stopsareforwimps wrote:I will report back in due course.
TLDR: A heap of research showed me that when stops and profit targets are quite tight, they can affect the skew and kurtosis of the monthly returns. But otherwise they seem not to. So Sluggo was right. My flippant comment was flawed.
Ultimately the fact that the long term CTA survivors have positive skewness of monthly returns and positive kurtosis of monthly returns, may reflect nothing more than the fact that they have survived.
You can probably stop reading here unless you are a masochist.
Possible Explanation - Hypothesis 1
Unless stops and targets are quite tight, the periodic fluctuations in equity are dominated by the daily moves of the underlying markets not by the stops and targets.
For a tight stop loss of 1.1 ATRs there was a strong positive relationship between the skew of monthly returns and of the trades as we increase the profit target. Both skews start negative
at low targets and go positive as the targets are increased. The skew of trade returns goes positive at a lower PT than the skew of monthly returns. In between those two values, the skews are of different signs.
In contrast, with a tight Profit Target of 2.1 ATRs there was a strong inverse relationship between the skew of trade returns and the skew of monthly returns as we increase the stop. The skew of the trades returns starts off positive and the skew of monthly returns starts off negative
. As the stop is increased, the skew of trade returns declines and goes negative, while the skew of monthly returns increases and goes positive.
So you can indeed generate the kinds of phenomena Sluggo described.
In my simulations - with different data than the international set originally described - having such tight stops and targets reduced risk-adjusted returns markedly eg -30% PA. This result may vary depending on the underlying strategy.
Possible Explanation - Hypothesis 2
When trade or periodic returns are compounded, the distribution tends to increasingly resemble a normal distribution, with zero skewness and kurtosis - provided certain conditions are met. This means that letting winners run and cutting losses would not generate positive skew when measured over long intervals. Instead it could generate higher compound returns by reducing volatility drag and increasing positive-skew lift. In that way it might increase your chances of survival.
With financial market return data, these conditions tend not to be met. For example, according to my calculations, the US stock market's real annual returns from 1820 (sic) to 2009 show a fair bit of skew (in the low single digit range) even for 30-year returns measured over this 189 year period. According to theory the skew and kurtosis should be minuscule at these time frames.
The issues of a) What are the underlying statistical distributions of financial market returns, and b) How do these returns compound to longer periods, are not at all resolved in the theory so it is hard to say anything much about this.
I did not test trailing stops or trailing profit targets. The results there may be different. I used the blox free data as at January this year for the test (Futures only).
Apart from learning possibly more than I wanted to know about the statistical distributions of financial market returns, I also found and fixed a significant bug in my trading code during this exercise which was costing me 2% pa. So it was time very well spent. Which also raises some troubling questions. I will be hanging out in the testing forum a bit.
Jarrod Wilcox "Investing by the Numbers"
Jean-Phillipe Bouchaud "Theory of Financial Risks"
Hudson, Richard L.; Mandelbrot, BenoÃ®t B. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward.