1
Performance Persistence Of Equity Mutual
Funds In US And China
*Name: Jun Guo ID number: S2171376 Master of science in Finance Master thesis
Thesis advisor: Prof. Roberto Wessels Faculty of Economics and Business University Of Groningen
2
ABSTRACT
This study examines the performance persistence of 216 and 125 equity mutual funds from the US and China, respectively. These mutual funds are mainly invested in domestic stock markets, and the sample is free of survivorship bias. I employ the contingency table and the Spearman rank correlation coefficient (SRCC) to test the general performance persistence of the equity mutual funds in each market and the del test to predict if the winner (loser) in the first period will remain as a winner (loser) in the second period. The empirical evidence shows that US equity funds have significant performance persistence, whereas those from China have weak performance persistence. The performances of both winners and losers demonstrate predictability for US equity funds, while only the performance of losers display predictability for China equity funds.
3
1. INTRODUCTION
Mutual funds have become the most popular investment tool in the capital market. According to the 2012 Investment Company Fact Book (52nd edition), the total net assets of the US mutual funds industry have grown from about US$ 17 billion in 1960 to about US$ 11,600 billion in 2011. Besides the market in the US, the past 15 years had seen the rapid development of mutual funds in other emerging markets. As the largest developing market, China established its mutual funds in 1998, which dramatically grew to approximately RMB ¥ 2200 billion (about US$ 350 billion) in total net assets by 2011. Equity mutual funds comprise the largest part of mutual funds. Being diversified and invested in equity markets, equity mutual funds are likely to have low volatilities and can avoid idiosyncratic risks, thus becoming increasingly attractive.
Both individual and institutional investors are concerned about the performance of mutual funds when they choose to invest them. They apparently select mutual funds that have previously demonstrated better performance and disregard poor performers to avoid the risk of losing money. They follow this rule because they believe that the performance of mutual funds can be persistent.
Performance persistence of mutual funds refers to the tendency of mutual funds to maintain their superior or weak performance to the next period. Essentially, performance persistence of mutual funds is subject to evaluation on whether the past performance of mutual funds can predict their future performance.
4
I attain the objectives of this study by implementing three steps. Firstly, I adopt the Sharpe ratio to measure the monthly performance of equity mutual funds in the two countries. Secondly, I perform the contingency table and Spearman rank correlation coefficient (SRCC) to test the general performance persistence of equity mutual funds in each market, and finally, the del test, which is based on the three-way contingency table, to precisely predict if a winner (loser) in the first period can be predicted as a winner (loser) in the second period for equity funds from the US and China.
In this study, I select 216 and 125 equity mutual funds from the US and China, respectively, as the sample. The timeframe of the study is from January 2008 to December 2012, thus a total of 60 months. To test performance persistence, I divide the sample period into two sub-periods, with each sub-period consisting of 30 months.
In previewing my results, I find that US equity funds demonstrate significant performance persistence, whereas China equity funds demonstrate weak performance persistence. Given that the two samples are based on the ranking according to the magnitude of the Sharpe ratio, findings on persistence explain relative performance among the mutual funds, but not the prediction of future return based on the historical return. Therefore, my results on the persistence phenomenon are useful indicators in identifying the funds to avoid. Moreover, by further precise research, I discover that being a winner or loser in the first period reduces the error in predicting the status of US equity funds in the second period, whereas being a loser in the first period helps predict future performance of China equity funds.
I contribute via this study by comparing performance persistence of equity funds from the US and China. Literature in English comparing the mutual funds of the two countries is limited. Most English references only focused on US mutual funds, while Chinese scholars focused on China mutual funds.
5
2. LITERATURE REVIEW
The past several decades have witnessed the rapid development of mutual funds in developed markets, such as the US and Europe, and in emerging markets, such as China. This massive growth trend has instigated much research about the performance of mutual funds. Measuring the performance of mutual funds becomes a common topic in research. However, recently, a large number of studies have focused on whether the performance of mutual funds can be persistent or not.
This section highlights a portion of the literature that discussed on performance persistence of mutual funds. Some literature is also mentioned on survivorship bias that is an important and unavoidable problem in studying performance persistence of mutual funds.
