When Indexing Fails
When an asset class does relatively well, an index fund in that class does even better. ­ "Dunn's Law"

Yea, the wise Prophet Bogle brought knowledge to the masses, and they saw that it was good. In fact, better than good. S&P indexing has done so well that sometime this year, failing apostasy or Armageddon, the Vanguard 500 Index Fund (VFINX) will surpass Fidelity Magellan as the planet's biggest mutual fund.

The reason is simple. VFINX has beaten 83, 93, 95, 89, and 92 percent of all mutual funds in its Morningstar class over the past 1, 3, 5, 10, and 15 year periods, respectively.

Unfortunately, the news for indexing is not that sunny elsewhere. Consider that the same numbers for the granddaddy of all small cap index funds, the DFA 9-10 US Small Company Portfolio (DFSCX), are 31, 29, 70, 57, and 43 percent, respectively. And for foreign funds the data are all over the place: 86, 46, 71, 9, and 100 percent, respectively.

What are we to make of this? Is indexing really that good for domestic large cap stocks? And is it that bad for small cap stocks? And just how good is it, really, for foreign stocks?

The Importance of Style

The plaintive cry of the active money manager goes something like this: "Just you wait. Of course we've not been able to beat the S&P over the past several years. Our portfolios hold smaller stocks, and we carry cash for a rainy day as well. Some day the market leadership will shift away from the megacaps, or we may even have a bear market. Then you'll be sorry you didn't heed our warnings against the false gods of indexing." Still others admit the superiority of indexing large cap stocks but argue that small cap and foreign markets are less efficient and therefore require active portfolio management.

Well, there is a grain of truth to all this. It turns out that when small stocks outperform large stocks, indexing doesn't look quite as good. I've plotted the annual percentile ranking of VFINX for 1987-98 in each year versus the large stock advantage, i.e., the difference in return between large and small stocks. (The percentile rankings are for the combination of Morningstar Growth and Growth/Income categories, and the large stock advantage is calculated as the return of VFINX minus the return of DFSCX.)

As you can see, in those years when large stocks out performed small stocks (right side of graph), VFINX's percentile rankings were superb. And, when small stocks outperformed large stocks (left side of graph), VFINX did not do quite so well. Using statistical regression techniques, it is possible to calculate that in a hypothetical year when the returns of large and small stocks are the same, VFINX should land in the 38^th percentile.

Small May Still be Beautiful

The same phenomenon applies in reverse to small caps. Because many, if not most, small cap funds are contaminated with some larger stocks, one might reasonably expect small cap indexing to work best when small cap returns exceed those of large caps. For 1987-98 this is exactly what happens:

This graph shows that when small caps outperform large caps (left half of graph) DFSCX does best relative to its peers (in this case, Morningstar's small cap prospectus objective category). And when small caps underperform large caps (right half of graph) DFSCX underperforms its small cap peers. Regression techniques show that in a hypothetical year when long term small and large caps have equal returns, DFSCX should perform at the 48^th percentile. Although DFSCX's "regressed" performance assuming equal large and small cap returns is not spectacular, if one assumes that there is in fact a small cap return premium over larger cap stocks, then in an average year, a small cap index fund which is wholly invested in small cap stocks should do relatively better. Whether or not there actually is a small cap premium is a matter of some dispute, but it's interesting to note that if the small cap premium does exist, it would act to boost the relative ranking of small cap index funds, and reduce that of large cap index funds.

The Japan Problem

A similar problem plagues the analysis of foreign indexing, and it sticks out like a sore thumb. Had you decided to index your foreign holdings 10 years ago to the most widely used foreign stock benchmark, the MSCI-EAFE (Europe, Australia, and Far East), then when you started on January 1, 1989 your portfolio would have been more than 50 percent Japanese. Look out below! Had you been able to buy the EAFE as an index fund, it would have ranked 40^th of 44 foreign funds Morningstar lists for the period. I've performed the same sort of analysis for foreign funds for 1987-98, using annual percentile rankings for the MSCI-EAFE as if it were a fund. In this case, the performance of the Japanese market relative to the EAFE as a whole was plotted on the x axis:

Again, when the Nikkei performed well relative to the rest of the non US markets (right side of graph) international indexing did well. On the left side of the graph, the reverse is true. Regressing assuming equal Japanese and EAFE performance, in an average year an EAFE index fund should perform at the 41^st percentile. Over longer periods, it should do much better. In fact, Morningstar lists 12 international funds with 15 year track records, and the EAFE beat all of them, in spite of the fact that over this period the Nikkei trailed the EAFE by 5.49 percent per annum.

