" Jurnal Reksadana dalam Bhs Inggris "

MUTUAL FUNDS PERFORMANCE PERSISTENCE: USING MARKOV TRANSITION PROBABILITY MATRIX


Wen-Tao Lee
Department of Finance, National Sun Yat-sen University
No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC
capm2000@ms63.hinet.net


ABSTRACT

We explore performance persistence in Taiwan’s mutual funds using absolute and relative performance. We use the Markov transition probability instant of traditional Spearman order correlation or winner-loser method. Our sample, largely free of survivorship bias, that the performance of mutual funds persists; however, persistence most due to relative performance. A probit analysis indicates that poor performance increases the probability of disappearance.

Keywords: Mutual Funds, Performance, Persistence, Transition Probability Matrix

1. INTRODUCTION

Since the beginning in 1986, there are now a total of close to 700 mutual funds raised in Taiwan by the end of 2006. At the end of 2006, 522 mutual funds still survived. Owing to great increase of number of mutual funds in Taiwan, a lot of investors are unable to select appropriate funds. Most of the investors take past performance of funds as the major reference. Starting from 1996, Securities Investment and Consulting Association of the R.O.C. published periodical ranks of funds issued by domestic investment trust companies . A lot of wealth management companies also offer return performance of mutual funds in the past. Yet, is the historical performance persistent? If the answer is yes, how strongly the persistence is ? Can investors take the past performance as the reference in investment decision making?

In earlier research on mutual funds performance persistence, both foreign and domestic empirical studies adopted dichotomy of winners and losers or grades of historical performance ranks in evaluation. The two methods do provide evidence of whether mutual funds performance is persistent. Nevertheless, dichotomy of winners and losers fail to provide investors with sufficient information. Coefficients of historical ranks show the relation between current and past performance of mutual funds. Investors still are unable to make investment decision with such information only.

To increase the reference value in decision making, the researcher expanded the dichotomy model of winners and losers by adding the number of divisions of mutual funds performance ranks. With estimation of Markov Chain Transition Probability matrix, the research provides richer transition probability matrix in funds performance ranks so that investors can have an overview of changes of mutual funds performance ranks in the past. Through Markov Chain joint test and likelihood ratio test, the research examines whether transition probability of mutual funds performance in the past obeys random and has clarified whether domestic mutual funds performance is persistent.

Earlier evaluation on funds performance persistence in Taiwan mostly ignored survivorship bias. For the first time, the research takes survivorship bias into consideration, making measurement of mutual funds performance persistence more accurate. Also, the research makes statistics of the performance of funds before liquidation or merge.

This research aims at 315 mutual funds raised in Taiwan and invested in domestic stocks between 1990 and 2006. Estimation of performance indexes each year is made through daily funds net value and dividends in the past years to verify the several common fund performance indexes are persistent. Such indexes include absolute return and three relevant indexes--Sharpe index, Jensen index and Treynor index. The empirical results show the three relevant indexes are significantly persistent while absolute return persistence is not very significant. Mutual funds with poorer performance are more likely to be liquidated or merged than those the historical average.
The major contribution of the research is the use of the most comprehensive and rich domestic mutual funds data to evaluate performance persistence of mutual funds raised in Taiwan and invested in domestic stocks. With transition probability matrix for estimation funds performance ranks in contingency tables, the paper provides more information than earlier studies using dichotomy, regression analysis or grades to serve as reference for investment decision making.
In addition to the foreword, the paper includes literature discussions and study methods in the second part, sample data and funds performance evaluation in the third part, empirical results of funds performance ranks stability in the fourth part, sub-sample test and performance of liquidated or merged funds in the fifth part and conclusions and suggestions in the sixth part.

2. LITERATURE REVIEW AND STUDY METHODS

2.1 Measurement of funds performance

Treynor (1965) adopted the idea of Security Market Line (SML) to propose the mutual funds model. The performance model is the index value of funds return after deduction risk free interest rate in excess return to be divided by unit system risk:
Treynor Indices (1)
Is the value from the market model?
Treynor index represents how many units of excess return a single unit system risk can have. Greater value means better performance of mutual funds allocation. Treynor (1965) made ranks of mutual funds through Treynor index and examined the performance was persistent with Spearman index. Carlson (1970) studied 57 mutual funds in the U.S. with not only Sharpe index but also Treynor index to evaluate funds performance. The conclusion also showed lack of performance persistency in funds market.

Sharpe (1966) developed the performance evaluation model based on Capital Market Line (CML). Different from Treynor, Sharpe believed mere consideration of system risk failed to include all risk. Impacts of total risks on performance must be taken into consideration. Estimation of Sharpe index is:

(2)is the average return; is the return variable; is average risk free return.
Sharpe index evaluation refers to the return of each unit total risk. Greater value means better performance. Sharpe (1966) studied 34 open mutual funds between 1944 and 1963 in the U.S. and made ranks with Sharpe index. Test was made through Spearman order correlation and the results showed funds in the two cycles were not in significant positive correlation. Carlson (1970) studied 57 funds in the U.S. by using Sharpe index and Treynor index. The conclusion showed lack of performance persistency in funds market.

Jensen (1968) proposed Market Model of absolute performance evaluation index to evaluate whether funds had abnormal return. The abnormal return means performance higher orlower the performance of benchmark allocation. Also, Jensen (1968), with this model, evaluated ability of fund managers to predict individual stock prices fluctuation and general pricing level of securities in the future. The measurement model is:

(3)is the return of funds in ; is the risk free return in ; is the return of benchmark allocation in ; is intercept of regression estimation, representing the excess return of the fund; is coefficient of regression estimation, representing the system risk of the fund; regression residual variance. As , fund performance exceeds performance of market benchmark allocation; when , fund performance in inferior to performance of market benchmark allocation. Therefore greater value means better fund performance.

2.2 Funds performance persistence examination

In study of funds performance persistence, some found persistency of mutual funds performance and some found evidence of persistent depended on the period. Grinblatt and Titman (1992) examined mutual funds performance from 1974 to 1987. The results showed funds performance was persistent in the long run.
Goetzmann and Ibbotson (1994) used Jensen index and regression to eamine whether funds performance was persistent. Empirical results showed, in most periods, performance was statisticcally remarkable. In absolute return and Jensen index and winner/loser performance persistent, the results showed winners in this period are 60% likely to be winners again in the next period. For funds performance persistence, funds with good performance in the past were persistent. Those with poor performance may continue to perform poorly. The results only could suggest investors avoid funds with poor performance. It still does not greatly help in selecting funds.

Brown and Goetzmann (1995) and Malkiel (1995) all pointed out funds performance persistence was related to sample periods. Most of the empirical results showed more apparent evidence of persistent performance of funds in 1970’s. Performance of funds in 1980’s was not persistent with evidence of reversed performance. Chiu Xianbi and Lin Qinpei (1999) believed better classification would show abilities of fund managers. Reverse of performance might be due to inaccruate classification.
Kahn and Rudd (1995) used regeression to review relation of performance of fixed income and stock funds in earlier and later periods. The results showed bond market had significant persistent. Different classification affects study of funds performance persistence.

Other than dichotomy of winners and losers or regression estimation, test can be made with absolute return or performance indexes in Spearman order correlation. For example, Williamson (1972) studied 180. funds between 1961 and 1970 in the U.S. After grade test, the conclusion supported lack of persistency in fund performance.
In Taiwan, Wu Jinting (1998) used multiple performance indexes and Spearman grade correlation. It was found not all domestic funds performance was persistent. Wong Shihuei (2002) found funds performance persistence was related to performance period. In annual performance, funds performance was not persistent. Xu Qinjun and Jiang Zhijiang (1993) used data from 1998 to 2002 to estimate persistency of different funds through Spearman rank rank-order correlation. The empirical results showed not each period had persistency. More classified funds had more significant performance persistency.

Chen Anlin, Hong Jialing and Lee Wenzhi (2001) also used Spearman order correlation to estimate persistency of performance ranks of 64 funds prior to 1999. The results show funds performance in persistency. Lin Xiuwei and Wang Jiazhen (2003) studied 248 domestic funds from 1994 to 2001 through traditional Spearman order correlation to estimate funds performance persistence under different indexes. The empirical results showed relevant performance indexes were not stabily persistent. Indexed related to CPAM beta were mmore persistent in teh long run.
Neither Sharpe (1966), Jensen (1968), Carlson (1970) and Williamson (1972) aborad nor domestic studies with Spearman order correlation failed to provide sufficient information. The dichotomy of winners and losers offer basic persistence probability to investors . However, such diviiosn of winners and losers fail to meet needs of investors. Although both Spearman order correlation and dichoromy can be used to examine whether funds performance is persistent, they provide too little information of funds performance persistence. The research seeks a bettter methods than the two in simplicity and direct perception to provide investors with more information on persistency of funds performance.

In Contingency Table by Carhart (1997), ranks of funds performance was divided into ten divisions. The author estimated year-by-year rank division transition probability matrix. Fig. II is transition probability matrix by Carhart. The method included more information than dichotomy and enabled iinvestors to have a better view of funds performance persistence. Carhart only estimatd funds with best and worst performance in investment allocation to see if they had excess return. Statistics test was not made on transition probability to see if rank division was random in past years.

Earlier studies on domestic funds performance often had insuffient samples. Survivorship bias was often ignored in funds performance persistence studies. This study is the first one to take liquidation or merge of domestic mutual funds into consideration. Therefore, there is no survivorship bias issue in measurement of funds performance persistence.

2.3 Markov Chain Transition Probability statistics test

The greatest benefit of dichotomy to evaluate funds performance is simplicity. It is relevantly simple in null hypothesis test. Use of more than two divisions in transition probability to evaluate funds performance persistence requires joint test of persistency of funds performance. Markov Chain by Anderson and Goodman (1957) can have statistics test of transition probability matrix of funds performance ranks to examine whether transference of ranks obeys random or annual ranks are non-random but persistent. Simple introduction to Markov Chain transition probability matrix is as follows. See Appendix I for inference of transition probability.
Presuming relevant performance of same type funds is random and obeys interrupted uniform distribution, in N funds, we divide into m grades of performance from large to small funds. For example, we divided funds performance ranks into 10 grades. The 1st grade includes funds in the first 10%; the 2nd grade covers funds ranked between the first 11% and 20%. The 10th grade contains funds ranked between 91% and 100%.

Based on annual funds performance, we gave grades. Annual funds performance grade transference matrix had states. If time has funds, any random and year maximum number of funds is . Presuming is fund in state; in , it belongs to state, under , random variable obeys asymptotically normal distribution and expected value is 0; variable is . Under funds performance state and specific , to provide null hypothesis , one must have:

(4)to obey incremental Chi-square distribution.
Freedom is . To test all ( ), one can sum up all . The results will obey freedom Chi-square distribution .

2.4 Probability test of likelihood ratio

Other than Markov process transition probability test, Kupiec (1995) presumed events in binominal distribution. Provided null hypothesis is event occurrence ratio = , through Likelihood Ratio (LR), one can examine whether occurrence ratio of events equals to null hypothesis. Measurement of LR is as follows:

(5)and statistics obeys liberty 1 Chi-square distribution. The advantage of likelihood ratio test is direct test on occurrence ration. Provided ranks of funds performance is random, likelihood ratio tests whether transition probability occurrence ration is the same as random null hypothesis to verify whether absolute ranks of funds performance is random.

3. SAMPLE DATA AND FUNDS PERFORMANCE EVALUATION

3.1 Sample source

The source in this research is mutual funds database of Taiwan Economic Journal (TEJ) covering 1990 to 2006. The researcher selected two types of funds--“raised in Taiwan and invested in domestic stocks” and “raised abroad and invested in domestic stocks” investing four targets small stocks, tech stocks, stocks and stocks/bonds. Table 1 lists overview of funds raised in Taiwan and investment target in past years. This research aims at 315 funds from the sample data.
Funds performance index is evaluated with net values on trading days of the year. If new funds were raised in January, they are included in our funds performance ranks. Those raised after January are included in the next year performance. Funds liquidated or merged in December are included in the performance ranks of the year. Those prior to December are not included in ranks and evaluation of the year. There are 315 funds between 1990 and 2006 meeting the sorting principle.
The risk free return is based on agent variable of risk free interest rate of one-year time deposit interest rate on the website of Central Bank of Republic of China (Taiwan). The Benchmark Index is weighted stock price index by Taiwan Stock Exchange.

