The volatility index and style rotation: Evidence from the Korean stock market and VKOSPI*

Transcription

1 C Lee** and D Ryu*** The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP The volatility index and style rotation: Evidence from the Korean stock market and VKOSPI* ABSTRACT We investigate whether changes in the implied volatility index (VKOSPI) of the Korean market have predictive power for daily market s. We find that future s on large stocks are higher than those on small stocks on days that follow an increase in the VKOSPI. Additionally, we find that future s on growth stocks are larger than those on value stocks on days following an increase in the VKOSPI. We also provide empirical evidence that a potential trading rule based on changes in the VKOSPI might be profitable. Our findings indicate that the VKOSPI can be used in predicting the performance of large/small and value/growth stocks in practice. 1. INTRODUCTION * Constructing an optimal asset allocation rule has been one of the most important issues in the field of financial economics. Two major strategies have emerged in the literature. On one hand, investors pursue a buy-andhold strategy under the belief that, despite periods of decline in stock prices, this relatively static strategy will provide a good rate of in the long run. On the other hand, investors rebalance their portfolios based on publicly available information that helps in predicting future market price movements. This dynamic strategy is based on the conjecture that future s can be forecasted using certain economic indicators. There is an ongoing debate in the existing literature as to whether buy-and-hold strategies outperform portfolio-rebalancing strategies for maximum profit. In the interest of providing new empirical evidence to this literature, we examine whether a potential trading rule based on an implied volatility index has markettiming ability. We are particularly interested in the implied volatility index as an indicator for the following reasons. First, a large body of literature has documented the relationship between changes in volatility and future asset s. Prominent examples include studies by Merton (1980) and French, Schwert, and Stambaugh (1987). Merton (1980) investigates the association between market risk premium and volatility, documenting that market risk premium has a positive relationship with the variance of market portfolios. French, Schwert, and Stambaugh (1987) find that the expected market risk premium is positively related to the forecastable volatility of stock s. Second, even though macroeconomic variables have * The authors are grateful for the helpful comments and suggestions from Heidi Raubenheimer (the editor), Robert I. Webb, and the anonymous referees. Changjun Lee is grateful for the Hankuk University of Foreign Studies Research Fund of ** Changjun Lee, College of Business Administration, Hankuk University of Foreign Studies, Seoul, Republic of Korea. leechangjun@hufs.ac.kr *** Doojin Ryu, Corresponding author, School of Economics, Chung-Ang University, Seoul, Republic of Korea. Tel: , doojin.ryu@gmail.com frequently been employed as state variables, macroeconomic variables are not adequate for our research purposes. This is because we are interested in timing strategies that are applicable for traders in real time. Most macroeconomic variables are released on a quarterly basis and undergo revisions. In contrast, the volatility index changes every minute, and its variation over time is likely to reflect the risk preferences and future expectations of market participants. Accordingly, the volatility index is a powerful candidate for an informative trading indicator for investors. Although extensive literature has investigated market timing ability, the purpose of the present paper is to provide empirical evidence in an emerging market. There are at least two important motivations for studying the Korean market, which is the leading financial market among emerging economies. First, as suggested by Lo and MacKinlay (1990), out-of-sample experiments on emerging markets provide additional evidence for whether or not findings in developed markets can be generalized worldwide. Previous studies on the relation between volatility index and future stock s have focused on the U.S. market. For example, using the U.S. market data, Copeland and Copeland (1999) document that large stocks outperform small stocks and value stocks outperform growth stocks on days following an increase in the volatility index. Although the U.S. market is generally accepted as the predominant developed market, empirical findings on the U.S. market are not necessarily present in an emerging market due to differences in regulatory environment and capital investment opportunities. Second, we adopt the VKOSPI (Volatility Index of KOSPI 200), which is the official implied volatility index recently developed by the Korea Exchange (KRX), as a trading indicator. This is a meaningful measure in that the VKOSPI is derived from the prices of KOSPI 200 options, which are the world s most remarkable and liquid options that attract great investor interest both locally and globally. We believe that the VKOSPI precisely and quickly reflects investor sentiment and expectations. This makes the index an appropriate Investment Analysts Journal No

