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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 253566  
Subject: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 6:25 AM
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In the thread The Best Measure for the Best Blend it was suggested that I try testing using a revised Sharpe/GSD. This suggestion came from JeffLandon in post # 203950 and StevnFool in # 203972. I went ahead and had this programmed into my backtester such that I can now test the following:

CAGR / (GSD^x)
CAGR / (UI^x)
CAGR / (UPI^x)
Sharpe / (GSD^x)

x can be set to any value whether positive or negative. To illustrate, let me share a little table I put together that will hopefully make this simpler for those who are a bit challenged by all this -- like me. :)
Sharpe  GSD   Ratio  Parameter x                  Consequence
1.5 17.6 0.09 Default
1.5 17.6 6.29 -0.5 GSD Underweighted
1.5 17.6 3.07 -0.25 GSD Underweighted
1.5 17.6 1.50 0 GSD Underweighted -- Equal to Sharpe Alone
1.5 17.6 0.73 0.25 GSD Underweighted
1.5 17.6 0.36 0.5 GSD Underweighted
1.5 17.6 0.17 0.75 GSD Underweighted
1.5 17.6 0.09 1 Sharpe / GSD -- No Weighting
1.5 17.6 0.04 1.25 GSD Overweighted
1.5 17.6 0.02 1.5 GSD Overweighted
1.5 17.6 0.01 1.75 GSD Overweighted
1.5 17.6 0.00 2 GSD Overweighted
1.5 17.6 0.00 2.25 GSD Overweighted
1.5 17.6 0.00 2.5 GSD Overweighted
1.5 17.6 0.00 2.75 GSD Overweighted

Of course, when GSD is underweighted that means that Sharpe is overweighted and vice versa.

In the test I'm about to share I set it up with the following parameters:
Begin           01/03/1999
End 11/09/2007
Value Line 3 Screens
SIPRO 3 Screens
Ranks 1-4
Total Held 24
Sort Sharpe/(GSD^x)

So every year I invest in six screens -- three from VL and three from SIPRO. Each screen has ranks from one to four, resulting in a blend of 24 stocks in all.

The Results of the Backtest

These results show that there is little to no advantage to using this formula compared to just a default of Sharpe/GSD -- which is the 1.00 / 1.00 below. I'd guess the minor difference that there is isn't anything more than noise. The Parameter x on the left is the one for the Value Line screens while the one on the right is for the SIPRO sort.
Parameter x  Parameter x   CAGR    GSD   Sharpe  Ulcer Index
2.00 1.50 32.23% 15.65 1.75 4.25%
2.00 1.00 32.23% 15.65 1.75 4.25%
2.00 2.00 31.70% 15.5 1.73 4.50%
1.00 1.00 32.26% 15.88 1.73 4.69%
1.00 1.50 32.26% 15.88 1.73 4.69%
1.00 2.00 31.73% 15.74 1.71 5.08%
1.50 1.00 30.27% 15.22 1.69 4.19%
1.50 1.50 30.27% 15.22 1.69 4.19%
2.00 0.50 30.98% 15.79 1.67 4.31%
1.50 2.00 29.78% 15.09 1.67 4.41%
0.50 1.50 31.15% 16.15 1.65 5.04%
1.00 0.50 31.03% 16.06 1.65 4.76%
0.50 1.00 31.15% 16.15 1.65 5.04%
0.00 1.50 31.97% 16.89 1.63 5.48%
0.00 1.00 31.97% 16.89 1.63 5.48%
0.50 2.00 30.60% 16.01 1.63 5.53%
-0.50 1.00 37.49% 20.47 1.61 7.19%
-0.50 1.50 37.49% 20.47 1.61 7.19%
0.00 2.00 31.43% 16.76 1.61 5.90%
1.50 0.50 29.03% 15.37 1.6 4.26%
-0.50 2.00 36.86% 20.41 1.59 7.78%
0.50 0.50 29.94% 16.38 1.57 5.16%
0.00 0.50 30.76% 17.13 1.55 5.60%
-0.50 0.50 36.27% 20.85 1.54 7.34%
1.00 0.00 32.02% 20.49 1.4 5.96%
2.00 0.00 31.58% 20.12 1.4 5.99%
-0.50 0.00 37.50% 25.2 1.38 8.31%
0.00 0.00 32.20% 21.61 1.35 7.34%
0.50 0.00 31.31% 20.78 1.35 6.10%
1.50 0.00 29.66% 19.86 1.33 6.02%
-0.50 -0.50 27.80% 30.46 0.92 14.72%
2.00 -0.50 22.60% 24.08 0.89 12.25%
1.00 -0.50 23.07% 24.75 0.89 12.27%
0.50 -0.50 21.87% 25.18 0.84 13.00%
0.00 -0.50 22.62% 26.01 0.84 15.77%
1.50 -0.50 21.08% 23.86 0.83 12.11%

An Alternative Look

Just to be sure, I also did another test.
Begin           01/03/1989
End 11/09/2007
Value Line 5 Screens
Ranks 1-4
Total Held 20
Sort Sharpe/(GSD^x)