Brown and Goestzmann (1995) find that relative to the measurement of performance, persistence displays a significant difference. Therefore, a highly important problem investigated in my research is on how performance of mutual funds is measured. Performance measurement methods for mutual funds are divided to two categories, namely, standard methods and relative performance measurement. Standard methods include the Sharpe ratio, the Jensen’s alpha, and the Treynor ratio. Another method is by relative performance measurement, such as the information ratio.
In this study, I use the Sharpe ratio, which Sharpe (1966) and Vassilios et al. (2007) formulated to measure performance. I have adopted the Sharpe ratio because of its principal advantage in computing from any observed series of returns without requiring additional information about the source of profitability. Besides, the Sharpe ratio does not depend on any model, whereas relative performance measurements, such as the Jensen’s alpha, depend on other models such as the capital assets pricing model (CAPM). No joint hypothesis also exists in measuring the performance of equity mutual funds for the Sharpe ratio.
6
performance persistence of mutual funds, some early empirical findings indicated no performance persistence, whereas those from recent studies show otherwise.
Sharpe (1966) initially uses the Sharpe ratio to measure the performance of mutual funds. He selects 34 mutual funds and determined their performance from 1954 to 1963. He then divides the period into two sub-periods and ranks the funds according to the Sharpe ratio. Finally, he employs SRCC to test the correlation of the performances of the 34 mutual funds. He obtains SRCC of 0.36, which is not significant, implying that the performance of the mutual funds cannot be predicted. The limitation in the study by Sharpe is that his sample is small. Thus, the presence or absence of performance persistence is not sufficiently explained. The current study has numerous similarities to that by Sharpe.
Unlike Sharpe, Jensen (1968) uses CAPM to estimate the Jensen alpha, a risk-adjusted return that can measure the performance of mutual funds. Jensen assumes that the after-fee performances of 115 sample mutual funds are worse than that of a portfolio consisting of random stocks. He concludes that active management cannot overpower the market and that performance persistence of mutual funds does not exist.
Besides, many earlier studies support the viewpoint that performance of mutual funds is not persistent. Kahn and Rudd (1995) measures 300 equity funds in terms of total returns, selection returns, and information ratio by regression analysis and contingency tables to investigate the performance persistence of the funds from one period to the next. They fail to acquire evidence that demonstrate the existence of performance persistence of equity funds. Detzal and Weigand (1998) also fail to obtain evidence of performance persistence after implementing the regression residual technique to control the effects of investment style, size, and expense ratios.
7
superior-performing funds. Without considering the source of performance persistence, the history performance of the mutual funds can provide useful information to predict their future performance.
Hend, Patel, and Zeckhauser (1993) show that the returns for three months are positively related to those from the previous years. Their findings reveal that performance persistence can occur. They also determine the relative performance of 165 no-load, growth-oriented mutual funds and perform two different test methods, namely, cross-section regression and SRCC to analyse the short-term performance persistence of the mutual funds. They conclude the presence of the “hot hand” phenomenon in which superior-performing funds maintain their performance in a short period. Ranking the funds according to the previous three-month performances, they notice that the top-ranking funds performed slightly better than the market funds and significantly better than the average- and bottom-ranking funds. Using contingency tables, Brown and Goestzmann (1995) find that though performance persisted in most situations, the performance of mutual funds sometimes displays the opposite.
At present, most research on performance persistence of mutual funds has focused on the performance of equity mutual funds. In my study, the research object is likewise equity mutual funds from the US and China.
Based on the review of existing literature, scholars have adopted several methods in testing performance persistence, such as SRCC, regression analysis, and contingency tables. I have employed two methods, namely, the contingency table previously implemented by Brown and Goestzmann (1995) and SRCC by Sharpe (1966) and Hend, Patel, and Zeckhauser (1993). The advantages of these two non-parametric tests are the absence of a joint hypothesis and the non-requirement of a normally distributed performance of mutual funds. My results support the findings of Sharpe (1996) and of Goetzmann and Ibbotson (1994) that performance of mutual funds persists.
8
estimated the extent of survivorship bias. Moreover, Brown, Goetzmann, Ibbotson, and Ross (1992) conduct simulations to study the relationship between volatility and returns. They subsequently conclude that a small survivorship bias can significantly increase performance persistence. Many other studies indicate an opposite viewpoint on the effect of survivorship bias on performance persistence of mutual funds. Grinblatt and Titman (1992) and Wermers (1997) state the difficulty of finding evidence on performance persistence of mutual funds if the database merely includes surviving mutual funds.
