Have scale effects on cost margins of pension fund investment portfolios disappeared?

ABSTRACT

Investment costs of pension funds are crucial for their returns. Consolidation in the pension fund market proceeds continuously, often with cost savings as the main argument. Unused economies of scale in pension fund investment costs, however, have declined over the years to values close to zero, except for very small pension funds. This paper investigates investment economies of scale in the Netherlands and pays special attention to the non-linear relationship between investment costs and sizes of pension funds. Furthermore, investment cost margins are disaggregated into three cost types and into six asset categories. Performance fees are in particular paid for complex asset categories held by large pension funds. They reduce the traditional-scale economy results for the entire portfolio. Cost savings by consolidation is still possible but is very limited.

KEYWORDS:

• Scale economies
• cost elasticity
• pension funds
• investment costs
• non-linear cost–size relationship

JEL CLASSIFICATION:

• G23
• L10

I. Introduction

The costs of pension funds’ investments have a direct impact on their net returns. More than ever, these costs affect current and future pension benefits: now pension premiums are high, with pension premiums in the Netherland between 25% and 30% of the salaries, little room exists to increase them further. In recent years, numerous smaller pension funds have been terminated and taken over by other pension funds or life insurers. Annually, this concerns more than 110.000 participants and over 6 billion euro. A major argument for these mergers is lower costs per invested euro, due to scale economies. But are these scale economies still substantial? Research on the scale effects on investment costs of pension funds reveals, however, a remarkable development over time. At outset, large unused scale economies were found for the Netherlands of, on average, 22% during 1992–2004 (Bikker and de Dreu 2009) and 20% in 1992 (Bikker 2013). However, in the last decennium, there seems to be an absence of any economies of scale: 0% in 2009 (Bikker 2013) and 0% over 2002–2013 (Alserda, Bikker and van der Lecq 2018). This contrasts sharply with the continuing and significant economies of scale in the administration costs of pension funds as observed in the same studies, even though these followed a downward trend: from 36% in 1992–2004, to 29% in 1992–2009, to 10% in 2002–2013. A decline in the mean economies of scale is plausible: three-quarters of the pension funds in 1992, particularly the smaller ones, have since been discontinued. But the complete elimination of scale economies, as apparently seems to be the case with investments, is counter-intuitive.

Broeders, van Oord and Rijsbergen (2016), investigate more precise disaggregated data on investment costs, reported only since 2012. For 2013, they do find economies of scale, for the entire investment portfolio, as well as for a number of separate investment categories. These at first sight contrary results raise the question as to whether scale effects on cost margins of pension fund investments still exist. The primary objective of this paper is to thoroughly investigate the recent and current behavior of pension fund investment costs, where we distinguish three cost types (management cost, performance fees and transaction cost) and six investment categories (fixed income, stocks, real estate, hedge funds, commodities, and private equity). Our results reveal large differences in behavior across cost types and across asset categories.

The three studies cited in the first paragraph use a model with a non-linear relationship: more economies of scale for small pension funds and fewer for large ones. Classic economic theory proposes for short-term U-shaped economies of scale between unit costs and size: in the left leg when size increases declining per unit cost until the cost margin is constant and thereafter in the right leg, when size increases further, increasing costs. Strong economies of scale for small enterprises are quite obvious as – when growing – fixed costs can be allocated over larger production. We refer to this phenomenon as the left-leg effect. Numerous studies have also pointed to higher inefficiency for larger firms, contributing evidence to the ‘right leg effect’. Key factors are managerial problems in large and complex firms: ‘bureaucracy’, ‘additional layers of management and over hiring’ (Chatterton, Smyth, and Darby 2013), and increasing luxury in terms of buildings and salaries, extra costs due to scarcity of qualified staff and additional costs related to overconfidence (Griffin and Tversky 1992). Bauer, Cremers, and Frehen (2010) mention increasing costs of communication between the different sections of the company and the costs involved in monitoring employees, including managers. The motivation and commitment of employees may be lower in a large organization, as they contribute relatively little to the overall success of the organization, resulting in lower productivity (Canback, Samouel, and Price 2006). Lack of a clear overview of budget and liquidity in a large firm may cause inefficient spending with respect to recruitment, equipment or offices (Canback, Samouel, and Price 2006). Pension funds with large amounts of assets are unable to respond quickly to changes in the market, particularly when capital markets are stressed (McKenna and Kim 1986; Bauer, Cremers, and Frehen 2010; Andonov, Bauer, and Cremers 2011), and therefore face market impact costs when buying or selling (Bikker, Spierdijk, and van der Sluis 2007; Bikker et al. 2008; Bikker, Spierdijk, and van der Sluis 2010). The key question is whether such large firm inefficiencies outweigh the basic effect of monotonically declining fixed costs.

Shaffer (1998) investigates functional forms to model costs and explains that many models are too restrictive to describe both (right and left leg) aspects of scale economy changes in relation to firm size: the outcomes are forced in one or another direction. Broeders’ model is prone to this criticism as his model can only describe monotonically declining fixed costs. Hence, the second goal of this paper is to thoroughly investigate the optimal functional form of the pension fund cost model in order to distinguish the two main drivers of scale economies and pension fund size relationship for the various cost types and investment categories.

This paper fits the new disaggregated data in 2012–2019 to a model that encompasses all mentioned and other theoretical relationships between investment costs and size, and hence allows for a possible strong non-linear relation. This enables us to shed light on the puzzle of declining or even disappearing economies of scale in the costs of pension investments. Section II provides a literature survey and Section III describes the pension system in the Netherlands. Section IV presents the (disaggregated) data on pension fund costs and the next section the methodology for measuring economies of scale. Section VI shows the empirical results for total costs and their components as well as by asset class; furthermore, numerous robustness tests are presented. The last section presents conclusions.

II. Literature on scale economies in investment costs

Our definition of investment costs is as follows: the sum of management cost, performance fees and transaction costs, where management costs comprise expenses for market analysis research, risk management, and consulting fees. In practice, particularly in the past, not all cost components are reflected in the reported costs, as sometimes cost items are deducted from gross returns. Specially, when investment is outsourced, the hidden costs may not even be known by the pension fund. A number of studies consider total operating expenses of pension funds, which also include administration costs besides investment cost: Caswell (1976), Mitchell and Andrews (1981), Bateman and Mitchell (2004) and Dobronogov and Murthi (2005). Particularly in earlier years, administration costs dominated investment cost. As these studies are less informative for our purposes, we consider here only investment-cost-only studies. Bikker and de Dreu (2009), Bikker (2013) and Alserda, Bikker, and van der Lecq (2018) investigate investment cost of Dutch pension funds, separately from their administrative costs. These studies provide economies of scale that gradually decline towards zero, as said above. In contrast, Broeders, van Oord, and Rijsbergen (2016) do find statistically significant scale economies for the Netherlands. For the US, Bauer, Cremers and Frehen (2010) observe strong economies of scale in costs in domestic equity investments. Costs vary across equity categories and are also higher for small cap portfolios compared to large caps, and for portfolios that are actively managed or externally managed compared to those internally managed. Both Andonov, Bauer and Cremers (2011) and Dyck and Pomorski (2011) investigate investment costs as well as returns of an international sample of large pension funds. They observe significant economies of scale for both costs and returns. Most of the higher returns come from large pension funds’ increased allocation to alternative investments (mainly private equity) and realizing greater returns in this asset class. Other possible explanations are the greater bargaining power of larger pension funds (Andonov, Bauer, and Cremers 2011), and their possible advantages in internationalization (Dyck and Pomorski 2011).

