This article is one in a long series which I hope will help explain the ins and outs of DFA – Dimensional Fund Advisors. NOTE: This is my interpretation and explanation only. For the final word, please refer to the DFA Canada Website.

Picking The Right Benchmarks

For Canadian equity fund managers, beating the TSX Composite Total Return Index is a big deal. Not many managers can do it for long periods of time and those that do are celebrated with the holy label of “adding alpha”. The same can be said of US Equity Fund managers, International Equity Fund managers, et cetera with respect to their traditional benchmark indices. The problem is that the practice of comparing an equity fund manager’s performance using a CAPM world is that you assume that returns are simply a matter of exposure to the market factor (Rm – Rf). Given what we’ve learned about the dimensions of returns, namely that there are three factors (market factor, size factor and value factor) and not one factor that determines returns, ajudicating alpha based on exposure to only one factor seems a bit outdated. Yet this is how the industry operates. Why we are comfortable drawing on science and academic research from decades ago (CAPM) but have yet to adopt newer research (Three Factor or even other models that do a better job of explaining the variations in portfolio returns) is a bit puzzling… until you realize how much money is earned in an industry in which CAPM alpha falsely identifies value more readily.

Measuring Alpha In A Three Factor World

Things don’t look so rosy once we start recognizing that the performance expectations change when we examine the Size and Value loadings a manager’s portfolio takes. So for example, if a fund tilts towards smaller cap stocks than the index it is expected that the long term returns will be higher. Likewise, if a manager tilts towards value stocks (as measured by higher Book-to-Market ratios than the index) then again a long term increase in performance is expected.

Let’s take a look at this graphically. The following graph has quite a bit of information to digest, but we’ll tackle it bit by bit:

(Click to enlarge)

The first thing to notice is that we’re looking at two dimensions of the market and not three. We are assuming that we are dealing with an all equity portfolio and we can measure the size and value loadings on this graph. The total stock market is represented by the point at the cross-hairs. A portfolio can tilt towards Value or Growth, and towards Small Cap or Large Cap versus the total market portfolio (which is all stocks in the market together on a cap-weighted basis). You’ll also notice that the S&P 500 index is plotted on the graph and it is NOT the same as the total market portfolio. This is because the S&P 500 tilts towards Large Cap. Considering that the total market consists of thousands of stocks and the S&P 500 only consists of about 500 of the largest stocks on a cap-weighted basis it only makes sense for the S&P 500 to tilt towards Large.

Taking Loadings Into Account Changes Performance Expectations

The second thing to notice is the “sample fund” data point in blue. This sample fund tilts towards Small Cap stocks and as a result it’s return is expected to be quite higher than the total market over time. With a higher expected performance in the Three Factor world, alpha which appeared in a CAPM world may not exist. As I alluded to in Part II of this series, the Fidelity Magellan fund when helmed by Peter Lynch provided both CAPM alpha and Three Factor alpha, but post-Lynch it provided negative Three Factor alpha even though it beat the S&P 500. This is because once you take into account the Size and Value loadings of Magellan you’ll see that it’s performance was expected to be higher than the S&P 500, but the post-Lynch performance was somewhere between the performance of the S&P 500 and the expected performance – which muddies up the optics for most investors and advisors who are used to a CAPM world.

Next Time

Okay, I’m going to start getting into what I think is the true differentiator of DFA versus all other index funds – the engineered trading. Any “manager-less” portfolio normally has a mandate to reduce tracking error – DFA rejects this as a costly and potentially foolish objective. So if you’ve ever wondered why a DFA fund has a large tracking error when comparing it to a seemingly similar benchmark there is a method to their madness! :) …stay tuned.