Available via license: CC BY 4.0
Content may be subject to copyright.
Open Access
© The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original
author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third
party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the mate-
rial. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or
exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://
creat iveco mmons. org/ licen ses/ by/4. 0/.
RESEARCH
Alda Financial Innovation (2025) 11:79
https://doi.org/10.1186/s40854-025-00761-4
Financial Innovation
Importance ofportfolio optimization inSRI
andconventional pension funds
Mercedes Alda1*
Abstract
This study assesses the portfolio concentration of socially responsible investment (SRI)
pension funds, which may be subject to a potentially limited asset universe and have
a higher concentration and lower performance than conventional funds. Nonethe-
less, in contrast to previous studies on SRI funds, this study considers the information-
advantage theory, positing that skilled managers should increase their concentration
in assets in which they possess valuable information, departing from optimization
models to achieve outperformance. This study first compares actual fund concentra-
tion with concentration obtained from several traditional and modern portfolio opti-
mization techniques (minimum variance, global minimum variance, optimal portfolio,
naïve diversification, risk parity, and reward-to-risk timing) to understand whether SRI
pension funds concentrate portfolios and deviate from optimization model solutions.
Unlike previous studies, the actual fund assets are considered in the optimization mod-
els to take into account the real investment profiles of SRI funds. The results indicate
that SRI pension funds are less concentrated than conventional funds, and SRI and con-
ventional pension funds largely diversify their portfolios, presenting lower concentra-
tion than portfolios formed with the optimization models. Furthermore, concentration
strategies positively influence performance in SRI and conventional funds, revealing
the use of information advantage. However, SRI and conventional fund managers
present poor skills (picking, timing, and trading) to exploit information advantages due
to overconfidence issues, which affect performance with concentration strategies. This
situation may be modified if SRI funds follow modern optimization models and con-
ventional funds follow traditional optimization models, improving managers’ perfor-
mance and skills.
Keywords: Concentration, Managerial skill, Pension fund, Portfolio optimization, SRI
Introduction
Traditional asset-pricing theories propose that portfolios with a limited asset universe,
such as socially responsible investment (SRI) funds, are subsets of the optimal portfolio
(Barnett and Salomon, 2006; Gangi and Varrone 2018). As a result, SRI funds develop
more concentrated portfolios and achieve lower performance than traditional funds
focused on financial factors; that is, the so-called conventional funds (Barnett and
Salomon, 2006; Gangi and Varrone 2018). Nevertheless, this argument is empirically
underexplored because the SRI niche is still growing, and the SRI boundaries have been
*Correspondence:
malda@unizar.es
1 Faculty of Economics
and Business, University
of Zaragoza, C/Gran Vía, 2, C.P.
50005 Saragossa, Spain
Page 2 of 37
Alda Financial Innovation (2025) 11:79
insufficiently studied. With currently available information, only Helliar et al. (2022)
compared the concentration in the top-10 holdings of SRI and conventional mutual
funds with basic mean tests, yet did not examine the overall SRI-fund concentration.
Hence, whether SRI funds develop more concentrated portfolios than conventional
funds and whether this concentration results in underperformance remain unanswered
in the literature. is study attempts to fill this research gap by considering the overall
fund concentration and the novel perspective of information-advantage theory to better
understand SRI-fund concentration strategies.
Furthermore, the study of portfolio concentration in SRI pension funds deserves
special attention because their motivation, time horizon, clientele, and investment
restrictions may further limit their asset universe. Pension funds are subject to stricter
regulations than other institutional investors because they should manage large retire-
ment savings in the best interest of beneficiaries with long-term and prosocial invest-
ments (Sandberg 2013). Additionally, pension funds are one of the largest long-term
institutional investors in SRIs (Cox etal. 2004). Consequently, SRI pension funds might
face a narrower asset universe due to their dual nature as retirement-saving vehicles and
socially responsible investments. is may result in concentration patterns that differ
from mutual funds.
is study examines the concentration patterns of SRI and conventional equity pension
funds in the United Kingdom’s (UK) world-leading pension-fund industry. Specifically,
the SRI and conventional pension fund datasets are matched using the nearest-neighbor
matching with a propensity score estimated using a logistic similarity measure based on
fund features. Moreover, the fund concentration of SRI and conventional pension funds
is compared using nonparametric and parametric methodologies.
In addition, there are three aspects to consider when analysing the SRI-fund concen-
tration. First, if SRI funds are subsets of the optimal portfolio (Barnett and Salomon,
2006; Gangi and Varrone 2018), their asset allocation will differ from that provided by
optimization models. However, many portfolio optimization models exist, offering dif-
ferent solutions based on the rationale of each model. us, SRI portfolios may not
follow traditional optimization techniques but present correct diversification. Second,
traditional asset-pricing theories do not consider the informational advantage theory.
e latter theory proposes that more concentrated portfolios may be optimal when
fund managers concentrate on assets in which they possess valuable information, lead-
ing to outperformance (Choi etal. 2017). ird, the two previous considerations may
be affected by managerial skills because portfolio optimization models may not capture
managerial skills, and the success of concentration strategies with information advantage
is subject to managers’ skills in processing and exploiting valuable information. Hence,
in contrast with previous research, this study considers these three aspects.
is study first compares the actual fund concentration with the concentration that
the funds would have obtained using several traditional and modern portfolio optimiza-
tion models (the minimum variance, the global minimum variance, the optimal port-
folio, the naïve diversification, the risk-parity, and the reward-to-risk timing models).
Contrary to past research, optimization models start from the actual fund assets to
consider the funds’ investment profiles and managers’ information signals in the opti-
mization process. is study also addresses the scarcity of analyses on SRI optimization,
Page 3 of 37
Alda Financial Innovation (2025) 11:79
which simulated SRI portfolios without considering actual SRI-fund investment patterns
(Oikonomou etal. 2018). us, previous studies did not explore the argument that SRI
funds develop more concentrated portfolios and underperform due to a limited asset
universe. e results of this study will also determine whether the asset allocations
developed by the SRI and conventional pension funds deviate from the optimization-
model solutions, assessing the impact of the asset allocation technique on fund perfor-
mance. Furthermore, this study analyses the concentration–performance relationship
from an information-advantage perspective and whether optimization models can guide
managers’ asset allocations to exploit informational advantages and improve skills, con-
centration strategies, and performance.
e findings of this study demonstrate that SRI funds can overcome the limited asset
universe boundary and build less concentrated portfolios than conventional funds. Con-
trary to expectations, pension funds largely diversify their portfolios, approaching naïve
diversification. e results also indicate that SRI and conventional managers have poor
picking, timing, and trading skills to manage information advantages. Optimization
models can help managers improve fund performance and skills through better asset
allocation decisions. Overall, these results contribute to filling the gap in the concentra-
tion–diversification dilemma of UK SRI and conventional equity pension funds.
e remainder of this study is organized as follows. Sect. "Literature review and
research hypotheses" presents the literature review and the research hypotheses.
Sect."Market overview, data, and variables" presents a market overview, data, and vari-
ables. e methods and empirical findings are presented in Sect."Empirical findings".
Sect."Conclusions" presents the conclusions.
Literature review andresearch hypotheses
Diversification is the basis of portfolio asset allocation (Platanakis etal. 2019); however,
portfolios with a limited asset universe, such as SRI funds, may be forced to build con-
centrated portfolios, departing from optimization models’ asset allocation (Barnett and
Salomon, 2006; Gangi and Varrone 2018). Previous studies have found that conventional
mutual fund managers sometimes diversify portfolios to a lesser extent than the level
recommended by portfolio choice models, obtaining positive outcomes (Choi et al.
2017; Fulkerson and Riley 2019; Kacperczyk etal. 2005). is evidence is consistent with
the information advantage theory (versus the traditional asset-pricing theory), positing
that deviations from the perfectly diversified market portfolio may be optimal for some
investors due to the information advantages in some assets (Merton 1987; Van Nieuw-
ergugh and Veldkamp 2010). According to the information-advantage theory, manag-
ers who know more about a financial/nonfinancial risk factor than average managers
tilt their portfolios significantly toward assets loading on that factor, deviating from
the perfectly diversified market portfolio (Choi etal. 2017; Fulkerson and Riley 2019).
Hence, from the information advantage perspective, SRI managers may have more spe-
cialized knowledge about environmental, social, and governance (ESG) risks and use this
knowledge to concentrate their portfolios on some ESG assets. If SRI funds use valu-
able ESG information to select superior firms, the limited ESG asset universe may pro-
vide investment opportunities, undermining the argument that SRI funds concentrate
portfolios and underperform due to the limited asset universe. With currently available
Page 4 of 37
Alda Financial Innovation (2025) 11:79
information, only Helliar etal. (2022) compared cash percentages and the concentration
in the top-10 holdings of SRI and conventional mutual funds. Applying a t-test mean,
Helliar etal. (2022) found that SRI funds have smaller cash holdings and lower invest-
ments in the top-10 portfolio holdings. Although these authors did not research the
overall fund concentration (unlike this study), their results indicate that SRI funds can
develop less concentrated portfolios than conventional funds. us, portfolio concentra-
tion is expected to depend on managers’ information rather than on the conventional/
SRI nature of the fund. Considering these arguments, the first hypothesis is as follows:
H1. SRI pension funds do not present more concentrated portfolios than conventional
pension funds.
Although the concentration of SRI funds may pursue to exploit information advan-
tages, the problem of SRI-fund concentration is also related to the failure of the diver-
sification bases of modern portfolio theory in SRI funds because ethical portfolios are
subsets of the market portfolio due to complying with ESG standards (Barnett and
Salomon, 2006; Bauer etal. 2006; Gangi and Varrone 2018). Oikonomou etal. (2018)
explained that SRI funds may outweigh optimization model solutions. Nevertheless, no
previous studies have analyzed the portfolio optimization model followed by SRI funds
or whether SRI funds deviate from optimization model solutions. e scarce literature
on SRI optimization is limited to exploring how to construct SRI portfolios based on
Markowitz’s mean–variance optimization frameworks (Ballestero etal. 2012; Utz etal.
2014). However, Markowitz optimizations suffer from significant estimation risk, result-
ing in input-sensitive solutions and unstable and poorly diversified portfolios (DeMiguel
etal. 2009; Oikonomou etal. 2018). Moreover, Utz etal. (2014) found no significant dif-
ferences in SRI and conventional mutual fund asset allocations with the Markowitz opti-
mization after a screening stage.
Only Oikonomou etal. (2018) has analyzed the optimization model’s impact in simu-
lated SRI portfolios, finding that more formal optimization models result in SRI port-
folios with lower risk, higher risk–return trade-offs, more unstable intertemporal asset
allocations, and lower diversification than more simplistic optimization models. Oikono-
mou etal. (2018) also argued that the optimization method for SRI portfolios should
be based on models considering risk and return to capture the higher estimation risk
of SRI assets. However, despite the many models, previous studies have not identified a
winning optimization model due to contradictory performance outcomes (Jacobs etal.
2014). Many studies have found that the naïve portfolio selection is superior to more
sophisticated methods due to its stability (Fischer and Gallmeyer 2016; Kirby and Ost-
diek 2012, among others). is study attempts to fill the gap in the SRI funds’ optimiza-
tion strategy by comparing the real fund concentration with the concentration obtained
from six optimization models. e six optimization models are divided into three tradi-
tional models (minimum variance, global minimum variance, and optimal portfolio) and
three more modern approaches (naïve diversification, risk-parity, and reward-to-risk
timing models) because SRI funds may deviate from traditional mean–variance models
and the more modern models are based on investing intuition (Oikonomou etal. 2018).
Nonetheless, market conditions vary and managers must rebalance their portfolios;
that is, optimization models must be recalculated with new information. is process
can be costly, especially with the computing effort of some models, such as traditional
Page 5 of 37
Alda Financial Innovation (2025) 11:79
mean–variance frameworks (Oikonomou etal. 2018). Hence, SRI and conventional fund
managers are expected to rebalance their portfolios without recurrently implementing
the optimization models, and deviate from the optimization models. Considering these
arguments, the second hypothesis is as follows:
H2. SRI and conventional funds deviate from the asset allocations of optimization
models.
e dilemma of developing more concentrated SRI portfolios and deviating from the
perfectly diversified market portfolio is also due to performance penalties. Nonethe-
less, considering the information advantage theory, if managers choose stocks based on
valuable ESG information, ESG standards might not impose a boundary. Greater port-
folio concentration on valuable assets allows managers to raise the weight of the best
investments, increasing the expected alpha (Choi etal. 2017). Previous SRI literature has
found that intense ESG screening criteria may improve performance (Friede etal. 2015;
Oikonomou etal. 2018). Soler‐Domínguez etal. (2021) also found that funds with higher
sustainability intensity perform better.
e information advantage theory further proposes that when information is valuable
enough and the portfolio is sufficiently diversified, the marginal benefit of increasing
concentration offsets the marginal costs of higher volatility with greater concentration
(Fulkerson and Riley 2019; Kacperczyk etal. 2005). In other words, concentrated funds
may present correct diversification by investing in several assets that minimize the idi-
osyncratic fund risk.1 us, managers should balance the expected returns and volatil-
ity by considering whether greater concentration produces benefits (Fulkerson and Riley
2019). When managers follow the principles of the information advantage theory, con-
centration is expected to positively influence performance, despite the conventional/SRI
fund nature. In line with these premises, the third hypothesis is as follows:
H3. A higher portfolio concentration improves SRI and conventional pension fund
performance.
Another important factor in concentration strategies is that concentration is condi-
tioned by managerial skills (Chen and Lai 2015). Managers should be able to use and
process valuable information; otherwise, the information advantage is useless. Kacper-
czyk etal. (2014) defined skill as the cognitive ability to process information (public or
private) in a limited time to generate a high-performance portfolio. Specifically, selectiv-
ity (or stock-picking) and market-timing skills are representative of this cognitive abil-
ity, indicating the capacity to choose assets and invest/disinvest at the correct moment,
respectively (Bauer et al. 2006; Stein 2022). Managers with superior skills are able to
learn and specialize in assets in which they have information advantage, exploiting the
information advantage with more concentrated portfolios (Choi etal. 2017). at is to
say, skilled managers will present portfolios with a higher concentration.
Kacperczyk etal. (2008) pointed out that managers may also have hidden managerial
skills because of unobserved trading activities. Hence, these authors proposed the return
gap measure to evaluate unobserved trading fund actions. e return gap captures hid-
den benefits and hidden costs to assess the value added/subtracted by the manager
1 e author thanks an anonymous referee for pointing out this argument.
