In his recent blog, Dan Bortolotti, discusses the basics of factor analysis. If you are one of the few who are actually interested in running your own 3-factor regressions, pull up your sleeves and let’s get started.
I’ve attached the 2008-2012 monthly Canadian regression factors from Andrea Frazzini’s Data Library (along with various ETF and fund returns that Dan Bortolotti will be discussing in his upcoming posts. The data is all in US dollars (so don’t input any monthly fund returns in Canadian dollars).
You may also notice a 4th factor, UMD (up minus down) – this is the Canadian “momentum” factor. Dan will be sure to explain this factor in more detail when he discusses the Morningstar Canada Value and Momentum indices.
Please feel free to try it out for yourself and send me a quick email with any questions you may have.
In the example below, we’ve chosen to analyze the monthly returns of the Beutel Goodman Canadian Equity Fund Class D (BTG770) from January 2008 to December 2012. BTG770 had a 5-year annualized return of 2.6% as of December 2008, while its benchmark index, the S&P/TSX Composite, returned only 0.8% annualized over the same period.
If you do not see the Data Analysis option at the far right, please continue to Step 3. If this option is visible, please skip ahead to Step 6.
Input Y Range: Select all the cells with data in column D (including the Fund-TBill labels).
Input X Range: Select all the cells with data in columns E through G (including the Mkt-TBill, SMB and HML labels)
Labels: Select the Labels check-box
New Worksheet Ply: Give a name to your new worksheet – in the example below, we’ve used the fund code BTG770. Click OK
My colleague, Dan Bortolotti, did an excellent job explaining the main outputs of a regression analysis in his recent blog Going on a Factor-Finding Mission. We’ve summarized our results below for the Beutel Goodman Canadian Equity Fund Class D (BTG770):
Adjusted R Square: This tells you how well the data fit the model. In this case, a figure of +0.9644 indicates the three factors we’ve analyzed explain 96.44% of the monthly performance of BTG770. It’s a fairly tight fit (a value of +1 would be even better).
t Stat: This value tells you whether or not the results are significant. An absolute value of 2 or more (i.e. more than +2 or less than -2) means that you should probably pay attention to the results.
Intercept: You can think of this as a fund manager’s “alpha” (it can be either positive or negative). As this is a monthly regression, the alpha is also a monthly value (so multiply the result by 12 to get an approximate annual alpha value). In our example, the annual alpha is about +0.07% (0.005730188 × 12), but the results are not significant (with a t Stat of only 0.32).
Mkt-TBill: This is referred to in finance as “beta”. A fund with a beta of more than +1 is more equity-like (relative to the market index) while a fund with a beta less than 1 is less equity-like than the market index. Our fund has a beta of +0.85 (with a t Stat of +36.65), so it is less equity-like than the index.
SMB: This is the small cap “slope co-efficient” - it measures the portfolio’s sensitivity to the small cap risk factor. Since this value is -0.21 (with a t Stat of -2.94), we are probably dealing with a large cap fund.
HML: This is the value “slope co-efficient” – it measures the portfolio’s sensitivity to the value risk factor. Since this value is +0.28 (with a t Stat of +6.20), we are probably dealing with a value fund.
So what does all of this factor-based analysis tell us? In this example, it shows investors that the impressive outperformance of BTG770 over that 5-year period was almost entirely due to its exposure to known risk factors (which they could’ve gained exposure to through lower-cost index funds). Its true alpha plummets from 1.8% per year, to a measly 0.07% per year. As William Bernstein so eloquently put it in his Efficient Frontier blog:
“Factor analysis is to active money managers, what a light switch is to cockroaches.”