ssrn-id2370501

8/11/2019 SSRN-id2370501

1/34

Jensen alpha and market climate *

Bernhard Breloer 1

Friedrich-Alexander-Universitt (FAU) Erlangen-Nrnberg

Hendrik Scholz 2

Friedrich-Alexander-Universitt (FAU) Erlangen-Nrnberg

This Version: March 17, 2014

1 Bernhard Breloer, Friedrich-Alexander-Universitt (FAU) Erlangen-Nrnberg, Chair of Financeand Banking, Lange Gasse 20, 90403 Nrnberg, Germany, phone: +49 911 5302 429, fax: +49 911

530 2466, e-mail: [email protected] Hendrik Scholz, Friedrich-Alexander-Universitt (FAU) Erlangen-Nrnberg, Chair of Finance and

Banking, Lange Gasse 20, 90403 Nrnberg, Germany, phone: +49 911 5302 649, fax: +49 911 5302466, e-mail: [email protected].

* We are grateful to participants of the CFR Research Seminar of the University of Cologne 2008; theSWFA Annual Meeting 2008, Houston; the EFA Annual Meeting 2008, St. Pete Beach; the 2008FMA Annual Meeting, Dallas; the Annual Meeting of the German Finance Association 2008,Mnster; the Annual Meeting of the German Academic Association for Business Research 2009,

Nrnberg; the Southern Finance Association Annual Meeting 2009, Captiva Island; and, especiallyto Oliver Entrop, Alexander Kempf, Peter Lckoff, Oliver Schnusenberg, John Stowe, MarcoWilkens and Wenjuan Xie for helpful comments and suggestions on earlier drafts of this paper

previously titled Ranking of equity mutual funds: The bias in using survivorship bias-free

datasets. We are responsible for any remaining errors.

8/11/2019 SSRN-id2370501

2/34

Jensen alpha and market climate

Abstract

This paper studies the impact of market climate on the classic Jensen alpha (JA) of

funds. We show analytically that the one-factor JA of a fund consists of i) the funds

alpha based on the assumed multi-factor model and ii) further components that are

subject to market phases of factor realization. To account for this impact of market

phases in the performance evaluation of funds, we apply a time period-adjusted JA.

In our empirical study, we analyze JAs and respective fund rankings for a

survivorship bias-free data set of 3.102 US equity mutual funds. Our results show that

factor realizations during the specific lifetime of a fund clearly affect its rank

position. This impact is particularly strong for funds with shorter lifetimes. Using the

time period-adjusted JA clearly reduces this impact. Our main results are robust when

applying alternative multi-factor models as a return generating process.

Keywords : Equity mutual funds; Jensen alpha; Fund ranking; Market conditions

JEL Classification : G11

8/11/2019 SSRN-id2370501

3/34

1

1. Introduction

When evaluating the performance of equity funds, private and institutional investors

frequently compare fund performance to appropriate benchmarks. Moreover, fund

managers regularly present their performance with a comparison to benchmarks, e.g.,

in the fund prospectus. In this context, the CAPM-based one-factor Jensen alpha

(Jensen, 1968) measures the funds risk-adjusted return, accounting for its systematic

risk exposure related to a selected benchmark. Even today, the classic Jensen alpha

(JA) is still one of the most widely used performance measures (Aragon and Ferson,

2006; Goetzmann et al., 2007). Moreover, it is presented in many finance textbooks

(e.g., Elton et al., 2009; Bodie et al., 2011).

The academic literature suggests that beyond systematic risk, several anomalies in

stock returns should be considered when explaining fund returns. For example, Banz

(1981) describes a size anomaly indicating that small-cap stocks exhibit relatively

high returns. Likewise, Fama and French (1992) discover relatively high returns

among stocks with high book equity to market equity ratios. Consequently, Fama and

French (1993) introduced a three-factor model which contains a size and a value

factor next to the market factor. Then, Carhart (1997) added a momentum factor to the

Fama and French three-factor model based on findings of Jegadeesh and Titman

(1993). Until now, the four-factor alpha of the Carhart model has been regularly

applied in the academic literature when evaluating the performance of equity funds.

However, using the one-factor JA can be justified for several reasons. For example,

one could simply neglect potential factors like size, value or momentum factors in

performance models, as these lack a thorough theoretical foundation, e.g., in the

8/11/2019 SSRN-id2370501

4/34

2

context of an equilibrium model such as the CAPM. Moreover, the average investor

could consider fund returns due to exposures to size, value and momentum factors as

the success of the fund manager, since the investor herself might be unwilling or

unable to implement such trading strategies. Furthermore, Berkowitz and Kotowitz

(2000) and Del Guercio and Tkac (2002) document evidence for a positive

relationship between JAs and fund flows of US equity funds. Similarly, for Australian

funds Gharghori et al. (2007) find that fund inflows are driven by risk-adjusted

performance, e.g., measured based on JA. On a broader international basis, Ferreira et

al. (2012) confirm a respective positive relationship. These findings indicate the

relevance of JA with respect to evaluating fund performance.

In our analytical study, for the sake of simplicity, we first assume fund returns to

be driven by Carharts (1997) four-factor model. Our first objective is to reveal the

relationship between the one-factor JA and the Carhart four-factor alpha. Based on an

approach outlined in Pastor and Stambaugh (2002), the JA of a fund consists of two

components, these being i) the funds four-factor alpha and ii) the products of the

funds factor exposures to the size, value and momentum factor and the respective

factor alphas. The latter represent the intercepts of regressions of the respective factor

returns on the market factor. On this basis, we show analytically what drives the

difference between a funds JA and its four-factor alpha and discuss how this

difference may impact fund rankings based on these measures.

In a similar context, Krimm et al. (2012) investigate the performance of US equity

mutual funds based on the Sharpe ratio (Sharpe, 1966, 1994). They document that the

Sharpe ratio depends on the market climate of factor realizations. They thus suggest

the use of a normalized Sharpe ratio (Scholz, 2007) to avoid biased rankings of equity

8/11/2019 SSRN-id2370501

5/34

3

funds. Likewise, the classic JA can be subject to market phases of realizations of the

size, the value and the momentum factor.

In the context of evaluating fund performance, empirical studies commonly rely on

survivorship bias-free data to overcome a potential survivorship bias (see, e.g.,

Grinblatt and Titman, 1989; Brown and Goetzman, 1995; Malkiel, 1995; Elton et al.,

1996; Carhart et al., 2002; Rohleder et al., 2011). Including both full-data funds and

non-full-data funds results in datasets with different lengths of fund return history. In

turn, unequal lifetimes of funds can lead to biased performance evaluations, since

these funds are exposed differently to market phases of factor realizations.

