Russell's Visual Fama-French Tool, updated to 2008

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Russell
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Russell's Visual Fama-French Tool, updated to 2008

Post by Russell » Mon Jul 09, 2007 3:49 pm

Hi everybody!

I've been playing with Java some more and put together a (visual) Fama French Calculator -- please give it a try!

You can choose to analyze the returns from the given list of 22 portfolios -- or enter your own returns! Then get your choice of graphical presentations for the results of a one-factor fit, a three-factor fit, a five-factor fit, or your own "fit by eye" (that's the most fun :D ).

Just click the screenshot below to try it out:

Image

Enjoy -- and let me know what you think.

Best wishes,
Russell

p.s. If you're having any trouble with the technical issues (red 'X', etc), I would suggest running over to http://www.javatester.org/ to make sure your browser is Java-enabled and you are using Java 1.4 or later.... Or shoot me a P.M.

p.p.s. If you have any other mutual funds that you would like hardcoded (and you have at least 10 years of data) just send me a note and I'll try to get it included as quickly as possible -- for instance, if anybody's got the return series for older funds like the Fidelity Magellan or the like, I'd be happy to have them!

EDIT (January 24, 2008): Data sets have all been extended to include 2007!

EDIT (June 9, 2009): Data sets now include a dismal 2008 :oops: !
Last edited by Russell on Tue Jun 09, 2009 10:35 am, edited 4 times in total.

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Post by Ariel » Mon Jul 09, 2007 6:35 pm

Awesome!!! :D

I entered my own portfolio returns since 1992 (start of my investing), and think I might qualify as a hedge-fund manager! 8)

Excess return (alpha) = +1.31
Market exposure (beta) = +0.50
Value risk = +0.16
Size risk = -0.03
Duration risk = -0.20
Credit risk = -0.89

R-squared = 0.87

It seems to capture some real aspects of my portfolio. I've typically had about 40-50% equities. I've favored Value, but not small value or small equities of any sort. On the income side, until recently I've had most funds in TIAA Traditional (stable value fund) and Vanguard Prime MM, so few dips associated with long durations. And these, along with recent Vanguard TIPS fund holding, are high quality.

So where does my high alpha come from? Two things, I think. First, I sold most of my equities before 2000 and came through the last bear market pretty well intact, and have ridden things back up as well. (No, I don't claim perfect timing, and was never either completely out or all in.) Second, I've had 10-20% in the TIAA Real Estate fund for last several years, which has done very well -- not as well as REIT funds, but with low volatility.

Thanks, Russell, for creating such a fantastic tool!!! :D
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Post by alec » Mon Jul 09, 2007 6:49 pm

Russell,

FWIW. Here are a whole lot of Vanguard MF returns from 1984-2003.

And here are the returns of Wellington and Wellesley from inceptions to 2004.

- Alec

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Post by tfb » Mon Jul 09, 2007 8:40 pm

What are the blue and red dots and the squares they create?
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Post by Ariel » Mon Jul 09, 2007 8:43 pm

Russell,

Here's a fund to include in your database, the Vanguard Asset Allocation Fund Investor Shares (VAAPX). The following are returns from 1992-2006 (ordered first-last) according to the Vanguard website:

7.51, 13.49, -2.32, 35.46, 15.73, 27.32, 25.40, 5.21, 4.95, -5.34, -15.38, 26.42, 11.09, 5.00, 16.02

So, just how good are the market timers at Vanguard? :lol:

Stay the course? :P Or abandon ship and join the market-timing wannabes? :shock:
Last edited by Ariel on Mon Jul 09, 2007 8:51 pm, edited 1 time in total.
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Post by Ariel » Mon Jul 09, 2007 8:46 pm

tfb wrote:What are the blue and red dots and the squares they create?
I puzzled at the same things at first, but can answer that now. Red points are the actual returns of the fund in question. Blue points are the "predicted" returns according to the fitted model. The squares are a way of visualizing the deviations between observed and expected.

