short term persistance in mutual funds performance

8/10/2019 Short Term Persistance in Mutual Funds Performance

1/23Electronic copy of this paper is available at: http://ssrn.com/abstract=962829

SHORT-TERM PERSISTENCE IN MUTUAL FUNDS PERFORMANCE: EVIDENCE FROM INDIA

Prof. Sanjay Sehgal1 & Mr. Manoj Jhanwar2

AbstractIn this paper, we examine if there is any short-term persistence in mutual funds performance in the

Indian context. We find no evidence that confirms persistence using monthly data. Using daily data, weobserve that for fund schemes sorted on prior period four-factor abnormal returns, the winners portfolio

does provide gross abnormal returns of 10% per annum on post-formation basis. The economic feasibilityof zero-investment trading strategies that involve buying past winners and selling past losers is however in

doubt. This is owing to the fact that these strategies generate low gross returns and that the winners

portfolios involve higher investment costs than losers portfolios, thus destroying a major portion of extra-

normal returns. Our empirical findings are consistent with the efficient market hypothesis and haveimplications for hedge funds and other managed portfolios who rely on innovative investment styles,

including the "fund of funds" trading strategies that implicitly assume short-term persistence.

Key words: Mutual Funds, Fama- French Model, Performance Evaluation, Multifactor Asset Pricing,

Short Term Persistence, Hedge Funds.JEL Classification Codes: C12, C13, C51, G11, G12, G23

1. INTRODUCTION

Mutual funds are a primary vehicle for channelising savings of small investors

into financial markets. As on June 3, 1996, Association of Mutual Funds of India(AMFI) reports 29 mutual funds offering 592 schemes with an investment in assets of

about 60 billion USA dollars. There are public sector mutual funds sponsored by banksand other financial institutions as well as private sector mutual funds, including those

with from foreign ventures. Given the vast size of the industry and its implications for

financial markets it is important that a comprehensive evaluation of mutual fund schemesbe performed.

The performance evaluation shall bring to light if some mutual fund managers

possess better security selection skills and that this ability persists, allowing astuteinvestors to predict performance from past results.

From an academic perspective, assuming the existence and persistence of mutualfund managerial ability is an important test of efficient market hypothesis. Evidence of

persistence will support the rejection of the semi-strong form. Grossman and stiglitz

1University of Delhi, Email: [email protected], [email protected] Delhi, Email: [email protected]
mailto:[email protected]:[email protected]


2/23Electronic copy of this paper is available at: http://ssrn.com/abstract=962829

(1980) argue that there must be a reward for the costly endeavour of seeking new

information. In the context of mutual fund performance, some mutual fund managers areexpected to have an informational advantage. Berk and Green (2004), however, show

theoretically that such an informational advantage will be short-lived when the investors

direct their capital to recent winners. Thus making the industry competitive. The

superior performance will also be short-lived in the presence of managerial turnover.[See Chevalier and Ellison (1999)]. The objective of this paper is to determine

empirically if the ability persists over a short horizon. The study specifically examines

the following propositions. Is there a short-term persistence in the performance of mutualfund managers owing to stock selection skills? Do the abnormal returns provided by the

trading strategies based on persistence vary with alternative portfolio formation criteria?

Are these abnormal returns explained by common risk factors and persistent differencesin mutual fund expenses?

The study contributes to the literature in two ways. First, it provides evidence onshort-term persistence in mutual funds performance for India, an emerging market

setting. The out of sample test enriches the literature as the previous work has mainlyconcentrated on mature markets. Secondly, previous empirical work has used either

monthly or daily data. We use both daily and monthly data in our research. This helps usto analyse if any market micro-structure issues affect over results.

2. A BRIEF REVIEW OF LITERATURE

The empirical literature on persistence in mutual funds performance relates to

both long as well as short-term horizons. With some exceptions, the majority of studiesfind little evidence that fund managers generate positive abnormal returns over long

horizons by following either a stock selection or a market timing strategy. Examplesinclude Jensen (1969) and Elton, Gruber, Das and Hlavka (1992) for stock selection over

periods of 10-20 years, and Treynor and Mazuy (1966) and Henriksson (1984) for market

timing over periods of 6-10 years. A number of studies, however, find evidence thatstock selection ability persists over periods as short as one year.

These studies include Hendricks, Patel and Zeckhauser (1993), Goetzmann and

Ibbotson (1994), Brown and Goetzmann (1995), Grinblatt Titman and Wermers (1995),Gruber (1996), Carhart (1997), Daniel Grinblatt, Titman and Wermers 1997), Nofsinger

and Sias (1999), Wermers (1999) and Grinblatt and Keloharju (2000) and Bollen and

Busse (2005).

Most of these papers attribute short-term persistence, at least in part, to fund

managers skill. Grinblatt, Titman and Wermers (1995) and Carhart (1997), however,argue that the superior performance of stock funds is a result of the momentum effect of

Jegadeesh and Titman (1993). After including a momentum factor in his return model,

Carhart finds that persistence largely disappears except among the lowest performer,where it arises from persistently high expenses. This result suggests that fund managers

possess little stock selection skill, since top performing funds generate their superior

returns simply by holding stocks that have recently had high returns.

