An Empirical Analysis of the Volatility in the Open-End Fund Market: Evidence from China

50 Emerging Markets Finance & Trade An Empirical Analysis of the Volatility in the Open-End Fund Market: Evidence from China Shiqing Xie and Xichen Huang ABSTRACT: This paper applies a set of GARCH models to investigate the three characteristics, including time persistence, leverage effect, and risk premium, of the volatilities of the four China Securities Index (CSI) fund indices. This study made the following four findings: () a strong ARCH effect exists in the returns; (2) time persistence is significant in all the CSI fund indices, namely, stock, hybrid, and bond in descending order of significance; (3) the leverage effect is not statistically significant, yet there may be a positive leverage effect on the bond funds; (4) a risk premium effect exists in the open-end fund market, especially in the bond fund market. KEY WORDS: leverage effect, open-end fund, persistence, risk premium, volatility. Open-end funds have experienced rapid development in China ever since the first fund, Bank of Communications-Hua An ChuangXin Securities Investment Fund (Hua An ChuangXin) was launched in 200. They now compose most of China s mutual fund market. As an illustration, there were 964 open-end funds (only 55 closed-end funds) in the Chinese fund market at the beginning of 202, with net asset value estimated to be RMB 2.07 trillion and accounting for 94 percent of the total net asset value of the mutual funds market. Nonetheless, Chinese investors enthusiasm for open-end funds and fund investment s specific advantages over other investments can never dispel the concern over the underlying investment risk. In the classical modern portfolio theory proposed by Markowitz (952), volatility of returns is regarded as a good proxy for risk, despite its difference from risk in essence. Nowadays, volatility has become an essential input for portfolio management, option pricing, and market regulation (Poon and Granger 2003). Hence, it is appropriate and necessary to investigate the characteristics of the return volatility of the Chinese openend funds to gain an understanding of the Chinese market. There are already some Chinese scholars studying the characteristics of volatility in the mutual funds in China. However, their investigations are hardly comprehensive or systematic. The investigation in this paper, which contributes to a better understanding of the Chinese mutual fund market, especially the open-end fund market, can be important in three ways. First, we develop a thorough empirical analysis of open-end fund volatility by investigating three different main characteristics, namely time persistence, leverage effect, and risk premium, which are all typical features in the returns and the volatility of financial assets. Second, though centering on the whole open-end fund market, we are also interested in whether behaviors of different subtypes of funds constituting the market vary, and possibly lead to a mixed phenomenon in the market. Shiqing Xie (xie@pku.edu.cn) is an associate professor of finance in the Department of Finance, School of Economics, Peking University, Beijing. Xichen Huang (xhuang43@illinois.edu) is a Ph.D. student in the Department of Statistics, University of Illinois, Urbana Champaign. Emerging Markets Finance & Trade / September October 203, Vol. 49, Supplement 4, pp. 50 62. 203 M.E. Sharpe, Inc. All rights reserved. Permissions: www.copyright.com ISSN 540 496X (print)/issn 558 0938 (online) DOI: 0.2753/REE540-496X4905S4 xie.indd 50 3/3/204 8:57:7 AM

September October 203, Volume 49, Supplement 4 5 Third, stock funds, bond funds, and hybrid funds are explored in this paper as they are the main constituents of the Chinese open-end fund market, with accounting in 202 for 44. percent, 26 percent, and 4.4 percent, respectively, of the sample funds constituting our sample. 2 In recent years, the research methodology on return volatility has evolved rapidly. Engle (982) first proposed the autoregressive conditional heteroskedasticity (ARCH) model, making it possible to quantify the volatility in financial markets. Bollerslev (986) then used the general ARCH (GARCH) model to better characterize the volatility persistence. Engle et al. (987) then developed the ARCH in mean (ARCH M) model, which incorporates the conditional variance in the mean equation to describe the impact of volatility on the rate of returns. Since then, some scholars have proposed asymmetric GARCH models to explain the leverage effect in the volatility of the financial asset returns. For example, Glosten et al. (993), Nelson (99), and Zakoian (994) have all modeled the different impacts of positive and negative shocks on the returns due to information asymmetry using GJR-GARCH (Glosten-Jagannathan-Runkle GARCH), EGARCH (exponential GARCH), and TGARCH (threshold GARCH) models, respectively (see Poon and Granger 2003 for a comprehensive review of GARCH models and other volatility forecasting models). Many studies, most of which center on the stock market, have been conducted to evaluate the relative superiority of these different models, but there seems to be no consensus as to which one is better than the others. Specifically in the Chinese market, which consists of two stock exchanges, models perform differently in the two exchanges (Zhang and Pan 2006). For instance, in the Shenzhen stock market, the GJR-GARCH and EGARCH models perform better than other GARCH-type models, but in the Shanghai stock market, there is no evident superiority. In this paper, we investigate the volatility of open-end funds, which invest in both Chinese stock markets and the bond market. A biased and unsound conclusion may be reached if we rely on only one model. Therefore, we deploy a seemingly redundant analysis of the leverage effects using three different models. Literature Review The relevant research conducted in the early stage of the open-end funds makes no distinction between closed-end and open-end funds. Guo (2006) utilizes a sample composed of the China International Trust and Investment Corporation Fund Index, and the subsets of large and small fund indices to examine the volatility clustering, asymmetry, and risk premium characteristics of the market more comprehensively. The study shows that the returns of the three fund indices have significant volatility clustering and leverage effects, but do not have a significant risk premium effect. Niu and Lu (2005) analyze the return characteristics of the Shanghai Stock Exchange (SSE) Fund Index and find that the return of the SSE Fund is not normally distributed and the volatility of the return exhibits conditional heteroskedasticity. Research focusing on the volatility of the open-end fund returns has sprung up since 2005. This research falls into two rough categories. The first comprises studies basing their analysis on several representative open-end funds. Yang and Zhou (2006) use the GARCH models to study the returns of the Hua An ChuangXin and find that the EGARCH M(2, 2) model can depict the asymmetric features of the fluctuations in the fund return and that there exists a significant risk premium effect. Using a sample of six open-end funds, Yang et al. (2007) find that () the distribution of open-end fund returns has the characteristics xie.indd 5 3/3/204 8:57:8 AM

52 Emerging Markets Finance & Trade of leptokurtosis and volatility clustering, (2) open-end fund returns have a volatility leverage effect, and (3) open-end funds have a significant risk-premium effect. Yang and Dong (2008) then analyze seventeen selected funds and find that in a bear market there is no leverage effect in some funds and in others there is a negative leverage effect, while in a bull market there is a positive leverage effect in most of the funds. The other category of studies directly investigates the open-end fund indices instead of several samples of open-end funds. Since the conclusions of these studies are free from the influence of the specific characteristics of the sample funds, the conclusions are less biased and more valid. Dong et al. (2008) apply the GARCH(, ) model and the EGARCH M(, ) model to probe into the volatility of the open-end funds and find that () the returns exhibit strong volatility persistence, (2) the overall leverage effect is insignificant, and (3) there is only a weak risk premium effect. Compared with the existing studies, this paper is innovative in three ways. First, the employed sample and the sample period are more reasonable. The existing studies choose only a few specific open-end funds as a sample; this paper takes four different open-end fund indices as the sample. Such samples can more objectively reveal the volatility characteristics of the open-end fund market. Moreover, previous studies (e.g., Dong et al. 2008) concentrate mainly on the early period of the open-fund market and the conclusions may not apply to the current market. The selected sample period in this paper is from early 2006 to early 202, thus improving the study in two ways: () since a large number of open-end funds began list trading in 2005 when the market was much more volatile, the paper purposefully excludes