The effect of short-term return reversals on momentum profits

The authors investigate the effect of a short-term stock return reversal on the term structure of momentum profits in the Korean stock market following Goyal and Wahal (2015). Their empirical findings show that the term structure of momentum is more pronounced when a return reversal lasts up to two months but is


Introduction
This study examines the term structure of momentum profits reported by Novy-Marx (2012) in the Korean stock market. Jegadeesh and Titman (1993, JT hereafter) find that past returns can predict future returns: the strategy of buying past winners and selling past losers generates significantly positive profits. Since then, various studies have documented that momentum, defined as the tendency of winners to win and losers to lose, exists in stock prices. Indeed, the momentum phenomenon is prevalent and robust in different countries, asset classes and sample periods (Rouwenhorst, 1998;Jegadeesh and Titman, 2001;Chui et al., 2010;Fama and French, 2012;Asness et al., 2013).
However, the profitability of the momentum strategy remains controversial in the Korean stock market. While most studies conducted in the late 1990s argue that no momentum exists in the Korean stock market (Kho, 1997;Kim and Eom, 1997), more recent studies find that the significance of JT momentum profits depends on firm characteristics and sample periods (Chung and Kim, 2002;Eom, 2013) [1]. Chung and Kim (2002) investigate stock samples from 1998 to 2001 and find that the momentum phenomenon exists depending on the size of the company and holding period of portfolios. Eom (2013) investigates both the KOSPI and the KOSDAQ markets over 1980-2009 and shows that momentum profits are more significant in the 2000s. Kim (2012), Jang (2017) and Kim and Lee (2018) also find that momentum profits have become more significant in the Korean stock market [2]. Jang (2017) investigates the term structure of momentum profitability in the Korean stock market according to Novy-Marx (2012). She finds that momentum profits are primarily driven by returns over the intermediate (past t-12 to t-7 months) rather than the recent (past t-6 to t-2 months) horizon. This finding is puzzling because it is inconsistent with the traditional view of momentum that stock prices continue moving in the same direction. "Echo," rather than momentum, thus seems to exist in Korean stock returns, consistent with the previous US-based results of Goyal and Wahal (2015).
In this study, we investigate the underlying cause of the echo effect in the Korean stock market. Our conjecture is that a return reversal over two months induces the difference in profits between strategies based on intermediate-horizon performance and recent performance. The conventional momentum strategy measures past performance over the preceding months, skipping the most recent month to avoid market microstructure effects, including a one-month return reversal [3]. Thus, the one-month reversal effect cannot contaminate the profitability of the conventional momentum strategy. However, if the return reversal occurs over a period of months, the reversal will affect the profitability of the momentum strategy, which might erode momentum profits.
Several studies have consistently reported that a short-term return reversal exists in the Korean stock market (Yun and Cho, 2006;Kim and Song, 2013;Kang and Jeong, 2018). The reversal can be explained by several theories, among which the widely accepted explanation is based on compensation for providing liquidity. Campbell et al. (1993) present a model in which liquidity providers absorb the excess supply of a stock at a lower price and expect a positive return. Their model implies that a subsequent reversal in the stock price reflects the premium required by liquidity providers. An alternative explanation of short-term reversals is that they are associated with investor overreaction (Lehmann, 1990). The overreaction and subsequent correction of prices can lead to the return reversal.
We hypothesize that the difference in profits between intermediate return-based and recent return-based momentum strategies, that is, the term structure of momentum, arises because of a carryover from a short-term reversal from months before portfolio formation. Based on a large sample spanning 1999-2021, we provide the supporting evidence for the hypothesis. First, we observe a term structure of momentum profits in the Korean stock market, consistent with Novy-Marx (2012) and Jang (2017). Specifically, the intermediate return-based strategy constructed 12 to seven months before outperforms the recent returnbased strategy constructed six to two months before. The magnitude of the difference in returns from the two strategies is as high as 0.615% per month based on the five-factor alpha. Second, we find that the term structure of momentum profits is more prominent when a return reversal occurs over two months. The difference in profits between the intermediate returnand recent return-based strategies is greater when the reversal strategy suggested by Nagel (2012) earns positive returns, which suggests that the reversal drives the term structure of momentum. Lastly, but most importantly, we find that the term structure of momentum weakens when we exclude the most recent two months for the recent return definitions. This implies that the return difference between the intermediate return-and recent return-based strategies is primarily driven by the underperformance of the former, which is due to the inclusion of the second month in recent return portfolios. Overall, our findings strongly support the hypothesis that the term structure of momentum profits is a manifestation of the short-term (two-month) return reversal effect.