Parameter x   CAGR    GSD   Sharpe  Ulcer Index
0.25 33.68% 17.78 1.57 6.35%
0.00 34.20% 19.85 1.46 8.06%
1.00 27.32% 15.34 1.45 4.96%
2.00 26.10% 14.47 1.45 4.90%
1.75 26.23% 14.66 1.44 4.92%
1.50 26.22% 14.83 1.43 4.97%
0.50 28.57% 16.26 1.43 6.32%
0.75 27.31% 15.84 1.41 5.05%
1.25 26.26% 15.14 1.4 5.13%
-0.25 32.03% 21.85 1.27 10.14%
-0.50 33.61% 27.13 1.14 12.54%

I don't see a mound of toast in this data, but it may be my eyes are a bit blurred at this point in the game. Let me know what the proposers think of these results.
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Author: klouche Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203986 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 1:13 PM
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I don't see a mound of toast in this data, but it may be my eyes are a bit blurred at this point in the game. Let me know what the proposers think of these results.

On the Valueline only I get correlations below:


Param x CAGR GSD Sharpe Ulcer Index
-0.5 33.61% 27.13 1.14 12.54%
-0.25 32.03% 21.85 1.27 10.14%
0 34.20% 19.85 1.46 8.06%
0.25 33.68% 17.78 1.57 6.35%
0.5 28.57% 16.26 1.43 6.32%
0.75 27.31% 15.84 1.41 5.05%
1 27.32% 15.34 1.45 4.96%
1.25 26.26% 15.14 1.4 5.13%
1.5 26.22% 14.83 1.43 4.97%
1.75 26.23% 14.66 1.44 4.92%
2 26.10% 14.47 1.45 4.90%


Correlations
CAGR GSD Sharpe Ulcer Index
Param x (0.89) (0.86) 0.49 (0.85)
CAGR 0.81 (0.25) 0.78
GSD (0.77) 0.99
Sharpe (0.79)


Looks like not much variation with parameter .75 to 2.

The correlation between GSD and Ulcer is near perfect.

KL

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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: 203988 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 3:04 PM
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Zee,

Thanks for doing this. You indicate that your first test started in 1999. Did you mean 1989?

I don't believe there is evidence here to suggest that any other value is superior to the default value of 1.00. It is interesting that in terms of resulting Sharpe, using Sharpe/GSD (X = 1) instead of Sharpe (X = 0) seems to help when there are SIPRO screens in the mix, but has little impact on resulting Sharpe when limited to Valueline screens. It does result is a lower GSD though which is not a bad thing.

My vote would be to stick with Sharpe/GSD (X=1). I'm not sure how much better it is as a predictor over Sharpe alone, but your results would suggest that it is not any worse.

StevnFool

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203990 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 5:00 PM
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Parameter x CAGR GSD Sharpe Ulcer Index
0.25 33.68% 17.78 1.57 6.35%
0.00 34.20% 19.85 1.46 8.06%
1.00 27.32% 15.34 1.45 4.96%


This indicates no difference between using the Sharpe ratio and using Sharpe/GSD to rank screens. (And there's an odd outlier at Sharpe/GSD^.25).

In message 203942 you presented the following table -


But our goal is risk-adjusted return, not raw return, so what is the best measure for finding the highest Sharpe Ratio?


Well, you'll be surprised to learn that what is at the absolute bottom of the list above, comes out at the absolute top of the list for risk-adjusted return -- StevnFool's Sharpe/GSD. BTW -- I just added this measure to my backtester after he suggested it yesterday. As a result I had to run a special test just for that indicator and add it to all my other tests.


Sharpe Minimum Maximum Median Average
Sharpe/GSD 1.25 1.67 1.62 1.58
Treynor 1.38 1.62 1.54 1.52
UPR 0.16 1.62 1.47 1.33
Sortino 1.02 1.45 1.37 1.36
CAGR/GSD 0.98 1.58 1.34 1.33
Sharpe 1.03 1.45 1.33 1.34
...



Can you explain the difference between the two results?

Elan

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Author: JeffLandon One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203993 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 6:21 PM
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I always thought that the ultimate goal was to increase CAGR, not Sharpe. I thought people shot for high Sharpe because they thought that was how to get high CAGR. "Can't predict CAGR, but maybe we can predict Sharpe, so maybe we should aim for that."

I agree it would be silly to aim for high arithmetic mean return. But isn't a high geometric mean the absolute ultimate final goal to measure by? The way you know you won?

If we're aiming for high CAGR, the study looks a bit different.

And if you're not aiming for high CAGR, why aren't you? If your answer is "pain" or "short time horizon," well, you're already investing in a manner than can cause great pain. I want a better answer.

At this point, what do you think you can predict, and how confident are you? CAGR? Sharpe? GSD? Anything?

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Author: ilmostro Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203994 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 6:54 PM
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At this point, what do you think you can predict, and how confident are you? CAGR? Sharpe? GSD? Anything?