3.2 Funds performance estimation

From simulation study of funds performance evaluation, Chiu Xianbi (1994) found Sharpe, Treynor, Jensen indexes and fund return before risk adjustment did not have significant difference in accuracy of distinguishing profitability of funds. The most widely used Sharpe, Treynor, and Jensen relevant performance indexes are also used in this study. Daily net values and dividends from TEJ are used to estimate daily return of funds in continuous time. The daily return is:

(6)is net value in t period.

is cash dividend issued in t period.
Treynor index, Sharpe index and Jensen index for measurement of relevant performance of funds are in formulas (1), (2) and (3):

3.3 Measurement of survivorship bias

Few domestic empirical studies of funds performance measured survivorship bias. To accurately measure whether funds performance is persistent, probability of fund liquidation or merge is considered. In the 315 funds, 74 were liquidated or merged during the sample period. To measure survivorship bias or probability of liquidation or merge, there a total 2,017 pieces of effective samples in the 315 funds between 1990 and 2006. Probability of funds to be liquidated or merged each year is 3.67%.

3.4 Statistics test and null hypothesis

For funds performance transition matrix, other than annual funds performance rank transition probability matrix, the research also includes new funds and liquidated or merged funds each year into transition probability matrix estimation. That is, funds raised this year are listed in the previous year as new funds. Those existing in the previous year but liquidated or merged this year are listed in liquidation division this year. Null hypothesis is set as funds performance obedience random. Fund ranks are not necessarily affected by ranks in previous year. In consideration of survivorship bias and presumption of funds performance rank obeying random, likelihood ratio test by Kupiec (1995) is null hypothesis as:

means probability of funds being liquidated or merged each year; is number of divisions of funds performance ranks. In ranks under two divisions, provided probability of liquadatoin or merge in the past , the likelihood ratio test null hypothesis is Pij=48.18%. In Markov Chain transition probability joint test, performance of funds in division in the previous year have the same probability of falling into each division in the next year. Probability of liquidation or merge ratio is . That is, null hypothesis is:

4. FUNDS PERFORMANCE RAND STABILITY EMPIRICAL RESULTS

4.1Performance persistent of two divisions

Goetzman and Ibbotson (1994), Brown and Boetzman (1995) and Malkiel (1995) used winner and loser dichotomy, which is also used here. See estimated winner and loser transition probability matrix in Table 2 and likelihood ratio test. Table 3 lists transition probability joint test of whether ranks of funds performance in the previous year obey random in the next year.
S1 refers to funds ranked 0～50% in the previous year; S2 shows funds ranked in the 2nd 50% in the previous year. From Table 2, one can see both absolute return and Sharpe, Jensen and Treynor indexes refuse transition probability as random null hypothesis . In the 4th column, funds ranked in the first 50% are less likely to be liquidated or merged than the historical average. The probability of their refusal to be liquidated or merged is the same at 3.46% of historical average in liquidation or merge. Those in the 2nd 50% are more likely to be liquidated or merged than historical average. The refusal to be liquidated or merged is also 3.46%.
Table 3 offers joint test of Markov Chain transition probability. Through test of transition probability matrix, no matter what the state of funds performance was in the previous year, all states refused transition probability equal null hypothesis, meaning transition of funds performance in the previous and next years is not random. Test of transition probability matrix where all probabilities are equal also refuses null hypothesis.

4.2 Performance persistence of ten divisions

Probability estimation and test in two divisions tell whether funds performance is persistent. The information is too simple. Carhart (1997) used funds performance Contingency Table. He divided absolute performance ranks of funds into ten divisions in the unit of one year to estimate funds abosulte performance rank transition probability. Through transition possibility table, one can better grab funds performance transition probability. With transition probability in contingency table of Carhart (1997), the research estimates funds performance index rank transition probability. With Markov Chain by Anderson and Goodman (1957), the paper tests transition probability, including the process of funds performance being random anmd not persistent and funds performancetransition probability in stationary Markov Chain.

With rank division method by Carhart (1997), funds performance is ranked from top to bottom in 10 divisions. Funds with performance in the first 10% are in the 1st division; those in the first 10%~20% are in the 2nd division. Those in the last 10% are in the 10th division. To begin, if funds performance is in random effect, it is not persistent. Each transition probability in transition probability matrix is equal. Providing is transition probability of division in the previous year and this year, after giving previsous year performance , Markov Chain joint test null hypothesis is 且 and Kupiec (1995) likelihood ratio test is .
Table 4 lists test results of transition probability matrix and likelihood ratio of the ten performance rank division in absolute return and Sharpe, Jensen and Treynor relevant performance indexes. The first colmn S1 to S10 refer to funds performance with ten quantile in the first to tenth divisions in the previous year. R1 to R10 in teh first row mean funds performance in the next year in ten quantile in the first to tenth divisions. Table 5 is joint test results of Markov Chaintransition probability matrix.

In Table 4 a. Absolute Performance, Funds S1 ~ S3 in teh first 30% in the previous year have transition probability to be still in the first 30% the next year. Likelihood ratio in S3 to R1 test refuse random null hypothesis. No matter in any area between S1 and R3 of the performance in the previous year, probability of funds performance the next year in the last division R10 refuses null hypothesis. This means, in absolute performance index, funds ranked in the first 30% in the previous year have lower probability to be inthe last division than random probability. In Table 4 a. Absolute Performance, funds in S10 are very likely to be in the last division R10 the next year, significantly refusing performance as random null hypothesis. In absolute return performance, although funds with good performance do not have significant persistency, funds with poor performance are very likely to keep the poor performance the next year.

In Table 4 b. Sharpe Index, funds with either good or poor performance have a lot of evidence of persistency. Funds with good performance have greater probability than random hypothesis to keep good performance, especially those with Sharpe index ranked in the first 10% in S1 division. They have as high as 16.8% probability to be in R1 the next year and 15.2% of S2 into R2. Funds with good performance in the previous year have lower probability than random hypothesis to be in the second half divisions. Example: funds in S1~S3 in the previous year have around 5.5% probability to be in the last 10% of R10 the next year. This is lower than random null hypothesis Pij = 9.645%. Table 4 c. Jensen Index and d. Treynor Index have similar performance as Sharpe index does. Funds with good performance in the previous year still have good performance the next year. Probability from S1 to R1 is over 15%. That from S1 to S2 to R10 is below or around 6%. Funds with poor performance as in S10 have probability as high as over 17% to be in the last 10% of R10 division the next year.
Brown and Goetzmann (1995) pointed out funds with poor performance were more likely to be terminated. Similar results are found in this resonance. In either absolute performance or relevant performance index, most of funds in S1～S3 refuse liquidation or merge equaling to historical average; those in S9～S10 are over 8% likely to be liquidated or merged the next year. Probability of refusal to be liquidated or merge equals to historical average.
Table 5 is the joint test of the 10 divisions. In the joint test of performance obedience random the next year, funds ranked in the first 10% only have Sharpe, Jensen and Treynor indexes significantly refusing random null hypothesis the next year. Absolute return performance fails to refuse transition probability non-random. Absolute return performance persistency is not distinctive. Funds with poor performance such as in the last 20% of S9～S10 refuse funds performance as random null hypothesis the next year. This means they are more likely to keep bad performance.

4.3 Classification sub-sample performance persistency

To understand whether nature of funds lead to different results, funds are divided into four sub-samples based on the investment target to reevaluate persistency of funds performance. The sub-samples are tech stocks, small stocks, stocks, and stocks + bonds. Tech stocks have 41 funds including 264 samples; small stocks and stocks have 260 stocks including 1,592 samples; stocks + bonds have 87 funds including 339 samples.
Tech stocks and small stocks do not cover many samples. With too many rank divisions in the sub-sample ttransition probability matrix, transition probability will have poor estimation representation and test performance of statistics is not high. As a result, only 3 divisions are used . S1~S3 means fund ranked in the first to third group in the previous year; R1~R3 refer to funds ranked in the first to third divisions the next year. The empirical results of tech stocks and small stocks in Table 5 show absolute performance transition probability matrix do not have distinctive transition probability different from random. On the contrary, new funds in small stocks had good performance in the first year. In absolute return, new funds are 51.9% likely to be in the first 1/3 ranks. Sharpe, Jensen and Treynor indexes show similar results. In either absolute performance or relevant performance indexes, the probability of funds in the first 1/3 of S1 division in the previous year to be in the first 1/3 of R1 division is not higher than random probability.

Empirical results of stocks sub-samples in Table 6 show absolute return performance is similar to Sharpe, Jensen and Treynor indexes. The four performance indexes have quite high persistency evidence. In absolute performance, funds in S1 in the previous year have 39.7% probability to be in the first 1/3 of R1 the next year and 21.8% probability to be in the last 1/3 rank. The two reach distinctive refusal probability of null hypothesis in statistics. This proves stocks funds with good performance have high persistency. In absolute performance, funds ranked in the last 1/3 in the previous year have only 22.1% probability to be in the first 1/3 rank the next year. They have 41.9% probability to be in the last 1/3 rank the next year. This shows stocks funds with poor performance in the previous year still tend to do poorly the next year.
In Table 6 of stock + bonds funds do not show evidence of persistence in absolute return. The threerelevant performance indexes do have high persistence. What is worth attention is funds of the four indexes ranked the last 1/3 of S3 in the previous year have probability of as high as 10% to be liquidated or merged than the historical average 3.46%.

Table 7 lists joint test of sub-samples empirical transition probability. Except for small stocks funds, the rest three sub-samples performance ranked in S1 or S3 mostly refuse randomnull hypothesis the next year. Funds with better performance in the previous year have grezter probability to perfrom well under good ranks. Those with poor performance under bad ranks have greater probability of liquidation or merge than thehistorical average. The probability of being in the poor ranks is higher than random hypothesis.

5. PERFORMANCE OF LIQUIDATED OR MERGED FUNDS

In the 229 fund samples in the study, 85 were liquidated or merged between 1990 and 2006. No estimation was available in earlier studies on performance of liquidated or merged funds. Scale and history of mutual funds in Taiwan already suffice statistics of liquidated or merged funds. The research made statistics of absolute return performance rank percentage of these 85 funds of the two years prior to liquidation or merge, or then rank of these funds in tow years, the previous year and the year of liquidation or merge with other funds. Table 8 shows average performance of these funds are in 65% of total fund market, which means 65% of the total funds over-performed the liquidated funds. Both liquidated or merged funds were defeated by over 70% of funds prior to liquidation or merge. Liquidated funds were defeated by 77.1% of funds in average; merged funds were beaten by 74.4% of funds in average.
In Table 8, merging funds had performance rank of 53% and 61.4% in the two years prior to and previous of the merge year in overall market. In the year of merging other funds, their average performance ranked at 57.9% of overall market. After merging other funds, these funds had performance rank at 54.3% and 52.6% in the 1st and 2nd year after merge. From such data, one can learn these merging funds had around the same performance of the overall market average. After merging other funds, the performance significantly improved or declined.

6. CONCLUSIONS AND SUGGESTIONS

This paper aims at funds raised in Taiwan and invested in domestic stocks between 1990 and 2006. Through Markov Transition Probability matrix, statistics is made to see if funds performance were persistent in the 17 years. To better estimate funds performance persistency, the research for the first time takes survivorship bias into domestic funds performance persistence consideration to reduce survivorship bias and more faithfully estimate funds performance ranks persistency.
Empirical results show that, in absolute return performance, persistence is lower. Sharpe, Jensen and Treynor relevant performance indexes have more distinctive persistence. Funds with good performance in the previous year had lower probability than historical average of liquidation or merge; on the contrary, those with poor performance will have greater probability than historical average of liquidation or merge.
In empirical results of tech stocks, small stocks, stocks and stock + bond funds, small stocks funds have less performance persistency. Stocks and stock + bond funds have more distinctive performance persistency. For stock + bond funds, if they performed poorly in the previous year, they had very high probability of liquidation or merge.
Statistics were made on performance of liquidated or merged companies prior to liquidation or merge. The performance was mostly below the average in the previous year or two years ahead. The performance in the year of liquidation or merge is below 70% of market rank. This means liquidated or merged funds were mostly those with poor performance. Before and after merging other funds, merging funds did not have great changes in performance.
In light of past performance of funds, performance did have certain persistency evidence, although it still fails to serve as the final single criterion for fund investment. What is clear is investors shall avoid funds with bottom performance in the same type, as they may continue perform poorly and have high probability of being liquidated or merged.

