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An Alternative to Benchmarking Fund Returns

January 16, 2012 - 1 comment

Assessing a fund manager’s skill is a difficult task – most of the time, advisors would simply pick a benchmark index and compare its returns (and perhaps its standard deviation) to that of their fund. For example, if we wanted to compare the 5-year performance of the DFA Canadian Core Equity Fund Class F (a fund we have used with many of our PWL clients in the past 5 years) to an appropriate benchmark index, we may choose the MSCI Canada Investable Market Index and compile the following information: 

At first glance, it would appear DFA had generated significant “alpha” over this time frame – they were able to beat their index, and with a lower standard deviation. Good enough explanation for our clients, right?


DFA is a Canadian fund company that consistently tilts their portfolios toward smaller companies (with smaller market capitalization than bigger companies) and value companies (with higher book-to-market ratios than “growth” companies). Their past outperformance could simply be due to taking on more small cap and value risk than the index, and not alpha at all. This would make intuitive sense, because as advisors, we do not expect DFA to generate alpha at all – we expect them to provide our clients with efficient and low-cost access to 3 of the risk factors that have historically been shown to compensate investors over a long-term investment horizon:

  1. The Market Factor
  2. The Size Factor
  3. The Value Factor

So how can we tell if DFA (or any other manager for that matter) has done their job?

This question leads us to the Fama-French 3-Factor Model:



The model can be used (among other things) to more accurately assess the true nature of a fund manager’s performance (whether it is good or bad). Determining the equation inputs for a Canadian equity fund is another matter. Unfortunately for Canadians, there is no easily accessible database where you can obtain the monthly return data necessary to run a 3-factor regression analysis (unlike in the U.S., where Ken French’s online data library is available to the public). Instead, I’ve created a “makeshift” Canadian version of the database that seems to work fairly well for this exercise – I’ve made notes below for the source of the monthly returns: 

After running a 3-factor regression analysis with the above data and monthly returns for the DFA Canadian Core Equity Fund Class F (minus the monthly Canadian One-Month T-Bill returns), we get the following results: 

 all show t-statistics greater than 2, indicating a high level of significance in the results. I find it easier to illustrate the main results of the small cap and value factors in a chart:

The chart above is divided into four quadrants, relative to the market portfolio. The further to the right and up a fund plots (the more small cap and value tilt it has), the higher the expected return of the fund (and the higher the risk). The opposite is also true. We are now ready to plug in the data (I’ve included it again below for convenience) and calculate a more appropriate benchmark return for the DFA Canadian Core Equity Fund Class F (DFA256).

Comparing this result (+1.92%) to the 5-year annualized return of the DFA Canadian Core Equity Fund Class F (+1.93%) appears to make more sense now. DFA did not in fact add alpha – they merely did what they said they were going to do – consistently tilt their portfolios in such a way to capture the small cap and value factors (which happened to be positive over this 5-year period, but could have just as easily been negative). There will be periods when the small cap and value factors will be negative, and it is even more important at that time to not cast aside fund managers like DFA, whose returns will be expected to lag the broad market indices.

By: Justin Bender with 1 comments.
Filed under: Factor Investing
  16/01/2012 11:05:30 AM
Justin Bender
For more information on rolling your own 3-Factor Analysis, please see William Berstein's online article:

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