I predict that there will always be those that want high CAGR but fail to realize it won't be a smooth road.

That and that the Cowboys will be in their record 9th SuperBowl this year. ;-)

Bryan

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Author: JeffLandon One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203995 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 7:09 PM
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<blockquote>At this point, what do you think you can predict, and how confident are you? CAGR? Sharpe? GSD? Anything?

I predict that there will always be those that want high CAGR but fail to realize it won't be a smooth road.

That and that the Cowboys will be in their record 9th SuperBowl this year. ;-)

Bryan</blockquote>

I suspect that people looking for low GSD could be more mortified than people looking for a high cagr.

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203996 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 7:13 PM
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I always thought that the ultimate goal was to increase CAGR, not Sharpe. I thought people shot for high Sharpe because they thought that was how to get high CAGR. "Can't predict CAGR, but maybe we can predict Sharpe, so maybe we should aim for that."

I agree it would be silly to aim for high arithmetic mean return. But isn't a high geometric mean the absolute ultimate final goal to measure by? The way you know you won?

If we're aiming for high CAGR, the study looks a bit different.

And if you're not aiming for high CAGR, why aren't you? If your answer is "pain" or "short time horizon," well, you're already investing in a manner than can cause great pain. I want a better answer.

At this point, what do you think you can predict, and how confident are you? CAGR? Sharpe? GSD? Anything?


Retrospectively we all want high CAGR and nothing else matters. Prospectively we have to understand that we're only dealing with probabilities. We can't dial in a desired future CAGR and get it. So the name of the game is to maximize your expected return, not some illusion about absolute return. And since, for most people, the pain of potential underperformance is greater than the gain of potential outperformance, a goal that involves reduced risk is perfectly rational.

Think of it this way - even if a backtest was a perfect prediction of future behavior, it could only give us a mean expectation and some wide distribution around that mean. Through all possible future paths of a screen's return, there are many that would be undesireable, and you want to do something to avoid them if you can, even if you have to forego some of the potential CAGR.

Elan

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Author: JeffLandon One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203997 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 7:30 PM
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Elan,

I understand your point.

But I'm beginning to wonder if perhaps aiming for high CAGR is actually safer than aiming for high Sharpe. If it's just probabilities we're aiming at, maybe we need the extra cagr to actually outperform.

After all, again, optimizing for CAGR is already optimizing for smoothing returns out, as CAGR does best when absolute returns vary least.

Just thinking out loud here. I figure we're bad at predicting any of these measures. We're going to miss by wide margins, so we need extra room for slop.


An aside:

Optimizing for Sharpe lets the screen do relatively poorly when risk-free returns are low. That doesn't help your long-term results. Sharpe is looking for excess returns. Optimizing for CAGR is, in theory, superior in the sense that it forces the screen to be uncorrelated to the return of risk-free returns--it wants great absolute returns.

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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 203998 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 7:46 PM
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Elan asked:
Can you explain the difference between the two results?

The test in this thread is based on ranks 1-4, while the test in the previous thread is off of ranks 1-10. I purposefully chose a lookback of 20 years for this test because the Sharpe and Sharpe/GSD had the exact same resulting Sharpe from the backtests. I wanted to put them on an even footing. Here is a table showing Ranks 1-10 as I posted before with Ranks 1-4 on the right side for comparison.
Ranks 1-10                                       Ranks 1-4               
Sharpe Jensen Sharpe Sharpe/GSD Treynor Sharpe Sharpe Sharpe/GSD
1 0.94 1.26 1.67 1.39 1 0.91 1.24
3 0.96 1.03 1.25 1.38 3 0.97 1.07
5 0.99 1.39 1.65 1.39 5 1.32 1.53
7 1.00 1.32 1.61 1.45 7 1.17 1.38
9 1.18 1.34 1.51 1.62 9 1.24 1.47
11 1.17 1.42 1.57 1.60 11 1.26 1.35
13 1.21 1.45 1.53 1.57 13 1.36 1.29
15 1.21 1.42 1.51 1.57 15 1.37 1.40
17 1.22 1.38 1.62 1.50 17 1.44 1.40
19 1.16 1.37 1.62 1.54 19 1.44 1.44
21 1.19 1.33 1.63 1.60 21 1.35 1.45
23 1.19 1.33 1.63 1.54 23 1.35 1.45
25 1.19 1.33 1.63 1.58 25 1.35 1.45
27 1.16 1.33 1.63 1.52 27 1.35 1.45
29 1.16 1.33 1.63 1.59 29 1.35 1.45

StevnFool asked:
You indicate that your first test started in 1999. Did you mean 1989?

No, it has to start in 1999 to put VL and SIPRO on a more or less even footing. Remember, this is investing in six screens with three from each.

My vote would be to stick with Sharpe/GSD (X=1). I'm not sure how much better it is as a predictor over Sharpe alone, but your results would suggest that it is not any worse.