Against this background, our second objective is to investigate empirically the JAs

of actual equity funds that are exposed to market phases of factor realizations. First,

we document the impact of market climate on the JAs of funds and on respective fund

rankings. Second, to avoid a biased performance evaluation, we adjust the factoralphas of funds if necessary. In detail, we determine the JAs the funds would have

shown if they had existed during the full evaluation period. Differences in these time

period-adjusted JAs of funds are mainly due to fund-specific characteristics, but not to

the different lifetimes of funds. Before this adjustment, we find that funds with shorter

lifetimes are more strongly affected by the market phases of factor realizations. This

is reflected by larger differences between adjusted JAs and classic JAs for these

funds.

To test the robustness of our approach, we apply alternative multi-factor models in

this context and find high correlations between adjusted JAs based on these models

and adjusted JAs based on the Carhart model. Thus the choice of the respective multi-

8/11/2019 SSRN-id2370501

6/34

4

factor model used to explain fund returns does not seem to severely impact our

empirical results.

The remainder of this paper is organized as follows. Section 2 describes the applied

performance measures and the methodology for time period adjustments of the JA.

Section 3 presents the fund sample used as well as our empirical results explaining the

relationship between JA, lifetime of funds and market phases of factor realizations.

After applying the time period adjustment of the Jensen alpha, we investigate the

difference between adjusted JAs and the classic JAs and its impacts on respective

fund rankings. Finally, Section 4 concludes.

2. Jensen alpha and the market phases of factor alphas

In this study, we investigate how market phases of factor realizations impact the JA.

The classic one-factor JA of fund i is determined by regressing its monthly return in

excess of the risk free rate ER it on the monthly market excess return ERM t ,

ER it = i1F + i

1F ERM t + i t , (1)

where the funds JA is the constant term i1F in Equation (1), and i

1F denotes the

funds systematic risk.

As a second measure, we apply the four-factor alpha according to the Carhart

(1997) model, which additionally includes a size factor SMB, a value factor HML and

a momentum factor MOM to Equation (1),

ER it = i4F + 1 i

4F ERM t + 2i 4F SMBt + 3 i

4F HML t + 4 i 4F MOM t + i t , (2)

8/11/2019 SSRN-id2370501

7/34

5

where the funds four-factor alpha is the constant term i4F and the exposures to the

factors ERM, SMB, HML and MOM are represented by 1 i 4F , 2 i

4F , 3 i 4F and 4 i

4F ,

respectively. In the following, for the sake of simplicity, we first assume Carharts

four-factor model to be the return generating process of funds, which accounts for

potential investment opportunities represented by the factors SMB, HML and MOM.

Omitting SMB, HML and MOM in the one-factor regression model can lead to

potential differences between the JA and the four-factor alpha of a fund. To display

these differences, we now apply an approach outlined in Pastor and Stambaugh

(2002). According to Equation (1), we first regress each of the factors SMB, HML

and MOM on the market excess return ERM.

SMBt = smb1F + smb

1F ERM t + smb t (3)

HML t = hml 1F

+ hml 1F

ERM t + hml t (4)

MOM t = mom1F + mom1F ERM t + mom t (5)

We call the intercepts of these regressions factor alphas ( smb1F , hml

1F and mom1F ). For

each fund, these factor alphas are estimated based on an evaluation period according

to the fund-specific lifetime. Thus factor alphas of funds differ when the funds exhibit

different lifetimes.

Next, we substitute SMBt , HML t and MOM t in Equation (2) on the right hand side

of Equations (3) to (5), which reveals - after some rearrangement - the components of

the one-factor JA as follows:

8/11/2019 SSRN-id2370501

8/34

6

i1F = i

4F + 2 i 4F smb

1F + 3 i 4F hml

1F + 4 i 4F mom1F (6)

Accordingly, the JA of a fund i consists of its four-factor alpha and the sum of the

fund-specific factor contributions of SMB, HML and MOM. For example, the

contribution of the SMB factor equals the funds exposure to the SMB factor times

the SMB factor alpha.

Importantly, while a funds factor exposures on SMB, HML and MOM depend on

its investment style, factor alphas are not identical across funds with regard to fund-

specific lifetimes and hence are sensitive to market climate. Therefore, two funds with

identical four-factor alphas and identical factor exposures to SMB, HML and MOM,

but different lifetimes, may have different JAs due to different fund-specific factor

alphas. In turn, evaluating the performance of funds with different lifetimes can result

in a biased JA comparison, e.g., a biased JA fund ranking.

Thus to appropriately compare the performance of funds based on JA, we treat

funds as if they are exposed to the same market phases of the respective factors, i.e.,

to the same factor alphas. Hence we adjust the JA of each fund i by replacing the

fund-specific factor alphas in Equation (6) by full-period factor alphas smb1F_FP , hml

1F_FP

and mom1F_FP each estimated over the full evaluation period. 1

i1F_adj = i

4F + 2 i 4F smb

1F_FP + 3 i 4F hml

1F_FP + 4 i 4F mom

1F_FP (7)

where i1F_adj represents the time period-adjusted JA of fund i.

1 Alternatively, even longer time periods could be considered to estimate normal factor alphas that

contain no market climate impact (compare, e.g., Pastor and Stambaugh, 2002; Krimm et al., 2012).

8/11/2019 SSRN-id2370501

9/34

7

By subtracting Equation (6) from Equation (7), the adjusted JA of fund i equals its

classic JA plus the sum of differences between full-period adjusted and original factor

contributions of the fund.

i1F_adj = i

1F + 2 i 4F smb

1F_FP smb1F + 3 i

4F hml 1F_FP hml

1F + 4 i 4F ( mom

1F_FP mom1F (8)

According to Equation (8), the adjusted JA is lower than the classic JA, if the sum of

differences between the full-period adjusted and original factor contributions is

negative and vice versa.

3. Empirical analysis

3.1 Data and summary statistics

As the source of fund data, we use the mutual fund database from the Center for

Research in Securities Prices (CRSP). We select U.S. domestic equity mutual funds

for an evaluation period from January 1996 to December 2009. 2 From this sample, we

eliminate funds with the description of ETF, Index, Long-Short, Alpha-Only, Fixed

Income, Retirement, Variable Insurance or Target in their names (compare, e.g.,

Comer et al., 2009; Amihud and Goyenko, 2013; Breloer et al., 2014). If a fund offers

multiple share classes, we select the oldest one. For the remaining funds we extract

monthly returns. Moreover, we require funds to exhibit at least 36 months of

continuous monthly returns. To avoid data-errors and outliers, we eliminate all funds

with fragmentary return histories and with implausible monthly returns greater than

2 We choose funds with the following Lipper objective codes: Capital appreciation funds (CA), equityincome funds (EI), growth funds (G), growth and income funds (GI), mid-cap funds (MC), and

small-cap funds (SG). For fund selection, we rely on the most recent objective code.