9
3. RESEARCH STRATEGY
To test the persistence of the performance of mutual funds, I should compare the relationship of performance measures between two consecutive periods. Therefore, it is very important on the results of the study to select the length of both periods studied. In this study, the time frame will include 30-month study periods.
In the part of literature review, I discussed different measures about performance, such as the Sharpe ratio, Jensen’s alpha and other risk-adjusted return. In this thesis, I only employ one performance measure: the Sharpe ratio. The Sharpe ratio measures the risk premium per unit of standard deviation in an investment portfolio. I follow William Sharpe (1994) and the Sharpe ratio is defined as:
(1)1
where Rp is realized returns of each fund in US or in China, Rf is the risk-free rate of
return in each market, and σp is the standard deviation of returns.
In this thesis, I split the timeframe into two sub-periods. Firstly, I calculate the Sharpe ratio of the total sample of each market in each period. Then, funds in each market are ranked in order of the Sharpe ratio from highest to lowest for each study period.
To investigate the persistence of equity mutual funds in a two-period framework, I use two non-parametric methods, the contingency table-based method and the Spearman Rank Correlation Coefficient statistics.
For the contingency table-based method, I construct a two-way contingency table of winners and losers.
Firstly, I use a strong contingency table test. The reason why I call it “strong” is that I split the whole sample into quartiles. The general method is that the sample is split into two parts according to the median. (Kahn and Rudd (1995), Brown and Goetzmann (1995)). In this study, the top quartile that has the higher Sharpe ratio will
1
10
be defined as Winners in each period and the bottom quartile that has the lower Sharpe ratio will be defined as Losers in each period.
Combined the performance in both periods, I should define the following,
WW: the funds that are winners in two consecutive periods; LL : the funds that are losers in two consecutive periods;
WL: the funds that are winners in first period and losers in second period; LW: the funds that are losers in first period and winners in second period.
Period 2 Period 1
W L
W win in both periods WW
win in first but lose in second WL
L lose in first but win in second LW
lose in both periods LL
Besides this strong test, I also take a weaker test. I split the whole sample into two parts accoding to the median of the Sharpe ratio. In each period, the fund is a winner if the Sharpe ratio of the fund is greater than the median Sharpe ratio of all equity funds in US market or in Chinese market, otherwise it is a loser.
In this method, to test for persistence, I introduce a cross-product ratio (CPR)2, (Agarwal & Naik, 2000a). The CPR is defined as (WW*LL)/(WL*LW). If the CPR equals one, it indicates that there is no persistence, which is null hypothesis. The alternative hypothesis is that there is performance persistence of equity mutual funds. If the CPR is significantly larger than one, it indicates that there is positive correlation in the performance of equity mutual funds between two periods. In other words, there is performance persistence of equity mutual funds. If the CPR is significantly smaller than one, it means that there is negative correlation in the performance of equity funds between two periods. In other words, it illustrates that the performance has been reversal, in which case the winners in first period become the losers in the second periods and vice versa.
2
11
To test the statistical significance of the CPR, I employ a Z statistic, which measures the ratio of the standard deviation of the natural logarithm of CPR. The standard error of the natural logarithm of the CPR is calculated as the square root of [(1/WW)+(1/WL)+(1/LW)+(1/LL)] 3. For significance, a two-tailed Z-statistic value of 1.96 corresponds to significance at the 5% level and that of 2.58 corresponds to significance at the 1% level. The Z-statistic will indicate whether the CPR is statistically greater than one. In practical, it means that the performance persistence of equity funds exists.
To further substantiate the results, I employ an additional quantitative measure of inter-period performance consistency, the Spearman Rank Correlation Coefficient (SRCC). SRCC is also a nonparametric test. As discussed in the part of literature review, the Spearman Rank Correlation Coefficient is adaptable and efficient when the distribution of the sample does not follow the normal distribution, when the style of the population is unknown, or when it is ordered data.
The SRCC can be calculated for the Sharpe ratio data based upon absolute rank in the period. The Sharpe ratios in US market are ranked from 1 to 216 or in Chinese market are ranked from 1 to 125 where 1=highest and 216 (or 125 in Chinese market) = lowest.
Then, I calculate the correlation between the rank in first period and the rank in second period. The following equation is employed to calculate the SRCC, denoted as γs :
∑ (2)4 Where di= Rankt-1-Rankt, n is the number of the sample.