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Most persistence studies have in general used monthly returns. Bollen and Busse(2005) re-examine the issue of persistence in mutual funds performance using daily data

and focus on a relatively short measurement period of three months. They rank funds

quarterly by abnormal returns and measure the performance of each decile the following

quarter. The average abnormal return of the top decile in the post ranking quarter is 39basis point. The post-ranking abnormal return disappears when funds are evaluated over

longer periods. These results suggest that superior performance is a short-lived

phenomenon.

3. DATA

The data comprises of dividend-adjusted Net Asset Values (NAVs) for 59 natural

fund schemes from January 2000 to December 2004. 57 of the sample schemes have a

re-investment option and hence we use their re-investment based NAVs. All the sample

schemes are open-ended in nature and are predominantly equity-based with growth and

growth-income as their objectives. The NAV values are used to estimate - percentagedaily and monthly returns for the sample schemes. We also collect information about

entry load and management expenses for the sample funds. The data source is ICRAMutual Funds Software. The data set is limited due to non-availability of regular NAV

and expenses information both cross-sectionally as well as over long periods of time.

We also use individual securities data for the construction of size, value and

momentum factors in returns both on daily and monthly basis. The data includes daily

share prices for 452 companies that form part of the BSE-500 index from January 1999 toDecember 2003. The sample securities account for more than 90% of market

capitalisation and market trading activity. Hence, the sample set is fairly representativeof market performance. The share prices are adjusted for capitalisation changes, such as

bonus, rights and stock splits and they are used to compute percentage returns on the

sample securities. The share prices are obtained from Smart Investor, a technicalsoftware.

The Bombay Stock Exchange (BSE)-500 index is used as the surrogate for

aggregate economic wealth. The BSE-500 series is available from January 2000onwards. We therefore splice this series with the BSE-100 series for the year 1999 as the

correlation between the two indices is 0.93 for the 2000-2004 period. BSE-500 is a

broad-based and value weighted market proxy constructed on lines of Standard & Poor,USA. The data source is BSE website. The 91-day treasury-bills are used as a risk-free

proxy and are compiled from the Reserve Bank of India (RBI) website.

We also collect information for company characteristics such as market

capitalisation (price times number of shares outstanding) and book equity to market

equity (BE/ME) ratios for the sample companies. The annual figures for marketcapitalisation and BE/ME are obtained for December-end and March-end respectively

from CMIE Provess, a financial software.

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4. EVALUATING SHORT-TERM PERSISTENCE IN MUTUAL FUNDS

PERFORMANCE

4.1 Estimation Procedure

In this section, we evaluate if mutual fund managers exhibit persistently superiorstock selection skills over a short-horizon of one year. We estimate daily percentage

returns from Net Asset Values (NAV) for the sample funds for the purpose.

At the end of year t (2000), we rank the sample funds on the basis of their average

daily returns for calendar year t. The ranked funds are then classified into five portfolios

such that P1comprises of the top 20% sample funds while P5 includes the bottom 20%fund schemes. We then estimate the equally-weighted daily returns on the sample

portfolios for the year t+1. The portfolios are re-formed at the end of t+1 based on the re-

ranking of the funds on the basis of their average daily returns for the same year. Theprocess is repeated till we reach the end of our study period.

Thus for we have used a ranking criterion based on prior returns not adjusted for

risk, also termed as unadjusted returns or UR, for portfolio formation purposes. We nowuse additional ranking criteria based on risk-adjusted abnormal returns (RAR) provided

by alternative asset pricing models. The aim is to examine if the choice of criteria has an

impact on the return differential between post-formation winner and loser portfolios. Wespecifically use three measures of abnormal returns, RAR based on (1) one-factor capital

asset pricing model or CAPM, (2) three-factor Fama-French model and (3) four-factor

Carhart model.

The one-factor RAR is estimated using the standard CAPM of Sharpe (1964),Lintner (1965) and Mossin (1966) as

RPt- RFt= a + b RMt- RFt+ et (1)

where

RPt- RFt is excess return on portfolio PRMt- RFtis excess market return

b is sensitivity coefficient

a is risk-adjusted abnormal return or RAR (One-factor)et is error term

The three-factor RAR is estimated using Fama-French (1993) equation

RPt- RFt= a + b RMt- RFt+ s SMBt+ h HMLt+ et (2)

where

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SMBtis minicking portfolio that proxies for size factor in asset returns.

HML is mimicking portfolio that proxies for value factor in asset returns.a is RAR (three-factor)

s and h are sensitivity coefficients

The other terms have the same meaning as in (1).

Next, we estimate the RAR using factor model of Carhart (1997). Carhartmodified the Fama-French equation and included on additional factor to incorporate the

momentum effect highlighted by Jegadeesh and Titman (1993). The four-factor RAR is

obtained in the equation

RPt- RFt= a + b RMt- RFt+ s SMBt+ h HMLt+ m WMLt+ et (3)

where

WML is mimicking portfolio that proxies for momentum factor in returns.

m is the sensitivity of asset returns to the returns on WML factora is RAR (four-factor)

The additional risk factors involved in by the three-factor model are estimated as

follows.

