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Author: spazz7 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 252528  
Subject: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 10:28 AM
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Starting is message http://boards.fool.com/Message.asp?mid=26810031, fred04 indicated the positive results of switching between the YEY screen and the EG screen based on the crossover of the 200 day moving average of the SP500. The switch return of 40% was significantly higher than the individual screen returns of 33 and 29%.

Later, in post http://boards.fool.com/Message.asp?mid=26812041, Zeelotes completed a more extensive analysis of this switch. His work had a switch based on short and long EMA's on the SP500. One other change from fred04's work was that Zeelotes used a 10 stock hold, where fred04's was 5.

Zeelotes made a statement which I'd like to address later in the post. Specifically, said 'No matter what EMA levels you choose all of them beat out holding these two individually'. From a sharpe perspective, I'll go about to prove this wrong.

It's probably obvious from my introduction as well as my subject title, but the intention of my work is to see if this positive result will hold up to multi start date testing via the GTR1 backtester.

For clarification and completeness, the following are statements comparing my analysis to Zeelotes. For the most part, I believe the work I completed is almost identical to Zeelotes, except for:
1. I used the daily returns for a 10 stock hold, 21 cycle, 21 day hold screen from Jamie's GTR1 backtester. I believe Zeelotes used a 10 stock, single cycle, monthly returns/stock picks from Jamie's monthly backtester
2. My results are an average of these 21 starts
3. My results contain returns up to Dec 31 2007, as Zeelotes went to March of 2008. The impact of this difference should be minimal.

Before I display the results, I'll state a quick executive summary:
1. From a pure Sharpe perspective, this switch idea is torpedoed when using all start dates.
2. My highest EMA switch CAGR of 34.2% is not much higher than Zee's lowest EMA swithc CAGR of 31.17%, and doesn't even come close to his highest switch return of 41.49%.
3. Although it could be said that the switch CAGR's are categorically higher than the individual screens, it must be added that the switch Sharpe's are categorically lower than YEY's.
4. Reversing the screens (where YEY is the high screen and EG the low screen), deteriotes the sharpe's minimally. (due to size, I won't display the results that back up this statement). It should follow that if the switch truly increased performance above the performance of the individual screens, then the reverse strategy should be the opposite. It doesn't.
5. A 50/50 blend of these two screens would have provided a larger sharpe, lower ulcer index and lower maxDrawDown (DD) than any one my 156 EMA switch tests.
5. One's optimal play, at least historically, would have been to blend the two screens, with a blend of 11% EG, 89% YEY, which gives a Sharpe of 1.403

What follows are the matrices of the relevant metrics. I've bolded the high and lows for the respective group. The rows are the shorter EMA levels, and the columns are longer EMA levels. At the very bottom is return metrics for differing blend percentages.

Lance

                 150        155        160        170        180        190        200        210        220        230        240        250
CAGR 20 32.2% 32.3% 32.4% 32.7% 33.2% 33.8% 34.1% 34.1% 34.1% 34.2% 34.2% 34.1%
25 32.2% 32.3% 32.6% 33.0% 33.7% 34.1% 34.1% 34.0% 34.0% 33.9% 33.6% 33.4%
30 32.4% 32.6% 32.8% 33.6% 34.0% 34.0% 34.0% 33.9% 33.6% 33.3% 33.3% 33.2%
35 32.7% 32.9% 33.4% 33.9% 33.9% 33.9% 33.7% 33.5% 33.2% 33.1% 33.2% 33.0%
40 33.1% 33.7% 33.8% 33.9% 33.8% 33.6% 33.3% 33.1% 33.1% 32.9% 32.7% 32.6%
45 33.7% 33.7% 33.7% 33.7% 33.4% 33.2% 33.0% 33.0% 32.8% 32.5% 32.5% 32.2%
50 33.6% 33.5% 33.5% 33.4% 33.1% 33.0% 32.8% 32.5% 32.5% 32.3% 31.7% 31.6%
55 33.4% 33.4% 33.4% 33.1% 32.9% 32.7% 32.3% 32.3% 32.3% 31.7% 31.6% 31.5%
60 33.4% 33.2% 33.2% 32.9% 32.6% 32.3% 32.3% 32.3% 31.6% 31.5% 31.4% 31.4%
65 33.1% 33.1% 32.8% 32.6% 32.3% 32.3% 32.2% 31.6% 31.5% 31.3% 31.3% 31.4%
70 32.9% 32.7% 32.5% 32.3% 32.2% 32.1% 31.6% 31.5% 31.3% 31.3% 31.4% 31.4%
75 32.5% 32.4% 32.3% 32.2% 32.1% 31.6% 31.6% 31.4% 31.3% 31.3% 31.4% 31.5%
80 32.4% 32.3% 32.2% 32.2% 31.6% 31.5% 31.4% 31.3% 31.3% 31.4% 31.4% 31.5%

