A Test of the Persistence in the Performance of UK Managed Funds

A Test of the Persistence in the

Performance of UK Managed Funds

D.E.Allen and M.L. Tan* 1. INTRODUCTION

This paper features tests of the persistence of investment trust company managers' rates of return and risk-adjusted returns in the United Kingdom (UK), on funds from 1989±1995. We analyse the relative performance of the funds and examine whether fund managers can maintain their inter-fund performance rankings over time (that is, whether past per-formance is a good predictor of future perper-formance). We assess persistence in performance in the short-run and long-run based on four major empirical tests: contingency table analysis of winners and losers, chi-squared independence testing on these tables, Ordinary Least Square (OLS) regression analysis of CAPM risk-adjusted excess returns and independent Spearman Rank Correlation Coefficient (SRCC) calculations. If past performance is a predictor of future performance, first half `superior' managers in the first period would remain as `superior' managers in the next period, second half `inferior' managers in the second half and so on. Overall, we find that both raw returns and risk-adjusted returns exhibit strong evidence of persistence in the long-run (over one-year and two-year-intervals) but this evidence appears to reverse in the short-run (semi-annually and monthly).

* The authors are respectively from Edith Cowan University, Joondalup, Western Australia and Citibank, Singapore. They are grateful to Professor L. Thomas of the Department of Business Studies, the University of Edinburgh, for comments on an earlier draft. Any remaining errors are the authors' own. (Paper received March 1998, revised and accepted November 1998)

Address for correspondence:D.E. Allen, Professor of Finance, Edith Cowan University, Joondalup Campus, Joondalup Drive, Joondalup, Western Australia 6027.

In exploring the relationship with volatility, funds are divided into high-variance and low-variance and their relative per-formance results exhibit repeat-winner pattern as well. Given these results, we then present a discussion of the implications both from the practitioners' and academicians' point of view.

To interpret relative performance, two major issues are addressed: types of measurement ± the need for risk adjustment and the possibility of survivorship bias. These issues will be discussed in Section 2 together with previous studies. Section 3 describes the data and research methods are presented in Section 4. Section 5 presents the results, indicating evidence of persistence in performance in the long-run but not in the short-run. In Sections 6 and 7, we analyse the validity of our study and provide a discussion on the implications of our results. The final section provides a summary and conclusion.

2. PREVIOUS RESEARCH AND SURVIVORSHIP BIAS

It is a common belief that empirical evidence about mutual fund performance confirms the original version of the EMH. According to Grossman and Stiglitz (1980), participants that do collect information may earn higher gross returns, but with the inclusion of expenses (on information collection), informed investors' net returns are equivalent to those obtained by uninformed investors. Others question this. Black (1973) concluded that:

the Value Line rankings definitely contain significant information and are certainly one of the exceptions to my rule that active portfolio management is generally worthless.

Similarly, Moles and Taylor (1977) and Gurney (1976) and Black, Fraser and Power (1992) reported some superiority in fund performance with Luther, Matatko and Corner (1992) finding weak evidence in studies of the performance of UK mutual funds. Jensen's Classic (1968) study looked at the performance of 115 mutual funds over the 1945±1964 period and found that 72 out of 114 mutual funds in his sample realised negative risk-adjusted returns after accounting for management fees and transaction costs. Thus, he concludes that there is a lack of persistence.

Ippolito (1989) resolved that funds with higher turnover, fees and expenses apparently earn risk-adjusted returns that are

sufficient to offset the higher charges. These results are consistent with the notion that mutual funds are efficient in their trading and information-gathering activities (Grossman, 1976; and Grossman and Stiglitz, 1980).

The potential for survivorship bias exists because not all mutual funds are typically included in sample data. Mutual funds that have proven to be unsuccessful do not tend to survive. Often, mutual fund complexes (that run large numbers of funds) will allow the unsuccessful funds to die away by merging the fund into one of the more successful funds in the complex, thereby burying the fund's bad record with it. Thus, there will be a tendency for more of the successful funds to survive. As a result, measures of fund performance will tend to overstate the success of mutual fund management.

However, some recent studies produce contrary evidence. Unfortunately, it is difficult to devise a simple adjustment to standard performance measures that will eliminate such bias totally. Brown, Goetzmann, Ibbotson and Ross (1992) examined the relationship between volatility and returns by using simulations to illustrate that even a small degree of survivorship bias can increase the evidence of persistence of performance significantly. Malkiel (1995) examined how mutual funds perform relative to various benchmarks and estimated the extent of survivorship bias. Shukla and Trzcinka (1992a and 1992b) argue that survivorship bias depends heavily on the ability of consumers to penalise managers with poor Jensen alphas. Since there is no evidence that consumers do so, survivorship bias should not be a major issue. Moreover, Hendricks, Patel and Zeckhauser (1993) and Sirri and Tufano (1992) provide evidence that consumers base their investment on total returns, and not on risk-adjusted returns.

Garcia and Gould (1993), suggest the term survivor bias refers to `the conceptual incorrectness of measuring performance of a portfolio that could have been defined at some time in the past only with a crystal ball'. They argue that there is no answer to survivor bias in the data. It exists because there are no true performance measures due to the non-existence of the index. Furthermore, there are no rules telling us what the exact composition would have been, if there had been one. Therefore, from the very beginning it is a leap of faith to test the way in which such an index, had it existed, would have performed.

Blitzer (1995) suggests attempts to adjust results for bias may create even more errors. Grinblatt and Titman (1989a) estimate the bias in measured performance that is due to survival providing evidence that investors are unable to make abnormal performance after accounting for all expenses. Grinblatt and Titman (1989b) present conditions under which the mean-variance efficient portfolio of tradable assets can be used as a benchmark to evaluate portfolio performance. Likewise, Elton, Gruber and Rentlzer (1990) found no performance persistence in that sample of 51 publicly offered mutual funds from 1980± 1988. Elton, Gruber, Das and Hlavka (1993) argued that Ippolito's results have low power because the benchmark he selected ± the S&P 500 is inefficient since it did not appropriately account for the performance of non-S&P assets. Grinblatt and Titman (1992) employed Jensen measures for 279 funds over the period 1974±1984 and found evidence of positive persistence with the existence of survivorship bias. Hendricks, Patel and Zeckhauser (1993) show that three-month returns are positively correlated to returns over the previous years.

Goetzmann and Ibbotson (1994) in a study of 728 surviving funds over a 13 year period (1976±1988) suggested that past returns and relative rankings are useful in predicting future returns and rankings. It appears that past alphas predict future alphas. Kahn and Rudd (1995) also found evidence of persistence of performance in fixed-income selection returns and information ratios even after taking into account fees and expenses. However, Shukla and Trzcinka (1992) suggest that persistence occurs only for inferior funds and not for superior funds.