In December of t-1 we rank all the 452 sample securities that form part of BSE-

500 index and for which data is regularly available on the basis of the company size(market capitalisation). We form two groups: S and B, S represents the bottom 50% of

companies, while B includes the top 50% companies on basis of size. We then rank the

sample securities in March, t-1 on the basis of their book equity to market equity(BE/ME) ratio and form three groups L (bottom 33.3%), M (middle 33.3%) and high (top

33.3%).

The annual BE/ME ratios are observed at March-end of each year as financialclosing in India is at the end of this month and the financial statements and related

information are available accordingly.

From the inter-section of two size and three BE/ME groups we construct six

portfolios namely - S/L, S/M, S/H, B/L, B/M and B/H. While S/L is a portfolio of small

and low BE/ME stocks, B/H is a portfolio of big and high BE/ME securities. Weestimate equally weighted daily returns for the six portfolios in year t. Tthe portfolios are

re-balanced at the end of t and the process is repeated for the study period. The six

double-sorted portfolios are then used to construct the size and value (BE/ME) factors instock returns.

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The size (SMB) factor is calculated as the difference between the average returns

on all small stock portfolios and the average returns on all big stock portfolios, i.e.

(S/L + S/M + S/H) (B/L + B/M + B/H)

SMB = ----------------------- - ------------------------3 3

The size factor is constructed in a way that it is neutral of BE/ME effect.

The value or BE/ME (HML) factor is constructed as the average returns on thehigh BE/ME portfolios minus the average returns on low BE/ME portfolios, i.e.,

(S/H +B/H) (S/L + B/L)HML = --------------- - --------------

2 2

The value factor is neutral of size effect by construction.

We also construct the Carhart momentum factor using the one-year prior averagedaily returns for portfolio formation purposes. We rank the sample securities at the end

of t-1 on the basis of their one-year average returns and form five groups, i.e., P1to P5

while P1includes top 20% of stocks on past performance, P5comprises of bottom 20% ofstocks. We refer to P1 and P5 as winners and losers portfolios. The equally-weighted

daily returns are estimated for the year t. The portfolios are re-formed at the end of t andthe process is repeated on year to year basis. We use the information on winners and

losers to construct the momentum (WML) factor as follows:

WML =- Return on winners portfolio minus return on losers portfolio

The excess returns on post-formation basis on the four types of momentumportfolios (a) unadjusted return momentum portfolios, (b) one-factor RAR momentum

portfolios, (c) three-factor RAR momentum portfolios, and (d) four-factor RAR

momentum portfolios are then regressed on (1) the excess returns on the market factorand (2) excess returns on the market factor and returns on size, BE/ME and one-year

momentum factors.

The unadjusted mean excess returns and the standard deviation of returns are also

estimated for the fund momentum portfolios. The above specified procedure for the

estimation of fund momentum portfolios, construction of risk factors and performingregression analysis is repeated for monthly mutual funds return data.

4.2 Empirical Results

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We provide mean descriptive statistics for the sample schemes and the market

index in Table 1. The average skewness and kurtosis for the sample funds are 3.86 and21.40 using daily data, where the latter is statistically significant. The similar figures for

the market index are 0.32 and 6.69 respectively. The average sample fund therefore

seems to be more option-like compared to the market index. Jagannathan and Korajczyk

(1986) show that this may lead to an underestimtion of selectivity skills and overestimation of market timing skills of fund managers. We shall refer to the selectivity bias

in our daily regressions later in this section. The average skewness and kurtosis measures

seem to sober down when we use monthly data, as shown in Table 1. The meanskewness and kurtosis values based on monthly data for the sample funds are 0.27 and

3.90. While similar figures for the market index are 0.28 and 3.05.

Table 2-5 provide empirical results based on daily data for the four models that

use different ranking criterion for the formation of fund momentum portfolios. The

ranking criterion in models 1,2,3 and 4 are UR, RAR (one-factor), RAR (3-factor) andRAR (4-factor) respectively as discussed in the previous sub-section. Each table contains

three panels. Panel A provides summary statistics for the post-formation fundmomentum portfolios. Panel B and C give regression results for these portfolios using

one-factor and four-factor benchmarks. The critical value is the intercept (a) of theseregressions which is a measure of risk-adjusted "extra-normal return".

The results in Panel B and C provide an interesting comparison as it is possiblethat some of the abnormal return reported by one-factor framework may simply be a

compensation for missing risk factors that is absorbed by more comprehensive four-

factor model. The difference in abnormal returns may also reflect the differences inunconditional and conditional benchmarks where the additional factors in the four-factor

model act as instruments that represent the time-varying nature of corporate betas andmarket returns, which the one-factor unconditional CAPM fails to account for.

There seems to be some evidence of short-term persistence in mutual fund returnsusing model 1 (UR ranking criterion) as shown in Table 2. P1, the winners portfolio

reports a significantly positive alpha (at 5% level) based on one-factor benchmark. [See

Panel B]. The abnormal return of P1, however, disappears in the four-factor framework.

[See Panel C]. The results for model 2 (RAR-one-factor criterion) and model 3 (RAR-three-factor criterion) are again not encouraging as shown in Tables 3 and 4 respectively.