Ain't it a thing of beauty?! 8)
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Post by Ariel » Mon Jul 09, 2007 9:09 pm

To answer my own question ...
Ariel wrote: Here's a fund to include in your database, the Vanguard Asset Allocation Fund Investor Shares (VAAPX). The following are returns from 1992-2006 (ordered first-last) according to the Vanguard website:

7.51, 13.49, -2.32, 35.46, 15.73, 27.32, 25.40, 5.21, 4.95, -5.34, -15.38, 26.42, 11.09, 5.00, 16.02

So, just how good are the market timers at Vanguard? :lol:

Stay the course? :P Or abandon ship and join the market-timing wannabes? :shock:
Stay the course wins! High beta (market risk) of 0.83, a moderate value tilt 0.26, slight tilt away from small at -0.08, tiny duration risk at 0.06, and large negative credit risk at -0.78 ... but with a disappointing negative alpha (excess return) of -0.98.

On the other hand, the fund doesn't explicitly tilt toward value, but that loading may well result from the fund having reduced market exposure when growth was frothy.

Russell -- I would still suggest you include this fund as an illustrative reference. Also, the negative signs are very tiny and can be easily overlooked on the model results screen; maybe you can make them more conspicuous somehow? Again, thank you and congratulations on producing this great tool! :D
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Post by tfb » Mon Jul 09, 2007 9:21 pm

Ariel wrote:Red points are the actual returns of the fund in question. Blue points are the "predicted" returns according to the fitted model. The squares are a way of visualizing the deviations between observed and expected.

Ain't it a thing of beauty?! 8)
It is beautiful but wouldn't a simple bar chart or line chart showing the deviations be more straight forward? You get to see the sizes of the deviations, the frequency of positive deviation vs negative deviation and when they occur. Right now it's very hard for me to get those info by looking at the dots and the squares. I can't tell if D&C Balanced deviated more often to the upside or more often to the downside. The positive alpha can be caused by large outperformance in a few years ("luck") or consistent small outperformance ("skills").
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Post by Russell » Mon Jul 09, 2007 9:50 pm

Hi everybody --

Thanks for the enthusiastic feedback!

Alec: Thanks for the link to the data you've collected --I'll extend the Wellington and Wellesley datasets tomorrow for sure. (Also, it was great chatting with you at Diehards VI -- hope all is well with you and yours....)

Ariel: Thanks for putting my applet through the paces! I've always been curious about the Asset Allocation Fund -- I almost can't believe I didn't think to put it in there first thing. I'm not quite sure how to interpret these negative exposures to credit risk -- it could be that that variable is generally just not particulary helpful. I was a little worried I had entered that data set wrong -- but I just tried out the Lehman US Long Credit A/Better Idx (the benchmark for Vanguard's LongTerm Corporate Bond Fund, 1992-2006) and it gave negligible MARKET, SMB and HML, with TERM of 1.10 and DEFAULT of 1.43 (and R^2 at 0.99) -- so it looks ok....

Finance Buff: Yeah, I didn't put a whole lot of explanation -- sorry about that. On the bright side, Ariel got it exactly right. The red square is the portfolio itself. The blue circle is the approximating portfolio.
One way to visualize the Fama-French 3 and 5-factor approximations is that these are the portfolios that minimize the sum of the squares of the errors between the portfolio returns and the returns of the approximation. Any other factor weighting would increase this measurement of the error.
By actually shading in those squares, we get a visual indication of the error we are measuring in our approximation -- we would like the total area covered by the gray squares to be as small as possible.... (Actually, depending upon the lighting and my angle to the screen, I sometimes can't even see those gray squares even when they're there.... :oops: )

Best to all,
Russell

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Another time series of interest

Post by Ariel » Tue Jul 10, 2007 12:46 am

The BXM index has been trumpeted as a way of getting market (S&P500) returns with lower volatility, and based on Sharpe Index (using monthy data) it apparently does. Basically, the index (strategy) involves owning the S&P500 index and writing (selling) at-the-money monthly calls against the index.

Here's the time series for 1989-2003: 31.49, -3.17, 30.55, 7.67, 9.99, 1.31, 37.43, 23.07, 33.37, 28.58, 21.03, -9.10, -11.88, -22.11, 28.69.