The investment operations of pension funds are similar to those of mutual funds and many pension funds invest assets through mutual funds. Therefore, the – extended – literature on the investment costs of mutual funds may provide meaningful insights into the investment operations of pension funds as well.¹ Empirical evidence suggests the existence of substantial cost-related economies of scale in the mutual fund industry, which decrease as the fund size increases and become zero as soon as the optimal size has been reached, see Malhotra and Mcleod (1997), Collins and Mack (1997) and Indro et al. (1999). Of course, mutual funds may incur higher costs in hunting for higher returns. Ippolito (1989) compares the expenses and returns of mutual funds and index funds and found that mutual funds offset higher expenses with better results. Possibly, however, this outcome may be sensitive to the particular benchmark used, or can be explained by survivorship bias (e.g. Malkiel 1995). Many other studies have found that higher costs are not related to superior performance relative to the risk-adjusted rate of return (e.g. Jensen 1968, Malkiel 1995, and Malhotra and Mcleod 1997). Thus, the evidence suggests that, in general, higher costs incurred by mutual funds do not lead to higher returns. Since the investment operations of pension funds and mutual funds are similar, it seems reasonable to expect this result to hold for pension funds as well.²

We may therefore conclude that, ceteris paribus, stakeholders are likely to be best served by pension funds with low investment costs. Furthermore, in the investment market, scale economies tend to exist but, according to some studies, only as long as institutions are below the optimal scale.

III. The pension system in the Netherlands

The institutional structure of the Dutch pension system is made up of three-pillars, similarly as in most other developed countries. The first pillar consists of a public pension scheme and is financed on a pay-as-you-go basis. It offers a basic flat-rate pension to all retirees and aims to link the benefit level to the legal minimum wage. The pension benefit age moved gradually from 65 years until 2012 to 66.3 years in 2020 and will go up to 67 years in 2024. The second pillar provides former employees with additional income from a collective, contribution-based supplementary scheme. The prescribed pension age is 68 years. The third pillar is composed of tax-deferred personal savings, which individuals undertake at their own initiative and expense. The supplementary or occupational pension system in the Netherlands is typically organized as a funded defined-benefit (DB) or collective defined contributions (CDC) plan. The benefit entitlement is determined by years of service and a reference wage, which is in more recent years linked to wages over the years of service. The second pillar takes the public scheme benefits into account, while the third pillar’s tax deduction takes the sum of the benefits from the first two pillars into account.

Supplementary schemes are usually managed collectively by pension funds. Three types of pension funds exist. The first is the industry pension fund, which is organized for a specific industry sector (e.g. construction, health care, transport). Participation in an industry pension fund is mandatory for all employers operating in the sector, with a few exceptions. An employer may opt out if it establishes a corporate pension fund that offers a better pension plan to its employees. Where a supplementary scheme is agreed by employers and employees, managed by either a corporate pension fund or an industry pension fund, participation by the workers is mandatory, governed by collective labor agreements. The third type of pension fund is the professional group pension fund, organized for a specific group of professionals, such as the medical profession or notaries.

The Dutch pension fund system is comprehensive, covering as much as 81% of the active labour force in 2019. Almost all employees are covered, but the self-employed need to arrange their own old-age savings. At the end of 2019, total pension fund assets in the Netherlands amounted to some € 1,471 billion, or 182% of GDP, ranking the Dutch pension system, in terms of the assets-to-GDP ratio, as the largest in the industrial world. The government, employees and employers have agreed to transform the pension system into a kind of defined contribution system, which will come into force in 2022 beginning with a transition period of five years. This system may have a collective buffer to soften setbacks, at the choice of the pension funds.

IV. Disaggregated data of pension fund investment costs

This paper is based on unique and extended reports of 280 pension funds of investment costs over 2012–2019 to their financial supervisor De Nederlandsche Bank (DNB). Data on funds discontinued before 1 January 2019 have been deleted for all years. When figures of a pension fund are in any year incomplete, then this fund is deleted for that year. In 2019, the selected funds together manage 94.6% of the total pension investments of € 1.471 billion. Investment costs are split into three components: management, performance and transactions, and available for each of six investment categories: fixed income, stocks, real estate, hedge funds, commodities and private equity.³ Since 2015, private equity has been called an alternative investment, due to a minor change in the definition. We stick to the old name, as private equity is the dominant category of alternative assets. There is a residual item ‘other investments,’ which is not analysed further as a separate asset class, as costs of other investments also include general costs such as liquidity costs, CEM benchmarking, as well as currency and interest rate derivatives, as far as not directly related to investment categories. Each considered investment category may be more or less heterogeneous across the pension funds. For instance, stock portfolios may differ in terms of geographical origin, industry sector, company size and management style. Such heterogeneity may result in cost differences.

Table 1 presents the investment cost margins by investment category and cost type. The upper panel shows that the total costs decline from 0.54% in 2012 to 0.49% in 2019. This decline also holds for the costs of all asset classes, except private equity. Management costs fall by even a quarter, and such a decrease is observed for all six asset classes. Developments in performance fees and transaction costs over time vary across the asset categories.