APPENDIX I: PERFORMANCE RANK MARKOV PROCESS

To give grades of each fund performance, each funds performance grade transition matrix has state. If in time there are funds, any and maximum number of funds is . Provided is fund at in state to in state, under of number of funds in state. When Individual funds is at time 0,1,…, is in states , ,…, . Given initial state , its performance rank state joint probability is:
(Annex 1)
Presuming transition probability is stationary, when ( ) means number of observation of in state and in state, will have a total of observation value; when is fund transition state after , ,…, number,
(Annex 2)
It is the sum of state and state. In dimension space, to describe all funds in initial state, funds transition state joint probability is:
(Annex3)
Statistics quantity of is in the preceding formula. According to Anderson and Goodman (1957), providing actual distribution is (Annex1) to be multiplied by a factorial function. Under the conditions of , , conditional probability distribution is:
(Annex4)
In which

This distribution will be the same. Providing number of observation is probability multi normal distribution and number of observation is and in conditional probability distribution:
(Annex5)
If Markov Chain transition probability is stationary transition probability, formula (Annex 1) can rewrite sufficient statistics. Therefore, if

Annex 3 can be rewritten as
(Annex6)
When transition probability is not required to be stationary, is the minimum assembly of sufficient statistics.
Stationary transition probability can be estimated with formula (9) maximum likelihood. Under probability axiom limit, all and
(Annex7)
Supposing transition probability distinctively has the same form and does inter-depend on state ( ), in sample, and, under probability, there is consistent multinomial trials distribution. Under such a sample, maximum likelihood estimate leads to:
(Annex8)
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Table 1: Mutual Funds Raised in Taiwan between 1990 and 2006 and Investment Target Classification
Investment target Raised and invested in Taiwan Raised in Taiwan and invested in domestic and foreign target Raised outside Taiwan and invested in Taiwan Total
Small stocks 29 1 30
Real property securitization 8 8
Real estate 8 1 9
Stocks 164 67 4 235
Stocks + bond 85 25 110
Principle guarantee 11 2 13
Index stocks 6 1 1 8
Tech stocks 41 10 51
Energy stocks 2 2
Funds 8 74 82
Currency 2 2 4
Bones 93 28 121
Asset securitization 5 5
Total 447 226 5 678
Remark: Data of fund raising and investment target are from TEJ database.
Table 2: Funds Performance Transition Probability Matrix in Two Divisions
1990~2006 ( R1 ) ( R2 ) ( C )
a. absolute return
( S1 ) 52.7*** 44.6** 2.67
( S2 ) 45.3* 48.8 5.98***
(New) 44.6 55.4** 0***
b. Sharpe index
( S1 ) 56.8*** 40.9*** 2.32**
( S2 ) 42.4*** 51.2* 6.33***
(New) 40.9** 59.1*** 0***
Jensen index
( S1 ) 53*** 44.5** 2.56*
( S2 ) 45* 48.9 6.1***
(New) 44.6 55.4** 0***
Treynor index
( S1 ) 56.4*** 41.2*** 2.32**
( S2 ) 42.6*** 51.1* 6.33***
(New) 41.6** 58.4*** 0***
Remark: Unit is %. Symbols *, ** and *** refer to refusal of the transition probability as (1-Pc)/2 null hypothesis at 10%, 5% and 1% significance levels in likelihood ratio test. Pc is past average of liquidation or merge. New means funds not raised in the previous year; C refers to next funds liquidated or merged. Statistics sample period is from 1990 to 2006.
Table 3: Joint Test of Whether Dichotomy Funds Performance Transition Probabilities Equal
Null hypothesis Absolute return Sharpe index Jensen index Treynor index
P(S1,R1)=P(S1,R2) 8.3*** 27*** 9.5*** 25.1***
P(S2,R1)=P(S2,R2) 14*** 23.9*** 15.5*** 23.6***
P(New,R1)=P(New,R2) 15.3*** 21.9*** 15.3*** 20.5***
All probabilities equal.等 37.6*** 72.9*** 40.3*** 69.1***
Remark:1. P (S1, R1) is the probability of being winners this and previous year; P (S1, R2) refers to probability of being the winners in the previous year and losers this year;; P (S2, R2) shows probability of being losers in the two years in a row; P (S2, R1) is the probability of being losers in the previous year and winners this year. 2 The last column null hypothesis refers to all transition matrix transition probabilities being equal. 。


Table 4: Funds Performance Transition Probability Matrix in Ten Divisions
1990~2006 ( R1 ) ( R2 ) ( R3 ) ( R4 ) ( R5 ) ( R6 ) ( R7 ) ( R8 ) ( R9 ) ( R10 ) ( C )
a. absolute return
( S1 ) 12.8 8.94 13.4 7.26 13.4 10.1 8.38 8.38 10.6 5.59** 1.12**
( S2 ) 8.19 13.5 11.1 7.6 8.77 12.3 11.7 7.02 12.9 5.26** 1.75
( S3 ) 14.5** 9.83 9.25 9.25 8.67 7.51 15** 12.1 7.51 5.2** 1.16**
( S4 ) 10.6 13.5 10.6 8.82 14.1* 6.47 11.8 7.06 5.88* 8.24 2.94
( S5 ) 8.93 11.9 10.7 10.7 7.14 7.14 8.93 11.9 8.33 7.74 6.55*
( S6 ) 9.25 12.7 9.83 9.83 9.25 6.36 13.3 8.67 11.6 5.78* 3.47
( S7 ) 9.83 7.51 12.1 7.51 9.25 11.6 8.09 15** 7.51 6.94 4.62
( S8 ) 11.8 4.71** 6.47 11.8 9.41 14.7** 8.24 9.41 11.2 6.47 5.88
( S9 ) 8.62 8.05 9.77 13.8* 8.05 9.2 12.1 8.05 4.02*** 10.9 7.47**
( S10 ) 5.52* 6.13 8.59 8.59 7.36 12.9 4.91** 7.36 11.7 18.4*** 8.59***
(New) 9.57 9.24 6.93* 9.9 8.91 9.24 6.6* 9.9 13.5** 16.2*** 0***
b. Sharpe index
( S1 ) 16.8*** 11.2 10.6 10.6 9.5 7.82 10.6 8.94 8.38 5.03** 0.56***
( S2 ) 9.94 15.2** 11.1 9.36 10.5 8.77 10.5 11.7 6.43 5.26** 1.17**
( S3 ) 10.4 10.4 10.4 8.09 13.3 12.7 11.6 9.83 4.05*** 6.94 2.31
( S4 ) 16.5*** 10.6 11.2 11.8 10 8.82 8.24 5.88* 5.88* 5.88* 5.29
( S5 ) 7.74 10.1 15.5** 14.9** 8.33 7.14 5.95* 11.9 9.52 6.55 2.38
( S6 ) 9.83 9.25 7.51 12.1 10.4 8.09 8.09 9.25 15** 6.94 3.47
( S7 ) 7.51 5.78* 8.09 8.67 9.83 12.7 13.9* 11 13.3 4.62** 4.62
( S8 ) 5.88* 10 10.6 11.8 10.6 12.4 8.82 10.6 7.06 6.47 5.88
( S9 ) 8.05 8.62 12.1 5.75* 8.62 9.77 12.6 8.05 6.32 11.5 8.62***
( S10 ) 6.75 4.91** 7.36 5.52* 6.13 9.2 8.59 7.36 16.6*** 18.4*** 9.2***
(New) 9.9 9.57 5.61** 7.92 7.92 9.57 8.58 10.2 12.9* 17.8*** 0***


Table 4 (continued)
1990~2006 ( R1 ) ( R2 ) ( R3 ) ( R4 ) ( R5 ) ( R6 ) ( R7 ) ( R8 ) ( R9 ) ( R10 ) ( C )
c. Jensen index
( S1 ) 15.1** 12.3 14* 7.26 9.5 12.3 7.26 8.94 6.7 6.15* 0.56***
( S2 ) 9.94 13.5 11.1 9.94 8.19 9.36 6.43 14.6** 10.5 4.68** 1.75
( S3 ) 12.1 8.67 11 7.51 10.4 7.51 13.9* 12.1 9.25 6.36 1.16**
( S4 ) 12.9 9.41 10.6 11.2 9.41 8.24 7.06 8.24 8.82 10.6 3.53
( S5 ) 10.1 7.74 11.9 13.7* 7.14 8.33 7.74 8.33 10.1 8.93 5.95
( S6 ) 8.67 12.1 9.25 11 10.4 8.67 7.51 9.25 10.4 9.83 2.89
( S7 ) 9.83 9.25 7.51 9.83 10.4 10.4 10.4 12.1 10.4 4.05*** 5.78
( S8 ) 9.41 8.82 8.82 10.6 9.41 14.7** 12.4 8.82 7.65 6.47 2.94
( S9 ) 6.32 10.9 7.47 8.62 9.77 11.5 10.9 8.05 4.6** 12.6 9.2***
( S10 ) 5.52* 5.52* 8.59 8.59 7.98 9.2 10.4 5.52* 11 17.8*** 9.82***
(New) 9.57 8.25 7.92 8.25 10.6 7.92 11.6 9.24 14.5*** 12.2 0***
d. Treynor index
( S1 ) 16.2*** 12.8 12.8 8.94 10.6 7.82 10.6 7.82 6.7 4.47*** 1.12**
( S2 ) 9.36 12.3 11.1 12.3 8.19 9.94 9.36 13.5 7.02 5.26** 1.75
( S3 ) 13.3 10.4 8.67 8.67 13.3 9.25 11 11 5.78* 6.94 1.73
( S4 ) 12.9 10 14.7** 10 8.24 12.9 8.24 6.47 5.29** 6.47 4.71
( S5 ) 9.52 11.9 11.9 13.7* 10.1 10.1 7.14 9.52 7.14 6.55 2.38
( S6 ) 8.09 8.67 12.7 9.25 12.1 8.09 5.2** 11.6 16.2*** 5.2** 2.89
( S7 ) 8.09 5.78* 7.51 9.25 10.4 13.3 13.3 11.6 11 5.78* 4.05
( S8 ) 4.71** 8.82 8.82 13.5 8.24 13.5 11.8 8.24 7.06 8.24 7.06**
( S9 ) 6.32 9.77 6.9 8.05 9.77 9.77 12.1 8.62 8.05 11.5 9.2***
( S10 ) 9.2 4.91** 9.2 7.36 4.91** 6.13 8.59 5.52* 17.8*** 17.8*** 8.59***
(New) 10.9 9.9 5.61** 6.6* 8.58 7.59 9.57 10.6 13.2** 17.5*** 0***
Remark: S1 through S10 refer to funds performance ranked to the 1st and 10th divisions in ten decimal; S1 has the best performance while S10 has the poorest performance. R1 through R10 refer to the first ten divisions of fund performance this year in. R1 has the best performance; R10 has the worst performance. New means funds not raised in the previous year; C means funds liquidated or merged the next year. Statistics sample period is from 1990 to 2006. Unit is %. Symbols *, ** and *** refer to refusal of the transition probability as (1-Pc)/10 null hypothesis at 10%, 5% and 1% significance levels in likelihood ratio test. Pc is past average of liquidation or merge.

Table 5 Joint Test of Whether Dichotomy Funds Performance Transition Probabilities Matrixes
Equal in the Ten Divisions
States absolute return Sharpe index Jensen index Treynor index
( S1 ) 15.4 20.1** 22.4** 23.3**
( S2 ) 14.4 15.2 15.8 12.2
( S3 ) 18.9* 13.3 12.6 11.7
( S4 ) 13.5 18.8* 4.7 16.5
( S5 ) 9.3 18.5* 9.2 9.3
( S6 ) 9.6 9.5 3.2 19.6**
( S7 ) 11.6 16.7 10.1 12.6
( S8 ) 17* 10.4 9.1 18.2*
( S9 ) 18.6* 20.9** 25.4*** 20.6**
( S10 ) 37.1*** 46.8*** 37.9*** 46.9***
( New ) 34.8*** 42.9*** 25.3*** 45***
(All) 200.2*** 233.2*** 175.7*** 235.8***
Remark: S1 through S10 refer to funds performance ranked to the 1st and 10th divisions in ten decimal in the previous year. S1 has the best performance; S10 has the worst performance. The last column (All) shows whether all transition probabilities are equal. Symbols *, ** and *** refer to refusal of the joint test transition probability of null hypothesis of Pij, j=1,2,…10 all equaling under previous states (S1~S10) at 10%, 5% and 1% significance levels in likelihood ratio test. Pc is past average of liquidation or merge. (All) means joint test in which probabilities in transition probability matrix equaling to (1-Pc)/10.