3-factor results:
Excess return (alpha) = +0.47
Market exposure (beta) = +0.99
Value risk = +0.04
Size risk = -0.17
R-squared = 1.00

:) The good news, a decent +0.47 (half percent) alpha. As expected, nearly 1 beta, and slightly negative size risk (since only S&P500). And R-squared is perfect at 1.00. So a free half-percent return, right?

:oops: The bad news: It's an index, not actual returns, and so it doesn't include trading costs (and taxes, which would be very high in a taxable account). Even those trading costs will eat up far more than 0.5% for any normal investor, and the few funds I've seen that want to sell this product charge 1-2% ... plus they will still have some hefty trading costs.

Description of index and strategy:
http://www.cboe.com/micro/bxm/introduction.aspx

Source of data:
http://corporate.morningstar.com/ib/doc ... yWrite.pdf
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Post by tfb » Tue Jul 10, 2007 2:17 am

Russell,

Thanks for the explanation. I still think a bar chart for excess returns (actual - fitted) tells a better story.

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.

The same can happen the other way. Suppose in a period when small beat large, value beat growth, a small value fund performed poorly. Its returns look more like a large growth fund. Fitting the returns to a model shows it had small or negative small and value load factors, and alas, it had a positive alpha!

The number of data points makes a big difference too. I think quarterly or monthly data should be used, not annual. There should be t-test, F-test stuff (forgot which one) which indicate whether the alpha, beta, and the loading factors are significant or not.

Please don't get me wrong. You've done a great job. I only want to make the tool better and more meaningful.
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Post by alec » Tue Jul 10, 2007 8:22 am

Russell,

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.

See Rolling Your Own: Three-Factor Analysis.

- Alec

ps - is it hot enough in Annapolis for you. :wink:

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Post by Ariel » Tue Jul 10, 2007 8:51 am

Some suggested funds for anyone who can dig up, post, and test long time series. These would all be quite interesting, in my view:

International stock index. I know that's not one of the FF factors, but that's what would make it interesting, since so many use it in real-life portfolios.

REIT index. Some logic for including as above.

Coffee House Portfolio in two flavors, all equity and balanced, say, 60:40.

Berkshire stock, both share price and book value. (The Oracle of Omaha favors the latter as his metric.)

Magellan fund, Lynch years, post-Lynch years, and all years combined.
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Vanguard historical returns

Post by simba » Tue Jul 10, 2007 9:13 am

Russell,

I haven't played with your tool yet but I compiled the historical returns of ALL the Vanguard funds. You can download Spreadsheet here.

I discussed this topic here

Regards,
Simba

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Dumb question

Post by troyboy » Tue Jul 10, 2007 9:31 am

I'm probably missing something obvious, but how do you enter your own portfolio? I selected "(enter your own)" and click "Set!," but the applet never prompts me to enter my portfolio...

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Post by matt » Tue Jul 10, 2007 11:29 am

If alpha exists, Vanguard Asset Allocation has captured it. It has outperformed the S&P 500 (which is the most aggressive position it can take) with substantially lower risk. The ever-shifting allocation, however, means that factor modeling is not likely to work very well.

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Post by Russell » Tue Jul 10, 2007 1:36 pm

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 :wink: . 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
Last edited by Russell on Fri Jul 13, 2007 10:56 am, edited 1 time in total.

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Re: Dumb question

Post by Russell » Tue Jul 10, 2007 1:50 pm

Hi TroyBoy --
troyboy wrote:I'm probably missing something obvious, but how do you enter your own portfolio? I selected "(enter your own)" and click "Set!," but the applet never prompts me to enter my portfolio...
Hmm.... If you select "(enter your own)" and then press "Set!" that should unlock tab ii and take you straight there automatically. Once there, you have to specify the first and the last year for which you have data (by clicking on the first year, then holding SHIFT and clicking on the last year, then pressing "Set!"). That'll unlock tab iii and take you there, where you actually get to enter your data.

It's a little clunky, but it seemed like a reasonable (if not particularly elegent) way to put it together.

I hope you can get it to work!

Best, Russell

p.s. I just uploaded a version including the expanded data sets and several more portfolios (including Berkshire Hathaway, VFINX and VAAPX). If you don't see the new datasets, you might need to close and reopen your browser to get the old version out of your browser's memory.

