create a profitable trading strategy that is based on choosing stocks that performed well in the past.
An early challenge to the market efficiency theory was the study by De Bondt and Thaler (1985). These researchers documented that past losing stocks over three- to five-year periods outperform past winners over the subsequent three- to five-year periods. Jegadeesh (1990) and Lehmann (1990) also found that losers over the past week or month outperform winners over the following week or month. The finding that a contrarian strategy leads to abnormal returns suggests that stock prices overreact to information.
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lower past returns in the future. To investigate which formation period generates the highest average return, they used four different periods, J-months (J-3, J-6, J-9, J-12), and four different holding periods, K-months (K-3, K-6, K-9, K-12). This is also known as the J-month/K-month strategy. In each period, each stock is ranked according to its past performance during the different formation periods. Based on the rankings, ten equally weighted portfolios were formed. The best-performing stocks were assigned to the “winners” portfolio and the worst-performing stocks to the “losers” portfolio. At the beginning of every period, a long position in the winners’ portfolio and a short position in the losers’ portfolio was taken. These positions were held for K months. Each strategy resulted in abnormal returns. The strategy that has been analyzed the most in the paper was the six-month formation and six-month holding strategy [6:6] with an annual average return of 12.01%. Jegadeesh and Titman (1993), Grinblatt and Moskowitz (2004) and Agyei-Ampomah (2007) all argue that the main momentum return comes from the short position in the loser portfolio.
Momentum strategies have been tested around the world and across different asset classes. Griffin, Ji and Martin (2003) and Chui, Titman and Wei (2000), for example, investigate the profitability of momentum strategies around the world. They found that it yielded positive returns on most markets, with the exception of certain Asian countries (e.g. Japan).
2.2 Predictability of momentum returns: Empirical evidence
Stivers and Sun (2010) studied the impact of CSV on future momentum returns on the US stock market. They measured CSV as the standard deviation of 100 size and book-to-market monthly portfolio returns and created a three-month moving average. Their study found that recent CSV predicts lower subsequent momentum returns. Their findings are significant and robust. Consequently, they conclude that recent CSV does contain information about subsequent momentum returns.
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Cooper et al. (2004) use a standard macroeconomic variable to predict momentum returns. Their study employs a three-year lagged market return proxy to predict momentum returns. They found that momentum strategies generate significant positive returns following up markets (defined as positive value for the three-year lagged market returns) and significant negative returns following down markets (defined as negative values for the three-year lagged market returns.
2.3 Predictability of momentum returns: Theoretical evidence
Several researchers have proposed market state variables to predict time-series variation in momentum returns. Indeed, Chorida and Shivakumar (2002), Zhang (2005), Gulen et al. (2008) and Stivers and Sun (2010) found proof that momentum returns are procyclical, meaning that a better market state leads to higher momentum returns.
Explanations for the impact of the market state on momentum returns have been derived from behavioral theories that try to explain the momentum anomaly. Most theories about momentum returns stem from the investor’s overconfidence and overreaction/underreaction. Daniel et al. (1998, 2002) and Odean (1998) argue that investors are overconfident about their own private signals and overreact/underreact to public information, thus leading to momentum returns. In this context, Daniel et al. (1998) and Cooper (2004) state that the overconfidence of investors is greater following market gains. Based on this theory, the momentum returns should increase as overconfidence increases.
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another explanation for these momentum crashes. They suggest that during a turbulent market state with a volatile stock market, the short position of the momentum strategy becomes highly leveraged and acts as a call option on the index portfolio, which make crashes more likely.
In general, the literature suggests a negative relationship between volatility and momentum returns. Therefore, the following hypothesis will be investigated:
H1: Volatility has a significant negative impact on subsequent momentum returns.
3. Data and Methodology
This chapter introduces the data and provides a description of the methodology that this paper follows.
3.1 Data
The data set used in this study consist of stocks traded on the Frankfurt Stock Exchange. Monthly data were gathered from Thomas Reuters Datastream from January 1995 to January 2015 and the data for the Carhart four factors and Fama-French model for the German market can be retrieved from the Humbold-Universität zu Berlin website.2 Following Demir et al. (2004) and Galariotis (2010), this study accounts for the survivorship bias. Survivorship exists because, for example, companies that did not survive due to bankruptcy have extreme values and lead to different results than without them. Survivorship bias can be eliminated by including stocks that were delisted within the time period. Stocks may be delisted from the stock market because they went bankrupt or because of mergers and acquisitions. Furthermore, stocks must be active for at least 24 months in order to test the [12:12] holding/formation period. The data retrieved from Datastream includes: the total return index (RI), the turnover (VO), the market capitalization (MV), and the VDAX. The maximum number of stocks for a period is 692 and the minimum number of stocks is 166, with a total average of 444 stocks per period.