2 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSPI trading indicator for the Korean market and other emerging markets. Despite these important features of the VKOSPI, there is little research on the contents and applicability of the VKOSPI. 1 Previous research does not elucidate the behavior of the VKOSPI as it relates to the performance of investment strategies among market participants. Considering that the VKOSPI has begun to play an important role as a major leading trading indicator for emerging economies, and given that the KOSPI 200 options market has some unique properties in contrast to the derivatives markets of developed countries, 2 more indepth studies of the utilization of the VKOSPI are urgently needed. Specifically, we investigate the relative performance of small versus large and value versus growth stocks according to changes in the implied volatility index of the Korean financial market. Our choice of specific styles reflects the fact that portfolio s based on firm size and value/growth orientation have been widely used in practice as well as in academics. In industry, equity funds are generally classified based on their market capitalization and value/growth orientation. For instance, the funds of Morningstar Groups are classified into the cells of a nine-square box according to firm size and orientation toward value or growth. In academics, Basu (1977) and Banz (1981) document the effects of firm size and price earnings ratio on stock s. In a series of seminal papers, Fama and French (1993, 1996) develop a three-factor model with factors related to firm size and book-tomarket ratio. Since the work of Fama and French (1993, 1996), numerous studies have investigated the behavior of size and book-to-market sorted portfolios (Levis and Liodakis, 1999; Lettau and Ludvigson, 2001; Petkova and Zhang, 2005; Auret and Cline, 2011; Strugnell, Gilbert, and Kruger, 2011, Muller and Ward, 2013). We report two main findings. First, we find that future s on large stocks are higher than those on small stocks on days that follow an increase in the VKOSPI. Our empirical evidence on market capitalization is consistent with the findings of Copeland and Copeland (1999), who document that large stocks outperform small stocks on days following an increase in the volatility index of the U.S. market. Given that previous studies have documented that large stocks are safer than small stocks in bad economic times (Quiros and Timmerman, 2000), our empirical findings support flight-to-quality and flight-to-liquidity hypotheses because large stocks indeed outperform small stocks after an increase in the VKOSPI. Additionally, we find that future s on growth stocks are higher than future s on value stocks on days following an increase in the VKOSPI. This finding is opposite to the results of Copeland and Copeland (1999), which support the hypothesis that value stocks outperform growth stocks on days following an increase in the volatility index of the U.S. market. We believe that our empirical finding on value/growth stocks also supports the flight-to-quality phenomenon because value stocks are riskier than growth stocks in bad economic times (Lettau and Ludvigsion, 2001; Petkova and Zhang, 2005; Kang, Kim, Lee, and Min, 2011). Second, we find that a potential trading rule based on change in the VKOSPI may be profitable. A trading rule that takes a long position on large (small) stocks and a short position on small (large) stocks when the daily percentage change in the VKOSPI is positive (negative) yields economically huge s for holding periods of up to twenty days. In addition, when we implement a trading rule in which we construct a zerocost portfolio that is long on growth (value) stocks and short on value (growth) stocks at a time when changes in the VKOSPI are positive (negative), the trading rule creates consistently positive s. Our empirical evidence also indicates that the VKOSPI can be useful in predicting the performance of large/small and value/growth stocks. These results again support the flight-to-quality hypothesis. Our empirical findings have some important implications. Since the VKOSPI is estimated from the most remarkable and liquid options market, the KOSPI 200 index options market, it is very likely that market participants refer to the changes in the VKOSPI when they make investment decisions. Indeed, we find that the volatility index does a good job in capturing the future stock s of particular styles. Thus, one implication of the present study is that stock market participants can be better off by paying attention to the current variability of the volatility index. The present paper contributes to the existing literature on market timing and style rotation. Our empirical work on market timing is related to studies by Treynor and Mazuy (1966), Henriksson and Merton (1981), Ferson and Schadt (1996), Pesaran and Timmermann (2002), and Bhaduri and Saraogi (2010). Our paper is different from previous papers in that we directly investigate market timing ability by calculating future s based on a potential trading rule. Our empirical study of style rotation is linked to the works of Chan, Chen, and Lakonishok (2002), Barberis and Shleifer (2003), Ainsworth, Fong, and Gallagher (2008), and Brown, Harlow, and Zhang (2009). Our work adds to the literature by providing empirical evidence on the Korean market and using the VKOSPI. 2. THE KOSPI 200 OPTIONS MARKET AND VKOSPI Since the introduction of KOSPI 200 index options by the Korea Exchange (KRX) in 1997, the trading volume of index options has sharply increased. In fact, the index options product has now become the most actively traded and liquid derivatives asset in the world. Even though highly speculative and noisy individuals were major market players in the KOSPI 30 Investment Analysts Journal No

