## Statistical approach to trailing stops

Discussions about the testing and simulation of mechanical trading systems using historical data and other methods. Trading Blox Customers should post Trading Blox specific questions in the Customer Support forum.
janvir17
Full Member
Posts: 16
Joined: Mon Aug 09, 2004 9:00 pm
Location: Tampa, FL

### Statistical approach to trailing stops

Guys,

I've been a long time lurker who has learned a ton from this site. I have programmed my own testing harness and have the following approach to trailing stops.

Stops are moved based on how many ATRs of profit we have. The stop locks in a percentage of the profit. For example, one profitable version has the following schedule:

Profit in ATRs | Stop (percent of profit locked in)
1 | 0%
2 | 0%
3 | 0%
4 | 15%
5 | 40%
6 | 50%
7 | 60%
8 | 70%
9 | 75%
10 | 75%

A separate schedule determines how stops are moved before breakeven. If the profitable stop schedule above shows 0%, then the following schedule shows how much of the initial stop is left exposed:

Profit in ATRs | Stop (percent of initial stop left exposed)
1 | 100%
2 | 80%
3 | 50%
4 | 0%
5 | 0%
6 | 0%
7 | 0%
8 | 0%
9 | 0%
10 | 0%

In my model each of these numbers can be changed so that you have a lot of room to play around with trailing stop movement. I have tried linear movements where the stop goes up by a set amount (say 10%) for each ATR. This doesnt work too well b/c early in the trend you must give the trade more room to breath than linear moves allow. I find that exponential moves where the percent lockin moves slowly at first and then starts to move higher much quicker at around 4 or 5 ATRs works much better.

I would be curious to see what people think about my version of stop movement for exiting compared to the usual simpler versions (e.g. turtle stops where you exit on a 10 day low for example).

I have found some counterintuitive results however, when testing my model. For example using the schedules above I have systems that generate CAGRs of 15-20% and Max drawdowns of 50% over the past 10 years (I plan on testing over 20 years once i upgrade my CSI subscription).

However, when I try modifiying the schedule such that I set the stop at 100% at 2 ATRs or 100% at 3 ATRs, my CAGR jumps to over 50% with Max drawdowns below 25%. The funny thing is that these results seem somewhat robust as well. Am I missing something here? Or is the long-term trend following model I painstakingly coded telling me that short-term profit taking is the key to a smooth equity curve and better profitability. It doesn't feel right to me. c.f./fellow board members, any thoughts on this?

Roundtable Knight
Posts: 101
Joined: Mon Apr 28, 2003 11:07 am
Location: Zimbabwe
Some people, let's call them "purists", insist that the only logical prices to trade at, are those directly calculated from market action. Chart points (such as recent highs or lows), trendline prices, indicator values (such as moving averages) are fair game.

But, the purists insist, it is wrong to use your "trade entry price" in the calculations for where/when to trade. The market doesn't care where you happened to get in, and the market is going to do what it is going to do, regardless of insignificant little you. So, the thinking goes, it is stupid to use your "trade entry price" to calculate stops or to determine any other trading action. Instead, base your decisions on the market's activity. Not your activity.

Moving your stops around based upon your trade profit would be, according to these folks, silly. Your profit is based on your entry point, which is utterly unimportant to the market's action. So your profit-based trailing stops are, in their opinion, silly.

Often these "purists" take quite a preachy and condescending tone. The real dead giveaway is when they start quoting William Eckhardt or other Big Names to justify their rather rigid views.

Luckily there's an easy way to disarm them. Just use the high price (or the low, or the close, or H+L+C/3) of the signal day, to calculate a "system theoretical gain", and move your stops around based on that. Now you're using "pure" technical analysis, and you've eliminated your own entry fill (which the market disregards) from the computation. Order has been restored, purity has been preserved.

As to your final question, is it stupid to trade an LTTF system with a profit target of +2R?, my answer would be: Read Ralph Vince's book "The Mathematics of Money Management". If you believe his Fundamental equation of trading ( p. 58 ), then you have theoretical justification for intentionally cutting off the right hand tail of the trade distribution of R values: it might reduce the variance faster than it reduces the mean. If so then the desirability (for which MAR is a good proxy) goes up.

