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No. of Recommendations: 89
Conclusions Up Front

I've been trying to find an optimal strategy for using the Superior Six as outlined in the "Investing at the end of the month" thread using ETFs. The purpose for using ETFs is to simplify the diversification process while investing in more liquid investments that are easily traded and do not have the restrictions of Mutual Funds. In my pursuit of this I came across a secondary observation which may be helpful to others as well. This secondary observation flows from attempting to use What Works Lately (WWL) methodology for selecting the ETFs to invest in each month end.

I took all the ETFs with a history from 1/1/1999 to 11/17/2006 and ran tests employing the Superior Six approach. At the end of the month I would invest in the ETF for the last five days and then sell at the close of the first day of the next month. Using the results of these tests I then attempted to find the optimal measure for predicting which ETF would be best held at the next month end using the previous twelve months of history. I only evaluated which ETFs to use quarterly, rather than monthly -- so at the beginning of a new quarter I would decide the three ETFs to use and then use these for the next three months and repeat the method at the beginning of each new quarter. The purpose in doing this was to simplify the process.

What I found was quite remarkable -- the absolute best predictor of future performance was the Ulcer Performance Index. The next two produced almost exactly the same results -- Sortino and Sharpe with the former slightly better.

The Ulcer Performance Index produced a CAGR of 22.58% over the period tested with a GSD of 9.42, a Sharpe of 1.85, and an Ulcer Index of just 0.98%! The drawdown over this period was a remarkable -6.8% and 97% of all rebalances produced a positive return -- the only losing rebalance was -0.30%.

Here is a comparison of the five best measures for finding the best forward returns -- note the significant improvement over holding SPY:
Begin:          1/1/1999          Sort     Descending    All ETFs          
End: 11/17/2006 Lookback 12 Months Avg CAGR: 12.54%
Time Invested: 30.52% Granularity Daily Avg GSD: 12.76
S&P 500 CAGR: 1.68% Evaluation Quarterly Avg DD: -23.70%
S&P 500 GSD: 19.78 Days Held Six
S&P Drawdown: -49.15% ETFs Held Three

        Based On           ROI     CAGR    GSD   Sharpe  Ulcer Index  Drawdown  Signal  Stock
Ulcer Performance Index 392.65% 22.58% 9.42 1.85 0.98% -6.80% 97% 88%
Sortino 335.82% 20.67% 9.82 1.69 1.45% -7.66% 84% 80%
Sharpe 317.67% 20.02% 10.05 1.57 1.40% -7.66% 84% 76%
Alpha 248.36% 17.27% 15.46 0.91 6.99% -19.95% 75% 70%
Jensen 248.36% 17.27% 15.46 0.91 6.99% -19.95% 75% 70%

So here we have a strategy where we are only invested 31% of the time, but we produce a 22% CAGR with less than a ten on GSD and a Sharpe of 1.85. I'm seriously considering this as the safe part of my asset allocation strategy. Take what I'd normally put into cash and put it into this method by only investing in it 31% of the time. At these levels of GSD and Ulcer Index I believe it would still be accomplishing my primary purpose to be in a safe investment, especially in light of the major bear market that this strategy went through.

Here are the annual results and the running cumulative ROI between this strategy and holding the S&P 500 -- SPY as an ETF:
                           Strategy     SP500
Strategy SP500 Cumulative Cumulative
Years ROI ROI ROI ROI
1999
16.64% 19.53% 16.64% 19.53%
2000 34.20% -10.14% 56.53% 7.41%
2001 26.34% -13.04% 97.77% -6.60%
2002 21.97% -23.37% 141.21% -28.43%
2003 15.80% 26.38% 179.32% -9.54%
2004 24.87% 8.99% 248.78% -1.41%
2005 15.44% 3.00% 302.63% 1.55%
2006 22.37% 12.25% 392.71% 13.99%

As I've found many times before, the UPI is one of the best predictors of future performance.

This brings me to a secondary point. Many, including myself, are fond of stating that past GSD has a very high correlation with future GSD. In other words, GSD does a great job of predicting itself. But how exactly does this help the investor. Can you actually use GSD to predict risk-adjusted return? Does past GSD tell you anything about which is the best investment to employ in the future?

Absolutely not!

Here are the results using GSD to select the ETFs to invest in for the next quarter:
Based On     Sort       ROI     CAGR    GSD   Sharpe  Ulcer Index  Drawdown  Signal  Stock
GSD Ascending 34.72% 3.88% 1.52 0.29 0.44% -1.96% 94% 93%
GSD Descending -25.47% -3.68% 27.08 -0.2 40.22% -56.73% 59% 73%

Certainly an ascending GSD enables you to have a very high win ratio -- 94% and produce a very low forward GSD of just 1.52 -- amazing! Yet, when it comes to what every investor is really looking for -- risk adjusted return -- it provides you with nothing. You'd be better off investing in a CD or some other fixed safe investment.