8/11/2019 SSRN-id2370501

10/34

8

100 percent or less than 100 percent. Our final data set contains 3,102 domestic

equity funds.

Table 1 shows the total yearly number of funds as well as the number of annual

fund starts and disappearances. 3 Basically, we find that the number of funds almost

continuously increases, peaking at the end of 2006 (2,283 funds). Since 1999, funds

disappear from our sample while new funds enter. Thus the lifetimes of funds in our

fund sample differ.

Insert Table 1 about here

To account for different lifetimes of funds, we divide our fund sample as follows.

The first subsample contains those funds that exist throughout the full evaluation

period, so called full-data funds (FD funds). The remaining non-full-data funds

are sorted into three subsamples based on the length of their return histories: a long

lifetime sample (LLT funds), a medium lifetime sample (MLT funds) and a short

lifetime sample (SLT funds). In total, we count 638 FD funds, 829 LLT funds, 819

MLT funds and 816 SLT funds. On average, FD (LLT, MLT, SLT) funds have a

lifetime of 168 (136, 88, 51) months.

In this context, Figure 1 shows the monthly number of funds in our subsamples.

The number of LLT funds increases until the end of 2000, remains on the same level

until the start of 2005 (829 funds) and decreases thereafter. MLT funds show a similar

pattern. That is, most MLT funds exist from December 2000 to December 2004

(about 570 funds on average). In contrast, SLT funds exhibit a relatively high number

of funds during the last third of the evaluation period. On average, we count about 170

3 Since each fund has at least 36 months of monthly returns, no funds disappear in the first three years

and no new funds start after January 2007.

8/11/2019 SSRN-id2370501

11/34

9

SLT funds from December 1996 to December 2004, while more than 350 SLT funds

exist from January 2005 to December 2009.

Insert Figure 1 about here

To analyze the performance of our funds, we use monthly excess returns of the

market ERM and the factors SMB, HML and MOM. 4 Table 2 presents descriptive

statistics for the four factors and factor alphas according to Equations (3) to (5). The

factors ERM, SMB, HML and MOM exhibit positive but not statistically significant

monthly means measuring 0.38, 0.26, 0.35 and 0.44, respectively. Similar, monthly

factor alphas of SMB, HML and MOM are positive but statistically not significant,

measuring 0.192, 0.428 and 0.596, respectively. Moreover, the four factors exhibit

low correlations, measuring between 0.39 and 0.23, which is also reflected by low

variance inflation factors (VIF) of about 1.3. Thus, multicollinearity should not be a

concern.


Focusing on the variation of factor alphas over time, Figure 2 shows the SMB,

HML and MOM factor alphas based on a 12-month rolling window. In general,

monthly factor alphas vary largely. For example, the SMB factor alpha is often

negative during the period from 1996 to 1999, but shows large fluctuations.

Conversely, from 2000 to 2004 it is mostly positive, exhibiting lower variability.

Similarly, the HML and MOM factor alphas clearly show variations over time.


4 The monthly factor and T-bill returns are downloadable from Kenneth Frenchs website(http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html), which also contains

information about the factor construction.

8/11/2019 SSRN-id2370501

12/34

10

To illustrate the variation in factor alphas during the individual lifetimes of our

non-full-data funds, Figure 3 shows absolute frequencies of factor alphas for our

subsamples of LLT, MLT and SLT funds. In addition, the bold vertical lines indicate

the respective full-period factor alphas of SMB, HML and MOM. Referring to LLT

funds in Panel A, their factor alphas vary only slightly with respect to full-period

factor alphas. Particularly, SMB and HML factor alphas of LLT funds are exclusively

positive. In comparison, factor alphas of SLT funds in Panel C vary clearly around

full-period factor alphas. Thus, SLT funds exhibit larger shares of negative SMB and

MOM factor alphas as well as relatively high positive SMB and MOM factor alphas.

Figure 3 about here

Against the background of these findings, we expect these differences in factor

alphas to impact JA fund rankings. In the next Section 3.2, we therefore investigate

the relationship between JAs, lifetime of funds and factor contributions.

3.2 Jensen alpha, four-factor alphas and factor contributions

We now take a closer look at descriptive statistics and factor alphas for our fund

subsamples. Table 3 shows average JAs, alphas and betas of the four-factor model and

corresponding standard deviations for the cross-sections of FD, SLT, MLT and LLT

funds. In addition, the average factor alphas for each fund subsample are presented.

Focusing on the FD fund sample in Panel A, JAs are positive on average, measuring

0.025%, while four-factor alphas are negative, measuring 0.045%. Furthermore, the

cross-sectional standard deviation of JAs is higher than that of four-factor alphas.

Noteworthy is the difference between JAs and four-factor alphas of FD funds, which

is driven solely by variation in the funds factor exposures, as the factor alphas of all

8/11/2019 SSRN-id2370501

13/34

11

FD funds coincide with the full-period factor alphas. Hence, based on Equation (6),

funds with exclusively negative factor exposures exhibit higher four-factor alphas and

vice versa given the positive SMB, HML and MOM factor alphas during the lifetime

of FD funds.

Focusing on LLT, MLT and SLT funds, in Panel B, C and D we observe lower

four-factor alphas compared to FD funds. Given the disappearance of many funds,

particularly in the SLT fund subsample, the relatively high performance of FD funds

could be due to a survivorship bias (see, among others, Brown and Goetzman, 1995;

Elton et al., 1996; Rohleder et al., 2011). Furthermore, these subsamples exhibit

higher cross-sectional standard deviations of four-factor alphas compared to FD

funds.

In contrast to FD funds, the difference between JAs and four-factor alphas of LLT,

MLT and SLT funds is not only driven by the variation in fund-specific factorexposures, but also by different factor alphas during the funds lifetimes. While the

average factor exposures of all four subsamples are similar, cross-sectional means and

standard deviations of factor alphas based on funds lifetimes differ considerably

among the subsamples (see also Figure 3). For example, the SMB factor alphas of

LLT funds show a mean and a standard deviation of 0.318% and 0.145%,

respectively, while for SLT funds these numbers are 0.246% and 0.436%,

respectively. Thus, the JAs of SLT funds tend to be more affected by variations in the

SMB factor alphas. We have similar findings regarding HML and MOM factor

alphas.