Table 6 Performance Transition Probability Matrix of Sub-samples
1990~2006 ( R1 ) ( R2 ) ( R3 ) ( C ) ( R1 ) ( R2 ) ( R3 ) ( C )
a. tech stocks b. small stocks
1.absolute return
( S1 ) 39.7 38.5 21.8* 0*** 36.7 34.7 26.5 2.04
( S2 ) 36 34.7 28 1.33 29.5 36.4 27.3 6.82
( S3 ) 25.4 26.8 42.3* 5.63 26.8 29.3 39 4.88
(New) 35 30 35 0** 51.9** 22.2 25.9 0
2.Sharpe index
( S1 ) 41* 39.7 19.2** 0*** 40.8 26.5 30.6 2.04
( S2 ) 34.7 38.7 26.7 0*** 27.3 36.4 29.5 6.82
( S3 ) 23.9 22.5* 46.5*** 7.04 26.8 36.6 31.7 4.88
(New) 37.5 27.5 35 0** 48.1* 25.9 25.9 0
3.Jensen index
( S1 ) 41* 37.2 20.5** 1.28* 36.7 30.6 30.6 2.04
( S2 ) 32 40 28 0*** 31.8 38.6 22.7 6.82
( S3 ) 25.4 23.9 45.1** 5.63 26.8 29.3 39 4.88
(New) 40 27.5 32.5 0** 48.1* 25.9 25.9 0
4.Treynor index
( S1 ) 44.9** 34.6 20.5** 0*** 36.7 32.7 28.6 2.04
( S2 ) 28 41.3* 30.7 0*** 31.8 34.1 27.3 6.82
( S3 ) 25.4 26.8 40.8 7.04 26.8 31.7 36.6 4.88
(New) 40 25 35 0** 48.1* 25.9 25.9 0
c. stocks d. stocks + bonds
1.absolute return
( S1 ) 39.7*** 32.5 25.8*** 1.97*** 39.8 30.1 25.8 4.3
( S2 ) 32.7 31 31.6 4.65 28.6 36.9 31 3.57
( S3 ) 29.6 30.7 32.3 7.4** 40 22.5* 25 12.5***
(New) 22.9*** 35.2 41.9*** 0*** 26.8 34.1 39 0***
2.Sharpe index
( S1 ) 39.5*** 36.5** 22.3*** 1.75*** 46.2*** 32.3 18.3*** 3.23
( S2 ) 33.4 29.6 32.7 4.2 33.3 32.1 29.8 4.76
( S3 ) 28.7 30.5 32.7 8.07*** 27.5 32.5 27.5 12.5***
(New) 23.7*** 30.5 45.8*** 0*** 26.8 26.8 46.3*** 0***
3.Jensen index
( S1 ) 39.7*** 32.3 26.4** 1.53*** 45.2*** 26.9 23.7* 4.3
( S2 ) 32.7 29.4 33 4.87 28.6 35.7 32.1 3.57
( S3 ) 28.5 32.1 31.8 7.62*** 33.8 31.2 22.5* 12.5***
(New) 25** 36 39** 0*** 26.8 30.5 42.7** 0***
4.Treynor index
( S1 ) 40*** 33.6 24.5*** 1.97*** 48.4*** 26.9 21.5** 3.23
( S2 ) 32.5 32.3 31 4.2 31 38.1 23.8 7.14
( S3 ) 28.3 31.6 32.3 7.85*** 26.2 32.5 31.2 10*
(New) 25.4** 28.8 45.8*** 0*** 28 26.8 45.1** 0***
Remark:1. S1 through S3 refer to divisions 1 to 3 in the 3 decimal of performance rank in the previous year. S1 has the best performance; S3 has the worst performance. R1 through R3 refer to divisions 1 to 3 in the 3 decimal of performance rank this year. R1 has the best performance; R3 has the worst performance. New funds not raised in the previous year; C means funds liquidated or merged the next year. Units are %. Symbols *, ** and *** refer to refusal of the transition probability as (1-Pc)/3 null hypothesis at 10%, 5% and 1% significance levels in likelihood ratio test. Pc is past average of liquidation or merge.
2. Tech stocks include 41 funds. In the sample period, there were 264 samples; small stocks have 29 funds and there were 161 samples in the sample period. Stocks contain 260 funds with 1,592 samples in the sample period. Stocks + bonds cover 87 funds of 339 samples in the sample period.

Table 7 Joint Test of Sub-samples
States absolute return Sharpe index Jensen index Treynor index
a. Tech stocks
( S1 ) 8.8** 11.2*** 7.9** 11.2***
( S2 ) 2.8 5.5 5.5 6.1*
( S3 ) 4.1 8.9** 6.4* 4.1
(New) 2.2 2.7 3 3.5
(All) 17.8** 28.3*** 22.7*** 24.9***
b. Small stocks
( S1 ) 1.7 2.5 1.2 1.3
( S2 ) 1 1 2.2 0.8
( S3 ) 1.1 0.6 1.1 0.6
(New) 5.8 4.1 4.1 4.1
(All) 9.6 8.3 8.6 6.8
c. Stocks
( S1 ) 21.9*** 33.5*** 23.3*** 25.3***
( S2 ) 0.2 1.4 1.1 0.5
( S3 ) 7.6** 12.2*** 9.4** 10.9***
(New) 25.6*** 30.6*** 19.8*** 29.4***
(All) 55.3*** 77.8*** 53.6*** 66.1***
c. Stocks + bonds
( S1 ) 3 11.9*** 7.9** 12.3***
( S2 ) 1.2 0.2 0.9 3.8
( S3 ) 15.2*** 11.1*** 12.5*** 5.5
(New) 6* 10.6*** 7.6** 9.5**
(All) 25.5*** 33.8*** 28.9*** 31.1***
Remark: S1 through S3 refer to divisions 1 to 3 in the 3 decimal of performance rank in the previous year. S1 has the best performance; S3 has the worst performance. (All) examines whether all transition probabilities are equal. Symbols *, ** and *** refer to refusal of the joint test transition probability of null hypothesis of Pij, j=1, 2, 3 all equaling under previous states (S1~S3) at 10%, 5% and 1% significance levels in likelihood ratio test. Pc is past average of liquidation or merge. (All) means joint test in which probabilities in transition probability matrix equaling to (1-Pc)/3.

Table 8 Average Ranks of Liquidated or Merged Funds
Classification Two years prior to liquidation One year before liquidation Liquidation/merge Number Average survival years
Liquidation 65.1% 65.5% 77.1% 33 4.09
Merged funds 61.5% 67.9% 74.4% 52 4.14

Merging funds performance Two years prior to liquidation One year before liquidation Liquidation/merge One year after liquidation Two years after liquidation
53% 61.4% 57.9% 54.3% 52.6%
Remark: As number of funds each year differed, rank is made in by percentage. Lower percentage means higher performance rank.

" Jurnal Reksadana dalam Bhs Indonesia "

KINERJA REKSADANA kegigihan: MENGGUNAKAN MATRIX Transisi Markov PROBABILITAS

Wen-Tao Lee Lee Wen-Tao
Department of Finance, National Sun Yat-sen University Departemen Keuangan, Yat-sen Nasional Universitas Ming
No.70, Lien-Hai RD. No.70,-Hai RD Lien. Kaohsiung City, 80424, Taiwan ROC Kaohsiung City, 80424, Taiwan ROC
capm2000@ms63.hinet.net capm2000@ms63.hinet.net

ABSTRAK

Kami mengeksplorasi kegigihan kinerja reksa dana yang relatif Taiwan menggunakan dan kinerja mutlak Kami menggunakan transisi Markov instan probabilitas korelasi urutan Spearman tradisional atau metode pemenang-pecundang. sampel kami, terutama bebas dari bias keberlangsungan hidup, bahwa kinerja reksa dana tetap, namun, kegigihan paling karena kinerja relatif. Sebuah analisis probit menunjukkan bahwa kenaikan kinerja yang buruk kemungkinan hilangnya.
Kata Kunci: Reksa Dana, Kinerja, Ketekunan, Matriks Probabilitas Transisi


1. PENDAHULUAN


Sejak awal tahun 1986, sekarang ada total mendekati 700 reksadana dibesarkan di Taiwan pada akhir tahun 2006. Pada akhir tahun 2006, 522 reksadana masih bertahan. Karena untuk meningkatkan besar jumlah reksadana di Taiwan, banyak investor tidak dapat memilih dana yang sesuai referensi. Sebagian besar investor mengambil kinerja masa lalu dana sebagai utama. Mulai dari 1996, Investasi dan Konsultasi Efek Asosiasi ROC berkala menerbitkan peringkat dana yang dikeluarkan oleh perusahaan investment trust domestik 1. Banyak perusahaan manajemen kekayaan juga menawarkan kinerja pengembalian reksa dana di masa lalu,. Namun adalah kinerja historis terus-menerus? Jika jawabannya adalah ya, bagaimana kegigihan kuat itu? Dapat investor mengambil kinerja masa lalu sebagai acuan dalam pengambilan keputusan investasi?
Dalam penelitian sebelumnya pada ketekunan kinerja reksa dana, baik asing dan domestik empiris studi mengadopsi dikotomi pemenang dan pecundang atau nilai dari peringkat kinerja historis dalam evaluasi. Kedua metode tidak memberikan bukti apakah kinerja reksa dana yang terus-menerus. Meskipun demikian, dikotomi pemenang dan pecundang gagal untuk menyediakan investor dengan informasi yang memadai. Koefisien peringkat sejarah menunjukkan hubungan antara masa lalu dan kinerja reksa dana saat ini. Investor masih tidak dapat membuat keputusan investasi dengan informasi seperti itu hanya.

Untuk meningkatkan nilai acuan dalam pengambilan keputusan, peneliti memperluas model dikotomi pemenang dan pecundang dengan menambahkan jumlah divisi peringkat kinerja reksa dana. Dengan estimasi Probabilitas Transisi Rantai Markov matriks, penelitian ini menyediakan lebih kaya matriks probabilitas transisi dana kinerja jajaran sehingga investor dapat memiliki gambaran tentang perubahan peringkat kinerja reksa dana di masa lalu. Melalui kerjasama Rantai Markov uji dan uji rasio kemungkinan, penelitian ini menguji apakah transisi probabilitas dari kinerja reksa dana dalam mematuhi lalu acak dan telah mengklarifikasi apakah kinerja reksa dana dalam negeri adalah persisten.

Sebelumnya evaluasi kinerja dana kegigihan di Taiwan kebanyakan bias diabaikan keberlangsungan hidup. Untuk pertama kalinya, penelitian ini mengambil bias keberlangsungan hidup ke dalam pertimbangan, ketekunan membuat pengukuran kinerja reksa dana lebih akurat. Selain itu, penelitian ini membuat statistik kinerja dana sebelum likuidasi, atau penggabungan.
Penelitian ini bertujuan mengangkat 315 reksa dana di Taiwan dan diinvestasikan dalam saham dalam negeri antara 1990 dan 2006. Perkiraan indeks kinerja setiap tahun dilakukan melalui dana harian nilai bersih dan dividen dalam tahun terakhir untuk memverifikasi kinerja indeks beberapa dana bersama persisten. indeks tersebut termasuk kembali mutlak dan tiga indeks yang relevan - indeks Sharpe, indeks Treynor dan indeks Jensen.. empiris menunjukkan hasil yang relevan tiga indeks secara signifikan gigih kembali absolut sementara ketekunan tidak terlalu signifikan Reksa dana dengan kinerja yang lebih miskin lebih mungkin dilikuidasi atau digabung daripada rata-rata historis.

Kontribusi utama penelitian ini adalah penggunaan data negeri reksa dana yang paling kaya dan komprehensif untuk mengevaluasi kegigihan kinerja reksa dana dibesarkan di Taiwan dan diinvestasikan dalam saham domestik. Dengan matriks probabilitas transisi untuk kinerja jajaran estimasi dana dalam tabel kontingensi, kertas menyediakan informasi lebih dari studi sebelumnya dengan menggunakan dikotomi, regresi analisis atau nilai untuk melayani sebagai acuan untuk pengambilan keputusan investasi.
Selain prakata, kertas itu termasuk diskusi sastra dan metode belajar di bagian kedua, data sampel dan evaluasi kinerja dana di bagian ketiga, hasil empiris dana kinerja peringkat stabilitas di bagian keempat, sub-sampel uji dan kinerja dilikuidasi atau digabung dana di bagian kelima dan kesimpulan dan saran di bagian keenam.

