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

Figures & data

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).

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.

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.

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.

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.

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.

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

See note below Figure 2.

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.

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.