Table 5 provides better results using model 4 (RAR-four factor criterion). However, not

only P1(winners portfolio) but also the runners up portfolios (P2and P3) provide superiorreturns as per both one-factor and four-factor benchmarks. Overall results for daily data

are not encouraging for models 1, 2 and 3. Short-term persistence evidence definitely

gets weaker for a multi-factor specification implying that the winners portfolio tend toload on additional risk factors.

However, winners portfolio based on model 4 does report abnormal returns onfour-factor basis, thus signalling short-term persistence in fund performance. The results

are consistent with those of Bollen and Busse (2005) who found that short-term

persistence for portfolios formed on abnormal returns but not for those that are sorted on

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unadjusted returns. Interestingly, our losers portfolios do not report any serious under-

performance as in case of Carhart (1997). However, this may be due to the fact Carhartused monthly data and hence we can arrive at a better conclusions by using the same

observation frequency, which we do in the next step.

We now evaluate short-term persistence in mutual funds performance usingmonthly data. Such an analysis is warranted to verify if persistence results are impacted

by any market micro-structure effects that are more pronounced on daily data.

Tables 6 - 9 show short term persistence results based on monthly data for the

post-formation fund momentum portfolios formed on different sorting criteria. The

results for monthly data are weaker compared to those for daily data. P1 (the winnersportfolio) provide significantly positive returns on post-formation basis only for model 3

(RAR-three-factor criterion) using the one-factor benchmark. However, short-term

persistence is not visible on the basis of four-factor benchmark.

We next evaluate the trading strategies based on short-term persistence in fundperformance. These strategies involve zero outlay as one short sells the past losers and

buys the past winners with the same amount. We explore a variety of such tradingstrategies based on alternative ranking criteria and those that involve use of daily/monthly

data.

We are specifically interested in finding if these trading strategies provide

abnormal returns based on differences in alphas for winners and losers generated on post-

formation basis using a four-factor benchmark. Table 10 shows that on four factor basis,these strategies seem to provide statistically significant payoffs at 5% level mainly for

daily data. However, the economic feasibility of the trading strategies seems doubtful.The best performing strategy is based on model 4 (daily data) ranking criterion which can

provide a daily return of .02% per month (annualised return at 5.5% on the assumption of

250 trading days) using the four factor benchmark. The second best strategy is the onebased on model 1 (daily) ranking criterion which gives a gross monthly return of .015%

(annualised 3.75%). The other daily data based as well as all monthly data based

investment strategies seem to be providing extremely low returns casting a shadow on

their economic feasibility. However, in the light of Jagannathan and Korajczyk (1986)bias that leads to an underestimation of selectivity measures (alphas) due to distributional

characteristics of daily data on fund returns, there is a possibility that our alpha

differentials may contain some estimation errors. To the extent these underestimationerrors in winners and losers portfolio alphas are self cancelling our estimation errors may

be small.

5. SHORT-TERM PERSISTENCE AND INVESTMENT COST

Carhart (1997) shows that persistence in mutual funds perforamnce can partly beexplained by persistent differences in mutual fund expense and transaction costs between

the winner and losers portfolios. This implies that persistence-based trading strategies

may not be feasible on net return basis.

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We analyse the entry loads and management expenses for momentum fundportfolio formed on alternative ranking models and based on daily as well as monthly

data.

Mutual funds in India charge an entry load generally on three-tier basis based onthe level of investment. The entry load is a decreasing function of the amount of

investment. However, different fund schemes follow varying investment slabs to charge

entry loads thus making inter-scheme comparison difficult. We try to overcome thisproblem by standardising these investment slabs for all the fund schemes using an

"averaging procedure". We form three investment slabs, i.e., upto 1 crore (Rs.10

million), between Rs.1 crore to Rs.5 crores (Rs.10 million to Rs.50 million) and morethan Rs.5 crore( more than Rs.50 million). If a hypothetical fund scheme has the

following investment slabs: upto 50 lakhs (.5 million), between 50 lakhs (.5 million) and

1.5 crores (15 million) and beyond 1.5 crores (15 million). The mean entry load for thehypothetical schemes are computed as follows.

ULH1 ULS1 ULH1

L1= ------- x L1+ ---------------- x L2ULS1 ULS1

ULH2- LLS2 ULS2 ULH2

L2= ---------------- x L2+ ---------------- x L3

ULS2 - LLS2 ULS2 LLS2

L3= L

3

Where

Liis mean entry load for investment slab i.

ULsiand LLSiare standardized upper and lower limits for slab i.

ULHiis the upper limit of slab i for the hypothetical scheme.

The entry loads shown in Table 11 are a percentage of the investment made by theinvestors. One can clearly see that the entry loads for the winner portfolio (P1) are

substantially larger than those entry loads for losers portfolio (P5) for all ranking models

and for all investment slabs. Thus, better performing fund schemes seem to be charginghigher.

There, however, does not seem to be much of a difference between managementexpenses of winner and loser fund portfolios as shown in Table 10 where the

management expenses are depicted as a percentage of fund corpus. Carhart (1997)

exhibits that winner portfolios comprise of sample schemes which are more actively

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managed compared to loser portfolios. The winner portfolio schemes therefore report a

higher asset turnover implying greater transaction costs which destroy some of theabnormal returns provided by them. We could not obtain portfolio turnover information

for our sample schemes and hence an explicit test of the relationship between fund

persistence and transaction costs is not possible. However, given the evidence in

previous literature, such a possibility can theoretically not be ruled out.

