attribute dimension. However, in terms of PE, PB, Inc and s, the separation between the two groups increased.
The Mahalanobis distances are shown in Panel B of Table 3. Comparing this table with Panel B of Table 2, we see that the attributes-based objective groups are much more
distinct than the stated fund objective groups. The Mahalanobis distances for the nearest neighbor objective groups are always higher for the attributes-based objectives than for
stated objectives groups. Examining aggressive growth and small capitalization funds, we see that the Mahalanobis distance between these neighboring groups increases from 10.38
to 28.31.
VI. Misclassification
The null hypothesis tested in this paper is:
Funds within a stated objective group are homogeneous in terms of their attributes fund characteristics, investment styles, and risk-return measure, and are distinct from the funds in other objective groups.
Table 4 provides evidence to test this hypothesis. This table shows how funds of various stated objectives are classified into the attributes-based objectives. If the fund
objectives are unique with respect to their attributes and most funds follow their stated objectives, we should see very high values along the diagonal in the classification table.
Large values off the diagonal would suggest that the funds do not follow their stated objectives.
On an average, the attributes-based objectives of 46 484 out of 1,043 funds are the same as their stated objectives. The worst consistency is for funds with the stated objective
of asset allocation where only 22 13 out of 57 are classified as asset allocation based
Table 3. Attributes of Attributes-based Objective Groups
Panel A: Attributes of attributes-based objective groups Objective
Stk DC
MktCap PE
PB Inc
r s
R
2
b ASAL
32.86 31.18
4592.57 23.16
3.21 2.77
9.92 7.04
41.48 0.49
BLNC 54.86
29.91 9140.26
20.78 3.55
3.13 10.83
6.92 79.43
0.68 EQIN
86.46 32.16
6877.77 20.35
3.22 2.09
13.59 8.97
74.02 0.85
GRIN 91.81
29.02 14651.12
20.69 3.85
1.90 12.64
8.93 88.33
0.93 GRTH
91.38 26.54
5151.06 24.12
4.40 0.36
12.37 11.59
64.72 1.02
SMCP 88.04
27.20 1359.46
20.94 2.88
0.62 15.27
10.53 42.79
0.75 AGGR
90.92 22.39
1411.67 30.99
5.49 20.36
15.87 16.61
38.80 1.11
Overall 82.85
28.27 6846.85
22.45 3.82
1.38 12.97
10.17 67.47
0.88 Panel B: Mahalanobis distances between attributes-based objective groups
ASAL BLNC
EQIN GRIN
GRTH SMCP
AGGR ASAL
0.00 32.71
54.71 77.76
59.27 50.41
82.71 BLNC
32.71 0.00
17.73 21.85
33.14 45.42
73.98 EQIN
54.71 17.73
0.00 9.51
10.85 21.48
49.38 GRIN
77.76 21.85
9.51 0.00
20.10 37.99
63.79 GRTH
59.27 33.14
10.85 20.10
0.00 13.11
22.58 SMCP
50.41 45.42
21.48 37.99
13.11 0.00
28.31 AGGR
82.71 73.98
49.38 63.79
22.58 28.31
0.00
Note: All Mahalanobis distances are significant at 1 level.
Mutual Fund Objective Misclassification 317
on their attributes, and the best consistency is for balanced funds where 83 of the funds are classified as balanced.
For every fund except the asset allocation funds the classification table has the highest percentages along the diagonal. Nevertheless, a significant number of funds are off the
diagonal. The x
2
statistic for the null hypothesis that the classification table is diagonal is 2799, which is significant at the 1 level. Therefore, we reject the null hypothesis that the
funds within a stated objective group are homogeneous, and distinct from the funds in other stated objective groups. In other words, some funds in the stated objective groups
have attributes distinct from the majority of the funds in their objective groups.
Table 4 also shows that the attributes-based objectives of a significant number of funds are far away from their stated objectives. For example, seven out of 57 12 asset
allocation funds are classified into growth-income, growth or small capitalization funds, and four out of 48 8 of the aggressive growth funds are classified into asset allocation,
balanced and equity income groups based on their attributes. To get an idea of the extent of this severe misclassification, consider the three broad fund groups: income-oriented
fund group asset allocation, balance, and equity income funds, growth-oriented fund group growth and growth-income funds, and aggressive capital appreciation-oriented
fund group aggressive growth and small capitalization funds. A misclassification outside of these broad fund groups may be considered severe. Panel B of Table 4 shows that 353
out of 1,043 34 funds are severely misclassified. This degree of severe misclassifica- tion casts serious doubt on the current fund objective classification system. The x
2
statistic for the diagonality of classification table in Panel B of Table 4 is 1,718, which is also
Table 4. Funds From Various Stated Objectives Classified into their Own Attributes-Based Objectives
Panel A: Results for individual objectives Stated
Objective Attributes-based objective
ASAL BLNC
EQIN GRIN
GRTH SMCP
AGGR Total
ASAL 13 22
34 60 4 7
3 5 2 3
2 3 0 0
57 5 BLNC
10 9 91 83
4 3 2 1
2 2 2 1
0 0 110 11 EQIN
3 5 15 24
25 40 18 28
1 1 2 3
0 0 64 6
GRIN 3 1
13 5 75 32 115 49
19 8 9 4
0 0 233 22 GRTH
6 2 4 1
94 24 61 15 148 38
44 11 37 9 394 38
SMCP 0 0
0 0 4 3
0 0 14 10
68 49 53 38 138 13
AGGR 2 5
1 1 1 2
0 0 14 30
5 11 25 52
48 5 Total
37 4 157 15 207 20 198 19 199 19 131 13 115 11 1043
Panel B: Results for aggregated objectives Stated
Objective Attributes-based objective
Income Growth
Aggressive Total
Income 198 86
27 12 5 2
230 22 Growth
195 31 342 55
90 14 627 60
Aggressive 8 4
28 15 150 81
186 18 Total
401 38 397 38
246 24 1043
Notes: The numbers in the parentheses show the number of funds, expressed as a percent of the number of funds in the stated objective group, classified into an attributes-based objective group. For example, 22 of funds that stated asset allocation as their
objective are classified as being asset allocation, while 60 are classified as balanced.
318 M. Kim et al.
significant at 1 level, again leading to rejection of the null hypothesis that mutual funds in even these three aggregated objective classes are homogeneous in their attributes. This
degree of disagreement between the stated and attributes based objectives is a genuine cause for concern.
VII. Objective Stability and Consistency