this period in order to incorporate more reliable information; (2) the sample period in this paper contains three subperiods that reflect different market trends (upward, downward, and fluctuations). Consequently, the results in this paper are more comprehensive. Second, this study compares the volatility characteristics of the open-end funds with different investment styles. At present, studies on open-end funds that take into account different investment styles are rare. Wang and Sun (20) investigate three open-end funds employing different investment styles. However, they can hardly represent the entire market and may lead to selection bias. By contrast, this paper utilizes the China Securities Index (CSI) Stock Fund Index, the CSI Hybrid Fund Index, and the CSI Bond Fund Index and then conducts a comparative study of these three fund indices to better capture the volatility characteristics of funds operating with different investment styles. Finally, a family of asymmetric GARCH models is employed to study the asymmetry of the return volatility in the open-end fund market. Previous studies have often used a single model, which can lead to the model specification problem. To avoid this problem, this paper uses three different kinds of GARCH models to investigate the leverage effect and obtain more robust conclusions. Empirical Strategies and Data Empirical Strategies Heteroskedasticity Test The ARCH model was first proposed by Engle (982). It models with the random disturbance term e t, which is in effect the residual of the mean equation, to extract the information contained in the residuals. ARCH (q) can be expressed as xie.indd 52 3/3/204 8:57:8 AM

September October 203, Volume 49, Supplement 4 53 iid... εt ηtσt, ηt ~ N 0, q 2 σt = α0 + αε i t i, i= = ( ) where a 0 > 0, a i 0, i =,..., q, and e t is the random disturbance term. Hereinafter, we use h t instead of s t 2 to represent the conditional variance. The ARCH model well describes the leptokurtosis and volatility clustering of time series, which are the two most typical characteristics of financial time series. Therefore, we can use the ARCH model to detect whether heteroskedasticity exists in the return volatility of open-end funds. Volatility Persistence Analysis Bollerslev (986) introduced the GARCH model, which extends the conditional variance equation of the ARCH model. The conditional variance equation of the GARCH model is specified as h q 2 = α + α ε + β h t 0 i t i j t j i= j= where a 0 > 0, a i 0, i =,..., q, b j 0, j =,..., p, and h t, the conditional variance, is nonnegative. In order to ensure the stationarity of the sequence, the coefficients should be subject to q 0< α + β <. i= i Through several iterations of h t, it is not hard to find that the GARCH model is actually an infinite-order ARCH model. In practice, a high-order ARCH model is usually replaced by a low-order GARCH model since fewer parameters need to be estimated and the specification is much easier. Moreover, the GARCH model features the property of lasting impact from lagged exogenous shocks. The conditional variance in the ARCH (q) model depends solely on the residuals of the past q periods, thus it can capture only the short-term effects of exogenous shocks. The GARCH model, corresponding to the infinite-order ARCH model, on the contrary, depends on exogenous shocks during all lagged periods and is therefore able to depict the long-term effects. More specifically, if at a certain point in time a large external shock occurs, it immediately increases the conditional variance in the next period and continues to have considerable influence until several periods later. The ARCH parameter a i s, together with the GARCH parameter b j s, individually determines the short-term behavior of the fluctuations of the time series. If the value of (S q i=a i + S p j=b j ) is high, persistence of the fluctuations in the sequence is strong; otherwise, persistence is weak. In addition, parameters a i and b j each reflect a different effect produced by new and historical information on current volatility. In other words, the larger a i is, the stronger the influence of new information from the lagged i period on the current volatility; the larger b i is, the greater the impact of historical shocks on current volatility. p j= j p, xie.indd 53 3/3/204 8:57:8 AM

54 Emerging Markets Finance & Trade Leverage Effect Analysis Although the GARCH model can accurately characterize volatility clustering, it fails to explain asymmetric volatility upon the release of good and bad news in the financial market, that is, the so-called leverage effect. Because extended models of GARCH, such as EGARCH, GJR-GARCH, and TGARCH, can reveal the influence of both the quantity and quality of the lagged residuals on volatility, they can be applied for the analysis of the leverage effect in the open-end fund market. The EGARCH model was proposed by Nelson (99). The conditional variance is accordingly expressed as follows: q p t i t i ln( ht) = α + α ε ε 0 i + γ i + β j ln ( ht j ). i= h h j= t i The g i parameters in this model are leverage terms depicting the impact of the historical shocks from different directions on the current conditional variance. If the g i parameters are significantly different from zero, the volatility is asymmetric. Specifically, if g i < 0, negative leverage effect exists in the volatility, indicating that when bad news hits the market (when external shock e t i < 0), the conditional variance tends to increase correspondingly. When good news reaches the market (external shock e t i > 0), the conditional variance tends to decrease. Glosten et al. (993) proposed the GJR-GARCH model, expressed as t i q p 2 2 h = α0 + ( α ε + γ d ε )+ β h t i t i i t i t i j t j i= j= where d t i = if e t i < 0; 0 if e t i > 0. The g i parameters in this model are the leverage terms. The identification in this model is slightly different from the EGARCH model. When g i > 0, negative leverage effect exists. Zakoian (994) proposed the TGARCH model, expressed as q σt = ω+ ( αi εt i γε i t i)+ βσ j t j. i= The g i parameters in this model are the leverage terms. When g i > 0, there is negative leverage. p j=, Risk Premium Analysis In financial markets, the returns on securities are closely correlated to their risks. Engle et al. (987) propose the ARCH M model and introduce conditional variance terms into the mean equation to model this relationship. The ARCH M model is expressed as y u gh εt = η t ht, = + ( ) + ε t t t t where u t denotes the mean equation, h t is the conditional variance following an ARCH process or more complicated model, and g(h t ) is a monotonic function of h t. As an illustration, when h t follows a GARCH(, ) process, the whole mean-variance model is xie.indd 54 3/3/204 8:57:8 AM

September October 203, Volume 49, Supplement 4 55 referred to as a GARCH(, ) M model. In this paper, we assume that g(h t ) = qh t /2. If q is positive, the returns and volatility are positively correlated, indicating the presence of a risk premium. Data and Descriptive Statistics This paper uses four indices developed by the China Securities Index (CSI) Company Ltd. to detect the volatility characteristics of open-end funds in China. The four indices comprise the CSI Open-End Fund Index ( code: H020, hereinafter CSI Fund ), which is constituted by all open-end funds in the Chinese market (excluding money funds, capital guaranteed funds, and QDII [Qualified Domestic Institutional Investor] funds) and three subtype indices comprising the subsets of the CSI Fund, including the CSI Stock Fund Index ( code: H02, hereinafter Stock Fund ), the CSI Hybrid Fund Index ( code: H022, hereinafter Hybrid Fund ), and the CSI Bond Fund Index ( code: H023, hereinafter Bond Fund ). The CSI indices are weighted by average growth rate and calculated as Current Close Index = Previous Day s Close Index * Simple Average Growth Rate of the Constituent Funds Net Asset Value. December 3, 2002 is set as the base day of each and has a basis point of,000. As each fund comprises almost all funds of the same type, our sample can adequately capture the volatility characteristics of the whole open-end fund market. The closing prices of the fund indices used in this paper are all from the RESSET database. This paper takes the time period from February 6, 2006, to January, 202, as the sample period, with a total of,455 daily observations. During this period, the Chinese stock market experienced dramatic changes and witnessed three different market trends including upward and downward trends and fluctuations. The performance of the Shanghai Shenzhen Index 300 (CSI 300) reflects this trend well. First, from the beginning of 2006 to October 2007, the market experienced a bull market and the CSI 300 once reached 589.72 points on October 7, 2007. Second, in 2008, the Chinese stock market went through a bear market partially resulting from the global financial crisis, with the CSI 300 decreasing by about 60 percent and reaching its lowest level at,606.73 points on November 4, 2008. Third, after a short period of increase, the stock market ran into an adjustment phase. Since the fund market is highly correlated with the stock market, with the