In sum, the winner portfolios do exhibit higher mutual fund expenses mainly

related to entry loads which may make them economically unviable on net return basis.

6. SUMMARY AND CONCLUSIONS

The paper demonstrates that short-term persistence in equity mutual fundsperformance does not necessarily imply superior stock selection skills. Common factors

in stock returns explain some of the abnormal returns in top ranking mutual fundschemes. Only the winner portfolios sorted on four-factor alphas' provide an annual

abnormal return of about 10% on post-formation basis using daily data. The short-termpersistence results are much better when we use daily data rather than monthly

observations, thus implying that data frequency does affect inferences about fund

perofrmance.

The zero-investment trading strategies involving buying of past winners and

selling of past losers do not seem to provide statistically significant payoffs. Using dailydata and a ranking criterion based on four-factor alpha, the zero-outlay trading strategy

does provide 5.5% returns on annualised basis. However, the higher load expenses ofwinner schemes and a theoretical possibility that they may involve higher transaction

costs due to more active portfolio management makes them relatively less attractive on

net return basis. Thus, the economic feasibility of persistence-based strategies may be indoubt in light of the differences in investment costs.

Our findings are consistent with those for the mature market. We thus offer little

evidence that supports management skills or informational advantage. Overall theevidence is in conformity with the efficient market hypothesis. Our results have

implications for hedge funds and other managed portfolios who consistently follow `fund

of funds' strategy to generate extra-normal returns. Interpreting, the persistence evidence,it will be difficult to implement such a strategy in India at least on net return basis. In

sum, though the Investment gurus and the financial press may continue to glamorize fund

persistence strategies their economic viability (net of investment costs) is yet to beuniversally proved.

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Table 1

Descriptive Statistic for Sample Mutual Fund Schemes and the Market Index

Portfolio Mean SigmaSkewness

(1)Skewness

(1)

Excess

KurotosisKurotosis

Daily

Fund Schemes 0.00123 0.017352 0.000872 3.858437 18.40438 21.40438

Daily BSE 500 0.0007 0.017094 -0.56165 0.315451 3.686799 6.686799

Monthly

Fund Schemes 0.022266 0.08357 -0.32379 0.269727 0.899073 3.899073

Monthly BSE

500 0.013572 0.087812 -0.52643 0.277133 0.049493 3.049493

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Table 2

Summary Statistic For The Fund Momentum Portfolios Sorted On One-Year Prior Unadjusted

Returns Using Daily Data (Model 1- Daily)

Panel A: Post holding unadjusted return

Portfolio Mean Sigma t-stat

P1 0.000737 0.015147 0.000429P2 0.000440 0.015574 0.000441

P3 0.000510 0.015788 0.000447P4 0.000405 0.013929 0.000394

P5 0.000329 0.013756 0.000389

Panel B: Post Holding Risk-Adjusted Returns Using One Factor Model (CAPM)

Portf

olio

a B t(a) t(b) R2

P1 0.0004995 0.7716664 2.29686 60.0026 0.742385

P2 0.0001836 0.8327812 0.97666 74.8987 0.817872

P3 0.0002409 0.8760998 1.56224 96.0983 0.880853

P4 0.0001643 0.7840680 1.36279 109.9923 0.906416

P5 0.000092384 0.769540941 0.73348 103.3201 0.895244832

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Panel C: Post Holding Risk-Adjusted Returns Using Four Factor Model

P1 P2 P3 P4 P5

A 0.00027196 0.000066725 0.000241418 0.000110747 0.000118269

B 0.755417164 0.812932175 0.876614416 0.787459317 0.789261992

S 0.271437673 0.166388636 0.091912586 0.101463521 0.065329587

H -0.057579418 0.000835942 0.063067589 0.004707665 0.05384233

M 0.261170543 0.239304115 0.074020043 0.04145657 -0.076664999

t(a) 1.331435217 0.377707005 1.59312396 0.924825391 0.950294163

t(b) 59.25913728 73.73480313 92.69218831 105.3678253 101.6157699

T(s) 8.864618524 6.282945967 4.046047382 5.65211868 3.501638299

T(h) -2.733616005 0.045887698 4.035919698 0.381230123 4.195324211

T(m) 11.41909756 12.09783047 4.362374762 3.091807009 -5.501437376

R2 0.777016458 0.842244752 0.88704802 0.909381787 0.899640499

Table 3

Summary Statistic For The Fund Momentum Portfolios Sorted On One Year Prior Risk Adjusted

Returns Based n One Factor Model Using Daily Data (CAPM)