The SRCC can be ranged from -1 to 1. The larger of the absolute value of SRCC, the stronger correlation it is. When the γs=1, it indicates that the two group of viable is
perfect positive correlation. Whereas the γs=-1, it is perfect negative correlation.
The null hypothesis is that there is no correlation between the ranks in two periods. In other words, there is no performance persistence of the equity mutual
3 See Christensen (1990) p.40. 4
12
funds in US market or in Chinese market. The alternative hypothesis can have three situations. The first one is that there is correlation between the ranks in two periods. In this situation, the performance can be persistent or reversal. The second one is that there is positive correlation, which indicates that there is performance persistence. The third one is that there is performance reversal.
To test the statistical significance of the SRCC, we can use a student t-statistic whose degree of freedom is (n-2). The student t-statistic of this measure can be calculated by following equation:
√
√ (3)
The significance of the statistic can be discussed at 5% confidence level (two-tailed test) and at 1% confidence level (two-(two-tailed test).
However, the two above-mentioned tests, CPR test and SRCC test, only examine the general performance persistence but cannot identify the more precise inference, such as “does being a winner (loser) in the first period predict being a winner (loser) in the second period?”. Therefore, in order to determine whether being a winner (loser) in the first period predict being a winner (loser) in the second period, a different test is introduced. Suppose that the theory being evaluated can be expressed in a statement of the form “ if x then y”. The empirical problem is that how much does information of the state of x contribute towards correctly predicting y. Hildebrand, Laing and Rosenthal (1977) develop the ∇-statistic to perform this evaluation. To be specific, the del-statistic indicates the reduction in errors by using the theory versus predictions without using the theory.
To develop an index for measuring prediction success, considering the two-way contingence table and the prediction X1→Y1 from the below table.
Y1 Y2
X1
X2
13 The ∇-statistic is following,
∇
Where the ratio P21/P.1 is the estimated error rate using the theory, and P2. is the
estimated error rate without using the theory. If the use of the theory results in zero errors of prediction, the ∇-statistic will equal one. It means a 100% increase in the amount of error reduction.
The implication of the ∇-statistic is that how much there is reduction in errors by using the information of the state of X over not using it at all to classify the state of Y. For example, by combing the hypothesis that being a winner in the first period predict being a winner in the second period, if the ∇-statistic equals 0.352, it indicates that there is a 35.2% reduction in errors by using the information of being a winner in the first period over not using it at all to estimate whether being a winner in the second period or not. In order to test the statistical significance of the ∇-statistic, the formulas of the standard deviation of the ∇-statistic has been derived by Hildebrand et al., (1977:200). Because the ∇-statistic can be nomalized, we can use the t-statistic to judge the statistical significance.
14
4. THE DATA
I investigate active equity mutual funds in China and US. These equity mutual funds, no matter in China or in US, mainly focus on their domestic stock markets. The time period studied is from January 2008 to December 2012, 60 months. To test the performance persistence, I divide the whole sample period into two parts and each period includes 30 months. The period 1 is from January 2008 to June 2010 and the period 2 is from July 2010 to December 2012.
The sample of Chinese Equity funds which are focus on their domestic stock market includes 125 funds. Among these Chinese funds, they include 65 Growth Equity Funds and 60 Value Funds. The sample of US equity funds includes 216 funds, which is 108 Growth Funds and 108 Value Funds. For the sample of Chinese equity funds, I draw out the sample from Sina Mutual Funds Database. The Sina Mutual Funds Database (SMFD) includes the information about fund objective, fees, dividends, daily net asset values and so on. It also provides the information of the inactive funds.
For the sample of US equity funds, I select the sample from the database called The Centre for Research in Security Prices (CRSP). The CRSP is only a provider of the information of the whole active and inactive mutual funds. The CRSP information includes fund objectives, fees, total net assets, monthly and daily net asset values, returns, and distributions. The key characteristic of the CRSP, which is also the reason why I select this database, is the CRSP is a survivorship bias free database, which is regarded as a foundation for research and benchmarking for this asset class.
The survivor-bias-free nature of the database ensures accurate performance benchmarks and valid analysis, which is very important for research in mutual funds. Survivorship bias, discussed in Fung and Hsieh (2000), may occur if the reported data includes the funds that exist today but excludes the returns of nonsurviving mutual funds that went out of business over the sample period because nonsurviving funds probably have poorer performance.