3.2 Momentum
In order to construct the momentum portfolios, this paper uses a method similar to that of Jegadeesh and Titman (1993). This is the most common method used in the existing literature and is called the J-month/K-month strategy, where J stands for the formation period of the past returns and K for the holding period. Jegadeesh and Titman (1993) divide stocks into ten equally weighted portfolios, depending on their past J-month return, at the end of each month t. Unlike
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Jegadeesh and Titman (1993) this paper creates five equally weighted portfolios due to the smaller size of the German stock market. The stocks with the highest returns are assigned to the “winners” portfolio and the stocks with the lowest return are assigned to the “losers” portfolio. To create the momentum returns, the latter portfolio, the “losers,” will be subtracted from the first portfolio, the “winners.” There are four different formation periods: J-3, J-6, J-9 and J-12. This paper follows the study by Cooper et al. (2004) who skip month t when calculating the formation period. For example, the formation period J-3 means that the stock returns are measured over the last 3 months. The time starts at t=-3 and ends at t=-1. The portfolios are held for K subsequent months: K-3, K-6, K-9 and K-12.
The stock returns are calculated arithmetically: 𝑅𝑖𝑡= 𝑅𝐼𝑖(𝑡 − 1) − 𝑅𝐼𝑖(𝑡 − 𝑗)
𝑅𝐼𝑖(𝑡 − 𝑗) (1)
where Rit is the return of stock i for the period t-J to t-1; RIis the lagged return of the
respective stock i at time t-J and t-1; and J denotes the formation period. To calculate the K-month returns, the following equation is used:
𝑅𝑖(𝑡 + 𝐾)= 𝑅𝐼𝑖(𝑡 + 𝑘) – 𝑅𝐼𝑖𝑡
𝑅𝐼𝑖𝑡 (2)
According to the momentum strategy, the winner portfolio must be bought and the losing portfolio must be sold after every month t. This portfolio is held for K months. Thus, it is possible to vary the formation period J and holding period K. The monthly returns of the constructed portfolios are calculated as follows:
𝑅𝑝𝑥(𝐽, 𝐾) = ∑ 𝑅𝑖𝑡 (𝐽 ,𝐾)
𝑁 (3)
where 𝑅𝑝𝑥(𝐽, 𝐾) is the monthly portfolio return at time t of the respective formation (J) and holding (K) period; N is the number of stocks in the portfolio; and Rit denotes the stock
return as calculated in Eq. 1.
In the next step the zero-sum portfolio is calculated, as Jegadeesh and Titman (1993):
Rpn(J;K) = Rpw (J;K) – Rpl (J;K) (4)
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Jegadeesh and Titman (1993) argue that using overlapping portfolios helps to reduce the effect of the bid-ask bounce, which means that the stock price tends to move back and forth between the bid- and ask-price. Since the portfolios are formed on a rolling basis, autocorrelation can be expected in the sample. Autocorrelation can be accounted for by using autocorrelation-consistent Newey-West (1987) standard errors to calculate the t-test (Agyei-Ampohmah, 2007).
The returns used in this paper are risk-adjusted. In order to create the risk-adjusted returns, the Carhart-four factor model (1997) can be used. The excess momentum returns are regressed to a constant and the corresponding factors:
(Rpt - Rf) = ap + β1p (Rm - Rf) + β 2p SMB + β 3p HML + β 4p MOM + ɛpt (5)
where Rpt denotes the portfolio return and Rf the risk-free rate; (Rpt-Rf) represents the
market return; SMB stands for small-minus-big factors, HML for market-to-book factor for the value premium and MOM represents the momentum premium (winner portfolio minus loser portfolio).
Table 1: Descriptive statistics of the unadjusted monthly momentum returns and the monthly returns on the market from 1995 to 2015
[3:3] [6:6] [9:9] [12:12] Rm Mean 0.0081 0.0099 0.01 0.0106 0.0079 Median 0.0065 0.0109 0.0111 0.0091 0.0126 Maximum 0.1145 0.8913 0.0498 0.0442 0.1644 Minimum -0.0942 -0.077 -0.0524 -0.0344 -0.2047 Std. Dev. 0.019 0.0199 0.0017 0.0166 0.0549 Skewness 0.0487 -0.2981 -0.912 -0.4214 -0.5163 Kurtosis 3.8226 3.7898 2.2317 0.682 1.583
Note: The table displays the average unadjusted monthly returns of the [3:3], [6:6], [9:9] and [12:12] strategies and the average monthly returns of the market.