One can demolish the market inefficiency argument for active foreign management in a heartbeat by examining actual emerging market performance. Surely, if there are exploitable inefficiencies abroad they are to be found in places like Brazil, Korea, and Indonesia. Yet the emerging market index funds from DFA and Vanguard have 3 year percentile rankings of 30 and 38, respectively. Both index funds are just shy of having a 5 year track record, but if one substitutes emerging market index returns to fill in the missing months, despite some shorter periods of subpar performance the DFA and Vanguard funds would rank 3^rd and 4^th of 20 funds, respectively, for the 1994-8 period.

Dunn's Law: Other Asset Classes

My friend and portfolio theory colleague Steve Dunn nicely codified the observation that the short term fortunes of an index fund are tied to to that of its asset class. In other words, if asset class X is doing relatively poorly, then an index fund which is wholly invested in that category will tend to lag actively managed funds even in that asset class given their more diffuse portfolios. Examples other than those cited above abound. If the MSCI Japan was an index fund, then it would rank only 4^th of 7 Japan funds with a 5 year track record. In fact, the worst was the DFA Japan Small Company Fund, cursed by both that market and its hideously negative small cap premium. (This particular fund makes the list of "worst" or "best" fund in the foreign category with alarming regularity, depending on the year. In fact, it is neither a good nor a bad fund—it is an index fund whose fortunes, unlike its managed cousins, are wholly tied to the fate of a single narrow asset class.)

The DFA Real Estate Index fund ranks 9^th of 12 REIT funds over the past 5 years. On the other hand, the Vanguard Index European Fund ranks 3^rd of 23 continental funds during the same period. It is no accident that over the past 5 years REITs and Japan have been poorly performing asset classes, while European stocks have done about as well as the S&P 500. The point, of course, is this: over long enough time periods the returns of various equity asset classes tend to converge, washing away the short term deleterious effects of Dunn's Law. What remains is:

The Index Fund Advantage

In fact, index funds possess advantages over actively managed funds which become almost insurmountable over the long haul. To demonstrate this I've extracted from the Morningstar fund universe data which allows us to calculate this advantage. Let's start with simple fund expense ratios and turnover:

	Expense Ratio	Turnover
Average Morningstar Large Blend Fund	1.21%	68%
Vanguard Index 500 Fund	0.19%	5%
Average Morningstar Small Blend Fund	1.44%	72%
Vanguard Small Cap Index Fund	0.23%	29%
Average Morningstar Foreign Fund	1.71%	72%
Vanguard Total International Index Fund	0.37%	6%
Average Morningstar Emerging Markets Fund	2.11%	91%
Vanguard Emerging Market Index Fund	0.57%	19%

Consider the large cap category. The Vanguard Index 500 Fund has an expense advantage of 1.02 percent (1.21 minus 0.19) over the average managed fund in its class. But that's not all. Note that it has 63 percent less portfolio turnover than the average managed fund (68 minus 5). The average buy/sell spread for large cap stocks is about 0.40 percent, so the decreased turnover results in another 0.25 percent advantage (0.63 times 0.40 percent). But we're still not done. Buying and selling the large blocks involved in fund transactions results in so-called "impact costs." In other words, when the Amalgamated Capital Depreciation Fund decides to dump a million shares of XYZ widgets, the resultant price decrease will reduce the price those shares will fetch. The opposite happens on the buy side. This effect is difficult to measure and, of course, varies with the size of the fund. Let's estimate it as equal to the spread, adding another 0.25 percent. Thus, in the large cap arena the "index advantage" is about 1.5 percent.

The advantage of indexing is even more impressive in small caps and abroad. In these arenas buy/sell spreads start at about 1 percent and increase as company size falls. Performing the same calculation for these two categories gives a total index advantage of about 2.5-3.0 percent. Finally, in the emerging markets arena the buy/sell spread averages about 2 percent, yielding an index fund advantage of about 4.5 percent. So, contrary to the conventional wisdom, indexing should be most advantageous in the least efficient markets.

Summing Up

Because of the recent dominance of large cap performance, large cap indexing looks much better than one would expect and small cap indexing much worse. However, it must be realized that the recent prolonged large cap dominance is unprecedented, and unlikely to continue. Over the long term, because of its relatively greater cost advantages, and the small cap premium to the extent it exists, small cap indexing should actually do better than large cap indexing. The 15 year record of international fund performance and the more recent data with emerging markets seems to confirm the enormous theoretical advantage of indexing these markets.

So yes, Virginia, indexing works almost everywhere, but over periods as long as 15 years its rewards may be distorted in either direction by factors such as the small stock premium and returns divergence among nations. Over the long haul, though, the benchmark is your friend. Use the force, and not just at home.

copyright (c) 1999, William J. Bernstein