I see it as better mainly because it consistently results in a much lower GSD. Let me illustrate:
  Years   Ranks 1-10              Ranks 1-4       
Lookback Sharpe Sharpe/GSD Sharpe Sharpe/GSD
1 29.78 16.42 21.20 10.91
3 27.80 20.73 22.14 13.16
5 22.46 14.58 16.05 9.75
7 20.25 15.17 16.52 9.82
9 19.91 14.54 18.03 9.84
11 20.17 15.11 16.56 9.71
13 19.81 15.23 16.89 10.06
15 19.66 15.47 16.67 10.01
17 19.72 15.40 16.49 10.00
19 19.72 15.48 16.19 10.06
21 20.29 15.34 16.33 10.09
23 20.29 15.34 16.33 10.09
25 20.29 15.34 16.33 10.09
27 20.29 15.34 16.33 10.09
29 20.29 15.34 16.33 10.09

Average 21.38 15.66 17.23 10.25
Median 20.29 15.34 16.49 10.06
StDev 3.10 1.47 1.87 0.85

Note how the standard deviation across all lookbacks is half in both rank cases between Sharpe and Sharpe/GSD. Also take note of the fact that the Median and Average GSD is about 40% lower for Ranks 1-4. I consider a GSD at or around 10 to be a significant lure.

The same thing as above on Sharpe -- here I'm seeing a 20% improvement in Sharpe/GSD over Sharpe alone on ranks 1-10, with a 7-8% improvement on ranks 1-4 -- which I'd just call noise if it wasn't for the ranks 1-10 results, and the results in GSD above.
  Years   Ranks 1-10              Ranks 1-4       
Lookback Sharpe Sharpe/GSD Sharpe Sharpe/GSD
1 1.26 1.67 0.91 1.24
3 1.03 1.25 0.97 1.07
5 1.39 1.65 1.32 1.53
7 1.32 1.61 1.17 1.38
9 1.34 1.51 1.24 1.47
11 1.42 1.57 1.26 1.35
13 1.45 1.53 1.36 1.29
15 1.42 1.51 1.37 1.40
17 1.38 1.62 1.44 1.40
19 1.37 1.62 1.44 1.44
21 1.33 1.63 1.35 1.45
23 1.33 1.63 1.35 1.45
25 1.33 1.63 1.35 1.45
27 1.33 1.63 1.35 1.45
29 1.33 1.63 1.35 1.45

Average 1.34 1.58 1.28 1.39
Median 1.33 1.62 1.35 1.44
StDev 0.10 0.10 0.16 0.11

Jeff asekd:
And if you're not aiming for high CAGR, why aren't you? If your answer is "pain" or "short time horizon," well, you're already investing in a manner than can cause great pain. I want a better answer.

It's really quite simple, CAGR is much less predictive than GSD -- in fact, there is no comparison. Consequently, I have a whole lot more confidence in the GSD side of the Sharpe equation staying pretty much static between the backtest and real-time results. I don't have anywhere near that level of confidence in the CAGR side. So when I find a backtest result with a relatively high CAGR, but extremely low GSD, and resulting high Sharpe, I prefer that over the other options. When you examine the yearly returns you also see a much higher degree of consistency. The Jensen, for example, tends to produce a very high CAGR, but a lot of that comes from three or four exceptional years.

This and what I've shown above is the reason why I'm grateful to have Sharpe/GSD as a new tool in my box -- thanks go to StevnFool for this!

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204000 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 7:52 PM
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But I'm beginning to wonder if perhaps aiming for high CAGR is actually safer than aiming for high Sharpe. If it's just probabilities we're aiming at, maybe we need the extra cagr to actually outperform.

That's why we have CAGR in the numerator of the Sharpe ratio. A high CAGR with a low level of uncertainty is what we're shooting for, and that is exactly the Sharpe ratio.

After all, again, optimizing for CAGR is already optimizing for smoothing returns out, as CAGR does best when absolute returns vary least.

No. A high CAGR is not necessarily a smooth CAGR. You're creating an incorrect rule by extending the fact that, given two series with equal average returns, the series with lower volatility will produce a higher CAGR.

Elan

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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204001 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 8:04 PM
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Jeff wrote:
After all, again, optimizing for CAGR is already optimizing for smoothing returns out, as CAGR does best when absolute returns vary least.

Elan replied:
No. A high CAGR is not necessarily a smooth CAGR. You're creating an incorrect rule by extending the fact that, given two series with equal average returns, the series with lower volatility will produce a higher CAGR.

That cannot be emphasized enough. A high CAGR is more often than not, far from smooth. When you compare the Jensen yearly returns with the Sharpe/GSD yearly returns you see a vast contrast -- the former is one bumpy, bumpy road.

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Author: sailrmac Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204003 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 8:28 PM
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Sharpe / GSD is roughly equivalent for ranking to CAGR / GSD squared. This means that GSD isn't just overweighted, it is heavily overweighted. Sticking some example numbers: CAGR = 30, GSD = 20 (20%)

CAGR / GSD squared = 30 / 20 * 20 = 30 / 400

When you are already overweighting GSD by this much vs. CAGR, it stands to reason a change in GSD doesn't effect the ranking result much.