Volkman and Wohar (1994 and 1995), concluded that there is no consistent relation between fund size and persistent fund performance. Similarly, Droms and Walker (1994) also find no relation between performance and size (which is consistent with Volkman and Wohar, 1995), but they also find no relation between performance and expense ratios, and turnover rates. In addition, Kahn and Rudd (1995) found evidence of persistence on fixed-income selection returns and information ratios even after taking into account the fees and expenses.

Grinblatt, Titman and Wermers (1995) analyse the extent to which mutual funds purchase stocks based on past returns and their tendency to exhibit `herding' behaviour, that is, buying and

selling the same stocks at the same time. Their evidence indicates that mutual funds have a tendency to buy stocks based on their past performance, and they tend to herd in excess of what one would expect from pure chance. The tendency of individual funds to buy past winners as well as to herd was shown to be highly correlated with fund performance.

Elton, Gruber and Blake (1996) use a sample free of survivorship bias to measure mutual fund predictability for common stock funds based on risk-adjusted returns. Like Hendricks, Patel and Zeckhauser (1993), they find that previous high returns can predict high returns in the short-run. In addition, they find evidence of persistence even in the longer run. In contrast to Ippolito (1989), performance still persists even after taking into account the impacts of expenses.

It is known widely that mutual funds, on average, have under-performed compared to index funds. Gruber (1996) explains why investors buy actively managed open-end mutual funds and pay for an amount equal to one with management skill. Several measures of performance are employed1 _{and the results show} that future performance is predictable from past performance.

While the above studies have examined the performance of all mutual funds, other studies have assessed the performance of international mutual funds such as Cumby and Glen (1990), Eun, Kolodny and Resnick (1991), Rao and Aggarwal (1987). Rao and Aggarwal (1987) examine the performance persistence of these funds. They conclude that these funds have earned a rate of return that is commensurated with the risk assumed and that there is no evidence of persistence.

Studies of market-timing abilities include: Alexandra and Stover (1980), Veit and Cheney (1982), Kon (1983), Chang and Lewellen (1984), Henriksson (1984), and Lee and Rahman (1990) ± all concluded that there was little evidence of successful marketing-timing. Some of the prominent mutual fund studies are summarised in Table 1.

3. THE DATA

Managed fund data, consisting of the weekly returns for 131 funds over the period 1989±1995 was obtained from the

Table 1

Summary of Some Prominent Mutual Fund Studies

Study Year Period Type of Survivor Performance Funds Bias Persistence

Friend, Brown, Herman

& Vickers '62 1953±58 All Yes No

Treynor & Mazuy '66 1954±63 All Yes n/c

Sharpe '66 1954±63 All Yes No

Jensen '68 1945±64 All Yes No

Friend et al. '70 1960±68 All Yes No

Carlson '70 1948±67 Stock Yes Yes

McDonald '74 1960±69 All Yes No

Mains '77 1955±64 All Yes Partiallya

Kon & Jen '79 1960±71 All Yes Yes

Alexandra & Stover '80 1966±71 All Yes n/t

Shawky '82 1973±77 All Yes No

Veit & Cheney '82 1944±78 All Yes n/t

Kon '83 1960±76 All Yes n/t

Chang & Lewellen '84 1971±79 All Yes No

Henriksson '84 1968±80 All Yes No

Lehman & Modest '87 1968±82 All Yes Yes

Robson '86 1969±78 All Yes No

Grinblatt & Titman '89 1974±84 Stock No Nob

Ippolito '89 1965±84 All No No

Cumby & Glen '90 1982±88 International Yes No

Elton et al. '90 1980±88 All Yes No

Hendricks, Patel

& Zeckhauser '93 1974±88 Equity Yes Yes

Goetzmann & Ibbotson '94 1976±88 All Yes Yes

Dromes & Walker '94 1971±90 Internationl Yes n/t

Kahn & Rudd '95 1983±90 Equity

1986±90 Fixed-Income Yes Yes Volkman & Wohar '95 1980±89 International Yes Yesc Grinblatt, Titman

& Wermers '95 1974±84 All Yes Yes

Malkiel '95 1971±90 Equity Yes Partiallyd

Elton, Gruber & Blake '96 1977±93 Stock No Yes

Gruber '96 1984±94 All Yes Yes

Notes:

n/r = not reported; n/t = not tested; n/c = no conclusion.

a_{Using annual data (as Jensen did), Mains found an average alpha ofÿ62 basis points,} but the average alpha becomes 9 basis points when the monthly data is employed. b_{There is no abnormal performance in the actual returns, net of all expenses bu the} risk-adjusted gross returns do exhibit some positive performance.

c_{The persistence in performance can be found in some low-management-fee funds but} not in the high-management-fee funds when the net returns are employed.

Datastream International data base. The return data is calculated on the basis of the reinvestment of gross dividends and therefore ignores tax and reinvestment charges. All dividends are assumed to be reinvested to purchase additional units of an equity or unit trusts at the closing price applicable on the ex-dividend date.2 Also, it is assumed that the effect of any informed trading on market-clearing prices is negligible (denoted as the i.i.d. assumption).3 _{All funds included in the study are funds with} mixed objectives and are survivors over the sample period. By using only those funds for which an annual return may be calculated, we omit all funds that existed for less than one year. We therefore exclude from the sample the year that funds do poorly and merge or fail.

(i) Weekly Returns

For each week, the return index (RI) is calculated as follows: RIt ˆRItÿ1_PIPIt

tÿ1 …1‡DYt† …1†

where: RIt = return index on dayt;

RItÿ1 = return index on previous day;

PIt…PItÿ1† = price index on day t(previous day);

DYt = gross dividend yield of the price index. With the return index, weekly returns for each fund can be calculated in a continuously compounded manner by taking the natural log of the return index for both individual stocks and for the market portfolio:

Continuously compounded returns…Rj† ˆX5

tˆ1

LN RIt RItÿ1: (ii) Market Rate of Return (Rm)

Grinblatt and Titman (1994) find that the choice of a benchmark has a large effect on inferences about performance. Fletcher (1995) added that these indices will probably be less accurate since the proportions and the composition of the index may vary greatly over time. Furthermore, the importance of a `fair' bench-mark is emphasised by Friend, Blume and Crockett (1970) when

the authors found some difference in performance that is not fully reflected in the estimated beta.

Grinold (1992) used a statistical test called the GRS4 _{test to} determine if a benchmark portfolio is efficient. The benchmarks tested were: the S&P 500, the FTA. the ALLORDS, the TOPIX, and the DAX. The results indicated that all of these benchmarks are not efficient except the DAX. Therefore, instead of using FTA as a benchmark, our study employs the UK fund managers return index as a proxy for market returns.5_{This return index is} a datastream-calculated index based on a representative group of equities in the same sector, and is derived similarly to the weekly returns index.

(iii) Risk-Free Rate of Interest (Rf)

A weekly risk-free rate of interest was derived from the 3-month Treasury bill as recorded in Datastream over the study period. The effective weekly rate of return is annualised as follows:

iˆ …1‡j=m†mÿ1; …2†

where: iis the effective interest rate per period;

j is the nominal interest rate, compounding mtimes per period.