3 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP 200 options market in its early stages, the trading volume of professional investors and experienced institutions has continuously increased to the point that their trading activity now accounts for a substantial portion of the total trading volume in the market. Meanwhile, the trading volume of foreign investors has also grown rapidly. Together with the continual increase of institutional trades and the trades of global investors, the rapid growth and abundant liquidity of the KOSPI 200 options market indicate that the market is of great concern and interest to both global and local investors. 3 It is generally understood that the KOSPI 200 options prices instantly reflect information shocks related to the Korean market and global markets due to the fierce competition among professional options traders who critically analyze and immediately react to the Korean market to maximize profits. Meanwhile, the views and expectations of global investors regarding the Korean market directly affect the dynamics of options prices. As a result, the options prices themselves become quite informative and reflect market-wide expectations about the future state of the Korean financial market. 4 The VKOSPI, which is the official and representative volatility index for the KOSPI 200 stock index, is derived from the informative options prices. As such, it becomes an informative and meaningful trading indicator. In addition, the abundant liquidity of the KOSPI 200 options market and the 200 underlying stocks that comprise the KOSPI 200 spot index add to the VKOSPI s reliability as a market indicator. Related to the huge trading volume of the KOSPI 200 options, the bid-ask spreads of the options are extremely narrow, nearly equal to the minimum tick size (Ahn, Kang, and Ryu, 2008, 2010; Ryu, 2011). This mitigates the bid-ask bounce problem that frequently occurs when illiquid options are used for analysis. The underlying spot index (KOSPI 200 index), which is also used in calculating the VKOSPI, consists of the 200 most actively traded stocks on the Korean stock market. This property of the underlying spot index successfully eliminates any non-synchronous trading or stale price problems, which are often detected in other stock indices. The VKOSPI is designed to capture the one-monthahead volatility of the stock prices of the KOSPI 200 spot index. Although it is calculated using the market prices of options, the VKOSPI is constructed using a model-free variance expectation method (i.e., the fair variance swap method), which is similar to the new VIX in the U.S. market. Accordingly, the values of the volatility index series are not affected by the restrictive assumptions of option pricing models. 5 After sufficient preparation and research, the KRX published the VKOSPI in April of Although the data span is relatively short considering the time-series data of the VKOSPI since its publication date, long-run artificial VKOSPI data can be constructed using the historical data of the KOSPI 200 index and options prices. 6 Figure 1 presents the movements of the underlying KOSPI 200 index prices and of the VKOSPI during the sample period of this study, which spans from January 2003 to December As the figure shows, major macroeconomic and global shocks, such as the Iraq War and the U.S. subprime mortgage crisis, cause spikes in the VKOSPI activity KOSPI200 VKOSPI Figure 1: Time-series behavior of the KOSPI 200 index and the VKOSPI. 3. SAMPLE DATA AND PORTFOLIO RETURNS To investigate the style s based on changes in the VKOSPI, we use size- and book-to-market-sorted portfolios on a daily basis from January 2003 to December 2010, and we use common stocks listed on the KOSPI market division. The Korean stock market is divided into the KOSPI market division and the KOSDAQ market division. Since we use the volatility index of the VKOSPI, which is derived from 200 leading companies of the KOSPI market division, we only use common stocks on the KOSPI market division. 7 The stock prices, s, and accounting information come from the FnGuide database, Korea s most comprehensive provider of data. We begin with all firms listed on the KOSPI market and exclude financial and insurance companies. We also include delisting firms into our analysis to minimize the survivor bias. The average 655 stocks are included over the sample period. We employ two versions of size and book-to-market sorted portfolios. The versions include two-by-three and five-by-five size and book-to-market sorted portfolios. To construct these portfolios, we follow the Fama-French (1993) approach. For the two-by-three sorted portfolios, at the end of June in year t, all stocks are sorted into two size groups (split 50%, 50%). Independently, all stocks are classified into three bookto-market groups (split 30%, 40%, 30%) based on the ratio of book equity in the prior fiscal year to market equity at the end of December in the prior year. To be Investment Analysts Journal No

4 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSPI included in our sample, a firm must have stock prices for December of year t-1 and June of year t and financial statements for year t-1. The six portfolios are held for one year and rebalanced at the end of June in year t+1. The on the large-minus-small portfolio is defined as the difference between the average s of the three large stocks and the three small stocks. The on the growth-minus-value portfolio is the difference between the average s of the two growth stocks and the two value stocks. In a similar way, we construct the five-by-five size and book-to-market sorted portfolios by dividing stocks into five groups (split 20%, 20%, 20%, 20%, 20%). Table 1 presents the average monthly s of portfolios sorted by size and book-to-market ratio. Panel A shows the results for the six portfolios, and Panel B shows the mean s for 25 portfolios. Small-Large is the difference between small stocks and large stocks, and High-Low is the difference between stocks with a high book-to-market ratio and stocks with a low book-to-market ratio. The numbers in parentheses are t-values. Table 1: Summary statistics Panel A: 2 by 3 sorts B/M MV Low 2 High High-Low Small (3.22) Large 0.32 (2.19) Small-large 0.10 (0.93) (4.13) 0.32 (2.59) 0.12 (1.33) (5.47) 0.53 (4.34) 0.00 (0.03) (1.55) 0.21 (1.65) Panel B: 5 by 5 sorts B/M MW Low High High- Low Small 0.36 (2.66) 0.34 (2.68) 0.40 (3.40) 0.3 (3.01) 0.57 (5.35) 0.21 (2.05) (2.57) 0.45 (3.42) 0.37 (3.07) 0.52 (4.65) 0.53 (4.89) 0.17 (1.51) (3.58) 0.65 (5.01) 0.55 (4.17) 0.58 (5.14) 0.63 (5.50) 0.10 (0.93) (4.27) Large 0.29 (1.92) Small-Large 0.07 (0.56) (4.90) 0.30 (2.03) 0.05 (0.39) (6.38) 0.27 (2.06) 0.13 (1.17) (5.57) 0.32 (2.42) 0.01 (0.07) (5.06) 0.47 (3.41) 0.10 (0.77) (0.64) 0.18 (1.22) Notes: This table presents average monthly s of portfolios sorted by size (MV) and book-to-market ratio (B/M). Panel A shows the results for six portfolios, and Panel B reveals the mean s for 25 portfolios. Small-Large is the difference between small and large stocks, and High-Low is the difference between stocks with high and low book-to-market ratios. Numbers in parentheses are t-values. The sample period is January 2003 to December The results in Table 1 indicate that value stocks tend to have higher s than growth stocks. In Panels A and B, the average monthly increases as stocks book-to-market ratios go from low to high. For example, for small groups in Panel B, the average of stocks with a low book-to-market ratio is 0.36%, while the average of stocks is 0.57% in the highest book-to-market ratio group. This difference is statistically significant. However, s on zerocost portfolios that buy value stocks and sell growth stocks are not statistically significant for other size groups. Table 1 also implies that small stocks earn more than large stocks on average because all s on the Small-Large portfolios are positive. The difference, however, is not statistically significant. In sum, the s dispersion based on firm size and value/growth orientation supports the use of these characteristics as valid dimensions of investment style. Therefore, these dimensions are used in classifying stocks and equity funds in the Korean industry sector. Accordingly, our investigation of the s behavior of small-versus-large and value-versus-growth stocks based on changes in the VKOSPI is worthwhile. 4. PERFORMANCE BASED ON SIZE To investigate the relationship between changes in the VKOSPI and subsequent s on small and large stocks, we perform the following regressions: where and are h-day-ahead s for large and small stocks, respectively. is the percentage change in the VKOSPI and is defined as the difference between today s VKOSPI and the recent 75-day average, divided by the recent 75-day average. To minimize any estimation errors in the VKOSPI, we use the moving average of the most recent 75 days, or approximately three months. Table 2 presents the estimation results. Panel A shows the results for the two-by-three portfolios, and Panel B shows the results for the five-by-five portfolios. We use holding periods of up to twenty days. For each regression, the intercept and the estimation slope are presented and the values in parentheses represent t-values. In Panel A, future s on large stocks are higher than those on small stocks, except for the case of a holding period of one day after an increase in the VKOSPI. For example, for one percentage point increase in the VKOSPI, large stocks outperform small stocks by 0.38% in the next ten days. In addition, estimated slopes are statistically significant for holding periods exceeding eight days. Although estimated slopes in Panel B are smaller than estimated slopes in Panel A, the results in Panel B also show that statistically significant future s for the largeminus-small portfolios are generated after an increase in the VKOSPI. It is commonly understood in the literature that increases in volatility usually coincide with bad states of the economy. Empirical studies have found that investors tend to shift their portfolios toward less risky (1) 32 Investment Analysts Journal No

5 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP assets during these volatile periods, which is a phenomenon known as flight-to-quality (Naes, Table 2: Regressions of future s on large-minus-small portfolios on percentage changes in today s VKOSPI Panel A: 2 by 3 portfolios Panel B: 5 by 5 portfolios HP (days) Intercept t-statistic Slope t-statistic HP (days) Intercept t-statistic Slope t-statistic (0.31) (-0.33) (0.58) (-0.59) (1.25) (1.23) (-1.19) (1.16) (-1.66) (1.64) (-1.68) ) (1.66) (-1.67) (1.65) (-1.68) (1.64) (-1.61) (1.58) (-1.59) (1.55) (-1.64) (1.61) (-1.59) (1.55) (-1.95) (1.92) (-1.83) (1.79) (-2.35) (2.32) (-2.20) (2.15) (-2.54) (2.50) (-2.37) (2.32) (-2.71) (2.67) (-2.54) (2.49) (-2.95) (2.90) (2.83) (2.78) (-3.04) (2.99) (-2.96) (2.91) (-3.00) (2.95) (-2.98) (2.93) (-3.00) (2.96) (-3.01) (2.96) (-3.07) (3.03) (-3.12) (3.07) (-2.97) (2.92) (-3.06) (3.00) (-2.76) (2.71) (-2.92) (2.87) (-2.63) (2.57) (-2.86) (2.80) (-2.50) (2.44) (-2.77) (2.70) (-2.58) (2.53) (-2.87) (2.81) Notes: This table reports regression results of future s on large-minus-small portfolios on percentage changes in the VKOSPI today. A percentage change in the VKOSPI is defined as the difference between today s VKOSPI and the recent 75-day average, divided by the recent 75-day average. Panel A shows the results for the two-by-three portfolios, and Panel B displays the results for the five-by-five portfolios. For the two-by-three portfolios sorted on size and book-to-market ratio, the on large portfolios is defined as the average of the three large portfolios, and the on small portfolios is the average of the three small portfolios. For five-by-five portfolios sorted by size and book-tomarket ratio, the on large portfolios is defined as the average of the five large portfolios, and the on small portfolios is the average of the five small portfolios. The sample period is January 2003 to December Skjeltorp, and Ødegaard, 2011). Similarly, Longstaff (2004) reports that investors increase the liquidity of their assets during bad economic states, defining this phenomenon as flight-to-liquidity. In empirical asset pricing literature, Quiros and Timmerman (2000) find that small stocks are riskier than large stocks in highly volatile markets. In addition, small stocks are usually regarded as less liquid stocks. 