15
sample period but disappear over the sample period. After selecting the sample respectively from the US CRSP database and Chinese SMFD database, the US sample includes 36 funds that disappear over the period and the Chinese sample includes 5 funds that have this characteristic.
In some cases, some of these funds didn’t report their return directly so that we should do some calculation to get the monthly return. To calculate the monthly return of these funds, we follow below equation:
Where the NAV is the net asset value per share, ∆NAVt is the change in net asset
value per share between two consecutive time t and t-1, Dt is the dividend per share at
time t, and NAVt-1 is the net asset value per share at the time t-1.
I draw out the US funds monthly net asset value per share (NAV) from the CRSP database and obtained the NAV of Chinese equity funds from the Sina Mutual Funds Database. After that, I calculate the monthly return of each fund. Table 1 will illustrate the average, maximum, and minimum value of the equity mutual funds invested in domestic stock market in China and US.
Table 1
The Descriptive Statistics Of The US And Chinese Equity Mutual Funds’ Return
US Equity Funds Chinese Equity Funds
16
From above table, we can see that the average monthly return of US Equity Funds for the whole sample period, from January 2008 to December 2012, is 0.84%, which is higher than that of Chinese Equity funds, -0.43%.
From the perspective of maximum and minimum, the best performer of US equity funds experienced the 10.78% monthly return and the worst one had a negative return, -0.95% over the sample period. Compared with the 0.60% monthly return of the NASDAQ Composite that is the important index which indicates the whole market performance, most of the US equity funds have a better performance than the market. In other words, it turns out that most managers of US Equity Funds have the skills to actively manage the funds to beat the market and get a better performance during the sample period.
In the mean time, the Chinese Equity Funds experienced a negative monthly return, -0.43%. The maximum and minimum is 0.96% and -1.25% respectively. Meanwhile, the index of SHANGHAI Composite average monthly return is -0.974%.
After dividing the whole sample period, the US Equity funds monthly return, reported in the raw of Period 1, varies between -1.90% and 19.19% and there is some variation in the fund returns. At the same time, the monthly return of Chinese funds had the range from -2.34% to 1.00% and there is much smaller variation.
In the Period 2, it is apparent that there is much reduction of variation of the US equity funds’ monthly return, which varies from 0.00% to 4.64%. In the mean time, the Chinese funds had a monthly return varying from -0.75% to 1.00% and there is also a small variation. It is obvious that the Chinese equity funds have a low return and small variation no matter in which period.
To measure the performance of the funds, I choose the Sharpe ratio. To calculate the Sharpe ratio, I need the risk-free rate of interest (Rf).
For the US risk-free rate, I downloaded the one-month Treasury Bill as recorded in the Datastream over the study period.
17
the one –year treasury bill. I obtained the three-month China Shibor (Shanghai Interbank Offered Rate) from the China National Interbank Offered Center.
The effective monthly rate of the risk-free rate can calculated as follows:
where: i is effective interest rate per month;
j is the nominal annualised interest rate.
After obtaining the monthly return of each fund, I can easily calculate the standard deviation. Then, it’s time to calculate the Sharpe ratio, the measurement I used in this study. The table 2 gives us some descriptive statistics of the Sharpe ratio about the US and Chinese Equity Funds.
Table 2
The Descriptive Statistics Of The US And Chinese Equity Mutual Funds’ Sharpe Ratio
US Equity Funds Chinese Equity Funds
2008.01-2012.12 Average 0.137 -0.079 Max 0.693 0.105 Min -0.207 -0.251 2008.01-2010.06 Period 1 Average -0.005 -0.126 Max 0.343 0.083 Min -0.413 -0.251 2010.07-2012.12 Period 2 Average 0.279 -0.032 Max 1.042 0.105 Min 0.000 -0.177
18
In the meantime, it is very erratic and unbelievable that the Chinese Equity Funds has a negative average Sharpe ratio that indicates that when increasing the risk, the extra return obtained from the risk is negative, -0.079. This phenomenon doesn’t make sense but indeed happen in China. From the perspective of the range, the Sharpe ratio of US Equity Funds varies from -0.207 to 0.693 and there is quite some variation in US equity funds Sharpe ratio. Whereas, the Chinese Equity funds experienced a small variation, ranging from -0.251 to 0.105.