Panel A: Post holding unadjusted return


P1 0.000626 0.017116 0.000485

P2 0.000476 0.015065 0.000426

P3 0.000604 0.014455 0.000409P4 0.000287 0.013882 0.000393

P5 0.000387 0.013364 0.000378


Portfolio a b t(a) t(a) R2

P1 0.000362 0.888973 1.565517 64.97817 0.771812

P2 0.000233 0.819153 1.391043 82.79115 0.845952

P3 0.000367 0.8006 2.563202 94.67513 0.877771

P4 0.000052986 0.788789657 0.489121 123.1477 0.92396

P5 0.000164989 0.747908439 1.353914 103.7997 0.896185028

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P1 P2 P3 P4 P5

A 0.000237 0.000216 0.000226 0.000030421 0.00012379

B 0.88243 0.811694 0.788807 0.78663913 0.76586286

S 0.244802 0.11622 0.160389 0.06736924 0.09394768

H 0.028325 0.065357 -0.04069 0.02152431 -0.00137514

M 0.207048 0.145046 0.167722 0.06385607 -0.06467844

t(a) 1.069718 1.342542 1.668462 0.284621 1.027115

T(b) 63.75334 81.0189 93.34011 117.9445 101.8361

t(s) 7.362884 4.829293 7.900999 4.205076 5.200521

t(h) 1.238653 3.948639 -2.91417 1.953406 -0.11068

t(m) 8.336401 8.068338 11.06047 5.33567 -4.79286

R2 0.794216 0.860842 0.892447 0.92736 0.90035433

Table 4

Summary Statistic For The Fund Momentum Portfolios Sorted on One Year Prior Risk Adjusted

Returns Based on Three Factor Model Using Daily Data (CAPM)

Panel A: Post Holding Unadjusted Return


P1 0.00051 0.017408 0.000493P2 0.00068 0.015681 0.000444

P3 0.00051 0.013334 0.000377

P4 0.000246 0.014109 0.000399

P5 0.00047 0.013707 0.000388


Portfolio a b t(a) t(b) R2

P1 0.000231 0.907281 0.994923 65.97846 0.77701

P2 0.00042 0.842795 2.273275 77.07983 0.82627

P3 0.00028 0.746958 2.320757 104.7396 0.897777

P4 0.000004979 0.78386075 0.036483 97.12158 0.883059

P5 0.00023362 0.76972515 1.926648 107.3455 0.90220079

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P1 P2 P3 P4 P5

A 0.000168 0.000384 0.000201 -0.00005970 0.000133757

B 0.906208 0.826822 0.745467 0.777727713 0.782788537

S 0.209649 0.126768 0.078187 0.113679354 0.14220485

H 0.072299 0.062088 -0.03551 0.010229269 -0.03047623

M 0.161063 0.207988 0.047333 0.115885267 -0.01063368

t(a) 0.746519 2.204883 1.666404 -0.45032 1.120669

t(b) 64.49108 76.03419 99.18014 93.99792 105.0897

t(s) 6.211348 4.853196 4.330655 5.719969 7.947887

t(h) 3.113921 3.45546 -2.85936 0.748233 -2.47616

t(m) 6.388613 10.66042 3.509912 7.80653 -0.79568

R2 0.794875 0.848617 0.899967 0.891733 0.907026923

Table 5Summary Statistic For The Fund Momentum Portfolios Sorted On One Year Prior Risk Adjusted

Returns Based On Four Factor Model Using Daily Data (CAPM)



P1 0.001026 0.013964 0.000431P2 0.000931 0.012625 0.00039

P3 0.000897 0.012194 0.000376

P4 0.000619 0.012107 0.000374

P5 0.000821 0.012823 0.000396



P1 0.000428 0.868119 2.917247 89.75435 0.88966

P2 0.000384 0.793883 3.206944 100.6163 0.910175

P3 0.000365 0.773628 3.485818 112.2905 0.926583

P4 0.000092441 0.76394727 0.834771 104.7274 0.916512

P5 0.00026813 0.80337573 2.126328 96.71435 0.90349379

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P1 P2 P3 P4 P5

a 0.000396 0.000307 0.000329 -0.000013373 0.000171689

b 0.886303 0.801103 0.772736 0.766281592 0.805958737

s 0.113724 0.088829 0.017823 0.09503348 0.112915265

h 0.042892 -0.00762 -0.01577 -0.03760336 -0.04140982

m -0.01254 0.04398 0.033924 0.053015902 -0.00380433

t(a) 2.718747 2.573722 3.118186 -0.12212 1.37548

t(b) 88.21552 97.26241 106.3134 101.4994 93.65463

t(s) 5.200786 4.95526 1.126687 5.783709 6.0287

t(h) 2.804851 -0.60749 -1.42507 -3.27248 -3.16151

t(m) -0.69003 2.953146 2.581304 3.883802 -0.2445

R2 0.893572 0.9125 0.926953 0.92006 0.907409922

Table 6Summary Statistic For The Fund Momentum Portfolios Sorted On One Year Prior Unadjusted

Returns Using Monthly Data (Model 1-Monthly)