correlation between the CSI Fund Index and the CSI 300 estimated to be 0.89 in our sample period, having a sample period during which the stock market fluctuates dramatically can ensure the adequacy of our sample space and thus facilitate reaching comprehensive results. In this paper, we take the difference of the logarithm of daily closing price as the daily return, namely, R t Pt = 00% ln P. Table reports the descriptive statistics of the four fund indices returns used to detect whether the distributions are left-skewed and fat-tailed. All kurtosis values are greater than 3, indicating a fat tail; all skewness values are negative, implying the distributions are left-skewed. For more rigorous detection, the Jarque Bera test is employed and the t xie.indd 55 3/3/204 8:57:9 AM

56 Emerging Markets Finance & Trade Table. Descriptive statistics of the four fund indices returns Index Mean Standard deviation Skewness Kurtosis Jarque Bera CSI Fund Index 0.067578.29636 0.4586 5.05235 306.53*** Stock Fund Index 0.073602.6378 0.45438 4.75802 237.272*** Hybrid Fund Index 0.06848.40495 0.47585 4.83834 259.63*** Bond Fund Index 0.029752 0.90724 0.4723 5.59765 462.823*** * p < 0.; ** p < 0.05; *** p < 0.0. Table 2. Stationarity tests on the four fund indices returns Index ADF statistic Lag length CSI Fund Index 36.22955*** 0 Stock Fund Index 36.45675*** 0 Hybrid Fund Index 36.45675*** 0 Bond Fund Index 32.34235*** 0 * p < 0.; ** p < 0.05; *** p < 0.0. statistics are shown in the last column in Table. They are significant at the level of percent, which indicates the four returns are not normally distributed. Therefore, for significance tests, we assume that the error terms of the mean equations hereinafter modeled in this paper follow a generalized error distribution. Empirical Analysis Stationarity and ARCH Test We utilize the augmented Dickey Fuller (ADF) test with no intercept and time trend to test the stationarity of the four indices returns and present the results in Table 2. 3 The lag order is chosen according to Akaike information criterion (AIC). The p values of the ADF test statistics are far less than percent, indicating that the four return sequences are stationary. Hence we can model them directly without differencing. Prior to conducting the ARCH test, we need to estimate the mean models of the returns. First we use the Ljung Box Q test to see whether the fund returns are white noise. As the observations of the four indices returns are all,454, the 95 percent confidence interval for the Ljung Box Q statistic is ( 0.054, +0.054). We calculate the autocorrelation functions, partial autocorrelation functions, and then the Ljung Box Q statistics of each lag order within 3 for the returns. The results show that when the lag order is 4, the Ljung Box Q statistic for each fund return sequence is significant at the 5 percent level, implying the returns are not white noise. 4 Second, we estimate autoregressive (AR) models to fit the fund indices returns; the lag orders of the mean model are reported in Table 3. The ARCH-LM test is used in this paper to inspect the ARCH effect. We first estimate AR models, with lag orders ranging from to 5, for the squared values of the residuals drawn from the estimated mean models of the four fund indices returns and then run an F test for the significance of all lagged terms. If the coefficients of the lagged squared xie.indd 56 3/3/204 8:57:9 AM

September October 203, Volume 49, Supplement 4 57 Table 3. Lag orders in the mean model of the four fund indices returns Index Lag order CSI fund 4, 6, 3, 5 Stock fund 6, 3, 5 Hybrid fund 4, 6, 0, 3, 5 Bond fund, 3, 6, 0, 7 Table 4. ARCH-LM tests of the four fund indices returns Lagged orders CSI fund Stock fund Hybrid fund Bond fund 20.2928*** 4.0897*** 9.2468*** 24.050*** 2 26.67*** 9.6962*** 25.2844*** 38.6770*** 3 44.645*** 37.3940*** 45.4599*** 50.0878*** 4 50.6549*** 44.284*** 5.099*** 57.2232*** 5 56.6795*** 47.3575*** 55.992*** 60.60*** * p < 0.; ** p < 0.05; *** p < 0.0. residuals are jointly 0, there is no ARCH effect; conversely, if the coefficients are significantly different from zero, there is an ARCH effect. Results of the first five lag orders of ARCH-LM statistics are reported in Table 4, from which we can that see the ARCH-LM statistics of the four indices are significant at the percent level for each order. Moreover, the higher the lagged order is, the more significant the statistic. Hence, it can be concluded that there are ARCH effects in the volatility of all four fund indices returns. Persistence of the Volatility of the Open-End Fund Return As high-order ARCH