Page 6 of 37
Alda Financial Innovation (2025) 11:79
(Kacperczyk etal. 2008). Although no previous studies have examined the relationship
between the return gap and concentration, skilled managers who undertake unobserved
trading actions may exploit this skill with concentration strategies. Hence, the following
hypotheses are proposed:
H4. e managers of more concentrated funds present superior stock-picking skills.
H5. e managers of more concentrated funds present superior market-timing skills.
H6. e managers of more concentrated funds present superior unobserved trading
skills (i.e., a larger return gap).
Superior skills will likely lead to better performance because the stock-picking skill is
based on holding more stocks with higher realized returns; that is, picking stocks that
outperform others at the same level of non-diversifiable risk (Kacperczyk etal. 2014).
Similarly, correct market timing refers to increasing holdings when market returns are
high, expanding exposure to the market portfolio (Kacperczyk etal. 2014). In addition, a
positive return gap shows the trading ability to add value due to hidden trading benefits
regarding the value subtracted due to hidden trading costs (Kacperczyk etal. 2008). If
concentration strategies’ success depends on managerial skills, managers with superior
skills will likely develop more concentrated portfolios and obtain higher performance.
us, the final hypothesis is proposed as follows:
H7. e combined effect of superior skills (stock-picking, timing, or unobserved trad-
ing -return gap) and higher concentration results in greater performance.
Market overview, data, andvariables
Market overview anddata
is study examines UK SRI and conventional pension funds because of the UK pension
fund industry’s unique characteristics. e UK pension fund industry is the second-larg-
est global pension fund market, with more than €2.7 trillion in 2023 (INVERCO 2024).
Additionally, the UK is a pioneer in developing a specific regulation on pension funds’
ESG disclosure (UKSIF 2018; UK Statutory Instruments No. 988 Pensions, 2018). e
development of the UK SRI pension fund niche makes it possible to study the portfolio
concentration of SRI pension funds and investigate whether SRI and conventional pen-
sion funds have distinct concentration patterns.
e data are drawn from several sources. e pension fund data are obtained from
the Morningstar Direct database and include all equity pension fund share classes domi-
ciled in the UK from January 1999 to August 2021. Morningstar Direct does not con-
tain data at the fund level but provides data for all the fund’s share classes. e data are
divided into conventional- and SRI-fund share classes with the dichotomous “Socially
Conscious” label (yes/no) provided by Morningstar. Hence, the data include 580 share
classes labeled as “Socially Conscious” (i.e., SRI-fund share classes) and 14,216 share
classes not labeled as “Socially Conscious” (i.e., conventional-fund share classes).
e data collected for each share class include the monthly and daily return, monthly
total net assets (TNA, in pounds), monthly portfolio sustainability score, inception fund
date, obsolete fund date (i.e., the end date of the fund if applicable), annual expense
ratios, investment area (the UK, Europe, the USA -United States of America-, Japan,
global markets, and emerging markets), firm name, quarterly portfolio holdings (weights
invested in each stock), a load/no-load dummy, and an institutional investor dummy.
Page 7 of 37
Alda Financial Innovation (2025) 11:79
Following previous studies, because the data are not at the fund level, all share classes
belonging to a fund are aggregated to operate at the fund level (Kacperczyk etal. 2014;
Renneboog etal. 2011). us, the following variables are calculated at the fund level:
monthly weighted average return, expense ratios, and sustainability scores of a given
fund’s share classes. e monthly TNAs of all the share classes of a fund are also aggre-
gated. Nonetheless, quarterly portfolio holdings of all the share classes belonging to a
fund are common; thus, this information is already at the fund level. In addition, the
pension fund data are monthly, but the portfolio holdings are quarterly; hence, quarterly
holding data for the three months of each quarter are used to obtain monthly portfo-
lio holdings, following Brown etal. (2021). Finally, the qualitative fund characteristics
(inception and obsolete dates) are those of the oldest share class.2 e final data com-
prise 80 SRI pension funds and 1548 conventional pension funds. Live and dead funds
are included to avoid survivorship bias.
Size differences between the SRI and conventional fund datasets may produce biased
results and prevent adequate comparisons (Ammann etal. 2019; Bilbao-Terol etal. 2017).
Hence, the r:1 nearest-neighbor matching method is applied for selecting matched con-
ventional funds (Ammann etal. 2019; Bilbao-Terol etal. 2017; Rubin 1973). is method
is widely used in comparative studies of SRI and conventional funds because it provides
a balance between samples, improves parametric statistics with reduced standardized
bias across covariates, and reduces endogeneity issues and omitted variable concerns
(Ammann etal. 2019; Bilbao-Terol etal. 2017; Joliet and Titova 2018). is technique
matches the control group (conventional funds) and the treated group (SRI funds) by
the smallest distance regarding fund characteristics. e propensity score is used as a
similarity measure between funds and is estimated using a logistic regression on the fol-
lowing fund characteristics: fund size, fund age, expense ratio, investment area, and firm
name. is method allows control funds to be matched several times. erefore, the 4:1
nearest-neighbor matching is applied, providing two balanced datasets comprising 80
SRI funds and 84 matched conventional funds.
Additionally, stock market information is obtained on the 11,688 different stocks in
which the 80 SRI and the 84 matched conventional funds invested over the study period
to calculate skill measures (see the skill variable description in Sect."Variables"). e
stock market information is obtained from the Datastream database and includes
monthly stock prices, monthly stocks’ market capitalization, each stock’s market bench-
mark name, monthly market index prices of the benchmarks, and monthly market
capitalization of the benchmarks. e market benchmarks are the equity market indi-
ces associated with each stock developed by Datastream.3 e price data are used to
2 e oldest share class in a fund is usually the first established share class by a fund firm.
3 Each market index represents all the stocks traded in each of the 66 stock markets analyzed. Specifically, the equity
market indices are from: Argentina, Australia, Austria, Bangladesh, Belgium, Brazil, Bulgaria, Canada, Chile, China,
Colombia, Croatia, Cyprus, the Czech Republic, Denmark, Egypt, Finland, France, Germany, Greece, Hong Kong,
Hungary, Iceland, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Lithuania, Luxemburg, Malaysia, Malta, Mauri-
tius, Mexico, Morocco, the Netherlands, New Zealand, Nigeria, Norway, Oman, Pakistan, Peru, the Philippines, Poland,
Portugal, Qatar, the Republic of Namibia, Romania, Russia, Saudi Arabia, Singapore, Slovenia, South Africa, Spain,
Sri Lanka, Sweden, Switzerland, Taiwan, ailand, Turkey, the United Arab Emirates, the UK, the USA, and Vietnam.
Clarify that some stocks have no stock market indices from Datastream and/or no information about the market index;
however, these stocks are part of the Financial Times Stock Exchange (FTSE) All-World index, in which case the FTSE
All-World index is used as the benchmark.
Page 8 of 37
Alda Financial Innovation (2025) 11:79
calculate the stock returns and market index returns. Next, the stock fund weights from
the Morningstar database are matched with the stock returns of each stock held by a
fund.
Finally, the monthly Organization for Economic Cooperation and Development
(OECD) based recession indicators for the UK, Europe, the USA, Japan, OECD mem-
bers, and non-OECD members are obtained from the Federal Reserve Economic Data4
to detect recession and expansion periods in funds investing in the UK, Europe, the
USA, Japan, global markets, and emerging markets, respectively. ese indicators are
equal to 1 in recessions and 0 otherwise.
Variables
Following previous studies, two portfolio concentration measures are calculated. First,
the Herfindahl–Hirschman Index measures the security concentration by considering
the weights of all the stocks in a fund and period (Hirschman 1964). e Herfindahl–
Hirschman Index (HHI henceforth) is obtained as follows:
where
HHI i
t
is the Herfindahl–Hirschman concentration index of fund i in month t and
ωi
j
,
t
is the weight of stock j in fund i in month t (where j = 1, …, N; and N are the total
stocks held by fund i in month t). HHI varies between 0 and 1, showing the lowest and
the highest portfolio concentration, respectively.5
Second, following Bu and Harrisburg (2017), the concentration level of a fund’s stocks
is measured using the portfolio weighting of the top 10 weighted stocks by a fund.
Although some funds hold many stocks, the weights of the most representative portfo-
lio stocks concentrate most of the portfolio investments, distorting fund diversification.
Measure (2) controls this issue. A higher/lower measure (2) shows a higher/lower con-
centration of the top 10 holdings in fund i in month t.6
In addition, multiple fund characteristics relevant to the concentration analysis are
considered. First, fund volatility is calculated because higher fund concentration may
increase fund risk (Fulkerson and Riley 2019; Kacperczyk et al. 2005; Sapp and Yan
2008). e fund risk of fund i in month t (Riski,t) is obtained as the standard deviation of
the daily fund returns each month. Second, fund flows are calculated because previous
studies found higher fund flows in more concentrated funds (Pandey and Sharma 2024).
Monthly percentage fund flows are obtained following Sirri and Tufano (1998):
(1)
HHI
i
t
=N
j=
1ωi
j,t
2
(2)
Top
10i
t
=
10
j=1
ωi
j,t
2
(3)
Flowsi,t=
[(
TNAi,t−TNAi,t−1
(
1+Ri,t
)]/
TNAi,t−1
4 e data are obtained from the Federal Reserve Economic Data (https:// resea rch. stlou isfed. org/ fred2/).
5 See Appendix A for a further explanation of HHI.
6 See Appendix A for a more detailed explanation of Top10.
Page 9 of 37
Alda Financial Innovation (2025) 11:79
where TNAi,t are the total net assets of fund i in month t, and Ri,t is the return of fund i
in month t.7
ird, the valuation certainty of fund i in month t (Valuation_certaintyi,t) is obtained
because managers have fewer opportunities to diversify valuation errors when concen-
tration increases; that is, the precision of managerial estimations may be affected if funds
concentrate on stocks with lower certain intrinsic values (Fulkerson and Riley 2019). Fol-
lowing Fulkerson and Riley (2019), the fund valuation certainty is estimated as the addi-
tion of the fund exposures to profitability (RMW: robust minus weak) and investment
(CMA: conservative minus aggressive) factors of Fama and French’s (2015) model. ese
factors indicate whether funds invest in firms that are less profitable and firms that make
larger investments because the intrinsic value of these stocks is often more difficult
to assess. When a fund has a joint negative exposure to RMW and CMA, it invests in
stocks that are difficult to value. e RMW and CMA factors for each investment area
are obtained from French’s data library.8
Moreover, the explicit and implicit costs of concentration are considered. On the one
hand, transaction costs explicitly increase as the trading size of more concentrated funds
grows, increasing expense ratios (Keim and Madhavan 1997). Hence, the Expense_ratioi,t
of fund i in month t is used. In contrast, implicit costs may emerge due to liquidity moti-
vations. When more concentrated funds face forced sales, the costs increase because
funds hold fewer stocks to develop liquidity-motivated trades (Fulkerson and Riley
2019). e cash liquidity fund weight is calculated as the holdings in cash of fund i in
month t (Cash_liquidityi,t).
Investor sophistication is also considered because less sophisticated retail investors are
more prone to react adversely to greater concentration due to potentially poor results
(Fulkerson and Riley 2019). e institutional ownership dummy (Institutionali,t) and the
load/no-load fund dummy (Loadi,t) are included. ese dummies are dichotomous vari-
ables (yes/no) transformed into numerical dummies. e institutional (load) dummy is
equal to 1 when a fund is owned by institutional investors (a fund is a load fund) and
0 otherwise. Institutional ownership could bear a greater fund concentration because
institutional investors are more sophisticated and rely more on managers (Barber etal.
2016). Alternatively, no-load fund investors are more sophisticated because they are
more informed and better understand managerial decision-making, such as concentra-
tion strategies (Zheng 1999).
e crisis dummy (Crisist) was explained in Sect. "Market overview and data" and
controls for instable scenarios. Managers may require greater expected benefits before
increasing their concentration during recessions (Fulkerson and Riley 2019). In addi-
tion, the fund performance is Carhart’s (1997) four-factor alpha because this measure is
commonly used in concentration analyses (Choi etal. 2017; Ivkovic etal. 2008; among
7 Flows are winsorized at the bottom and top 1% levels of the distribution to ensure that extreme values do not drive the
results.
8 French’s website: https:// mba. tuck. dartm outh. edu/ pages/ facul ty/ ken. french/ data_ libra ry. html. Clarify that Applied
Quantitative Research (AQR) provides some UK risk factors at www. aqr. com; however, AQR does not provide UK
RMW and CMA factors. us, the European RMW and CMA factors provided by French’s website are used as UK fac-
tor proxies.
Page 10 of 37
Alda Financial Innovation (2025) 11:79
others).9 e alpha is estimated using 36-month return rolling windows; thus, the analy-
ses are restricted to the period from January 2002 to August 2021.
Finally, three skill variables are developed. e stock-picking and market-timing meas-
ures of Kacperczyk etal. (2014) are calculated because these measures are unconditional
and independent portfolio-style measures. e picking measure (4) determines how
fund holdings co-move with the idiosyncratic component of stock returns relative to the
market. Skilled managers will underweight (overweight) stocks with regard to the mar-
ket weights that have subsequently low (high) idiosyncratic returns (Kacperczyk etal.
2014).
where
Pickingi
t
is the stock-picking skill measure of fund i in month t,
wi
j
,
t
is the weight
of stock j in fund i in month t (where j = 1, …, N; and N are the total stocks held by fund
i in month t),
wm
j
,
t
is the weight of stock j in the market portfolio (m) in month t, and βj,t
measures the covariance between the return of stock j (
Rj
,
t
) and the market return (
Rmt
)
in month t divided by the variance of the market return.
e market-timing measure (5) indicates how fund holdings co-move with the system-
atic component of the stock return relative to the market. Skilled managers present tim-
ing ability when they overweight/underweight assets with high betas in anticipation of a
market increase/decline (Kacperczyk etal. 2014).
where
Timingi
t
is the market-timing skill measure of fund i in month t, and the remain-
ing variables are defined in (4).
e third skill measure (measure 6) is the return gap developed by Kacperczyk etal.