P1 0.008278 0.082274 0.010711

P2 0.008886 0.077939 0.010147

P3 0.012409 0.074853 0.009745

P4 0.007977 0.072517 0.009441

P5 0.003393 0.068991 0.008982



P1 0.002367 0.899985 0.685461 22.44333 0.894962

P2 0.003204 0.864984 1.13494 26.37675 0.921723

P3 0.00689 0.840219 2.985673 31.34508 0.943297

P4 0.002585 0.820876 1.369624 37.45156 0.959606

P5 -0.00161 0.761099 -0.60136 24.52429 0.91053

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P1 P2 P3 P4 P5

a -0.00135 0.001894 0.007649 0.003239 0.000868

b 0.868153 0.855459 0.859372 0.836511 0.812046

s 0.274437 0.170002 0.076553 0.083707 0.05713

h -0.04063 0.025634 0.07337 0.07397 0.139526

m 0.290446 0.151623 -0.05028 -0.02061 -0.23447

t(a) -0.44018 0.676496 3.149842 1.67452 0.374422

t(b) 24.86846 26.76704 31.00238 37.88235 30.68954

t(s) 3.833656 2.594018 1.346772 1.848597 1.052914

t(h) -0.84058 0.579321 1.911794 2.419502 3.808648

t(m) 4.769228 2.719551 -1.03976 -0.53493 -5.07952

R2 0.929224 0.9339 0.94609 0.963549 0.942176

Table 7Summary Statistic For the Fund Momentum Portfolios Sorted On One Year Prior Risk Adjusted

Returns Based On One Factor Model Using Monthly Data (CAPM)



P1 0.007936 0.083591 0.010883

P2 0.011769 0.06831 0.008893P3 0.008339 0.078252 0.010188

P4 0.007874 0.071304 0.009283

P5 0.004335 0.072492 0.009438



P1 0.00178 0.93722 0.677465 30.71079 0.941068

P2 0.006764 0.761977 2.917546 28.29873 0.931301

P3 0.00257 0.878352 1.064721 31.32935 0.943243

P4 0.002545 0.811363 1.587001 43.56676 0.969837

P5 -0.00095 0.805151 -0.36658 26.64532 0.923174

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P1 P2 P3 P4 P5

a 0.000663 0.005 0.002528 0.00319 0.000139

b 0.934725 0.755628 0.881426 0.819644 0.847547

s 0.179137 0.147154 0.128762 0.032112 0.186633

h 0.036816 -0.01663 0.067826 0.04997 0.137281

m 0.111823 0.07905 0.083506 -0.00431 -0.13026

t(a) 0.253836 2.083255 1.047236 1.862319 0.061136

t(b) 31.33812 27.58291 31.98569 41.92543 32.6577

t(s) 2.928816 2.619528 2.278631 0.801009 3.506941

t(h) 0.891531 -0.43846 1.777769 1.846169 3.820665

t(m) 2.149069 1.654102 1.73707 -0.12647 -2.87722

R2 0.949949 0.936777 0.951249 0.970448 0.949616

Table 8Summery Statistic For The Fund Momentum Portfolios Sorted On One Year Prior Risk Adjusted

Returns Based On Three Factor Model Using Monthly Data (CAPM)


Portfolio Mean Sigma t-statP1 0.008906 0.081006 0.010546

P2 0.007922 0.077333 0.010068

P3 0.007474 0.072176 0.009397

P4 0.007849 0.068836 0.008962P5 0.007796 0.074392 0.009685



P1 0.002926 0.910422 1.197118 32.06953 0.945695

P2 0.002279 0.859169 0.824149 26.74984 0.923729

P3 0.002174 0.806774 0.914344 29.21105 0.935256

P4 0.002751 0.776178 1.408933 34.23016 0.952021

P5 0.002277 0.840179 1.115974 35.45475 0.955134

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P1 P2 P3 P4 P5

a 0.002003 0.001241 0.002024 0.00515 0.00071

b 0.912168 0.858735 0.807371 0.80764 0.852252

s 0.161871 0.223289 0.128441 0.002747 0.174736

h 0.03525 0.064798 0.063124 0.119456 -0.00365

m 0.072476 0.137369 0.097702 -0.12277 -0.03998

t(a) 0.8044 0.483429 0.860204 2.803876 0.365745

t(b) 32.09868 29.31134 30.06411 38.52541 38.43948

t(s) 2.777785 3.716736 2.332367 0.063897 3.843339

t(h) 0.895944 1.59751 1.697762 4.115687 -0.11901

t(m) 1.461965 2.687799 2.0855 -3.35695 -1.03363

R2 0.951621 0.94358 0.945578 0.963539 0.965083

Table 9Summary Statistic For the Fund Momentum Portfolios Sorted On One Year Prior Risk Adjusted

Returns Based On Four Factors Model Using Monthly Data (CAPM)



P1 0.015064 0.072982 0.010646P2 0.017707 0.063358 0.009242P3 0.016063 0.063094 0.009203P4 0.016191 0.071307 0.010401

P5 0.016631 0.071454 0.010423



P1 0.001992 0.871529 0.721603 25.74065 0.93367

P2 0.006305 0.760131 2.828369 27.79577 0.942585

P3 0.004611 0.763445 2.46325 33.24402 0.959172

P4 0.003219 0.864822 1.614442 35.35809 0.96374

P5 0.00374 0.859446 1.555825 29.14798 0.947521

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P1 P2 P3 P4 P5

a 0.002104 0.005513 0.003865 0.003907 0.00306

b 0.896777 0.769547 0.77243 0.880561 0.876578

s 0.127347 0.098267 0.063424 0.036865 0.184785

h 0.094981 0.022553 0.018251 0.068173 0.05877

m -0.01185 0.004921 0.042085 -0.00811 -0.06539

t(a) 0.726057 2.259551 1.864284 1.807922 1.372845

t(b) 26.42028 26.92717 31.81214 34.79327 33.58221

t(s) 1.937968 1.776099 1.349256 0.752418 3.656701

t(h) 2.125487 0.599402 0.570941 2.046058 1.710177

t(m) -0.19556 0.096488 0.971207 -0.17952 -1.40382

R2 0.939655 0.943238 0.958683 0.964856 0.96277

Table 10Statistical Feasibility of Trading Strategies Based on Fund Momentum Portfolios

a1 a5 a1-a5 (a1-a5)%t(a1-a5)/SE(a1-

a5)

