The topics of portfolio asset allocation and diversifying among screens with low correlations have been discussed quite a bit recently (attributions would include many, but gelasmus has posted a lot, including his spreadsheet tool). In this post, I show how I've tackled finding the "best" blend of 3 quarterly screens of 3 stocks each. Note that "best" may be defined differently by people with different risk aversion profiles, so a curve is built to define the "efficient frontier", which allows users to identify where they want to be on the risk/reward curve.As a side note, I should mention that in this process I have used a tool that was mentioned last fall by JoeLiar (and seconded by klouche): MvoPlus from Efficient Solutions. You can find it at http://www.effisols.com on a trial basis (with some limited capabilities). Although I didn't use this for the final form of what I'm presenting, it does offer a useful tool when considering alternative investments, either screens or stocks. And it seems to match results with what I have prepared here.At the end of this post I address how this might be used in picking stocks within a screen.The following summary refers to an Excel spreadsheet that is in my Yahoo briefcase:http://briefcase.yahoo.com/barrydtoClick on Mechanical Investing Stuff, and find the 12th file down (Quarterly Efficient Frontiers). You'll have to download and unzip this 730K file (the Excel file is over 2 meg). It should open showing the efficient frontier chart for 1986-1999. In addition, there is a chart for using only 1986-1994 data. You might want to see the "ReadMe" tab at the beginning of the worksheet first to get a feel for what all is included.Summary of ResultsUsing the methods described below, 12 combinations (or blends) of three 3-stock quarterly screens were found along a "sort of" efficient frontier. This is from a total of 1,140 3-screen blends examined, with a universe of 20 screens to choose from. For the GSD of each of these combinations, there were no other combinations that yielded a higher CAGR. Five of the combinations are shown below: 1986 - 1999Screen 1 Screen 2 Screen 3 CAGR GSD(Q) CAGR - 2 Sigma RS4 LowPBV Spark 34.9% 25.0% -13.6% RS4 LowPBV RSCAP 45.2% 27.4% -10.5% LowPBV RSCAP CAPRS 52.0% 31.5% -12.0%PEG-O (1-7) LowPBV CAPRS 52.1% 31.9% -12.5%PEG-O (1-7) RSCAP CAPRS 59.4% 39.3% -17.8%When you look at the efficient frontier chart showing all 12 efficient frontier blends, you'll understand why I picked these combinations to list -- they seemed to give the most bang for the buck as you moved up the chart, or they were one of the two endpoints.Method Used to Generate Resultso The following 20 screens were drawn from to form blends of three screens at a time. All were examined for the first 3 stocks of each screen. Peg-Overlap was defined as using 1-7 of the component screens, using a max score of 10.EG PEG RS52 RSCAPEGRSW PEG13 RS26 CAPRSKey100 PEG-O RS13 SOS-PEGs1-3 LowPBV PEGRSW RS4 (an SOS of PEG13, PEG26, PEGRSW, 1-3 each)Plow RSO Spark RSW RSFOGo For each screen, quarterly results for each month (all cycles) were obtained from the backtester.o For a given blend, each screen was assumed to be invested in evenly (33 1/3% each). The portfolio was rebalanced each "quarter". This is in quotes since there are three separate cycles going at once. To get a CAGR/GSD measure for the blend overall, the quarterly return for each month (all 168 months for 1986-1999) were used. The GSD used is the GSD(Q), if you will, based on all 168 points. I believe this is the best way to combine the data from the various cycles, and is consistent with the way Alan Levine presents his results. And whenever I have looked at either averaging all three quarterly results or at CASM, the results have been very close.o To find the "efficient frontier" I wrote a macro that looped through all possible combinations of these 20 screens, 3 at a time. For the probabilistically-inclined, you'll recognize this as 1,140 combinations (= 20x19x18/(3x2x1)). For each combination, various statistics were stored for later processing.o The spreadsheet in my briefcase contains all the input data, output data, the macro used to generate the combinations, and the charts.Observationso Alevine and Mrtoast should be proud that their relatively new screens are prominent in the "best mix" blends, whichever you may wish to choose. (If I'm missing a proper attribution for these, please let me know.)o It may seem unusual for RS4 to pop up in the low-GSD blends, but I have consistently seen RS4 as one of the screens with low correlations with other screens. Although it does not add enough juice to bump up the CAGR very high, if low GSD is a goal, it can help.o Why did I attack this problem this way? I realize that the above results are taking advantage of "low correlation" among the various screens. I could never figure out how to translate any observed low pair-wise correlations into getting the right mix of 3 or more screens. So, I decided to go directly to the end results to see which combinations yielded the best performance, rather than trying to interpret the correlations. Clearly, the "best mixes" are finding the low correlations.Reaching further back in time, I should mention that this is really just an extension of the approach