2. TINJAUAN LITERATUR DAN STUDI METODE
2,1 Pengukuran dana kinerja

Treynor (1965) mengadopsi ide Keamanan Pasar Line (SML) untuk mengusulkan model reksa dana. Model kinerja adalah nilai indeks dana kembali setelah dikurangi risiko suku bunga bebas dalam kembali kelebihan untuk dibagi oleh sistem risiko unit:
Indeks Treynor

(1) Apakah nilai dari model pasar?
indeks Treynor menggambarkan seberapa banyak unit pengembalian kelebihan sistem unit risiko yang dapat memiliki nilai yang lebih besar. berarti kinerja yang lebih baik alokasi reksa dana indeks. Treynor (1965 dibuat) peringkat reksa dana Treynor melalui dan memeriksa kinerja itu terus-menerus dengan indeks Spearman. Carlson (1970) mempelajari 57 reksa dana di AS dengan indeks Sharpe tidak hanya tetapi juga indeks Treynor untuk mengevaluasi kinerja dana. Kesimpulan ini juga menunjukkan kurangnya persistensi kinerja reksa dana pasar.
Sharpe (1966) mengembangkan model evaluasi kinerja berdasarkan Pasar Modal Line (CML).
Berbeda dengan Treynor, Sharpe percaya hanya pertimbangan risiko sistem gagal untuk memasukkan risiko semua. Dampak dari total risiko pada kinerja harus dipertimbangkan indeks. Estimasi Sharpe dari adalah:

(2) pengembalian rata-rata; return; adalah rata-rata return bebas risiko.
evaluasi indeks Sharpe mengacu pada kembalinya setiap unit total risiko nilai lebih besar. berarti dan performa yang lebih baik. Sharpe (1966) mempelajari reksa dana terbuka 34 di antara 1944 dan 1963 di AS dan dibuat peringkat dengan indeks Sharpe. Test dilakukan agar korelasi Spearman melalui hasil menunjukkan dana dalam dua siklus tidak korelasi positif yang signifikan dalam pasar. Carlson (1970) mempelajari 57 dana di Amerika Serikat dengan menggunakan indeks Sharpe dan Indeks Treynor. Kesimpulan menunjukkan kinerja persistensi kurangnya dana.
The measurement model is: Jensen (1968) mengusulkan Pasar Model indeks evaluasi kinerja mutlak untuk mengevaluasi apakah dana itu abnormal return. The abnormal return yang lebih tinggi berarti kinerja orlower kinerja alokasi benchmark. Selain itu, Jensen (1968), dengan model ini, evaluasi kemampuan fund manager untuk memprediksi fluktuasi harga saham individu dan tingkat harga umum efek di masa depan. Model pengukuran adalah:

(3) kembalinya dana dalam ; pengembalian bebas risiko ; kembalinya alokasi benchmark dalam ; mencegat estimasi regresi, mewakili kembali kelebihan dana tersebut; koefisien estimasi regresi, mewakili sistem risiko dana tersebut. Sebagai Kinerja melebihi dana alokasi benchmark kinerja pasar; ketika , kinerja rendah terhadap kinerja benchmark alokasi pasar. Oleh karena itu lebih besar berarti nilai kinerja dana yang lebih baik.


2,2 pemeriksaan kinerja ketekunan

Dalam studi dana ketekunan kinerja, beberapa persistensi ditemukan kinerja reksa dana dan beberapa bukti yang ditemukan dari terus-menerus bergantung pada periode dan. Grinblatt Titman (1992) meneliti kinerja reksa dana 1974-1987. Hasil penelitian menunjukkan kinerja dana persisten dalam jangka panjang lari.
Empiris Hasil penelitian menunjukkan, kebanyakan, kinerja statisticcally luar biasa. Sebagai imbalannya mutlak dan indeks Jensen dan pemenang / pecundang kinerja terus-menerus, hasil menunjukkan pemenang dalam periode ini adalah 60% kemungkinan untuk menjadi pemenang lagi di periode berikutnya. Untuk dana kinerja ketekunan, dana dengan kinerja yang baik di masa lalu yang terus-menerus. 2 Mereka yang memiliki kinerja yang buruk dapat terus berkinerja buruk kinerja. Hasil hanya bisa menyarankan investor menghindari dana miskin dengan. Ia masih tidak sangat membantu dalam memilih dana. 2

Brown dan Goetzmann (1995) dan Malkiel (1995) semua menunjukkan kinerja kegigihan dana sehubungan dengan periode sampel ini. Sebagian besar empiris hasil yang lebih jelas menunjukkan bukti terus-menerus dari kinerja reksa dana pada tahun 1970 dari itu. Kinerja dana pada tahun 1980 tidak gigih dengan bukti kinerja terbalik Xianbi. Chiu dan Lin Qinpei (1999) percaya klasifikasi yang lebih baik akan menunjukkan kemampuan dari manajer dana. Reverse kinerja mungkin karena inaccruate klasifikasi.
Kahn dan Rudd (1995) regeression digunakan untuk meninjau hubungan kinerja dana pendapatan tetap dan saham dalam dan kemudian periode sebelumnya.. Hasil obligasi menunjukkan pasar yang cukup signifikan telah terus-menerus mempengaruhi studi yang berbeda-beda klasifikasi dana ketekunan kinerja.

Selain dikotomi pemenang dan pecundang atau estimasi regresi, pengujian dapat dilakukan dengan kembali absolut atau kinerja indeks dalam rangka korelasi Spearman. Sebagai contoh, Williamson (1972) mempelajari 180 1970. Dana antara 1961 dan di AS Setelah uji kelas, kesimpulan didukung kurangnya dana persistensi kinerja.
Di Taiwan, Wu Jinting (1998) digunakan beberapa indeks kinerja dan kelas korelasi Spearman. Ternyata tidak semua kinerja dana domestik gigih Shihuei. Wong (2002) menemukan dana kegigihan kinerja sehubungan dengan periode kinerja. Tahunan Dalam kinerja, dana kinerja tidak gigih Qinjun. Xu dan Jiang Zhijiang (1993) 3 data yang digunakan dari tahun 1998 sampai 2002 untuk mengestimasi persistensi dana yang berbeda melalui peringkat-peringkat urutan korelasi Spearman. Hasil empiris menunjukkan setiap periode tidak memiliki persistensi. dana diklasifikasikan Lebih memiliki lebih persistensi kinerja yang signifikan.
Chen Anlin, Hong Jialing dan Lee Wenzhi (2001) juga digunakan agar korelasi Spearman untuk memperkirakan peringkat persistensi kinerja dari 64 dana sebelum tahun 1999. Hasil penelitian menunjukkan kinerja dana dalam persistensi Xiuwei. Lin dan Wang Jiazhen (2003) mempelajari 248 dana dalam negeri dari 1994-2001 melalui korelasi Spearman rangka tradisional untuk menilai kinerja kegigihan dana indeks yang berbeda.. empiris Hasil indeks menunjukkan kinerja yang relevan tidak stabily gigih Indexed terkait dengan beta CPAM adalah mmore terus-menerus dalam jangka panjang.
Baik Sharpe (1966), Jensen (1968), Carlson (1970) dan Williamson (1972) aborad studi domestik maupun dengan korelasi Spearman agar gagal menyediakan informasi yang cukup.. Dikotomi pemenang dan pecundang kegigihan dasar probabilitas menawarkan kepada investor Namun, seperti diviiosn pemenang dan pecundang gagal untuk memenuhi kebutuhan investor. Meskipun kedua Spearman korelasi dan dichoromy agar dapat digunakan untuk memeriksa apakah dana kinerja yang gigih, mereka juga memberikan sedikit informasi dana ketekunan kinerja. Penelitian ini bertujuan metode bettter daripada dua di kesederhanaan dan persepsi langsung untuk menyediakan investor dengan informasi lebih lanjut tentang dana persistensi kinerja.
Dalam Tabel Contingency oleh Carhart (1997), peringkat kinerja dana dibagi menjadi sepuluh divisi. The. Penulis diperkirakan tahun-tahun peringkat pembagian dengan transisi-probabilitas 4. Matriks. Gambar II adalah matriks probabilitas transisi oleh Carhart Metode yang menyertakan informasi lebih dari dikotomi dan memungkinkan iinvestors untuk memiliki pandangan yang lebih baik dana ketekunan kinerja. Carhart hanya estimatd dana dengan kinerja terbaik dan terburuk dalam alokasi investasi untuk melihat apakah mereka telah kembali kelebihan uji. Statistik tidak dilakukan pada probabilitas transisi untuk melihat apakah divisi peringkat adalah acak di tahun terakhir.

Penelitian sebelumnya terhadap kinerja dana dalam negeri sering sampel insuffient. keberlangsungan hidup. prasangka sering diabaikan dalam kinerja ketekunan dana studi penelitian ini adalah yang pertama untuk mengambil likuidasi atau gabungan dari reksa dana dalam negeri menjadi pertimbangan. Oleh karena itu, tidak ada masalah keberlangsungan hidup bias dalam pengukuran kinerja ketekunan dana.

2 2,3 Rantai Markov Probabilitas Transisi statistik uji

Manfaat terbesar dari dikotomi untuk mengevaluasi kinerja dana adalah kesederhanaan.. Hal ini relevan sederhana hipotesis nol dalam ujian Penggunaan lebih dari dua divisi dalam transisi probabilitas untuk mengevaluasi kinerja kegigihan memerlukan dana tes bersama dana persistensi kinerja Rantai. Markov oleh Anderson dan Goodman (1957) dapat memiliki uji statistik matriks transisi probabilitas dana kinerja peringkat untuk memeriksa apakah pemindahan peringkat mematuhi atau tahunan peringkat non-acak acak tapi persisten. Wikipedia pengantar probabilitas transisi Rantai Markov matriks adalah sebagai berikut. Lihat Lampiran I untuk inferensi transisi probabilitas.

Kinerja yang relevan menganggap dana jenis yang sama adalah acak dan mematuhi sela distribusi seragam, dana N, kita membagi menjadi nilai m kinerja dari besar ke kecil dana. Sebagai contoh, kami membagi kinerja jajaran dana menjadi 10 kelas. The kelas 1 st mencakup dana dalam 10% pertama; itu dn grade 2 meliputi dana peringkat antara 11% pertama dan 20%. The grade th 10 berisi dana peringkat antara 91% dan 100%.
Berdasarkan dana tahunan kinerja, kami memberikan grades. Tahunan kinerja dana transferensi kelas matriks telah negara. waktu Jika memiliki dana, setiap acak and dan tahun jumlah maksimum dana . Presuming . Menganggap adalah dana di negara; di , Itu milik state, negara, di bawah , , Variabel acak obeys asymptotically normal distribution and expected value is 0; variable is mematuhi distribusi asimtotik dan nilai yang diharapkan adalah 0; variabel . Di bawah funds performance state dana kinerja negara dan spesifik , , Untuk memberikan hipotesis nol , , Seseorang harus memiliki:

(4) mematuhi distribusi Chi-kuadrat incremental. Kebebasan . . Untuk menguji semua. Kita dapat jumlah semua. Hasil akan mematuhi kebebasan . Chi-square distribusi 5.

2,4 Probabilitas uji rasio kemungkinan

Selain probabilitas transisi proses uji Markov, Kupiec (1995) peristiwa diduga dalam distribusi binomial. Hipotesis nol yang disediakan adalah event rasio Melalui Kemungkinan Ratio (LR), seseorang dapat menguji apakah rasio terjadinya peristiwa sama dengan null hipotesis LR. Pengukuran adalah sebagai berikut:

(5) dan mematuhi statistik kebebasan 1-persegi distribusi Chi. Kelebihan uji rasio kemungkinan adalah tes langsung pada ransum terjadinya dana. Diperoleh peringkat kinerja adalah rasio kecenderungan acak tes, apakah transisi probabilitas terjadinya rasio adalah acak null hipotesis sebagai sama untuk memverifikasi apakah mutlak peringkat kinerja dana adalah acak.

3. 3. SAMPEL DATA DAN EVALUASI KINERJA DANA

3,1 Contoh sumber

Sumber dalam penelitian ini adalah reksa dana database Jurnal Ekonomi Taiwan (Thailand Tej) meliputi 1990-2006. Peneliti dipilih dua jenis dana - "dibesarkan di Taiwan dan diinvestasikan dalam saham domestik" dan "dibesarkan di luar negeri dan diinvestasikan dalam saham domestik" empat target investasi saham kecil, saham teknologi, saham dan saham / obligasi 1. Tabel daftar ikhtisar dana dibesarkan di Taiwan dan target investasi di tahun terakhir. Penelitian ini bertujuan 315 dana dari data sampel.