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However, to test whether volatility explains and predicts momentum returns, this paper uses the same approach as Stivers and Sun (2010). In their study, each month’s payoff represents the outcome of a single [J:K] event. They argue that this approach is more appropriate because the explanatory variable directly corresponds to the momentum return in month t. This approach differs from those of Jegadeesh and Titman (1993) and Chordia and Shivakumar (2002), who use the average return of each investment every month. Consequently, each month’s return reflects multiple ranking periods.
Table 2: Descriptive statistics of the momentum returns from 1995 to 2015
[3:3] [6:6] [9:9] [12:12] Mean 0.0296 0.07 0.1064 0.1219 Median 0.0248 0.0762 0.1256 0.1179 Maximum 0.3789 0.6077 0.5021 0.5505 Minimum -0.2578 -0.5163 -0.5169 -0.4117 Std. Dev. 0.0767 0.1305 0.173 0.1828 Skewness 0.0408 -0.2972 -0.901 -0.445 Kurtosis 6.7167 6.6917 5.1632 3.7361
Note: This table shows the outcome of the average momentum return where every month represents the outcome of a single momentum strategy.
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Figure 1: Density function of the [9:9] strategy
Figure 2: Returns of the [9:9] strategy from 1995 to 2015
Figure 1 shows the density function of the [9:9] strategy. The long tail on the left displays the downside risk and the potential crash risk for an investor. Figure 2 shows the returns for the [9:9] of the zero-sum portfolio, as well as the winner and loser portfolio. In this figure the crashes of the strategy are visible. One notable crash occurred from October to December 2002, where the returns dropped from 12.67% to -45.28% within two months. The prior
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months’ WCSV moving average increased from 10.08% to 12.95% and the CSV moving average also increased from 20.82% to 23.27%. Another notable crash occurred from October 2008 to January 2009, when the momentum returns dropped from 8.91% in October 2008 to -51.68% in January 2009. The prior months’ WCSV increased from 11.71% to 17.68%, while the CSV increased from 13.48% to 20.32%. The figure also shows that the extreme crashes are driven by the loser portfolio, due to the rebound effect of the loser portfolio, as explained by Bohl, Czaja and Kaufmann (2016).
3.3 State variables
This paper considers two relevant market states, both related to volatility. According to several researchers,3 momentum gains are procyclical, meaning that if the market state improves, subsequent momentum returns are expected to be higher.
The first measure is cross-sectional volatility. Stivers and Sun (2010) find evidence that CSV is a countercyclical measure. This paper uses the following equally-weighted measure of CSV: CSVt = √∑ (𝑅 𝑖𝑡−𝑅µ𝑡)² 𝑁 𝑁 𝑖=1 (6)
where CSVt is the equally-weighted cross-sectional volatility in month t; N denotes the
number of available stocks in month t; Rit represents the return of stock i in month t; and Rµt is
the arithmetic mean of the return of the total stocks included in the metric at month t. I also use a market weighted measure of CSV (WCSV), calculated as follows:
WCSVt=√∑𝑛𝑖=1𝑤𝑖𝑡 (𝑅𝑖𝑡− 𝑅𝑤𝑡)² (7)
where: Rwt=∑𝑛𝑖=1𝑤𝑖𝑡∗ 𝑅𝑖𝑡 (8)
WCSVt is the market-weighted cross-sectional volatility in month t; Wit represents the
weight of stock i in month t. The weights are calculated by dividing the return index of each share by the total return index at every period t. Rit is the return of stock i in month t; and Rwt
denotes the total weighted return, as calculated in equation 8, in month t.
The advantage of the CSV measure is that it can be estimated across countries, markets and industries. The drawback of this estimation is that the calculation depends on past returns, making it a backward-looking measure of current volatility (Goltz, Guobuzaite and Martellini, 2011).
