Good afternoon!
tfb wrote:This kind of quantitative analysis is interesting but can also produce weird results. I think this is called "returned based style analysis." It tries to deduce a portfolio's style by looking at its returns. For example the Vanguard Asset Allocation Fund is shown with a good value tilt and only a very small tilt toward large. It sure didn't tilt toward value and it should have a much larger tilt toward large because it uses S&P 500 for the equity part. When measured against a value tilted and not as large model, it had negative alpha. Buy and holders proclaim market timing didn't work. But if the fund is measured against a value neutral, large tilted benchmark, it probably had a solid positive alpha.
I agree. My first Java project for the board was an efficient frontier applet (see thread
here) and I do prefer that way of looking at portfolios -- purely on a risk/reward basis. But I think this has its own interest as well. And, hopefully, a low R^2 will reflect it if the 3-factor analysis doesn't work so well. And you can always "roll your own" one-factor (beta) analysis with this tool as well -- just set the other four factors to zero!
Note to self: I just put in Simba's data for VAAPX and got a wicked good R^2 (better than 0.96) -- so my theory above about the low R^2 is maybe a little rough. To be fair though, VAAPX hasn't really varied that much over its lifetime for a TAA fund --see my (slightly outdated) graph
here....
tfb wrote:The number of data points makes a big difference too. I think quarterly or monthly data should be used, not annual.
In general, I agree again -- but I'm viewing this basically as an online learning and intuition building tool -- and (I believe) it's much easier for people to run down annual returns and try them out. Actually, I believe the pages Alec put together above provide more of the stats and shorter time intervals that you're interested in (but they aren't nearly as pretty

)
tfb wrote:Please don't get me wrong. You've done a great job. I only want to make the tool better and more meaningful
No problem -- I appreciate it!
alec wrote:When doing these sorts of regressions, one should always look at the t-stat and p-value to see if the coefficient of Mkt-Rf, SMB, HML, DEF, and TERM is statistically significant.
Yes, one should (although I didn't notice where Bill mentioned that at all in your link...). I'm probably not gonna, though

. I'm teaching a Matrix Algebra course in the fall, and I thought that this was a nice application -- using projections onto the space spanned by the factors to find the least squares fit. Maybe if I teach Probs and Stats in the Spring I'll code up the t-stats and p-values....
[EDIT/UPDATE: I lied -- and have now relented and included standard errors in the calculations -- see posts below.]
alec wrote:ps - is it hot enough in Annapolis for you.
I like it! After 8 years exiled in New England, it's nice to get back to a real Southern summer....
Best, Russell