8/11/2019 SSRN-id2370501

14/34

12

While the factor exposures of our fund subsamples tend to be similar on average,

their factor alphas clearly differ. These should be reflected in variations in the

corresponding factor contributions to the JA. Thus we now focus on the relationship

between JAs and four-factor alphas with respect to factor contributions as outlined in

Equation (6). Positive factor contributions result in higher JAs compared to the four-

factor alphas and vice versa. As the majority of funds exist during positive market

phases of factor alphas, the sign of factor contributions is mostly affected by the sign

of the funds factor exposures. Therefore, we first split each fund subsample, based on

the sign of the funds SMB exposures, into a positive and a negative SMB exposure

group. Similarly, we group funds with respect to their HML and MOM exposures for

each subsample. Table 4 reports the cross-sectional averages of JAs, four-factor

alphas and corresponding factor contributions for our four subsamples in Panels A

to D.

In Panel A of Table 4, we observe that FD funds with positive SMB exposures

exhibit an average JA of 0.078%. Therefore, in line with Equation (6) and our

expectations, JAs mainly corresponds to the sum of the four-factor alphas of 0.036%

and the positive SMB factor contribution of 0.071%. Additionally, positive HML and

MOM factor contributions further increase the positive difference between the

average JA and four-factor alpha for this fund group. While we expect opposite

results for FD funds with negative SMB exposure, on average, these funds exhibit a

slightly higher JA (0.044%) than four-factor alpha (0.056%). Here, the negative

SMB factor contribution of 0.024% is more than compensated by the positive HML

factor contribution of 0.047%, resulting in an overall positive factor contribution.

Findings for the FD funds group with positive (negative) HML exposures reveal that,

8/11/2019 SSRN-id2370501

15/34

13

on average, the positive (negative) HML factor contribution results in a higher (lower)

JA compared to the four-factor alpha. In contrast, FD funds with negative MOM

exposure show a higher JA compared to the four-factor alpha, as the negative MOM

factor contribution is overcompensated by a positive HML factor contribution.

Since the lifetimes of non-full-data funds differ, in Panels B to D we now also

account for variations in factor alphas. That is, we further sort funds in each non-full-

data subsample into fund groups with high or with low SMB factor alphas. If the

SMB factor alpha during the fund-specific lifetimes is higher (lower) than the full-

period SMB factor alpha, the fund is sorted into the high (low) SMB factor alpha

group. In Panel B of Table 4, we observe for LLT funds in the high SMB factor alpha

group that funds with positive SMB exposures show, as expected, average JAs higher

than corresponding four-factor alphas. This positive difference is largely driven by a

positive SMB factor contribution. In contrast, funds with negative SMB exposure

exhibit lower JAs than corresponding four-factor alphas, as expected, mainly due to

negative SMB factor contributions. Furthermore, we observe comparable findings for

funds in the low SMB factor alpha group as well as for respective groups of funds

based on HML and MOM factor alphas and corresponding exposures. Moreover,

results for MLT funds are largely in line with LLT funds (see Panel C). Importantly,

on average, LLT and MLT funds show higher absolute factor contributions than FD

funds, due to variations in factor alphas.

Regarding the SLT funds in Panel D, we document for the high factor alpha fund

groups that funds with positive factor exposures show among the highest factor

contributions. Conversely, SLT funds in the low factor alpha groups have minor

factor contributions, as these groups are exposed to small factor alphas on average

8/11/2019 SSRN-id2370501

16/34

14

(compare Figure 3). 5 In addition, the SMB and MOM factor alphas of these SLT fund

groups are negative on average (compare Figure 3). Therefore, respective groups with

positive factor exposures have negative factor contributions and lower JAs compared

to four-factor alphas. Accordingly, SLT funds with positive factor exposures exhibit

higher JAs than four-factor alphas due to positive factor contributions.


In short, differences between JAs and four-factor alphas are substantially

influenced by variations in factor contributions which are driven by factor alphas

during the funds lifetimes. In particular, the factor contributions of SLT funds

substantially vary due to the market phases of factor alphas.

3.3 Time period adjustment of Jensen alpha

So far, we have observed that the JAs of our fund subsamples are differently affected

by factor contributions. After accounting for the sign of factor exposures, this is

mainly caused by market phases of factor alphas. To eliminate the market climate

impact on JAs, we now control for fund-specific factor alphas by replacing those with

full-period factor alphas. Consequently, we determine the adjusted JA for each fund

according to Equation (7). As result, we expect adjusted JAs of funds in the high

factor alpha fund groups to be lower (higher) than the classic JAs given positive

(negative) factor exposures. Since LLT funds mainly consist of funds with factor

alphas closer to full-period factor alphas, the JAs of this subsample should be less

affected by time period adjustments. In contrast, JAs of SLT funds should

5 In results not reported, we find that factor alphas are the higher (lower) for SLT funds in the high(low) factor alpha groups compared to corresponding LLT and MLT fund groups. These results are

available from the authors upon request.

8/11/2019 SSRN-id2370501

17/34

15

substantially change due to time period adjustments, as the factor alphas during their

lifetimes deviate substantially with respect to full-period factor alphas (see Section

3.2).

We sort LLT, MLT and SLT funds into the same fund groups as in Section 3.2.

Based on Equation (8), Table 5 refers to the adjusted JA, the classic JA and the

differences between adjusted and original factor contributions of LLT, MLT and SLT

fund groups in Panel A, B and C, respectively. In line with expectations, LLT funds

with positive SMB exposures in the high factor alpha group exhibit smaller adjusted

JAs (0.109%) than corresponding JAs (0.161%). This is mainly caused by a

downward adjustment of the SMB factor contribution (0.059%). For funds with

negative SMB exposure, a positive adjustment of the SMB factor contribution

(0.021%) leads to a higher adjusted JA (0.049%). However, funds in the low factor

alpha group with positive HML (MOM) exposure also exhibit lower adjusted JAs.

This is because the positive adjustment of the HML (MOM) contribution of 0.016%

(0.026%) is exceeded by a negative adjustment of the SMB factor contribution of

0.026% (0.046%). For MLT funds in Panel B and SLT funds in Panel C, we find

that the differences between adjusted JAs and classic JAs are mostly in line with our

expectations. Not surprisingly, most substantial are observed for the groups

containing SLT funds. For example, for SLT funds with positive SMB exposures in

the high factor alpha group, the difference on average between adjusted JA and JA

measures 0.16%. Thus, strong deviations in factor alphas lead to substantial

adjustments in factor contributions and hence to adjustments in JAs.