Table 1. Investments and cost margin by investment category (2012 and 2019)

	Investments		Costs (in percentages)
	(billion €)		Total		Management		Performance		Transactions
	2012	2019	2012	2019	2012	2019	2012	2019	2012	2019
	All pension funds
Fixed income	441	815	0.19	0.16	0.11	0.10	0.01	0.00	0.07	0.06
Stocks	251	438	0.28	0.23	0.21	0.14	0.03	0.03	0.04	0.05
Real estate	79	136	0.92	0.72	0.82	0.53	0.06	0.12	0.03	0.07
Hedge funds	26	26	3.38	2.68	1.84	1.43	1.52	0.83	0.02	0.42
Commodities	2	4	2.45	2.24	1.69	1.26	0.30	0.07	0.46	0.90
Private equity	40	71	3.08	3.70	1.90	1.60	1.18	1.96	0.00	0.14
Total ^a	838	1,471	0.54	0.49	0.36	0.27	0.13	0.14	0.06	0.08
	Largest pension funds^a
Fixed income	235	431	0.17	0.14	0.10	0.07	0.02	0.00	0.11	0.06
Stocks	152	264	0.22	0.20	0.18	0.12	0.03	0.04	0.03	0.04
Real estate	56	92	0.95	0.68	0.84	0.49	0.07	0.15	0.07	0.05
Hedge funds	22	22	3.62	2.69	1.90	1.44	1.70	0.83	0.07	0.41
Commodities	0	4	7.92	2.10	5.53	1.19	1.44	0.07	1.51	0.84
Private equity	34	67	3.12	3.71	1.88	1.53	1.23	2.04	0.00	0.13
Total ^a	492	864	0,65	0.58	0.42	0.29	0.19	0.21	0.08	0.08
	Smallest pension funds^a
Fixed income	34	51	0.28	0.23	0.15	0.16	0.02	0.00	0.16	0.07
Stocks	15	22	0.38	0.31	0.29	0.22	0.07	0.02	0.07	0.08
Real estate	3	4	1.10	0.71	1.01	0.52	0.01	0.10	0.11	0.15
Hedge funds	1	0	1.30	1.01	0.97	0.79	1.12	0.11	0.03	0.11
Commodities	1	0	0.74	6.83	0.64	3.50	0.02	0.00	0.11	3.34
Private equity	1	1	1.96	3.58	1.83	1.66	0.09	2.42	0.03	0.11
Total ^b	54	77	0.39	0.33	0.27	0.22	0.04	0.08	0.13	0.08

Source: DNB.

^aLargest pension funds have each an amount of total assets of more than, in 2012, 6,6 billion euro and, in 2019, 11,7 billion euro. Smallest pension funds have each an amount of total assets of less than, in 2012, 0,13 billion euro and, in 2019, 0,17 billion euro; ^b Residual item ‘other investments’ has not been shown. Private equity is called ‘alternative investment’ since 2015. For the all pension funds sample, the total investment cost margin is the sum of the management, performance and transaction cost margins (horizontal aggregation). The total investment cost margins follow from the investment category margins, but each category weighted with its own share (vertical aggregation).

Investment cost margins are much higher for complex investment types compared to fixed income and stocks. In 2019, private equity investments were 23 times as expensive as those in fixed income. The management costs are also higher (16 times), but the majority of cost differences across asset types are related to performance fees. Commodities have high investment costs. This is a more speculative investment asset with more frequent buying and selling. These observations highlight the differences across asset categories.

The middle panel of Table 1 presents key data for the class of the sixth-largest pension fund (covering 59% of all investments) and the lower panel for the class of the 91st-smallest pension fund (holding 5% to 6% of all assets).⁴ For the largest funds, the cost margins of particularly fixed income, stocks and real estate are lower than those of the smallest pension funds, reflecting economies of scale. The largest funds have many more investments in the expensive complex categories (hedge funds, commodities and private equity), so that their average cost margin is still higher than that of the class of smaller funds.

The higher costs of complex products are expenses that are ‘compensated’ by higher expected returns: costs contribute to benefits. We split the costs into two fictitious components: (1.) costs which we consider waste, of which we want to know possible economies of scale. These costs are related to all necessary activities for investments, which are roughly the same for all investments – comparable to pension funds’ administration costs – which should be as low as possible; and (2.) costs which exclusively relate to the higher risk and the higher complexity of particular categories – related to risk management and market analyses – which are offset by expected higher returns. For our analysis, it is of great importance to correct for the latter type of product-related costs. We do so in the model presented below.

The composition of the management costs in terms of asset categories and the impact of the size of pension funds is illustrated in Figure 1. Five size classes from large to small show for 2012 and 2019 that the costs are highest for the large pension funds. The main drivers are their huge costs of private equity (in 2019 around 40% of all costs) and hedge funds. The economies of scale of larger pension funds, clearly present in fixed income and stocks, are offset by the relative high costs of their larger hedge funds and private equity portfolios.

Figure 1. Management costs of pension funds in basis points, and the asset allocation, by five size classes

The general ‘other costs’ (among which covering of interest- and exchange risk) are here allocated to the tiny item ‘other investments’. The five size class groups are defined based on total assets. The four borders that define the groups are, in 2012: 30, 7.5, 1.5 and 0.4 billion euro, and in 2019: 52, 12, 3 and 0.7 billion euro.

V. Methodology of measuring economies of scale

This section discusses the functional form of cost models and their underlying assumptions with respect to the shape of the average cost per unit curve, which determines the magnitude of scale economies. In the literature, the translog cost function (TCF) to describe costs dominates other model specifications. Christensen and Greene (1976) proposed the TCF as a second-order Taylor expansion, usually around the mean, of a generic function with all variables appearing as logarithms. This TCF is a flexible functional form that has proven to be an effective tool for the empirical assessment of efficiency, both in banking and elsewhere (Christensen and Greene 1976; Dietsch 1993; Nauriyal 1995; Edirisuriya and O’Brien 2001). It is an extension of the Cobb-Douglas function that is capable of fitting the theoretical U-shaped short-term unit cost functions.⁵ A simple TCF is as follows:

(1) $\mathrm{l}\mathrm{n}I{C}_{it}=c+\alpha \left(\mathrm{l}\mathrm{n}T{A}_{it}\right)+\beta (\mathrm{l}\mathrm{n}T{A}_{it}-\overline{lnTA}{)}^2$(1)

with IC for investment costs and ‘TA’ for total assets or investments, as the measure of size. Subscripts i and t refer to, respectively, pension fund i and year t. Note that, in the squared term, we take the logarithm of TA_it in deviation from its arithmetic average, that is over the logarithms of TA_it over all years and all pension funds (denoted by the bar above the variable).⁶ This is in line with the Taylor expansion.⁷ Unused scale economies exist where α < 0, while concavity, or a U-shaped unit cost function, requires β > 0.

Shaffer (1998, 94) proves that for a sample of monotonically declining unit costs, the TCF would estimate a concave function with an optimal scale, so that the existence of an optimal size and diseconomies of scale for larger firms is (incorrectly) imposed.⁸ Indeed, the left leg of the TCF can be fitted to the hyperbolically declining average costs, with the optimal scale in the right-hand tail of the sample, or beyond the largest observation. Therefore, Shaffer (1998) suggests cost functions to estimate scale economies that do not impose this U-shaped average-cost function. The main alternative is the unrestricted Laurent function (ULF), which is similar to the TCF, but with two inverse terms added..

(2) $\mathrm{l}\mathrm{n}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /ln\hspace{0.17em}T{A}_{it}+\delta /(lnT{A}_{it}{)}^2$(2)

The ULF can describe monotonically declining average cost, does not impose an optimal scale and allows different degrees of concavity for smaller and larger pension funds. For the concave properties to hold, the coefficients γ and δ should both be positive, next to β. Under γ = δ = 0, Equation (2)(2) $\mathrm{l}\mathrm{n}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /ln\hspace{0.17em}T{A}_{it}+\delta /(lnT{A}_{it}{)}^2$(2) would become equal to the TCF. Cost elasticity (CE) is defined as the proportional increase in cost as a result of a proportional increase in output. In mathematical terms, this results in the following expression for elasticity: $C{E}_{it}=\mathrm{\partial }\mathrm{l}\mathrm{n}I{C}_{it}/\mathrm{\partial }\mathrm{l}\mathrm{n}T{A}_{it}$. Using Equation (2)(2) $\mathrm{l}\mathrm{n}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /ln\hspace{0.17em}T{A}_{it}+\delta /(lnT{A}_{it}{)}^2$(2) , this is equal to:

(3) $C{E}_{it}=\alpha +2\beta (\mathrm{l}\mathrm{n}T{A}_{it}-\overline{lnTA})-\gamma /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^2-2\delta /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^3$(3)

The second term of CE becomes zero when the CE is evaluated around the mean of the sampled logarithms of TA_it, that is: $\overline{lnTA}$. The CE is then equal to the sum of α and the last two terms that depend on the sample observations. The scale economies (SE) can easily be calculated from the above by subtracting CE from unity: SE = 1 – CE. If the calculated CE has a value larger than one, this indicates diseconomies of scale; a value smaller than one indicates economies of scale and a value of exactly one indicates constant returns to scale.

Our empirical model for investments costs (IC) reads as:

(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4)

The IP_ikt stands for investment products or categories k (as listed in Table 1), as each product brings its own investment costs. In general, it holds that greater risk is attached to higher costs of risk management market analyses. The coefficient ε_k denotes the extra costs attached to investments in category k, compared to fixed income.This way, costs are corrected for the varying composition of the investment portfolio and, particularly, for the fact that larger pension funds have more risky and costly investment products. R_ijt denotes rating class j of the fixed income investments of pension fund i in year t, as the rating of bonds are also attached to cost: the lower the rating, the more risk they carry and the more cost of risk management and market analyses are involved. Further, TA/P represents investments per participant, as investment strategies and costs may relate to the average pension wealth. Other explanatory variables are type of pension fund organisation (industry, company or professional group pension funds), pension scheme (defined premiums versus defined benefits) and age and working position of participants (working, inactive or retired). They are included in the estimated model, but appear not to be significant.

Note that both the sum of all investment products and the sum of all ratings amount to 1, so that we (twice) delete one category to avoid singularity in the explanatory variables. We delete fixed income, so that all other coefficients of investment products reflect cost differences with fixed income. And, similarly, we delete the AAA rating class, so that all other rating coefficients show cost differences with the AAA rating.

We use the model of Broeders et al. as a robustness check. This model deviates from our Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) in two respects. First, the dependent variable is not the logarithm of investments costs (ln IC_it) but the cost margin C_it/TA_it, and second, the non-linear terms of total investments are absent (so that scale economy does not vary with pension fund size, expressed as total investments):

(5) $I{C}_{it}/T{A}_{it}=\alpha ln\hspace{0.17em}T{A}_{it}+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(5)

Broeders, van Oord, and Rijsbergen (2016) have two other explanatory variables related to duration, not available to us or considered as less relevant. The main disadvantage of this model, in our view, is that the relationship between economies of scale and pension fund size is imposed, as in the TCF model, explained above. An advantage is that the simple relationship between scale economies and pension fund size more easily results in significant effects. A minor disadvantage is that scale economies cannot directly be derived from the estimation results as in Equation (5)(5) $I{C}_{it}/T{A}_{it}=\alpha ln\hspace{0.17em}T{A}_{it}+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(5) , where they follow directly from Equation (4), see Equation (3)(3) $C{E}_{it}=\alpha +2\beta (\mathrm{l}\mathrm{n}T{A}_{it}-\overline{lnTA})-\gamma /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^2-2\delta /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^3$(3) .

VI. Estimation results

Models of total costs and their components

Table 2 provides the estimates of Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) , using pooled OLS and Newey–West estimates of heteroscedasticity and autocorrelation consistent (HAC) standard errors. In this presentation, we drop the constant and the insignificant other explanatory variables discussed below that equation: organizational types of pension funds, pension schemes, as well as age and working position of participants. The negative coefficients of the quadratic total assets term reveal that the unit cost function is concave, that is, costs decrease less than proportionally with size, reflecting large economies of scale for small pension funds and smaller economies of scale for larger pension funds. Positive coefficients of the inverse terms of total assets would indicate that fixed costs exist which may be allocated to ever-increasing investments. This can reflect a component to economies of scale that exist for any pension fund size. This is indeed the case for total costs, management costs and transaction costs, as the positive effect of the first inverse term outweighs the effect of the second (quadratic) inverse term. The opposite is true for performance fees, where the classical scale economy theory does not (fully) apply.

Table 2. Estimates of the investment costs of pension funds Equation (4) over 2012–2019

	Total costs		Management costs		Performance costs		Transaction costs
Column	1		2		3		4
ln(total assets)	3.17	(0.78*)	1.78	(0.94°)	1.90	(1.62)	2.61	(2.46)
(ln(total assets)-ln(gem.))^2	-0.08	(0.03*)	-0.04	(-0.04°)	-0.08	(0.05)	-0.delete v	(0.04°)
1/ln(total assets)	774.21	(271.73*)	309.23	(334.91)	-233.13	(736.20)	368.80	(369.83)v
1/(ln(total assets))^2	-2474.8	(874.17*)	-1010.04	(1099.23)	2748.52	(2936.8)	-598.86	(1181.91)
ln (assets/participants)	-0.04	(0.02°)	-0.04	(0.02°)	0.09	(0.07)	-0.08	(0.03*)
Stocks^#	0.37	0.12*	0.34	(0.12*)	2.02	(0.69*)	0.24	(0.30)
Real estate^#	1.82	(0.26*)	2.00	(0.26*)	-2.62	1(.59)	1.02	(0.59)
Hedge funds^#	6.09	(0.45*)	5.89	(0.47*)	15.01	(1.78*)	-1.19	(2.50)
Commodities^#	4.61	(1.71*)	6.18	(1.77*)	0.97	(9.47)	-8.60	(3.87°)
Private equity^#	7.67	(0.52*)	7.14	(0.57*)	23.30	(2.85*)	2.37	(1.26)
AA^#	-0.58	(0.10*)	-0.54	(0.09*)	-0.70	(0.58)	-0.53	(0.20*)
A^#	-0.19	(0.13)	-0.07	(0.15)	-1.28	(0.85)	0.15	(0.26)
BBB^#	0.78	(0.14*)	0.70	(0.14*)	2.62	(0.90*)	-0.30	(0.35)
lower than BBB^#	1.35	(0.17*	1.52	(0.17*)	-1.05	(1.00)	1.28	(0.52°)
no rating^#	0.55	(0.13*)	0.72	(0.13*)	-1.21	(0.55°)	-0.25	(0.33)
Cost elasticity (average p.f.)	0.941		0.911		1.173		1.104
Economics of scale	0.059		0.089		-0.173		-0.104
R^2 adjusted for d.o.f.	96.2		96.0		74.0		82.5
Number of observations	1486		1486		667		1387

Newey-West estimates of heteroscedasticity and autocorrelation consistent (HAC) standard errors are shown in italics and between parentheses. ^# indicates that the shares are expressed as per units. * and ° indicate statistical significance at the respectively 99% and 95% confidence level.

