Planning for potential increases in disbursements and risk of managed funds conditional on desired short-term performance levels

Figures & data

Figure 1. Two-stage production process.

Figure 2. Superannuation fund assets (financial resource) management process.

Table 1. Summary statistics of input, intermediate and output variables.

Statistic (n=69)	Stage A process				Stage B process
	Input variables		Output variable	Intermediate variable	Input variables				Output
	Administration and operating expenses (000’ $)	Beginning period net assets (000’ $)	Benefit payments (000’ $)	Total investments (000’ $)	Investment expenses (000’ $)	Portfolio risk	Total risk (SD)	Leverage risk	Investment income (000’ $)
Mean	54,726	17,037,037	712,695	20,859,262	44,063	4.2983	0.0623	0.0296	559,140
Median	20,270	5,344,720	250,764	6,204,255	9,065	4.3393	0.0623	0.0252	182,958
SD	94,179	32,169,094	1,280,710	39,612,499	95,916	0.5004	0.0100	0.0274	992,675
Maximum	548,846	182,378,081	7,166,105	241,601,963	522,990	5.1830	0.0863	0.2034	5,091,052
Minimum	240	79,926	4,842	86,533	37	1.0046	0.0354	0.0025	40
Range	548,606	182,298,155	7,161,263	241,515,430	522,953	4.1783	0.0509	0.2008	5,091,012
CV	1.72	1.89	1.80	1.90	2.18	0.12	0.16	0.93	1.78

Table 2. Overall efficiency by fund type.

Fund type	Number of funds	Average efficiency	Standard deviation	Minimum	Number of efficient funds (%)
Corporate	6	0.6751	0.1824	0.4599	1 (4.76)
Industry	28	0.7991	0.1815	0.4739	9 (42.86)
Public sector	10	0.6864	0.1683	0.4255	1 (4.76)
Retail	25	0.8243	0.1769	0.4583	10 (47.62)
All funds	69	0.7811	0.1829	0.4255	21 (100.00)

Table 3. Observed input, intermediate and output variable values of selected funds.

Fund label	Administration and operating expenses (000’ $)	Beginning period net assets (000’ $)	Benefit payments (000’ $)	Total investments (000’ $)	Investment expenses (000’ $)	Portfolio risk	Total risk (SD)	Leverage risk	Investment income (000’ $)
SF1	209,214	111,998,948	3,917,904	112,071,653	125,417	3.7531	0.0528	0.0237	1,638,330
SF2	35,066	12,668,020	505,006	14,626,599	38,454	4.321	0.0451	0.0316	400,865

Table 4. Intermediate and output targets that attains desired performance levels of SF1 with observed inputs.

	Stage A output target	Intermediate measure target	Stage B output target
	Benefit payments (000’ $)	Total investments (000’ $)	Investment income (000’ $)
Observed value	3,917,909	112,071,653	1,638,330
Desired relative performance
0.9	4,105,982 (4.80)	152,749,403 (36.30)	2,055,550 (25.47)
0.95	4,334,092 (10.62)	152,749,403 (36.30)	2,169,747 (32.44)
0.975	4,448,147 (13.53)	152,749,403 (36.30)	2,226,846 (35.92)
0.99	4,516,580 (15.28)	152,749,403 (36.30)	2,261,105 (38.01)

Table 5. Intermediate and output targets for SF1 to reach different performance levels when its administration and operating expenses and investment expenses increase.