(2008), measuring managerial skills due to unobserved fund trading activity:
where RG
i
t
is the return gap of fund i in month t,
RF i
t
is the net return of fund i in month
t,
RH i
t
is the holding portfolio return of fund i in month t,
wi
j
,
t−1
is the weight of stock j
in fund i in month t − 1 (where j = 1, …, N; and N are the total stocks held by fund i in
month t − 1),
Rj
,
t
is the return of stock j in month t, and Expense_ratioi,t is the expense
ratio of fund i in month t.
e return gap captures unobserved actions between fund-holding disclosure dates,
including hidden benefits and hidden costs (trading costs, agency costs, or negative
investor externalities). Hidden benefits mainly arise from the interim trades of skilled
(4)
Picking
i
t
=N
j=
1wi
j,t
−
wm
j,t
Rj,t
+
1
−
βj,tRmt
+
1
(5)
Timing
i
t
=N
j=1
wi
j,t
−
wm
j,t
βj,tRmt
+
1
(6)
RG
i
t=RFi
t−RHi
t−Expense_ratioi,t=RF i
t−
N
j
=
1
wi
j,t−1Rj,t−Expense_ratioi,t
9 e market size (SMB: small minus big), book-to-market (HML: high minus low), and momentum factors of Carhart
(1997) are obtained from the AQR data (www. aqr. com) for funds investing in the UK and from French’s data library
(https:// mba. tuck. dartm outh. edu/ pages/ facul ty/ ken. french/ data_ libra ry. html) for funds investing in Europe, the USA,
Japan, other developed markets, and emerging markets.
Page 11 of 37
Alda Financial Innovation (2025) 11:79
managers that create value and increase the fund return (RF); however, the return of
the disclosed holdings (RH) remains unaffected until the new fund-holding position
is disclosed. Kacperczyk et al. (2008) indicated that the return gap is positively/nega-
tively related to hidden benefits/costs and measures the value added/subtracted by the
manager.
Table1 presents the summary statistics of the variables. e HHI (Top10) of the SRI
and conventional funds are 1.98% and 2.18% (1.19% and 1.32%), respectively. e con-
centration differences between the SRI and conventional funds are significant, showing
higher concentration (HHI and Top10) in conventional funds. ese figures are consist-
ent with the argument that fund concentration depends on valuable information rather
than on the conventional/SRI-fund nature (i.e., H1). Furthermore, SRI and conventional
fund managers have negative picking, timing, and return gap skills, which is consistent
with previous literature (Knigge etal. 2004; Matallín‐Sáez etal. 2019, among others).
Empirical ndings
is section presents the analyses of the concentration distributions, the difference
between the actual fund concentration and the concentration obtained from the asset-
allocation solutions of the six optimization models, the concentration determinants, the
effect of concentration on performance, and the influence of concentration and skills on
performance.
Preliminary concentration analysis
First, a preliminary analysis of the portfolio concentration distributions is conducted
with a nonparametric methodology to identify concentration patterns in isolation
from other fund variables. is allows for a better understanding of the concentration
Table 1 Summary statistics
This table presents the summary statistics of the monthly fund variables from January 2002 to August 2021 for all SRI
and matched conventional pension funds. The last column shows the dierence between the SRI-fund and matched
conventional-fund variables. The signicance levels of the dierence in means are based on t-tests. *, **, and *** indicate
signicance at the 10%, 5%, and 1% levels, respectively
All SRI funds Matched
conventional SRI versus matched
HHI 0.0209 0.0198 0.0218 − 0.002***
Top10 0.0126 0.0119 0.0132 − 0.0013***
Sustainability score 0.4221 0.4250 0.4192 0.0058**
Alpha 0.0009 0.0013 0.0005 0.0008***
Return 0.0062 0.0061 0.0062 − 0.0001
Risk 0.0073 0.0083 0.0065 0.0018**
Flows 0.0625 0.0491 0.0716 − 0.0225***
Fund assets (pounds) 2.53*1073.20*1072.25*1079.5*106***
Age (months) 10.6017 10.2533 10.9226 − 0.6693***
Expense ratio 0.0153 0.0151 0.0155 − 0.0004***
Valuation certain 0.0763 0.0234 0.1278 − 0.1043***
Cash_liquidity 0.0283 0.0276 0.0289 − 0.0012**
Picking − 0.0096 − 0.0123 − 0.0074 − 0.0049*
Timing − 0.0127 − 0.0131 − 0.0123 − 0.0008
Return gap − 0.0137 − 0.0148 − 0.0129 − 0.0019*
Page 12 of 37
Alda Financial Innovation (2025) 11:79
differences with regard to the portfolio concentration calculated using the optimization
model solutions in the next section (Sect."Analyzing the deviations from the portfolio
optimization models"). e nonparametric methodology detects distribution param-
eters, such as skewness and kurtosis, and compares distributions better than parametric
methods (Abbasi 2022). Table2 and Fig.1 present the results.
Panel A of Table2 shows that conventional funds’ HHI and Top10 concentrations are
greater than SRI fund concentrations (considering the mean, median, and interquartile
range). is evidence is in line with H1: SRI funds do not present more concentrated
portfolios than conventional funds. e Kolmogorov–Smirnov and Epps–Singleton
tests confirm the existence of differences in the HHI and Top10 distributions of SRI and
conventional funds. Figure1 shows the concentration distributions for further study of
these differences.
Graphs 1 and 2 of Fig.1 illustrate the HHI and Top10 kernel density plots. Both graphs
show similar shapes around the mean; however, a few SRI funds exhibit large concentra-
tion deviations (greater sharpness). Moreover, the right-skewed conventional-fund dis-
tributions show conventional funds with a significantly higher concentration than the
average. Graphs 3 and 4 illustrate the cumulative distribution function (CDF) and con-
firm the lower SRI-fund concentration (CDFs above the diagonal). However, the SRI-
fund concentration is greater at the beginning of the function; therefore, Graphs 5–10
illustrate the probability density function (PDF) to determine whether the concentra-
tion relation varies over the distribution. Graph 5 confirms that the SRI-fund HHI is not
lower than the conventional-fund HHI in the entire concentration distribution. e SRI-
fund HHI PDF is significantly larger than the conventional-fund HHI PDF in regions
higher/lower than the 10%/60% quantile (PDF higher than 1). In contrast, the SRI cohort
is underrepresented in regions below 10% and above 60% quantiles (non-significantly
Table 2 Nonparametric analysis of the concentration variables
This table is divided into three panels. Panel A presents the summary statistics of HHI (panel A.1) and Top10 (panel A.2)
concentration measures for SRI and conventional (Conv.) funds. Panel B shows the divergence measures of SRI-fund and
conventional-fund concentration distributions for HHI and Top10 in percentage. Panel C displays the polarization indices of
HHI and Top10 concentration distributions between the SRI and conventional funds. MRP, LRP, and URP indicate the median,
lower, and upper relative polarization index, respectively. *** indicates signicance at the 1% level
Panel A. Concentration summary statistics
Mean Standard
deviation Median Interquartile
range Kolmogorov–
Smirnov (p-value) Epps-
Singleton
(p-value)
Panel A.1. HHI summary statistics
SRI 0.0198 0.0086 0.0191 0.0097 0.000*** 0.000***
Conv 0.0218 0.0132 0.0218 0.0128
Panel A.2. Top10 summary statistics
SRI 0.0119 0.0077 0.0101 0.0095 0.000*** 0.000***
Conv 0.0132 0.0122 0.0120 0.0108
Panel B. Divergence measures (%) Panel C. Polarization indices
HHI Top10 HHI Top10
Location 0.4808 − 85.2333*** MRP − 0.1449*** − 0.0988***
Shape 99.5193*** 185.2333*** LRP − 0.1998*** − 0.1945***
URP − 0.0902*** − 0.0031
Page 13 of 37
Alda Financial Innovation (2025) 11:79
different from 1). ese differences are further studied by decomposing the PDF into
“location” and “shape” effects (Handcock and Morris 1999). Graph 6 illustrates that the
bottom-quintile differences in Graph 5 are due to location differences (i.e., mean differ-
ences), and Graph 7 illustrates that the middle-top differences are due to outlier-con-
centrated SRI funds (i.e., differential shape due to dispersion and skewness). Consistent
with this evidence, Graphs 8–10 show variability in the Top10 concentration among
SRI funds because this distribution is overrepresented in quantiles higher/lower than
10%/50% (Graph 8), and the differences in the lower/middle quintiles are due to loca-
tion/shape differences (Graph 9/10).
e location and shape effects are quantified in panel B of Table2 (Handcock and
Morris 1999). e divergence measures indicate a large dispersion in the HHI concentra-
tion of SRI and conventional funds (significant shape and non-significant location). In
contrast, the concentration strategies in the top 10 fund assets differ on average and in
dispersion (significant location and shape differences). Additionally, panel C of Table2
Fig. 1 Concentration distributions in SRI and conventional pension funds. This figure is divided into ten
graphs. Graphs 1 and 2 show the kernel density of HHI and Top10 concentration measures for SRI and
conventional funds. Graphs 3 and 4 show the cumulative distribution functions (CDF) between SRI and
conventional funds for HHI and Top10, respectively. Graphs 5, 6, and 7 show the probability density function
(PDF), the location effect in PDF, and the shape effect in PDF between SRI and conventional funds for HHI,
respectively. Graphs 8, 9, and 10 show the probability density function (PDF), the location effect in PDF, and
the shape effect in PDF between SRI and conventional funds for Top10, respectively
Page 14 of 37
Alda Financial Innovation (2025) 11:79
quantifies the degree of inequality between distributions, confirming that the conven-
tional-fund concentration is more unequal than the SRI-fund concentration (negative
median, lower, and upper relative polarization indices -MRP, LRP, and URP).
is preliminary concentration analysis shows that SRI and conventional funds
develop diverse concentration strategies and conventional funds generally present
greater and more varied concentration. Furthermore, the analysis displays the exist-
ence of outliers, a feature that should be considered. Specifically, the remaining analy-
ses in Sect."Empirical findings" are undertaken with the initial HHI and Top10 variables
(described in Sect. "Market overview, data, and variables"); however, all analyses are
repeated with HHI and Top10 winsorized at the bottom and top 5% and 10% levels. e
results obtained using the winsorized concentration measures demonstrate that the
findings of the remaining sections are unaffected by outliers.10
Analyzing thedeviations fromtheportfolio optimization models
is section compares the concentrations obtained using the six optimization-model
asset allocations with the fund concentration calculated using actual portfolio hold-
ings. Previous literature has provided a variety of optimization models; however, some
models may be difficult to apply by fund managers due to their complexity, assumptions,
and sophistication. Moreover, sophisticated optimization techniques do not always pro-
vide the best solution in terms of diversification (Oikonomou etal. 2018). Among the
existing models, six well-known optimization models are considered because these are
widely applied in professional portfolio management (Oikonomou etal. 2018). e first
three models (minimum variance, global minimum variance, and optimal portfolio) are
based on the traditional mean–variance bases established by Markowitz (1952). e
remaining models (naïve diversification, risk-parity, and reward-to-risk timing) are more
recent approaches that have less mathematical sophistication and are based on investing
intuition (Oikonomou etal. 2018). ese six models make it possible to build optimal
portfolios on the basis of different premises, representing the primary rationales of opti-
mization techniques among professional managers.
e first model is the minimum variance portfolio; that is, Markowitz’s (1952) optimi-
zation framework. is model minimizes the portfolio risk (variance) among all feasible
portfolios, subject to the following constraints: a required return, the sum of the weights
is equal to 1 (normalization of portfolio weights), and the model does not allow short
sales. is model assumes that the expected return (µ) and the variance–covariance
matrix of asset returns (Σ) are known with certainty. e minimum-variance portfolio
problem is expressed as follows:
(7)
min
ww
′
�w
s
.t.
µ
′w≥θ
1
′w=1
wj≥
0
∀
j
=
1, ...,
N
10 e results with winsorized HHI and Top10 are not included for the sake of brevity and are available upon request.
Page 15 of 37
Alda Financial Innovation (2025) 11:79
where
w=[w1,t
,
w2,t
, ...,
wN,t]′
is the column vector of portfolio weights with N assets
in the portfolio at period t, and the purpose is to select a portfolio w that minimizes the
variance among all possible portfolios at period t. Σ is the variance–covariance matrix
of asset returns, and
µ=[
µ
1,t,
µ
2,t, ...,
µ
N,t]′
is the column vector of asset returns at
period t. e constraints are:
µ′w≥θ
, which establishes a lower bound on the portfolio
return,11
1′w=1
requires that the portfolio weights sum to one (
1
is a vector of ones),
and
wj≥0
is the non-negativity constraint, which discards short selling.
e second model is the global minimum variance portfolio, which is based on the
minimum variance portfolio model (7) but does not require a lower bound on the port-
folio return, assuming that all stocks have equal expected returns to reduce estimation
risks (Ledoit and Wolf 2003; Jagannathan and Ma 2003, among others). Hence, the
unique efficient portfolio is the portfolio with the smallest risk (global minimum vari-
ance). e optimization problem is expressed as follows:
e third model is the optimal or tangency portfolio model. is model provides an
optimal and efficient portfolio by maximizing the Sharpe ratio (Sharpe 1966) because
the portfolio that maximizes the Sharpe ratio lies on the mean–variance efficient fron-
tier, a point at which the capital market line is tangent to the efficient frontier (Markow-
itz 1952; Jagannathan and Ma 2003). For this reason, the optimal portfolio is also called
tangency portfolio. e optimization problem is expressed as follows:
where
w′
µ−Rf,t
√w′�w
is the Sharpe ratio and Rf,t is the risk-free asset rate at period t. e
remaining variables are described in (7).
e fourth model is the naïve diversification with rebalancing. is model assigns
a portfolio weight of 1/N to each portfolio asset (wj,t = 1/N; where wj,t is the portfolio
weight of asset j at period t, and N is the total number of portfolio assets considered);
therefore, the portfolio is equally weighted. is method is characterized by its simplic-
ity because it does not consider return, risk, or other return moments. However, pre-
vious literature points out that this approach is not inferior to mean–variance models
(8)
min
ww
′
�w
s
.t.
1
′w=1
wj≥
0
∀
j
=
1, ...,N
max
w
w
′
µ−Rf,t
√w′�w
s.t.
(9)
1′w=1
11 e lower bound of the portfolio return (θ) is the minimum positive return of the assets considered because it is
assumed that this is the minimum expected return of an investor to accept the investment in a risky portfolio. Nonethe-
less, Oikonomou etal. (2018) point out that the value assumed of θ is not crucial in this model. Consistent with this
argument, the value of θ does not affect the conclusions reached in this study.
Page 16 of 37
Alda Financial Innovation (2025) 11:79
or Markowitz-optimization extensions (Bloomfield etal. 1977; DeMiguel etal. 2009).