8 Therefore, our empirical findings support the flight-to-quality and flight-to-liquidity hypotheses because large stocks indeed outperform small stocks after an increase in the VKOSPI. Our empirical findings are also consistent with those of Copeland and Copeland (1999), who document that portfolios of large capitalization stocks outperform portfolios of small capitalization stocks after an increase in the VIX of the U.S. market. Our empirical evidence further suggests that a trading strategy based on changes in the VKOSPI may be profitable. To fully investigate this suggestion, we construct a simple trading rule and examine whether the rule consistently creates profit. The results are shown in Table 3. Specifically, for each day, we calculate the difference between today s VKOSPI and the recent 75-day average of VKOSPI, divided by the recent 75-day average of the VKOSPI. This change is represented in the first column. The term No. of days is the total number of days out of the examined 1,915 days for which percentage changes in the VKOSPI are included for each group. For example, No. of Days of 243 in Change [-20, -15) indicates that out of 1,915 days, there are 243 days when today s VKOSPI is 15~20% lower than its 75-day moving average. Out of 1,915 days, the VKOSPI decreased during 1,154 days and increased during 761 days. In each group, we construct a simple trading strategy: when changes in the VKOSPI are positive (negative), the proposed trading rule is to take a long position on large (small) stocks and a short position on small (large) stocks. Subsequently, the holding period s in each group are computed for one day to twenty days without changing the position during our holding periods. 9 The geometric and arithmetic daily average s are displayed in basis points. Finally, we report the Sharpe ratios of the thirteen groups. The results for the two-bythree portfolios and the five-by-five portfolios are presented. Investment Analysts Journal No

6 Change (%) No of days HP (days) HP (days) The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSPI Table 3: Future s on zero-cost portfolios formed on firm size 2 by 3 portfolios 5 by 5 portfolios 2 by 3 portfolios 5 by 5 portfolios [-Inf,-20] [-20,-15] [-15,-10] [-10,-5] [-5,0] [0,5] [5,10] [10,15] [15,20] [20,30] [30,40] [40,50] [50,Inf] [-Inf,-20] [-20,-15] [-15,-10] [-10,-5] [-5,0] [0,5] [5,10] [10,15] [15,20] [20,30] [30,40] [40,50] [50,Inf] Notes: This table reports future s on zero-cost portfolios formed on firm size depending on changes in the VKOSPI. Specifically, daily percentage changes in the VKOSPI are divided into thirteen groups. No. of days is the total number of days out of the examined 1,915 days that a percentage change in the VKOSPI is included in each group. When changes in the VKOSPI are positive (negative), the trading rule is to take a long position on large (small) stocks and a short position on small (large) stocks. Then, the holding period s in each group are computed for one day to twenty days. The geometric and arithmetic daily average s are displayed in basis points. In addition, the Sharpe ratios are reported. A percentage change in the VKOSPI is defined as the difference between today s VKOSPI and the recent 75-day average, divided by the recent 75-day average. The results for the two-by-three and five-by-five portfolios are presented. For the two-by-three portfolios sorted by size and book-to-market ratio, the on large portfolios is defined as the average of the three large portfolios, and the on small portfolios is the average of the three small portfolios. For five-by-five portfolios sorted by size and book-to-market ratio, the on large portfolios is defined as the average of the five large portfolios, and the on small portfolios is the average of the five small portfolios. The sample period is January 2003 to December Table 3 indicates that a potential strategy based on changes in the VKOSPI generates positive s in either direction. Several features of the empirical findings are worth highlighting. First, the average s are generally positive. For a holding period of one day, the average s are positive in nine out of thirteen cases. For other holding periods, the positive s pattern is largely retained. Second, although the potential strategy is usually profitable, the average does not monotonically increase as the change in the VKOSPI becomes more extreme. For example, for the size strategy, the average s are negative for large increases in the VKOSPI such as ranges of 20 30% and 40% 50%. 10 Since the s are calculated from the zero-cost portfolios, some of the s are negative. For comparison, the mean excess of the stocks listed on the KOSPI is 0.049% per day with a Sharpe ratio of Table 3 reveals that most of the Sharpe ratios from our strategies are higher than that of the market s, which implies that our trading strategy, on the average, outperforms the passive strategy. In sum, this empirical evidence indicates that the VKOSPI may be used to capture periods when large stocks outperform small stocks and vice versa. Our empirical findings are consistent with the results shown in Table 2, supporting the flight-to-quality and flight-toliquidity hypotheses. 5. PERFORMANCE BASED ON BOOK-TO- MARKET RATIO Constructing value-based and growth-based portfolios is a well-known investment strategy in practice, and the differences between value and growth stocks have been well-documented (Banz, 1981; Fama and French, 1993). Our investigation of the performance of these two types of portfolios based on changes in the VKOSPI makes a worthwhile contribution to this literature. In this subsection, we analyze the empirical relationship between changes in the VKOSPI and subsequent s on value and growth stocks. To this end, we run the following regressions: (2) 34 Investment Analysts Journal No