Increase in disbursements	Stage A output target	Intermediate measure target	Stage B output target
	Benefit payments (000’ $)	Total investments (000’ $)	Investment income (000’ $)
Observed value	3,917,909	112,071,653	1,638,330
Desired relative performance: 0.8588 (observed efficiency level)
2%	3,958,844 (1.04)	153,048,762 (36.56)	1,968,987 (20.18)
5%	4,020,247 (2.61)	153,497,800 (36.96)	1,980,373 (26.68)
7.5%	4,071,416 (3.92)	153,871,998 (37.30)	1,989,861 (27.29)
10%	4,122,585 (5.22)	154,246,196 (37.63)	1,999,349 (27.89)
(b) Desired relative performance: 0.9
2%	4,148,882 (5.90)	153,048,762 (36.56)	2,063,505 (25.95)
5%	4,213,232 (7.54)	153,497,800 (36.96)	2,075,437 (33.72)
7.5%	4,266,858 (8.91)	153,871,998 (37.30)	2,085,381 (34.36)
10%	4,320,483 (10.28)	154,246,196 (37.63)	2,095,324 (35.00)
(c) Desired relative performance: 0.95
2%	4,379,375 (11.78)	153,048,762 (36.56)	2,178,144 (32.95)
5%	4,447,301 (13.51)	153,497,800 (36.96)	2,190,739 (33.72)
7.5%	4,503,905 (14.96)	153,871,998 (37.30)	2,201,235 (34.36)
10%	4,560,510 (16.40)	154,246,196 (37.63)	2,211,731 (35.00)

Intermediate and output targets are estimated in model (8). Parentheses give the percentage increase from the observed value.

Table 6. Intermediate and output targets for SF2 to reach different performance levels when its administration and operating expenses and portfolio risk increase.

Increase in administration and operating expenses and portfolio risk	Stage A output target	Intermediate measure target	Stage B output target
	Benefit payments (000’ $)	Total investments (000’ $)	Investment income (000’ $)
Observed value	505,006	14,626,599	400,865
Desired relative performance: 0.7112 (observed efficiency level)
2% and 0.25SD	505,006 (0.00)	11,678,779 (−20.15)	516,731 (28.90)
5% and 0.5 SD	505,006 (0.00)	11,967,688 (−18.18)	529,249 (32.03)
7.5% and 0.75SD	505,006 (0.00)	12,208,446 (−16.53)	539,681 (34.63)
10% and 1SD	505,006 (0.00)	12,449,203 (−14.89)	550,113 (37.23)
(b) Desired relative performance: 0.75
2% and 0.25SD	505,006 (0.00)	14,246,568 (−2.60)	662,460 (65.26)
5% and 0.5 SD	505,006 (0.00)	14,551,334 (−0.51)	676,390 (68.73)
7.5% and 0.75SD	505,006 (0.00)	14,805,305 (1.22)	687,999 (71.63)
10% and 1SD	505,006 (0.00)	15,059,277 (2.96)	699,607 (74.52)
(c) Desired relative performance: 0.8
2% and 0.25SD	505,006 (0.00)	16,662,207 (13.92)	824,399 (105.65)
5% and 0.5 SD	505,006 (0.00)	16,995,729 (16.20)	840,660 (109.71)
7.5% and 0.75SD	505,006 (0.00)	17,273,664 (18.10)	854,210 (113.09)
10% and 1SD	505,006 (0.00)	17,551,599 (20.00)	867,761 (116.47)

Intermediate and output targets are estimated in model (8). Parentheses give the percentage increase from the observed value. SD = standard deviation of the distribution of portfolio risk.

Table 7. Intermediate and output targets under different weighting schemes when SF2 administration and operating expenses increases by 10% and portfolio risk increases by 1SD.

Weighting scheme	Stage A output target	Intermediate measure target	Stage B output target
	Benefit payments (000’ $)	Total investments (000’ $)	Investment income (000’ $)
Maintains efficiency at 0.75
(1, 1)	505,006	15,059,277	699,607
(5, 1)	548,194	12,057,035	562,381
Maintains efficiency at 0.8
(1, 1)	505,006	17,551,599	867,761
(5, 1)	584,740	12,860,838	639,063

The parentheses in the first column give the weights assigned to benefit payments and investment income. The reported values of total benefit payments, total investments and investment income are obtained in model (8).