Over the period 1 from January 2008 to June 2010, the Sharpe ratio of US equity funds ranges from -0.413 to 0.343, comparing with the Sharpe ratio of Chinese equity funds which varies between -0.251 to 0.105. It is interesting that we find that the US equity funds has more variation than Chinese equity funds in the Sharpe ratio.
19
5. EMPIRICAL ANALYSIS
I will divide two categories to discuss the test results and implications. First, I will present the results of contingency table and SRCC, which are used to test the general performance persistence of Chinese equity funds and US equity funds. The test result of the three-way contingency table is firstly discussed to indicate the performance persistence of Chinese equity funds and US equity funds. After that, the performance persistence of Chinese equity funds and US equity funds are analysed by using a weaker test, the two-way contingency table. Finally, I state the test result of Spearman Rank Correlation Coefficient method and analyse the implication of this result. Second, I will show the results of the del-test, which is applied to answer whether being a winner (loser) in the first period predicts being a winner (loser) in the second period or not.
5.1 Tests Of The General Performance Persistence
A. The Results of Three-Way Contingency Table Test
TABLE 3
The Three-Way Result Of Chinese Equity Funds
Jul 10-Dec 12
Winners Losers Others SUM
Jan 08-Jun 10 Winners 8 4 19 31 Loses 5 14 12 31 others 18 13 32 63 SUM 31 31 63 125 CPR=5.600 Z=2.143
20
In the part of Research strategy, I have stated that I use the cross-product ratio to test the performance persistence. Table 3 states that the cross-product ratio (CPR) is 5.600, which is larger than one. It indicates that there is performance persistence of Chinese equity funds. The z-statistic is 2.143, which indicates that the persistence is significant at the 5% level but not significant at the 1% level.
Table 3 also shows that the winners in both periods are 8. However, from the perspective of the probability, unconditionally, the probability of ending up in the winners/winners cell is 0.25^2, which equals 6.25%.and 6.25% of 125 is 7.8 which is very, very close to the result, 8. This situation indicates that the performance persistence of Chinese equity funds don’t come from the winners but is derived from the losers, because the losers in both period is 14, larger than 8.
The winners in the second but losers in the first, which means the performance reversal, is 5, and the alternative reversal situation is just 4. It indicates that there is little probability that the performance of the Chinese equity funds reverse.
Compared to the performance of Chinese Equity Funds, we use the same three-way contingency table to test the performance of US Equity Funds. The result is the table below:
TABLE 4
The Three-Way Result Of US Equity Funds
Jul 10-Dec 12
Winners Losers Others SUM
21
From Table 4, we can easily see that the past performance has definite information about the future performance. This performance persistence sources from not only the winners but also the losers, because in the table 4, the winners in both periods are 34 and the losers in both periods are 31, both significantly larger that 0.25^2*216, 13.5. The winners in both periods and losers in both periods equally contribute to the persistence.
From the perspective of the performance reversal, we can be sure that almost no fund performance will be reversal in two successive periods.
The CPR of the test about the performance persistence of the US equity funds is 263.5, which is prominently larger than one, and it indicates that there is significant performance persistence, as can be seen from the Z-statistic, reported in the last row, which is 4.867, which means that the persistence is significant at the 5% level and at the 1% level.
To be concluded, there is difference about the performance persistence between the Chinese equity funds and the US equity funds. First, the persistence of US equity funds is more significant than that of Chinese equity funds. Next, the persistence of Chinese equity funds only come from the losers while that of US equity funds is equally derived from the winners and losers.
B. The Results Of Two-Way Contingency Table Test
In addition, we take a weaker two-way contingency table test.
TABLE 5
The Two-Way Result Of Chinese Equity Funds
Jul 10-Dec 12
Winners Losers SUM
Jan 08-Jun 10
Winners 33 29 62
Loses 29 34 63
SUM 62 63 125
CPR= 1.334 Z=0.804
22
In table 5, it is easily to find that the CPR is 1.334, very close to 1, which indicates that there is no performance persistence of Chinese equity funds. Therefore, the investor cannot determine their fund invested by the previous performance, because there is no correlation between them. The Z-statistic is 0.804, which is very below 1.96 corresponds to significance at the 5% level and that of 2.58 corresponds to significance at the 1% level. So we cannot reject the null hypothesis that there is no performance persistence about the Chinese equity funds.