Note that multicollinearity may exist between the four total assets terms, which may prevent statistical significance of the separate terms. A Variance Inflation Factor (VIF) test confirms the multicollinearity among the four size terms, but reveals that multicollinearity among all other explanatory variables, and between the size variables and the other explanatory variables, are very low, with VIF values below 2.5. In Section “Robustness tests” below, we test whether one or more of the non-linear total assets variables may be excluded. This is not the case: these tests reveal that all exclusion restrictions are rejected. This confirms that the model specification, as in Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) , is necessary to describe the scale economies in full detail.

The four coefficients of the size terms together determine the cost elasticity (CE), as explained by Equation (3)(3) $C{E}_{it}=\alpha +2\beta (\mathrm{l}\mathrm{n}T{A}_{it}-\overline{lnTA})-\gamma /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^2-2\delta /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^3$(3) . For total costs, this CE is 0.941 for the average pension fund, where the squared term becomes zero.⁹ The average pension fund is defined as the geometric mean of the pension funds’ investments, which corresponds to € 751 million. This implies average economies of scale of 5.9%. For management costs, these economies of scale are larger at 8.9%, while for performance costs and transaction costs, diseconomies of scale exist, at least for the average pension fund. For performance costs, the traditional-scale economy theory may not be applicable, as performance fees are expected to be compensated by higher returns from investments. However, Broeders, van Oord and Rijsbergen (2019) do not find such ‘compensation’ effect in their empirical investigation. Also, for transaction costs, one likely expects that the additional (transaction) costs of active management are compensated by higher returns. Here too, traditional-scale economy theory may not be applicable.

We start with the first two columns referring to estimates of the total cost and management cost models. As the category management costs is the main component of total costs, these estimates are rather similar. The model variables reflecting the composition of the investment portfolio show that all investment products have attached to them considerably more, and statistically significantly more total and management costs than fixed income (which are chiefly bonds). This is plausible because market analysis and risk management of these products are, on average, more complex. If investments in stocks, real estate, hedge funds, commodities or private equity were doubled at the cost of fixed income investments, total investment costs would increase by, respectively, 10%, 20%, 16%, 1% or 29%.¹⁰ Cost difference across asset types are better reflected, if we considered marginal cost, and increase investment for each asset category by, say, 10% points. Total costs would then increase by, respectively, 3%, 20%, 66%, 45% or 52%.¹¹ For management costs, the outcomes are roughly the same.

In addition to the decomposition of the entire investment portfolio, we have the decomposition of the rating distribution for fixed income. Total and management costs increase significantly with the rating: investment in relatively safe AA and A bonds bring much less costs along, while those in the riskier BBB and below BBB bonds go with more costs. If investments in BB and BBB bonds would be doubled at the cost of AAA bonds, total investment costs would increase with 6%,¹² or for an increase in investment for each of these categories by, say, 1% point: respectively, 0.85% and 1.47%. The rating class costs are compared to those of AAA bonds. It is remarkable that they are higher than those of AA and A rating classes. We observe this also for all individual years. This may be because the risk of the safest counterparties is more difficult to assess, as the probability on default or credit quality downgrading in this class is extremely rare or absent. Wealth per participant (investment per participant) is accompanied by lower costs. The total investment cost and management cost models explain around 96% of all variation in costs (R², adjusted for degrees of freedom).

Performance costs are only paid by a minority of pension funds (those who invest more in complex assets), see the relative low number of observations (663, see 3rd column of Table 2). They increase strongly with investments in hedge funds and private equity, while they increase slightly, but significantly with investments in stocks, all compared to fixed income. The coefficients of hedge funds and private equity of above 15 imply that total performance costs would increase by, respectively, 44% and 65%, if these asset categories were to double their investment, at the cost of fixed income investments,¹³ or increase in both cases by 17%, when the respective investments would increase with 1% point.¹⁴ Significant effects are not found for real estate and commodities nor for the rating classes, except for rating BBB. Relatively wealthy pension funds have higher performance costs, as they invest more in hedge funds and alternative assets. The performance cost model explains around 73% of all variation in costs, a much lower percentage than for e.g. managements cost. Transaction costs are high for commodities but do not vary much for the other categories (last column in Table 2).

Scale economies by size classes and cost type

Figure 2 shows how the cost elasticity of our Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) varies with pension fund size. The nine points in each graph represent the cost elasticity for the 10^th to the 90^th percentile of the size distribution. Note that pension funds that matter from an economic perspective are all in the highest size class. Clearly, the cost elasticity of the total costs (straight line) increases – and economies of scale decrease – with size, so that substantial economies of scale occur mainly in the smaller pension funds. For the 50^th percentile (the median) of the pension funds, the CE is close to 0.94, equal to the CE of the geometric average of pension funds, which is € 751 million. For total costs, economies of scale for the smallest institutions are 10%, declining for larger funds to 6% and becoming 5% for the largest organizations.¹⁵

Figure 2. Cost elasticities of total investments of pension funds by their size (2012–2019).

This figure shows the nine percentile borders of 10% to 90%. The total investments of the 10%-percentile amounts €°110 million and that of the 90%-percentile € 8.6 billion.

Disaggregation to cost types reveals that cost elasticities for management costs (light grey dotted line) are fairly constant at around 0.91 for smaller and medium-sized pension funds, so that scale economies are around 9%. Scale economies increase to 10% for the largest pension funds. This is remarkable, as the classic economy of scale mechanism – constant costs can be allocated across a large group of participants – is expected to have the greatest impact on small pension funds. Performance fees have large economies of scale for the small pension funds (47%), declining to zero for larger funds (where CE is equal to 1, for pension funds with investments of almost a half a billion euro), and thereafter diseconomies of scale up to 22% for the largest pension funds. For transaction costs, we observe diseconomies of scale ranging from 0% via 10% to 5%.