As with most mutual fund studies, the mutual fund return data are subjected to survivorship bias. Funds that went out of business prior to December 31, 1995 are excluded from the data set. Brown, et al. (1992) have suggested that the survivorship bias effect on persistence of performance studies is accentuated by analysing a group of funds with divergent risk levels. However, survivorship bias in our study will be partially mitigated because we will be comparing survivors to other survivors' relative performance, instead of comparing each surviving fund to some absolute market index benchmark such as the FT100 Index. Moreover, there has been no major recession or unexpected event such as the October 1987 Crash during this 1989±1995 period.

The investment performance of an individual mutual fund is likely to contain both a skill component and a noise component. The skill component would cumulate over time, while the noise component would usually be serially independent so that its average would tend toward zero over time. Thus, there is a need

to choose a reasonably long period to diminish noise in performance, and at the same time to ensure that the skill level of the manager of the fund is unlikely to change. In our study, a five-year performance sample period is chosen so that both the management skill level and strategy for the fund are incor-porated in the results.

Since these funds are operating in different security classes, there is a need to adjust for the amount of risk each fund carries before they can be compared with each other. To solve this problem, risk-adjusted returns are also used to rank funds to test for persistence over the 1989±1995 period.

it ˆRpitÿ ‰Rft‡Bi…Rmt ÿRft†Š …3†

where: it is the Jensen risk adjusted performance measure;

Rpitis the return on fund iin period t; Rftis the riskfree treasury bill return;

Rmt is the return on the index (UK fund manager's return);

Bi is the beta coefficient for fund i.

The Jensen (1968) measure as mentioned above in equation (3) is employed. In applying the Jensen measure, several assumptions have to be made. They are the unconditional mean-variance efficiency of the benchmark portfolios, the existence of a riskless asset, and no binding constraints on investors6 _{(Fletcher, 1995). While studies have shown that the} Jensen measure is biased in the presence of timing information, there are studies showing that this bias of the Jensen measure is of little empirical significance. In particular, Grinblatt and Titman (1994), Cumby and Glen (1990) and Draper and Fletcher (1995) report similar inferences between the Jensen and positive period weighting measures, indicating the insigni-ficance of such bias.

In employing the Jensen measure in our study, each resulting

t will be paired with t‡1 and an ordinary least squares (OLS)

regression will be performed to determine the slope of the relationship between two periods as well as the statistical significance of the relationship. This will be conducted for the one-year, half-year, and monthly period. The risk-adjusted performance will improve consistency because all five periods ±

1990, 1991, 1992, 1993, 1994 and 1995 are now consistent with the proposed effect.

4. METHODOLOGY

To test for persistence in return rankings, funds are ranked in order of total cumulative raw as well as risk-adjusted returns for the entire study period. This comparison allows the effect of different manager holding horizons to be considered and also allows a comparison between the raw and risk-adjusted returns for each sub-period. However, those funds which did not exist for the entire period will be at a disadvantage in terms of overall raw return rankings.

(i) One-Year Mutual Fund Raw Returns

First, the total fund return over each successive one-year interval is studied. For each one-year period, only funds that existed for the entire one-year interval are considered. The prior one year's performance for the year 1990 is used to predict the performance for the subsequent year 1991 by employing the capital asset pricing model (CAPM):

E…Ri† ˆRf ‡Bi…RmÿRf† …4† whereE…Ri†is the expected return on portfolioi,Rfis the return on the risk-free asset,Rmis the return on market portfolio andBi is the portfolioi's (relative) systematic risk.

Similarly, the prior one year's performance is used to predict the performance for the subsequent one year ± 1992, 1993, 1994 and 1995. In particular, the performance of funds in 1990 are ranked and categorised as winners and losers, with accordance to whether their performance are above or below the median performance. Funds that are top half of the list are defined as winners and the bottom half as losers. If the statistical evidence shows that winners in period 1 remain as winners in period 2, the case for persistence of performance is proven. In a like manner, the same procedure is followed for the remaining one-year period of the study.

To analyse performance persistence, contingency tables similar to Goetzmann and Ibbotson (1994) are used. By definition, half

the funds are winners and half are losers in each period. And if performance does not persist, the numbers in each bin should be the same. There is evidence for persistence provided that the number of funds are higher in the diagonal bins (top left and bottom right).

OLS regression analysis is also used to investigate the performance persistence of these mutual funds.

Performt2ˆ‡BPerformt1‡" …5†

where `perform' is the raw returns or risk-adjusted returns. Henriksson and Merton (1981) suggest the managed portfolio's return will exhibit conditional heteroscedasticity because of the fund manager's attempt to time the market, even when stock returns are independently and identically distributed through time. Breen, Jagannathan, and Ofer (1986) show the importance of correcting for heteroscedasticity7 _{in return studies and} document the adequacy of White's (1980) correction. We use White's heteroscedasticity-consistent variance-covariance matrix.8 The adjustedt-statistic is calculated as follows:

t-statisticˆCoefficient

HSCE

where HSCEis the heteroscedastic-consistent standard errors. In addition, chi-square tests are employed so as to provide a more substantive measure of the interperiod performance consistency from one period to the next. This can be represented as (Keller et. al., 1990):

2_ˆ…OiÿEi†2

EI ; …6†

where: Oiis the observed number in each bin; Eiis the expected number in each bin;

2 _{follows a chi-square distribution with 1 degree of}

free-dom in the case of a two-by-two table and …Rÿ1† …Cÿ1† degrees of freedom in an R by C contingency matrix.

The chi-square statistic tests are used to the hypothesis that the actual distribution is 50% in every bin.9_{The critical value is 3.841} at the 95% confidence level.

To further substantiate the results, an additional quantitative measure of inter-period performance consistency is used ± the Spearman Rank Correlation Coefficient (SRCC) which is a nonparametric test of the predictability of performance ranks. The SRCC is calculated for the yearly return data based upon absolute rank in the period. The returns are ranked from 1 to 131 where the rank 1 = lowest and 131 = highest. Since there are not many ties in the rankings of the sample data, the following equation is employed to calculate the SRCC, denoted as Rs (Siegel et al., 1988):

Rs ˆ1ÿ_n6_n2di_ÿ2_1†; …7†

where di= returntÿ1ÿreturnt.

Following Vos, Brown and Christie (1995), these SRCC were then averaged, and the standard deviation of results was obtained giving an indication of the overall correlation between yearly rankings. The standard deviation of coefficient is represented as (Keller et al., 1990):

Rs ˆp_n1_ÿ1:

(ii) One-Year Mutual Fund Risk-Adjusted Returns

To correct for risk, Jensen's measure in equation (3) is employed. The one-year prior is a measure of the unanticipated portion of the fund return for each week. This can also be defined as the distance of the fund return above or below the security market line. The average weekly alpha over the one-year period is calculated and distinguished winners from losers in a similar manner to the raw returns.