Nonetheless, a rebalancing method is followed to vary 1/N weights over time instead of
applying a 1/N buy-and-hold strategy (Platanakis etal. 2019).
e risk-parity portfolio is the next model, broadly applied by long-term institutional
investors, such as pension funds (Anderson etal. 2012). is model requires that each
portfolio asset must contribute to the portfolio variance to the same extent. As a result,
asset weights are anti-proportional to the variance of each asset (Maillard etal. 2010).
e portfolio weights are obtained as follows:
where wj,t is the weight of portfolio asset j at period t, and
σ2
j,t
is the variance of the
returns of portfolio asset j at period t.
Finally, the reward-to-risk timing model proposed by Kirby and Ostdiek (2012) is
applied. is model is based on the reward-to-risk ratio (i.e., return divided by variance),
mitigating the estimation risk and overcoming the instability of portfolios obtained
using Markowitz mean–variance methods (Kirby and Ostdiek 2012). is model pro-
vides more stable portfolios with lower transaction costs by overweighting assets with
higher return and lower variance; that is, assets with a higher reward-to-risk ratio. is
strategy allocates asset weights in proportion to the contribution of each asset’s mean–
variance ratio to the mean–variance ratio of the universe of assets (Oikonomou etal.
2018). e portfolio weights are obtained as follows:
where
µ+
j,t=
max(µj,t,0
)
to discard short selling. In the case of all negative asset returns,
portfolio assets are equally weighted (1/N).
To estimate portfolio weights using the six optimization models over the time period
for the 80 SRI and 84 conventional funds studied, it is assumed that the universe of
assets in the optimization models is the actual quarterly fund assets in which the SRI
and conventional funds invest quarterly. is assumption makes it possible to start from
the actual portfolio asset allocation to consider the investment profile of each fund by
observing whether the optimization models vary the real portfolio asset weights. e
optimization models are estimated quarterly because the real fund-holding weights
are quarterly. Nonetheless, the remaining pension-fund data are monthly; thus, quar-
terly estimated weights are used in the three months of each quarter to obtain monthly
weights (Brown etal. 2021). is replicates the process explained with the real fund
weights in Sect."Market overview and data".
Concentration measures (1) and (2) are calculated from the weights obtained from the
six optimization models over the study period. Table3 presents the results. e SRI and
conventional funds are less concentrated with the actual holdings than with the hold-
ings of the optimization-model solutions (significantly negative differences), except with
the naïve diversification. ese results indicate that funds deviate from the optimization
(10)
w
j,t=
1/σ
2
j,t
N
j
=
1
1/σ 2
j,t
∀j=1, ...,N
(11)
w
j,t=
µ
+
j,t/σ
2
j,t
N
j
=
1
µ+
j,t/σ 2
j,t
∀j=1, ...,N
,
Page 17 of 37
Alda Financial Innovation (2025) 11:79
Table 3 Estimated variables with portfolio optimization model solutions
This table presents the summary statistics of concentration measures (1) and (2), performance (four-factor alpha), and
skill measures (4)–(5) calculated with the weights obtained from the six optimization models applied (minimum variance,
global minimum variance, optimal portfolio, naïve diversication, risk parity, and reward-to-risk timing) for all, SRI, and
conventional funds. Columns (3), (5), and (7) show the dierences between the variables calculated with the actual fund
All Actual vs
optimization
variables
SRI SRI actual vs SRI
optimization
variables
Conv Conv actual vs
conv optimization
variables
HHI minimum
variance
0.3564 − 0.3355*** 0.3567 − 0.3369*** 0.3562 − 0.3344***
HHI global mini-
mum variance
0.4812 − 0.4603*** 0.4797 − 0.4599*** 0.4823 − 0.4605***
HHI optimal
portfolio
0.6820 − 0.6611*** 0.6808 − 0.661*** 0.6830 − 0.6612***
HHI naïve 0.0195 0.0014*** 0.0161 0.0037*** 0.0222 − 0.0005
HHI risk parity 0.0432 − 0.0223*** 0.0405 − 0.0207*** 0.0454 − 0.0236***
HHI reward-to-risk
timing
0.0879 − 0.067*** 0.0898 − 0.0701*** 0.0862 − 0.0645***
Top10 minimum
variance
0.3568 − 0.3442*** 0.3586 − 0.3467*** 0.3554 − 0.3422***
Top10 global mini-
mum variance
0.4813 − 0.4687*** 0.4838 − 0.4719*** 0.4793 − 0.4661***
Top10 optimal
portfolio
0.6751 − 0.6625*** 0.6723 − 0.6605*** 0.6772 − 0.664***
Top10 naïve 0.0071 0.0054*** 0.0045 0.0073*** 0.0093 0.0039***
Top10 risk parity 0.0367 − 0.0241*** 0.0339 − 0.022*** 0.0389 − 0.0257***
Top10 reward-to-
risk timing
0.0803 − 0.0677*** 0.0751 − 0.0633*** 0.0845 − 0.0713***
Alpha minimum
variance
0.01402 − 0.0131*** 0.0140 − 0.0127*** 0.01404 − 0.0135***
Alpha global mini-
mum variance
0.00929 − 0.0084*** 0.00928 − 0.0079*** 0.0093 − 0.0088**
Alpha optimal
portfolio
0.0424 − 0.0415*** 0.0453 − 0.0439*** 0.0397 − 0.0392***
Alpha naïve 0.0060 − 0.0051*** 0.0067 − 0.054*** 0.0049 − 0.0044***
Alpha risk parity 0.0058 − 0.0049*** 0.0065 − 0.0052*** 0.0046 − 0.0041***
Alpha reward-to-
risk timing
0.0494 − 0.484*** 0.0497 − 0.0484*** 0.0488 − 0.0483***
Picking minimum
variance
0.0228 − 0.0324*** 0.0199 − 0.0322*** 0.0251 − 0.0325***
Picking global mini-
mum variance
0.0156 − 0.0252*** 0.0102 − 0.0225*** 0.0199 − 0.0273***
Picking optimal
portfolio
0.1053 − 0.1148*** 0.0983 − 0.1105*** 0.1109 − 0.1183***
Picking naïve − 0.0142 0.0046** − 0.0122 − 0.0001 − 0.0159 0.0085***
Picking risk parity − 0.0145 0.005** − 0.0142 0.0019 − 0.0148 0.0074***
Picking reward-to-
risk timing
0.1009 − 0.1105*** 0.1005 − 0.1128*** 0.1013 − 0.1087***
Timing minimum
variance
0.0023 − 0.015*** 0.0025 − 0.0156*** 0.0022 − 0.0145***
Timing global mini-
mum variance
0.0014 − 0.014*** 0.0014 − 0.0145*** 0.0013 − 0.0136***
Timing optimal
portfolio
0.0142 − 0.0268*** 0.0193 − 0.0324*** 0.0100 − 0.0223***
Timing naïve − 0.0127 0.0001 − 0.0154 0.0023 − 0.0105 − 0.0018
Timing risk parity − 0.0113 − 0.0013 − 0.0133 0.0002 − 0.0097 − 0.0026
Timing reward-to-
risk timing
0.0051 − 0.0177*** 0.0029 − 0.016*** 0.0070 − 0.0192***
Page 18 of 37
Alda Financial Innovation (2025) 11:79
model solutions; hence, H2 cannot be rejected. Additionally, SRI and conventional funds
greatly diversify their portfolios and develop asset allocations similar to the naïve diver-
sification. is evidence aligns with multiple studies pointing out that the naïve portfolio
selection is a preferred method due to its stability (Fischer and Gallmeyer 2016; Kirby
and Ostdiek 2012; among others). is indicates that SRI pension funds do not present
problems when diversifying their portfolios due to the limited ESG-asset universe and
stricter regulations. Furthermore, the concentration measures from the optimization
models illustrate a lower SRI-fund concentration and, consistent with previous literature
(DeMiguel etal. 2009; Oikonomou etal. 2018), traditional mean–variance models show
poorly diversified portfolios relative to the more recent optimization approaches.
e performance and skill measures (4)–(5)12 are also calculated from the weights
obtained from the six optimization models. Table 3 shows that deviations from the
optimization models affect fund performance (lower actual performance than optimi-
zation-model performance). us, managers should assess the consequences of deviat-
ing from some optimization models. Although the optimization skill measures (4)–(5)
do not capture real managerial skills because all managers’ information regarding future
market movements is not included in the optimization models, the optimization models
calculate the weights starting from the actual fund assets to consider funds’ investment
profiles and managers’ information signals. Hence, optimization skill measures (4)–(5)
make it possible to explore whether optimization models can guide managers to improve
their skills. e results indicate that fund managers would have achieved better selectiv-
ity and timing skills with the optimized asset allocations, except with the naïve diversi-
fication and risk-parity optimizations. us, optimization models can help managers in
asset allocation decisions to improve performance, picking, and timing skills if managers
specify the asset universe in the optimization model.
Concentration determinants
is section studies the determinants of the actual fund concentration to analyze
whether funds develop different concentration on the basis of fund characteristics. e
concentration determinants using optimization models are not studied because the opti-
mization solutions are subject to model specifications and do not consider fund char-
acteristics. However, actual concentration strategies may depend on fund features, as
explained in Sect."Variables". Accordingly, model (12) is as follows:
(12)
Conc
i,t
=
β0
+
β1SRI_dummyi,t
−
1
+
β2Sust_scorei,t
−
1
+13
j=
3βjControli,t
−
1
+
FE
+
εi,t
weights and the variables obtained from the optimization model solutions. The signicance levels of the dierences in
means are based on t-tests. ** and *** indicate signicance at the 5% and 1% levels, respectively
Table 3 (continued)
12 e return gaps are not calculated from the optimization solutions because the optimization models do not consider
unobserved trading activities between the fund-holding disclosure dates. In other words, optimization models provide a
solution for a specific date, and it is necessary to recalculate the model with new information on another date to obtain a
new solution. Consequently, the net return (RFti) is the same as the holding portfolio return (RHti) in measure (6) using
the optimization model solutions.
Page 19 of 37
Alda Financial Innovation (2025) 11:79
where Conci,t is the fund concentration, either
HHI i
t
(measure 1) or
Top
10
i
t
(measure 2),
of fund i in month t. SRI_dummyi,t is equal to 1/0 when fund i is an SRI/conventional
fund. Sust_scorei,t−1 is the sustainability score of fund i in month t − 1.13 e control vari-
ables are Returni,t−1, Riski,t−1, Assetsi,t−1 (logarithm of TNAs of fund i in month t − 1),
Flowsi,t−1, Agei,t−1 (obtained from the inception and obsolete dates), Expense_ratioi,t−1,
Valuation certaintyi,t−1, Cash_liquidityi,t−1, Institutionali,t−1, Loadi,t−1, and Crisist−1. All
independent variables are lagged to avoid endogeneity issues (Anantharaman and Lee
2014). FE are time fixed effects to eliminate bias from unobservable factors that change
over time and are constant over funds as well as to control for factors differing across
funds that are constant over time.14 Finally, εi,t is the error term. Robust standard errors
clustered by fund and month are estimated for obtaining standard errors that are robust
to heteroskedasticity and within serial correlation, addressing concerns about correlated
errors within fund and time dimensions (Newey and West 1987).
Table4 presents the results of model (12).15 e significantly negative SRI_dummy in
columns (1)–(2) supports H1; that is, SRI funds do not develop more concentrated port-
folios than conventional funds. is finding is also consistent with the lower SRI-fund
concentration found in the nonparametric analysis (Sect. "Preliminary concentration
analysis"). Contrary to previous studies indicating the limited ESG asset universe, this
evidence is consistent with the increasing supply and demand of SRIs and the evolution
of the SRI from a niche to the mainstream (Revelli 2017). In this line of argument, funds
with superior ESG criteria develop less concentrated portfolios (significantly negative
Sust_score at 5% and 1% levels in columns 1–2). erefore, the ESG asset universe is not
a limitation.
Consistent with previous literature, Table416 also shows that a larger fund size may
imply information advantages, thus, managers of larger funds increase the fund concen-
tration (Qin and Wang 2021). More expensive funds also present greater concentration
(Keim and Madhavan 1997). e concentration in stocks with lower intrinsic value indi-
cates managers’ confidence in their information because they have fewer opportunities
to diversify valuation errors with higher concentration (Fulkerson and Riley 2019). Addi-
tionally, more liquid funds concentrate the portion of noncash portfolio holdings to have
sufficient liquidity for liquidity-motivated trades (Fulkerson and Riley 2019). Contrary to
previous arguments (Fulkerson and Riley 2019), more sophisticated investors (institu-
tional and no-load) react adversely to concentration (negative Institutional and positive
Load). Finally, managers take refuge in fewer assets during crises (significantly positive
Crisis).
13 e sustainability score denotes the ESG fund standards of conventional and SRI funds because both SRI and conven-
tional funds consider ESG criteria in their portfolio allocations (Revelli 2017).
14 e significant results of the test for time-fixed effects show the need to control for these effects. ese results are
available upon request.
15 e variance inflation factors (VIFs) do not show multicollinearity problems.
16 Some coefficients are close to 0 (e.g. Assets or Valuation_certain); that is, the impact of these variables on the
dependent variable is limited. However, the coefficient magnitudes are monthly, and the annual effect is larger.