This study contributes to the literature as follows. First, we provide a convincing explanation for the term structure of the momentum and echo effects in the Korean stock market. This is primarily driven by a return reversal occurring over two months. Second, we provide practical implications for the design of more profitable trading strategies. A stock selection criterion that excludes the performance of the most recent two months can significantly improve the profitability of a momentum strategy. Lastly, we confirm that the echo effect exists in the Korean stock market like the US market based on a large sample covering 1999-2021. By expanding the sample to the latest period in which COVID-19 has affected the global financial market, we also contribute to the existing literature.
The remainder of this paper is organized as follows. Section 2 explains the data source and methodology, and Section 3 examines momentum profits and their term structure. Section 4 investigates whether the term structure is related to a short-term return reversal. Section 5 concludes.

Data and methodology
To examine the term structure of momentum returns, we employ the conventional momentum strategy suggested by JT. Specifically, at the end of month t, we sort stocks based on pret (p, q) , denoting the cumulative returns from months t-p to t-q (inclusive), and construct a long-short strategy by buying stocks in the top quintile and selling stocks in the bottom quintile. Hereafter, we denote the long-short strategy based on pret (p, q) as "the pret (p, q) strategy." Our sample consists of all the firms listed on the Korea Stock Exchange from January 1999 to February 2021. We obtain market and accounting data from DataGuide and KIS-VALUE. To be included in our sample, a stock must have at least 14 days in the month. We exclude stocks priced below 500 Korean won at the end of the previous month. The final sample includes, on average, 658 firms per month. Table 1 presents the summary statistics for the variables of interest, including the mean, standard deviation and 5th, 25th, 50th, 75th and 95th percentiles. r (À1) is a stock's monthly return, SIZE is the natural logarithm of market capitalization and BM is the book-to-market ratio. OP is the operating profitability ratio calculated by dividing EBIT by the book value to equity, and INV is asset growth computed following Fama and French (2015). IVOL is the idiosyncratic volatility estimated as the standard deviation of the residuals obtained from a regression of daily excess stock returns based on Fama and French's (2015) five-factor model over a one-month window. ILLIQ is the natural logarithm of Amihud's (2002) illiquidity measure computed as the absolute daily return divided by the daily dollar trading volume, averaged over all the trading days in a month.  and pret (p, q) is the cumulative return over months t-p to t-q (inclusive). return is a stock's monthly return, SIZE is the natural logarithm of market capitalization and BM is the book-tomarket ratio. OP is the operating profitability ratio calculated by dividing EBIT by the book value to equity, and INV is asset growth computed following Fama and French (2015). IVOL is the idiosyncratic volatility estimated as the standard deviation of the residuals obtained from a regression of daily excess stock returns on the Fama and French's (2015) five factors over a one-month window. ILLIQ is the natural logarithm of Amihud's (2002) illiquidity measure computed as the absolute daily return divided by the daily dollar trading volume, averaged over all the trading days in a month. All the returns and IVOL are reported in percentage Table 1.

Summary statistics
The reversal effect on momentum profits First, we examine the term structure of momentum using Fama-MacBeth (1973) regression, as in Novy-Marx (2012) where r i,t is the rate of return of stock i in month t. pret ðp 1 ; q 1 Þ and pret ðp 2 ; q 2 Þ , respectively, refer to the cumulative intermediate-horizon returns and recent-horizon returns. z is a set of control variables. In the most general specification, z i,tÀ1 includes size (SIZE), the book-to-market ratio (BM), operating profitability (OP), investment (INV), illiquidity (ILLIQ), idiosyncratic volatility (IVOL) and a one-month reversal (r À1 ) [4]. The positive and significant coefficient of pret ðp i ; q i Þ implies that the momentum strategy based on pret ðp i ; q i Þ is profitable. Our main interest is in the difference between the pret ðp 1 ; q 1 Þ and pret ðp 2 ; q 2 Þ slopes. This difference implies the presence of the term structure of momentum. In particular, a lower slope of pret ðp 2 ; q 2 Þ indicates the inferior performance of momentum strategies based on recent past returns.