Likewise, four empirical tests ± contingency table analysis of winners and losers, chi-squared independence tests, Ordinary Least Square (OLS) regression analysis of CAPM risk-adjusted excess returns, and an independent Spearman Rank Correlation Coefficient (SRCC) calculation are used to test the persistence of mutual fund managers' rates of risk-adjusted returns. Since alpha is a risk-adjusted standard of relative fund performance, any persistence in relative alphas is expected to be due to relative levels of management skill.

(iii) Half-Yearly and Monthly Mutual Fund Returns

The cross-sectional results of managers within a period are likely to be cross-correlated for style and other reasons. These `styles' can be defined as the relationship between fund characteristics and performance, and are not necessarily correctable by risk adjustment. In order to correct for cross-sectional dependence due to hidden factors such as the `style' factors or unidentified common variables in the funds, the number of independent time-period observations is increased by studying both six-month and one-month period results.

In the one-month period test, there are 60 independent time series observations of the multivariate distribution of mutual fund returns. Since there are 131 funds that have survived over the five-year period, we have a total of 7,860 observations. As for the six-month period test, there are 10 independent time series observations which give us a total of 1,310 observations. The Jensen measure uses the beta estimated from one-year of weekly data in the preceding tests. Using Jensen's performance measure, we rank these 131 funds each month. Regressions are performed relating each fund's rank to its prior month's rank.

(iv) Fund Variance

In each year, there will be funds shutting down due to their poor performance. As a result, some funds are missing in our data which leads to the problem of survivorship bias. Suppose that some of the funds have more volatile returns than other funds, the more volatile funds are less likely to survive. In the surviving funds, the more volatile funds will tend to have the best performance. This may then lead to a predominance of repeat-winners, as winner/losers would not survive.

To avoid potential selection bias, another test is conducted by studying the total fund performance over one-year periods covering the 1989±1995 time period. Essentially, it is suggested that the high-variability funds have more selection bias than low-variability funds. In particular, Brown et al. (1992) find that differential volatilities among funds have attributed to such bias. Therefore, we will then split the one-year results into high- and low-variability funds so as to see if the results are related to fund variance.

Specifically, the variances of the returns of all funds are measured over the entire period, and then ranked. The funds with variance above the median are classified as high-variance, while funds with variance below the median are classified as low-variance funds. Again, these high- and low-low-variance funds are further classified into winners and losers based on the median of the funds' returns.

5. RESULTS

In Table 2a and Table 3a, the two-way contingency table shows the numbers of funds that were winners in both periods, losers in both periods, winners then losers, and losers then winners. In addition, the percentage of period 1 winners and losers that become period 2 winners and losers are calculated. The combined results of all five periods can be seen in the last panel of each table.

From Table 3a, we can see that the numbers of funds in the diagonal bins (top left and bottom right) are relatively higher, providing evidence of persistence in each one-year interval period. However, this evidence of persistence is not very strong for the 1991±1992 period and 1994±1995 period. Confirmed by the chi-squared test with insignificant statistics of 0.619 and 0.191 respectively. This implies that the 1991 and 1994 performances are independent of the consecutive 1992 and 1995 performances respectively.

Table 2b reports the regression analysis which exhibits significant evidence of persistence at the 95% confidence level in all except the 1991±1992 period and the 1993±1994 period. Thus, we see, there is an apparent inconsistency between the two sets of results. This could be due to the raw returns not being normally distributed. As such, a nonparametric test such as the chi-squared tests may be more accurate.10_{Nevertheless, there is still} evidence that past performances are predictors of future returns since the estimated coefficients are all positive. As for the combined results, they indicate that the ratio associated with picking a winner is about 56/44 on the basis of past winning performance. Overall, there is strong evidence of persistence with a significantt-statistic of 4.257 and a chi-squared statistic of 12.094.

Table 2a

Two-Way Tables of Ranked Fund Raw Returns Over Successive One-Year Intervals 1991 Winners Losers Winners 38 27 (58.5%) (41.5%) 1990 Losers 27 39 (40.9%) 59.1% 2_ˆ4:039* 1992 Winners Losers Winners 35 31 (53.0%) (47.0%) 1991 Losers 30 35 (46.2%) (53.8%) 2_ˆ0:619 1993 Winners Losers Winners 40 25 (61.5%) (38.5%) 1992 Losers 25 41 (37.9%) (62.1%) 2_ˆ7:336* 1994 Winners Losers Winners 38 28 (57.6%) (42.2%) 1993 Losers 27 38 (41.5%) (58.5%) 2_ˆ3:368 1995 Winners Losers Winners 34 32 (51.5%) (48.5%) 1994 Losers 31 34 (47.7%) (52.3%) 2_ˆ0:191

Table 2a (Continued)

Combined Results in Successive Periods

Winners Losers Initial 185 143 Winners (56.4%) (43.6%) Initial 140 187 Losers (42.8%) (57.2%) 2_ˆ12:094* Notes:

Winner-winner indicates the number of above median funds in the year that were also above median funds in the following year. Loser-winner, Winner-loser, and Loser-loser are defined similarly. The percentage of period 1 winners and losers that become period 2 winners and losers can be seen in parentheses. Chi-squared statistics are calculated as:

2_ˆ…OiÿEi†2

Ei

whereOiis the observed number in each bin andEiis the expected number in each bin.

2_{follows a chi-square distribution with 1 degree of freedom in the case of a two-by-two} table and…Rÿ1† …Cÿ1†degrees of freedom in anRby contingency matrix. * Significant at the 0.05 level (two-tailed test) with a critical value of 3.841.

Table 2b

Regression of Last Year Ranked Raw Returns Over Successive One-Year Intervals

Dependent Independent Intercept Slope T-Stat R2

Variable Variable 1991 1990 0.2526 0.3428 4.0040* 0.1552 1992 1991 0.3781 0.0071 0.0748 0.0562 1993 1992 0.3306 0.2691 2.7835 0.0737 1994 1993 0.3934 0.0771 0.8389 0.0282 1995 1994 0.2792 0.2019 2.1546* 0.0815

Combined Regression Results: Following Preceding

Period Period 0.3186 0.1765 4.2575* 0.0572

Notes:

Regression analysis is used to investigate the persistence of these mutual funds. Coefficientbis estimated through the `market model' using an ordinary least squares (OLS) technique, from a regression of period 2 performance with period 1 performance. The market model can be represented as:

Performance…t2† ˆa‡b Performance…t1† ‡"

where `performance' is the raw returns or risk-adjusted returns anda,bas constants with"

as a disturbance term.