Page 20 of 37
Alda Financial Innovation (2025) 11:79
Performance–concentration relationship
is sections examines the influence of concentration on fund performance to test
H.3; that is, whether a higher portfolio concentration improves the performance of
SRI and conventional pension funds, per the information advantage theory (Van
Nieuwergugh and Veldkamp 2010). Model (13) is proposed on the basis of previous
concentration studies (Chen and Lai 2015; Fulkerson and Riley 2019):
(13)
Performance
i,t=
β
0+
β
1
SRI_dummy
i,t−1+
β
2
Conc
i,t−
1
+β3Sust_scorei,t−1+13
j
=4βjControli,t−1+FE +εi,t
Table 4 Influence of fund characteristics on fund concentration
This table presents the results of model (12), with HHI and Top10 concentration measures as dependent variables in columns
(1) and (2), respectively. All models are estimated with time xed eects and robust standard errors clustered by fund and
month. T-statistics are in parentheses. ** and *** indicate signicance at the 5% and 1% levels, respectively
(1) (2)
SRI_dummy − 0.0025*** − 0.0022***
(− 11.57) (− 11.14)
Sust_score − 0.0043** − 0.0064***
(− 2.19) (− 3.46)
Return 0.0038 0.0037
(1.57) (1.62)
Risk 0.0016*** 0.1598***
(4.02) (4.26)
Assets 0.0007*** 0.0005***
(9.48) (8.79)
Flows − 0.0002 − 0.0003
(− 0.54) (− 0.69)
Age − 0.0003*** − 0.0002***
(− 15.38) (− 15.20)
Expense_ratio 0.2222*** 0.2259***
(8.58) (11.65)
Valuation_certain − 0.0006*** − 0.0009***
(− 3.43) (− 5.96)
Cash_liquidity 0.0101*** 0.0087***
(8.25) (5.75)
Institutional − 0.0012*** − 0.0007**
(− 3.57) (− 2.49)
Load 0.0009*** 0.0008***
(4.12) (3.78)
Crisis 0.0012*** 0.0014***
(4.18) (5.69)
Constant 0.0129*** 0.0064***
(7.7) (4.36)
R-squared 0.1244 0.1242
VIF 1.18 1.18
No. Obs 4875 4975
Page 21 of 37
Alda Financial Innovation (2025) 11:79
where Performancei,t is the four-factor alpha of fund i in month t, SRI_dummyi,t is equal
to 1/0 when fund i is an SRI/conventional fund, Conci,t−1 is either
HHI i
t−1
or
Top
10
i
t−1
of fund i in month t − 1, Sust_scorei,t−1 is the sustainability score of fund i in month t − 1,
and the control variables are Riski,t−1, Assetsi,t−1, Flowsi,t−1, Agei,t−1, Expense_ratioi,t−1,
Valuation certaintyi,t−1, Cash_liquidityi,t−1, Institutionali,t−1, Loadi,t−1, and Crisist−1. FE
are time-fixed effects.
Table5 presents the results of model (13). Panel A shows that SRI funds outperform
conventional funds (significantly positive SRI_dummy), and SRI funds are able to use
ESG information to increase concentration and improve performance (positive HHI
and Top10 in column 2). is result again demonstrates that the ESG asset universe pro-
vides investment opportunities. Additionally, the Top10 concentration positively affects
conventional funds’ performance (column 3). ese results do not reject H3, indicating
that the SRI and conventional funds use information advantages to increase their perfor-
mance through concentration. However, conventional fund managers have an informa-
tion advantage in a few stocks (Top10); thus, they focus on the stocks in which they enjoy
an information advantage to enhance performance (Johnson and Moggridge 2012).
Panels B–G show the results of model (13) with the fund variables calculated from the
weights obtained in the optimization models.17 Unlike the generalized positive concen-
tration–performance relation found in panel A, panels B–G show that the significance of
the concentration variables is lower, and the results are mixed, prevailing a generalized
negative influence of concentration on performance. e results of panels B–D are con-
sistent with previous studies using traditional optimization models that find lower per-
formance with higher concentration (Gangi and Varrone 2018). Moreover, although the
actual fund concentration is similar to the naïve portfolio concentration (see Table3),
panel E indicates that the naïve portfolio concentration has a diverse effect on perfor-
mance. is shows that the actual fund concentration responds to managers’ valuable
information, which improves performance (Choi etal. 2017; Fulkerson and Riley 2019;
Kacperczyk etal. 2005). It is also noted that the reward-to-risk timing model may help
managers exploit informational advantages with concentration to improve performance
(panel G). e latter result is due to the idiosyncrasy of this model; that is, out-weight-
ing assets with higher return and lower volatility improves performance with higher
concentration.
Importance ofmanagerial skills whendeveloping concentration strategies
Although managers with information advantages can improve performance through
concentration strategies, the success of these strategies also depends on managerial skills
(Chen and Lai 2015). is section examines the relationship between skills, concentra-
tion, and performance.
Skills byconcentration level
Table6 shows skills by concentration level to test H4, H5, and H6 about whether
managers of more concentrated funds present superior picking, timing, and return
17 Control variables are not included and are available upon request.
Page 22 of 37
Alda Financial Innovation (2025) 11:79
Table 5 Performance-concentration relation
HHI as concentration measure Top10 as concentration measure
All SRI Conv All SRI Conv
Panel A: Results with the variables calculated from the actual fund weights
SRI_dummy 0.0022*** 0.0023***
(16.33) (16.55)
Concentration 0.0291*** 0.1109*** 0.0149 0.0605*** 0.1151*** 0.0520***
(3.39) (6.67) (1.41) (5.91) (6.25) (4.00)
Sust_score 0.0074*** 0.012*** 0.007*** 0.0076*** 0.0121*** 0.0072***
(6.98) (6.41) (5.81) (7.29) (6.56) (5.94)
Risk 0.2125*** 0.1488*** 0.1534*** 0.2065*** 0.1611*** 0.1420***
(11) (5.71) (6.95) (10.71) (6.28) (6.36)
Assets − 0.0001 − 0.0001* − 0.0002*** − 0.0000 − 0.0001 − 0.0002***
(− 0.01) (− 1.68) (− 3.56) (− 0.32) (− 1.42) (− 3.77)
Flows − 0.0001 − 0.0002 − 0.0001 − 0.0001 − 0.0001 − 0.0001
(− 0.45) (− 0.37) (− 0.3) (− 0.41) (− 0.34) (− 0.23)
Age − 0.00002** − 0.0001*** 0.00003** − 0.0000 − 0.0001*** 0.0000***
(− 1.99) (− 6.93) (2.37) (− 1.62) (− 7.28) (3.20)
Expense_ratio − 0.044*** − 0.1076*** − 0.0612*** − 0.0510*** − 0.1235*** − 0.0723***
(− 2.92) (− 4.73) (− 3.37) (− 3.42) (− 5.50) (− 4.01)
Valuation_certain − 0.0044*** − 0.0063*** − 0.0012*** − 0.0044*** − 0.0062*** − 0.0011***
(− 12.93) (− 19.97) (− 4.36) (− 12.78) (− 19.70) (− 4.10)
Cash_liquidity 0.0015* − 0.0043 0.0037*** 0.0012 − 0.0098** 0.0037***
(1.75) (− 1.02) (5.09) (1.46) (− 2.27) (5.20)
Institutional − 0.0015*** − 0.0008*** − 0.0015*** − 0.0015*** − 0.0009*** − 0.0014***
(− 8.12) (− 4.68) (− 5.09) (− 8.14) (− 5.36) (− 4.89)
Load − 0.0005*** 0.0017*** − 0.0016*** − 0.0005*** 0.0016*** − 0.0016***
(− 2.92) (6.68) (− 7.38) (− 3.06) (6.40) (− 7.48)
Crisis − 0.0032*** − 0.0029*** − 0.0025*** − 0.0032*** − 0.0030*** − 0.0025***
(− 15.87) (− 11.33) (− 10.43) (− 16.09) (− 11.57) (− 10.66)
Constant − 0.0003 − 0.0004 0.0025** − 0.0003 0.0006 0.0023**
(− 0.34) (− 0.24) (2.33) (− 0.35) (0.41) (2.09)
R-squared 0.3786 0.6057 0.1962 0.3818 0.6057 0.2009
No. Obs 4874 2063 2811 4874 2063 2811
Panel B: Results with the variables calculated from the minimum variance model solution
Concentration − 0.0037 − 0.0049 − 0.0018 − 0.0012 0.0157*** − 0.0084
(− 1.05) (− 0.94) (− 0.39) (− 0.32) (3.27) (− 1.54)
Control variables Yes Yes Yes Yes Yes Yes
R-squared 0.1113 0.1978 0.1233 0.1063 0.1997 0.1173
No. Obs 4212 1706 2506 4777 2012 2765
Panel C: Results with the variables calculated from the global minimum variance model solution
Concentration 0.0010 0.0139*** − 0.0088*** 0.0007 − 0.0002 − 0.0002
(0.51) (5.19) (− 3.05) (0.38) (− 0.09) (− 0.07)
Control variables Yes Yes Yes Yes Yes Yes
R-squared 0.1227 0.2402 0.1104 0.1052 0.2144 0.0891
No. Obs 4296 1728 2568 4728 2012 2716
Panel D: Results with the variables calculated from the optimal portfolio model solution
Concentration − 0.0097* − 0.0214*** − 0.0035 − 0.0014 − 0.0172** 0.0098
(− 1.85) (− 2.80) (− 0.52) (− 0.22) (− 2.24) (1.04)
Control variables Yes Yes Yes Yes Yes Yes
R-squared 0.2113 0.5966 0.1523 0.2512 0.5338 0.2819
Page 23 of 37
Alda Financial Innovation (2025) 11:79
gaps. Panels A and B show the results obtained using actual fund holdings. e most
concentrated funds display significantly better picking, timing, and a larger return gap
than the least concentrated funds (Q1 versus Q5). However, panel A shows general-
ized poor managerial skills (broadly negative picking, timing, and return gap), and the
managers of the most concentrated funds are only able to develop one skill correctly
(picking in SRI funds and timing in conventional funds). Additionally, the generalized
negative return gaps indicate that managers do not have investment ability to cre-
ate enough value to offset trading costs and other hidden costs with hidden benefits.
us, H4, H5, and H6 are rejected.
Although no prior studies examined the relationship between concentration and skills,
Zambrana and Zapatero (2021) also find differential behaviours between pickers and
timers, arguing that the behaviour depends on the information collected and processed
by managers. ese authors report that pickers rely on firms’ information, whereas tim-
ers rely on macroeconomic information. Considering these premises, SRI fund managers
are specialized in ESG-firm information and develop picking skills considering ESG-firm
issues, leading them to leverage their information advantages through concentration
(Choi etal. 2017; Fulkerson and Riley 2019; Kacperczyk etal. 2005). In contrast, conven-
tional fund managers process more heterogeneous information and are more exposed to
multiple investment objectives, receiving insights into a broad range of macroeconomic
This table presents the results of model (13) for all, SRI, and conventional pension funds with the HHI and Top10
concentration measures calculated from the actual fund weights (panel A), the minimum-variance (panel B), the global
minimum variance (panel C), the optimal portfolio (panel D), the naïve diversication (panel E), the risk parity (panel F),
and the reward-to-risk timing (panel G) optimization-model solutions. All models are estimated with time xed eects
and robust standard errors clustered by fund and month. Control variables are not shown in panels B-G and the results
are available upon request. T-statistics are in parentheses. *, **, and *** indicate signicance at the 10%, 5%, and 1% levels,
respectively
Table 5 (continued)
HHI as concentration measure Top10 as concentration measure
All SRI Conv All SRI Conv
No. Obs 678 227 451 612 273 339
Panel E: Results with the variables calculated from naïve-diversification model solution
Concentration − 0.0066 0.3524** − 0.1507*** 0.0190 0.1302 − 0.0652**
(− 0.32) (2.44) (− 3.63) (0.66) (0.72) (− 2.21)
Control variables 0.0819 0.2758 0.1864 0.0820 0.2144 0.1592
R-squared 1643 913 730 1643 913 730
No. Obs − 0.0066 0.3524** − 0.1507*** 0.0190 0.1302 − 0.0652**
Panel F: Results with the variables calculated from the risk-parity model solution
Concentration 0.0084 0.0261 − 0.0345*** 0.0128** 0.0169 − 0.0227**
(1.30) (1.47) (− 3.33) (2.04) (1.20) (− 2.47)
Control variables Yes Yes Yes Yes Yes Yes
R-squared 0.0523 0.2033 0.1696 0.0533 0.2003 0.1642
No. Obs 1680 947 733 1677 944 733
Panel G: Results with the variables calculated from the reward-to-risk timing model solution
Concentration 0.0071** − 0.0007 0.0260*** 0.0060*** 0.0094*** − 0.0000
(2.52) (− 0.29) (3.21) (2.83) (2.88) (− 0.00)
Control variables Yes Yes Yes Yes Yes Yes
R-squared 0.2842 0.4335 0.2587 0.2415 0.3921 0.1386
No. Obs 1146 754 392 1671 938 733
Page 24 of 37
Alda Financial Innovation (2025) 11:79
Table 6 Managerial skills by actual and estimated concentration level
All funds SRI funds Conventional funds
Picking Timing Return gap Picking Timing Return
gap
Picking Timing Return
gap
Panel A. Skills by actual HHI level
Q1 0.0002 − 0.0009 − 0.0122 0.0023 − 0.0031 − 0.0168 − 0.0018 0.0015 -0.0121
Q2 0.0025 − 0.0028 − 0.0129 − 0.0167 − 0.0077 − 0.0135 0.0044 − 0.0046 -0.0119
Q3 − 0.0054 − 0.0016 − 0.0151 0.005 0.0144 − 0.0114 − 0.0002 0.0007 -0.0134
Q4 − 0.0095 − 0.0109 − 0.0121 − 0.0195 − 0.0094 − 0.0109 − 0.0035 − 0.0205 -0.0153
Q5 − 0.0365 − 0.0482 − 0.0182 − 0.0326 − 0.0597 − 0.022 − 0.0372 − 0.0405 -0.0154
Q1–Q5 0.0367*** 0.0473*** 0.0060*** 0.0349*** 0.0566*** 0.0052** 0.0354*** 0.042*** 0.0034**
Panel B. Skills by actual Top10 level
Q1 − 0.0034 − 0.0018 − 0.0121 − 0.0024 − 0.002 − 0.014 − 0.0044 − 0.0016 -0.0121
Q2 0.0019 − 0.0035 − 0.0112 − 0.0081 − 0.0118 − 0.0132 0.0031 − 0.0007 -0.0095
Q3 0.0003 − 0.0029 − 0.0155 0.0002 0.0105 − 0.0147 − 0.0008 0.0002 -0.0142
Q4 − 0.0112 − 0.0027 − 0.0138 − 0.0176 − 0.0108 − 0.0127 − 0.0032 − 0.0087 -0.0152
Q5 − 0.0346 − 0.0536 − 0.0179 − 0.0347 − 0.0525 − 0.0201 − 0.0326 − 0.0522 -0.0168
Q1–Q5 0.0312*** 0.0518*** 0.0058*** 0.0323*** 0.0505*** 0.0061** 0.0282*** 0.0506*** 0.0047**
Panel C. Skills by HHI level calculated with the weights from the minimum variance optimization
Q1 − 0.0029 0.0204 − 0.0020 0.0150 − 0.0028 0.0257
Q5 0.0139 0.0299 0.0233 0.0304 0.0073 0.0296
Q1–Q5 − 0.0168*** − 0.0094* − 0.0252*** − 0.0154 − 0.0101* − 0.0040
Panel D. Skills by HHI level calculated with the weights from the global minimum variance optimization
Q1 0.0026 0.0166 0.0131 0.0022 − 0.0055 0.0256
Q5 0.0045 0.0234 0.0046 0.0217 0.0040 0.0263
Q1–Q5 − 0.0018 − 0.0068 0.0085 − 0.0195*** − 0.0095 − 0.0007
Panel E. Skills by HHI level calculated with the weights from the optimal portfolio optimization
Q1 0.0158 0.1040 0.0243 0.1039 0.0083 0.1041
Q5 0.0172 0.1000 0.0103 0.1082 0.0226 0.0959
Q1–Q5 − 0.0014 0.0041 0.0141 − 0.0043 − 0.0143 0.0083
Panel F. Skills by HHI level calculated with the weights from the naive diversification
Q1 − 0.0329 − 0.0095 0.0040 0.0032 − 0.0518 − 0.0161
Q5 − 0.0231 − 0.0332 − 0.0320 − 0.0440 − 0.0149 − 0.0167
Q1–Q5 − 0.0098 0.0237*** 0.0359*** 0.0472*** − 0.0370*** 0.0006
Panel G. Skills by HHI level calculated with the weights from the risk-parity optimization
Q1 − 0.0129 − 0.0230 − 0.0032 − 0.0178 − 0.0182 − 0.0325
Q5 − 0.0287 − 0.0255 − 0.0375 − 0.0331 − 0.0176 − 0.0157
Q1–Q5 0.0158** 0.0025 0.0343*** 0.0153* − 0.0006 − 0.0169
Panel H. Skills by HHI level calculated with the weights from the reward-to-risk timing optimization
Q1 0.0483 0.1572 0.0375 0.1494 0.0573 0.1636
Q5 − 0.0753 0.0610 − 0.0732 0.0600 − 0.0707 0.0631
Q1–Q5 0.1236*** 0.0962*** 0.1106*** 0.0893*** 0.1279*** 0.1005***
Panel I. Skills by Top10 level calculated with the weights from the minimum variance optimization
Q1 0.0114 0.0241 0.0138 0.0256 0.0090 0.0243
Q5 − 0.0095 0.0078 − 0.0209 − 0.0163 − 0.0022 0.0217
Q1–Q5 0.0210*** 0.0164*** 0.0347*** 0.0419*** 0.0113** 0.0025
Panel J. Skills by Top10 level calculated with the weights from the global minimum variance optimization
Q1 − 0.0017 0.0118 − 0.0056 − 0.0220 − 0.0005 0.0323
Q5 − 0.0081 0.0132 − 0.0097 0.0215 − 0.0069 0.0068
Q1–Q5 0.0065 − 0.0014 0.0041 − 0.0436*** 0.0064 0.0255***
Panel K. Skills by Top10 level calculated with the weights from the optimal portfolio optimization
Q1 0.0202 0.1320 0.0187 0.1237 0.0220 0.1421
Q5 0.0393 0.1082 0.0438 0.0879 0.0357 0.1247
Q1–Q5 − 0.0191 0.0238* − 0.0251 0.0359** − 0.0137 0.0173
Panel L. Skills by Top10 level calculated with the weights from the naive diversification
Q1 − 0.0329 − 0.0095 0.0040 0.0032 − 0.0518 − 0.0161
Page 25 of 37
Alda Financial Innovation (2025) 11:79
variables. ese factors generate informational externalities, enabling them to develop
timing skills and exploit macroeconomic-information advantages with concentration.