We have calculated how much investment costs the smaller and medium-sized pension funds together may save, when they would become equal to, say, the five but largest funds by growth, mergers or takeovers. The scale economy savings would be € 36 million, that is only 1,4% of the costs of the respective smaller and medium-sized pension funds, or less than 0.5% of the investment costs of all funds together. The savings percentage increases (but the savings amount decreases) when we consider smaller pension funds only. For instance, the smallest ten pension funds would save 6%, or € 0.3 million. On the other hand, when two large pension funds merge, they can, mutatis mutandis, save 2.5–3% of their investment costs.¹⁶

Analyses by asset class

In order to better explain the outcomes presented in Figure 2, we disaggregate our analyses by estimating CEs (and, hence, economies of scale) separately for the six asset classes and for the three cost types. Table 3 presents these CEs of investment costs of the – in terms of size – average pension fund over 2012–2019 based on Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) . The first row refers to the total investment costs estimates from Table 2: for the total cost-total investment case the economies of scale for the average pension fund are 6%, and for the management cost-total investment case the economies of scale are 9%. The CE coefficients below 1 reflect the existence of (unused) economies of scale. For both total costs and management costs, we observe economies of scale for all investment categories, except real estate and private equity. Total costs of economies of scale of the key investment categories fixed income and stocks are around 5%, while they are somewhat lower for hedge funds and commodities. All these economies of scale are much larger for management costs, particularly for commodities. For real estate and private equity, the cost margins increase with size instead of decrease. This unexpected result for real estate may be explained by the fact that larger pension funds have more complex real estate categories, such as shopping centres and office buildings, to which higher management and analysis costs are attached, but where expected returns may also be higher. A similar argument may apply to private equity: large pension funds may hold more laborious private equity types, which require more management and analysis costs. Table 3 also shows that the number of observations falls sharply for the more complex and more sophisticated investment categories, confirming that these categories are held only by a limited number of pension funds, particularly the larger ones. This has also been observed in Table 1.

Table 3. Cost elasticities of investment costs of the average pension fund (2012–2019)

	Total costs	Management costs	Performance costs	Transaction costs	Total costs	Management costs	Performance costs	Transaction costs
	Cost elasticity				Number of observations
Total investment	0.941**	0.911**	1.173	1.104	1486	1486	667	1387
Fixed income	0.954**	0.910**	0.910	1.064	1461	1453	178	1308
Stocks	0.953**	0.931**	0.799**	0.998	1475	1471	326	1276
Real estate	1.107**	1.085**	1.168	0.835**	1213	1208	273	736
Hedge funds	0.980	0.915	1.243	0.905	272	270	179	107
Commodities	0.967	0.772	0.860	0.449**	283	189	39	96
Private equity	1.095**	1.042**	1.024	0.854	522	521	286	225

Cost elasticities below 1 imply that economies of scale exist. Two asterisks point to significance of economies of scale on the 95% confidence level, based on the ‘constant returns to scale’ test, see text.

Performance fees also show substantial scale economies for fixed income, stocks, and commodities, but diseconomies of scale for real estate, hedge funds, private equity and, remarkably, total investments. These – implausible – diseconomies of scale in the total costs-performance fees case are likely caused by the complex investment products real estate, hedge funds and private equity. We will investigate this in Section ”Cost elasticities of the classic investments versus those of the complex assets” below. In any case, we conclude that disaggregation of asset classes appears to increase our insight here.

We apply a constant returns to scale (CRS) test with null hypothesis ‘no scale economies’ or CE = 1, which simultaneously tests the four restrictions α = 1 and β=γ=δ = 0 in Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) . The asterisks in Table 3 show where the CRS hypothesis has been rejected.

Broeders’s model estimates

We estimate Broeder’s model of Equation (5)(5) $I{C}_{it}/T{A}_{it}=\alpha ln\hspace{0.17em}T{A}_{it}+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(5) as a robustness test. The disadvantage of this model is that it only distinguishes a very simple relationship between costs and size, but the advantage is that it provides statistically significant results much more easily. Table 4 presents the coefficient α in Equation (5)(5) $I{C}_{it}/T{A}_{it}=\alpha ln\hspace{0.17em}T{A}_{it}+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(5) , which is the effect of pension fund size (i.e. total investments) on investment costs over 2012–2019. For total investments, fixed income and stocks, for all three cost components the negative size effects in this table correspond to the economy of scale effects in Table 3.¹⁷ All these effects are now significant on the 1% level, except the stock-performance fees case, where the significance level is 5%. Hence, these results are robust. For the other investment categories, the results differ in various places compared to those in Table 3. Statistically significant results at the 5% level are found only for the real estate-performance fee case (diseconomies of scale) and the commodity-management cost case (economies of scale). Here, the lower number of observations is likely the cause of the lower significance. For 2013, Broeders et al. (2016) did find similar effects, with a few exceptions, both for our 2013 results (not shown here)¹⁸ and our full period results.

Table 4. Effect of pension fund size on investment costs (α) of Equation (5) over 2012–2019

	Total costs	Management costs	Performance costs	Transaction costs
Total investment	-3.98***	-4.45***	0.29***	-0.28
Fixed income	-3.00***	-2.98***	-0.88***	-0.43**
Stocks	-2.73***	-2.43***	-1.09**	-1.03***
Real estate	1.10	-0.47	1.54**	-2.01*
Hedge funds	-2.54	-8.30*	-8.31	-0.87
Commodities	4603.32*	-625.36**	-6.20	15,546*
Private equity	-752.60	-660.14	5.62*+	-3.25

Two and three asterisks refer to significance on the, respectively, 5% and 1% level, using a one-sided test. Negative coefficients reflect the existence of economies of scale. Numbers of observations are equal to those in Table 3.

Cost elasticities of the classic investments versus those of the complex assets

Using the results of Tables 3 and 4, we now investigate the outcomes when we drop either real estate, hedge funds or private equity, or all three categories together, to see whether the less plausible results of the total investment-performance fee case are attributable to these categories. Dropping each of these asset categories moves its CE curve down, compared to the initial situation in Figure 2. In Figure 3, we present the outcome when all three complex asset categories are excluded. Hence, this graph represents the fixed income, stocks and commodity investments portfolio, which is 85% of the total portfolio.

Figure 3. Cost elasticities of fixed income, stocks and commodity investments of pension funds by their size (2012–2019).

See note below Figure 2.

The total investment cost economies of scale of this classic investment portfolio range from 8% for the smallest pension funds via 5% of the medium-sized funds to 7% for the largest institutions. The management cost economies of scale now range from 7% for the smallest pension funds to 14% for the largest ones. For performance fees and transaction costs, economic theory has less predictive power with respect to economies of scale. We observe economies of scale for performance fees ranging from 11% (for small pension funds) to 29% (medium-sized) back to 10% (large) and diseconomies of scale for transaction costs, with values similar to those in Figure 2 (0%, 11% and 5%).