Bernd
Roundtable Knight
Posts: 126
Joined: Wed Apr 30, 2003 6:39 am
Last edited by Bernd on Fri Apr 18, 2008 10:25 am, edited 1 time in total.

janvir17
Full Member
Posts: 16
Joined: Mon Aug 09, 2004 9:00 pm
Location: Tampa, FL

- The 100% level before breakeven indicates that the full amount of my initial stop is left exposed. My initial stop is similar to the turtle stop. It's an ATR multiple. So I can set my initial stop at 0.75 ATRs, 2 ATRs, etc. The bet sizing algorithm is separate from this, so for any given level of initial stop I can change what percent of equity to risk.

- The 100% refers to 100% of profit locked in (i.e. immediately exit when the ATR level is reached). So, for example, using my profitable stop schedule and a 2 ATR target I set it to the following:

Profit in ATRs | Stop (percent of profit locked in)
1 | 0%
2 | 100%
3 | 100%
4 | 100%
5 | 100%
6 | 100%
7 | 100%
8 | 100%
9 | 100%
10 | 100%

Note that all of the numbers past the 2 ATR mark are redundant as the position is exited as soon as 2 ATRs are reached. And yes, different variations on this theme (I've tried modifying the initial stop, the betting algorithm, portfolio selection, among other things) still indicate that I am better of with a profit target of 2 or 3 ATRs instead of the conventional approach of letting profits at that level fully retrace in order to go for the big moves.

Tigerline
Full Member
Posts: 10
Joined: Mon Jun 23, 2003 12:30 pm
Location: Cumbria, UK
Note that all of the numbers past the 2 ATR mark are redundant as the position is exited as soon as 2 ATRs are reached. And yes, different variations on this theme (I've tried modifying the initial stop, the betting algorithm, portfolio selection, among other things) still indicate that I am better of with a profit target of 2 or 3 ATRs instead of the conventional approach of letting profits at that level fully retrace in order to go for the big moves

By better off, do you mean a smoother equity curve with less drawdown or increased total profit when tested against a number of markets?

janvir17
Full Member
Posts: 16
Joined: Mon Aug 09, 2004 9:00 pm
Location: Tampa, FL
Tigerline,

I've been getting both a smoother equity curve and larger profits. I know this seems strange which is why I'm almost inclined to believe that there is an error in my code. I haven't found anything as of yet but am continuing to look.

On this subject, has anyone else out there found that they've achieved smaller drawdowns AND higher profits with a smaller (short-term) profit target? Or are my results truly out of the norm (again, leading me to the conclusion that it's probably a bug in the way I've coded)?

One of the reasons that I tried testing 2 and 3 ATR profit targets is that I wanted to find a short-term system that I could trade along with a longer-term traditional trend following system. I'm not sure that I can personally withstand the drawdowns associated with pure trend following. In addition, I noticed that traders who have had the best MAR ratios out there are typically those that take profits quicker. Paul Tudor Jones and Monroe Trout come to mind (sure, they're also more discretionary, I know).

richard
Roundtable Fellow
Posts: 94
Joined: Tue May 18, 2004 10:17 pm
I think your profit target method makes some sense.

Some strategies that I am interested in:

1. tightening your profit targets as time goes by, so that as time progresses your targets get nearer than they were.

2. tightening profit targets in accordance with volatility, so that as volatility increases, you take profits sooner. This is what I do with discretionary trading. Volatility tends to oscillate. You could monitor a ratio of historical volatility, short term to long term, like 6 day / 100 day, and as this decreases (short term diverges from long term) take profits sooner.

Sam
Senior Member
Posts: 41
Joined: Wed May 14, 2003 5:40 pm
Location: London, United Kingdom
Why would you decrease your profit target if volatility has increased? If vol has increased, then surely you would be more likely to be stopped out on trades. In order to compensate, would you not need to increase your profit targets?

I suppose if you are measuring vol using ATR, then adjustments due to changes in vol are made automatically if your targets/stop loss levels are measured in ATR.