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Re: Dumb question

Post by troyboy » Tue Jul 10, 2007 2:37 pm

Russell wrote:Hi TroyBoy --
troyboy wrote:I'm probably missing something obvious, but how do you enter your own portfolio? I selected "(enter your own)" and click "Set!," but the applet never prompts me to enter my portfolio...
Hmm.... If you select "(enter your own)" and then press "Set!" that should unlock tab ii and take you straight there automatically. Once there, you have to specify the first and the last year for which you have data (by clicking on the first year, then holding SHIFT and clicking on the last year, then pressing "Set!"). That'll unlock tab iii and take you there, where you actually get to enter your data.
This works for me, but I had assumed that I would have to enter the composition (or at least AA) of my own portfolio at some point, not just the annual returns. Maybe I just misunderstand what the calculator is supposed to do. Sorry for the confusion.

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Post by alec » Tue Jul 10, 2007 2:50 pm

Russell,
although I didn't notice where Bill mentioned that at all in your link
See the second paragraph after the blue tables:
The second group is far more interesting. First, the "intercept" is the fund’s alpha, negative 0.206 per month, or about 2.5% per year. In other words, the managers, after expenses, underperformed the regression-based benchmark by that amount. However, the t-stat and p-value tell us that this is not statistically significant. Next, we have the "loadings" for the three factors. The Mkt loading is 1.06. This is the traditional beta of the fund. Most equity-only funds have values very close to 1.0. The SmB loading is -.05. This means that the fund is primarily large cap. (A zero value signifies large cap, and a value of greater than 0.5, small cap.)

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The Oracle of Omaha - Oh My Goodness!

Post by Ariel » Tue Jul 10, 2007 3:07 pm

Russell wrote:p.s. I just uploaded a version including the expanded data sets and several more portfolios (including Berkshire Hathaway, VFINX and VAAPX). If you don't see the new datasets, you might need to close and reopen your browser to get the old version out of your browser's memory.
I'm tempted to sell everything and buy Berkshire Hathaway. I knew WB was great, but this tool shows just how amazingly great his returns have been. :shock:

Were these stock prices, by the way? Or book value, which is WB's own preferred metric?
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Re: The Oracle of Omaha - Oh My Goodness!

Post by Russell » Tue Jul 10, 2007 3:23 pm

Ariel wrote: Were these stock prices, by the way? Or book value, which is WB's own preferred metric?
Ooo -- good point. I grabbed these numbers off of the latest Berkshire Hathaway annual report -- and thus they reflect per-share book value rather than share price -- not exactly an apples to apples comparison. :oops:

If anybody's got the share price history, that's probably a more reasonable data set to regress....

Best, Russell

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Re: Another time series of interest

Post by Olav2 » Tue Jul 10, 2007 3:24 pm

Ariel wrote:The BXM index has been trumpeted as a way of getting market (S&P500) returns with lower volatility, and based on Sharpe Index (using monthy data) it apparently does. Basically, the index (strategy) involves owning the S&P500 index and writing (selling) at-the-money monthly calls against the index.

...
:oops: The bad news: It's an index, not actual returns, and so it doesn't include trading costs (and taxes, which would be very high in a taxable account). Even those trading costs will eat up far more than 0.5% for any normal investor, and the few funds I've seen that want to sell this product charge 1-2% ... plus they will still have some hefty trading costs.
Ariel- Did you see BWV, the BXM index etn product? .75% ER, so sounds like you are still not going to come out ahead, unfortunately.

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Post by Russell » Tue Jul 10, 2007 3:43 pm

The good folks at fundadvice.com had an article with over 30 years of Berkshire's market returns (through 1999). I've just uploaded the applet with that data set instead of the previous....

Best, Russell

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Re: The Oracle of Omaha - Oh My Goodness!

Post by alec » Tue Jul 10, 2007 7:02 pm

Ariel wrote:
Russell wrote:p.s. I just uploaded a version including the expanded data sets and several more portfolios (including Berkshire Hathaway, VFINX and VAAPX). If you don't see the new datasets, you might need to close and reopen your browser to get the old version out of your browser's memory.
I'm tempted to sell everything and buy Berkshire Hathaway. I knew WB was great, but this tool shows just how amazingly great his returns have been. :shock:
Well, not really. The R2 for the BK regressions is only around 0.50, which is not all that great. Generally, you'd want an R2 over 80%.

- Alec

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Post by alec » Tue Jul 10, 2007 7:04 pm

Russell,

Is there a way to only do a certain number of years for the funds you've uploaded. For example, if I just wanted to do Windsor from 1965-1995 [when John Neff was managing].

thanks,
Alec

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Re: The Oracle of Omaha - Oh My Goodness!

Post by Ariel » Tue Jul 10, 2007 7:25 pm

alec wrote:
Ariel wrote:
Russell wrote:p.s. I just uploaded a version including the expanded data sets and several more portfolios (including Berkshire Hathaway, VFINX and VAAPX). If you don't see the new datasets, you might need to close and reopen your browser to get the old version out of your browser's memory.
I'm tempted to sell everything and buy Berkshire Hathaway. I knew WB was great, but this tool shows just how amazingly great his returns have been. :shock:
Well, not really. The R2 for the BK regressions is only around 0.50, which is not all that great. Generally, you'd want an R2 over 80%.

- Alec
I respectfully disagree. R^2 of 0.5 means R around 0.7. With 30+ data points and 4 or 6 degrees of freedom used to estimate parameters (including alpha + 3 or 5 factor FF model), that's very highly significant -- if you want to be a statistical purist. (There are other issues that make me think statistical purism is wrong-headed in these contexts anyhow, such as viewing years as independent observations.)

EDIT: I see that R^2 is a bit lower now using stock prices, 0.44 for the 5 factor model. Still, R then is 0.66 and with 30+ data points highly significant. WB, btw, actually thinks book value is what captures BRK's performance best, not the share price ... and that yielded higher R^2 values.

The fact that the R is so low relative to familiar funds (like balanced ones) shows, I think, the effects of this being a different beast -- a single stock (albeit fund-like in many respects) and, moreover, one with a very unusual and successful manager.

Ah, if only I had these data when WB was young ... too bad the future is hard to predict, eh?
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Post by Russell » Tue Jul 10, 2007 8:03 pm

First, thanks again to everybody for your feedback (and especially to Simba, Alec and Ariel for help with the data).
alec wrote:Is there a way to only do a certain number of years for the funds you've uploaded. For example, if I just wanted to do Windsor from 1965-1995 [when John Neff was managing].
Sure! The way I would do that is:
  • 1. On the first screen (tab 'data i') select "Windsor" and click "Set!".
    This will load the Windsor data, but will also automatically take you to the 'compute' tab and lock up the data.

    2. Now click the tab at the top marked 'data i' to return to the start -- and this time select "(Compute your own)" and press "Set" again.
    The Windsor data set is still in the memory but is now unlocked for editing!

    3. You should now be at the tab 'data ii'. Scroll down and click '1965'. Scroll down some more, hold 'SHIFT' and click '1995'. Then press "Set!".
    This will take you to tab 'data iii', where the Windsor return data for 1965 to 1995 should now be displayed (and editable, if you so desired).

    4. Just press "Set!" again to finalize the data set -- this will take you to the 'compute' tab and you can proceed with your regressions!
Again, it's a little clunky but it gets the job done.

Best,
Russell

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Post by Russell » Wed Jul 11, 2007 11:48 am

Just a quick note --

I've added the option of doing a 1-factor CAPM regression, in addition to the 3 and 5 factor regressions -- I hope folks find it useful....

Best, Russell

p.s. Once again, if you don't see the new functionality, you may need to close and reopen your browser to purge the older version of the applet from your browser's memory.

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Suggestion - Graph Style

Post by Vegomatic » Wed Jul 11, 2007 10:55 pm

Suggestion - Graph Style

If/when you have the time .... might it also be interesting to see the data plotted as a "scatter plot" (using MS Excel terminology).

That way ... if FF3F predictions were "on top" of actuals, believe you would see a 45 degree straight line... (right?)