Table 3a

Two-Way Tables of Ranked Fund Raw Alphas Over Successive One-Year Intervals 1991 Winners Losers Winners 40 18 (69.0%) (31.0%) 1990 Losers 18 40 (31.0%) (69.0%) 2_ˆ16:69* 1992 Winners Losers Winners 40 26 (60.6%) (39.4%) 1991 Losers 25 40 (38.5%) (61.5%) 2_ˆ6:421 1993 Winners Losers Winners 40 25 (61.5%) (38.5%) 1992 Losers 25 41 (37.9%) (62.1%) 2_ˆ7:336* 1994 Winners Losers Winners 36 29 (55.4%) (44.6%) 1993 Losers 29 37 (43.9%) (56.1%) 2_ˆ1:717 1995 Winners Losers Winners 33 33 (50.0%) (50.0%) 1994 Losers 32 33 (49.2%) (50.8%) 2_ˆ0:007

Table 3a (Continued)

Combined Results in Successive Periods

Winners Losers Initial 189 131 Winners (59.1%) (40.9%) Initial 129 191 Losers (40.3%) (59.7%) 2_ˆ22:5* Notes:

Jensen's (1968) risk-adjusted performance measure is used to evaluate the mutual fund performance. This is defined as:

tˆRptÿ ‰Rft‡B…RmtÿRft†Š

whereRptis the individual fund portfolio unadjusted total return for periodt;Rfis the treasury bill return; Rmt is the UK fund managers return; B is the regression slope coefficient. The(alpha) estimates the excess returns averaged over the sample period used to estimate the characteristic line regression. It indicates whether the portfolio manager is superior or inferior in market timing and/or stock selection. A significant positive value giving consistent positive residuals would imply that the manager is superior.

* Significant at the 0.05 level (two-tailed test) with a critical value of 3.841.

Table 3b

Regression of Last One-Year Ranked Alphas Over Successive One-Year Intervals

Dependent Independent Intercept Slope T-Stat R2

Variable Variable 1991 1990 0.1839 0.5407 6.8602* 0.3202 1992 1991 0.1432 0.4006 5.0350* 0.2758 1993 1992 0.3965 0.2056 2.0714* 0.0423 1994 1993 0.4195 0.0509 0.5545 0.0246 1995 1994 0.3278 0.1179 1.2287* 0.0509

Combined Regression Results: Following Preceding

Period Period 0.2885 0.2613 6.4055* 0.0930

Notes:

Like the raw returns, regression analysis is used to investigate the persistence of these mutual funds. Coefficientbis estimated through the `market model' using an ordinary least squares (OLS) technique, from a regression of period 2 performance with period 1 performance.

The Spearman Rank Correlation Coefficient is calculated for the yearly return. For the one-year observation interval between 1990±1995, the mean coefficient calculated is 0.188 with a standard deviation of 0.088. Since the mean coefficient is positive, this indicates that there is correlation between the annual performance rankings. That is, winners in period 1 have a higher chance of being winners in period 2. The standard deviation is small indicating a substantial amount of stability ± providing further evidence that past performance shows predictive power.

Contingency tables have also been constructed based on Jensen measures in order to adjust returns to take into account the different levels of risk and to provide a more robust measure of excess performance. Table 3a shows the results with the repeat-winners phenomenon occurring in four out of five one-year periods in the study. Interestingly, the 1994±1995 period shows weak evidence of persistence. There are almost an equal number of funds in each bin, especially during the 1994±1995 period. However, the combined results still exhibit evidence of persistence.

Like the contingency analysis, the regression analysis in Table 3b shows positive slope of coefficients for all one-year intervals. Yet the evidence is weak in the 1993±1994 and the 1994±1995 period with insignificant t-statistics. Nevertheless, the combined regression results exhibit strong evidence of persistence, becoming even more significant after adjustment for risk.

The chi-squared tests exhibit consistent results with the regression analysis. There is a strong evidence of persistence in all one-year intervals except for the 1993±1994 and 1994±1995 periods. The chi-squared statistics of 1.717 and 0.007 for the 1993±1994 and 1994±1995 periods are lower than the critical value, showing that we can be 95% confident that the data is independent from one period to the next. Thus, we can see that even though most years' winners and losers repeat, occasionally there is no such effect. Such an outcome could be due to two possibilities. One, persistence is correlated across managers. This is most likely due to a common strategy that is not captured by `style' factor or risk adjustment procedures. Brown and Goetzmann (1995) suggest that this correlation in persistence is probably due to individual managers selecting stocks that are

overlooked or ignored by other managers. Winning could also be due to a group phenomenon. This correlation in persistence is consistent with the findings of Grinblatt, Titman and Wermers (1995) and Connor and Korajczyk (1991) suggesting herding behaviour amongst equity fund managers and correlated dynamic portfolio strategies such as the portfolio insurance respectively.

Secondly, this is because the market fails to fully discipline underperformers, allowing their presence in the sample to contribute to the relative persistence phenomenon. While there is an increased probability for the losing funds to disappear or merge, not all of them are eliminated.

The results of the Spearman Rank Correlation Coefficient for risk-adjusted returns yield similar conclusions to the raw returns.

Table 4

Two-Way Tables of Ranked Fund Raw Returns Over Successive One-Year Periods. Grouped by High-Variance Funds, Low-Variance Funds,

and Total Sample

High-Variance Low-Variance Total Sample Next Year Next Year Next Year Winners Losers Winners Losers Winners Losers

Initial Year 1990 Winners 33 27 5 0 38 27 Losers 26 39 1 0 27 39 1991 Winners 34 18 1 13 35 31 Losers 30 18 0 17 30 35 1992 Winners 12 0 28 25 40 25 Losers 15 4 10 37 25 41 1993 Winners 8 14 30 14 38 28 Losers 3 10 24 28 27 38 1994 Winners 6 12 28 20 34 32 Losers 3 18 28 16 31 34 Notes:

Winners and Losers are ranked and determined over one-year periods, and then ranked again over the subsequent one-year periods. This gives us five separate periods in which to compare our results. Each one-year result is split into the high- and low-variance funds (using median over the entire period 1990±1995 as the benchmark), and then combined to the total sample.

The mean coefficient is positive at 0.3110 with a sufficiently stable coefficient, showing persistence in the ranking relationship.

As suggested by the models of selection bias, the high-variability funds have more selection bias than low-high-variability funds. In light of the potential selection bias, the yearly results are split into high- and low-variability funds. Table 4 presents the two-way tables of ranked fund raw returns over successive one-year periods. The groupings are quite different from one another. There is no repeat-winner hypothesis in all groupings: while sometimes the hypothesis prevails in both groupings, in others it only prevails in one or in none of the categories.