Next, we examine which months contribute to (or erode) the profitability of momentum strategies. We run the full-term structure regressions suggested by Jegadeesh (1990): where r i,t is the rate of return of stock i in month t. z is a set of control variables. The b k is interpreted as the return responses at various lags of k. If b k is significantly negative, it indicates that the return in month t − k reverses in month t. For example, if a return reversal carries over two months, b 2 is negative and significant. Finally, we examine whether the term structure of momentum is more pronounced in the presence of return reversals using the following time-series regression: where r dif t is the difference in returns between the pret ðp 1 ; q 1 Þ and pret ðp 2 ; q 2 Þ strategies. f t is a vector of the risk factors of the CAPM, Fama and French (1993) three-factor and Fama and French (2015) five-factor models in month t. H t is a dummy variable equal to 1 if the reversal strategy suggested by Nagel (2012) generates a positive return and 0 otherwise; hence, H is an indicator of the presence of return reversals. The reversal strategy involves assigning the portfolio weights w i,t to stock i at time t based on the past return of stock i (r i,tÀk ) relative to the returns on the equal-weighted market portfolio (r m,tÀk ): where N is the number of stocks in month t. In Equation (4), the weight implies buying stocks whose returns are less than the market return in month tÀk and selling stocks whose returns are greater than the market return in month tÀk. Thus, the higher the reversal strategy returns, the stronger is the return reversal from months tÀk to t [5]. In Equation (3), the coefficients of interest are α, the intercept, and β, the slope of the reversal dummy. The insignificant α indicates that the term structure of momentum disappears in the absence of a short-term return reversal. The significant and positive β implies that the term structure is more prominent in the presence of a return reversal. Table 2 shows the average monthly returns for the long-short portfolios for the momentum strategy based on different past performances [6]. Columns (1), (2) and (3) show the returns based on pret (12,2) , pret (12,7) and pret (6,2) , respectively. Column (4), labeled "pret (12,7) -pret (6,2) ," shows the difference in returns between the two long-short portfolios based on pret (12,7) and pret (6,2) . We report the raw returns and alphas from the CAPM, three-factor model and fivefactor model [7]. First, we find that the conventional momentum strategy, based on pret (12,2) , does not generate positive returns, consistent with previous studies finding no price momentum in the Korean stock market (Chung and Kim, 2002;Ahn and Lee, 2004;Park and Jee, 2006;Chui et al., 2010). The strategy based on recent past returns also does not earn significant profits; indeed, it is even negative. The five-factor alpha of pret (6,2) is À0.084 (t-statistic 5 À0.28). However, the strategy based on the intermediate past returns exhibits different results. The pret (12,7) strategy generates a positive five-factor alpha of 0.531% (t-statistic 5 2.05). Accordingly, momentum strategies formed on pret (12,7) outperform strategies formed on pret (6,2) by 0.615% per month with a t-statistic of 2.01. The superior profitability of intermediate strategies implies that momentum strategies have the term structure of returns in the Korean market like the US market. Our finding confirms Jang (2017) for our extended sample, which includes recent years. Figure 1 plots the trends of the cumulative returns of the momentum strategies based on intermediate-horizon and recent past performance, respectively. Consistent with the earlier results, the pret (12,7) strategy (solid line) generates significantly higher cumulative returns than the pret (6,2) strategy (dashed line) over the sample period. Specifically, an investor investing 1 Korean won in the first month of the sample period would have earned 3.11 Korean won with the pret (12,7) strategy and 0.67 Korean won with the pret (6,2) strategy. Figure 2 presents the momentum profits across holding periods. We construct the longshort momentum portfolio and hold the portfolio over subsequent K (K 5 3, 6, . . ., 24) months using JT's overlapping approach. The blue and red bars represent the five-factor alphas of the pret (12,7) and pret (6,2) strategies, respectively, and the asterisk above the bar represents statistical significance. First, the profits of the pret (2,7) strategy decrease with the holding period. The profits are statistically positive with one-and three-month holding periods but become not significant with holding periods longer than six months [8]. On the contrary, we find no evidence of a decreasing pattern with the pret (6,2) strategy; indeed, this strategy generates even higher returns with three-, six-and nine-month holding