7 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP where and are h-day-ahead s for growth and value stocks, respectively. Panel A of Table 4 presents the estimation results for the two-bythree portfolios, and Panel B presents the results for the five-by-five portfolios. For each regression, the intercept and slope coefficients are given and t-values appear in parentheses. Table 4: Regressions of future s on growth-minus-value portfolios on percentage changes in today s VKOSPI Panel A Panel B HP (days) Intercept t-statistic Slope t-statistic HP (days) Intercept t-statistic Slope t-statistic (-0.01) (0.02) (0.84) (-0.84) (-1.44) (1.45) (-0.63) (0.65) (-2.34) (2.35) (-1.39) (1.41) (-2.96) (2.98) (-1.93) (1.95) (-3.55) (3.57) (-2.33) (2.36) (-3.96) (3.99) (-2.60) (2.63) (-4.21) (4.23) (-2.81) (2.84) (-4.46) (4.49) (-3.04) (3.08) (-4.85) (4.88) (-3.33) (3.37) (-5.18) (5.21) (-3.58) (3.62) (-5.53) (5.57) (-3.87) (3.91) (-5.78) (5.82) (-4.17) (4.21) (-6.08) (6.12) (-4.49) (4.53) (-6.23) (6.27) (-4.65) (4.70) (-6.44) (6.48) (-4.82) (4.87) (-6.73) (6.77) (-4.96) (5.01) (-6.98) (7.02) (-5.11) (5.16) (-7.15) (7.19) (-5.19) (5.25) (-7.11) (7.16) (-5.13) (5.18) (-7.16) (7.21) (-5.10) (5.16) Notes: This table reports regression results of future s on growth-minus-value portfolios on percentage changes in the VKOSPI today. A percentage change in the VKOSPI is defined as the difference between today s VKOSPI and the recent 75-day average, divided by the recent 75-day average. Panel A shows the results for the two-by-three portfolios, and Panel B displays the results for the five-by-five portfolios. For the two-by-three portfolios sorted by size and book-to-market ratio, the on value portfolios is defined as the average of the two value portfolios, and the on growth portfolios is the average of the two growth portfolios. For the five-by-five portfolios sorted by size and bookto-market ratio, the on value portfolios is defined as the average of the five value portfolios, and the on growth portfolios is the average of the five growth portfolios. The sample period is January 2003 to December In Panel A, the estimated slope from the regression equation (Equation (2)) is positive for any holding period, and the slope coefficient is statistically significant when the holding period is greater than two days. The empirical results in Panel B are qualitatively similar to the results in Panel A. The estimated slopes are positive and statistically significant, even though the absolute values of the estimated slopes for the five-by-five portfolios are smaller than the values for the two-by-three portfolios. Copeland and Copeland (1999) find that in the U.S. market, value stocks outperform growth stocks after an increase in the VIX. In sharp contrast, our empirical findings on the Korean market reveal that on days following increases in the VKOSPI, s on growth stocks are higher than s on value stocks. It has been accepted that value stocks are riskier than growth stocks in bad states of the economy (Lettau and Ludvigsion, 2001; Kang, Kim, Lee, and Min, 2011). If investors pursue a flight-to-quality strategy during bad times, they are likely to switch their portfolios into growth stocks. Thus, the fact that growth stocks outperform value stocks after an increase in the VKOSPI supports the flight-to-quality phenomenon. To examine whether a value/growth strategy based on changes in the VKOSPI creates profits, we implement a simple trading rule in which we construct a zero-cost portfolio that is long on growth stocks and short on value stocks when changes in the VKOSPI are positive. We construct an opposite position when the VKOSPI decreases. Then, we hold the portfolio for up to twenty days without changing the position. Table 5 displays the geometric and arithmetic daily average s in basis points and also displays the Sharpe ratios. For robustness, we present results for the twoby-three portfolios and the five-by-five portfolios. Investment Analysts Journal No

8 Change (%) No of days HP (days) HP (days) The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSPI Table 5: Future s on zero-cost portfolios formed on book-to-market ratios 2 by 3 portfolios 5 by 5 portfolios 2 by 3 portfolios 5 by 5 portfolios [-Inf,-20) [-20,-15) [-15,-10) [-10,-5) [-5,0) [0,5) [5,10) [10,15) [15,20) [20,30) [30,40) [40,50) [50,Inf) [-Inf,-20) [-20,-15) [-15,-10) [-10,-5) [-5,0) [0,5) [5,10) [10,15) [15,20) [20,30) [30,40) [40,50) [50,Inf) Notes: This table reports future s on zero-cost portfolios formed on book-to-market ratios depending on changes in the VKOSPI. Specifically, daily percentage changes in the VKOSPI are divided into thirteen groups. No. of days is the total number of days out of the examined 1,915 days that a percentage change in the VKOSPI is included in each group. When changes in the VKOSPI are positive (negative), the trading rule is to take a long position on growth (value) stocks and a short position on value (growth) stocks. Then, the holding period s in each group are computed for one day to twenty days. The geometric and arithmetic daily average s are displayed in basis points. In addition, the s are reported. A percentage change in the VKOSPI is defined as the difference between today s VKOSPI and the recent 75-day average, divided by the recent 75-day average. The results for the two-by-three and five-by-five portfolios are presented. For the two-by-three portfolios sorted by size and book-to-market ratio, the on large portfolios is defined as the average of the three large portfolios, and the on small portfolios is the average of the three small portfolios. For the five-by-five portfolios sorted by size and book-tomarket ratio, the on large portfolios is defined as the average of the five large portfolios, and the on small portfolios is the average of the five small portfolios. The sample period is January 2003 to December Compared to the zero-cost portfolios formed on size, we find striking patterns of profitability. For the two-bythree portfolios, the average s are positive in twelve out of thirteen cases in any holding