# FTSE RAFI Methodology

As discussed yesterday, there are actually many variants of fundamental indexation out there and most are based on single metrics. For example, Jeremy Siegel of “Stocks For The Long Run” fame has teamed with Wisdom Tree to produce ETFs that index on either a dividend weighted basis, or an earnings weighted basis. FTSE RAFI (to my knowledge) is the only one that uses multiple metrics – four to be exact: 1)Sales, 2) Cash-Flow, 3) Book Value and 4) Dividends.

# Index Construction

It’s probably helpful to go over how a cap-weighted index (vernacular for Market Capitalization Weighted) is constructed. If we had 100 companies in a market, and the total sum market capitalization of all the companies put together was \$100 Billion, then if Company 1 had a market cap of \$4 Billion, it would have a 4% weighting in a cap weighted index. If Company 100 had a market cap of \$50 million it would have a weighting of 0.05% in the cap weighted index.

To weight on fundamentals is very much the same process, you just use different numbers. So let’s say our 100 companies have combined sales of \$100 Billion, and Company 1 had sales of \$2 Billion. In the sales-weighted index it has a weighting of 2%.

With FTSE RAFI there’s a bit more to it. You do the same for Cash-Flow, Book Value and Dividends. You then take the average of the four weightings to create a composite weighting. (If a company does not pay dividends, then you take an average of the first three only.) There’s one more step: you then take the rolling 5 year average of this composite to create the final FTSE RAFI Weightings (the index is reconstituted once per year, based on receiving all the audited annual financial statements for the market constituents once per year).

So you can see, none of these metrics or calculations have anything to do with the stock market price – therefore the structural link between portfolio weight and pricing error is removed. Pricing errors still occur, but the point is that they are random and they cancel each other out – instead of having most of your over-pricing errors magnified and most of your under-pricing errors diminished.

Preet Banerjee
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• Jordan

Even though DFA doesn’t provide a stand alone index formula, don’t their index funds also use multiple metrics to construct?

• Preet

@ Jordan – They offer funds that allow you to tilt towards small stocks and value stocks, but they are cap-weighted from there. So for example, you could buy a core fund which gives you exposure to the cap-weighted index, and then you could purchase a “small” fund or a “value” fund which are parsed from the larger market to encapsulate only those stocks which fall into those categories (the core fund may hold all of those stocks as well), but by tinkering with your mix of these three funds, you could create a custom amount of tilting towards small or value (or both) in your portfolio. The link to cap-weighting still exists as far as I know.

• Jordan

What would happen to an asset allocation if you mixed different indexes for the same asset class? For example if you had 50% of the TSX index and 50% of the FTSE RAFI Canadian Fundamental index?

Is it possible that the two would blend well… having some benefit of the traditional price based cap weighted model and lower pricing errors based on the fundamental. Is it possible that together their movements might have a slight negative correlation so you could reduce the standard deviation of both without adding more risk?

The reason I’m thinking of this is I fully believe in traditional indexing, it’s an investment style I’m very comfortable with and it has a long track record of success. But I also want to believe that fundamental indexing can out perform a standard index going forward. My caution comes from a fundamental index being more expensive, having lower adoption in the market and relying more on back testing to show it’s success instead of having an actual long term history. So without going all into one or the other, is it possible to straddle the fence in the middle with a foot in each with positive results?

• Preet

@Jordan – a couple of points to address here:

1. In the context you are framing, standard deviation is equivalent to risk.

2. The two would blend fine – and either by themselves is not a bad bet compared to what’s out there. I do personally prefer the FI versus cap-weighting.

3. If you are serious, pick up Arnott’s book on The Fundamental Index. It’s actually a pretty easy read, given how data intensive it is.

4. You need to be careful with lower volume ETFs as the premium/discount to NAV can far exceed the value-add (or hopeful value-add) depending on when you buy/sell.

5. You could very easily straddle the fence – best of both worlds, not a bad approach. The theory that any new strategy (or back-tested one) has its advantage negated by its discovery is valid, but consider that you would know exactly when this happens as the FI would approach the cap weighted index in composition. Until that time, the drag of cap-weighting would continue to exist.

• Patapia

This idea of fundamental Indexation is very interesting! I am wondering if the weights are multiplied with the returns of each stock, like capitalization indexes.