periods than with a pret (12,2) pret (12,7) pret (6,2) pret (12,7) -pret (6,2) (12,2) , pret (12,7) and pret (6,2) strategies and the difference in returns between the pret (12,7) and pret (6,2) strategies. We report the raw returns and alphas from the CAPM, three-factor model and five-factor model. The pret (p,q) strategy refers to the momentum strategy constructed each month by buying winners and selling losers, which are defined as the top and bottom quintiles of cumulative returns over months t-p to t-q (inclusive). All the returns are reported in percentage. Numbers in parentheses are the t-statistics calculated using the Newey and West's (1987) robust standard errors. ***, ** and * denote significance at the 1, 5 and 10% levels, respectively The reversal effect on momentum profits one-month holding period, although they are insignificant. A possible explanation is that profits from the intermediate-horizon strategy carry over to profits from the recent returnbased strategy as the holding periods increase because we revise the weight on 1/K of the momentum portfolio in any month [9]. Table 3 reports the estimation results of the Fama-MacBeth (1973) regression of Equation (1). Columns (1) and (2) show that while the coefficient of pret (12,7) is 0.733% and statistically significant at the 1% level, the coefficient of pret (6,2) is not significant. Our primary interest is in the difference between the pret (12,7) and pret (6,2) coefficients. The difference, reported in Column (3), is 0.475% (t-statistic 5 1.98), positive and significant at the 5% level. Columns (4)- (6) report the results when we use risk-adjusted returns as the dependent variable in Equation (1) [10]. Consistently, the coefficient of pret (12,7) is significantly positive, whereas that of pret (6,2) is insignificant. The difference between the coefficients of pret (12,7) and pret (6,2) is significant and positive.

Term structure of momentum profits
The estimated coefficients of the control variables are consistent with our expectations: the price reverses at monthly horizons (Jegadeesh, 1990;Lehmann, 1990;Yun and Cho, 2006), high idiosyncratic volatility is associated with lower subsequent returns (Ang et al., 2006;Kang et al., 2014a) and firms with more aggressive investment earn higher average returns (Aharoni et al., 2013). On the contrary, we find that the illiquidity effect (Amihud, 2002) and profitability effect (Novy-Marx, 2012;Fama and French, 2015) are insignificant in the Korean market unlike in the US market.

Term structure of momentum profits and short-term return reversal
To investigate which months contribute to or erode the profitability of momentum strategies, we run the cross-sectional regressions in Equation (2). Table 4 presents the results of the estimation. First, r tÀ1 has a negative coefficient of À2.950% (t-statistic 5 À3.77), consistent with previous studies finding the existence of a one-month return reversal in the Korean stock Note(s): This figure plots the cumulative returns of the pret (12,7) strategy (solid line) and pret (6,2) strategy (dashed line). For comparison purposes, we report the cumulative profits of the market index (dotted line). The pret (p,q) strategy refers to the momentum strategy constructed each month by buying winners and selling losers, which are defined as the top and bottom quintiles of cumulative returns over months t-p to t-q (inclusive) Figure 1. Cumulative profits of the momentum strategies market. Next, and most importantly, the coefficient of r tÀ2 is À1.108 (t-statistic 5 À2.01), significant at the 5% level. As we suspect, the return reversal occurs over more than one month [11].
To further examine whether a return reversal is carried over up to two months, we use the reversal strategy suggested by Nagel (2012), which involves buying stocks whose returns are less than the market return and selling stocks whose returns are greater than the market return. Panel A of Table 5 presents the returns of the reversal strategy, as shown in Equation (4). When k 5 1, we find significant raw returns and a five-factor alpha of 1.293% (t-statistic 5 3.32) and 1.275% (t-statistic 5 3.22) per month, respectively. The positive and significant profit is consistent with our earlier findings. Comparing the result reported by Hameed and Mian (2015), who study the US stock market, the profit is relatively high, implying that the short-term return reversal is strong in the Korean market. More importantly, the reversal strategy exhibits significantly positive returns, even when k 5 2. The raw return and five-factor alpha are 0.432% (t-statistic 5 1.83) and 0.514% (t-statistic 5 1.99), respectively. Consistent with Table 5, we find a carryover of a return reversal from month tÀ2. However, when k 5 3, the reversal strategy does not exhibit significant results. Hence, the reversal effect does not appear to last for more than three months.