Developments over time

We repeat the estimates of Table 2 for each single year and present the annual cost elasticities in the upper panel of Table 5. Remarkably, the economies of scale in total investment costs were close to zero over 2012–2016 and did disappear fully in the year 2014, but returned in later years, increasing to 8% in 2019. This is in part due to the management costs that had smaller economies of scale over 2012–2014. For performance fee elasticities, we observe a substantial rise over the years, as well as fluctuations. Transaction cost diseconomies of scale peaked in the years 2014 and 2015.

Table 5. Cost elasticities of investment costs of average pension fund by year

	2012	2013	2014	2015	2016	2017	2018	2019	2012-2019
Total costs	0.97	0.99	1.00	0.98	0.96	0.94	0.94	0.92	0.94
Management costs	0.95	0.96	0.94	0.91	0.92	0.92	0.93	0.91	0.91
Performance fees	1.01	0.98	1.17	1.33	1.06	1.27	1.44	1.44	1.17
Transaction costs	1.11	1.20	1.23	1.27	1.16	1.10	1.05	0.99	1.10
Exclusive of complex investments in real estate, hedge funds and private equity
Total costs	0.98	1.01	1.02	1.00	0.98	0.95	0.96	0.93	0.95
Management costs	0.95	0.97	0.96	0.93	0.93	0.93	0.94	0.91	0.92
Performance fees	0.89	0.55	0.42	0.71	0.81	0.96	1.12	1.03	0.75
Transaction costs	1.12	1.20	1.30	1.32	1.21	1.11	1.06	1.03	1.12

Values below 1 indicate that scale economies are present.

When the costs of the complex investments in real estate, hedge funds and private equity are excluded (lower panel), we observe that performance fees show economies of scale in most years (except 2018 and 2019), particularly in the first part of the sample period. This is in line with what we have seen in Figure 3. For the other cost components, the picture in the lower panel hardly differs from that in the upper panel. These results confirm that economies of scale in pension fund investment costs indeed disappeared almost or fully around 2012–2015, but did return somewhat in later years.

Robustness tests

This section presents a number of variants on the model and an alternative estimation approach, in order to observe how robust our estimation outcomes are, in addition to the variants of the last two Sections above. Column 1 of Table 6 shows the original model also presented in Table 2. In the next three models, one or two inverse ‘total assets’ terms have been excluded, whereas Column 5 displays the linear model. We use F-tests for the exclusion restrictions. The key outcome is that the F-tests reject the restrictions with high levels of confidence: the test statistics range from 19 to 54 while the 99% critical values range from 3.9 to 6.4. Hence, the four total assets terms are all needed to describe the cost–size relationship precisely. A further test is on ‘constant returns to scale’ or ‘no scale economies’, that is simultaneously on the four restrictions α = 1 and β=γ=δ = 0 in Equation (4)(4) $ln\hspace{0.17em}I{C}_{it}=c+\alpha lnT{A}_{it}+\beta (lnT{A}_{it}-\overline{lnTA}{)}^2+\gamma /lnT{A}_{it}+\delta /(lnT{A}_{it}{)}^2+\sum _k{\epsilon }_{k}I{P}_{ikt}/T{A}_{it}+\sum _j{\phi }_j{R}_{ijt}+\nu T{A}_{it}/P_{it}+u_{it}$(4) . This no-scale-economies hypothesis is also rejected firmly. Secondly, cost elasticities range from 0.93 to 0.95, that is, scale economies are rather similar with values between 5% and 7%. Some non-linear ‘total assets’ coefficients shift heavily when restrictions are applied, but – and this is the third result – the other coefficients are fairly stable across the variants. This also holds for Column 6 where we present the results of a size-weighted regression, where each invested euro counts equally, instead of each pension fund. A final test is pictured in Figure 4, where the cost elasticities (and, hence, scale economies) are presented for various pension fund sizes. Weighted and unweighted cost elasticities are fairly similar, which points to robust CE estimates. Furthermore, we see the effect of the exclusion restrictions, but we have to hold in mind that they are rejected. With the dropping of inverse terms, the higher scale economies for smaller pension funds are not present anymore. The linear model excludes variation with the pension fund size, hence we see a constant line, not reflecting the U-formed unit cost qualities.

Figure 4. Cost elasticities of total investments of pension funds by their size for various specifications (2012–2019).

See note below Figure 2.

Table 6. Estimates of the total investment costs of pension funds Equation (4) for various specifications of ‘size’ over 2012–2019

	Original model		Without squared inverse term		Without simple inverse term		Without the two inverse terms		Linear		Weighted regression
Column	1		2		3		4		5		6
ln(total assets)	3.17	(0.78*)	0.64	(0.20*)	0.78	(0.10*)	0.95	(0.01*)	0.95	(0.01*)	3.92	(1.65°)
(ln(total assets)-ln(gem.))^2	-0.08	(0.03*)	-0.02	(0.01*)	0.01	(0.01)	-0.01	(0.00)	—	—	-0.11	(0.03*)
1/ln(total assets)	774.21	(271.73*)	-52.02	(33.88)	—	—	—	—	—	—	1021.73	(183.36*)
1/(ln(total assets))^2	-2474.8	(874.17*)	—	—	-176.13	(105.81)	—	—	—	—	-3225.62	(674.75*)
ln (assets/participants)	-0.04	(0.02°)	-0.03	(0.02)	-0.04	(0.02)	-0.03	(0.02)	-0.02	(0.03)	-0.04	(0.02°)
Stocks^#	0.37	(0.12*)	0.36	(0.12*)	0.35	(0.12*)	0.42	(0.13*)	0.41	(0.13*)	0.42	(0.13*)
Real estate^#	1.82	(0.26*)	1.74	(0.25*)	1.76	(0.26*)	1.64	(0.26*)	1.67	(0.25*)	1.74	(0.27*)
Hedge funds^#	6.09	(0.45*)	5.89	(0.44*)	5.90	(0.44*)	5.94	(0.44*)	5.86	(0.43*)	6.10	(0.46*)
Commodities^#	4.61	(1.71*)	4.50	(1.70°)	4.48	(1.71°)	4.68	(1.73°)	4.71	(1.73°)	6.17	(2.31°)
Private equity^#	7.67	(0.52*)	7.80	(0.51*)	7.78	(0.51*)	7.85	(0.49*)	7.31	(0.66*)	7.69	(0.54)*
AA^#	-0.58	(0.10*)	-0.59	(0.10*)	-0.59	(0.10*)	-0.59	(0.10*)	-0.58	(0.10*)	-0.56	(0.10*)
A^#	-0.19	(0.13)	-0.34	(0.19)	0.3	(0.18)	-0.41	(0.27)	-0.40	(0.28)	-0.28	(0.17)
BBB^#	0.78	(0.14*)	0.83	(0.15*)	0.82	(0.14*)	0.87	(0.16*)	0.88	(0.17*)	0.85	(0.14*)
lower than BBB^#	1.35	(0.17*)	1.42	(0.17*)	1.42	(0.17*)	1.38	(0.17*)	1.39	(0.16*)	1.37	(0.18*)
no rating^#	0.55	(0.13*)	0.55	(0.14*)	0.55	(0.14*)	0.52	(0.13*)	0.52	(0.13*)	0.60	(0.15*)
Cost elasticity (average p.f.)	0.941		0.928		0.926		0.950		0.948		0.948
Economics of scale	0.059		0.072		0.074		0.050		0.052
R^2 adjusted for d.o.f.	96.2		96.1		96.1		96.1		96.0		92.3
F-test on restriction(s)	—		54.9		33.2		19.2		39.8		—
Number of observations	1486		1486		1486		1486		1486		1486

See note below Table 2.