One apple in a truckload of oranges or one apple in two truckloads of orange's ain't going to make the orange juice taste much different.

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Author: Syvash Two stars, 250 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204004 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 8:31 PM
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Zee,

Looking at your last table:

If you ignore the row with the Sharpe value of 1.57 then One would see a VALLEY of TOAST (min.) by ploting Sharpe vs. Ulcer Index.

Or the best choice would be the Ulcer Index at min. with Sharpe at almost max value.

Best

Syvash

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Author: sailrmac Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204005 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 8:32 PM
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Aiming for extra CAGR only helps if can stand the heat. Can you stay invested after losing 20% a year three years in a row when the market made money? (I can't)

Even if you can, you have a finite amount of money on the downside (which is the main reason the house makes money from craps). A 100% wipeout followed by a 300% gain, doesn't do you much good.

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Author: lsmr409 Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204007 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 9:00 PM
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Param x	CAGR	GSD	Sharpe	Ulcer Index
-0.5 33.61% 27.13 1.14 12.54%
-0.25 32.03% 21.85 1.27 10.14%
0 34.20% 19.85 1.46 8.06%
0.25 33.68% 17.78 1.57 6.35%
0.5 28.57% 16.26 1.43 6.32%
0.75 27.31% 15.84 1.41 5.05%
1 27.32% 15.34 1.45 4.96%
1.25 26.26% 15.14 1.4 5.13%
1.5 26.22% 14.83 1.43 4.97%
1.75 26.23% 14.66 1.44 4.92%
2 26.10% 14.47 1.45 4.90%
Hmm, with the data in the table that klouche presented, it looks as if the CAGR stays relatively constant from x = -0.5 to 0.25 while GSD decreases significantly. After 0.25, CAGR drops and then stays fairly constant, while GSD continues to decrease gradually. Why wouldn't we say that x = 0.25 is the best value for risk-adjusted return?

Todd

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Author: JeffLandon One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204008 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 9:20 PM
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1) Whether CAGR optimizes for smooth returns.

It does in this sense: When you write an optimizing backtester that looks for highest arithmetic mean, the results are much less even than when you write a backtester that optimizes for highest geomean. Bad years beat down CAGR unmercifully, at least compared to how arithmetic average is affected. (There is one interesting case where arithmetic is what you want--a young person who so far has little saved, but who is investing a fair amount monthly, can take advantage of volatility and is well served by optimizing for arithmetic average.)

2) Concerning the knowledge that GSD predicts GSD, but CAGR does not predict CAGR.

True. I never disputed that. But that's not my point at all. I agree that GSD is a better predictor of GSD than CAGR is of CAGR, but that doesn't mean something else doesn't predict CAGR.

Ever time you find a measuring stick, you should find out what it's good at measuring. Perhaps for some x, CAGR/(GSD^x) does turn out to be a good predictor of CAGR. By default, you're focusing on how it measures Sharpe.

Perhaps if you go back through all the screens pre- and post-discovery, you'll see that CAGR/(GSD*GSD) does predict CAGR. You'll never find what does because you've given up looking.

(And if you're convinced that you can't predict returns but only volatility, why are you even looking at Sharpe? You should only be interested in GSD if that's all you have a good handle on predicting.)

3) The idea that a measure which predicts CAGR would be good only for those who can stand the heat, and that pursuing such a path could lead to a 100% loss.

If a measure were to be found that predicts CAGR as well as GSD predicts GSD, would you still have this opinion? These high Sharpe screens can be very nearly as terrifying as the high cagr screens. And do you trust the prediction of the return portion of Sharpe? One is always served by some amount of distrust of these screens. That's where diversification and portfolio management come into play. Telling yourself you are safe because the backtested Sharpe is good can be very dangerous.

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204010 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 9:48 PM
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Elan asked:
Can you explain the difference between the two results?

The test in this thread is based on ranks 1-4, while the test in the previous thread is off of ranks 1-10. I purposefully chose a lookback of 20 years for this test because the Sharpe and Sharpe/GSD had the exact same resulting Sharpe from the backtests. I wanted to put them on an even footing. Here is a table showing Ranks 1-10 as I posted before with Ranks 1-4 on the right side for comparison.