Dana PI ini dievaluasi dengan nilai-nilai bersih pada hari-hari perdagangan tahun ini. Jika dana baru dibesarkan pada bulan Januari, mereka termasuk dalam performa kinerja jajaran dana kami. Mereka dibangkitkan setelah tanggal termasuk dalam tahun depan. Dana dilikuidasi atau digabung pada bulan Desember termasuk dalam jajaran kinerja tahun ini. Mereka sebelum tanggal tidak termasuk dalam barisan dan evaluasi tahun. Ada 315 dana antara 1990 dan 2006 pertemuan prinsip penyortiran.
Kembalinya bebas risiko didasarkan pada variabel agen dari suku bunga bebas risiko bunga deposito satu tingkat tahun 6 pada website Bank Sentral Republik Cina (Taiwan). Benchmark Indeks tertimbang indeks harga saham oleh Bursa Saham Taiwan.
,2 kinerja estimasi
Dari simulasi dana studi evaluasi kinerja, Chiu Xianbi (1994) menemukan Sharpe, Treynor, indeks Jensen dan kembali dana sebelum penyesuaian resiko tidak mempunyai perbedaan signifikan dalam akurasi membedakan profitabilitas dana. Yang paling banyak digunakan Sharpe, Treynor, dan Jensen yang relevan indeks kinerja juga digunakan dalam studi ini bersih nilai harian. dan dividen dari Thailand Tej digunakan untuk memperkirakan kembali setiap hari dana di waktu kontinu. Pengembalian harian:

(6) nilai bersih pada periode t.

dividen tunai yang dikeluarkan pada periode t.
indeks Treynor, indeks Sharpe dan indeks Jensen untuk pengukuran kinerja yang relevan dana dalam rumus (1), (2) dan (3):

3,3 keberlangsungan hidup bias

Beberapa studi empiris domestik dana kinerja bias diukur keberlangsungan hidup.. Untuk akurat mengukur apakah dana kinerja yang terus-menerus, kemungkinan dana likuidasi atau menggabungkan dianggap. Pada dana 315, 74 yang dilikuidasi atau digabung sampel selama periode Untuk mengukur keberlangsungan hidup atau probabilitas bias likuidasi atau merger, ada total 2.017 buah sampel yang efektif dalam 315 dana antara 1990 dan 2006. Probabilitas dana yang akan dilikuidasi atau digabung setiap tahun adalah 3,67%.

3,4 pengujian dan hipotesis null

Untuk dana kinerja matriks transisi, selain dana tahunan probabilitas transisi peringkat kinerja matriks, penelitian ini juga mencakup dana baru dan dilikuidasi atau digabung dana setiap tahun ke estimasi matriks transisi probabilitas. Artinya, dana yang dihimpun tahun ini tercatat di tahun sebelumnya seperti baru dana. Mereka yang ada di tahun sebelumnya tetapi dilikuidasi atau digabung tahun ini tercatat di divisi likuidasi tahun ini hipotesis. Null ditetapkan sebagai dana kepatuhan kinerja jajaran acak. Dana tersebut belum tentu dipengaruhi oleh peringkat pada tahun sebelumnya. Dalam pertimbangan keberlangsungan hidup dan bias praduga dana kinerja peringkat mematuhi acak, uji rasio kemungkinan oleh Kupiec (1995) adalah hipotesis nol sebagai:

berarti kemungkinan dana yang dilikuidasi atau digabung setiap tahun; adalah jumlah dana divisi peringkat kinerja. Pada peringkat bawah dua divisi, memberikan probabilitas liquadatoin atau penggabungan di masa lalu , the likelihood ratio test null hypothesis , Rasio kemungkinan uji hipotesis null is P ij =48.18%. Dalam transisi bersama probabilitas uji Rantai Markov, kinerja reksa dana di divisi pada tahun sebelumnya memiliki probabilitas yang sama untuk jatuh ke dalam masing-masing divisi di tahun berikutnya. Probabilitas likuidasi atau menggabungkan rasio .


4. 4. KINERJA DANA STABILITAS RAND HASIL EMPIRIS

4.1Performance gigih dari dua

Goetzman dan Ibbotson (1994), Brown dan Boetzman (1995) dan Malkiel (1995) pemenang dan dikotomi digunakan pecundang, yang juga digunakan di sini. Pemenang dan pecundang Lihat estimasi probabilitas transisi matriks pada Tabel 2 dan uji rasio kemungkinan daftar. Tabel 3 transisi probabilitas gabungan uji apakah kinerja jajaran dana pada tahun sebelumnya mematuhi acak di tahun berikutnya.
S1 mengacu pada dana peringkat 0 ~ 50% di tahun sebelumnya; S2 menunjukkan peringkat dana dalam 2 dn 50% di tahun sebelumnya. Dari Tabel 2, kita dapat melihat kedua kembali mutlak dan Sharpe, Jensen dan indeks Treynor menolak transisi probabilitas sebagai hipotesis null acak 7. Pada kolom 4 September, dana di peringkat pertama 50% lebih kecil kemungkinannya untuk dilikuidasi atau digabung dari rata-rata historis. Probabilitas penolakan mereka akan dilikuidasi atau digabung adalah sama pada 3,46% dari rata-rata historis dalam likuidasi, atau penggabungan. Those in the 2 nd 50% are more likely to be liquidated or merged than historical average. The refusal to be liquidated or merged is also 3.46%. Mereka dalam 2 dn 50% lebih mungkin dilikuidasi atau digabung dari rata-rata historis atau The. Penolakan akan dilikuidasi digabung juga 3,46%.
Tabel 3 menawarkan sambungan tes probabilitas transisi Rantai Markov matriks. Melalui uji probabilitas transisi, tidak peduli apa keadaan dana kinerja pada tahun sebelumnya, semua negara transisi probabilitas menolak hipotesis nol yang sama, berarti transisi dana kinerja sebelumnya dan tahun berikutnya adalah tidak acak transisi. uji matriks probabilitas dimana semua probabilitas yang sama juga menolak hipotesis null.

4,2 kegigihan dari sepuluh divisi

Probabilitas estimasi dan uji dalam dua divisi tahu apakah dana kinerja yang persisten. Informasi yang terlalu sederhana Tabel. Carhart (1997) menggunakan dana kontingensi kinerja dibagi. Dia peringkat kinerja absolut dana ke divisi sepuluh unit satu tahun untuk memperkirakan dana abosulte kinerja peringkat transisi probabilitas. Melalui tabel kemungkinan transisi, yang lebih baik bisa ambil dana transisi probabilitas kinerja. Dengan transisi probabilitas dalam tabel kontingensi Carhart (1997), perkiraan dana penelitian kinerja indeks probabilitas transisi peringkat. Dengan Markov Chain oleh Anderson dan Goodman (1957 ), kertas tes probabilitas transisi, termasuk proses dana kinerja yang acak anmd tidak gigih dan probabilitas performancetransition dana dalam Rantai Markov stasioner.
Dengan metode pembagian peringkat oleh Carhart (1997), dana kinerja adalah peringkat dari atas ke bawah dalam 10 divisi;. Dana dengan kinerja di 10% pertama adalah dalam 1 st divisi mereka yang berada di 10% pertama ~ 20% dalam 2 nd divisi. Mereka yang berada di 10% terakhir berada di divisi th 10. Providing Untuk memulai, jika dana kinerja berlaku acak, tidak terus-menerus.. Transisi Setiap probabilitas dalam matriks probabilitas transisi sama transisi probabilitas dari divisi in the previous year and pada tahun sebelumnya dan tahun ini, setelah memberikan kinerja tahun previsous , Markov Chain joint test null hypothesis is , Rantai Markov null hipotesis gabungan uji and Kupiec (1995) dan Kupiec (1995) uji rasio kemungkinan . .
Tabel 4 hasil tes daftar matriks probabilitas transisi dan rasio kecenderungan dari divisi peringkat sepuluh performance kembali mutlak dan Sharpe, Jensen dan relevan performance indeks Treynor. Yang pertama colmn S1 untuk S10 lihat dana kinerja dengan sepuluh kuantil pertama untuk divisi kesepuluh di tahun sebelumnya. R1 untuk R10 pada baris pertama yang berarti kinerjanya dana pada tahun berikutnya dalam sepuluh kuantil pertama untuk divisi kesepuluh. Tabel 5 hasil tes bersama Chaintransition probabilitas Markov matriks.
Absolute Kinerja, Dana S1 ~ S3 di 30% pertama pada tahun sebelumnya memiliki probabilitas transisi harus masih dalam 30% pertama tahun depan rasio. Kemungkinan di S3 untuk menguji R1 menolak hipotesis nol secara acak. Tidak peduli di daerah manapun antara S1 dan R3 kinerja pada tahun sebelumnya, kemungkinan dana kinerja tahun depan di divisi R10 terakhir menolak hipotesis nol, ini. berarti dalam indeks kinerja absolut, dana yang masuk dalam 30% pertama pada tahun sebelumnya memiliki probabilitas yang lebih rendah harus inthe terakhir divisi dari probabilitas acakAbsolute Kinerja, dana di S10 sangat mungkin berada di divisi R10 terakhir tahun berikutnya, menolak secara signifikan kinerja sebagai hipotesis nol secara acak. Pada pertunjukan kembali absolut, walaupun dana dengan kinerja yang baik tidak memiliki persistensi signifikan, dana dengan kinerja buruk sangat mungkin untuk menjaga kinerja yang buruk pada tahun berikutnya.
Indeks Sharpe, dana dengan baik atau buruk kinerja yang baik memiliki banyak bukti persistensi.. Dana yang baik dengan performa yang lebih memiliki probabilitas acak dari hipotesis untuk menjaga performa baik, terutama yang Sharpe dengan indeks peringkat pertama di 10% di S1 divisi Mereka memiliki setinggi 16,8% probabilitas berada di R1 tahun berikutnya, dan 15,2% dari S2 ke R2. Dana dengan kinerja baik pada tahun sebelumnya memiliki probabilitas lebih rendah daripada hipotesis acak untuk berada di babak kedua divisi:. Contoh dana S1 ~ S3 pada tahun sebelumnya memiliki sekitar 5,5% probabilitas berada di 10% terakhir R10 tahun berikutnya. ini lebih rendah dari hipotesis nol secara acak ij P = 9,645%. Indeks Treynor memiliki kinerja yang sama dengan indeks Sharpe tidak.. Dana yang baik dengan kinerja di tahun sebelumnya masih baik memiliki kinerja berikutnya tahun Probabilitas dari S1 ke R1 adalah lebih dari 15%. Itu dari S1 ke S2 ke R10 di bawah atau sekitar 6%. Dana dengan kinerja yang buruk seperti pada S10 memiliki probabilitas setinggi lebih dari 17% menjadi 10% dalam divisi R10 terakhir tahun berikutnya.
Brown dan Goetzmann (1995) mengatakan dana dengan kinerja buruk lebih cenderung dihentikan hasil. Serupa ditemukan di resonansi ini. Dalam salah kinerja absolut atau indeks kinerja yang relevan, sebagian besar dana dalam likuidasi menolak S1 ~ S3 atau setara untuk menggabungkan sejarah rata-rata; mereka yang S9 ~ S10 lebih dari 8% kemungkinan akan dilikuidasi atau digabung pada tahun berikutnya. Probabilitas penolakan akan dilikuidasi atau menggabungkan sama dengan rata-rata historis.
Tabel 5 adalah ujian bersama dari 10 divisi. Pada uji bersama acak kepatuhan kinerja tahun depan, dana yang masuk dalam 10% pertama hanya memiliki Sharpe, Jensen dan indeks Treynor signifikan menolak hipotesis nol secara acak tahun berikutnya kembali kinerja Absolut. gagal untuk menolak transisi probabilitas non-acak. Absolute kembali persistensi kinerja tidak khas.. Dana yang miskin dengan kinerja seperti dalam 20 terakhir% dari S9 ~ S10 menolak dana kinerja null acak sebagai hipotesis berikutnya tahun ini berarti mereka lebih cenderung untuk menjaga performa buruk.