150 155 160 170 180 190 200 210 220 230 240 250
GSD 20 32.2% 32.3% 32.3% 32.3% 32.4% 32.5% 32.5% 32.6% 32.7% 32.7% 32.8% 32.9%
25 32.3% 32.3% 32.3% 32.4% 32.5% 32.6% 32.6% 32.7% 32.8% 32.8% 33.0% 33.1%
30 32.4% 32.4% 32.5% 32.6% 32.6% 32.7% 32.8% 32.8% 32.9% 33.1% 33.1% 33.1%
35 32.5% 32.5% 32.6% 32.6% 32.7% 32.8% 32.9% 32.9% 33.1% 33.1% 33.1% 33.2%
40 32.6% 32.6% 32.7% 32.7% 32.8% 32.9% 33.0% 33.1% 33.1% 33.2% 33.2% 33.3%
45 32.7% 32.7% 32.7% 32.9% 32.9% 33.1% 33.1% 33.2% 33.2% 33.3% 33.3% 33.4%
50 32.7% 32.8% 32.9% 33.0% 33.1% 33.1% 33.2% 33.2% 33.3% 33.3% 33.5% 33.6%
55 32.9% 32.9% 32.9% 33.1% 33.1% 33.2% 33.2% 33.3% 33.3% 33.5% 33.5% 33.6%
60 33.0% 33.0% 33.1% 33.1% 33.2% 33.3% 33.3% 33.3% 33.5% 33.5% 33.6% 33.6%
65 33.1% 33.1% 33.1% 33.2% 33.2% 33.3% 33.3% 33.5% 33.5% 33.6% 33.6% 33.7%
70 33.1% 33.2% 33.2% 33.2% 33.3% 33.3% 33.5% 33.5% 33.6% 33.6% 33.6% 33.7%
75 33.2% 33.2% 33.2% 33.3% 33.3% 33.5% 33.5% 33.6% 33.6% 33.6% 33.7% 33.7%
80 33.2% 33.3% 33.3% 33.3% 33.5% 33.5% 33.6% 33.6% 33.6% 33.7% 33.7% 33.7%

150 155 160 170 180 190 200 210 220 230 240 250
Ulcer 20 12.7% 12.7% 12.7% 12.7% 12.6% 12.6% 12.6% 12.6% 12.7% 12.6% 12.6% 12.7%
25 12.7% 12.7% 12.7% 12.6% 12.6% 12.6% 12.6% 12.7% 12.7% 12.7% 12.8% 12.8%
30 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.7% 12.7% 12.8% 12.9% 12.9% 12.9%
35 12.7% 12.6% 12.6% 12.6% 12.7% 12.7% 12.8% 12.8% 12.9% 12.9% 12.9% 12.9%
40 12.7% 12.6% 12.6% 12.7% 12.7% 12.7% 12.8% 12.9% 12.9% 12.9% 13.1% 13.2%
45 12.6% 12.7% 12.7% 12.7% 12.8% 12.8% 12.9% 12.9% 13.0% 13.2% 13.3% 13.4%
50 12.7% 12.7% 12.8% 12.8% 12.9% 12.9% 13.0% 13.1% 13.2% 13.3% 13.6% 13.6%
55 12.7% 12.8% 12.8% 12.9% 12.9% 13.1% 13.2% 13.3% 13.3% 13.6% 13.6% 13.6%
60 12.8% 12.9% 12.8% 13.0% 13.1% 13.3% 13.3% 13.4% 13.6% 13.6% 13.7% 13.7%
65 12.8% 12.8% 13.0% 13.1% 13.3% 13.3% 13.4% 13.6% 13.6% 13.6% 13.7% 13.7%
70 12.9% 13.0% 13.1% 13.3% 13.3% 13.4% 13.6% 13.6% 13.6% 13.7% 13.7% 13.8%
75 13.1% 13.2% 13.3% 13.3% 13.4% 13.6% 13.6% 13.6% 13.7% 13.7% 13.8% 13.7%
80 13.2% 13.3% 13.3% 13.4% 13.6% 13.6% 13.6% 13.6% 13.7% 13.7% 13.7% 13.8%