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The second measure of volatility is calculated by the implied volatility (VDAX). The implied volatility is a measure of the market expectation about the near-future volatility of the underlying stock. The VDAX represents the implied volatility for the German stock market. Implied volatility is estimated from option prices. It measures how much the return of an asset fluctuates between the present and the expiration date of the option. Thus, the key advantage of this measure is that implied volatility is a forward-looking measure, which represents the market expectations. A drawback of implied volatility is that the volatility is based on auxiliary option markets rather than actual stock or index returns (Goltz, Guobuzaite and Martellini, 2011). Furthermore, the measure is only available for markets that include a liquid option market.
Similar to Stivers and Sun (2010), this paper uses a three-month moving average for the volatility measures. Stivers and Sun (2010) argue that three months reasonably reflects changing market condition and eliminates noise in month-to-month variations.
Table 3: Descriptive statistics of the CSV, WCSV and VDAX three-month moving average from 1995 to 2015 CSVt-3 WCSVt-3 VDAXt-3 Mean 0.175766 0.115413 0.241500 Median 0.161621 0.102036 0.220767 Maximum 0.441381 0.317520 0.555100 Minimum 0.073346 0.056521 0.123233 Std. Dev. 0.060551 0.048043 0.093367 Skewness 1.575383 1.981283 1.284028 Kurtosis 6.449708 7.604477 4.323348
Note: The table shows the descriptive statistics of the three-month moving average of the CSV, WCSV and VDAX.
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Table 4: Correlations between the volatility measures and the momentum returns CSVt-3 WCSVt-3 VDAXt-3 [3:3] [6:6] [9:9] [12:12] CSVt-3 1 0.3156 0.1311 -0.0068 -0.0834 -0.1765 -0.128 WCSVt-3 0.3156 1 0.3342 0.006 -0.1338 -0.1232 -0.1016 VDAXt-3 0.1311 0.3342 1 -0.0989 -0.2977 -0.387 -0.3285 [3:3] -0.0068 0.006 -0.0989 1 0.2941 0.2436 0.1658 [6:6] -0.0834 -0.1338 -0.2977 0.2941 1 0.6029 0.4621 [9:9] -0.1765 -0.1232 -0.387 0.2436 0.6029 1 0.7977 [12:12] -0.128 -0.1016 -0.3285 0.1658 0.4621 0.7977 1
Note: The table displays the results for the correlations between the volatility measures and the momentum returns.
Table 4 illustrates the correlations between the volatility measures and the momentum strategies. It shows that the volatility measures are negatively correlated with the momentum strategies, except for the WCSV and the [3:3] strategy. Furthermore, the table shows that the VDAX has the highest correlation with the momentum strategy. In general, there appears to be a connection between volatility and momentum returns. After testing for autocorrelation, it can be concluded that it appears to be present. Consequently, the Newey-West standard errors are also used in the empirical analysis.
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Figure 3: three-month moving average of the CSV, WCSV and VDAX from 1995 to 2015. The graph in the upper left presents the CSV, in the upper right the WCSV and lower left the
VDAX.
3.4 Control variable
This paper also includes a more conventional measure of the market state to test whether this adds any predictive power to the volatility measures. Similar to Cooper et al. (2004), this paper includes the 36-month lagged returns of the German stock market at every month t. In addition, this study also includes the 12-month and 24-month lagged returns.
3.5 Empirical estimation
In order to investigate the impact of cross-sectional volatility on the subsequent momentum returns, the following equations have been formulated:
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where MOM are the returns of the momentum strategy for the four different holding periods; ΔMOMt, t-k is the change in the momentum return between MOMt and MOMt-k;CSVt-3
denotes the equally-weighted cross-sectional volatility three-month moving average, WCSVt-3
the market-weighted volatility three-month moving average, and VDAXt-3 the three-month
moving average of the implied volatility; and StRt denotes the lagged returns at t-12, t-24 and
t-36. D (CSVd, WCSVd, VDAXd) represents a dummy variable with which the volatility
measures are regressed. This dummy variable was created for each volatility measure and equals 1 when the difference of the three-month moving average of CSV from one period to another period is positive, and 0 otherwise. This dummy variable captures the direct increase in each volatility measure.
The estimations in equations (9) and (10) try to determine whether the different volatility measures (CSV, WCSV and VDAX) have intertemporal information about the subsequent momentum returns. As stated in the introduction, volatility is expected to be a countercyclical state variable that increases in times of distress (Gomes, Kogan, and Zhang, 2003; Zhang, 2005; Stivers and Sun, 2010), while the momentum returns are expected to be procyclical. This suggests that we should expect a negative relationship between volatility and the subsequent momentum returns in equation (9). Consequently, when higher volatility indicates a weaker market state, not only are the subsequent momentum returns expected to be lower, but the momentum return preceding the higher volatility state is also expected to be higher. When volatility increases, the previous economic state was stronger. If this is indeed the case, then the volatility can be seen as informative about changes in the momentum return. Equation (10) tries to captures this by regressing the subsequent momentum return minus the previous momentum return that precedes the volatility terms. Thus, the coefficients in equation (10) are expected to be lower than the coefficients estimated in equation (9).
