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On The Wrong Track (Tracking Errors Among the Major Indexes)
by Craig L. Israelsen
From Financial Planning Magazine, July 2000. Reprinted with permission.
There are dozens of indexes tracking thousands of mutual funds. However, after boiling the data down there are four dominant U.S. equity indexes utilized in Morningstar's Principia Pro database, namely the Standard & Poor's 500 (large cap stocks), Standard & Poor's Midcap 400 (mid cap stocks), Russell 2000 (small cap stocks), and the Wilshire 4500 (mid & small cap stocks).
Four Major Equity Indexes Used by Morningstar
S&P 500
A market capitalization-weighted index of 500 widely held stocks often used as a proxy for the stock market. It measures the movement of the largest issues. Standard and Poor's chooses the member companies for the 500 based on market size, liquidity and industry group representation. Included are the stocks of industrial, financial, utility, and transportation companies. Since mid 1989, this composition has been more flexible and the number of issues in each sector has varied.
S&P Midcap 400
Includes approximately 10% of the capitalization of U.S. equity securities. These are comprised of stocks in the middle capitalization range. At the original time of screening, this was a $200 million to $5 billion market value range. Any midcap stocks already included in the S&P 500 are excluded from this index, which started on December 31, 1990.
Russell 2000
Consists of the smallest 2000 companies in the Russell 3000 Index, representing approximately 7% of the Russell 3000 total market capitalization.
Wilshire 4500
Measures the performance of all U.S. common equity securities excluding the stocks in the S&P 500.
This article examines the amount of tracking error which exists between these four main indexes and the domestic equity mutual funds which have one of the four as their "best-fit index". The term "best fit index" refers to the fact that, even though the S&P 500 is a popular index, it is not an appropriate index for say, a small cap mutual fund. The word "fit" refers to a statistical measure known as R2, or R-squared. An R2 of 1.00 represents perfect correlation between two entities, say an equity index and an equity mutual fund. Conversely, an R2 of zero indicates no correlation between the two.
As explained by Morningstar, R-squared "reflects the percentage of a fund's movements that can be explained by movements in its benchmark index. An R?squared of 100 [or 1.00] indicates that all movements of a fund can be explained by movements in the index. Thus, index funds that invest only in S&P 500 stocks will have an R?squared very close to 100. Conversely, a low R?squared indicates that very few of the fund's movements can be explained by movements in its benchmark index. An R?squared measure of 35, for example, means that only 35% of the fund's movements can be explained by movements in the benchmark index. R?squared can be used to ascertain the significance of a particular beta. Generally, a higher R?squared will indicate a more reliable beta figure. If the R?squared is lower, then the beta is less relevant to the fund's performance."
As of March 31, 2000 there were over 11,000 mutual funds in the Morningstar database. Of that total, 5,445 were distinct portfolios. Selecting out only distinct portfolios assures that funds with multiple share classes will not be over-represented. 2,706 funds remained after removing portfolios which were not domestic stock funds. Of that total, 2,023 funds had a "best fit index" assigned (which requires at least three years of performance). Finally, 1,838 funds had one of the previously mentioned four indexes as their best fit index. The S&P 500 was the best-fit index for 960 funds, the S&P Midcap 400 for 271 funds, Russell 2000 for 145 funds, and the Wilshire 4500 for 462 funds.
As shown in Figure 2, the average R-Squared (or "fit") in recent years has been somewhere near 80% for all but the S&P Midcap 400. The S&P Midcap 400 index evidently has funds which use it as the best possible benchmark index even though the "fit" may not be very good.
Figure 1. The "Fit" in Recent Years
|
Index
|
Number
of “Best Fit”
Equity Funds over 3 Year Period
|
Average
3 Year
R-Squared for
Best-Fit Funds
(1997-1999)
|
|
S&P
500
|
934
|
.84
|
|
S&P
Midcap 400
|
266
|
.73
|
|
Russell
2000
|
137
|
.78
|
|
Wilshire
4500
|
454
|
.78
|
As seen in Figures 3 and 4 the index tracking error has widened in recent years (1997-1999) for funds which best-fit the S&P 500. This is likely, at least in part, a function of a growing number of equity funds which must be assigned to a benchmark index, even though the S&P 500 is not a perfect match. However, recent growth in the number of index funds, which will obviously have R-Square coefficients near 100 [or 1.00], would work toward minimizing index tracking error.
The last three years has also seen more tracking error among funds which best-fit the S&P Midcap 400 (Figure 5) and the Wilshire 4500 (Figure 9). Funds which best-fit the Russell 2000 (Figure 7) have been fairly well behaved during the nineties, with the exception of 1990. As before, the increase in tracking error is undoubtably linked to a growing number of equity funds which seek to carve out specific niches and, as such, are not good matches with any specific benchmark. Therefore, the term "best-fit" index is a statement of hope, rather than promise.
The range of return among the four groups of "best-fit" funds is enormous (see Figures 4, 6, 8, 10). With such wide ranging returns, a portfolio of equity funds could easily have two or three funds which share a common benchmark without creating high intra-portfolio correlation. Said differently, it is clear from the information in Figures 3-10 that even though funds may share a common benchmark index they can have dramatically different performance patterns. And, in fact, it appears that benchmark deviation is becoming even more pronounced as the number of equity funds proliferates.