The results of Table 4 are then summarised and interpreted in Table 5, showing the number and percentage of repeat-winners or repeat-losers. At the same time, the time series results are also presented by counting the number of years that there are a majority of repeat winner or repeat-losers in each category. Since the high-variance funds demonstrate this repeat-winner phenomenon as strongly as the low-variance funds, this indicates

Table 5 Summary of Table 4

High-Variance Low-Variance Total Sample Next Year Next Year Next Year Winners Losers Winners Losers Winners Losers

By Count Initial Year Winners 93 71 92 72 185 143 Losers 77 89 63 98 140 187 By Percentage Initial Year Winners 56.7 43.3 56.1 43.9 56.4 43.6 Losers 46.4 53.6 39.1 60.9 42.8 57.2 By Number of Years* Initial Year Winners 4 1 4 1 5 0 Losers 1 3 0 3 0 5 Notes:

* Number of years in which winner (loser) funds from the prior year were in the majority in the winner or loser category in the successive year. Ties are not counted.

that survivorship bias is mitigated in our performance study. From Table 5, we can see that the results support the repeat-winner/loser hypothesis with a percentage of 56.4% and 57.2% respectively.

(i) Half-Yearly and Monthly Mutual Fund Returns

To maximise the number of independent time periods, the half-yearly and monthly returns are also studied. Not surprisingly, there is no evidence supporting the winner-loser hypothesis. This is because the prediction of each half-yearly and monthly result is much noisier than the predictions based upon longer-period results. Tables 6, 7 and 8 present the coefficients, t-statistics and R-squared for both raw returns and risk-adjusted returns over the half-yearly and monthly interval respectively. From the tables we can see that all coefficients are negatively sloped, exhibiting no evidence of persistence. This means that funds which are winners (losers) in the first period did not remain as winners (losers) in the subsequent period. The t-statistics are not significant at the 95% confidence level for all except the monthly alpha ranks. Since the t-statistics for the monthly alpha appear significant, what does this tell us? This question will be answered below.

Table 6

Regression of Monthly Relative Performance on Preceding Monthly Relative Performance

Coefficient T-Statistic R2

Raw Returns Ranks ÿ0.0069 ÿ0.6557** 0.0000

Alpha Ranks ÿ0.0502 ÿ4.3583 0.0025

Notes:

Monthly raw returns and Jensen measures are used to test performance persistence. There are 60 independent time series observations of the multivariate distribution of mutual fund returns. Since there are 131 funds that have survived over the five-year period, we will have a total of 131 60 or 7,860 observations. The Jensen measure uses the beta estimated from one-year period of weekly data in the preceding tests. Using the Jensen's performance measure, we then rank these 131 funds each month. Regressions are performed on each fund's rank on its prior month's rank.

We have:

a_ˆR

tÿbRtÿ1: …8†

In our study, we have 131 observations for period 1 and 2. WithRt andRtÿ1 as 0.50 andb*asÿ0.0502 (refer to Table 6), substitute

the values into equation (8). This gives the following: a_{ˆ0:5ÿ0:5…ÿ0:0502†;}

ˆ0:5251:

Given the values of a*, the estimated return equation can be represented as:

Table 7

Regression of Annually Relative Performance on Preceding Semi-Annually Relative Performance

Coefficient T-Statistic R2

Raw Returns ± Ranks ÿ0.0504 ÿ1.9033** 0.0025

Alpha Ranks ÿ0.0298 ÿ1.0639** 0.0009

Notes:

Like the monthly relative performance test, semi-annual raw returns and Jensen measures are used to test performance persistence. The independent and dependent series for the regression of raw returns is a vector of 131 10 or 1,310 observations. The Jensen measure uses the beta estimated from one-year period of weekly data in the preceding tests. Using the Jensen's performance measure, we then rank these 131 funds each month. Regressions are performed on each fund's rank on its prior month's rank.

** Not significant at the 0.05 level (two-tailed test).

Table 8

The Alpha Results of the Standard Errors of and HCSEs

Dependent Independent

Variable Variable Standard Error HSCEs

1991 1990 0.0795 0.0788 1992 1991 0.0778 0.0796 1993 1992 0.0876 0.0992 1994 1993 0.0895 0.0917 1995 1994 0.0881 0.0959 Combined 0.0381 0.0408

R_tˆa‡bRtÿ1;

R

t ˆ0:5251‡Rtÿ1…ÿ0:0502†:

If the ranked returns for period 1 is 1, that is Rtÿ1ˆ1, then: Rt ˆ0:5251‡1…ÿ0:0502†;

ˆ0:4749;

and if Rtÿ1ˆ0, then:

Rt ˆ0:5251‡0…ÿ0:0502†

ˆ0:5251:

Thus, the coefficient can be interpreted that the bottom fund (with a ranking of one) is expected to be in the 47th percentile, while the top ranked fund (with a ranking of zero) would be expected to be in the 53rd percentile for the monthly alpha returns since the regression line is negatively sloped.

(ii) Further Analysis

In the following section we report tests to see whether heteroscedasticity and serial correlation are a problem. The tests in Tables 8 and 9 suggest these are not a problem.

Table 9

Durbin-Watson Results for Both Raw Returns and Alpha Returns Over the One-Year Interval

Dependent Independent Raw Returns Alpha Returns Variable Variable Durbin±Watson Durbin±Watson

1991 1990 2.02 1.87 1992 1991 2.01 2.01 1993 1992 2.01 1.99 1994 1993 2.00 1.98 1995 1994 2.11 2.08 Combined 2.06 2.05 Notes:

In our study, the DW values for both raw returns and alpha returns are pretty close to 2 in all cases (see Table 9) Since there is no evidence of serial correlation, we need not pursue further into the first-order autoregressive AR1 and Augmented Dickey-Fuller (ADF) test.11

6. CONTEXT: VALIDITY OF THIS STUDY (i) Bootstrapped

Though we have adjusted the returns using Jensen's measure, we are still concerned that alpha has not been adequately adjusted for relative risk. Brown et. al. (1992) regarding survivors' samples:

A manager who takes a great deal of risk will have a high probability of failure. However, if he/she survives, the probability is that this manager took a large bet and won. High returns persist . . . this is total risk effect; risk adjustment using beta or other measure of non-idiosyncratic risk may not fully correct it.

As a result, this has called into question whether the evidence of persistence is due to ability to predict or whether it is just a long-term phenomenon that is related to risk.

In order to distinguish the two possibilities, we performed a bootstrapped test 100 times on the yearly returns (Efron and Gong, 1983). Specifically, we bootstrapped the joint distribution of yearly fund returns by randomising with replacement over the 1989±1995 period. In doing this, the cross-sectional relationship for each year is preserved, but the time series relationship is destroyed. A regression test of this year's rankings upon last year's rankings is then performed 100 times. From each iteration, we derive the coefficient, t-statistic and R2_{. The distribution of} these three statistics then provides a sample with which the significance of the original regression may be tested.12

Unlike Monte Carlo results, the bootstrap method allows the construction of significance levels of the test statistics which are free from distributional assumptions. In addition, the presence of small sample bias due to the lagged correlation between the independent and the lagged dependent variable is minimised by employing the bootstrap method.