4. Empirical Results
This chapter presents the empirical results. The first part describes the risk-adjusted momentum returns. The second part addresses the impact of the volatility measures on the subsequent momentum returns and the changes therein.
4.1 Risk-adjusted momentum returns on the Frankfurt Stock Exchange
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holding that portfolio for a short to long term. These returns were risk-adjusted using the Carhart-four factor model (1997). The table also contains information about the Newey-West t-values and whether the mean momentum return is significantly different from zero. Furthermore, it shows the size and volume of each portfolio. The size of a portfolio measures the average market value of stocks in that portfolio, while the volume measures the average turnover by volume and is used as a proxy for liquidity.
As we see, every strategy generates a higher return than the general market return except for the [3:12] strategy. It is notable that longer ranking periods generated higher returns for each holding period. The lowest return was generated by the [3:12] strategy, where the return from the winner portfolio was 0.69% and the return from the loser portfolio was -0.08% for a total return of 0.77%. This is just below the monthly return on the market. The strategy that is most discussed in literature is the [6:6] strategy. The winner portfolio of that strategy had a return of 0.83% and the loser portfolio a return of -0.37%, which leads to a total return of 1.2%. The [6:3] and [12:3] strategies generated the highest returns. The winning portfolio of the [6:3] strategy had a return of 0.78% and the loser portfolio was -0.72%, which resulted into a total return of 1.5%. The [12:3] strategy yielded the same monthly return of 1.5%, with a return of 2.11% for the winning portfolio and a 0.61% for the losing portfolio. In comparison, the highest return that Jegadeesh and Titman (1993) found in their study was also the [12:3] strategy, which generated an annual return of 15.72% on the US stock market, which would be roughly 1.31% per month.
The zero-sum portfolios are all significant at the 1% level, meaning that the momentum anomaly challenges the market efficiency theory, which states that it is impossible to beat the market over the long term. The winner portfolio also shows high significance, except for the [3:3], [3:6] and [12:12] strategies, while the loser portfolio is not significant in any time frame. Jegadeesh and Titman (1993), Grinblatt and Moskowitz (2004) and Agyei-Ampomah (2007) argue in their studies that the largest share of the momentum returns is generated through the short position in the loser portfolio. In this paper, the loser portfolio did contribute to the momentum profits, except for the J=12 strategies, but the main momentum return was generated from the winner portfolio in every other case. Consequently, it can be concluded that short-selling on the German stock market is not as profitable as on other stock exchanges.
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liquid. This contradicts the theory proposed by Amihud (2002), who argues that stocks contain an illiquidity premium. In this sample the winner portfolio is more liquid and also generates higher returns than the relatively less liquid loser portfolio.
Table 5: Monthly risk-adjusted momentum returns on the Frankfurt Stock Exchange from 1995 to 2015
Holding period Ranking
Period
Portfolio K=3 K=6 K=9 K=12 Size Volume
W (t-value) 0.0062 (1.3845) 0.0058 (1.4822) 0.0068** (2.0135) 0.0069** (2.3362) 1789 36810 J=3 L (t-value) -0.004 (-0.6962) -0.0041 (-0.8375) -0.001 (-0.2309) -0.0008 (-0.2298) 751 31168 W-L (t-value) 0.0102*** (4.1773) 0.0099*** (4.9395) 0.0078*** (4.2671) 0.0077*** (5.1012) W (t-value) 0.0078* (1.9557) 0.0083** (2.3069) 0.0091*** (2.8082) 0.0088*** (2.9906) 2010 34642 K=6 L (t-value) -0.0072 (-1.2824) -0.0037 (-0.7584) -0.0022 (-0.5275) -0.0008 (-0.2319) 535 29453 W-L (t-value) 0.015*** (4.6315) 0.012*** (4.3026) 0.0113*** (4.5902) 0.0096*** (4.3879) W (t-value) 0.0098** (2.2856) 0.0101** (2.5975) 0.0105*** (2.9585) 0.0098*** (3.1158) 2239 33522 J=9 L (t-value) -0.0039 (-0.6287) -0.0028 (-0.5308) -0.0007 (-0.1575) -0.0001 (-0.0028) 441 30259 W-L (t-value) 0.0138*** (3.5227) 0.0129*** (4.0295) 0.0112*** (3.8968) 0.0099*** (4.0795) W (t-value) 0.0211* (1.9357) 0.0216* (1.729) 0.0246* (1.6529) 0.0244 (1.6266) 3134 38401 J=12 L (t-value) 0.0061 (0.5228) 0.009 (0.7013) 0.0137 (0.9165) 0.0148 (0.9901) 1071 36970 W-L (t-value) 0.015*** (3.8534) 0.0126*** (3.7801) 0.0109*** (3.997) 0.0096*** (4.2463)
Note: The table shows the monthly risk-adjusted momentum returns of the German stock market for the period from 1995 to 2015. The returns have been risk-adjusted with the Carhart four factor model. Furthermore, the Newey-West t-test was used to test whether the returns are significantly different from zero. W represents the winner portfolio, L the loser portfolio and W-L the zero-sum portfolio. J and K represent the formation and holding periods. Size stands for the average market value of stocks in that portfolio. Volume represents the turnover by volume and is used as a proxy for liquidity. *, ** and *** denote significance levels of 10%, 5% and 1%, respectively.