--------------------------------------------------------------------
Additional Suggestion for 'Scatterplot'

Since X and Y axes would each be returns, if possible, include "year labels" floating near points...
Last edited by Vegomatic on Sat Jul 14, 2007 10:41 pm, edited 1 time in total.

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Re: Suggestion - Graph Style

Post by Russell » Thu Jul 12, 2007 2:49 pm

Vegomatic wrote:Suggestion - Graph Style

If/when you have the time .... might it also be interesting to see the data plotted as a "scatter plot" (using MS Excel terminology).
Thanks for the suggestion, Veg!

I've been looking for an excuse to use a tabbed pane for the plots -- and that sounds like just the option to have! (Apologies to The Finance Buff, that I'll probably shade my squares there as well :) -- but it should make the "over/under" comparisons he's interested in more obvious, too.)

Actually, that graph would look similar to the one we have now -- it would just translate each gray square horizontally so that the red markers all fell on your line of slope one. If I had any animation skills, that could be a cool segue between the two graphs as the squares all slowly and seamlessly shifted into place -- oh well....

Also, Alec has shamed me into at least computing the standard errors for the coefficients :oops: -- the interested reader should be able to convert those into t-stats and p-values without much trouble.

I'll try to get to both of those things shortly....

Best, Russell

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Re: Suggestion - Graph Style

Post by alec » Thu Jul 12, 2007 3:12 pm

Russell wrote:Also, Alec has shamed me into at least computing the standard errors for the coefficients :oops: -- the interested reader should be able to convert those into t-stats and p-values without much trouble.

I'll try to get to both of those things shortly....

Best, Russell
Man, if I didn't know any better, I'd think you were a professor or something. Making us learn. C'mon. :evil:

btw - in case anyone wants to know how to convert the standard error into t-stats, see EXCEL: Multiple Regression [the section called KEY REGRESSION OUTPUT] or Interpreting Regression Output
The t statistic is the coefficient divided by its standard error.
- Alec

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Standard Errors....

Post by Russell » Fri Jul 13, 2007 10:23 am

Good morning --
alec wrote:Man, if I didn't know any better, I'd think you were a professor or something. Making us learn. C'mon. :evil:
Well, it's a good thing you know better! :wink:

Anyway, the applet will now automatically compute the standard errors for ya....

For example, if I plug in Vanguard Wellington, 1940-2006, and ask for a five-factor analysis, I get:

Code: Select all

alpha:  -0.23 [ +/- 0.472]
beta:    0.58 [ +/- 0.025]
hml:     0.13 [ +/- 0.032]
smb:    -0.00 [ +/- 0.032]
term:    0.29 [ +/- 0.048]
default: 0.05 [ +/- 0.144]
--------------------------
R^2:     0.93
That's the regression coefficients on the left and their standard errors on the right. As Alec noted, the t-statistic for each term is the coefficient divided by its standard error. For a statistician, a t-statistic larger than 2 (or so) suggests that we can reject the null-hypothesis with probability around 95% (or so), and say that a coefficient is significant.

For instance, in the regression above, beta, hml and term would all be considered significant, while alpha, smb and default are insignificant. The R^2 near one suggests a good fit with the data....

Best, Russell

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Re: Standard Errors....

Post by tfb » Fri Jul 13, 2007 10:09 pm

Russell wrote:That's the regression coefficients on the left and their standard errors on the right. As Alec noted, the t-statistic for each term is the coefficient divided by its standard error. For a statistician, a t-statistic larger than 2 (or so) suggests that we can reject the null-hypothesis with probability around 95% (or so), and say that a coefficient is significant.

For instance, in the regression above, beta, hml and term would all be considered significant, while alpha, smb and default are insignificant. The R^2 near one suggests a good fit with the data....
I think the null hypothesis for beta should be whether it equals 1.0, not whether it equals 0. So you subtract 1.0 from the beta coefficient and then divide by the standard error. The above stats suggest that the beta for that fund is statistically significantly different from 1.0.
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Re: Standard Errors....

Post by Ariel » Sat Jul 14, 2007 7:05 am

tfb wrote: I think the null hypothesis for beta should be whether it equals 1.0, not whether it equals 0. So you subtract 1.0 from the beta coefficient and then divide by the standard error. The above stats suggest that the beta for that fund is statistically significantly different from 1.0.
Interesting issue, TFB. It's actually a bit more complicated, depending on circumstances. In essence, the issue is what's the "null" hypothesis. In the case of an all-equity portfolio, I agree with you that beta = 1 is the null. In the case of a zero-equity portfolio, however, then the null would be beta = 0. For a balanced portfolio, then the stated average equity in the portfolio might be the best null. In general, though, beta out to be and usually will be one of the most informative aspects of this tool, showing how a portfolio is correlated with the overall equity market.
Do what you will, the capital is at hazard ... - Justice Samuel Putnam (1830), as quoted by John Bogle (1994)

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Re: Standard Errors....

Post by tfb » Sat Jul 14, 2007 9:52 am

Ariel wrote:For a balanced portfolio, then the stated average equity in the portfolio might be the best null.
Agreed. So for Wellington, the null hypothesis should be whether the beta is 0.6. Stats showed the beta didn't vary significantly from 0.6. Another suggestion for Russell would be in addition to showing the coefficient in the slider, also include a shaded range for the 95% confidence interval. Yeah, users can calculate themselves, but I'm lazy :o
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Re: Suggestion - Graph Style

Post by Russell » Thu Jul 19, 2007 3:45 pm

Hi All --
Vegomatic wrote:Suggestion - Graph Style

If/when you have the time .... might it also be interesting to see the data plotted as a "scatter plot" (using MS Excel terminology).

That way ... if FF3F predictions were "on top" of actuals, believe you would see a 45 degree straight line... (right?)

--------------------------------------------------------------------
Additional Suggestion for 'Scatterplot'

Since X and Y axes would each be returns, if possible, include "year labels" floating near points...
Sorry for the delay -- your scatterplot is ready for you now! Enjoy! :D

I hope I didn't break anything too badly -- I'm skipping town for a couple 'o days and won't be able to fix it 'til next Wednesday!
The best material model for a cat is another, or preferably the same, cat. - A. Rosenblueth and N. Wiener (1945).

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Post by Russell » Wed Jul 25, 2007 10:07 am

Hi everybody --

Back safe and sound!

Just a quick update -- there are now two views for visualizing the fit of the regressions, and 11 portfolios pre-entered in the applet.

These include 8 Vanguard Funds:
  • Vanguard Wellington (1930-2006)
  • Vanguard Wellesley (1971-2006)
  • Vanguard Windsor (1965-2006)
  • Vanguard Morgan Growth (1970-2006)
  • Vanguard Explorer (1972-2006)
  • Vanguard 500 Index (1977-2006)
  • Vanguard Small Cap Index (1962-2006)
  • Vanguard Asset Allocation Fund (1989-2006)
Two other funds:
  • Dodge and Cox Balanced (1961-2006)
  • Janus Fund (1971-2006)
And good old Berkshire-Hathaway:
  • Berkshire Hathaway (share price, 1967-1999)
If anybody has any other funds that they would like hard-coded, just let me know (and send me the data) via PM....
The best material model for a cat is another, or preferably the same, cat. - A. Rosenblueth and N. Wiener (1945).

johndcraig

Post by johndcraig » Wed Jul 25, 2007 11:26 am

Russell

Glad to hear you are back safe and sound. Now about that Hussman fund... :)

http://www.diehards.org/forum/viewtopic ... 2513#52513

John

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Post by Russell » Thu Jan 24, 2008 3:00 pm

Good afternoon --

I've just updated all of the data series in this applet to include 2007 -- thanks again, Simba et al!

Enjoy!
The best material model for a cat is another, or preferably the same, cat. - A. Rosenblueth and N. Wiener (1945).

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Updated through 2008

Post by Russell » Tue Jun 09, 2009 10:45 am

Good morning!!

I've finally updated the applet with all of the (dismal :cry:) calander year 2008 data. It now includes the six Fama and French Model Portfolios and several of the TSP funds.

Enjoy! Russell
The best material model for a cat is another, or preferably the same, cat. - A. Rosenblueth and N. Wiener (1945).

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