effects are detected in the fund indices returns, we employ GARCH(,) based on the results of the AIC to model the variance equations. The estimated results are reported in Table 5. The ARCH a parameters and the GARCH b parameters of the four fund indices are all significant at the 5 percent level; these parameters comply with the nonnegative and stationary conditions. A comparison among the three subset fund indices shows that the sums of the ARCH and GARCH parameters of each fund follow a descending order of bond funds, stock funds, and hybrid funds. This indicates that the persistence of volatility in the bond fund return is the strongest, followed by the hybrid fund, while persistence is weakest in the stock fund. This conclusion is consistent with the efficiency of the underlying stock and bond markets these fund indices are tracking: the degree of informational efficiency in the stock market is higher than that in the bond market, thus external shocks can be more rapidly absorbed in the stock market, accounting for the weaker volatility persistence in the stock funds. Furthermore, it can be learned that the ARCH parameters of each follow a descending order of the bond funds, hybrid funds, and stock funds, while the exact opposite is true of the GARCH parameters. Due to the fact that the dynamic fluctuation characteristics of the time series in the short term are jointly determined by α and β in the GARCH model, it can be inferred that the dynamic fluctuation of the three funds xie.indd 57 3/3/204 8:57:9 AM

58 Emerging Markets Finance & Trade Table 5. Estimation of the GARCH model of the four fund indices returns CSI fund Stock fund Hybrid fund Bond fund C 0.0269007** (2.07) 0.05285** (2.9) 0.0396595** (2.25) 0.00047385** (2.002) a 0.0657478*** (4.386) 0.064505*** (4.25) 0.070978*** (4.485) 0.0978747*** (5.004) b 0.92007*** (49.5) 0.9847*** (45.87) 0.905*** (44.6) 0.895657*** (44.27) a + b 0.98589 0.982658 0.982029 0.993532 * p < 0.; ** p < 0.05; *** p < 0.0. varies from each other to some extent. Transactions in the stock market are flexible and the information emerging during the day can be responded to by the market in a timely manner, thus the volatility of stock funds is less fragile to current shocks than hybrid and bond funds. On the contrary, the transmission of new information in the bond market is far slower than in the stock market, thus the new information of the day is not fully reflected in the current market and has a larger impact in the following periods. Nevertheless, the smaller GARCH parameters of the bond fund, by contrast with those of the stock fund, suggest that although the bond fund is sensitive to new information shocks, the effect does not last long and the returns on bond funds are less affected by historical information than by new information. Asymmetry of the Volatility of the Open-End Fund Return Three different models, the EGARCH(, ), GJR-GARCH(, ) and TGARCH(, ), are employed to analyze the asymmetry of the volatility so as to reduce the potential configuration bias arising from drawing conclusions from a single model. Table 6 reports the estimated leverage coefficients for the four indices. The signs of leverage effects detected in each model for the CSI Fund Index contradict each other but fortunately they are not significant. As this tracks the characteristics of the entire open-end fund market, the insignificance indicates that no significant leverage effect exists in China s open-end fund market. This conclusion is consistent with Dong (2008), but contrary to Guo (2006). In addition, the stock funds and the hybrid funds have negative leverage effects, which is consistent with the convention of negative leverage effects verified in the stock market. However, on the grounds that the leverage terms are not significant in a statistical sense, we can conclude that there are no evident leverage effects in stock funds and hybrid funds. Another interesting finding is that the sign of the leverage effect of the bond fund is different from those of the other two funds. Xu et al. (2006) find that the Chinese exchangetraded bond market has significant negative leverage effect, a finding confirmed by Zhu and Tian s (2008) research on the corporate bond. Bond funds invest mainly in bonds and other fixed income instruments, so the volatility characteristics of bond funds should be similar to those of the bond market. However, we find that the bond funds leverage effect is positive in all three models despite significance being found only in the GJR GARCH(, ) model. This implies that the bond funds respond more intensely xie.indd 58 3/3/204 8:57:9 AM