M1-Daily-1Factor 0.00049952 0.00009238 0.00040714 0.04071370 57.25252623

M1-Daily-4Factor 0.00027196 0.00011827 0.00015369 0.01536910 22.70846581

M1-Monthly-1Factor 0.00236700 -0.00161000 0.00397700 0.39770000 6.99126774

M1-Monthly-4Factor -0.00135000 0.00086800 -0.00221800 -0.22180000 -4.43145397

M2-Daily-1Factor 0.00036200 0.00016499 0.00019701 0.01970110 26.62729583

M2-Daily-4Factor 0.00023700 0.00012379 0.00011321 0.01132100 15.85710414

M2-Monthly-1Factor 0.00178000 -0.00095000 0.00273000 0.27300000 5.68210289

M2-Monthly-4Factor 0.00066300 0.00013900 0.00052400 0.05240000 1.16230686

M3-Daily-1Factor 0.00023100 0.00023362 -0.00000262 -0.00026200 -0.35349873

M3-Daily-4Factor 0.00016800 0.00013376 0.00003424 0.00342430 4.75075130

M3-Monthly-1Factor 0.00292600 0.00227700 0.00064900 0.06490000 2.03868524

M3-Monthly-4Factor 0.00200300 0.00071000 0.00129300 0.12930000 3.14559743

M4-Daily-1Factor 0.00042800 0.00026813 0.00015987 0.01598700 26.76500628

M4-Daily-4Factor 0.00039600 0.00017169 0.00022431 0.02243110 37.87382883

M4-Monthly-1Factor 0.00199200 0.00374000 -0.00174800 -0.17480000 -3.27380763

M4-Monthly-4Factor 0.00210400 0.00306000 -0.00095600 -0.09560000 -1.79271320

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Table 11Mean entry load and management expenses for the fund momentum portfolios panel a:

Daily data

UR-sorted portfolios (Model 1)

L1 L2 L3 Expense Ratio

P1 2.074639 1.193693 0.67125 2.202380712

P2 1.95075 1.187619 0.345 2.317057319

P3 1.992837 1.349554 0.672321 2.342686398

P4 1.992931 1.237535 0.549722 2.374731702

P5 1.938754 0.892451 0.553463 2.161679173

RAR-sorted portfolio (Model 2)


P1 1.973304 1.170893 0.67125 2.305122

P2 1.993093 1.384953 0.615471 2.228313

P3 2.142426 1.078175 0.307341 2.343787

P4 1.913528 1.228785 0.687917 2.213265

P5 1.942367 0.972024 0.485065 2.281058

RAR-3 Factor model sorted portfolio (Model 3)

L1 L2 L3 Expense RatioP1 1.992321 1.193214 0.6275 2.309789

P2 1.986902 1.253249 0.523162 2.259211

P3 2.21942 1.353943 0.539583 2.353899

P4 1.961389 1.10066 0.554583 2.16248

P5 1.813864 0.952469 0.529004 2.28763



P1 2.009375 1.413672 0.903125 2.301789

P2 2.042358 1.296425 0.39929 2.277693P3 2.203342 1.39605 0.516493 2.334196

P4 1.931944 0.858507 0.370833 2.140631

P5 1.822538 0.948213 0.57197 2.328195

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Panel B: Monthly Data

UR-sorted portfolios (Model 1)

L1 L2 L3 Expense RatioP1 2.00789 1.502293 0.751981 2.255075

P2 1.998141 1.30059 0.538909 2.310551

P3 2.164881 1.174157 0.385119 2.334383

P4 1.996364 1.063998 0.563254 2.27419

P5 1.786409 0.811959 0.56123 2.217295

RAR-sorted portfolio (Model 2)


P1 2.032675 1.23418 0.699821 2.170234969

P2 2.007179 1.331845 0.292857 2.336216931

P3 2.052738 1.390179 0.766369 2.359275904

P4 1.966145 1.117912 0.500813 2.377973765

P5 1.897298 0.813383 0.554841 2.138431878



P1 2.091648 1.280291 0.569176 2.294137

P2 2.090229 1.385728 0.644618 2.305808

P3 2.156764 1.55542 0.61066 2.242246

P4 1.885955 0.908681 0.500347 2.196612

P5 1.797396 0.780469 0.44375 2.327462



P1 1.899552 1.417378 0.739838 2.242906

P2 2.169319 1.196736 0.418016 2.336595

P3 2.165119 1.250149 0.481944 2.244173

P4 1.874331 0.948254 0.470813 2.325223

P5 1.857266 1.047822 0.697659 2.229239

short term persistance in mutual funds performance

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