4,3 Klasifikasi sub-sampel persistensi kinerja

Untuk memahami apakah alam dana menyebabkan hasil yang berbeda, dana dibagi menjadi empat sub-sampel berdasarkan target investasi untuk mengevaluasi kembali dana persistensi kinerja. Sub-sampel saham teknologi, saham kecil, saham, dan saham + obligasi. Tech 41 dana saham memiliki termasuk 264 sampel; saham kecil dan memiliki saham 260 saham termasuk 1.592 sampel; saham obligasi + memiliki 87 dana termasuk 339 sampel.
Tek saham dan saham kecil tidak mencakup banyak sampel. Dengan peringkat terlalu banyak divisi di ttransition sampel probabilitas-sub matriks, probabilitas transisi akan memiliki perwakilan estimasi miskin dan kinerja uji statistik tidak tinggi. Akibatnya, hanya 3 divisi digunakan 8S1 ~ S3 adalah dana peringkat pertama untuk kelompok ketiga di tahun sebelumnya; ~ R1 R3 lihat dana peringkat pertama di divisi ketiga dan tahun depan. Empiris Hasil tech saham saham kecil pada Tabel mutlak menunjukkan kinerja transisi 5 matriks probabilitas tidak memiliki probabilitas transisi yang khas yang berbeda dari acak. Pada dana baru Sebaliknya, dalam saham kecil memiliki kinerja yang baik di tahun pertama. Sebagai imbalannya mutlak, dana baru 51,9% cenderung berada di peringkat pertama 1 / 3. Sharpe , Jensen dan indeks Treynor menunjukkan hasil serupa. Dalam salah kinerja absolut atau indeks kinerja yang relevan, kemungkinan dana dalam pertama 1 / 3 dari S1 divisi di tahun sebelumnya berada di pertama 1 / 3 dari pembagian R1 tidak lebih tinggi dari probabilitas acak.
hasil empiris dari saham sub-sampel pada Tabel mutlak kembali menunjukkan kinerja 6 adalah mirip dengan Sharpe, Jensen dan indeks Treynor.. Kinerja empat indeks persistensi tinggi cukup memiliki bukti absolut Dalam kinerja, dana di S1 pada tahun sebelumnya memiliki 39,7% kemungkinan untuk berada di 1 / 3 dari R1 berikutnya tahun pertama dan 21,8% probabilitas untuk berada di peringkat 1 / 3 terakhir.. Kedua mencapai probabilitas penolakan berbeda null hipotesis dalam statistik. Ini membuktikan dana saham yang baik dengan kinerja tinggi memiliki persistensi Dalam kinerja mutlak, dana peringkat terakhir dalam 1 / 3 di tahun sebelumnya memiliki 22,1% kemungkinan hanya berada di pertama 1 / 3 peringkat tahun berikutnya. Mereka memiliki 41,9% kemungkinan berada di terakhir 1 / 3 peringkat tahun berikutnya menunjukkan. ini dana saham dengan kinerja yang buruk di tahun sebelumnya masih cenderung payah tahun berikutnya.
Pada Tabel 6 dari saham + obligasi dana tidak memperlihatkan bukti mutlak kegigihan dalam kembali. Threerelevant Indeks-indeks kinerja memiliki ketekunan yang tinggi. Apa yang bernilai perhatian adalah dana dari empat indeks peringkat yang terakhir 1 / 3 dari S3 pada tahun sebelumnya telah probabilitas setinggi 10% akan dilikuidasi atau digabung daripada rata historis 3,46%.
Tabel 7 daftar uji bersama sub-sampel probabilitas transisi empiris dana. Kecuali saham kecil, sisanya tiga sub-sampel kinerja peringkat S1 atau S3 sebagian besar menolak hipotesis randomnull tahun berikutnya. Dana dengan kinerja yang lebih baik di tahun sebelumnya telah probabilitas grezter untuk perfrom baik di bawah rata-rata peringkat yang baik. Orang-orang miskin dengan kinerja buruk di bawah peringkat yang lebih besar memiliki kemungkinan likuidasi atau menggabungkan thehistorical dari. Probabilitas berada di barisan miskin lebih tinggi dari hipotesis acak.

5. Dilikuidasi atau digabung DANA

Dalam dana 229 sampel dalam studi, 85 telah dilikuidasi atau merger antara 1990 dan 2006. Estimasi Tidak ada yang tersedia dalam studi sebelumnya terhadap kinerja dilikuidasi atau digabung dana dan. Skala sejarah reksadana di Taiwan sudah cukup statistik dilikuidasi atau digabung dana membuat The. penelitian statistik persentase absolut kembali peringkat kinerja dari 85 dana dari dua tahun sebelum likuidasi atau merger, atau kemudian peringkat dana tersebut tow tahun, tahun sebelumnya dan tahun likuidasi atau merger 9 dengan dana lainnya. Tabel 8 menunjukkan kinerja rata-rata dana ini di 65% dari total dana pasar, yang berarti 65% dari total dana yang dilakukan selama-dana dilikuidasi. Kedua dilikuidasi atau digabung dana dikalahkan oleh lebih dari 70% dari dana sebelum likuidasi atau menggabungkan . Dilikuidasi. dana dikalahkan oleh 77,1% dari dana dalam rata bergabung; dana dikalahkan oleh 74,4% dari dana dalam rata
Pada Tabel 8, dana penggabungan telah kinerja peringkat dari 53% dan 61,4% dalam dua tahun sebelum dan sebelumnya penggabungan tahun di pasar secara keseluruhan. Pada tahun dari penggabungan dana lain, kinerja mereka yang berada di peringkat rata-rata 57,9% dari pasar secara keseluruhan. Setelah penggabungan dana lain, dana tersebut sudah peringkat kinerja pada 54,3% dan 52,6% pada tanggal 1 dan 2 tahun dn setelah bergabung. Dari data tersebut, kita bisa belajar penggabungan dana tersebut memiliki sekitar kinerja yang sama rata-rata pasar secara keseluruhan. Setelah menggabungkan dana lain, kinerja meningkat secara signifikan atau ditolak.

6. KESIMPULAN DAN SARAN

Tulisan ini bertujuan untuk dana dibesarkan di Taiwan dan diinvestasikan dalam saham dalam negeri antara 1990 dan 2006 tahun. Transisi Markov Melalui Probabilitas matriks, statistik ini dilakukan untuk melihat apakah dana kinerja yang terus-menerus dalam 17. Untuk dana persistensi memperkirakan kinerja yang lebih baik, penelitian untuk waktu pertama kali bias kesintasan mempertimbangkan dana domestik kegigihan kinerja untuk mengurangi bias keberlangsungan hidup dan lebih setia memperkirakan dana persistensi kinerja jajaran.
Hasil empiris menunjukkan bahwa, dalam performa kembali mutlak, ketekunan yang lebih rendah,. Sharpe Jensen dan relevan kinerja indeks Treynor memiliki lebih kegigihan khas,. Dana yang baik dengan kinerja tahun sebelumnya telah probabilitas yang lebih rendah daripada rata-rata historis likuidasi atau merger



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Table 1: Kenaikan Reksadana di Taiwan antara 1990 dan 2006 dan Klasifikasi Terget Investasi
Target Investasi Kenaikan investasi di Taiwan Kenaikan di Taiwan dan Taget investasi di dalam dan luar negeri Kenaikan di Luar Taiwan dan investasi di Taiwan Total
Small stocks 29 29 1 1 30 30
Real property securitization 8 8 8 8
Real estate 8 8 1 1 9 9
Stocks Saham 164 164 67 67 4 4 235 235
Stocks + bond 85 85 25 25 110 110
Principle guarantee 11 11 2 2 13 13
Index stocks 6 6 1 1 1 1 8 8
Tech stocks 41 41 10 10 51 51
Energy stocks 2 2 2 2
Funds Dana-dana 8 8 74 74 82 82
Currency Mata uang 2 2 2 2 4 4
Bones Bones 93 93 28 28 121 121
Asset securitization 5 5 5 5
Total Total 447 447 226 226 5 5 678 678
Catatan : Data dari kenaikan dana dan target investasi diperoleh dari TEJ database.
Table 2:Bagan Dana Transisi Probabilitas Matrix di Dua Divisi
1990~2006 ( R1 ) ( R2 ) ( C )
a. absolute return
( S1 ) 52.7*** 44.6** 2.67 2,67
( S2 ) 45.3* 45,3 * 48.8 48,8 5.98***
(New) (Baru) 44.6 44,6 55.4** 0*** 0 ***
b. Sharpe index
( S1 ) 56.8*** 40.9*** 2.32**
( S2 ) 42.4*** 51.2* 6.33***
(New) 40.9** 59.1*** 0*** 0 ***
Jensen index
( S1 ) 53*** 44.5** 2.56*
( S2 ) 45* 48.9 48,9 6.1***
(New) 44.6 44,6 55.4** 0*** 0 ***
Treynor index
( S1 ) 56.4*** 41.2*** 2.32**
( S2 ) 42.6*** 51.1* 6.33***
(New) (Baru) 41.6** 58.4*** 0*** 0 ***
Table 3: Kebersamaan dari Tes pembagian dalam dua bagian Bagan Dana Transisi Probabilitas Matrix yang sama
Null hypothesis Absolute return Sharpe index Jensen index Treynor index
P(S1,R1)=P(S1,R2) 8.3*** 27*** 9.5*** 25.1***
P(S2,R1)=P(S2,R2) 14*** 23.9*** 15.5*** 23.6***
P(New,R1)=P(New,R2) 15.3*** 21.9*** 15.3*** 20.5***
All probabilities equal. 等 37.6*** 72.9*** 40.3*** 69.1***

Table 4: Bagan Dana Transisi Probabilitas Matrix di Sepuluh Divisi

1990~2006 ( R1 ) ( R2 ) ( R3 ) ( R4 ) ( R5 ) ( R6 ) ( R7 ) ( R8 ) ( R9 ) ( R10 ) ( C )
a. absolute return
( S1 ) 12.8 12,8 8.94 8,94 13.4 13,4 7.26 7,26 13.4 13,4 10.1 10,1 8.38 8,38 8.38 8,38 10.6 10,6 5.59** 1.12**
( S2 ) 8.19 13.5 13,5 11.1 11,1 7.6 7,6 8.77 8,77 12.3 12,3 11.7 7.02 12.9 5.26** 1.75
( S3 ) 14.5** 9.83 9.25 9.25 8.67 7.51 15** 12.1 12,1 7.51 7,51 5.2** 1.16**
( S4 ) 10.6 13.5 10.6 10,6 8.82 14.1* 6.47 11.8 7.06 5.88* 8.24 2.94 2,94
( S5 ) 8.93 11.9 10.7 10.7 7.14 7.14 7,14 8.93 11.9 8.33 7.74 7,74 6.55*
( S6 ) 9.25 12.7 9.83 9.83 9.25 6.36 13.3 8.67 11.6 5.78* 3.47 3,47
( S7 ) 9.83 9,83 7.51 7,51 12.1 7.51 9.25 11.6 8.09 8,09 15** 7.51 6.94 4.62 4,62
( S8 ) 11.8 4.71** 6.47 11.8 9.41 14.7** 8.24 9.41 11.2 11,2 6.47 5.88 5,88
( S9 ) 8.62 8,62 8.05 8,05 9.77 9,77 13.8* 8.05 9.2 9,2 12.1 8.05 4.02*** 10.9 7.47**
( S10 ) 5.52* 6.13 8.59 8.59 8,59 7.36 12.9 4.91** 7.36 11.7 18.4*** 18,4 *** 8.59***
(New) 9.57 9.24 6.93* 9.9 8.91 9.24 6.6* 9.9 13.5** 16.2*** 0*** 0 ***
b. Sharpe index
( S1 ) 16.8*** 11.2 10.6 10.6 9.5 9,5 7.82 10.6 8.94 8.38 5.03** 0.56***
( S2 ) 9.94 15.2** 11.1 11,1 9.36 9,36 10.5 8.77 10.5 11.7 6.43 5.26** 1.17**
( S3 ) 10.4 10.4 10.4 8.09 8,09 13.3 12.7 11.6 9.83 4.05*** 6.94 2.31 2,31
( S4 ) 16.5*** 10.6 11.2 11,2 11.8 10 8.82 8.24 5.88* 5.88* 5.88* 5.29
( S5 ) 7.74 7,74 10.1 10,1 15.5** 14.9** 8.33 7.14 5.95* 11.9 9.52 6.55 2.38
( S6 ) 9.83 9.25 7.51 7,51 12.1 10.4 8.09 8,09 8.09 8,09 9.25 15** 6.94 6,94 3.47 3,47
( S7 ) 7.51 7,51 5.78* 8.09 8,09 8.67 8,67 9.83 12.7 13.9* 11 11 13.3 4.62** 4,62 ** 4.62 4,62
( S8 ) 5.88* 10 10.6 11.8 10.6 12.4 12,4 8.82 10.6 7.06 6.47 5.88
( S9 ) 8.05 8.62 12.1 5.75* 8.62 9.77 9,77 12.6 12,6 8.05 6.32 11.5 8.62***
( S10 ) 6.75 6,75 4.91** 7.36 5.52* 6.13 9.2 9,2 8.59 7.36 16.6*** 18.4*** 18,4 *** 9.2***
(Baru) 9.9 9.57 5.61** 7.92 7.92 9.57 8.58 8,58 10.2 12.9* 17.8*** 0*** 0 ***


