The BMW Method
Back-Testing a Timing System

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By DocM47
June 9, 2009

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On to business...I do have some news to report regarding some potential enhancements to the timing system described in an earlier post.

My pal with the computer degrees has made some interesting improvements which I shall report herein, and after much testing I'm prepared to say that from here forward I'll be following this new version of the system. Actually, it didn't change all that much except for the threshold values, but the little changes made for some good improvements.

So let's dig into it and see what's cooking.

As a brief review, the difference between the S&P dividend yield and the three-month treasury yield is compared to a threshold to determine the first of two decision points. I had been using a value of -3.0 for this threshold. My buddy changed this threshold as follows. If the difference is greater than -3.25, then the decision point is giving a positive signal. If the difference is less than -3.50, then a negative signal is being given. If the difference is between -3.25 and -3.50, then the prior week's signal is used.

Likewise, he changed the threshold for the decision point derived from comparing the S&P weekly close to its 52 week moving average. I had been simply comparing the two values. What he's changed is the way this comparison is done. He computes a ratio, dividing the S&P weekly closing price by the 52 week moving average, and gives the weekly close a 5% envelope around the moving average. If this ratio is 1.025 or higher, the decision point is giving a positive signal. If the ratio is 0.975 or lower, then it's a negative signal. Otherwise, as with the prior decision point, use the prior week's signal.

As before, the two decision points are combined into a single signal. If both are positive, then a buy signal is being given. Otherwise, a sell signal is being given.

So how does it do? This new approach gives results very similar to the original model. Using the S&P 500, the average compounded annual return since 1960 was 9.7% and the variability of the returns was 8.6%. Returns were up a little, but so was variability. In all, no great changes there. But the really nice feature is that there were only 20 trades during this period, with 16 winners and 4 losers. The average trade returned 19.3%. The worst trade was -6.1%. The average holding period was 67 weeks, with the longest being 243 weeks and the shortest being 2 weeks. This is particularly interesting to me because of the big drop in the number of trades (from 68 to 20) and the much longer holding period (on average, 67 weeks vs. 17 weeks). Having a longer "in" cycle opens some doors for a few interesting approaches to stock selection. More on that later.....

I went back and tested how my actual portfolio would have performed during this period, although the test results are probably a little suspect because I'm not sure I would have held a static basket of stocks for these longer "in" periods. However, even holding them as I had done with the shorter cycles, the results were good, actually beating what I had achieved since 1995 by about a percent per year. But again, these longer periods between buy and sell signals provide some interesting opportunities to apply a little stock-picked acumen, such as using the BMW method, or other value-oriented approaches, to pick out-of-favor companies. Another potential opportunity is doing some sort of stock basket re-balancing on a regular basis, such as monthly or so. More research needed there.....

Another interesting issue arose from my conversations with my buddy. He uses his own modified version of the commodity channel index (CCI) oscillator which he has built to trade stocks within the buy and sell signals from the system. He keeps a pool of about 100 stocks, and allows himself to hold up to 20 of them at any one time, buying and selling based on each stock's computed CCI indicator value. He uses weekly data so it's not very volatile, and his returns are quite good. I'm not a big fan of TA-style investing, but it's probably worth a look. As with other things, I'll need to research it more fully.

The other thing he brought to the table was a unique way of investing in industry (sector) funds. I mentioned earlier that I invest in a static basket of six such funds. He uses about twice that many, and has determined that some of them tend to follow the system's signals very well while others follow slightly different signals based on their own recent price history. I haven't tested it myself so in my opinion it's not ready for prime time, at least for me. His returns are a good bit better than my 6-fund basket, so it's worth taking a look when time allows.

From here on I'll be following the new signals, but I'll of course be tracking the old signals as well. It'll take a year or two for me to get comfortable with this new approach but it does seem to test well. Unfortunately there was nothing we could do to make the system more responsive on the front end of a market upturn (like the past few weeks). Any modifications in that direction caused variability and risk to go too far up.

My primary reason for reporting all this is that the longer "in" cycles of the new system may provide an opportunity for BMW-like regression analysis on price curves, and that may be of interest to this board. I've uploaded a set of charts to the BMW method website that shows the system's signals since 1950 for those who are interested. These charts show the signals overlaid on a chart of the index and also overlaid on the equity curves.

Doc M