Optimized Sampling in Vanguard's Total Stock Market Index Fund By John Spence April 18, 2002

Recently we discussed why optimized sampling is critical to the managers of the iShares MSCI EAFE, an exchange-traded fund that covers a broad international index.

Another well-known index fund that uses a representative sample of an index is the Vanguard Total Stock Market Index Fund, which holds nearly $15.7 billion in its coffers. The fund tracks the Wilshire 5000, the most commonly cited measuring stick for the broad U.S. economy. The name is really a misnomer because the index held 5,948 securities as of the end of March. However, the Vanguard fund was comprised of only 3,446 stocks at the time. Some investors might assume the fund is a full replication of the index, but for a few reasons it's too expensive to hold every stock in the index.

Portfolio	1 mo	3 mo	1 yr	3 yr*	5 yr*
Wilshire 5000	4.38%	0.96%	2.56%	-1.56%	9.77%
TSM fund	4.38%	0.97%	2.47%	-1.36%	9.81%

Not surprisingly, Vanguard isn't about to divulge any secrets about the actual optimization programs or techniques. ("We could tell you . . . but then we'd have to kill you," joked one Vanguard spokesperson.)

"We're not too concerned with the daily returns - hedge funds are more interested in short-term trends and spikes," said Jim Troyer, a principal at the Vanguard Group. "We're looking at longer periods like the monthly or quarterly data. If the fund is exposed to the big risk factors, then the correlations will be there."

Launched in 1992, the Vanguard Total Stock Market Index Fund has tracked its bogey very closely over the years. The rather lengthy chart below shows monthly returns of the fund versus the Wilshire 5000 index.