Ranks 1-10 Ranks 1-4
Sharpe Jensen Sharpe Sharpe/GSD Treynor Sharpe Sharpe Sharpe/GSD
1 0.94 1.26 1.67 1.39 1 0.91 1.24
3 0.96 1.03 1.25 1.38 3 0.97 1.07
5 0.99 1.39 1.65 1.39 5 1.32 1.53
7 1.00 1.32 1.61 1.45 7 1.17 1.38
9 1.18 1.34 1.51 1.62 9 1.24 1.47
11 1.17 1.42 1.57 1.60 11 1.26 1.35
13 1.21 1.45 1.53 1.57 13 1.36 1.29
15 1.21 1.42 1.51 1.57 15 1.37 1.40
17 1.22 1.38 1.62 1.50 17 1.44 1.40
19 1.16 1.37 1.62 1.54 19 1.44 1.44
21 1.19 1.33 1.63 1.60 21 1.35 1.45
23 1.19 1.33 1.63 1.54 23 1.35 1.45
25 1.19 1.33 1.63 1.58 25 1.35 1.45
27 1.16 1.33 1.63 1.52 27 1.35 1.45
29 1.16 1.33 1.63 1.59 29 1.35 1.45



This demonstrates how easy it is to lie, or be misled, by statistics. I don't think you meant to lie or mislead. But by presenting only the 20 lookback for the 4 stock screens in the prior message, I thought you were saying there was no difference between ranking by Sharpe and ranking by Sharpe/GSD. I don't think that was the intended conclusion.

Elan

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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204012 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 11:01 PM
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I reran the 1999 to present test separating VL and SIPRO screens. The results are a bit more clear it seems to me. What I'm seeing here is that a standard Sharpe/GSD is still optimal -- any slight rise above this at higher values is not sufficient to warrant adopting a higher weighting of the GSD.
VL Screens                                
Parameter x CAGR GSD Sharpe Ulcer Index
-0.5 3.34% 39.93 0.16 44.42%
-0.25 14.05% 30.42 0.49 13.21%
0 19.64% 29.3 0.7 8.36%
0.25 25.15% 21.77 1.05 5.65%
0.5 19.75% 16.15 1.04 5.23%
0.75 20.09% 16.42 1.05 5.28%
1 22.36% 15.99 1.19 4.76%
1.25 22.36% 15.99 1.19 4.76%
1.5 22.36% 15.99 1.19 4.76%
1.75 22.94% 15.97 1.23 4.74%
2 21.08% 15.62 1.14 5.47%

SI Screens                                     
Parameter x CAGR GSD Sharpe Ulcer Index
-0.5 46.40% 32.27 1.38 13.74%
-0.25 38.27% 24.91 1.41 10.48%
0 39.89% 23.45 1.53 9.13%
0.25 39.32% 22.09 1.58 7.62%
0.5 38.47% 21.96 1.56 7.79%
0.75 40.55% 21.42 1.67 7.02%
1 40.96% 21.08 1.7 6.85%
1.25 42.11% 20.84 1.76 6.48%
1.5 36.66% 19.62 1.63 6.09%
1.75 40.58% 20.19 1.75 6.04%
2 40.58% 20.19 1.75 6.04%
2.25 38.58% 18.97 1.76 5.89%
2.5 36.40% 18.87 1.67 5.92%
2.75 34.56% 18.61 1.61 6.21%
3 33.62% 18.38 1.59 6.22%


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Author: TGMark Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204013 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 11:04 PM
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I'm in the middle of Taleb's book Fooled by Randomness. Unfortunately, that means that not only does this thread seem like noise, so does this board and my whole investing foundation. Eh, philosophy will do that to you, I'll recover.

Earlier in the book, I felt OK. Everything is relative, and I think that this board is not fooled by randomness as much as the general public, or perhaps even many investment professionals. Over time, that should be an advantage.

However, he discusses backtesting, and not favorably. He mentions Tradestation and legions of data hounds searching for the optimum strategy. However, his treatment is a little shallow, from what I've read so far. Sure, tuning a backtest for a particular parameter value is a suspicious activity, obviously; whereas the simplicity of using a few fundamental parameters and a sort that takes advantage of past human behavior would seem qualitatively different. I also think the quality of our backtesters and datasets are better than what he's familiarized himself with. Of course, I could easily be wrong.

I agree it would be silly to aim for high arithmetic mean return.

Some time back I made these control charts of MI screens. They were made using, by definition, arithmetic averages. However, it is a difficult way of thinking, and doesn't translate into the normal metrics without assumptions about serial autocorrelation, or whatever.

But CAGR magnifies the noise, the random variation, especially for high volatility screens. You happen to get 5 months of great returns in a row, and your CAGR looks fantastic, and you attribute greatness to the screen. So I wonder if simpler statistics might have some value after all. Something like arithmetic average cycle return/GSD^x ;) ?

(Don't take anything I say about this book too seriously; I usually have to read things a couple times for them to make sense, if they ever do).


Mark

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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204015 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 11:09 PM
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Elan wrote:
This demonstrates how easy it is to lie, or be misled, by statistics. I don't think you meant to lie or mislead. But by presenting only the 20 lookback for the 4 stock screens in the prior message, I thought you were saying there was no difference between ranking by Sharpe and ranking by Sharpe/GSD. I don't think that was the intended conclusion.

The reason I set it to 20 was to avoid stacking the deck in favor of Sharpe/GSD, which is what would have resulted if I had set the lookback to the value that is optimal for Sharpe/GSD. Setting it to a value that produced an equal Sharpe, put the two on an equal footing.