The results can be seen in Table 10, providing the median coefficient, t-statistic and R2_{. These statistics derived from the} bootstrapped test are rather close to the original regression. The median t-statistic is 4.984, indicating that there are long-term differences in means across funds. As for the coefficient, it is observed as 0.188 which is below the others in the bootstrap sample. The R2 _{is similar. There is little difference between the} observed variables and the bootstrap variables, indicating little

bias in our study. Overall, our study is slightly weakened by the bootstrapped test, but is still valid.

(ii) Survivorship Bias

In a recent study, Grinblatt and Titman (1989) report that the survivorship effect only impacts about 0.1 to 0.4 percent return per year measured on a risk-adjusted basis before transaction costs and fees. Likewise, Brown, Goetzmann, Ibbotson and Ross (1992) show that the net effect of survivorship bias on average risk-adjusted returns for all managers is very small (approximately 0.4 to 0.6 percent per year on a risk-adjusted basis for the 5 to 10 percent cutoff examples).

7. IMPLICATIONS (i) Investment Implications

To ensure that our results were not due to unusual and extreme persistence high performance of one or two funds, we removed the two funds that appeared most often in the top quantile of the periods and recalculated the performance period averages. A two-year period 1990±1991 is used to categorise the subsequent two-year period 1992±1993; 1992±1993 is the initial period for the

Table 10

Regression Statistics From Yearly Relative Performance Bootstrapped Tests

(Based on 100 Bootstrapped Iterations)

Observed Median 0.95 Quantile 0.99 Quantile

Coefficient 0.1881 0.1927 0.2024 0.2051

T-Statistic 4.8956 4.9842 5.2680 5.3375

R2 _{0.0354 0.0367 0.0422 0.0432}

Notes:

The bootstrapped test is performed 100 times on the yearly returns. Specifically, we bootstrapped the joint distribution of yearly fund returns by randomising with replacement over the 1989±1995 period. A regression test of this year's rankings upon last year's rankings is then performed 100 times. From each iteration, we derive the coefficient, t-statistic andR2_{. The distribution of these three statistics then provides a} sample with which the significance of the original regression may be compared.

1994±1995 rankings. The funds are then ranked and classified as winners and losers by employing median as a benchmark. The two-year risk-adjusted return performance result is presented in Table 11. The resulting average performance alpha for the remaining funds still exhibits evidence of persistence for the combined periods. In particular, the ratio associated with picking a winner based upon past performance is about 54/46.

From Table 11, we can see that past performance has definite information about future performance, and this information works for periods 2-years into the future as well as 1-year into the future (shown in Table 4). `Hot hands' may be an important phenomenon, but there is a longer persistence in performance than has been expressed in the hot hands literature.

From our results in Table 11 it appears that an investor may be better off hiring top-performers based upon past performance results since the current high-flier manager is likely to be next period's top-performer. Therefore, it may be possible to fashion investment strategies that will permit investors to earn excess returns.

In addition, we present the two-year period risk-adjusted return performance into four different quartiles ± top1/4, second1/4, third1/4 and fourth1/4. Our results in Table 12 are pretty similar to Goetzmann and Ibbotson (1994) with the top-quartile showing

Table 11

Two-Way Tables of Ranked Alphas Over Successive Two-Year Intervals. Combined Results Over the Periods 1990±1991, 1992±1993, 1993±1994

and 1994±1995

Two-Way Results by Count and Percentage

Successive Period Winners Losers Initial 66 57 Winners (53.7%) (46.3%) Initial 56 68 Losers (45.2%) (54.8%) Notes:

The initial two-year period 1990±1991 is used to predict performance for the subsequent two-year period 1992±1993. Similarly, 1992±1993 is the initial two-year period for 1994± 1995 period rankings. The funds are then ranked and classified as winners and losers by employing median as a benchmark.

by far the best results in the successive periods. The lower the initial quartile ranking, the worse the subsequent performance. This can be seen when you compare the initial top-quartile of 34 and fourth-quartile of 19 with the initial second-quartile of 16 and fourth-quartile of 10. The results in the four rows were compared with a random distribution usingX2 _{tests. Rows 2 and} 4 are not random at the 1% level and 1 is not random at the 10% level. The results in rows were compared with each other: 1 and 2, 1 and 4, 2 and 3 and 2 and 4 are significantly different at the

Table 12

Four-Way Tables of Ranked Alphas Over Successive Two-Year Intervals. Combined Results Over the Periods 1990±1991, 1992±1993, 1993±1994

and 1994±1995 PlusX2_{Tests of Significance} Part A: Four-Way Results by Percentage

Successive Period

Top1/4 Second1/4 Third1/4 Fourth1/4 Initial Period (%) (%) (%) (%)

Top1/4 34 26 21 19

Second1/4 16 36 40 10

Third1/4 25 21 24 31

Fourth1/4 24 16 16 40

Part B:X2_{Tests on Quartile Rows}

A number ofX2_{tests were undertaken to see if the performance in the various} quartiles is significantly different working across the rows.

First the results for rows 1, 2, 3 and 4 were compared with a random

distribution. TheX2_{values were 7.54, 32.12, 3.24 and 18.54 respectively. This} means that rows 2 and 4 are significantly different from a random distribution at the 89% level and 1 is significantly different at the 10% level.

Then the rows were compared with each other:

1 compared with 2 X2_{= 22.48 1% significance}

1 compared with 3 X2_{= 6.85 1% significance}

1 compared with 4 X2_{= 14.20 1% significance} 2 compared with 3 X2_{= 28.03 1% significance} 2 compared with 4 X2_{= 47.69 1% significance} 3 compared with 4 X2_{= 3.40 50% significance.}

Notes:

Instead of classifying the funds into winners and losers, the combined results are presented in four different quartiles ± Top1/4, Second1/4, Third1/4 and Fourth1/4.

1% level. Thus the behaviour and persistence of performance of managers in these different quartiles is significantly different.

The other interesting observation from the two-year performances is that funds which are in the third or fourth initial quartile turn up to be top in the subsequent quartile. Thus, it is tempting to assume that there is a tendency for certain managers to alternate between first and second quartiles but the results do not exhibit any strong evidence supporting such alternate phenomenon.13 _{Though this result may not be a good} guide to beat the market, it does help investors to improve their chances of superior relative performance based on past performance.

Since there is evidence of persistence in our study, this may suggest that there are two types of investors in the market. The first type being the `superior' investors (that is, investors with superior information) while the latter type being known as the `momentum' investors (one who buys past `winners' and sells past `losers') as suggested by Grinblatt and Titman14_{(1989 and} 1993) and Grinblatt, Titman and Wermers15_{(1995) respectively.} It is said that both types of investors contribute to the positive performance of mutual funds.

8. CONCLUSION

In the United Kingdom, Brown and Draper (1992) demonstrated evidence of persistence using data on 550 pension managers from 1981 to 1990. Our research examined managed funds from 1989 onwards and provided evidence of persistence performance. We investigated persistence of performance for raw returns and risk-adjusted returns and found that past returns and relative rankings are useful in predicting returns and rankings, even after adjusting for risk. Both 1- and 2-year alphas convey information about future performance. We controlled for volatility by dividing funds into high-variance and low-variance funds but their relative performance results continue to exhibit repeat-winner patterns.