The existence of a return reversal: return responses to the prior 12 months Table 3. Term structure of momentum profits: cross-sectional regressions our focus is a carryover of a reversal from the penultimate month [12]. Columns (1)-(3) report the estimation results for the reversal strategy assigning portfolio weights based on raw returns, risk-adjusted returns and market-adjusted returns, respectively [13]. We control for exposure to risk factors based on the CAPM, Fama and French (1993) three-factor and Fama and French (2015) five-factor model.
We obtain consistent results with the Fama-MacBeth (1973) regressions. As shown in Table 3, we run the regression of Equation (2), but with return lags that mitigate the negative effect of month tÀ2 on recent returns. Table 8 presents the estimation results [15]. Each column contains a slightly different definition of intermediate-horizon and recent returns. In Columns (1), (5) and (6), we use pret (6,2) instead of pret (6,3) as an independent variable to examine the impact of month tÀ2. Columns (2), (3) and (4) are used for a comparison with the other columns. Overall, the coefficient of intermediate-horizon returns is larger than that of recent returns. However, the difference is insignificant with only pret (6,2) , not with pret (6,3) , implying that the influence of month tÀ2 is significant for the term structure of the momentum strategy.
Finally, Figure 3 illustrates the cumulative returns of momentum strategies. Consistent with the previous results, the pret (12,3) strategy (dashed line) has higher cumulative returns than the pret (12,2) strategy (red solid line). Investing 1 Korean won in the first month of our sample period would have earned 2.43 Korean won based on the pret (12,3) strategy, which is much higher than the 1.43 Korean won gained from the pret (12,2) strategy. Similarly, the pret (6,3) strategy generates higher cumulative returns than the pret (6,2) strategy. The earlier comparison provides practical implications for the design of more profitable trading strategies. Ignoring performance over the last two months in the stock selection criteria can improve the profitability of momentum strategies.
Our empirical results provide practical implications for the design of profitable trading strategies. By ignoring recent performance (especially the last two months of portfolio formation) in portfolio selection criteria, portfolio managers can improve the profitability of momentum strategies. Additionally, we provide a plausible explanation for the relatively weak momentum in Korean stock prices. According to Chui et al. (2010), the momentum phenomenon is insignificant in the Korean market. Our findings suggest that a long-lasting return reversal reduces the profitability of the JT momentum strategy. Such a reversal also provides a clue to understanding the trend that momentum profits are insignificant (or even negative) before the Asian crisis but become more significant thereafter (Kim, 2012;Kim and Lee, 2018). Kim and Lee (2018) explain that the difference between the pre-and postcrisis periods is driven by a change in market illiquidity. Our results can be reconciled with their findings because a short-term return reversal is closely related to the illiquidity premium (Campbell et al., 1993).

Notes
1. Additionally, Ahn and Lee (2004), based on data from 1994 to 2001, find that the stock price does not show momentum but tends to reverse. Park and Jee (2006), based on data from 1980 to 2003, find that the momentum phenomenon exists only in stocks with low price volatility.
2. Kim (2012) shows that momentum strategies earned significant profits after the 1997 Asian crisis, while contrarian strategies were able to generate profits in the precrisis period. The author argues that the increased participation of foreign and/or institutional investors after the crisis affected the profitability of momentum strategies. Kang et al. (2014b) also link the trading behavior of foreign investors to the momentum effect. Meanwhile, Kim and Lee (2018) argue that the momentum phenomenon has become significant as overall market liquidity has increased since 2000. The liquidity premium offsets momentum profits as losers tended to have less liquidity than winners Note(s): This figure plots the cumulative profits of the momentum strategies, calculated at the end of January 2021, with 1 Korean won invested at the beginning of July 2002. The pret (p, q) strategy refers to the momentum strategy constructed each month by buying winners and selling losers, which are defined as the top and bottom quintiles of cumulative returns over months t-p to t-q (inclusive) The reversal effect on momentum profits