How to Beat the Benchmark

Indexing's Ultimate Irony

Something funny is going on in the financial skunkworks of Valley Forge and Santa Monica. The high priests of indexing, George U. ("Gus") Sauter and Rex Sinquefield, have created funds which are beating their benchmarks. Even after expenses. Like clockwork. Spookier still, they are doing it with index funds.

The ultimate measure of the efficiency of an index fund is its "tracking error" (TE). This is the difference between the return of the fund and its benchmark. If an index fund is doing its job perfectly, then its TE will be a small negative number, equal to the opposite of its expense ratio. For example, the Vanguard Index Trust 500 has an expense ratio of 0.20%. If it is performing as advertised, it should thus have a return 0.20% less than the S&P500 each and every year. In fact, it pretty much does that. (Well, actually slightly better. More about that later.)

One of the small pleasures of being a Vanguard shareholder are the handsome and informative annual reports. Chairman Bogle is always entertaining, and the reports contain a wealth of data. There's also something satisfying about being reminded of your connection, no matter how minuscule, with thousands of corporations. Even better, you get to explain ownership of a few shares of McDonalds, Coke, Disney, or Electronic Arts to your children. For the past several years the careful reader has noticed something else: The tracking error of the Vanguard Small Cap Index Fund (symbol NAESX) has been persistently positive, and by no small amount either - about 1.38% annually since 1994. And that's after expenses.

The first few years I wrote this seeming anomaly off to statistical noise - the fund does not own all 2000 stocks in the index, and a TE much larger than with the S&P500 was expected. But with succeeding annual reports the same positive TE was noted. So, with a little help from Morningstar's Principia software, I computed the monthly TE for the fund since it converted to an index fund in 1990, and plotted the 24 month trailing TE: (The y axis plots the average monthly TE, in %. Since the numbers are small you can convert this to an annualized rate by multiplying by 12.)

For the entire history of the index fund, it beats the benchmark by 0.038% per month, or 0.46% annually . Remember that this includes the fund's expense ratio of 0.25%. The actual before expense TE is the sum of these two figures, +0.71%, per year, since 1990. This is highly statistically significant, with p = 0.038 after expenses, and p=0.0083 before expenses.

Look closely at the graph - it looks as though Gus learned something around 1994, because after that the average net TE increases to +0.095% per month (+1.15% annually), or +0.115% (+1.39% annually) before expenses. The post 1994 rise in TE may not be due to random noise, as the p values for this period are 0.0036 after expenses and 0.00063 before expenses. In the world of mutual funds, benchmark outperformance of such statistical power is unparalleled, sort of like batting .450 ten seasons in a row.

The granddaddy of small cap indexing actually resides in Santa Monica, in the form of the DFA (Dimensional Fund Advisors) 9-10 Small Cap Index Fund (symbol DFSCX). Founded in 1982 by Rex Sinquefield and David Booth, the fund's benchmark is the CRSP (Center for Research in Security Prices) 9-10 Decile Index, which comprise stocks in the smallest quintile of the NYSE/AMEX, and NASDAQ stocks with the same capitalization included as well. Again, I've plotted the 24 month TE of the fund since inception:

As you can see, its TE is also persistently positive, but if anything seems to be declining over time. In fact, the average net TE for the whole period is +0.155% per month, or an astounding +1.88% pa net after expenses. The fund expense ratio is 0.61% annually, for a whopping before expense TE of +2.5% annually. This is once again highly statistically significant, with p values of 0.015 after expenses and 0.0022 before expenses. (The SD of the TE is higher for DFSCX than for NAESX, lowering its degree of statistical significance.) It is remarkable enough for any fund to beat its benchmark by 2.5% annually over 17 years, but it is downright eerie to see this done by an index fund.

To complete the picture, since 1992 the Vanguard Extended Index Fund has beaten its benchmark (the Wilshire 4500) by 0.56% per year after expenses (0.81% net of expenses), and even the Vanguard Index Trust 500 has beaten its benchmark by a razor thin 0.08% annually before (but not after) expenses in the same period.

So what is going on here? A hint is found in DFA's 1996 Reference Guide:

The 9-10 Portfolio captures the return behavior of U.S. small company stocks as identified by Rolf Banz and other academic researchers. Dimensional employs a "patient buyer" discount block trading strategy which has resulted in negative total trading costs, despite the poor liquidity of small company stocks. Beginning in 1982, Ibbotson Associates of Chicago has used the 9-10 Portfolio results to calculate the performance of small company stocks for their Stocks, Bonds, Bills, and Inflation yearbook.

A small cap index fund cannot possibly own all of the thousands of stocks in its benchmark; instead it owns a "representative sample." Further, these stocks are usually thinly traded, with wide bid/ask spreads. In essence what the folks at DFA learned was that they could tell the market makers in these stocks, "Look old chaps, we don't have to own your stock, and unless you let us inside your spread, we'll pitch our tents elsewhere. Further, we're prepared to wait until a motivated seller wishes to unload a large block." In a sense, this gives the fund the luxury of picking and choosing stocks at prices more favorable than generally available. Hence, higher long term returns. It appears that Vanguard did not tumble onto this until a decade later, but tumble they did.

To complete the picture, this strategy works best in the thinnest markets, so the excess returns are greatest in the smallest stocks, which is why the positive TE is greatest for the DFA 9-10 Fund, less in the Vanguard Small Cap Fund, less still in the Vanguard Index Extended Fund, and minuscule with the S&P500.

There are some who say the biggest joke in the world of finance is the idea of value added active management. If so, then the punch line seems to be this: If you really want to beat the indexes, then you gotta buy an index fund.

copyright (c) 1998, William J. Bernstein