APPENDIX A1

The Managed Fund Sample

1. Murray Enterprise 2. Scottish Mortgage 3. TR Property Investment 4. Brunner Investment 5. Martin Currie Pacific 6. General Cons Capital 7. Jupital Intl. Green Ord. 8. Mercury Keystone 9. Dunedin Enterprise 10. North American Gas 11. Fleming Cont. Europe 12. Electric & General 13. Witan Investment Co. 14. Anglo & Overseas 15. Exploration

16. Mid Wynd International 17. Lowland Investment 18. Majedie Investment 19. British Investment 20. TOR Investment Capital 21. Yeoman Investment 22. Govett Strategic 23. Baring Tribune 24. Murray Income 25. Fleming Enterprise 26. Derby Trust Capital 27. Investment Company 28. Albany Investment 29. Overseas Investment 30. Fleming American 31. Temple Bar 32. Rights & Issues Inc. 33. Kleinwort Charter 34. Scottish Eastern 35. Merchants Trust 36. TR High Income 37. American Trust 38. Foreign & Colonial 39. Dunedin Worldwide 40. Dunedin Inc. Growth 41. Edinburgh Investment 42. Electra Investment 43. Hotspur Investment 44. Scottish American 45. Candover Investments 46. Shires Investment 47. Gartmore Emerging Pacific 48. TR Technology Ord. 49. First Philippine 50. Abtrust New Dawn 51. Edinburgh Dragon Trust 52. TR Pacific Investment 53. Pacific Assets

54. New Zealand Investment 55. North Atlantic SMCOs 56. Sumit

57. Abtrust New Thai 58. Turkey Trust 59. TR Far East Income 60. London American GW. 61. Jove Investment Capital 62. Kleinwort Overseas 63. Fleming Far Eastern 64. Thompson Clive 65. Pacific Horizon 66. Rit Capital Partners 67. Murray Smaller Markets 68. Govett Oriental 69. Gartmore American Secs. 70. Primadona 71. Law Debenture 72. Thornton Asian Emerging 73. Paribas French Investment 74. Gartmore European 75. Finsbury Trust 76. British Empire Secs 77. Throgmorton Trust 78. River Plate Capital 79. Murray Ventures 80. Bankers Investment 81. Henderson Strata 82. English & Scottish 83. Murray International 84. Olim Convertible Ord. 85. Fleming Overseas 86. Equity Consort Portfolio 87. Monks Investment

88. I & S Optimum Inc. Ord. 89. Greenfriar

90. M & G Dual Capital 91. Personal Assets 92. TR City of London 93. Fleming Fledging 94. Baring Stratton 95. Alliance Trust 96. Second Alliance 97. Glasgow Income 98. Securities Trust Sctl. 99. Ldn & St. Lawrence 100. Flem. Inc. & GW Cap. 101. Fleming Claverhouse 102. British Assets 103. Scottish Investment 104. TR Smaller Cos. 105. Fleming Merchantile 106. Danae Invt. Inc. 107. Fulcrum Invt. Inc. 108. Capital Gearing 109. Fleming High Income 110. Continental Assets 111. Lazard SM. Equities 112. Parambe

113. Flem. Geared I & A 114. Moorgate Investment 115. German Smaller Cos. 116. Dunedin Smaller 117. Fleming Japanese 118. Kleinwort Dev. F.D. 119. I & S UK Smaller 120. Baillie Shin Nippon 121. Baillie Giff Japan 122. New Throg. 83 Cap. 123. GT Japan Investment 124. Archimedes Inc. 125. Radiotrust 126. Gresham House 127. Exmoor Dual Inc. 128. Scottish Nat Capital 129. Kleinwort Smaller 130. Updown Investment 131. New Market Venture

NOTES

1 The measures include: (1) a measure of return relative to the market, (2) the excess return from a single index model, (3) the excess return from a four index model.

2 For unit trusts, the closing bid price is used.

3 Admati and Ross (1986) discuss the inappropriateness of the performance measures (Sharpe, Treynor and Jensen) should this assumption be relaxed. 4 The GRS test was introduced by Gibbons, Ross and Shanken (1989) to test the possibility of outperforming this benchmark based on Markowitz's mean-standard deviation notion of efficiency. Its assumptions are: the process that generates the returns does not change with time, and the returns are normally distributed.

5 Dybvig and Ross (1985) show that arbitrarily inefficient portfolios may yield positive Jensen measures if an inefficient benchmark portfolio is used. 6 In specific: Roll (1978) stresses on the importance of mean-variance

efficiency of benchmark; Dybvig and Ross (1985) and Green (1986) show the usefulness of the Jensen measure depends upon the existence of a riskless asset; Best and Grauer (1990) and Grauer (1991) highlight the importance of assuming that investors face no binding investment constraints by illustrating that the Jensen measure can be non-zero if investors face binding constraints on investment.

7 Henriksson (1984) examined the market timing performance of 116 mutual funds using monthly data from the 1968±1980 period. He found that only three funds (one fund) had market timing ability at the 5% (1%) confidence level. He also found evidence of heteroscedasticity. However, after correcting for heteroscedasticity in the regression model, the results remain similar. Chang and Lewellen (1984) examined monthly returns on 67 mutual funds during the 1971±1979 period by employing Henriksson± Merton parametric test. They ignore the presence of heteroscedasticity and relied on Henriksson's results that correction for heteroscedasticity did not change the nature of his conclusion.

8 Besides the White's test, we can also carry out a Monte Carlo evidence presented in Hsieh (1983) or to carry out generalised method of moments presented in Hansen (1982) so as to correct for heteroscedasticity. 9 Care must be taken in interpreting the statistical significance of the 2

values. Since the identification of managers as winners and losers is actually ex-post, we should expect to find the winners-following-winners result at least 50% of the time.

10 Moreover, when we test the regressions using PcGive, the results show that the distribution of returns are not normally distributed.

11 The purpose of these tests is to `whiten' the residual errors.

12 A detailed bootstrap test is illustrated in Efron and Gong (1983) where they explore the connections between the various non-parametric methods, and also the relationship to familiar parametric techniques. In particular, they examine the `error' which refers to the bias and standard error of an estimator, or the error rate of a prediction rule.

13 This alternate phenomenon is similar to Donald (1994) but we would think our results are more accurate because we take into account the risk. 14 Grinblatt and Titman observed a positive relation between momentum

trading and performance, suggesting that the positive performance of mutual funds may be generated by superior information.

15 Grinblatt, Titman and Wermers (1995) find that 77% of the mutual funds were `momentum investors' buying stocks that were past winners. However, this is not systematic with selling losers. In particular, their results indicate that both the tendency of individual funds to buy past winners as well as to `herd' (buying and selling stocks at the same time) are highly correlated with fund performance.

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