Panel B also shows generalized poor skills for Top10 quintiles. Picking and timing skills
are only positive in the middle-concentrated SRI and conventional funds.
Panels C-N show the skills in the top and bottom concentrated portfolios (Q1 and Q5)
obtained from the optimization model solutions18 to analyze whether the optimization
models can help managers obtain differential skills by concentration level. Panels C–E
show that the greater skills with higher concentration, as observed in panels A–B, are
not sustained with optimization models. In contrast, managers achieve superior picking
in the least concentrated funds (panel C) and superior timing in the least concentrated
SRI funds (panel D). is evidence is consistent with the diversification assumptions of
traditional optimization models (Markowitz 1952). Nonetheless, more modern models
(panels F–H) provide some significantly positive Q1–Q5 differences, indicating superior
skills in the top concentrated funds. e greater similarity of the latter results with those
found in panel A aligns with the rationality of these models; that is, more modern mod-
els are based on mangers’ investing intuition (Oikonomou etal. 2018). Panels I–N also
show mixed results for Top10 quintiles, confirming no rationalization between concen-
tration and skills in the optimization models because concentration and skills are not
included among the model premises.
This table is divided into fourteen panels. Panels A and B show the stock picking, market timing, and return gap obtained
from measures (4)-(6) for all, SRI, and matched conventional pension funds from top (Q1) to bottom (Q5) concentrated
funds according to the HHI and Top10 calculated from the actual fund weights, respectively. Panels C-H show the stock
picking and market timing obtained from measures (4)-(5) for all, SRI, and matched conventional pension funds in top
(Q1) and bottom (Q5) concentrated funds according to the HHI calculated from the minimum-variance (panel C), the
global minimum variance (panel D), the optimal portfolio (panel E), the naïve diversication (panel F), the risk parity (panel
G), and the reward-to-risk timing (panel H) optimization-model solutions. Panels I-N show the stock picking and market
timing obtained from measures (4)-(5) for all, SRI, and matched conventional pension funds in top (Q1) and bottom (Q5)
concentrated funds according to the Top10 calculated from the minimum-variance (panel I), the global minimum variance
(panel J), the optimal portfolio (panel K), the naïve diversication (panel L), the risk parity (panel M), and the reward-to-risk
timing (panel N) optimization-model solutions. Skills from Q2 to Q4 are not displayed in panels C-N and are available upon
request. The signicance levels of the dierence in means of quintiles 1 and 5 (Q1-Q5) are based on t-tests. *, **, and ***
indicate signicance at the 10%, 5%, and 1% levels, respectively
Table 6 (continued)
All funds SRI funds Conventional funds
Picking Timing Return gap Picking Timing Return
gap
Picking Timing Return
gap
Q5 − 0.0231 − 0.0332 − 0.0320 − 0.0440 − 0.0149 − 0.0167
Q1–Q5 − 0.0098 0.0237*** 0.0359*** 0.0472*** − 0.0370*** 0.0006
Panel M. Skills by Top10 level calculated with the weights from the risk-parity optimization
Q1 − 0.0128 − 0.0236 − 0.0030 − 0.0191 − 0.0177 − 0.0326
Q5 − 0.0327 − 0.0255 − 0.0374 − 0.0318 − 0.0218 − 0.0174
Q1–Q5 0.0199** 0.0019 0.0344*** 0.0127 0.0042 − 0.0152
Panel N. Skills by Top10 level calculated with the weights from the reward-to-risk timing optimization
Q1 − 0.0005 0.0898 0.0139 0.0977 − 0.0103 0.0963
Q5 − 0.0218 0.0726 − 0.0317 0.0662 − 0.0164 0.0791
Q1–Q5 0.0212** 0.0172*** 0.0456*** 0.0315*** 0.0061* 0.0173
18 e skills of the remaining quintiles are not shown for the sake of brevity but are available upon request.
Page 26 of 37
Alda Financial Innovation (2025) 11:79
The inuence ofskills onconcentration
is section presents the results of the influence of skills on concentration because the
analyses in Sect."Skills by concentration level" reveal distinct skills according to the level
of the actual fund concentration. Skill measures (4)–(6) are included in model (12) to
obtain model (14) as follows:
where
Pickingi
t−1
is the stock-picking skill of fund i in month t − 1,
Timingi
t−1
is the mar-
ket-timing skill of fund i in month t − 1, and RG
i
t−1
is the return gap of fund i in month
t − 1. e remaining variables are described in model (12).
Panel A of Table7 displays the results of model (14),19 which align with Table4’s find-
ings; that is, SRI funds have a lower concentration than conventional funds. Additionally,
managers with better picking and timing exploit their skills by increasing fund concen-
tration (significantly positive timing at 5% and 10% in columns 1 and 2). In contrast,
managers with a larger return gap diminish fund concentration. Although the latter con-
duct is not consistent with that found in Table6, it shows that managers aim to address
the negative return gaps by reducing concentration to offset hidden costs.
Skills, concentration, andperformance
is last section examines the joint effect of concentration and skills on performance
to test H7. Kacperczyk etal. (2014) found that skills can predict performance, and Choi
et al. (2017) pointed out the interaction effect of skills and concentration strategies
on performance. Skill measures (4)–(6) and skill–concentration interaction variables
(
Skilli
t−1
*Coni,t−1) are included in model (13) to obtain model (15). Model (15) allows
the analysis of the specific effect of picking, timing, and return gap skills on performance
and the joint effect of skills and concentration on performance as follows:
where
6
j=4
β
jSkilli
t−1
represents the picking, timing, and return gap measures (4)–(6) of
fund i in month t–1, and the interaction terms
9
j=
7βjSkill
i
t
−
1
∗
Coni,t
−1
allow to study
the impact of concentration according to picking, timing, and return gap on the perfor-
mance of fund i in month t − 1, respectively. e remaining variables are described in
model (13).
Panel B of Table7 presents the results of model (15). Comparing these results with
those shown in panel A of Table5, the persistent and superior evidence of the posi-
tive concentration–performance relationship after controlling for skills indicates that
(14)
Conc
i,t=
β
0+
β
1
SRI_dummy
i,t−1+
β
2
Sust_score
i,t−
1
+β3Pickingi
t−1+β4Timingi
t−1+β5RGi
t−1
+15
j
=5βjControli,t−1+FE +εi,t
(15)
Performance
i,t=
β
0+
β
1
SRI_dummy
i,t−1+
β
2
Conc
i,t−1
+β3Sust_scorei,t−1+6
j=4βjSkilli
t−1
+9
j
=7βjSkilli
t−1∗Coni,t−1+19
j
=10βjControli,t−1+FE +εi,
t
19 e control-variable results are available upon request and are in line with the findings presented in Table4.
Page 27 of 37
Alda Financial Innovation (2025) 11:79
Table 7 Relation between skills, concentration, and performance
This table is divided into two panels. Panel A shows the results of model (14) with the actual fund variables. The
concentration variable is HHI in column (1) and Top10 in column (2). Panel B shows the results of model (15) with the actual
fund variables. The concentration variable is HHI in panel B.1 and Top10 in panel B.2. All models are estimated with time
xed eects and robust standard errors clustered by fund and month. Control variables are not shown and the results are
available upon request. T-statistics are in parentheses. *, **, and *** indicate signicance at the 10%, 5%, and 1% levels,
respectively
Panel A. Concentration determinants
HHI Top10
SRI_dummy − 0.0027*** − 0.0022***
(− 12.4) (− 11.43)
Sust_score − 0.0037* − 0.0060***
(− 1.91) (− 3.23)
Picking 0.02*** 0.0086***
(9.54) (5.90)
Timing 0.0015** 0.0007*
(2.34) (1.73)
Return gap − 0.0055*** − 0.0047***
(− 3.34) (− 2.89)
Control variables Yes Yes
R-squared 0.1607 0.1340
No. Obs 4867 4867
Panel B. Inuence of concentration and skill on performance
Panel B.1. HHI as concentration measure Panel B.2. Top10 as concentration
measure
All SRI Conv All SRI Conv
SRI_dummy 0.0023*** 0.0023***
(16.45) (16.65)
Concentration 0.0417*** 0.116*** 0.0293*** 0.0736*** 0.1194*** 0.0663***
(4.58) (6.65) (2.65) (6.85) (6.09) (4.92)
Sust_score 0.0072*** 0.0118*** 0.007*** 0.0075*** 0.0120*** 0.0073***
(6.82) (6.31) (5.89) (7.13) (6.53) (5.95)
Picking − 0.0028** 0.0057 − 0.0058*** − 0.0023 0.0212*** − 0.0101***
(− 2.21) (1.51) (− 4.15) (− 1.23) (3.51) (− 4.97)
Timing − 0.0002 − 0.0029 − 0.0008** − 0.0000 − 0.0008 − 0.0015***
(− 0.56) (− 1.12) (− 2.49) (− 0.09) (− 0.23) (− 2.77)
Return gap − 0.0043 − 0.01 − 0.007** − 0.0090** − 0.0232** − 0.0085**
(− 1.39) (− 1.38) (− 2.01) (− 2.39) (− 2.41) (− 1.98)
Picking*Conc − 0.0045 − 0.3694** 0.3582*** − 0.0017 − 0.0642*** 0.0359***
(− 0.06) (− 2.31) (4.19) (− 0.25) (− 3.76) (4.59)
Timing*Conc − 0.0125 0.0269 0.1154*** − 0.0010 − 0.0047 0.0084***
(− 0.36) (0.25) (2.93) (− 0.36) (− 0.48) (2.78)
Return_gap*Conc 0.3512*** 0.5927* 0.4284*** 0.0370*** 0.0762** 0.0338***
(3.2) (1.71) (3.59) (3.65) (2.57) (3.20)
Control variables Yes Yes Ye s Yes Yes Yes
R-squared 0.3836 0.6097 0.2058 0.3880 0.6133 0.2104
No. Obs 4874 2063 2811 4859 2060 2799
Page 28 of 37
Alda Financial Innovation (2025) 11:79
managers exploit information advantages with concentration. e negative impact of
conventional fund skills (picking, timing, and return-gap) on performance relates to the
poor skills found in Sect."Skills by concentration level". Furthermore, the scarce influ-
ence of SRI managers’ skills on performance is also explained by the poor SRI fund skills.
e predictive margins of the significant interaction terms are presented in Appendi-
ces B–C to understand the results better because interaction terms are formed of non-
dummy variables (concentration and skills).
e graphs in Appendix B/C show the relationship between the HHI/Top10 and the
performance for three skill levels (maximum, average, and minimum). Graphs B.1–B.2
of Appendix B show increasing SRI-fund performance with greater HHI concentration
for all picking and return gap levels. Moreover, managers with the maximum picking/
return gap level achieve higher/lower performance levels than the managers with the
minimum picking/return-gap level. Hence, SRI-fund managers with superior pick-
ing skills can exploit this ability using concentration strategies to enhance fund per-
formance. However, more skilled traders do not achieve the performance level of less
skilled traders using concentration strategies. is evidence is consistent with the gener-
alized negative return gap found in Table6, revealing estimation errors in the marginal
benefit with regard to the marginal cost of increasing concentration (Fulkerson and Riley
2019; Kacperczyk etal. 2005).