150 155 160 170 180 190 200 210 220 230 240 250
maxDD 20 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3%
25 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.4% 46.4%
30 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.3% 46.4% 46.4% 46.4% 46.4% 46.4%
35 46.3% 46.3% 46.3% 46.3% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4%
40 46.3% 46.3% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.5%
45 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.5% 46.5% 46.7%
50 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.5% 46.5% 46.8% 46.8%
55 46.4% 46.4% 46.4% 46.4% 46.4% 46.4% 46.5% 46.5% 46.5% 46.8% 46.8% 46.8%
60 46.4% 46.4% 46.4% 46.4% 46.4% 46.5% 46.5% 46.5% 46.8% 46.8% 46.8% 47.2%
65 46.4% 46.4% 46.4% 46.4% 46.5% 46.5% 46.5% 46.8% 46.8% 46.8% 47.2% 47.3%
70 46.4% 46.4% 46.4% 46.5% 46.5% 46.5% 46.8% 46.8% 46.8% 47.2% 47.3% 47.9%
75 46.4% 46.4% 46.5% 46.5% 46.5% 46.7% 46.8% 46.8% 47.2% 47.3% 47.9% 48.2%
80 46.4% 46.5% 46.5% 46.5% 46.7% 46.8% 46.8% 47.1% 47.3% 47.5% 48.2% 48.6%

150 155 160 170 180 190 200 210 220 230 240 250
Sharpe 20 0.983 0.985 0.989 0.995 1.007 1.022 1.029 1.026 1.027 1.027 1.027 1.021
25 0.983 0.985 0.992 1.001 1.019 1.027 1.026 1.022 1.022 1.017 1.006 1.000
30 0.986 0.992 0.995 1.014 1.023 1.023 1.023 1.018 1.007 0.997 0.995 0.993
35 0.993 0.997 1.009 1.020 1.020 1.018 1.010 1.004 0.994 0.991 0.992 0.987
40 1.000 1.015 1.017 1.019 1.015 1.008 0.998 0.990 0.989 0.985 0.978 0.975
45 1.015 1.015 1.014 1.010 1.003 0.994 0.988 0.986 0.980 0.972 0.971 0.962
50 1.012 1.007 1.005 1.002 0.991 0.988 0.981 0.973 0.971 0.966 0.947 0.944
55 1.002 1.003 1.001 0.991 0.984 0.977 0.968 0.967 0.966 0.946 0.943 0.939
60 1.002 0.995 0.993 0.983 0.975 0.968 0.967 0.965 0.944 0.942 0.936 0.936
65 0.993 0.990 0.983 0.975 0.967 0.966 0.963 0.944 0.942 0.936 0.935 0.937
70 0.986 0.978 0.974 0.967 0.964 0.962 0.943 0.942 0.936 0.934 0.936 0.937
75 0.974 0.971 0.967 0.963 0.961 0.944 0.942 0.937 0.934 0.934 0.935 0.937
80 0.970 0.967 0.963 0.963 0.944 0.942 0.938 0.935 0.933 0.935 0.936 0.937


% EG  CAGR   GSD    MaxDD  Ulcer  Sharpe
0% 25.0% 14.7% 24.3% 5.5% 1.368
5% 25.4% 14.8% 24.2% 5.0% 1.393
10% 25.9% 15.0% 24.7% 4.7% 1.403
15% 26.3% 15.3% 25.2% 4.7% 1.400
20% 26.7% 15.8% 26.0% 4.9% 1.385
25% 27.0% 16.4% 26.7% 5.0% 1.360
30% 27.4% 17.2% 27.5% 5.3% 1.328
35% 27.7% 18.0% 28.3% 5.7% 1.291
40% 27.9% 19.0% 29.1% 6.1% 1.251
45% 28.2% 20.1% 30.0% 6.5% 1.210
50% 28.4% 21.2% 30.9% 7.1% 1.169
55% 28.6% 22.4% 32.1% 7.7% 1.129
60% 28.8% 23.7% 33.6% 8.5% 1.090
65% 29.0% 25.1% 35.7% 9.4% 1.053
70% 29.1% 26.5% 38.0% 10.4% 1.018
75% 29.2% 28.0% 40.7% 11.6% 0.984
80% 29.3% 29.5% 44.0% 13.0% 0.953
85% 29.3% 31.1% 47.7% 14.6% 0.923
90% 29.3% 32.8% 51.4% 16.4% 0.895
95% 29.3% 34.5% 55.0% 18.4% 0.869
100% 29.3% 36.2% 58.5% 20.5% 0.844
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Author: Zeelotes Big red star, 1000 posts Top Favorite Fools Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211116 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 10:45 AM
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Nice work Lance!

I pretty much came to the same conclusion myself since I posted that. I'm presently running a huge battery of tests with the aim of raising this whole subject to a whole new level. We'll see how that turns out.

