tomz said:
Thank you. This is exactly what I was looking for. I'm not sure I understand the regression results after a superificial look at them. I'll take a more detailed look when I'm, umm, not at work.... :
Hi Tom,
In a nutshell [well, kind of
], any regression model is looking to try to explain something, whether that be a drop in crime, college student test scores, or the returns of mutual funds. For a little backround, see Fama & French's
two papers on the subject of explaining portfolios of stock and bond returns. Also see
Frank Armstrong's explanation, and
Bill Bernstein's application of the three factor model. I just included the two bond factors [read: explanatory variables] because I was dealing with mutual funds with both stocks and bonds.
Basically, what you're looking for is a high R-squared, which means that your model explains most of the returns of said mutual fund. For example, if the R-squared is 87%, that tells you that 87% of the fund's monthly returns are explained by the 5 factors.
Then, look at the coefficient for the "Intercept." This is any extra monthly return that is not explained by the 5 factors. This is the value added by the mutual fund manager, or "alpha." Say the alpha is "0.05", then the yearly alpha is then [1+0.05%]^12-1 = 0.60% per year.
If the "t-stat" is greater than 1.96, then that coefficient is generally considered "statistically significant," and we can say that the alpha is different than zero.
Of course, any statistically signficiant alpha may or may not be due to the skill of the managers. It may totally be due to luck, we just can't know.
Also, finding a fund with alpha doesn't say anything about the possible persistence of this alpha, as the shareholders of Vanguard's Windsor Fund found out in the 1980's and 1990's with John Neff.
It should be noted that my results for Wellesley and Wellington don't say conclusively that their monthly returns are totally due to their exposure to stocks, value stocks, and longer term corporate bonds. It just says that their monthly returns are highly correlated with the returns of stocks, value stocks, and longer term corporate bonds. Of course, reading through
Bogle's Speech on Wellington and the prior investment policies of Wellington in its SEC filings [focusing on value stocks and longer term corporate bonds], does point to the conclusion that the returns of these two funds are mostly due to their focus on large cap value stocks and longer term corporate bonds.
hth,
- Alec