Peter Kuperman started in early 1999. Without looking back for the posts, I believe he came upon the "RKE" (Spark, Keystone, PEG?) approach as the blend with the best return vs risk mix. Based on that, I used an approach similar to Peter's for selecting my annual screen blend for 2000 last fall. And now I wanted to branch out to more quarterlies (moving some money from both monthlies and annuals) as I start thinking about next year. Given the discussions of asset allocation and portfolio management recently, this seemed to be the natural way.o The spreadsheet I built can also be used to enter any combination you want of the 20 screens. You can also vary percentages of each screen, but I have shied away from putting different percentages on screens or stocks so far. Note that I also entered data for the 4- and 5-stock versions of each screen, but have chosen not to examine them further. But you can easily examine different blends of these if you wish.One interesting way to use this is to examine other blends to see how close their results are to the frontier. If they are close, then the differences may just be statistical noise and if you are more comfortable with your screen selection than one actually lying on the frontier, that's fine. Each of us would have to define "close" for ourselves, though.o This approach (and/or the MvoPlus tool) can be used with individual stocks also. I am looking at using it as an extension of LorenCobb's exponential growth approach. Loren's approach looks at each stock individually, using the weekly (or daily) price history of each stock. I have a tool that uses this same daily price history to blend 5 stocks, this time looking at all possible combinations of 5 stocks chosen from the top 10. This again builds an efficient frontier of past six-month CAGR and GSD for the various blends, implicitly identifying blends that take advantage of historical low correlation. This allows one to choose the blend that best meets their risk preference. Naturally, this approach, as does Loren's, requires the assumption that the future will match the past in terms of growth and correlation. (LMS and IVX have provided recent examples that low past volatility makes no guarantee of short-term low future volatility. I guess we have to wait for the backtest to validate our trust in these methods!)OK, enough for now. Happy asset allocating and please offer any comments or questions.Regards,Tim
1986 - 1999Screen 1 Screen 2 Screen 3 CAGR GSD(Q) CAGR - 2 Sigma RS4 LowPBV Spark 34.9% 25.0% -13.6% RS4 LowPBV RSCAP 45.2% 27.4% -10.5% LowPBV RSCAP CAPRS 52.0% 31.5% -12.0%PEG-O (1-7) LowPBV CAPRS 52.1% 31.9% -12.5%PEG-O (1-7) RSCAP CAPRS 59.4% 39.3% -17.8%
EG PEG RS52 RSCAPEGRSW PEG13 RS26 CAPRSKey100 PEG-O RS13 SOS-PEGs1-3 LowPBV PEGRSW RS4 (an SOS of PEG13, PEG26, PEGRSW, 1-3 each)Plow RSO Spark RSW RSFOG
BarryDTO wrote:Reaching further back in time, I should mention that this is really just an extension of the approach Peter Kuperman started in early 1999. Without looking back for the posts, I believe he came upon the "RKE" (Spark, Keystone, PEG?) approach as the blend with the best return vs risk mix. Based on that, I used an approach similar to Peter's for selecting my annual screen blend for 2000 last fall. Outstanding contribution. Did you post the results of your annual screen blend analysis? I can go find it if you could just verify it is on the board.Thanks for sharing this work.Mick
Geez this place is fun... folks generate outstanding new research at a simply blistering pace!Thanks for all the work, Tim... can't wait to grab your worksheet and go fiddle. Nice methodology describing the Eff. Frontier for everybody.-gelasmus
Did you post the results of your annual screen blend analysis? No. It was not as complete an analysis as I just did for quarterlies and not as presentable. It was more along the lines of what Ben Goldman has done recently (and last year). Except I very strongly believe I need to include all starting months (even for annuals), and Ben prefers to use only the 14 points associated with January starts. I think the additional starting months are even more important to understand the correlation among screens, regardless of any January effect. But, each to their own preferences.By the way, I should revise one thing in the original post and add one other small note:o Kuperman's RKE actually referred to Foolish Four (RP4), Keystone and PEG semi-annual. I incorrectly included Spark originally.o The PEG-O 1-7, max score of 10 I used padded both PEG13 and PEG-RSW. It's so hard to remember to fully specifiy these things, and someone's bound to ask. :-)Tim
The concept of "efficient frontier" can be useful provided the frontier is fairly stable in time. One way to test the robustness of this approach is to determine the "efficient frontier" for the first half of the tested time period and then to see how investing in the selected screens performed in the second half of the tested time.Earlier research by Rahm Ytsami on this board indicated that the performance of the screens for the last 3 or 4 month predicted the best which screen would lead in the following month. Can one construct a "moving efficient frontier" based on the performance of the screens for the last several months rather than 14 years?