8/11/2019 SSRN-id2370501

18/34

16

One conclusion drawn from these findings is that comparing funds based on the

classic JA can result in biased fund rankings as soon as the investigated funds exhibit

different lengths of return history. To illustrate differences in fund rankings for our

fund subsamples, we present scatter plots similar to Bollen and Whaley (2009).

Therefore, we plot rank positions of funds based on adjusted JAs and JAs in one

diagram.

Figure 4 shows respective scatter plots for all funds as well as for the subsamples

of FD, LLT, MLT and SLT funds. In addition, corresponding mean absolute rank

changes (MARC) are reported. In the case of identical rank positions, coordinates of

funds would be located exactly on the bisecting line. For all funds in Panel A, we

observe that a larger share of funds is distributed closely to the bisecting line but

several funds are still widely dispersed. Against this background, FD funds in Panel B

and LLT funds in Panel C show relatively few differences in rank between those

based on adjusted JA and those based on JA. Since factor alphas of LLT funds are

only slightly adjusted, LLT funds exhibit an average MARC of only 163.5 ranks.

Importantly, the positions of SLT funds clearly deviate from the bisecting line

reflected by a relatively high average MARC of 357.9 ranks (see Panel E). Thus we

conclude that in this subsample, rank positions of funds based on the classic JA are

clearly influenced by market climate.


3.4 Robustness: Augmented factor models

Until now, our analysis is based on the assumption that the Carhart four-factor model

represents the return generating process of funds. However, recent literature offers

8/11/2019 SSRN-id2370501

19/34

17

alternative models that take additional performance factors into account. In the

following, we thus study whether our results are affected by choosing augmented

multi-factor models as the assumed return generating process of funds.

Taking the Carhart four-factor model (Model 1) as the point of departure, there are

several performance factors which could additionally be considered. For example,

Pastor and Stambaugh (2003) document that expected returns of stocks are sensitive

to market liquidity and suggest the use of a liquidity factor. Furthermore, Frazzini and

Petersen (2013) show that assets with high market exposure produce relatively low

alphas compared to assets with low market exposure. Consequently, they introduce a

so-called betting-against-beta (BAB) factor. Moreover, Asness et al. (2013) find high

quality stocks to exhibit higher risk-adjusted returns than low quality stocks. To

account for this potential anomaly, they introduce a quality-minus-junk (QMJ) factor

which may help to better explain stock returns. We consider these three potential

performance factors and hence augment the Carhart four-factor model either with a

liquidity, a BAB or a QMJ factor, resulting in three respective five-factor models

(Models 2 to 4). 6 Finally, we include these three additional factors at the same time,

resulting in a seven-factor model (Model 5).

Panel A of Table 6 presents Pearson correlations between adjusted JAs based on

the Models 1 to 5, respectively, which measure from 0.919 to 0.997. Likewise,

respective Spearman rank correlations in Panel B range between 0.907 and 0.997.

These high correlations indicate that the use of the Carhart (1997) four-factor model

6 The monthly return of the liquidity factor is downloadable from Lubos Pastors website(http://faculty.chicagobooth.edu/lubos.pastor/research/), which also contains information about thefactor construction. The monthly returns of the BAB and QMJ factors are downloadable from AndreaFrazzinis website (http://www.econ.yale.edu/~af227/data_library.htm), which also contains

information about the factor construction.

8/11/2019 SSRN-id2370501

20/34

18

as return generating process of funds is quite robust against the application of these

alternative multi-factor models.


4. Summary and conclusion

Our theoretical and empirical analyses indicate that using the classic JA to measure

and compare fund performance for a survivorship bias-free dataset can result in a

biased comparison. Different realizations of factor alphas during fund-specific

lifetimes result in varying factor contributions to the JA and thus impact respective

fund rankings.

To illustrate the impact of market phases of factor alphas on JA with respect to

lifetime of funds, we group funds based on the length of their return histories. We use

the Carhart four-factor model as the return generating process and show that

differences between the four-factor alphas and JAs of funds are driven by their SMB,

HML and MOM factor contributions. In detail, after accounting for the sign of the

factor exposures, factor contributions are driven by factor alphas and their respective

market phases. This is particularly the case for funds with short return histories. To

reduce the impact of market climate on factor contributions, we suggest standardizing

the evaluation period for all funds by replacing fund-specific factor alphas with full-

period factor alphas. We thus determine the JA which funds would have shown if they

had existed during the full evaluation period. This adjustment of factor alphas and

factor contributions has a stronger impact on funds with shorter return histories,

causing larger differences between adjusted JAs and corresponding classic JAs.

Against this background, fund rankings based on JA (instead of adjusted JA) are

8/11/2019 SSRN-id2370501

21/34

19

influenced by fund-specific factor alphas which can thus result in misleading

conclusions about the performance of the investigated fund sample. Comparing

correlations between adjusted JAs based on the Carhart four-factor model and based

on four augmented multi-factor models, our findings indicate only minor differences

and hence underline the robustness of our empirical results.

The findings reported here are not only important to researchers concerned with

fund performance and ranking, but also to investors and analysts comparing the

performance of individual funds. Moreover, our results are also useful for investment

company boards when rewarding fund managers for their performance relative to

others. Regarding future research, several possible directions emerge from these

results. In the context of empirical studies, the use of time period-adjusted alphas

could be applied to funds investing in different asset classes. Moreover, the approach

of adjusting JA could be transferred to other popular performance measures like the

Information ratio.

8/11/2019 SSRN-id2370501

22/34

20

References

Amihud, Y., Goyenko, R., 2013. Mutual funds R 2 as predictor of performance.

Review of Financial Studies 26, 667-694.

Aragon, G.O., Ferson, W.E., 2006. Portfolio performance evaluation. Foundations and

Trends in Finance 2, 83-190.

Asness, C.S., Frazzini, A., Pedersen, L. H., 2013. Quality minus junk. Working paper.

AQR capital management, New York University.

Banz, R., 1981. The relationship between return and market value of common stocks.

Journal of Financial Economics 9, 3-18.

Bodie, Z., Kane, A., Marcus, A.J., 2011. Investment and portfolio management.McGraw-Hill. 9th Edition.

Bollen, N.P.B., Whaley, R. E., 2009. Hedge fund risk dynamics: Implications for

performance appraisal. Journal of Finance 64, 985-1035.