period. For the five-by-five portfolios, the same pattern is observed. The magnitude of s is economically huge. For example, for the two-by-three portfolios, the daily average geometric s are 45.58, 53.01, 81.77, and basis points for holding periods of one, two, three, and twenty days. In addition, most of the s of our strategy are substantially higher than the of the market portfolio (0.032). In sum, we find that growth stocks outperform value stocks on days following increases in the VKOSPI, and that a potential trading rule developed on book-to-market ratios according to changes in the VKOSPI yields consistently positive s. 6. CONCLUDING REMARKS This study investigates whether the implied volatility index in the Korean market has market timing ability. We use the implied volatility index as a timing indicator for the following reasons. First, time variations in market volatility induce changes in the set of investment opportunities by revising the expectations of investors about future stock s. Accordingly, investors are likely to choose particular investment styles, such as large versus small and value versus growth, based on changes in market volatility. Second, although macro variables have been frequently used as economic indicators in the literature, the VKOSPI is better suited for our research purposes. The minuteby-minute changes in the VKOSPI are likely to reflect the risk preferences and future expectations of market participants. Specifically, we examine how the performance of small-versus-large and value-versusgrowth stocks is different on days following increases and decreases in the VKOSPI. We find that future s on large stocks are higher than those on small stocks on days that follow an increase in the VKOSPI. For value/growth stocks, we find that future s on growth stocks are larger than those on value stocks on days following an increase in the VKOSPI. Our empirical findings justify the flight-toquality hypothesis because small and value stocks are riskier than large and growth stocks in bad times. We 36 Investment Analysts Journal No

9 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP also provide empirical evidence for our assertion that a potential trading rule based on changes in the VKOSPI is profitable. Our findings indicate that the VKOSPI may be used in predicting the performance of largeversus-small and value-versus-growth stocks in practice to maximize profits. One implication of our study is that stock market participants can be better off by paying attention to current variability of the volatility index. Although this paper reports some interesting findings, it has some limitations. Our study does not evaluate traded indices that track the s behavior of specific investment styles. To further examine the profitability of the strategy, it may be beneficial for future research to investigate the use of traded indices such as the exchange-traded fund.. REFERENCES Ahn, H., J. Kang, and D. Ryu Informed trading in the index option market: The case of KOSPI 200 options. Journal of Futures Markets, 28: Ahn, H., J. Kang, and D. Ryu Information effects of trade size and trade direction: Evidence from the KOSPI 200 index options market. Asia-Pacific Journal of Financial Studies, 39: Ainsworth, A., K. Fong, and D. Gallagher Style drift and portfolio management for active Australian equity funds. Australian Journal of Management, 32: Amihud, Y Illiquidity and stock s: crosssection and time-series effects. Journal of Financial Markets, 5: Auret, C., and R. Cline Do the value, size, and January effects exist on the JSE? Investment Analysts Journal, 74: Banz, R The relationship between and market value of common stocks. Journal of Financial Economics, 9: Barberis, N., and A. Shleifer Style investing. Journal of Financial Economics, 68: Basu, S Investing performance of common stocks in relation to their price-earning ratios: A test of the efficient market hypothesis. Journal of Finance, 32: Bhaduri, S., and R. Saraogi The predictive power of the yield spread in timing the stock market. Emerging Markets Review, 11: Brown, K., W. Harlow, and H. Zhang Staying the course: The role of investment style consistency in the performance of mutual funds. Working paper, University of Texas. Chan, L., H. Chen, and J. Lakonishok On mutual fund investment styles. Review of Financial Studies, 15: Copeland, M., and T. Copeland Market timing: Style and size rotation using the VIX. Financial Analysts Journal, 55: Fama, E. F., and K. R. French Common risk factors in the s on stocks and bonds. Journal of Financial Economics, 33: Fama, E. F., and K. R. French Multifactor explanations of asset pricing anomalies. Journal of Finance, 51: Ferson, W. E., and R. Schadt Measuring fund strategy and performance in changing economic conditions. Journal of Finance, 54: French, K. R., G.W. Schwert, and R. Stambaugh Expected stock s and volatility. Journal of Financial Economics, 19: Guo, B., Q. Han, and D. Ryu Is the KOSPI 200 options market efficient? Parametric and nonparametric tests of the martingale restriction. Journal of Futures Markets, 33: Han, Q., B. Guo, D. Ryu, and R. I. Webb Asymmetric and negative -volatility relationship: The case of the VKOSPI. Investment Analysts Journal, 76: Henriksson, R., and R. Merton On market timing and investment performance II: Statistical procedures for evaluating forecasting skills. Journal of Business, 54: Jang, J., J. Kang, and C. Lee Liquidity risk and expected stock s in Korea: A new approach. Asia-Pacific Journal of Financial Studies, 41: Kang, B., D. Ryu, and D. Ryu Phase-shifting behaviour revisited: An alternative measure, Physica A: Statistical Mechanics and its Applications, 401: Kang, J., and D. Ryu Which trades move asset prices? An analysis of futures trading data. Emerging Markets Finance and Trade, 46: Kang, J., T. Kim, C. Lee, and B. Min Macroeconomic risk and the cross-section of stock s. Journal of Banking and Finance, 35: Investment Analysts Journal No

