Are Passive Funds Really Superior Investments? An Investor Perspective

Figures & data

Table 1. Representative Indexes for Each Group

Group	Index	Mean Squared Correlation
Large cap	S&P 500	0.496
Large value^a	Russell 1000 Value	0.666
Large growth^a	Russell 1000 Growth	0.643
Midcap	S&P MidCap 400	0.762
Midcap growth	Russell Midcap Growth	0.631
Midcap value^a	Russell Midcap Value	0.675
Small cap	S&P SmallCap 600	0.783
Small growth^a	Russell 2000 Growth	0.801
Microcap	Wilshire US Micro	0.811
Momentum	S&P 500 Momentum	0.590
Mixed value	S&P MidCap 400 Pure Value	0.671

Note: This table shows the index with the highest average-in-group squared correlation and the group name for each of the 11 groups we identified.

^aIndicates inclusion in the four-index model.

Table 2. Non-Base Regressions

Non-Base Index	Intercept	Russell 1000 Growth		Russell 1000 Value		Russell 2000 Growth		Russell Midcap Value		R ^2
S&P 500 Momentum	0.067		0.886*		0.152		0.136		–0.076		0.15
Wilshire US Micro	0.057		–1.149**		–0.436		0.737**		0.241		0.59
Russell Midcap Growth	–0.056		0.799**		–0.362		0.287**		0.400**		0.70
S&P 500	0.009		0.484**		0.594**		–0.027**		–0.100**		0.92
S&P MidCap 400	–0.020		–0.075		–0.541**		0.208**		0.735**		0.79
S&P SmallCap 600	0.054		–1.366**		–0.912**		0.464**		0.518**		0.81
S&P MidCap 400 Pure Value	–0.188		–2.353**		–1.856**		–0.338**		1.598**		0.65

Notes: This table shows the results of regressing the representative index from each group not in the base on the four base indexes. The returns on all indexes have the CRSP market index removed: We regressed each index on the market index and used the intercept plus the residual for the returns.

*Significant at the 5% level.

**Significant at the 1% level.

Table 3. Base Regression Slopes

Base Index	Intercept	Russell 1000 Growth		Russell 1000 Value		Russell 2000 Growth		Russell Midcap Value		R ^2
Russell 1000 Growth	–0.053**				–1.058**		–0.207**		0.109**		0.90
Russell 1000 Value	–0.055**		–0.799**				–0.203**		0.156**		0.93
Russell 2000 Growth	–0.239**		–2.731**		–3.542**				0.693**		0.74
Russell Midcap Value	0.224**		1.109**		2.108**		0.535**				0.57

Notes: This table shows the results of regressing each base index on the other three indexes in the base. The returns of each index have the CRSP market index removed: We regressed each index on the market index and used the intercept plus the residual for the returns.

**Significant at the 1% level.

Table 4. Average Regression Parameters

Morningstar Category	Freq.	Intercept	CRSPMarket	Russell 1000 Growth	Russell 1000 Value	Russell2000 Growth	Russell Midcap Value	R ^2
A. Short sales allowed
US Fund Large Value	131	–0.132	0.540	–0.048	0.536	–0.033	0.005	0.93
US Fund Large Blend	176	–0.143	0.586	0.205	0.228	0.001	–0.020	0.94
US Fund Large Growth	213	–0.154	0.403	0.668	–0.140	0.086	–0.017	0.93
US Fund Mid-Cap Value	28	–0.090	0.121	0.038	0.079	0.118	0.645	0.92
US Fund Mid-Cap Blend	37	–0.118	0.262	0.125	–0.130	0.230	0.513	0.92
US Fund Mid-Cap Growth	82	–0.127	0.076	0.510	–0.316	0.373	0.356	0.91
US Fund Small Value	40	–0.043	1.007	–0.800	–0.137	0.471	0.458	0.92
US Fund Small Blend	69	–0.091	0.897	–0.572	–0.245	0.546	0.374	0.93
US Fund Small Growth	107	–0.134	0.477	–0.051	–0.361	0.762	0.173	0.92
All	883	–0.130	0.490	0.161	–0.010	0.221	0.139	0.93
B. No short sales allowed
US Fund Large Value	131	–0.146	0.094	0.129	0.650	0.041	0.086	0.91
US Fund Large Blend	176	–0.164	0.180	0.340	0.346	0.065	0.069	0.92
US Fund Large Growth	213	–0.151	0.080	0.677	0.081	0.116	0.046	0.91
US Fund Mid-Cap Value	28	–0.063	0.072	0.096	0.147	0.145	0.539	0.91
US Fund Mid-Cap Blend	37	–0.080	0.083	0.174	0.078	0.278	0.387	0.91
US Fund Mid-Cap Growth	82	–0.078	0.049	0.365	0.019	0.421	0.146	0.89
US Fund Small Value	40	–0.007	0.017	0.008	0.122	0.427	0.426	0.89
US Fund Small Blend	69	–0.041	0.029	0.018	0.095	0.542	0.317	0.92
US Fund Small Growth	107	–0.108	0.027	0.082	0.026	0.756	0.110	0.91
All	883	–0.120	0.086	0.306	0.211	0.256	0.142	0.91

Note: This table shows the average parameters of a regression of each active fund on the ETFs following the five indexes indicated.

Table 5. Monthly Difference in Returns

Morningstar Category	Freq.	ETF Better	Return Diff.	Diff. in St. Dev.
A. Short sales allowed
US Fund Large Value	131	103	0.1218%**	–0.0346%
US Fund Large Blend	176	147	0.1357**	–0.0688
US Fund Large Growth	213	178	0.1210**	–0.1601
US Fund Mid-Cap Value	28	21	0.0726**	–0.0804
US Fund Mid-Cap Blend	37	31	0.1487**	–0.0489
US Fund Mid-Cap Growth	82	54	0.0804**	–0.2025
US Fund Small Value	40	28	0.1331**	–0.0776
US Fund Small Blend	69	48	0.1275**	–0.0567
US Fund Small Growth	107	71	0.1138**	–0.1175
All	883	681	0.1201**	–0.1030
B. No short sales allowed
US Fund Large Value	131	113	0.1386%**	–0.0058%
US Fund Large Blend	176	152	0.1474**	–0.0140
US Fund Large Growth	213	176	0.1129**	–0.1150
US Fund Mid-Cap Value	28	23	0.0632**	–0.1906
US Fund Mid-Cap Blend	37	30	0.1209**	–0.1059
US Fund Mid-Cap Growth	82	43	0.0176	–0.2828
US Fund Small Value	40	30	0.1652**	–0.4996
US Fund Small Blend	69	52	0.1046**	–0.2940
US Fund Small Growth	107	68	0.1054**	–0.3076
All	883	687	0.1143**	–0.1512

Notes: This table shows the difference in return between the risk-matching ETF portfolio and the corresponding active fund. It also shows the number of times the risk-matching ETF portfolio had higher returns. Differential returns are expressed in percentage per month.

**Significant at the 1% level.