Breloer, B., Scholz, H., and Wilkens, M., 2014. Performance of international and

global equity mutual funds: Do country and sector momentum matter? Journal of

Banking and Finance, forthcoming.

Brown, S.J., Goetzmann, W.N., 1995. Performance persistence. Journal of Finance50, 679-698.

Carhart, M.M., 1997. On persistence in mutual fund performance. Journal of

Finance 52, 57-82.

Carhart, M.M., Carpenter, J.N., Lynch, A.W., Musto, D.K., 2002. Mutual fund

survivorship. Review of Financial Studies 15, 1439-1463.

Comer, G., Larrymore, N., Rodriguez, J, 2009. Controlling for fixed-income

exposures in portfolio evaluation: Evidence from hybrid mutual funds. Review of

Financial Studies 22, 481-507.

Del Guercio, D., Tkac, P.A., 2002. The determinants of the flow of funds of managed

portfolios: Mutual funds vs. pension funds. Journal of Financial and Quantitative

Analysis 37, 523-557.

Elton, E.J., Gruber, M.J., Blake, C.R., 1996. Survivorship bias and mutual fund

performance. Review of Financial Studies 9, 1097-1120.

8/11/2019 SSRN-id2370501

23/34

21

Elton, E.J., Gruber, M.J., Brown, J.S., Goetzmann, W.N., 2009. Modern Portfolio

Theory and Investment Analysis. John Wiley & Sons. 8th Edition.

Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. Journal

of Finance 47, 427-465.

Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and

bonds. Journal of Financial Economics 33, 3-56.

Frazzini, A., Pedersen, L.H., 2013. Betting against beta. Journal of Financial

Economics, forthcoming.

Gharghori, P., Mudumba, S., Veeraraghavan, M., 2007. How smart is money? An

investigation into investor behaviour in the Australian managed fund industry.

Pacific-Basin Finance Journal 15, 494-513.

Goetzmann, W., Ingersoll, J., Spiegel, M., Welch, I., 2007. Portfolio performance

manipulation and manipulation-proof performance measures. Review of Financial

Studies 20, 1503-1546.

Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers:

Implications for stock market efficiency. Journal of Finance 48, 65-91.

Jensen, M.C., 1968. Problems in selection of security portfolios. Journal of Finance

23, 389-419.

Krimm, S., Scholz, H., Wilkens, M., 2012. The Sharpe ratios market climate bias:

theoretical and empirical evidence from US equity mutual funds. Journal of Asset

Management 13, 227-242.

Malkiel, B.G., 1995. Returns from investing in equity mutual funds 1971 to 1991.

Journal of Finance 50, 549-572.

Pastor, L., Stambaugh, R.F., 2002. Mutual fund performance and seemingly unrelated

assets. Journal of Financial Economics 63, 315-349.Pastor, L., Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal

of Political Economy 111, 642-685.

Rohleder, M., Scholz, H., Wilkens, M., 2011. Survivorship bias and mutual fund

performance: Relevance, significance, and methodical differences. Review of

Finance 15, 441-474.

Scholz, H., 2007. Refinements of the Sharpe ratio: Comparing aternatives for bear

markets. Journal of Asset Management 7, 347-357.

8/11/2019 SSRN-id2370501

24/34

22

Sharpe, W.F., 1966. Mutual fund performance. Journal of Business 39, 119-138.

Sharpe, W.F., 1994. The Sharpe ratio. Journal of Portfolio Management 21 (Fall),

49-58.

8/11/2019 SSRN-id2370501

25/34

23

Table 1: Yearly total numbers, starts and disappearances of fundsThis table shows the total numbers of funds as well as the numbers of annual fundstarts and disappearances within the evaluation period from January 1996 to December2009. Total number refers to the number of funds operating at the end of each year.

Funds

Year Total number Starts Disappearances

1995 1,097 1996 1,271 174 1997 1,500 229 1998 1,737 237 1999 1,946 213 42000 2,101 232 772001 2,198 173 762002 2,241 138 952003 2,219 120 1422004 2,217 132 1342005 2,260 190 1472006 2,283 145 1222007 2,174 22 1312008 2,049 1252009 1,849 200

8/11/2019 SSRN-id2370501

26/34

24

Table 2: Descriptive statistics of factorsThis table shows descriptive statistics for the monthly explanatory factors. The evaluation period is from January 1996 toDecember 2009. Monthly factor alphas are estimated based on Equation (1). Means and factor alphas are reported in percent. STDrefers to the standard deviation of monthly returns. VIF refers to the variance inflation factor. Numbers in brackets representt-statistics that are based on the null hypothesis H o: x = 0.

Factor Mean STD Factor

alphaVIF

Correlation

ERM SMB HML MOMERM 0.38 0.049 1.32 1

(1.02)SMB 0.26 0.039 0.192 1.21 0.23 1

(0.87) (0.65)HML 0.35 0.037 0.428 1.31 0.28 0.39 1

(1.20) (1.54)MOM 0.44 0.062 0.596 1.23 0.33 0.08 0.16 1

(0.92) (1.32)

8/11/2019 SSRN-id2370501

27/34

25

Table 3: Descriptive statistics of fund subsamplesThis table shows cross-sectional means and standard deviations (STD) of one-factor Jensen alphas as well as alphas and betas of the four-factor model for four fund subsamples. In addition, the table presents cross-sectional means and STD of corresponding factor alphas basedon fund lifetimes. Funds are first sorted into full-data funds (FD funds) and non-full-data funds. Non-full-data funds are then allocated tothree subsamples based on the length of fund return histories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes.Monthly (factor) alphas and STD are reported in percent.

1F-model 4F-modelFactor alpha

during fund lifetime

1F adj. R2 4F 4F 4F 4F 4F adj. R2 smb

1F hml 1F mom1F

Panel A: FD fundsMean 0.025 0.767 0.045 0.965 0.152 0.084 0.007 0.871 0.192 0.428 0.596STD 0.199 0.113 0.173 0.161 0.311 0.315 0.106 0.071Panel B: LLT funds Mean 0.034 0.767 0.052 0.988 0.16 0.052 0.024 0.873 0.318 0.533 0.549STD 0.305 0.129 0.242 0.146 0.314 0.337 0.125 0.076 0.145 0.159 0.334Panel C: MLT funds Mean 0.072 0.801 0.150 0.997 0.194 0.015 0.019 0.887 0.313 0.492 0.509STD 0.319 0.139 0.272 0.171 0.337 0.319 0.126 0.090 0.191 0.249 0.562Panel D: SLT funds Mean 0.121 0.804 0.155 1.001 0.194 0.005 0.001 0.889 0.246 0.298 0.165STD 0.477 0.166 0.393 0.183 0.337 0.321 0.153 0.102 0.436 0.371 0.825

8/11/2019 SSRN-id2370501

28/34

26

Table 4: Components of Jensen alphaThis table shows average one-factor Jensen alphas, four-factor alphas and factor contributions for four fund subsamples. Funds are firstsorted into full-data funds (FD funds) and non-full-data funds. Non-full-data funds are then allocated to three subsamples based on the lengthof fund return histories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes. Fund subsamples are further divided by

positive factor exposure and negative factor exposure (for each of the factors SMB, HML and MOM). In addition, LLT, MLT and SLT fundsare sorted based on the factor alpha of funds being higher than the corresponding full-period factor alpha (high factor alpha) or lower than thecorresponding full-period factor alpha (low factor alpha). Monthly alphas and factor contributions are reported in percent.