September October 203, Volume 49, Supplement 4 59 Table 6. Leverage effect on the four fund indices returns Index EGARCH(, ) GJR-GARCH(, ) TGARCH(, ) CSI fund Parameters 0.025 0.0028 0.03289 z-statistics 0.82 0.0666 0.224 Leverage effect + Stock fund Parameters 0.0846 0.006383 0.099324 z-statistics.26 0.285 0.8787 Leverage effect Hybrid fund Parameters 0.02206 0.00688 0.095277 z-statistics.9 0.399 0.848 Leverage effect Bond fund Parameters 0.04836 0.44422** 0.0897 z-statistics 0.7477 2.94.077 Leverage effect + + + Notes: The cells show estimated parameters of leverage terms with z statistics, and the sign of the leverage effect follows. + indicates a positive leverage effect, that is, volatility increases when good news arrives; indicates a negative leverage effect, that is, volatility increases when bad news arrives. * p < 0.; ** p < 0.05; *** p < 0.0. to good news than to bad news, which seems to be contrary to conventional wisdom. This result, however, accords to some extent with Andersen et al. (2007), who found that positive real shocks affect bond prices negatively in the U.S. market. In China, monetary policies and economic fundamentals are the main sources of real shocks (Xu et al. 2006), and if the Chinese bond market works in the way same as the U.S. bond market, positive real shocks, or news that is otherwise good for the whole financial market, can actually be bad news for the bond market and consequently the bond funds. Therefore, the expected negative leverage effect resulting from bad news turns out to be a positive leverage effect, that is, the bond fund reacts more intensely to good news. Risk Premium Effect on the Open-End Fund Return From the foregoing analysis, we know that the leverage effects of the four fund indices are not significant, so the variance equations can be fitted simply by using the GARCH model. We use the GARCH M(, ) to reveal the risk premium effect of volatility on the four fund indices. The lag order of the mean equation is determined in the mean equations estimated in our earlier analysis. To save space, Table 7 reports only the parameters of the risk premium terms of the four fund indices returns. Table 7 shows that the risk premium effect is significant at the 0 percent level in the entire open-end fund market. The risk premium parameter of bond funds (about 0.77 and significant at the percent level) is the largest of the risk premium parameters in the three different kinds of funds. The underlying assets of bond funds are mainly government bonds, corporate bonds, and other fixed income instruments, and therefore the risk is much lower than in stock funds, which invest mainly in stocks. However, results in xie.indd 59 3/3/204 8:57:9 AM

60 Emerging Markets Finance & Trade Table 7. Risk-premium effect on the four fund indices returns Index Parameters (θ) z-statistics CSI fund 0.095536*.842 Stock fund 0.098565*.766 Hybrid fund 0.09729.629 Bond fund 0.7727*** 4.93 * p < 0.; ** p < 0.05; *** p < 0.0. this paper indicate that risk is more obviously compensated in the bond funds than in the stock funds. This anomaly may be closely related to the fact that China s stock market is immature and is exposed to irrational trading and consequently the risk is not adequately reflected in the stock returns. Conclusions An in-depth study on the volatility characteristics of open-end fund returns helps us to further understand the basic characteristics and the current development status of open-end funds. This paper therefore utilizes the CSI open-end fund, stock fund, hybrid fund, and bond fund to conduct such an empirical analysis through a set of GARCH models. The results of our analysis lead to the following four conclusions. First, the return of each fund has a very significant ARCH effect. This means that China s open-end fund market has the characteristic of volatility clustering, that is, all other things being equal, large fluctuations are often followed by large fluctuations and small fluctuations are followed by small fluctuations. This is consistent with most existing research. Second, there is evident volatility persistence in the open-end fund market as a whole, while the characteristics of each specific fund vary. As a consequence of the higher information efficiency in the stock market than in the bond market, the volatility persistence of the stock fund is the weakest and the volatility persistence of the bond fund is the strongest; that of the hybrid fund lies in between. In addition, the values of the ARCH parameters in the GARCH model follow a descending order of bond fund, hybrid