VII. Conclusions

Over the years, the investment costs of pension funds, expressed in percentages, have declined substantially from 0.54% in 2012 to 0.49% in 2019. This holds for almost all investment categories for total costs as well as management costs. Economies of scale in total investment costs of pension funds are nowadays smaller than in the past, but not yet disappeared completely: during 2012–2019 ranging from 10% for the smaller pension funds to 5% for the largest ones. Disaggregation to cost types and pension fund size reveals that economies of scale in management costs are around 9% for all pension fund sizes. Remarkably, performance fees have huge economies of scale for small institutions but substantial diseconomies of scale for the large funds. Large pension funds invest more in the complex asset categories where high performance fees are paid. Disaggregation into asset categories reveals that performance fee diseconomies of scale do not exist for the key investment categories fixed income and stocks (as well as for commodities) and are mainly due to complex asset classes.

In the hypothetical case that all smaller and medium-sized pension funds would be equally large as the fifth but largest pension fund through growth, mergers or take-overs, then their investment costs in 2019 would decline by only 1.4% (or € 36 million). That is less than 0.5% of the total investment costs of all funds together. On the other hand, when two large pension funds merge, they can, mutatis mutandis, save 2.5–3% of their investment costs.

Finally, we turn to the question posed by the title of this paper: have scale effects on cost margins of pension fund investment portfolios disappeared? Not according to the benchmark model of Broeders: there is statistical evidence that the size of investment portfolios affects costs. But the limited economies of scale we find with our sophisticated economies of scale model are from an economic viewpoint rather mediocre. In a breakdown of the analysis in individual years, we find absence of economies of scale for a number of years. Our conclusion is that some economies of scale do exist (in most years) but that they are of moderate magnitude only. The argument for consolidation still exists but is limited.

VIII. Recommendations with respect to further research

The investment and administrative costs of pension funds in the Netherlands have been subject to increasing attention from pension funds themselves, their branch organizations and the various supervisory authorities. Reporting requirements are regularly strengthened, which has contributed to better cost figures, greater attention to costs, and to the huge consolidation of the Dutch pension sector. From an economic cost perspective, this is a positive development. Hence, the sector has responded to the existence of scale economies. However, an important characteristic of investment costs is that they increase in relation to the asset categories that are more demanding in terms of market analysis and risk management. Are the expectations of corresponding higher expected returns justified? Further research in this direction would be very welcome and could contribute to sound investment policy recommendations. A similar research question regards performance fee costs. Are they recovered through, on average, higher returns? Further research would be helpful here, too. Such research on the net performance of pension funds would allow evaluation of the overall economies of scale.

We also have recommendations with respect to further research in order to improve our approach. Each investment category considered may be more or less heterogeneous across the pension funds. For instance, stock portfolios may differ in terms of geographical origin, industry sector, company size and management style. Such heterogeneity may relate to pension fund sizes. Increasing the granularity of our dataset so it comprises more than the six asset classes that we considered could also offer greater insights.

Finally, it is possible that risk management and market analysis of larger pension funds are of higher quality, for instance, because greater numbers of staff may allow for more specialization. In that case, we expect lower risk and higher returns. This quality effect would imply underestimation of the scale economies, as the costs could be divided into true cost and quality improvement. Further research on risk and returns in relation to pension fund size would be both valuable and interesting.

Acknowledgements

The views expressed here are solely those of the authors and do not in any way represent the views of DNB. The authors are grateful to Maurice Bun for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that mutual fund expenses and investment costs of pension funds are different. For example, marketing costs and administration costs are important cost categories in the mutual fund industry. Pension funds have little if any marketing costs and administration costs are nowadays reported separately. Also, pension funds have to take the duration of their investment portfolio into account, given their liabilities. Finally, mutual funds often focus on investments in one asset class (e.g. stocks, bonds), while pension funds generally invest in various asset classes.

2 Lakonishok et al. (1992) report that the pension fund industry has consistently underperformed the market. The authors posit that pension fund managers may trade excessively, incurring large execution and transaction costs, and may be unlucky with their timing.

3 In some European countries, some costs, especially management costs, are limited by legal conditions. That is not the case in the Netherlands.

4 Largest pension funds have each an amount of total assets of more than, in 2012, 6,6 billion euro and, in 2019, 11,7 billion euro. Smallest pension funds have each an amount of total assets of less than, in 2012, 0,13 billion euro and, in 2019, 0,17 billion euro.

5 For shortcomings of the TCF, see Shaffer (1998, 91).

6 White (1980) and Shaffer (1998, 95) explain that this specification also helps to avoid multicollinearity.

7 As will follow below, in Equation (3)(3) $C{E}_{it}=\alpha +2\beta (\mathrm{l}\mathrm{n}T{A}_{it}-\overline{lnTA})-\gamma /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^2-2\delta /{\left(\mathrm{l}\mathrm{n}T{A}_{it}\right)}^3$(3) , α is equal to the cost elasticity of an average pension fund, because the squared term then becomes zero.

8 Except possibly over limited ranges of scale within which marginal costs are steeply declining.

9 CE is 0.9414 and its confidence interval is very tiny with (0.9409–0.9419).

10 The formula reads: exp(coeff. x change) − 1. ‘Coeff’. of the shares in investment by asset type are from Table 2, while ‘change’ here means doubling the current shares of the investment categories.

11 Here ‘change’ is 0.1.

12 See footnote 12.

13 See footnote 12.

14 Here ‘change’ is 0.01.

15 We do not show the confidence intervals: they would be too tiny to be seen.

16 A large pension fund can save 5–6% of the investment costs (the scale economies) when its size doubles, hence a saving of 50% of the costs of the two initial pension funds.

17 For transaction costs, Table 4 presents scale economies, statistical significant for fixed income and stocks, while comparable effects in Table 3 are not significant.

18 Differences in estimates for 2013 may come from later data revisions, small model differences and selection applied to the data.