1F 4F 2

4F smb1F 3

4F hml 1F 4

4F mom 1F

Panel A: FD funds pos. SMB 0.078 0.036 0.071 0.027 0.016neg. SMB 0.044 0.056 0.024 0.047 0.011

pos. HML 0.075 0.048 0.022 0.122 0.021neg. HML 0.058 0.039 0.040 0.104 0.045

pos. MOM 0.010 0.076 0.043 0.030 0.053neg. MOM 0.059 0.014 0.016 0.101 0.044

Panel B: LLT fundsHigh factor alpha pos. SMB 0.161 0.018 0.129 0.023 0.028neg. SMB 0.066 0.043 0.044 0.031 0.010

pos. HML 0.105 0.085 0.039 0.173 0.022neg. HML 0.146 0.083 0.052 0.158 0.044

pos. MOM 0.117 0.193 0.052 0.085 0.108neg. MOM 0.112 0.125 0.002 0.082 0.071

Low factor alpha pos. SMB 0.074 0.164 0.059 0.018 0.049neg. SMB 0.152 0.136 0.017 0.033 0.032

pos. HML 0.160 0.003 0.063 0.109 0.009neg. HML 0.040 0.015 0.065 0.097 0.057

pos. MOM 0.104 0.008 0.096 0.021 0.036neg. MOM 0.136 0.028 0.029 0.106 0.027

Panel C: MLT fundsHigh factor alpha pos. SMB 0.027 0.150 0.150 0.011 0.017neg. SMB 0.172 0.130 0.049 0.016 0.009

pos. HML 0.013 0.218 0.050 0.200 0.045neg. HML 0.279 0.236 0.076 0.191 0.073

pos. MOM 0.176 0.296 0.074 0.095 0.140neg. MOM 0.150 0.199 0.014 0.122 0.087


pos. HML 0.062 0.049 0.062 0.048 0.002neg. HML 0.035 0.052 0.059 0.052 0.010

pos. MOM 0.019 0.094 0.091 0.023 0.006neg. MOM 0.044 0.034 0.064 0.015 0.001

Panel D: SLT fundsHigh factor alpha pos. SMB 0.040 0.181 0.220 0.034 0.035neg. SMB 0.192 0.104 0.088 0.006 0.007

pos. HML 0.007 0.225 0.028 0.255 0.052neg. HML 0.361 0.302 0.118 0.224 0.046

pos. MOM 0.036 0.204 0.059 0.058 0.167neg. MOM 0.256 0.182 0.023 0.092 0.142


pos. HML 0.214 0.208 0.001 0.028 0.033neg. HML 0.005 0.020 0.030 0.018 0.014

pos. MOM 0.150 0.139 0.056 0.036 0.031neg. MOM 0.035 0.127 0.035 0.031 0.027

8/11/2019 SSRN-id2370501

29/34

27

Table 5: Time period adjustment of Jensen alphaThis table shows average time period-adjusted Jensen alphas, Jensen alphas and differences between full-period adjusted- and original factorcontributions for non-full-data fund subsamples. Non-full-data funds are sorted into three subsamples based on the length of fund returnhistories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes. Fund subsamples are further divided by positive factorexposure and negative factor exposure (for each of the factors SMB, HML and MOM). In addition, LLT, MLT and SLT funds are sorted

based on the factor alpha of funds being higher than the corresponding full-period factor alpha (high factor alpha) or lower than thecorresponding full-period factor alpha (low factor alpha). Monthly alphas and differences in factor contributions are reported in percent.

1F_adj 1F 2

4F ( smb1F_ FP smb

1F 3 4F ( hml

1F_F P hml ,1F 4

4F ( mom1F_F P mom 1F

Panel A: LLT fundsHigh factor alpha pos. SMB 0.109 0.161 0.059 0.001 0.006neg. SMB 0.049 0.066 0.021 0.004 0.000

pos. HML 0.049 0.105 0.017 0.051 0.011neg. HML 0.118 0.146 0.023 0.054 0.003

pos. MOM 0.131 0.117 0.006 0.029 0.038neg. MOM 0.108 0.112 0.000 0.020 0.025


pos. HML 0.148 0.160 0.026 0.016 0.002

neg. HML 0.008 0.040 0.021 0.013 0.001 pos. MOM 0.085 0.104 0.046 0.001 0.026neg. MOM 0.100 0.136 0.013 0.009 0.015

Panel B: MLT fundsHigh factor alpha pos. SMB 0.043 0.027 0.076 0.000 0.006neg. SMB 0.141 0.172 0.025 0.001 0.006

pos. HML 0.086 0.013 0.023 0.072 0.022neg. HML 0.266 0.279 0.036 0.072 0.022

pos. MOM 0.234 0.176 0.028 0.031 0.061neg. MOM 0.155 0.150 0.001 0.042 0.038


pos. HML 0.066 0.062 0.024 0.029 0.002neg. HML 0.070 0.035 0.012 0.036 0.014

pos. MOM 0.012 0.019 0.043 0.006 0.044neg. MOM 0.012 0.044 0.022 0.005 0.038

Panel C: SLT fundsHigh factor alpha pos. SMB 0.120 0.040 0.151 0.000 0.009neg. SMB 0.124 0.192 0.065 0.003 0.000

pos. HML 0.100 0.007 0.005 0.110 0.009neg. HML 0.325 0.361 0.080 0.108 0.008

pos. MOM 0.131 0.036 0.019 0.006 0.081neg. MOM 0.135 0.256 0.048 0.005 0.066


pos. HML 0.099 0.214 0.039 0.071 0.006neg. HML 0.053 0.005 0.012 0.075 0.004 pos. MOM 0.078 0.150 0.013 0.001 0.084neg. MOM 0.137 0.035 0.004 0.028 0.078

8/11/2019 SSRN-id2370501

30/34

28

Table 6: Rank correlation between adjusted Jensen alphasThis table presents Pearson correlations and Spearman rank correlations of funds between time period-adjusted Jensen alphas (JA adj) basedon several multi-factor models. The evaluation period is from January 1996 to December 2009. Model 1 is the Carhart four-factor model.Model 2 refers to a five-factor model that additionally includes a liquidity factor (Pastor and Stambaugh, 2003). Model 3 represents a five-factor model that additionally contains a betting-against-beta factor (Frazzini and Petersen, 2013). Model 4 refers to a five-factor model thataugments the Carhart model by a quality-minus-junk factor (Asness et al., 2013). Model 5 is a seven-factor model that contains the fourfactors of the Carhart model as well as the liquidity, the betting-against-beta and the quality-minus-junk factors.