10 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSPI Kim, H., and Ryu D Which trader s ordersplitting strategy is effective? The case of an index options market. Applied Economics Letters, 19: Kim, J., and D. Ryu Intraday price dynamics in spot and derivatives markets. Physica A: Statistical Mechanics and its Applications, 394: Lee, B., and D. Ryu Stock s and implied volatility: A new VAR approach. Economics: The Open-Access, Open-Assessment E-Journal, 7: Lee, J., and D. Ryu. forthcoming. Regime-dependent relationships between the implied volatility index and stock market index. Emerging Markets Finance and Trade. Lettau, M., and S. Ludvigson Resurrecting the (C)CAPM: A cross-sectional test when risk premia are time-varying. Journal of Political Economy, 109: Levis, M., and M. Liodakis The profitability of style rotation strategies in the United Kingdom. Journal of Portfolio Management, 26: Lo, A., and C. Mackinlay Data snooping biases in tests of financial asset pricing models. Review of Financial Studies, 3: Longstaff, F. A The flight-to-liquidity premium in U.S. Treasury bond prices. Journal of Business, 77: Merton, R On estimating the expected on the market: An explanatory investigation. Journal of Financial Economics, 8: Naes, R., J. Skjeltorp, and B. Ødegaard Stock market liquidity and the business cycle. Journal of Finance, 66: Muller, C., and M. Ward Style-based effects on the Johannesburg Stock Exchange: A graphical timeseries approach. Investment Analysts Journal, 74: Perez-Quiros, G., and A. Timmermann Firm size and cyclical variations in stock s. Journal of Finance, 55: Pesaran, M., and A. Timmermann Market timing and prediction under model instability. Journal of Empirical Finance, 9: Petkova, R., and L. Zhang Is value riskier than growth. Journal of Financial Economics, 78: Ryu D Intraday price formation and bid-ask spread: A new approach using a cross-market model. Journal of Futures Markets, 31: Ryu, D. 2012a. The effectiveness of the order-splitting strategy: An analysis of unique data. Applied Economics Letters, 19: Ryu, D. 2012b. The profitability of day trading: An empirical study using high-quality data. Investment Analysts Journal, 75: Ryu D. 2012c. Implied volatility index of KOSPI 200: Information contents and properties. Emerging Markets Finance and Trade, 48: Ryu, D. 2013a. Price impact asymmetry of futures trades: Trade direction and trade size. Emerging Markets Review, 14: Ryu, D. 2013b. What types of investors generate the two-phase phenomenon? Physica A: Statistical Mechanics and its Applications, 392: Ryu, D. forthcoming. The information content of trades: An analysis of KOSPI 200 index derivative. Journal of Futures Markets. Ryu, D., J. Kang, and S. Suh. forthcoming. Implied pricing kernels: An alternative approach for option valuation. Journal of Futures Markets. Strugnell, D., E. Gilbert, and R. Kruger Beta, size and value effects on the JSE, Investment Analysts Journal, 74: 1-17 Treynor, J., and K. Mazuy Can mutual funds outguess the market? Harvard Business Review, 44: FOOTNOTES i. To the best of our knowledge, only five recent articles, Ryu (2012c), Han, Guo, Ryu, and Webb (2012), and Lee and Ryu (2013), Kim and Ryu (2014), and Lee and Ryu (forthcoming) thoroughly examine the properties and forecasting ability of the VKOSPI. Most studies have focused on the VIX, the CBOE volatility index of the U.S. market. ii. The properties of the KOSPI 200 options market and VKOSPI are explained in Section 2. iii. Another driving force for the rapid development of the KOSPI 200 options market is the synergy effect of the simultaneous trading with the KOSPI200 index futures contract, which is one of the most liquid index futures. Implementing intraday trading strategies (e.g., daytrading, programming trading, and stealth trading) using both KOSPI 200 futures and options is a widespread convention among professional investors in the Korean market (Kang and Ryu, 2010; Kim and Ryu, 2012; Ryu 2011, 2012a, 2012b, 2013a, 2013b, forthcoming). iv. More detailed characteristics of the KOSPI 200 options market and the informational role of KOSPI 200 options trading are described well by Ahn, Kang, and Ryu (2008, 2010), Ryu (2011), Kim and Ryu 38 Investment Analysts Journal No

11 The Volatility Index and Style Rotation: Evidence from the Korean Stock Market and VKOSP (2012), Guo, Han, and Ryu (2013), Kang, Ryu, and Ryu (2014), and Ryu, Kang, and Suh (forthcoming). v. For the derivation and further discussion of the VKOSPI, refer to Ryu (2012c) and to the two official documents provided by the KRX, V-KOSPI 200 Methodology and VKOSPI 200_Brochure. The documents can be found on the KRX website ( vi. Because the number of options traded was insufficient to construct the VKOSPI before 2003, researchers and analysts use historical time-series data on the volatility index generated after This study also analyzes VKOSPI data starting from vii. In the Korean market, stocks traded in the KOSPI market are essentially all issued by sound and reliable companies. Extremely small stocks and/or stocks issued by small and/or venture companies (which therefore, contain substantial credit risk and are less liquid) are listed in a separate market, the KOSDAQ market. viii. Using the Amihud (2002) illiquidity measure, Jang, Kang, and Lee (2012) find that small stocks are less liquid stocks in the Korean stock market. ix. For the sake of brevity, we report future s on holding periods of one, two, three, and twenty days. Empirical results for holding periods of four to nineteen days are quantitatively similar, and the results are available upon request. x. For the two-by-three portfolios sorted by size, the s are not negative for all holding periods. We find positive s over 15- to 20-day holding periods (not reported). Investment Analysts Journal No

12 Forecasting winner IPOs 40 Investment Analysts Journal No