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URL:  http://boards.fool.com/elan-asked-can-you-explain-the-difference-between-26109676.aspx

Subject:  Re: Optimizing Blends with Sharpe/(GSD^x) Date:  11/17/2007  7:46 PM
Author:  Zeelotes Number:  203998 of 252746

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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