Dunn’s Law Review—Foreign Funds

In the spring edition we tested Dunn’s Law in the US style-box arena, and found that except for a disastrous showing in 1999 due to the performance of the NASDAQ, it had acquitted itself well.

In this edition we examine how accurately it explains fund performance across nations and regions. In other words, if Japanese equity has a particularly good year, as occurred in 1999, would that reflect favorably in the performance of a Japanese index fund relative to its peers? Last year I had begun to suspect that there was trouble in paradise; in 1999 the DFA and Vanguard emerging markets index funds had mediocre relative performance in spite of the superb emerging markets returns that year, and the exact opposite occurred in 1998.

In order to look at this more closely, I looked at the relative performance of 6 different global general equity assets, comparing the percentile performance of the index, assuming that it was a fund, versus the appropriate actively managed funds. For each year from 1990 to 1999 I looked at the following 6 classifications (except for 1990 and 1991, when there was <2 Latin funds):

Region/Nation	Index	Fund Classification
US	Wilshire 5000	Morningstar Diversified Domestic
Europe	MSCI-Europe	Morningstar European
Japan	MSCI-Japan	Morningstar Japan
Pacific Rim	MSCI-PacXJ	Morningstar Pacific Rim, Japan <10%
Emerging Markets	MSCI-EM	Morningstar Diversified EM
Latin America	MSCI-EM/Latin	Morningstar Latin American

To make a long story short, Dunn’s Law strikes out at the global level. Although in some years there was a strong positive relationship between relative fund and index performance, it is strongly negative in others. When the data are aggregated (58 data points in all) it produces an almost perfect scattergram:

Contrast this with the aggregated data for 1995-9 for the 10 domestic style boxes:

Although the neatness of the plot is marred by the 1999 results, there is still an easily appreciated relationship between relative index and fund performance; the results are highly statistically significant, with at t-stat/p-value of 3.41/0.0013 and an R-squared of 0.20.

So what’s going on here? In a word, asset class purity. The "purity hypothesis," extensively discussed by John Rekenthaler in a piece on the Morningstar site, is that fund managers frequently stray from their assigned market cap and valuation pigeon holes. After all, even if the prospectus pegs a fund as a small cap value offering, there’s no reason why the manager can’t sneak in a bit of Microsoft or Cisco. And, of course, many fund managers would categorically reject the entire style box paradigm as an externally imposed tyranny—"My job is to pick the best stocks, regardless of market cap and price/book ratio." So if small value has a bad year, then a small value index fund will do very poorly relative to its actively managed peers, since the active funds are free to invest beyond that year’s dismal style box playground.

And, as we’ve seen, this is in fact the case domestically. But Dunn’s Law fails abroad for a simple reason; the purity hypothesis does not operate across borders. Although it’s easy for a domestic small cap value manager to stray beyond her mandated style box, it’s much harder for a regional foreign manager to wander out his continent. After all, if you’re a European fund manager having a bet on Telmex blowing up in your face just won’t do.

The average domestic index funds' relative performance for 1995-9 was 32^nd percentile for each year. This is slightly better than predicted on theoretical grounds. (If an index fund has a 2% total expense advantage [fund expense ratio plus commissions, spreads, and market impact costs] over the average active fund, and the scatter of annual return funds is about 8%, then it is expected to perform 2/8 = .25 SD above the mean, which puts it at the 40^th percentile for one year returns. For a fuller discussion of this phenomenon click here.)

But the 1990-99 annual performance for global indexing is 40^th percentile, and only 48^th percentile when US funds are taken out of the picture. This is much worse that expected, since the average foreign index fund should have about a 4% expense advantage over its actively managed cousin. (4/8 = .5 SD above the mean, which is the 31^st percentile.)

How have active foreign funds managed to do so well? In a word, "growth." If you think that the past 10 years have been cruel to the US value investor, then take a look abroad. In 1999 alone, for example, the correlation of fund returns with aggregate P/B was 0.62, with a t-stat of 19.9 and a p value of 4 x 10^-69. In other words, the single most important determinant of foreign fund relative performance was growth/value orientation. And in the aggregate, the average P/B of actively managed funds was higher than that of the indexes—at the time of this writing, 5.5 for the average diversified foreign fund versus 4.7 for the EAFE index, so it is not surprising that indexing has not worked spectacularly abroad in recent years.

The best place to demonstrate this is with European funds, where a relatively large number of offerings are available that are fairly free of regional bias. For the 5-year period ending 2/00, the Vanguard European Index Fund ranks a disappointing 25^th out of 38. Again, growth appears to be the culprit, with the Vanguard fund having a P/B of "only" 6.2. The 24 funds ranked above it have an average P/B of 7.6; the top 10 funds, 8.2; and the top 5, 9.1. So growth orientation seems to be the culprit here as well.

Also, the Morningstar database is not survivorship-bias-free, and it is likely that this is a significant factor with foreign funds. In the domestic area Burton Malkiel estimates it at about 1.5% per year, which would put the Vanguard European fund in the top half of the pack.

I must admit that Dunn's Law has engendered more confusion than I had thought it would. Some advocates of passive management accuse it of being an excuse to buy actively managed funds in poorly performing asset classes. It does no such thing; one simply cannot predict which asset classes will perform well or poorly going forward. Others note with surprise that it in fact has no predictive value. Guilty as charged; Dunn's Law is simply a rebuttal to the hackneyed argument that some asset classes, like small stocks, are inefficient enough that it pays to use active management, but that passive management is better in the more efficient large stock arena. The first 2 months of this year, with its small-cap dominance, vividly disprove this so-called "efficiency argument. " Dunn's Law predicts that during this period small stock indexing should work better than large stock indexing, and in fact the Vanguard Index 500 Fund ranked in the 77^th percentile of all large cap funds for January-February, whereas the DFA 9-10 index fund and Vanguard Small cap index fund ranked in the 8^th and 19^th percentiles, respectively, of all small stock funds.

So, while Dunn's Law is a powerful explanation of indexing efficacy domestically, it does not travel well.

Copyright © 2000, William J. Bernstein. All rights reserved.