TABLE 6
The Two-Way Result Of US Equity Funds
Jul 10-Dec 12
Winners Losers SUM
Jan 08-Jun 10
Winners 73 35 108
Loses 35 73 108
SUM 108 108 216
CPR= 4.350 Z=5.057
23
C. The Results Of Spearman’s Rank Correlation Coefficient Test
TABLE 7
The Test Results Of SRCC
rho t-statistics
US Equity Funds 0.638 12.116
Chinese Equity Funds 0.248 2.824
Notes: rho is the Spearman’s Rank Correlation Coefficient. The sample of US Equity Funds has 216 observations and the Chinese has 125 equity funds.
From the table 7, it is apparent that there are performance persistence in both US equity funds and Chinese Equity Funds. The results undoubtedly support the alternative hypothesis that there is performance persistence.
In the first row, we find that the Spearman Rank Correlation Coefficient of US equity funds is 0.638, a high positive correlation and the t-statistic is 12. 116, larger than the 2.58, that is significant at the 1% level.
In the second row, we can see that the SRCC of Chinese Equity Funds is 0.248, which means that the correlation is not strong. However, the t-statistic is 2.824, which is also significant at the 1% level. Although the performance persistence of Chinese Equity Funds is weak, it indeed exists.
5.2 Tests of Winners’ and Losers’ Predictability
24 D. The Results of Winners’ Predictability
TABLE 8
Cross Classification Of Winners And Non-Winners Of Chinese Equity Funds
Note : Cell, row and column propotions are given in between parentheses
The assumed theory is that being a winner in the first period predicts being a winner in the second period for Chinese equity funds. Therefore, according the del-test mentioned in the Research Strategy, the shaded box reprensents an error cell based on the theory. Thurs, the del statistic to test the theory is computed as:
∇=1-[0.184/(0.248)(0.752)]=0.013
After that, we follow the formulas of the standard deviation of the ∇-statistic. The standard deviation is 0.091. Therefore, the t-statistic is 0.143, much smaller than 1,96, which is not significant at the 5% level. So it indicates that the theory does not work to predict a winner in the second period.
TABLE 9
Cross Classification Of Winners And Non-Winners Of US Equity Funds
Jul 10-Dec 12
Winners Non-Winners Total
Jan 08-Jun 10 Winners 34 (0.157) 20 (0.093) 54 (0.250) Non-Winners 20 (0.093) 142 (0.657) 162 (0.750) Total 54 (0.250) 162 (0.750) 216 (1.000)
Note : Cell, row and column propotions are given in between parentheses
Jul 10-Dec 12
Winners Non-Winners Total
25
The assumed theory is that being a winner in the first period predicts being a
winner in the second period for US equity funds. The del-ststistic can be calculated as:
∇=1-[0.093/(0.25)(0.75)]=0.504
The standard deviation of the del-statistic is 0.079 and the t-statistic is 6.405, much larger than 1.96, which is much significant at the 5% level. Therefore, the foregoing result means that there is a 50.4% reduction in errors by knowing the information of being a winner in the first period over not using it at all to predict being a winner in the second period for US equity funds.
E. The Results of Losers’ Predictability
TABLE 10
Cross Classification Of Non-Losers and Losers Of Chinese Equity Funds
Jul 10-Dec 12
Non-Losers Losers Total
Jan 08-Jun 10 Non-Losers 77 (0.616) 17 (0.136) 94 (0.752) Losers 17 (0.136) 14 (0.112) 31 (0.248) Total 94 (0.752) 31 (0.248) 125 (1.000)
Note : Cell, row and column propotions are given in between parentheses
The theory posits that being a loser in the first period predicts being a loser in the second period for Chinese equity funds. The shaded box reprensents an error cell because it contains the incorrect prediction. The del statistic to test the theory is computed as:
∇=1-[0.136/(0.752)(0.248)]=0.271
26
TABLE 11
Cross Classification Of Non-Losers and Losers Of US Equity Funds
Jul 10-Dec 12
Non-Losers Losers Total
Jan 08-Jun 10 Non-Losers 139 (0.644) 23 (0.106) 162 (0.750) Losers 23 (0.106) 31 (0.144) 54 (0.250) Total 162 (0.750) 54 (0.250) 216 (1.000)
Note : Cell, row and column propotions are given in between parentheses
The theory assumes that the Losers’ performance can be predicted for US equity funds. In other words, being a loser in the first period predicts being a loser in the second period for US equity funds. The del statistic can be calculated as:
∇=1-[0.106/(0.25)(0.75)]=0.435
27
6. CONCLUSION
This study compares the performance persistence of equity mutual funds between the US and China. The Sharpe ratio is used to measure the performance of all equity funds, while the contingency table analysis and SRCC are conducted to test the general performance persistence of equity mutual funds. Besides, I perform the del test, which is based on the three-way contingency table, to precisely predict whether a winner or a loser can retain its performance.