One way to test the robustness of this approach is to determine the "efficient frontier" for the first half of the tested time period and then to see how investing in the selected screens performed in the second half of the tested time.Although my own reasons for showing both 86-94 and 86-99 data/results differed from the above, I think the efficient frontier shown for 86-94 data provides some indication of the above. Several of the combinations that were "best" during 86-94 ranked either at or near the efficient frontier for 86-99. That's not a direct calculation of their performance of how they did 95-99, but it gives a fair indication they did better than average.The data is in the spreadsheets to make that calculation, or even generate an efficient frontier based only on 95-99 data, if one wanted to.Can one construct a "moving efficient frontier" based on the performance of the screens for the last several months rather than 14 years?Yes. Again, recemt data could be dropped into the spreadsheet and the formulas could easily be changed to develop those measures.However, it won't be by me. Primarily because I believe this approach would not generate useful or valid information to base one's investing decisions on. If someone believes it is, have at it!Regards,Tim
Tim,Is it possible for you to post unzipped version of your file if only for a few days? My unzipping program does not seem to work. It tells me that the date is wrong and I can not find the unzipped file. Alternative to posting unzipped file: is there any good unzip programs I can download from the net?A couple of comments to add to my previous message:1). Efficient frontier should be decided for the whole portfolio and not just for a portion of your assets. However, for obvious reasons, the numbers of possible combinations of screens to test becomes extremely large if one includes monthly, SOS, switching, yearly candidates, etc. as well. One possible solution is to do eliminate some screens based on CAGR and Sharpe ratios, for example. Would it work and can your tool be modified to look at the whole portfolio? Also, what is your motivation to use more of 3 month screens vs. monthly and yearly screens? 2). Autocorrelation for all the screens needs to be determined, IMO. This will tell us what is the appropriate look back period for the creation of efficient frontier. Like so many things in MI, the empirical evidence will be important in the final analyses. For example, as you know, RS type screens have done extremely well for the last few years and one would like to start capturing this outperformance as soon as possible.Thanks for posting your results -- I always read with interest your posts.Eugene
Alternative to posting unzipped file: is there any good unzip programs I can download from the net?This one works for me:http://www.pkware.com/shareware/pkzip_win.htmlBlissAK
BissAK,Thanks. Your zip program worked perfectly!
LionHeartM:First, thanks to BlissAK for pointing to a zip source.Efficient frontier should be decided for the whole portfolio and not just for a portion of your assets. ... One possible solution is to do eliminate some screens based on CAGR and Sharpe ratios, for example. Would it work and can your tool be modified to look at the whole portfolio? I agree on the whole portfolio thought, but find it a little unmanageable to attack right now. So, I focused on quarterlies for now. I've looked at monthlies in a similar vein, but simply converged on PEG-O and RSO, which I'm already doing. (Although I have not looked at the full range of screens as choices, so I haven't posted anything.)One reason for posting my work and especially my spreadsheet is to allow others to extend what I've done. And the best next step may not use anything I've built so far, but instead have someone read it and say "Oh yeah, that makes me think of doing it this other way ...". So, if you have some thoughts on following this approach for monthlies/quarterlies/annuals combined, I'd sure be interested in seeing the results of anything you come up with. I suppose there could be a number of ways to limit the screens used in a final run to define an efficient frontier. Note that I did not include all possible screens in my quarterly analysis. But you never know if you're missing the one screen to make the perfect combination, even though that screen on its own doesn't look good (as for RS4 quarterly).Also, what is your motivation to use more of 3 month screens vs. monthly and yearly screens? Even in taxable accounts, I think the backtests show quarterlies and monthlies outperform annuals. That is, if I can get 40% (backtested) in a quarterly, that will beat, after taxes in my situation, an annual making 30%. (Note: I tend to use 86-94 backtested returns to set my expecations, thus the percentages shown.)I'm mostly using monthlies as my "non-annuals" right now. I'd like to spread my taxable portfolio more evenly between monthlies, quarterlies and annuals, not knowing which will be best in the future. For my IRA, I will probably have a mix of monthlies and quarterlies only. Oh yeah, and options.Autocorrelation for all the screens needs to be determined, IMO. This will tell us what is the appropriate look back period for the creation of efficient frontier. ... RS type screens have done extremely well for the last few years and one would like to start capturing this outperformance as soon as possible.I don't follow the autocorrelation argument, so perhaps you could explain or demonstrate somehow. As for using only recent performance to guide my investment, it comes down to what we believe and our preferences. I don't find this convincing, but hold nothing against those who do. So feel free to perform the analyses that way, and to share your work. I think there are quite a few members of the board who would be interested.Rgards,Tim
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