fund, and stock fund, while this order is exactly the other way around in the GARCH parameters. Compared to the stock funds, the bond funds react intensively to new information but poorly to historical information. Third, leverage effects of the volatility in the entire open-end fund market are not significant in the EGARCH, GJR-GARCH, or TARCH models. Consistent with most prior research, negative leverage effects are found in the stock and hybrid funds, but the effects are not statistically significant. However, contrary to conventional wisdom, the leverage effect of the return on the volatility of the bond funds is positive despite its lack of significance, which means good news produces stronger responses in bond funds than does bad news. Fourth, there is a certain level of a risk premium effect in China s open-end funds on the whole, but the significance level is not statistically high. The risk premium is most significant in the bond funds in both an economic and statistical sense, followed by stock funds, and then hybrid funds. Therefore, the open-end fund market compensates xie.indd 60 3/3/204 8:57:9 AM

September October 203, Volume 49, Supplement 4 6 the risk assumed by bond fund investors, but the levels of risk premium in stock funds and hybrid funds are low. Despite our having conducted systematic empirical research into the volatility of returns on Chinese open-end funds, there are still two issues requiring further research. First, high-frequency data may be employed to study the volatility of open-end funds. Because this paper is based on daily data, the conclusions may not reflect any short activities, which account for most of the trading activities in the market. Second, a comparative analysis between open-end funds and closed-end funds can be carried out. As there are many institutional distinctions between these two kinds of mutual funds, there must be significant differences in the volatility characteristics of their returns. A comparative analysis will further our understanding of China s mutual fund market. Notes. Mutual funds mainly comprise closed-end funds and open-end funds. The two types of funds mainly differ in the way the shares are issued and traded/redeemed. Shares of closed-end funds are issued only at the beginning and can be traded only in the market, while shares of open-end funds can be issued and redeemed at any time after a lock-up period. The first mutual fund in China was a closed-end fund and was launched in 99. 2. There are also money funds and QDII funds in the Chinese open-end fund market, but they account for only 9.3 percent and 6. percent of the market. 3. We also implement the ADF test with intercept and trend. Not surprisingly, the statistics are all significant. 4. Due to space limitations, the results are not reported here; they are available from the authors upon request. References Andersen, T.G.; T. Bollerslev; F.X. Diebold; and C. Vega. 2007. Real-Time Price Discovery in Global Stock, Bond and Foreign Exchange Markets. Journal of International Economics 73, no. 2: 25 277. Bollerslev, T. 986. Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics 3, no. 3: 307 327. Dong, T.; L. Yang; J. Jiang; and L. Wang. 2008. An Empirical Study on the Volatility of China Open-Ended Fund Market. Journal of Industrial Engineering and Engineering Management 22, no. 3: 34 37 (in Chinese). Engle, R.F. 982. Autoregressive Conditional with Estimates of the Variance of United Kingdom Inflation. Econometrica 50, no. 4: 987 007. Engle, R.F.; D.M. Lilien; and R.P. Robins. 987. Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M Model. Econometrica 55, no. 2: 39 407. Glosten, L.R.; R. Jagannathan; and D.E. Runkle. 993. On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance 48, no. 5: 779 80. Guo, X. 2006. An Empirical Research on the Volatility of China Securities Investment Fund Market. Chinese Journal of Management Science 4, no. : 5 20 (in Chinese). Markowitsz, H. 952. Portfolio Selection. Journal of Finance 7, no. : 77 9. Nelson, D.B. 99. Conditional Heteroscedasticity in Asset Returns: A New Approach. Econometrica 59, no. 2: 347 370. Niu, F., and X. Lu. 2005. The Fund Market Volatility Research Based on A Class of ARCH Models. Statistics and Decision 24: 09 0 (in Chinese). Poon, S.-H., and C. Granger. 2003. Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature 4, no. 2: 478 539. Wang, X., and X. Sun. 20. An Empirical Analysis of the Open-End Fund Risk Based on the VaR-GARCH Model. Commercial Times, 20: 73 74 (in Chinese). xie.indd 6 3/3/204 8:57:9 AM

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