JA adj (M1) JA adj (M2) JA adj (M3) JA adj (M4) JA adj (M5)

Panel A: Pearson correlationJA adj (M1) 1JA adj (M2) 0.997 1JA adj (M3) 0.967 0.969 1JA adj (M4) 0.941 0.940 0.919 1JA adj (M5) 0.953 0.954 0.962 0.948 1Panel B: Spearman rank correlationJA adj (M1) 1JA adj (M2) 0.997 1JA adj (M3) 0.961 0.963 1JA adj (M4) 0.927 0.926 0.907 1

JAadj

(M5) 0.941 0.941 0.951 0.943 1

8/11/2019 SSRN-id2370501

31/34

29

Figure 1: Monthly number of funds in subsamplesThis figure shows the monthly number of funds in four subsamples. The evaluation period is from January 1996 to December 2009. Thefunds are first sorted into full-data funds (FD funds) and non-full-data funds. Non-full-data funds are then allocated to three subsamples

based on the length of fund return histories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes.

0

100

200

300

400

500600

700

800

900

1 2 . 1 9 9 6

1 2 . 1 9 9 7

1 2 . 1 9 9 8

1 2 . 1 9 9 9

1 2 . 2 0 0 0

1 2 . 2 0 0 1

1 2 . 2 0 0 2

1 2 . 2 0 0 3

1 2 . 2 0 0 4

1 2 . 2 0 0 5

1 2 . 2 0 0 6

1 2 . 2 0 0 7

1 2 . 2 0 0 8

1 2 . 2 0 0 9

FD funds (638) LLT funds (829) MLT funds (819) SLT funds (816)

8/11/2019 SSRN-id2370501

32/34

30

Figure 2: Rolling 12-month factor alphasThis figure presents monthly rolling 12-month factor alphas stemming from regressions of the monthly factors SMB, HML and MOM on themarket excess return ERM according to Equation (1). The evaluation period is from January 1996 to December 2009. The first windowranges from January 1996 to December 1996. The horizontal axis indicates the end dates of the respective rolling windows. Monthly factoralphas are reported in percent.

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

1 2 . 1 9 9 6

1 2 . 1 9 9 7

1 2 . 1 9 9 8

1 2 . 1 9 9 9

1 2 . 2 0 0 0

1 2 . 2 0 0 1

1 2 . 2 0 0 2

1 2 . 2 0 0 3

1 2 . 2 0 0 4

1 2 . 2 0 0 5

1 2 . 2 0 0 6

1 2 . 2 0 0 7

1 2 . 2 0 0 8

1 2 . 2 0 0 9

SMB factor alpha HML factor alpha MOM factor alpha

8/11/2019 SSRN-id2370501

33/34

31

Figure 3: Frequencies of factor alphas for different fund subsamplesThis figure shows the absolute frequencies of factor alphas with respect to each fund subsample and the factors SMB, HML and MOM.Factor alphas stem from regressing the factors SMB, HML and MOM on the market excess return ERM according to Equation (1) based oneach funds specific lifetime. The bold vertical lines refer to the corresponding full-period factor alphas of SMB, HML and MOM. Funds arefirst sorted into full-data funds and non-full data funds. Non-full data funds are then allocated to three subsamples based on the length offund return histories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes. Panels A, B and C show the absolutefrequencies of factor alphas for LLT, MLT and SLT funds, respectively. Monthly factor alphas are reported in percent.

LLT funds

SMB factor alpha

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

LLT funds

HML factor alpha

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

LLT funds

MOM factor alpha

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

MLT funds

SMB factor alpha

F r e q

u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

MLT funds

HML factor alpha

F r e q

u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

MLT funds

MOM factor alpha

F r e q

u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

SLT funds

SMB factor alphas

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

SLT funds

HML factor alpha

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

SLT funds

MOM factor alpha

F r e q u e n c y

-1.0 -0.5 0.0 0.5 1.0 1.5

0

1 0 0

2 0 0

3 0 0

Panel A: LLT funds

Panel B: MLT funds

Panel C: SLT funds

8/11/2019 SSRN-id2370501

34/34

Panel A: All funds (MARC: 210.1) Panel B: FD funds (MARC: 54.6)

Panel C: LLT funds (MARC: 163.5) Panel D: MLT funds (MARC: 234.1)

Panel E: SLT funds (MARC: 357.9)

Figure 4: Scatter plots of fund ranks based on Jensen alphas and time period-adjusted Jensen alphasThis figure shows scatter plots of rank positions for all funds and for four fund subsamples. The evaluation period is from January 1996 toDecember 2009. The rank positions are based on the classic Jensen alpha (JA) and the time period-adjusted JA. Funds are first sorted intofull-data funds (FD funds) and non-full-data funds. Non-full-data funds are then allocated to three subsamples based on the length of fundreturn histories. LLT (MLT, SLT) funds refer to funds with long (medium, short) lifetimes. Panel A presents the scatter plots of rank

positions with respect to all funds. Panels B to E present scatter plots of rank positions with respect to the FD, LLT, MLT and SLT fundsubsamples. MARC refers to the mean absolute rank change between the classic JA and the adjusted JA.

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

R a n

k s b a s e d

o n a d

j u s t e d

J A

Ranks based on JA

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

R a n

k s

b a s e d

o n a d

j u s t e d

J A

Ranks based on JA

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

R a n

k s b a s e

d o n a

d j u s g e d

J A

Ranks based on JA

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

R a n

k s b a s e

d o n a d

j u s t e d

J A

Ranks based on JA

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

R a n

k s b a s e

d o n a d

j u s t e d

J A

Ranks based on JA

ssrn-id2370501

Documents