Graphs B.3–B.5 show increasing performance with greater HHI for all skill levels in
conventional funds. Nevertheless, managers with the maximum/minimum skills achieve
the lowest/highest performance. Furthermore, Graph B.4 shows that more skilled timers
develop more concentrated portfolios to achieve the same performance as less skilled
timers. is evidence indicates that the positive timing of the most concentrated con-
ventional funds does not translate into better performance. Chen and Lai (2015) found
a negative relationship between performance and concentration due to overconfidence;
that is, a human bias that causes individuals to overestimate their skills, misjudge the
accuracy of their private information, and overestimate the value of assets (Fellner-Röh-
ling and Krügel 2014). ese results indicate that conventional-fund managers are over-
confident in their information signaling and timing skills, affecting their performance.
Graphs C.1–C.2 in Appendix C show higher performance with greater Top10 concen-
tration in SRI funds, and the SRI managers with the maximum picking (return gap) level
achieve the highest (lowest) performance level. Graphs C.3–C.5 also display a positive
Top10-performance relationship in conventional funds, and managers with the maxi-
mum/minimum skill levels achieve the lowest/highest performance level.
Consistent with the information-advantage principles, this section demonstrates that
the SRI and conventional funds employ concentration strategies to leverage informa-
tional advantages and improve performance. However, the generalized poor skills do not
allow managers to exploit concentration strategies, affecting performance. Only supe-
rior SRI-fund pickers can exploit the selectivity skills with concentration, improving per-
formance. Hence, H7 is rejected. It is noteworthy that conventional-fund managers can
improve performance with higher concentration, but skilled conventional-fund manag-
ers cannot exploit their skills with concentration. is evidence shows that conventional
managers make estimation errors about the marginal benefit relative to the marginal
cost of increasing concentration, and present managerial overconfidence in their skills
Page 29 of 37
Alda Financial Innovation (2025) 11:79
Table 8 Relation between skills, concentration, and performance obtained from the optimization-
model solutions
HHI as concentration measure Top10 as concentration measure
All SRI Conv All SRI Conv
Panel A: Results with the variables calculated from minimum variance optimization
Concentration − 0.0016 0.0010 − 0.0030 − 0.0023 0.0192*** − 0.0094*
(− 0.42) (0.20) (− 0.61) (− 0.62) (3.99) (− 1.69)
Picking 0.0202 0.0372** 0.0061 − 0.0467*** − 0.0662*** 0.0286
(1.57) (2.26) (0.31) (− 4.56) (− 6.83) (1.31)
Timing − 0.0036 − 0.0400** 0.0125 − 0.0163 − 0.0254* − 0.0137
(− 0.43) (− 2.05) (1.10) (− 1.55) (− 1.78) (− 1.08)
Picking*Conc − 0.0253 − 0.0897* 0.0403 0.1739*** 0.2236*** − 0.0224
(− 0.71) (− 1.95) (0.72) (6.18) (7.56) (− 0.40)
Timing*Conc 0.0089 0.1161* − 0.0285 0.0456 0.0692* 0.0396
(0.45) (1.88) (− 1.08) (1.48) (1.66) (1.04)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.1328 0.2102 0.1618 0.1426 0.2469 0.1594
No. Obs 4178 1677 2501 4741 1983 2758
Panel B: Results with the variables calculated from global minimum variance optimization
Concentration 0.0000 0.0123*** − 0.0077*** 0.0016 − 0.0002 − 0.0005
(0.01) (4.55) (− 2.65) (0.85) (− 0.07) (− 0.19)
Picking 0.0024 − 0.0107 0.0396** − 0.0102 − 0.0132 0.0076
(0.20) (− 1.17) (2.29) (− 0.99) (− 1.61) (0.62)
Timing − 0.0070 0.0100 0.0117 − 0.0086 − 0.0296*** 0.0175***
(− 0.80) (0.77) (0.87) (− 1.26) (− 3.32) (2.91)
Picking*Conc 0.0267 0.0336* − 0.0251 0.0589*** 0.0499*** 0.0435*
(1.15) (1.87) (− 0.70) (2.93) (3.06) (1.71)
Timing*Conc 0.0153 − 0.0170 − 0.0209 0.0168 0.0641*** − 0.0405***
(0.88) (− 0.77) (− 0.71) (1.18) (3.67) (− 3.28)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.1481 0.2454 0.1634 0.1388 0.2288 0.1508
No. Obs 4262 1699 2563 4692 1983 2709
Panel C: Results with the variables calculated from optimal portfolio optimization
Concentration − 0.0161*** − 0.0424*** − 0.0040 0.0050 − 0.0168** 0.0184**
(− 2.98) (− 4.78) (− 0.59) (0.78) (− 2.02) (2.18)
Picking − 0.0346*** − 0.0755*** 0.0055 0.0569*** 0.0101 0.0943***
(− 2.86) (− 4.55) (0.24) (3.28) (0.76) (4.15)
Timing − 0.0141 0.0781** − 0.0146 0.0369*** 0.0617* 0.0164
(− 1.40) (2.00) (− 1.27) (3.02) (1.96) (1.55)
Picking*Conc 0.0803*** 0.1315*** 0.0329 − 0.0674*** − 0.0114 − 0.1041***
(3.86) (5.26) (0.97) (− 2.65) (− 0.56) (− 2.88)
Timing*Conc 0.0199 − 0.1150** 0.0221 − 0.0484*** − 0.1057* − 0.0184
(1.46) (− 2.11) (1.43) (− 2.68) (− 1.95) (− 1.23)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.2871 0.6682 0.2482 0.3098 0.5396 0.4053
No. Obs 678 227 451 612 273 339
Panel D: Results with the variables calculated from naive diversification
Concentration − 0.0116 0.3497** − 0.1616*** 0.0066 0.1466 − 0.0752**
(− 0.54) (2.46) (− 3.32) (0.24) (0.84) (− 2.11)
Picking 0.0079 0.0289* 0.0043 0.0075** 0.0253** 0.0042
(1.45) (1.90) (0.82) (2.37) (2.49) (1.27)
Page 30 of 37
Alda Financial Innovation (2025) 11:79
Table 8 (continued)
HHI as concentration measure Top10 as concentration measure
All SRI Conv All SRI Conv
Timing − 0.0016 − 0.0080 − 0.0001 − 0.0009* − 0.0015 − 0.0005
(− 1.11) (− 1.44) (− 0.05) (− 1.66) (− 0.40) (− 0.82)
Picking*Conc − 0.2129 − 0.7588 − 0.1126 − 0.5427** − 1.8824 − 0.2725
(− 1.45) (− 0.97) (− 0.80) (− 2.41) (− 0.82) (− 1.16)
Timing*Conc 0.0384 0.9297** − 0.0190 0.0429 2.7503* 0.0028
(0.81) (2.14) (− 0.30) (1.03) (1.89) (0.06)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.0850 0.2920 0.1902 0.0868 0.2336 0.1631
No. Obs 1643 913 730 1643 913 730
Panel E: Results with the variables calculated from risk-parity optimization
Concentration 0.0105 0.0351* − 0.0365*** 0.0145** 0.0246 − 0.0231**
(1.62) (1.84) (− 3.15) (2.22) (1.54) (− 2.32)
Picking 0.0027 0.0247* 0.0015 0.0026 0.0216** 0.0014
(1.57) (1.85) (0.97) (1.58) (2.25) (0.93)
Timing − 0.0001 0.0105 − 0.0001 − 0.0001 0.0106 − 0.0001
(− 0.22) (1.14) (− 0.08) (− 0.18) (1.46) (− 0.21)
Picking*Conc − 0.0168 − 0.2213 − 0.0090 − 0.0160 − 0.1714 − 0.0071
(− 1.47) (− 0.56) (− 0.85) (− 1.45) (− 0.47) (− 0.69)
Timing*Conc 0.0016 − 0.0987 − 0.0032 0.0015 − 0.1434 − 0.0013
(0.18) (− 0.31) (− 0.32) (0.20) (− 0.42) (− 0.16)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.0533 0.1730 0.1676 0.0542 0.1688 0.1621
No. Obs 1643 913 730 1640 910 730
Panel F: Results with the variables calculated from reward-to-risk timing optimization
Concentration 0.0080 0.0099* 0.0235* 0.0069*** 0.0350*** 0.0004
(1.57) (1.89) (1.80) (3.10) (5.24) (0.14)
Picking 0.0172*** 0.0356*** 0.0026 0.0056*** 0.0564*** 0.0013
(3.75) (4.56) (1.54) (2.63) (5.02) (1.47)
Timing − 0.0010 − 0.0017 − 0.0010 − 0.0013 0.0446*** − 0.0009
(− 0.75) (− 0.13) (− 1.03) (− 1.49) (2.76) (− 1.37)
Picking*Conc − 0.0171 − 0.1702*** 0.0493 − 0.0132* − 0.1526*** 0.0044
(− 0.33) (− 3.26) (0.39) (− 1.80) (− 2.73) (1.35)
Timing*Conc 0.0015 0.3043** 0.0035 0.0016 − 0.1828*** 0.0038*
(0.34) (1.99) (0.31) (0.61) (− 4.25) (1.93)
Control variables Yes Yes Yes Ye s Yes Yes
R-squared 0.3140 0.4991 0.2582 0.2647 0.5024 0.1482
No. Obs 1131 741 390 1634 904 730
This table presents the results of model (15) with the HHI and Top10 concentration measures calculated from the minimum-
variance (panel A), global minimum variance (panel B), optimal portfolio (panel C), naïve diversication (panel D), risk parity
(panel E), and reward-to-risk timing (panel F) optimization-model solutions for all, SRI, and conventional funds. All models
are estimated with time xed eects and robust standard errors clustered by fund and month. Control variables are not
shown and the results are available upon request. T-statistics are in parentheses. *, **, and *** indicate signicance at the
10%, 5%, and 1% levels, respectively
Page 31 of 37
Alda Financial Innovation (2025) 11:79
and information signals in developing concentration strategies (Chen and Lai 2015;
Fulkerson and Riley 2019; Kacperczyk etal. 2005).
Table8 shows the results of model (15) with the variables calculated from the opti-
mization model solutions. e results confirm the diverse effects of concentration on
performance found in panels B–G of Table5. Skills from traditional optimization-model
solutions also affect performance in different ways (panels A–C). However, the picking
skills from modern optimization-model solutions positively influence SRI-fund perfor-
mance (panels D–F). e predictive margins of the significant interaction terms20 show
that only some models provide higher performance with superior skills and higher con-
centration, differing between the SRI and conventional portfolios. Specifically, the asset
allocation from the reward-to-risk timing model helps SRI funds exploit picking and
timing skills. In contrast, the asset allocation from the optimal portfolio model helps
conventional funds exploit picking skills, presenting higher performance with supe-
rior skills and greater concentration. Additionally, results from the optimal portfolio
(reward-to-risk timing) models show lower performance with superior skill levels and
a higher concentration in SRI (conventional) funds. e discrepancy between the same
models for the SRI and conventional funds is because the models must calculate asset
weights from actual fund holdings to consider the investment profile of the SRI and con-
ventional funds. Consistent with previous literature, these results indicate that the best
optimization models differ between the SRI and conventional funds because SRI portfo-
lios usually present higher uncertainty (Oikonomou etal. 2018).
Conclusions
is study analyzes whether the limited universe of ESG assets can lead SRI pension
funds to deviate from the asset allocations of six well-known portfolio optimization
models (minimum variance, global minimum variance, optimal portfolio, naïve diver-
sification, risk-parity, and reward-to-risk timing), presenting higher concentration and
lower performance than their conventional peers. Unlike previous research, this study
considers that SRI-fund concentration strategies may be related to informational advan-
tages. In addition, this study overcomes previous studies on simulated SRI portfolios
because the analyses consider the actual investment profiles of funds in the optimization
models. Hence, this study also demonstrates whether optimization models can guide
managers to improve their skills, concentration strategies, and performance.
e results indicate that the concentration of UK SRI equity pension funds is lower
than the concentration of UK conventional equity pension funds. Moreover, pension
funds largely diversify their portfolios, showing a concentration similar to the naïve
diversification. us, the actual fund concentration is lower than the concentration cal-
culated with the optimization-model solutions (except with the naïve diversification).
is finding contributes to the SRI literature by demonstrating that the ESG asset uni-
verse is not an endemic SRI fund restriction and can provide investment opportunities.
In addition, greater fund concentration improves the performance of SRI and con-
ventional funds, which is consistent with the principles of the information-advantage
20 Predictive margin graphs of the significant interaction terms in Table8 are available upon request.
Page 32 of 37
Alda Financial Innovation (2025) 11:79
theory. However, accomplishing concentration strategies also depends on manage-
rial skills, and the results indicate poor stock-picking, market-timing, and unobserved
trading skills. Only superior SRI-fund pickers can achieve higher performance than less
skilled SRI pickers for a particular concentration level. Skilled conventional managers
cannot achieve higher performance than less skilled managers for a specific level of con-
centration, revealing overconfidence in their information signal and skills. ese results
indicate that managers should know that deviating from the optimization models may
damage pension fund participants. Moreover, some optimization models can help man-
agers improve performance and skills through better asset-allocation decisions, such as
the reward-to-risk timing model in SRI funds. Nonetheless, managers may be motivated
to depart from optimization models because these models provide static solutions, and
constantly recalculating models to adapt to market movements may be costly and sub-
ject to each model’s idiosyncrasy.
e results of this study offer managers, market regulators, and fund participants a
better understanding of concentration patterns in the UK SRI and conventional equity
pension funds, identifying the benefits and limitations of concentration strategies and
the consequences of deviating from optimization models. Additionally, managers can be
aware of the risks of overconfidence and their real capabilities in concentration strate-
gies. Managers can also understand each optimization model’s complexity, assumptions,
and limitations to incorporate upcoming information to adapt to market movements
and rebalance portfolios. Moreover, fund participants can better understand the impact
of concentration decisions on their pension fund savings. us, market regulators should
pursue transparency and provide reliable information about concentration strategies to
improve the decision-making process of fund participants.
Nevertheless, some limitations should be highlighted, and further research should be
conducted. First, although the UK pension fund industry is the second most important
worldwide, some concentration patterns may differ in less developed markets and/or
markets influenced by distinct demographic patterns, such as population aging. Further
research that considers demographics in other countries will address the possible lim-
itations related to country-oriented analyses. Second, SRI fund data limitations result
from the continuing growth of the SRI pension fund niche. Furthermore, the analyses
are restricted to six optimization models, and the study of additional optimization mod-
els will complete the findings. In this sense, the assumption that optimization models
consider actual fund asset allocations might also constrain investment alternatives.