Date	TSM fund ret. (%)	Wilshire 5000 ret. (%)	Tracking Error
5/31/92	0.69	0.61	0.075
6/30/92	-2.05	-2.04	-0.011
7/31/92	3.98	4.05	-0.066
8/31/92	-2.20	-2.11	-0.090
9/30/92	1.27	1.20	0.077
10/31/92	1.17	1.21	-0.047
11/30/92	4.23	4.15	0.085
12/31/92	1.57	1.78	-0.209
1/31/93	1.01	1.23	-0.214
2/28/93	0.46	0.41	0.046
3/31/93	2.46	2.57	-0.107
4/30/93	-2.77	-2.76	-0.008
5/31/93	3.03	3.13	-0.102
6/30/93	0.55	0.47	0.081
7/31/93	-0.27	-0.01	-0.254
8/31/93	3.93	3.86	0.074
9/30/93	0.01	0.20	-0.190
10/31/93	1.64	1.67	-0.026
11/30/93	-1.62	-1.62	0.007
12/31/93	1.90	1.80	0.098
1/31/94	3.08	3.15	-0.070
2/28/94	-2.16	-2.24	0.086
3/31/94	-4.52	-4.53	0.004
4/30/94	0.89	0.96	-0.066
5/31/94	0.97	0.98	-0.005
6/30/94	-2.73	-2.68	-0.052
7/31/94	3.08	2.97	0.112
8/31/94	4.39	4.42	-0.023
9/30/94	-1.85	-1.94	0.086
10/31/94	1.55	1.63	-0.081
11/30/94	-3.65	-3.66	0.012
12/31/94	1.23	1.35	-0.114
1/31/95	2.20	2.16	0.038
2/28/95	4.04	3.98	0.062
3/31/95	2.65	2.64	0.017
4/30/95	2.51	2.49	0.025
5/31/95	3.48	3.39	0.089
6/30/95	2.98	3.19	-0.212
7/31/95	4.02	4.12	-0.094
8/31/95	1.07	0.98	0.099
9/30/95	3.61	3.81	-0.200
10/31/95	-1.17	-1.00	-0.163
11/30/95	4.17	4.24	-0.070
12/31/95	1.54	1.63	-0.090
1/31/96	2.66	2.68	-0.019
2/29/96	1.62	1.75	-0.130
3/31/96	1.14	1.09	0.051
4/30/96	2.41	2.47	-0.063
5/31/96	2.66	2.73	-0.073
6/30/96	-0.84	-0.82	-0.020
7/31/96	-5.37	-5.40	0.026
8/31/96	3.09	3.20	-0.104
9/30/96	5.38	5.32	0.056
10/31/96	1.43	1.40	0.031
11/30/96	6.81	6.63	0.187
12/31/96	-1.27	-1.13	-0.142
1/31/97	5.46	5.35	0.106
2/28/97	-0.11	-0.05	-0.061
3/31/97	-4.45	-4.42	-0.031
4/30/97	4.50	4.36	0.136
5/31/97	7.10	7.09	0.016
6/30/97	4.37	4.59	-0.225
7/31/97	7.77	7.69	0.082
8/31/97	-3.72	-3.76	0.042
9/30/97	5.77	5.90	-0.132
10/31/97	-3.40	-3.33	-0.064
11/30/97	3.33	3.27	0.058
12/31/97	1.70	1.85	-0.149
1/31/98	0.44	0.54	-0.101
2/28/98	7.34	7.28	0.064
3/31/98	5.06	5.01	0.057
4/30/98	1.10	1.19	-0.091
5/31/98	-2.71	-2.66	-0.050
6/30/98	3.54	3.51	0.038
7/31/98	-2.27	-2.19	-0.083
8/31/98	-15.65	-15.57	-0.082
9/30/98	6.68	6.53	0.147
10/31/98	7.51	7.44	0.073
11/30/98	6.17	6.30	-0.126
12/31/98	6.45	6.40	0.054
1/31/99	3.65	3.68	-0.029
2/28/99	-3.73	-3.63	-0.105
3/31/99	3.93	3.86	0.074
4/30/99	4.68	4.79	-0.115
5/31/99	-2.00	-2.19	0.192
6/30/99	5.16	5.18	-0.017
7/31/99	-3.20	-3.21	0.010
8/31/99	-0.92	-0.93	0.013
9/30/99	-2.44	-2.61	0.175
10/31/99	6.29	6.36	-0.074
11/30/99	3.42	3.35	0.073
12/31/99	7.59	7.59	-0.003
1/31/00	-4.18	-4.15	-0.033
2/29/00	2.54	2.24	0.305
3/31/00	5.69	5.94	-0.254
4/30/00	-5.21	-5.21	0.002
5/31/00	-3.41	-3.49	0.083
6/30/00	4.42	4.41	0.010
7/31/00	-1.95	-2.04	0.088
8/31/00	7.28	7.26	0.021
9/30/00	-4.67	-4.67	-0.001
10/31/00	-2.04	-2.12	0.076
11/30/00	-9.90	-9.99	0.087
12/31/00	1.78	1.78	0.001
1/31/01	3.83	3.83	-0.002
2/28/01	-9.41	-9.48	0.066
3/31/01	-6.72	-6.73	0.010
4/30/01	8.16	8.23	-0.066
5/31/01	1.01	1.00	0.015
6/30/01	-1.64	-1.68	0.044
7/31/01	-1.71	-1.65	-0.062
8/31/01	-6.00	-6.05	0.046
9/30/01	-9.00	-8.98	-0.017
10/31/01	2.52	2.54	-0.018
11/30/01	7.63	7.65	-0.016
12/31/01	1.78	1.80	-0.017
1/31/02	-1.24	-1.24	-0.003
2/28/02	-2.05	-2.06	0.014
3/31/02	4.38	4.38	-0.002

That's some pretty good index-hugging, especially when you consider the fund always holds significantly less stocks than there are in the index. The benefits of sampling include reduced turnover and transaction costs, which leaves more return for the fund shareholders. Vanguard index fund manager Gus Sauter and his team have a knack for closely tracking indexes while picking up a few basis points over the benchmark.

The graph below shows the number of stocks in the index and the fund on a quarterly basis since the inception of the Total Stock Market Index Fund.