BTW -- could you please post the dates in bullish and bearish periods for the 25 / 180 combination? Obviously, since these are run off of the S&P 500 whether you using daily starts or not they should remain exactly the same.

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Author: mungofitch Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Feste Award Winner! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211119 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 11:14 AM
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I wonder if here might be a more conservative way to go about this
which is more robust.

There is little doubt that bull and bear markets exist, and that different
screens are optimal in each case. So, here is an approach:

Pick a set of bull and bear market crossover dates from a chart.
This can be done with perfect hindsight, by hand---doesn't matter.
Though, ideally, it would be with a touch of lag, since no one knows
it's a bear until it starts if you're using technical indicators.
Build a blend of screens that do well overall, but do particularly well
in bull markets, and do the same for bear markets. A nice diverse
blend in each case---a few stocks from quite a few different screens.
Don't worry about overtuning, just get two blends, one of which is
full of bull market winners, and one full of bear market best-you-can-do.

Then, pick maybe four different very basic timing indicators for bull
versus bear. How much the S&P went up or down in the last month or three
might be one of them. I use one which is, how long since the index
crossed above a trendline which is the average of the (200-day high and
a 150-day SMA). Or, is that line rising or falling? Is the market above
its 200 day SMA? The VL 4% rule might be good. Whatever. All you need
is simple metrics which work pretty well most of the time---perfection is not needed.
Just pick things which give very few signals per year---under 1, ideally.

Then, much like QTAA, simply allocate 1/4 of your portfolio to each
of the four signals. If all are bullish, put all your money into the
bullish blend. If three are bullish, put 75% of your money in the
bullish blend and 25% in the bearish blend, etc.

Since all the screens do well on average, your risk is modest,
and you should benefit nicely on average. It doesn't really matter
if the individual signals are right or wrong at any given time, as
long as they work passably well on average. You can't be whipsawed,
since you're long at all times.

This could be done with more than 4 signals, of course. The fraction of
your portfolio in the bullish blend could be the percentage of bull/bear
indicators among dozens whcih are bullish on your rebalance day.
You could use 20 different crossovers or lookbacks that work on average,
which means you can avoid the entire issue of [over]tuning for the best one.
You could weight each subsignal by how good it is in backtest---the
magitude of the gap between CAGR's during its bull and bear periods in
the past---provided no individual signal is overtuned.

Jim

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Author: MainiacJoe Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211127 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 3:17 PM
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Lance,

Would you please share how you went about testing this at GTR1, that is, the mechanics of using the backtester. Like Zee I get the impression that Robbie has made it possible to directly test switch ideas with the GTR1 engine instead of massaging output files, but I havne't had the time to figure out how yet.

Thanks,

- Joe

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211133 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 5:26 PM
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Build a blend of screens that do well overall, but do particularly well
in bull markets, and do the same for bear markets. A nice diverse
blend in each case---a few stocks from quite a few different screens.
Don't worry about overtuning, just get two blends, one of which is
full of bull market winners, and one full of bear market best-you-can-do.



Jim,

If I understand you correctly, the screen selection would go something like this:

1. Select a pool of candidate screens that do reasonable well all of the time.
2. From this, select a subset of best screens for bull periods.
3. Similarly from the pool of screens selected in 1, select a subset of best screens for bear periods.
4. Figure out some method to switch between.

I like this logic, but it is not so easy to implement in real life. I tried doing this a few years ago. The issues I came up with were:

1. The pool of screens I trusted as "reasonably good" for all periods was pretty small.
2. I ended up with a lot of overlap between the bull and bear screens.
3. The backtested gain (relative to a blend) was not as much as I would like.
4. If you switch much, it messes up a HTD strategy for minimizing trading.

My final conclusion was just to construct the best blend I could; use HTD to minimize trading and stick with it through bull and bear.

I suppose I should say that I think the concept of a switch is OK, but it introduces the ability to do a good bit of extra tuning i.e.:

* The backtest of each half of the switch is cut approx in half so is less robust.
* You can tune by picking various indices and screens to switch on.
* You can tune the cut-off

All of this really means that the burden of stress testing the backtest is so much greater - i.e. it is that much more difficult to figure out if the backtest has predictive value.

StevnFool
Yes - a genuine Irishman. Born in Ireland and lived all my life here so far except for a few vacations.

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Author: mungofitch Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Feste Award Winner! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211137 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/16/2008 7:10 PM
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* The backtest of each half of the switch is cut approx in half so is less robust.
* You can tune by picking various indices and screens to switch on.
* You can tune the cut-off

All of this really means that the burden of stress testing the backtest is so much greater - i.e. it is that much more difficult to figure out if the backtest has predictive value.