Findings from empirical analysis reveal that the performance of US equity mutual funds has significant persistence, whereas that of China equity mutual funds is weak. The results of the del test for US equity funds show different degrees in error reduction with the knowledge of winner or loser status during the first period, in contrast to the non-utilization of the knowledge in predicting the status in the second period. Meanwhile, the results of the del test for China equity funds reveal that the information of being a winner in the first period is not helpful in predicting the status in the second period, whereas being a loser in the first period helps predict the performance in the second period.
However, I should emphasize that these methods are only based on the ranking determined by the magnitude of the Sharpe ratio. Persistence explains only the relative performance among the mutual funds, but does not show if the future return can be predicted by the historical return. Thus, the persistence phenomenon is a useful indicator in identifying the funds to avoid.
28
REFERENCES
Agarwal, V., Naik, N. Y., 2000. Multi-period performance persistence analysis of hedge funds. Journal of Financial and Quantitative Analysis 35, 327–342.
Agarwal, V., Naik, N. Y., 2000. On taking the alternative route: Risks, rewards, and performance persistence of hedge funds. Journal of Alternative Investments 2, 6–23.
Brown, S. J., Goetzmann, W. N., 1995. Performance persistence. Journal of Finance 50, 679– 698.
Brown, S. J., Goetzmann, W. N., Ibbotson, R. G., 1999. Offshore hedge funds: Survival and performance 1989–1995. Journal of Business 72, 91–118.
Brown, S.J., W.N. Goetzmann, Roger G. Ibbotson, Stephen A. Ross, 1992. Survivorship bias in performance studies. Review of Financial Studies 5, 553-580.
Christensen, R., 1990. Log-Linear Models. Springer-Verlag, New York.
Detzel, F. L., Weigand, R. A., 1998. Explaining persistence in mutual fund performance. Financial Services Review 7(1), 45-55.
David, K.H., James, D.L., Howard, R., 1977. Prediction Analysis of Cross Classifications. John Wiley & Sons, Inc.
Fama, E. F., French, K. R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56.
Frederick, M., 1968. Association and estimation in contingency tables. Journal of the American Statistical Association 63, 1-28.
Goetzmann, W.N., R.G. Ibbotson, 1994. Do winners repeat?. Journal of Portfolio Management 20, 9-18.
Grinblatt, M., S. Titman, 1992. The persistence of mutual fund performance. Journal of Finance 47, 1977-1984.
Grinblatt, M., S. Titman, 1993. Performance measurement without benchmarks: An examination of mutual fund returns. Jolurnal of Business 66, 47-68.
Jensen, M. C., 1968. The performance of mutual funds in the period 1945-1964. Journal of Finance 23, 389-416.
Kahn, R. N., Rudd, A., 1995. Does historical performance predict future performance?. Financial Analysts Journal 51, 43-52.
Lehman, B.N., D.M. Modest, 1987. Mutual fund performance evaluation: A comparison of benchmarks and benchmark comparisons. Journal of Finance 42, 233-265.
29
Sharpe, W.F., 1966. Mutual fund performance. Journal of Business 39, 119-138. Sharpe, W.F., 1994. The Sharpe ratio. The Journal of Portfolio Management 21, 49-58. Sharpe, W.F., 1996. The styles and performance of large seasoned US mutual funds, World Wide Web http://gsb-www .stanford.edu/wfsharpe/lslOO.htm.
Vassilio, B., Guglielmo, M.C., Alexandros, K., Nikolaos, P., 2007. Testing for persistence in mutual fund performance and the ex post verification problem: Evidence from the Greek market. European Journal of Finance 14, 735-753.