Tabel 4 (lanjutan)
1990~2006 ( R1 ) ( R2 ) ( R3 ) ( R4 ) ( R5 ) ( R6 ) ( R7 ) ( R8 ) ( R9 ) ( R10 ) ( C )
c. Jensen index
( S1 ) 15.1** 12.3 12,3 14* 14 * 7.26 9.5 12.3 12,3 7.26 8.94 8,94 6.7 6.15* 0.56***
( S2 ) 9.94 13.5 13,5 11.1 11,1 9.94 8.19 9.36 9,36 6.43 14.6** 10.5 4.68** 1.75 1,75
( S3 ) 12.1 12,1 8.67 8,67 11 11 7.51 7,51 10.4 10,4 7.51 7,51 13.9* 12.1 12,1 9.25 9,25 6.36 1.16**
( S4 ) 12.9 12,9 9.41 10.6 11.2 11,2 9.41 8.24 7.06 8.24 8.82 10.6 3.53
( S5 ) 10.1 10,1 7.74 7,74 11.9 11,9 13.7* 7.14 7,14 8.33 7.74 7,74 8.33 10.1 10,1 8.93 5.95 5,95
( S6 ) 8.67 8,67 12.1 12,1 9.25 9,25 11 11 10.4 10,4 8.67 8,67 7.51 7,51 9.25 9,25 10.4 10,4 9.83 9,83 2.89 2,89
( S7 ) 9.83 9,83 9.25 9,25 7.51 7,51 9.83 9,83 10.4 10,4 10.4 10,4 10.4 10,4 12.1 12,1 10.4 10,4 4.05*** 5.78
( S8 ) 9.41 9,41 8.82 8,82 8.82 8,82 10.6 9.41 9,41 14.7** 12.4 12,4 8.82 8,82 7.65 6.47 2.94 2,94
( S9 ) 6.32 10.9 7.47 7,47 8.62 9.77 9,77 11.5 11,5 10.9 8.05 4.6** 12.6 12,6 9.2***
( S10 ) 5.52* 5.52* 8.59 8,59 8.59 8,59 7.98 9.2 9,2 10.4 10,4 5.52* 11 11 17.8*** 9.82***
(Baru) 9.57 8.25 8,25 7.92 7,92 8.25 8,25 10.6 7.92 7,92 11.6 11,6 9.24 9,24 14.5*** 12.2 12,2 0*** 0 ***
d. Treynor index
( S1 ) 16.2*** 12.8 12,8 12.8 12,8 8.94 8,94 10.6 10,6 7.82 7,82 10.6 7.82 7,82 6.7 4.47*** 1.12**
( S2 ) 9.36 9,36 12.3 12,3 11.1 11,1 12.3 12,3 8.19 9.94 9.36 9,36 13.5 13,5 7.02 7,02 5.26** 1.75 1,75
( S3 ) 13.3 10.4 10,4 8.67 8,67 8.67 8,67 13.3 9.25 9,25 11 11 11 11 5.78* 6.94 6,94 1.73 1,73
( S4 ) 12.9 12,9 10 14.7** 10 10 8.24 12.9 12,9 8.24 6.47 5.29** 6.47 4.71 4,71
( S5 ) 9.52 9,52 11.9 11,9 11.9 11,9 13.7* 13,7 * 10.1 10,1 10.1 10,1 7.14 7,14 9.52 9,52 7.14 7,14 6.55 6,55 2.38 2,38
( S6 ) 8.09 8,09 8.67 8,67 12.7 9.25 9,25 12.1 12,1 8.09 8,09 5.2** 11.6 11,6 16.2*** 5.2** 2.89 2,89
( S7 ) 8.09 8,09 5.78* 7.51 7,51 9.25 9,25 10.4 10,4 13.3 13.3 13,3 11.6 11,6 11 11 5.78* 4.05 4,05
( S8 ) 4.71** 8.82 8,82 8.82 8,82 13.5 13,5 8.24 13.5 13,5 11.8 8.24 7.06 8.24 7.06**
( S9 ) 6.32 9.77 9,77 6.9 6,9 8.05 8,05 9.77 9,77 9.77 9,77 12.1 12,1 8.62 8,62 8.05 8,05 11.5 11,5 9.2***
( S10 ) 9.2 9,2 4.91** 9.2 9,2 7.36 7,36 4.91** 6.13 6,13 8.59 8,59 5.52* 17.8*** 17.8*** 8.59***
(New) (Baru) 10.9 10,9 9.9 5.61** 6.6* 6,6 * 8.58 8,58 7.59 7,59 9.57 10.6 10,6 13.2** 17.5*** 0*** 0 ***
Table 5 : Kebersamaan dari Tes pembagian dalam dua bagian Bagan Dana Transisi Probabilitas Matrix yang sama di sepuluh devisi

States Amerika absolute return Sharpe index Jensen index Treynor index
( S1 ) 15.4 20.1** 22.4** 23.3**
( S2 ) 14.4 14,4 15.2 15.8 15,8 12.2 12,2
( S3 ) 18.9* 13.3 12.6 12,6 11.7 11,7
( S4 ) 13.5 13,5 18.8* 4.7 16.5 16,5
( S5 ) 9.3 9,3 18.5* 9.2 9,2 9.3 9,3
( S6 ) 9.6 9,6 9.5 9,5 3.2 3,2 19.6**
( S7 ) 11.6 11,6 16.7 16,7 10.1 10,1 12.6 12,6
( S8 ) 17* 17 * 10.4 10,4 9.1 9,1 18.2* 18,2 *
( S9 ) 18.6* 18,6 * 20.9** 25.4*** 20.6**
( S10 ) 37.1*** 46.8*** 37.9*** 46.9***
( New ) 34.8*** 42.9*** 25.3*** 45***
(All) (Semua) 200.2*** 233.2*** 175.7*** 235.8***

Table 6 : Hasil Transisi Probabilitas Matrix dari Sub - Samples
1990~2006 ( R1 ) ( R2 ) ( R3 ) ( C ) ( R1 ) ( R2 ) ( R3 ) ( C )
a. tech stocks b. b. small stocks
1.absolute return
( S1 ) 39.7 39,7 38.5 38,5 21.8* 0*** 0 *** 36.7 36,7 34.7 34,7 26.5 26,5 2.04 2,04
( S2 ) 36 36 34.7 34,7 28 28 1.33 1,33 29.5 29,5 36.4 36,4 27.3 27,3 6.82 6,82
( S3 ) 25.4 25,4 26.8 26,8 42.3* 5.63 5,63 26.8 26,8 29.3 29,3 39 39 4.88 4,88
(New) (Baru) 35 35 30 30 35 35 0** 0 ** 51.9** 22.2 22,2 25.9 25,9 0 0
2.Sharpe index
( S1 ) 41* 41 * 39.7 39,7 19.2** 0*** 0 *** 40.8 40,8 26.5 26,5 30.6 30,6 2.04 2,04
( S2 ) 34.7 34,7 38.7 38,7 26.7 26,7 0*** 0 *** 27.3 27,3 36.4 36,4 29.5 29,5 6.82 6,82
( S3 ) 23.9 23,9 22.5* 46.5*** 7.04 7,04 26.8 26,8 36.6 36,6 31.7 31,7 4.88 4,88
(Baru) 37.5 37,5 27.5 27,5 35 35 0** 0 ** 48.1* 48,1 * 25.9 25,9 25.9 25,9 0 0
3.Jensen index
( S1 ) 41* 41 * 37.2 37,2 20.5** 1.28* 1,28 * 36.7 36,7 30.6 30,6 30.6 30,6 2.04 2,04
( S2 ) 32 32 40 40 28 28 0*** 0 *** 31.8 31,8 38.6 38,6 22.7 22,7 6.82 6,82
( S3 ) 25.4 25,4 23.9 23,9 45.1** 5.63 5,63 26.8 26,8 29.3 29,3 39 39 4.88 4,88
(Baru) 40 40 27.5 27,5 32.5 32,5 0** 0 ** 48.1* 48,1 * 25.9 25,9 25.9 25,9 0 0
4.Treynor index
( S1 ) 44.9** 34.6 34,6 20.5** 0*** 0 *** 36.7 36,7 32.7 32,7 28.6 28,6 2.04 2,04
( S2 ) 28 28 41.3* 41,3 * 30.7 30,7 0*** 0 *** 31.8 31,8 34.1 34,1 27.3 27,3 6.82 6,82
( S3 ) 25.4 25,4 26.8 26,8 40.8 40,8 7.04 7,04 26.8 26,8 31.7 31,7 36.6 36,6 4.88 4,88
(Baru) 40 40 25 25 35 35 0** 0 ** 48.1* 48,1 * 25.9 25,9 25.9 25,9 0 0
c. c. stocks saham d. d. stocks + bonds
1.absolute return
( S1 ) 39.7*** 32.5 32,5 25.8*** 1.97*** 39.8 39,8 30.1 30,1 25.8 25,8 4.3 4,3
( S2 ) 32.7 32,7 31 31 31.6 31,6 4.65 4,65 28.6 28,6 36.9 36,9 31 31 3.57 3,57
( S3 ) 29.6 29,6 30.7 30,7 32.3 32,3 7.4** 40 40 22.5* 25 25 12.5***
(New) (Baru) 22.9*** 35.2 35,2 41.9*** 0*** 0 *** 26.8 26,8 34.1 34,1 39 39 0*** 0 ***
2.Sharpe index
( S1 ) 39.5*** 36.5** 22.3*** 1.75*** 1,75 *** 46.2*** 32.3 32,3 18.3*** 3.23 3,23
( S2 ) 33.4 33,4 29.6 29,6 32.7 32,7 4.2 4,2 33.3 33,3 32.1 32,1 29.8 29,8 4.76 4,76
( S3 ) 28.7 28,7 30.5 30,5 32.7 32,7 8.07*** 27.5 27,5 32.5 32,5 27.5 27,5 12.5***
(Baru) 23.7*** 30.5 30,5 45.8*** 0*** 0 *** 26.8 26,8 26.8 26,8 46.3*** 0*** 0 ***
3.Jensen index
( S1 ) 39.7*** 32.3 32,3 26.4** 1.53*** 45.2*** 26.9 26,9 23.7* 23,7 * 4.3 4,3
( S2 ) 32.7 32,7 29.4 29,4 33 33 4.87 4,87 28.6 28,6 35.7 35,7 32.1 32,1 3.57 3,57
( S3 ) 28.5 28,5 32.1 32,1 31.8 31,8 7.62*** 33.8 33,8 31.2 31,2 22.5* 12.5***
(Baru) 25** 36 36 39** 0*** 0 *** 26.8 26,8 30.5 30,5 42.7** 0*** 0 ***
4.Treynor index
( S1 ) 40*** 33.6 33,6 24.5*** 1.97*** 48.4*** 26.9 26,9 21.5** 3.23 3,23
( S2 ) 32.5 32,5 32.3 32,3 31 31 4.2 4,2 31 31 38.1 38,1 23.8 23,8 7.14 7,14
( S3 ) 28.3 28,3 31.6 31,6 32.3 32,3 7.85*** 26.2 26,2 32.5 32,5 31.2 31,2 10* 10 *
(Baru) 25.4** 28.8 28,8 45.8*** 0*** 0 *** 28 28 26.8 26,8 45.1** 0*** 0 ***

Table 7 : Kebersamaan dari Test Sub-samples
Bagian Amerika absolute return Sharpe index Jensen index Treynor index
a. Tech stocks
( S1 ) 8.8** 11.2*** 7.9** 11.2***
( S2 ) 2.8 2,8 5.5 5,5 5.5 5,5 6.1*
( S3 ) 4.1 4,1 8.9** 6.4* 4.1 4,1
(Baru) 2.2 2,2 2.7 2,7 3 3 3.5 3,5
(Semua) 17.8** 28.3*** 22.7*** 24.9***
b. Small stocks
( S1 ) 1.7 1,7 2.5 2,5 1.2 1,2 1.3 1,3
( S2 ) 1 1 1 1 2.2 2,2 0.8 0,8
( S3 ) 1.1 1,1 0.6 0,6 1.1 1,1 0.6 0,6
(Baru) 5.8 5,8 4.1 4,1 4.1 4,1 4.1 4,1
(Semua) 9.6 9,6 8.3 8,3 8.6 8,6 6.8 6,8
c. Stocks
( S1 ) 21.9*** 33.5*** 23.3*** 25.3***
( S2 ) 0.2 0,2 1.4 1,4 1.1 1,1 0.5 0,5
( S3 ) 7.6** 12.2*** 9.4** 10.9***
(Baru) 25.6*** 30.6*** 19.8*** 29.4***
(Semua) 55.3*** 77.8*** 53.6*** 66.1***
c. Stocks + bonds
( S1 ) 3 3 11.9*** 7.9** 12.3***
( S2 ) 1.2 1,2 0.2 0,2 0.9 0,9 3.8 3,8
( S3 ) 15.2*** 11.1*** 11,1 *** 12.5*** 5.5 5,5
(Baru) 6* 6 * 10.6*** 7.6** 9.5**
(Semua) 25.5*** 33.8*** 28.9*** 31.1***
Table 8 : Peringkat Rata - rata odari Likuiditas atau Dana Merger
Klasifikasi Dua tahun sebelum Likuidasi Satu tahun sebelum Likuidasi Likuidasi / Merger Nomor Rata – rata pertahun
Likuidasi 65.1% 65,1% 65.5% 65,5% 77.1% 77,1% 33 33 4.09 4,09
Dana Merger 61.5% 61,5% 67.9% 67,9% 74.4% 74,4% 52 52 4.14 4,14

Hasil dari Dana Merger Dua tahun sebelum Likuidasi Satu tahun sebelum Likuidasi Likuidasi / Merger Satu tahun setelah Likuidasi Dua tahun setelah Likuidasi
53% 53% 61.4% 61,4% 57.9% 54.3% 54,3% 52.6% 52,6%