4.2 Impact of volatility on subsequent momentum returns
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forward-looking implied volatility (VDAX). As demonstrated by Gomes, Kogan and Zhang (2003), Zhang (2005) and Stivers and Sun (2010) volatility is a countercyclical state variable, while momentum returns are procyclical. Thus, a negative relationship was expected. A three-month moving average of each volatility measure is used, because this should be enough time to reflect changing market conditions (Stivers and Sun, 2010). The following empirical analysis focused on the most prominent momentum strategies in the literature, which are [3:3], [6:6], [9:9] and [12:12]. Every t-value has been regressed using Newey-West (1987) standard errors. Panel A of the table presents the results regarding the impact of the equally-weighted CSV on the subsequent momentum results. The equally-weighted CSV does not appear to affect the subsequent momentum returns. However, the dummy variable for the direct increase of CSV from one period to another does have a significant negative impact on the [3:3] strategy. This negative impact is significant at the 5% level and implies that an increase in the equally-weighted CSV from one period to another leads to a reduction in the subsequent momentum return for the [3:3] strategy. This implies that the equally-weighted CSV does contain information about the subsequent short-term momentum strategy.
Panel B of the table show the results for the market-weighted CSV (WCSV) variable on momentum returns. After controlling for the macroeconomic variables, the impact of the WCSV becomes significantly negative for the [6:6], [9:9], and [12:12] strategy at a 10% significance level. This indicates weak evidence that a high market-weighted CSV predicts lower subsequent momentum returns for mid- to long-term strategies. Furthermore, similar to the results in panel A, the dummy variable of the [3:3] strategy is negative and significant at a 5% level. Consequently, there is weak evidence that the market-weighted CSV does contain information about subsequent mid- to long-term momentum strategies and there is strong evidence that the WCSV does contain information about the short-term momentum strategy.
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Table 6: Impact of market volatility on subsequent momentum returns
21 | P a g e Panel C [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] VDAXt-3 -0.0953 (-1.6452) -0.4593** (-2.3518) -0.7609*** (-2.7262) -0.6136** (-2.0854) -0.0945 (-1.6395) -0.4545** (-2.3246) -0.7582*** (-2.6945) -0.6097** (-2.069) -0.1358 (-1.5114) -0.6646*** (-2.9333) -1.0896*** (-3.5182) -0.9092*** (-3.2496) Rm(-12) -0.0047 (-0.0709) 0.0205 (0.1734) -0.1023 (-0.6993) -0.0577 (-0.3756) Rm(-24) 0.0289 (0.5135) -0.0939 (-1.0695) 0.0344 (0.2953) 0.0929 (0.7824) 0.0288 (0.5101) -0.0944 (-1.0682) 0.0336 (0.29) 0.0911 (0.7702) 0.0337 (0.5794) -0.0791 (-0.9283) 0.0224 (0.1945) 0.0865 (0.7502) Rm(-36) 0.0615 (0.7769) 0.1282 (0.8144) -0.1008 (-0.557) 0.0208 (0.0999) VDAXd 0.0032 (0.2618) 0.02 (0.938) 0.0102 (0.3465) 0.0187 (0.5749) 0.008 (0.6098) 0.022 (0.9375) 0.0078 (0.256) 0.0074 (0.2312) Rsquared 0.0137 0.0995 0.1622 0.1041 0.0141 0.1049 0.1630 0.1067 0.0272 0.1868 0.2692 0.2138
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It can be concluded that the CSV measures in panel A and panel B do contain information about the subsequent short-term momentum strategy, while the VDAX measure contains information about the subsequent mid- to long-term momentum strategies. Furthermore, the coefficients are negative, which provides enough evidence to accept the hypothesis H1.