Moreover, the results are limited to the time horizon of the study; thus, it is necessary to
consider that investors’ ESG concerns evolve over time and that the rapid expansion of
ESG issues in society also influences the ESG asset diffusion. e analysis of other insti-
tutional investors may also expand the knowledge about concentration strategies.
Appendix A: Note onHHI andTop10 concentration measures
To illustrate the calculation of HHI, suppose Fund A and Fund B with the following port-
folio holdings at period t. Fund A invests in four stocks and the weights are: 25%, 25%,
25%, and 25%. Fund B invests in four stocks and the weights are: 70%, 20%, 5%, and 5%.
HHI of Fund A = 0.252 + 0.252 + 0.252 + 0.252 = 0.25.
Page 33 of 37
Alda Financial Innovation (2025) 11:79
HHI of Fund B = 0.702 + 0.202 + 0.052 + 0.052 = 0.535.
Although Funds A and B have the same number of stocks at period t, the higher HHI
of Fund B shows greater portfolio concentration because of the larger investment in two
assets (70% and 20%) and Fund A is equally weighted. HHI is recalculated with the new
weights and holdings of Funds A and B at period t + 1, and so on as long as the funds do
not disappear.
e calculations can be extrapolated to funds with diverse number of holdings; in fact,
the funds analysed in this paper hold, on average, 141.8 stocks per quarter (130 stocks
and 151.6 stocks in SRI and conventional funds, respectively).
In addition, to illustrate the calculation of Top10, suppose two funds. Fund A invests in
twenty stocks at period t and is equally weighted (the weight of each stock is 5%). Fund
B invests in twenty stocks and the weights of the ten stocks with the highest weights are:
20%, 20%, 15%, 15%, 10%, 5%, 2%, 1%, 1%, 1% (the remainder stocks have weights of 1%).
Top10 of Fund A = 0.052 + 0.052 + 0.052 + 0.052 + 0.052 + 0.052 + 0.052 + 0.052 + 0.052 + 0.
052 = 0.025, and HHI of Fund A is 0.05.
Top10 of Fund B is 0.1382, and HHI of Fund B is 0.1392.
HHI and Top10 indicate that Fund B is more concentrated than Fund A, and Top10 is
closer to HHI in Fund B than in Fund A because of the larger importance of a few stocks
with regard to the remaining holdings. ese results show the interest of including
Top10 as additional concentration measure when a small number of portfolio holdings
are overweighted. Top10 will be recalculated for Funds A and B with the new weights
and holdings at period t + 1, and so on as long as the funds do not disappear.
In addition, HHI and Top10 are equal in funds holding ten or less assets.
Appendix B: Predictive margins ofsignicant HHI‑skill interaction terms inSRI
andconventional funds
Graphs B.1–B.5 show the predictive margins of the significant picking-concentration,
timing-concentration, and ReturnGap-concentration interaction terms of SRI and con-
ventional funds in panel B.1 of Table7. e y-axis shows the performance (alpha) and
the x-axis shows the HHI concentration.
Page 34 of 37
Alda Financial Innovation (2025) 11:79
Page 35 of 37
Alda Financial Innovation (2025) 11:79
Appendix C: Predictive margins ofsignicant Top10‑skill interaction terms
inSRI andconventional funds
Graphs C.1–C.5 show the predictive margins of the significant picking-concentration,
timing-concentration, and ReturnGap-concentration interaction terms of SRI and con-
ventional funds in panel B.2 of Table7. e y-axis shows the performance (alpha) and
the x-axis shows the Top10 concentration.
Abbreviations
AQR Applied Quantitative Research
CDF Cumulative distribution function
CMA Conservative minus aggressive in the investment factor
ESG Environmental, social, and governance
FE Fixed effects
FTSE The Financial Times Stock Exchange
HHI Herfindahl–Hirschman fund concentration index
HML High minus low in the book-to-market factor
LRP Lower relative polarization
MRP Median relative polarization
OECD The Organization for Economic Cooperation and Development
PDF Probability density function
RMW Robust minus weak in the profitability factor
SMB Small minus big in the size factor
SRI Socially responsible investment
TNA Total net assets
Top10 Concentration of the top-10 fund holdings
UK The United Kingdom
URP Upper relative polarization
USA The United States of America
VIF Variance inflation factor
Page 36 of 37
Alda Financial Innovation (2025) 11:79
Acknowledgements
The author would like to express her gratitude to the Aragon Government for funding received as part of the Public
and Official Research Group (CIBER S38_20R), University of Zaragoza and Fundacion Ibercaja for the financial support
provided for the research Projects JIUZ-2021-SOC-03 and JIUZ2022-CSJ-24, and Ministerio de Ciencia e Innovación and
FEDER for the financial support provided for the research Project PID2022-136818NB-100.
Author contributions
The author read and approved the final manuscript.
Funding
This word was supported by Government of Aragon [Grant S38_20R], Ibercaja and University of Zaragoza [Grants JIUZ-
2021-SOC-03 and JIUZ2022-CSJ-24], and Ministerio de Ciencia e Innovación and FEDER [PID2022-136818NB-100].
Availability of data and materials
Due to the nature of the research, supporting data is not available.
Declarations
Competing interests
The author declares that she has no competing interests.
Received: 26 April 2023 Accepted: 20 January 2025
References
Abbasi AR (2022) Comparison parametric and non-parametric methods in probabilistic load flow studies for power
distribution networks. Electr Eng 104:3943–3954
Ammann M, Bauer C, Fischer S (2019) The impact of the Morningstar sustainability rating on mutual fund flows. Eur
Financ Manag 25:520–553
Anantharaman D, Lee YG (2014) Managerial risk taking incentives and corporate pension policy. J Financ Econ
111(2):328–351
Anderson RM, Bianchi SW, Goldberg LR (2012) Will my risk parity strategy outperform? Financ Anal J 68(6):75–93
Ballestero E, Bravo M, Pérez-Gladish B, Arenas-Parra M, Plà-Santamaria D (2012) Socially responsible investment: A multic-
riteria approach to portfolio selection combining ethical and financial objectives. Eur J Oper Res 216:487–494
Barber B, Huang X, Odean T (2016) Which factors matter to investors? evidence from mutual fund flows. Rev Financ Stud
10:2600–2642
Barnett ML, Salomon RM (2006) Beyond dichotomy: the curvilinear relationship between social responsibility and finan-
cial performance. Strateg Manag J 27:1101–1122
Bauer R, Otten R, Rad AT (2006) Ethical investing in Australia: Is there a financial penalty? Pac Basin Financ J 14:33–48
Bilbao-Terol A, Álvarez-Otero S, Bilbao-Terol C, Cañal-Fernández V (2017) Hedonic evaluation of the SRI label of mutual
funds using matching methodology. Int Rev Financ Anal 52:213–227
Bloomfield T, Leftwich R, Long JB (1977) Portfolio strategies and performance. J Financ Econ 5:201–218
Brown KC, Harlow WV, Zhang H (2021) Investment style volatility and mutual fund performance. J Invest Manag
19(1):25–61
Bu Q, Harrisburg P (2017) Mutual fund performance, diversification, and concentration. J Finance Account 21(1):94–105
Carhart M (1997) On persistence in mutual fund performance. J Financ 52(1):57–82
Chen X, Lai Y-J (2015) On the concentration of mutual fund portfolio holdings: evidence from Taiwan. Res Int Bus Financ
33:268–286
Choi N, Fedenia M, Skiba H, Sokolyk T (2017) Portfolio concentration and performance of institutional investors world-
wide. J Financ Econ 123:189–208
Cox P, Brammer S, Millington A (2004) An empirical examination of institutional investor preferences for corporate social
performance. J Bus Ethics 52:27–43
DeMiguel V, Garlappi L, Uppal R (2009) Optimal versus naive diversification: how inefficient is the 1/N portfolio strategy?
Rev Financ Stud 22(5):1915–1953
Fama E, French K (2015) A five-factor asset pricing model. J Financ Econ 116:1–22
Fellner-Röhling G, Krügel S (2014) Judgmental overconfidence and trading activity. J Econ Behav Org 107:827–842
Fischer M, Gallmeyer MF (2016) Heuristic portfolio trading rules with capital gain taxes. J Financ Econ 119(3):611–625
Friede G, Busch T, Bassen A (2015) ESG and financial performance: aggregated evidence from more than 2000 empirical
studies. J Sustain Finance Invest 5(4):210–233
Fulkerson JA, Riley T (2019) Portfolio concentration and mutual fund performance. J Empir Financ 51:1–16
Gangi F, Varrone N (2018) Screening activities by socially responsible funds: a matter of agency? J Clean Prod
197:842–855
Handcock MS, Morris M (1999) Relative distribution methods in the social sciences. Springer, New York
Helliar C, Petracci B, Tantisantiwong N (2022) Comparing SRI funds to conventional funds using a PCA methodology. J
Asset Manag 23:581–595
Hirschman AO (1964) The paternity of an index. Am Econ Rev 54:761
INVERCO (2024) Las Instituciones de Inversión Colectiva y los Fondos de Pensiones. Informe 2023 y perspectivas 2024.
INVERCO
Page 37 of 37
Alda Financial Innovation (2025) 11:79
Ivkovic Z, Sialm C, Weisbenner S (2008) Portfolio concentration and the performance of individual investors. J Financ
Quant Anal 43:613–656
Jacobs H, Muller S, Weber M (2014) How should individual investors Diversify? An empirical evaluation of alternative asset
allocation policies. J Financ Mark 19:62–86
Jagannathan R, Ma T (2003) Risk reduction in large Portfolios: why imposing the wrong constraints helps. Journal of
Finance 58(4):1651–1683
Johnson E, Moggridge D (2012) The collected writings of John Maynard Keynes. Economic Articles and Correspondence:
Investment and Editorial, Chapter I, 12. Cambridge University Press, New York
Joliet R, Titova Y (2018) Equity SRI funds vacillate between ethics and money: an analysis of the funds’ stock holding deci-
sions. J Bank Finance 97:70–86
Kacperczyk M, Sialm C, Zheng L (2005) On the industry concentration of actively managed equity mutual funds. J
Finance 60:1983–2011
Kacperczyk M, Sialm C, Zheng L (2008) Unobserved actions of mutual funds. Rev Financ Stud 21:2379–2416
Kacperczyk M, Van Nieuwerburgh S, Veldkamp L (2014) Time-varying fund manager skill. J Finance LXIX(4):1455–1484
Keim D, Madhavan A (1997) Transaction costs and investment style: an inter-exchange analysis of institutional equity
trades. J Financ Econ 46:265–292
Kirby C, Ostdiek B (2012) It’s all in the Timing: Simple active portfolio strategies that outperform naive diversification. J
Financ Quant Anal 47(2):437–467
Knigge A, Nowak E, Schmidt D (2004) On the performance of private equity investments: does market timing matter? J
Financ Transf 16(April):123–134
Ledoit O, Wolf M (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio
selection. J Empir Financ 10:603–621
Maillard S, Roncalli T, Teiletche J (2010) The properties of equally weighted risk contribution portfolios. J Portf Manag
36(4):60–70
Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91
Matallín-Sáez JC, Soler-Domínguez A, de Mingo-López DV, Tortosa-Ausina E (2019) Does socially responsible mutual fund
performance vary over the business cycle? New insights on the effect of idiosyncratic SR features. Bus Ethics Eur Rev
28(1):71–98
Merton R (1987) A simple model of capital market equilibrium with incomplete information. J Finance 42:483–510
Newey WK, West KD (1987) A simple, positive semi-definite heteroscedasticity and autocorrelation consistent covariance
matrix. Econometrica 55:703–705
Oikonomou I, Platanakis E, Sutcliffe C (2018) Socially responsible investment portfolios: does the optimization process
matter? Br Account Rev 50:379–401
Pandey A, Sharma AK (2024) The cumulative prospect theory and fund flows in emerging markets. Invest Anal J. https://
doi. org/ 10. 1080/ 10293 523. 2024. 23127 07
Platanakis E, Sutcliffe SA (2019) Harmful diversification: evidence from alternative investments. Br Account Rev 51:1–23
Qin N, Wang Y (2021) Does portfolio concentration affect performance? Evidence from corporate bond mutual funds. J
Bank Finance 123:06033
Renneboog L, Ter Horst J, Zhang C (2011) Is ethical money financially smart? Nonfinancial attributes and money flows of
socially responsible investment funds. J Financ Intermediat 20(4):562–588
Revelli C (2017) Socially responsible investing (SRI): From mainstream to margin? Res Int Bus Financ 39:711–717
Rubin DB (1973) Matching to remove bias in observational studies. Biometrics 29:159–184
Sandberg J (2013) (Re-)Interpreting fiduciary duty to justify socially responsible investment for pension funds? Corporate
Governance: an International Review 21(5):436–446
Sapp T, Yan X (2008) Security concentration and active fund management: do focused funds offer superior performance.
Financ Rev 43:27–49
Sharpe WF (1966) Mutual fund performance. J Bus 39:199–138
Sirri ER, Tufano P (1998) Costly search and mutual fund flows. Journal of Finance 53:1589–1622
Soler-Domínguez A, Matallín-Sáez JC, de Mingo-López DV, Tortosa-Ausina E (2021) Looking for sustainable development:
socially responsible mutual funds and the low-carbon economy. Bus Strateg Environ 30(4):1751–1766
Stein R (2022) Smart’ copycat mutual funds: on the performance of partial imitation strategies. Financial Innovation.
https:// doi. org/ 10. 1186/ s40854- 022- 00398-7
UK Statutory Instruments No. 988 Pensions (2018) UK legislation, Department for Work and Pensions
UKSIF (2018) New Government regulation makes clear existing pension scheme duty to consider ESG factors. UKSIF
Utz S, Wimmer M, Hirschberger M, Steuer RE (2014) Tri-criterion inverse portfolio optimization with application to socially
responsible mutual funds. Eur J Oper Res 234:491–498
Van Nieuwerburgh S, Veldkamp L (2010) Information acquisition and portfolio under-diversification. Rev Econ Stud
77:779–805
Zambrana R, Zapatero F (2021) A tale of two types: generalists vs. specialists in asset management. J Financ Econ
142:844–861
Zheng L (1999) Is money smart? A study of mutual fund investors’ fund selection ability. Journal of Finance 54:901–933
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