The main point on Sharpe/GSD is that if you take the results of all the tests and sort by Sharpe, the first Sharpe-based result is at position #45 out of 285 tests. In other words, Sharpe is no where near as good as Sharpe/GSD, Treynor, UPR or Sortino, but the values get closer as you go down in that list.

What conclusions can we reach in your view based on the data presented to date?

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Author: Zeelotes Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204017 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/17/2007 11:41 PM
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Mark wrote:
However, he discusses backtesting, and not favorably. He mentions Tradestation and legions of data hounds searching for the optimum strategy. However, his treatment is a little shallow, from what I've read so far. Sure, tuning a backtest for a particular parameter value is a suspicious activity, obviously; whereas the simplicity of using a few fundamental parameters and a sort that takes advantage of past human behavior would seem qualitatively different. I also think the quality of our backtesters and datasets are better than what he's familiarized himself with. Of course, I could easily be wrong.

What he is talking about is the backtesting of Technical Analysis, not fundamental analysis which is primarily what we do here. It is not an apples to apples comparison. I 100% agree with the idea that TA and Tradestation (and other similar software) enable one to be fooled by randomness day in and day out. It is a lesson in futility trying to find indicators that work in that field IMO. I've been there, done that.

But one interesting thing is that it appears that Tradestation can now use fundamental data as well -- check this out:

And now, new for TradeStation 8.3, in addition to building technical strategies, you can build and back-test strategies based on fundamentals. Enhance your strategy back-testing power by incorporating fundamental data into your strategies. With all-new indicators, PaintBar studies, strategy components and over 900 historical fundamental reference data fields added, you have the tools you need to create and test strategies for whatever your trading needs require.

http://www.tradestation.com/strategy_testing/st_creation.shtm

Check out the list of available "historical" fundamental data by clicking on 900 historical fundamental reference data fields.

Anyone know the source of their fundamental data?

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Author: MoeBruin Big gold star, 5000 posts Top Favorite Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204029 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 12:10 PM
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JeffLondon,

I am in some ways pretty much with you here. If I am young and looking long term who cares what the volatility as long as you get the highest maximum CAGR. I can tell you personally I have taken hits on my portfolio that make most people shudder and to be honest it isn't that bad. The pain of those hits has been far less painful to me then where my portfolio is now. Of course if you get older and/or closer to actually needing the money then you have to watch out for a hit coming when you need the money.

That said here is why Zee and Elan are for the most part correct in my opinion. Having successfully used these screens for many years I can tell you one thing for sure the future predictive power of these screens is much less then you can imagine. Most of the great screens I started with myself and most people on this board won't touch today with one or two exceptions.

What people have discovered is that the volatility around a screen is a much better predictor then the CAGR but again I personally don't consider even that as perfect a predictor as most people. That is in part why Elan has stated your expectation have to be at beating the market not getting the past return on these screens. Otherwise you are bound be disappointed with your returns and will tend to pick screens that minimize not maximize your returns especially if the market collapses. This again is said from knowing the past experience of many people who have invested in MI.

So when you try to maximize for CAGR you are fooling yourself with these screens. You are maximizing on a mirage.

It is for these reasons that the strategy I use is two fold.

1) I invest in simple screens that have been around for ever and have worked for a very long time like a the RS26. 26 week return has been something that has been known to work for decades and has been backtested with VL data since the 60s.

2) I use a blend geared toward volatility.

One final note I can tell you is that Elan is basically the pioneer of actually using a blend in his portfolio. He has always blended in part for volatility although it may not have been totally intentional in the early years. He always blended for variety which did give him a volatility edge in the early years.

I can also tell you that that nobody I know on this board including myself (must say I don't know what Zee gets but I wouldn't bet against him) has had overall higher returns throughout the years.

There were some very famous poster on this board who ran portfolios trying to just maximize CAGRs. One did it to the nth degree possible (cherry picking) any possible backtested screen you could find. The other just kept switching each year to what he thought high fliers were for the coming year (without the blending tool we have today to help). The first of these portfolios over a fairly long period of time lost money and way underperformed the market. The other portfolio over a number years also did not beat the market.

Moe

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Author: MoeBruin Big gold star, 5000 posts Top Favorite Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204030 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 12:12 PM
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Zee or anyone else:

I have the original blender with December coming along can you or someone else make an updated blender available so that I can run these factors and others in looking at my 2008 blend.

Moe

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Author: JeffLandon One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204032 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 3:24 PM
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Moe,

I simply point out that every time you explore a function that you haven't looked at before (say, CAGR/GSD^x), you have the opportunity to see what it might be good at measuring.

I still have not been convinced that shooting for high Sharpe is somehow safer than shooting for high CAGR, if we had a way to predict CAGR that rivaled how well we can predict GSD).

Note that's NOT the same as chasing screens with high CAGRs historically--we know that CAGR is a relatively poor predictor of CAGR. Some people seem to think I would like to chase screens with high historical CAGR when I'm saying that I would like to chase high future CAGR.