4.3 Impact of volatility on changes in momentum returns
This section investigates equation 10, which aims to determine whether volatility also explains changes in the subsequent momentum return. A negative relationship between volatility and momentum returns was expected, in which the coefficients are lower than in Table 6. This relationship is expected because it is presumed that high volatility indicates a change to a weaker market state. Thus, the subsequent momentum return is expected to be lower with the change to a weaker market state, and the prior payoff is expected to be higher since the market state has been stronger in the prior period. If this is the case, then volatility should also contain information about the changes in the subsequent momentum returns. Table 7 presents the results for equation 10. The table is constructed in the same way as Table 6 and uses the same variables to regress on the changes of the momentum returns.
Panel A shows that the equally-weighted measure for CSV does not explain the subsequent changes in momentum returns. The dummy variable is still significant at the 1% level and the coefficient is lower than that in Table 6. Thus, a direct increase in CSV leads to a reduction in the difference of the subsequent momentum returns.
Panel B presents the results for the market-weighted CSV. The WCSV appears to explain the changes in the momentum returns of the [9:9] strategy at a 5% significance level and the subsequent changes of the momentum returns of the [6:6] and [12:12] strategies at a 10% significance level. Furthermore, the coefficient for the dummy variable remains negative and significant at a 5% level. Each coefficient is negative and lower than those in Table 6.
The VDAX variable in panel C explains the changes of momentum returns of the [9:9] and [12:12] strategies at a 1% and 5% significance level and the changes of the momentum returns of the [6:6] strategy at a 10% significance level. The coefficients are negative and imply a negative relationship. Furthermore, they are lower than the coefficients in table 6.
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Table 7: Impact of volatility on the change in the momentum returns
Panel A [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] CSVt-3 0.0989 (0.6036) -0.1104 (-0.3929) -0.7073 (-1.598) -0.4542 (-1.1321) 0.1984 (1.2218) -0.0911 (-0.3004) -0.6656 (-1.3702) -0.4558 (-1.0935) 0.2173 (1.1243) -0.0252 (-0.0769) -0.6239 (-1.2363) -0.308 (-0.6886) Rm(-12) -0.0142 (-0.1706) -0.072 (-0.383) -0.3766 (-1.5511) -0.1801 (-0.8284) Rm(-24) 0.0238 (0.2795) 0.1168 (0.8142) 0.1587 (0.7214) 0.2658 (1.324) 0.0327 (0.3837) 0.1186 (0.8241) 0.1622 (0.7314) 0.2657 (1.3178) 0.0126 (0.1356) 0.0611 (0.4069) 0.1713 (0.7884) 0.2909 (1.4053) Rm(-36) 0.0511 (0.5957) 0.1468 (0.5677) -0.1125 (-0.3175) -0.1553 (-0.4855) CSVd -0.0457*** (-2.5588) -0.0091 (-0.3073) -0.0178 (-0.3899) 0.0007 (0.0162) -0.05*** (-2.6382) -0.0108 (-0.3541) -0.0271 (-0.5808) 0.0151 (0.2983) Rsquared 0.0021 0.0043 0.0219 0.0151 0.0349 0.0049 0.023 0.0151 0.0441 0.0292 0.0726 0.0384 Panel B [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] WCSVt-3 -0.0415 (-0.2101) -0.4332 (-1.5589) -1.0471** (-2.4884) -0.8211* (-1.8431) 0.0572 (0.305) -0.4711* (-1.701) -1.0503** (-2.4717) -0.7986* (-1.7458) 0.0292 (0.1588) -0.4469* (-1.6682) -0.7485 (-1.4739) -0.6656 (-1.2743) Rm(-12) -0.034 (-0.393) -0.0437 (-0.2155) -0.2798 (-1.0821) -0.1181 (-0.5262) Rm(-24) 0.026 (0.3058) 0.1331 (0.9662) 0.1884 (0.9155) 0.2959 (1.5954) 0.0345 (0.4174) 0.1298 (0.9605) 0.1881 (0.908) 0.2985 (1.606) 0.0158 (0.1755) 0.0669 (0.4782) 0.1879 (0.8958) 0.3163* (1.6868) Rm(-36) 0.0269 (0.3456) 0.1704 (0.6842) -0.1316 (-0.3904) -0.1175 (-0.3973) WCSVd -0.0449** (-2.1855) 0.0176 (0.6748) 0.0015 (0.0378) -0.0103 (-0.2304) -0.0498** (-2.3021) 