The real question every investor wants answered is what data from the past can help me most in choosing an investment for the future. GSD does not answer this question. It is true that it has the highest correlation with itself past to present, but this information provides us with nothing useable for our investing. What we want is to predict the best investment based on risk adjusted return, not just the standard deviation of the returns. In order to gain the former we need to rely on one of four measures -- Ulcer Performance Index, Upside Potential Ratio, Sortino, or the Sharpe.

It is very possible that I could take the returns of all the various ETFs using the Superior Six methodology and plug them into the Excel Solver and produce a return that beats what I've shown above, but this is optimizing history in hindsight, and cannot be compared to a method such as WWL which has a much higher probability of continuing to work in the future.

For the curious, here are all the various measures that I tried using both Ascending and Descending final sorts:
        Based On            Sort       ROI      CAGR    GSD   Sharpe  Ulcer Index  Drawdown
Ulcer Performance Index Descending 392.65% 22.58% 9.42 1.85 0.98% -6.80%
Sortino Descending 335.82% 20.67% 9.82 1.69 1.45% -7.66%
Sharpe Descending 317.67% 20.02% 10.05 1.57 1.40% -7.66%
Alpha Descending 248.36% 17.27% 15.46 0.91 6.99% -19.95%
Jensen Descending 248.36% 17.27% 15.46 0.91 6.99% -19.95%
Sharpe Ascending 204.80% 15.29% 16.5 0.76 4.16% -14.42%
Correlation Ascending 177.19% 13.90% 10.2 1 3.25% -16.47%
Sortino Ascending 162.59% 13.12% 14.83 0.68 3.15% -11.61%
GSD Ratio Descending 159.82% 12.96% 5.01 1.73 0.42% -3.94%
Treynor Descending 135.14% 11.53% 9.28 0.86 2.60% -11.59%
CAGR/SF Descending 124.23% 10.86% 3.38 2.13 0.24% -2.10%
CAGR/UI Descending 124.23% 10.86% 3.38 2.13 0.24% -2.10%
Upside Potential Ratio Ascending 123.99% 10.84% 19.21 0.48 9.07% -20.34%
Treynor Ascending 122.37% 10.74% 11.87 0.6 8.01% -21.11%
Ulcer Performance Index Ascending 101.06% 9.33% 6.71 0.69 1.22% -8.89%
CAGR/GSD Descending 91.64% 8.66% 2.55 2.08 0.24% -1.68%
Correlation Descending 69.13% 6.94% 11.45 0.32 15.82% -36.62%
Upside Potential Ascending 59.67% 6.16% 7.62 0.35 2.64% -13.58%
Upside Potential Ratio Descending 50.41% 5.35% 6.43 0.27 2.49% -13.58%
Downside Deviation Ascending 49.28% 5.25% 6.55 0.26 2.56% -13.58%
Sleep Ratio Ascending 40.22% 4.41% 1.25 0.62 0.10% -1.00%
Ulcer Index Ascending 40.22% 4.41% 1.25 0.62 0.10% -1.00%
GSD Ascending 34.72% 3.88% 1.52 0.29 0.44% -1.96%
Beta Descending 15.40% 1.85% 17.3 -0.01 34.73% -59.07%
CAGR/UPI Ascending 8.92% 1.10% 9.86 -0.17 20.08% -37.37%
CAGR/UPI Descending -0.04% -0.01% 9.73 -0.37 11.17% -30.05%
Upside Potential Descending -4.34% -0.56% 32.66 -0.02 49.04% -72.27%
Alpha Ascending -14.88% -2.04% 27.31 -0.11 54.86% -74.57%
Jensen Ascending -14.88% -2.04% 27.31 -0.11 54.86% -74.57%
Beta Ascending -19.42% -2.72% 23.54 -0.19 49.28% -71.03%
GSD Descending -25.47% -3.68% 27.08 -0.2 40.22% -56.73%
Downside Deviation Descending -53.47% -9.31% 32.04 -0.35 65.78% -84.60%
GSD Ratio Ascending -62.41% -11.74% 26.2 -0.53 62.13% -78.50%
Sleep Ratio Descending -62.41% -11.74% 26.2 -0.53 62.13% -78.50%
Ulcer Index Descending -70.13% -14.29% 28.24 -0.67 67.24% -81.34%
CAGR/GSD Ascending -71.52% -14.82% 25.69 -0.76 65.46% -77.57%
CAGR/SF Ascending -71.52% -14.82% 25.69 -0.76 65.46% -77.57%
CAGR/UI Ascending -71.52% -14.82% 25.69 -0.76 65.46% -77.57%
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