If I could predict CAGR as well as I could predict GSD, I'd go for the CAGR, not GSD or Sharpe. I realize we don't have such a tool now. That's why I'm saying, "When you pick up a new tool, don't always assume it's a hammer. try it out. See what it's good for."

My strategies are of many types. Many are low in GSD. I'm not talking about wise current practice given what we know, I'm talking about how we think about research.

Jeff

---

A Question (for anyone, not just Moe)

There were screens that acted great for 30 years until they hit 2000. Is there a way to know that some market event WON'T pick on low GSD screens catastrophically? Might it be worth diversifying among screens with a wide range of GSDs?

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204035 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 4:51 PM
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What conclusions can we reach in your view based on the data presented to date?

I accept the conclusion that Sharpe/GSD may be the best selection metric.

The reason for my comments was the sequence of your posts. In one, you presented data the led to that conclusion. In a subsequent message you presented selective data that appeared to contradict that conclusion, and it confused me.

Elan

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Author: elann Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204038 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 5:23 PM
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Sharpe / GSD is roughly equivalent for ranking to CAGR / GSD squared. This means that GSD isn't just overweighted, it is heavily overweighted. Sticking some example numbers: CAGR = 30, GSD = 20 (20%)

CAGR / GSD squared = 30 / 20 * 20 = 30 / 400

When you are already overweighting GSD by this much vs. CAGR, it stands to reason a change in GSD doesn't effect the ranking result much.


You've got your units wrong. I think it's more like -

CAGR / GSD squared = 1.30 / 1.20 * 1.20 = 1.30 / 1.44

Elan

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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: 204040 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 5:57 PM
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Jeff,

Forgive me if you know this already, but I am not sure if you fully understand the logic behind the Sharpe Ratio.

First, I assume you appreciate that for any strategy, you can increase or decrease the CAGR and GSD by adjusting your leverage (cash or margin).

The Sharpe Ratio was constructed in such a way (with one simplification - i.e. that the interest paid for margin is the same as the interest received for cash) that irrespective of the leverage employed on a given strategy, the Sharpe Ratio remains the same.

If you feel there is a max level of volatility that you can live with - say a GSD of 20 - then the way to maximize your CAGR is to find the strategy with the highest Sharpe Ratio and adjust the leverage to give you a GSD of 20.

I hope I have explained this sufficiently well that you can see that maximizing Sharpe is the best way to realise your goal of maximizing CAGR within your volatility tolerance.

StevnFool

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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: 204041 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 6:09 PM
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You've got your units wrong. I think it's more like -

CAGR / GSD squared = 1.30 / 1.20 * 1.20 = 1.30 / 1.44

Elan


Elan,

I am not sure if you are correct. Certainly for Sharpe/GSD, the GSD value in the above example would be 20 and not 1.20.

To confirm how Zeelotes calculates the Sharpe/GSD ratio, look at the first table in the first post in this thread.

StevnFool

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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: 204043 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 6:25 PM
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What conclusions can we reach in your view based on the data presented to date?

Zee,

I think you have made a compelling case that Sharpe/GSD is more predictive of future Sharpe than Sharpe. The additional data that you have posted since your initial post in the thread have helped confirm this in my mind.

In relation to Treynor, I don't know enough about it to comment. An advantage of Sharpe/GSD is that the public backtesters tend to spit out the data needed to calculate it easily.

Back to the prediction of the Sharpe Ratio of a future blend. Lets say you choose to use Sharpe/GSD as your metric to select your blend. Have you done any testing to indicate which of the following methodologies is more predictive of future Sharpe.

1) Optimizing to select a blend with max value of past Sharpe/GSD.

2) Sorting all screens by past Sharpe/GSD and picking the top X screens and possibly removing some high overlap screens and going down the list a bit deeper.

Option 1) will give a blend with a higher overall backtest Sharpe/GSD, but may include individual screens with significantly lower backtest Sharpe/GSD values. Will these lower Sharpe/GSD screens reduce the overall predictability of the blend?

I believe you tend to favour sorting over optimizing and I think this goes back to sorting or optimizing on Sharpe, but I am wondering have you done any testing to show if one method is superior to the other.

Thanks for all you have done. I think blend selection is a key part of MI. At this stage in the evolution of MI, I believe it is more important that finding new screens.

Thanks again.

StevnFool

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Author: emintz Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 204045 of 253566
Subject: Re: Optimizing Blends with Sharpe/(GSD^x) Date: 11/18/2007 8:08 PM
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I think you have made a compelling case that Sharpe/GSD is more predictive of future Sharpe than Sharpe. The additional data that you have posted since your initial post in the thread have helped confirm this in my mind.

I still think there is a limitation here - it may work well for screens only. My observation is that Sharpe/GSD does not produce blends that are all that different from Sharpe - it just picks ones that have lower GSDs (and lower CAGRs). If you blend with other asset classes, such as bond ETFs, you may find that Sharpe/GSD optimizations may put you almost entirely in bonds all the time.

Eric

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