Well, my thoughts were that you wanted to avoid much in the way of
backtest tuning at all. It's pretty easy to pick some blends just by
reputation: you're going to want things like RS26 and Screamers
in the bull periods, and YldEarnYear and ZLTDA in the bear periods.
It's pretty obvious once a bear is well under way (say, January
this year) that it's time to quit the momentum screens and think
about the dividend yield screens. So, if it's common sense, then
it can probably be usefully approximated in real life.

Doing it mechanically isn't hard, but it's circular: I'm using the
backtest results to pick what to use, then seeing how it works in
the backtest. Not so great for predictive value!

But taht never stopped me. I ranked all the VL screens by CAGR in bull
periods, CAGR in bear periods, and rolling-two-month downside deviation
calculated across all periods.

I figured rank(downdev)-rank(cagr-bull) would be a good way to find hot
stuff for bull markets with reasonable risk containment, and then use
rank(downdev)-rank(cagr-bear) for the bear periods.
In essence, I used a good rolling-2-month downside deviation across the
whole history as a proxy for a "good enough" screen. If it tends
not to lose money in two-month periods often, it's probably an OK
place for your money. (why 2 months? it reduces noise inherent in
only a few picks at a time, and eliminates problems the fact that a
lot of screens have positive or negative month-to-month correlations).

The funny thing is, the blend that this picks for the bear periods
works so well in the bull periods that you might as well use it
all the time and not bother switching!

Here's what it came up with.
For bear periods
8608BL(PIH_CSO_safe)13(YLDEARNYEAR)13(TVALUE)13(LPCF)13(ValueRatio)13(PIH_CSO_simple)13(YEYPayout)13(YLDYEAR)13(Fundamentals)13(PIH_MCP)13(LowPEsafe)13ps13
For bull periods
8608BL(PEG-Minimalist)13(Screamers)13qb13(TPEG13)13(PIH4)13(EG5_AT)13(AssRS26)13(CAPLOWEG)13(TREPPE_E)13(SLS_RS26)13(PLOW_PE2)13(RS2020)13

The bear screens backtest at around 35.2% overall, the bull screens
at about 37.8% overall, and the switch at around 41.1%.
That's using a simple "S&P above 12 month-end SMA" test.
For this purpose, the optimal is "above 6 month SMA", which ups it to 43%.
But, the bear blend is a steadier earner than the switch, and looking
at the equity curves, it's a much better and simpler choice!

Here are the bear blend returns.
1989   62.5
1990 -1.2
1991 76.7
1992 45.7
1993 45.2
1994 13.4
1995 55.3
1996 24.6
1997 48.7
1998 22.9
1999 43.7
2000 39.0
2001 101.4
2002 24.9
2003 40.3
2004 43.1
2005 44.6
2006 27.3
2007 33.8
2008 -2.9 (that's Q1 only--TTM is +22%)


Executive summary (one possible interpretation): if you can pick a
long-only blend that works in bear periods, it's probably an excellent
blend for bull periods too, so why bother with the switching?

Jim

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211151 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/17/2008 8:42 AM
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Executive summary (one possible interpretation): if you can pick a
long-only blend that works in bear periods, it's probably an excellent
blend for bull periods too, so why bother with the switching?

Jim


That was pretty much my conclusion.

StevnFool

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Author: MainiacJoe Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211153 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/17/2008 9:18 AM
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Executive summary (one possible interpretation): if you can pick a
long-only blend that works in bear periods, it's probably an excellent
blend for bull periods too, so why bother with the switching?


Because many of the screens that only do well during bull periods do really, really well during the bull periods. IOW, greed. Or more graciously put, wanting to avoid the opportunity cost of being in the bear-friendly blend during bull markets.

- Joe

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Author: mungofitch Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Feste Award Winner! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 211160 of 252528
Subject: Re: YEY/EG SP500 EMA Switch Torpedoed Date: 7/17/2008 11:28 AM
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IOW, greed.

Yup. I'm as guilty as anyone. Rather than using a sensible bear-friendly
blend at all times, I use a what's-working-lately approach that uses
trailing 2-month screen returns for the greed side, and long history of
rolling-2-month downside deviations for the safety side, with a coefficient on each.
I include the short screens, but not the SOS's.
Oddly enough, it works best with a small negative coefficient on
the long run CAGR of the screens---a way of avoiding the overtuned maybe?
It seems to have been pretty good this year. Had I followed it exactly
as designed, it would be up about 19% for the first half of this year.

Jim

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