Rob Arnott, the founder of Research Affiliates, was on the Masters in Business podcast a while back. He said something that, to me, was fascinating. He criticized Dimensional Fund Advisors for starting with market cap weights to build their products.

Arnott’s alternative to Dimensional’s approach is Fundamental Indexing which ignores market cap weights entirely, instead basing portfolio weights on the types of metrics that are used in fundamental security analysis. Metrics like sales, cash flow, book value, and dividends are used to weight securities in a Fundamental Index.

If this sounds like a quantitative approach to traditional active management, it is. Fundamental Indexing is based on markets being inefficient. You are underweighting stocks that are overpriced, and overweighting stocks that are underpriced, with no attention paid to market cap weights. If you believe that markets are efficient then a security cannot be over or under priced and this weighting scheme makes no sense.

Fortunately for investors, funds tracking these indexes are relatively low-cost and well diversified. Owning one of these funds would be far better than owning a traditional actively managed fund, and many of them have outpaced their benchmark index. For example, the FTSE RAFI US 1000 index has handily beaten the Russel 1000 index for the 10-year period ending July 31, 2018.

The question that I am more interested in answering is whether a fundamental index fund compares favourably to Dimensional Fund Advisors funds, which start with market cap weights and then tilt toward securities with higher expected returns based on risk premiums, or factors. A fundamental index does not intentionally target factors, but I suspect that the strategy leads to naïve factor exposure.

To satisfy my suspicions I ran 5-factor regressions on a fund tracking one of Research Affiliates’ Fundamental Indexes.

The Invesco FTSE RAFI US 1000 ETF tracks a fundamentally weighted index of large US stocks with the view of beating the Russell 1000 index. Over the period from January 2006 through July 2018 the FTSE RAFI US 1000 returned an annualized 9.42%, beating the Russell 1000 which returned an annualized 8.93%. What we care about is how the ETF tracked the index net of fees; the Invesco FTSE RAFI US 1000 ETF returned an annualized 9.05% over the same period.

As we might expect, the fund has slightly negative, but statistically insignificant, loading to size – this would be expected from a large cap fund, but interestingly the index has a larger, and statistically significant, negative loading to size. More importantly the fund has a higher loading to value than the Russell 1000. We might expect this based on the intention of the index to underweight overpriced securities. The fund and the index have the same loading to quality, but the fund’s loading is not statistically significant.

The fund has a negative loading to momentum which is statistically significant. Over the period in question the momentum factor happened to be negative, giving a boost to the fund relative to the index. The fund also benefitted relative to the index from a higher (less negative) loading to size, which was positive over the period. While the value premium was negative over the period in question, value is an established factor that might be sensible to target in portfolios.

The question for any investor becomes whether or not fundamental indexing is the most efficient way to get value loading, and whether or not it is a problem that other factor loadings are not statistically significant. Investing based on the evidence would suggest that consistent factor loading is more sensible than naïve factor loading as a by-product of fundamental indexing.


Invesco FTSE RAFI US 1000 ETF t Stat
Alpha 0.00 1.40
Market 1.00 50.22
Size -0.05 -1.50
Value 0.31 9.38
Quality 0.07 1.66
Momentum -0.13 -8.53


Russell 1000 Index t Stat
Alpha 0.00 -0.36
Market 1.01 149.11
Size -0.09 -8.30
Value 0.02 1.59
Quality 0.07 5.30
Momentum 0.00 -0.44


A somewhat comparable product from Dimensional Fund Advisors would be the DFA US Core fund, which starts with market cap weights and then intentionally loads up on factors. We see with a regression that this fund has statistically significant loading to the factors that we would hope to have consistent exposure to. DFA US Core has beaten the Russell 1000 and the Invesco FTSE RAFI US 1000 ETF for the trailing 10-year period ending July 2018 with an annualized return of 9.57%. To be fair, this can be attributed to a higher loading to small, which was positive, and lower loading to value, which was negative, over the period. The point remains, though, that DFA’s factor loading was intentional, while RAFI’s was naïve.

DFA US Core t Stat
Alpha 0.00 -2.94
Market 1.05 92.88
Size 0.15 7.65
Value 0.20 10.39
Quality 0.12 5.25
Momentum -0.02 -2.57


The question remains: what is Fundamental Indexing providing that deliberate factor loading is not? Based on the data that we have seen here the answer is not clear that there is a compelling case to abandon an efficient market risk-based premium approach for an inefficient behaviour-driven one.