0.0193 (0.6393) -0.0175 (-0.4068) -0.0056 (-0.1146) Rsquared 0.0006 0.0164 0.0416 0.0281 0.0325 0.0186 0.0416 0.0284 0.044 0.0418 0.0761 0.0475 Panel C [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] [3:3] [6:6] [9:9] [12:12] VDAXt-3 -0.0917 (-0.9473) -0.4278* (-1.8514) -1.0151*** (-3.1287) -1.0828*** (-2.7748) -0.0983 (-1.0562) -0.4275* (-1.8505) -1.0271*** (-3.2022) -1.0824*** (-2.7638) -0.0576 (-0.4217) -0.421 (-1.2793) -1.0689** (-2.4472) -1.146*** (-2.7143) Rm(-12) -0.001 (-0.011) -0.0317 (-0.1529) -0.2304 (-0.8736) -0.1014 (-0.4151) Rm(-24) 0.017 (0.1946) 0.0818 (0.543) 0.0639 (0.2747) 0.1764 (0.9107) 0.0174 (0.1987) 0.0818 (0.5417) 0.0673 (0.2913) 0.1762 (0.9123) 0.0061 (0.0652) 0.0465 (0.3072) 0.0631 (0.2599) 0.1905 (0.9451) Rm(-36) 0.0242 (0.2927) 0.1453 (0.6104) -0.1787 (0.2599) -0.138 (-0.5081) VDAXd -0.0246 (-1.1938) 0.0014 (0.0473) -0.0464 (-1.1977) 0.0019 (0.0422) -0.0236 (-1.0466) -0.0006 (-0.0183) -0.0383 (-0.5935) -0.0186 (-0.3597) Rsquared 0.005 0.0495 0.1371 0.1385 0.0149 0.0495 0.1452 0.1385 0.0157 0.0641 0.168 0.16
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5. Conclusion
The purpose of this paper is to study potential determinants of momentum strategies and in particular the impact of the recent volatility on momentum returns. The study was conducted on all traded shares on the Frankfurt Stock Exchange from 1995 to 2015. Similar to Jegadeesh and Titman (1993), this paper finds that investors can beat the market and receive abnormal returns of 1.5% per month over the long term through the momentum strategy. Although the short position contributed to the total momentum return in this sample, the main momentum return was generated through the long position, which contradicts the findings of Jegadeesh and Titman (1993), Grinblatt and Moskowitz (2004) and Agyei-Ampomah (2007). The zero-sum portfolios proved to be significant at a 1% level. However, as noted in this study, momentum returns come with occasional momentum crashes and short strings of negative returns. The most notable momentum crash occurred for the [9:9] strategy, with crashes up to -51.68% in this data set. Being able to explain the subsequent momentum returns would give investors indications about potential momentum crashes so that they would be able to hedge their exposure to avoid huge losses over the next period. This paper finds that volatility does explain subsequent momentum returns.
The impact of two volatility measures on the subsequent momentum returns has been analyzed. One was the CSV, which was measured as an equally-weighted CSV and as a market-weighted CSV. The other, implied volatility, was measured as the VDAX. The results indicate that volatility and momentum returns have a negative relationship, and therefore there was enough evidence to accept hypothesis H1: Volatility has a significant negative impact on subsequent momentum returns. The results also showed evidence that the CSV measures explain short-term momentum returns, while there is strong evidence that the implied volatility explains mid- to long-term momentum returns. The findings are similar to those of Stivers and Sun (2010) and Tang and Mu (2012), who found that their volatility measures do explain subsequent momentum returns and that there is a negative relationship between volatility and momentum returns. It can be concluded that recent market volatility can be seen as an indication for potential momentum crashes. As market volatility rises, subsequent negative momentum returns are more likely.
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might test whether a double-sorted approach, where winning and losing stocks are sorted and categorized as high- and low-volatility stocks, reduces risk and maximizes the return.
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