All of this suggests that choosing equity funds for inclusion in a diversified portfolio based upon each fund having a different best-fit benchmark index may not, in fact, produce the desired result of low correlation between the funds. There is enough tracking error between equity mutual funds and their respective best-fit indexes to warrant a closer look prior to making portfolio assignments. Moreover, as shown in Figure 11, the correlation between these four indexes is higher than some might suppose. Ironically, despite moderately to very high correlation between these four indexes, the presence of index tracking error among many of the "best-fit" funds creates ample opportunities to assemble diversified equity fund portfolios - regardless of a particular fund's best-fit index. So, whether or not index tracking error is a friend or foe depends entirely upon your objective.
Figure 2. S&P 500 Index and "Best Fit" Mutual Funds: 1990-1999 Returns
|
Year
|
Number
of Funds
|
Average
Return of Best-Fit Funds
|
S&P
500 Return
|
Best
Fund
Return
|
Worst
Fund
Return
|
|
1990
|
387
|
-3.9
|
-3.1
|
24.3
|
-31.4
|
|
1991
|
431
|
31.5
|
30.5
|
86.5
|
1.3
|
|
1992
|
476
|
9.4
|
7.6
|
57.9
|
-17.4
|
|
1993
|
575
|
11.9
|
10.1
|
49.3
|
-7.3
|
|
1994
|
667
|
-1.1
|
1.3
|
23.1
|
-37.2
|
|
1995
|
763
|
30.7
|
37.5
|
59.5
|
-20.1
|
|
1996
|
839
|
18.9
|
22.9
|
48.6
|
-12.4
|
|
1997
|
934
|
26.7
|
33.4
|
64.1
|
-21.0
|
|
1998
|
960
|
18.9
|
28.6
|
64.7
|
-19.0
|
|
1999
|
960
|
12.6
|
21.0
|
58.1
|
-20.5
|
Figure 3. Range of Return for Funds which Best-Fit the S&P 500
Left hash mark represents average return for best-fit funds. Right hash mark represents S&P 500 return.
Figure 4. S&P Midcap 400 Index and "Best Fit" Mutual Funds: 1990-1999 Returns.
|
Year
|
Number
of Funds
|
Average
Return of Best Fit Funds
|
S&P
Midcap 400 Return
|
Best
Fund
Return
|
Worst
Fund
Return
|
|
1990
|
108
|
-6.8
|
-5.1
|
16.3
|
-23.7
|
|
1991
|
114
|
31.3
|
50.1
|
99.1
|
-23.5
|
|
1992
|
128
|
12.1
|
11.9
|
42.4
|
-15.3
|
|
1993
|
141
|
15.9
|
13.9
|
43.3
|
-9.0
|
|
1994
|
168
|
-1.6
|
-3.6
|
19.8
|
-33.8
|
|
1995
|
194
|
26.3
|
30.9
|
49.1
|
.62
|
|
1996
|
224
|
21.0
|
19.2
|
70.3
|
-14.6
|
|
1997
|
266
|
24.5
|
32.3
|
51.9
|
-12.8
|
|
1998
|
271
|
2.1
|
19.1
|
85.3
|
-48.8
|
|
1999
|
271
|
10.7
|
14.7
|
72.2
|
-29.6
|
Figure 5. Range of Return for Funds which Best-Fit the S&P Midcap 400.
Left hash mark represents average return for best-fit funds. Right hash mark represents S&P Midcap 400 return.
Figure 6. Russell 2000 Index and "Best Fit" Mutual Funds: 1990-1999 Returns.
|
Year
|
Number
of Funds
|
Average
Return of Funds
|
Russell
2000 Return
|
Best
Fund
Return
|
Worst
Fund
Return
|
|
1990
|
32
|
-8.6
|
-19.5
|
44.4
|
-27.5
|
|
1991
|
35
|
45.9
|
46.1
|
99.1
|
2.0
|
|
1992
|
45
|
13.5
|
18.4
|
42.5
|
-13.7
|
|
1993
|
64
|
15.2
|
18.9
|
34.5
|
-24.8
|
|
1994
|
78
|
-0.5
|
-1.8
|
23.8
|
-21.6
|
|
1995
|
94
|
31.0
|
28.4
|
61.3
|
-1.3
|
|
1996
|
114
|
20.2
|
16.5
|
56.6
|
-23.0
|
|
1997
|
137
|
20.2
|
22.4
|
71.3
|
-39.5
|
|
1998
|
145
|
-2.4
|
-2.6
|
43.4
|
-42.9
|
|
1999
|
145
|
25.8
|
21.3
|
144.2
|
-15.9
|
Figure 7. Range of Return for Funds which Best-Fit the Russell 2000.
Left hash mark represents average return for best-fit funds. Right hash mark represents return of Russell 2000.
Figure 8. Wilshire 4500 Index and "Best Fit" Mutual Funds: 1990-1999 Returns.
|
Year
|
Number
of Funds
|
Average
Return of Funds
|
Wilshire
4500 Return
|
Best
Fund
Return
|
Worst
Fund
Return
|
|
1990
|
169
|
-5.4
|
-13.6
|
18.4
|
-36.4
|
|
1991
|
181
|
46.1
|
43.5
|
98.8
|
5.1
|
|
1992
|
189
|
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