Fixed vs. percentage based stop loss

N

NinjaTrader_Dierk

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Hi,

Currently I'm backtesting a interday strategy on NASDAQ stocks. I found a phemomena which I can't explain so far:

I use a percent value (0,5%, 1% 2% .. whatever) as stop loss. I experienced greater profit, when I add a fixed(!) dollar amount to the percent based stop loss. This profit can't be reached by "simply" adjusting the percent based value.

More info:
This effect still is there, when I set commission + slippage to zero.

Has anyone any idea what is going on there ? Am I simply "fooling myself", by having some "mysterious" fault in my testing system or is this proven to be a known effect ?

Any comment appretiated.

Droth
 
It's been known for years. The larger the % risked on each trade, the higher the negative expectancy the trader must overcome. I trade using 1/2% risk for my own account, but when I traded for the house we used a different method of sizing.

Here's some detail on problems with the % risk method:

One of the myths about money management is, "size your positions so that you can only lose a fixed percent of the account equity on every trade". The mythology goes on that when you're in a losing streak, you'll be cutting back your risk, so you theoretically can't ever lose all your money.
This myth is pervasive and spread by authors (not traders), analysts (not traders), and speakers (not traders).

Why is this a myth? Because if you follow it, you will increase your chances of losing money. By itself, it will provide a negative expectation.

How? Here's a example. Suppose you decide to risk 3% of your account on each trade of a 50k account. Assuming no slippage or commissions in a zero sum game you'll lose money.

Here's 10 trades using the method on a coin flip; 50% win, 50% lose. This is a neutral trading method (no advantage or disadvantage by the trading method), to show what happens to your equity when you trade a fixed percent of equity.

1). W 50,000 +1,500
2). W 51,500 +1,545
3). W 53,045 +1,591
4). W 54,636 +1,639
5). W 56,275 +1,688
6). L 57,963 -1,738
7). L 56,225 -1,686
8). L 54,539 -1,636
9). L 52,903 -1,587
10). L 51,316 -1,539

Ending balance = 51,316 -1,539 = 49,777

You can change the trade order anyway you want and the result will be the same....a net loss of 223 without slippage or commissions.
 
acrary -

In your risk example, it looks like you're assuming that you always exit your winning positions at the same amount of your initial risk.

It's an interesting arithmatic example - you either win your risk amount or you lose it. But it ignores position managment factors - like riding a position for a win of more than your initial risk, reducing your risk as a position proceeds, etc. - the things that can make your winning $/losing $ ratio much higher than just the simple winner/loser ratio.

Based on your entry selection and position management rules your winning $ to losing $ ratio can be over 50% even though the pure winner to loser ratio is less than 50%.
 
You're right. Positive expectancy was excluded. I was just trying to isolate the money management component. In a method with no postive or negative expectancy, the % of portfolio money management just adds another negative to overcome.

E = (PW *SW) - (PL*SL)
where E = expectancy
PW = probability of win
SW = size of win
PL = probabilty of loss
SL = size of loss

In the coin flipping example, where we had 5 winners and 5 losers with the same size win as a loss, the expectancy should have been:

E = (.5 * 1) - (.5 *1)
E = 0

Because we're using %'s, you get the imbalance in actual total dollars won to lost. Gains are arithmentic while losses are geometric (ex. $100 + 40 = 40% gain, while 140 - 40 = 28% loss)

The fact that it was negative with % money management, demonstrated that the method added drag. I'm sure all experienced traders are aware of the drag, but not some of the newcomers.

There's no method that can give a positive expectancy, so the best you can do with a different method is get one that doesn't contribute to your losses.
 
Thank you for your replies. I understand, that details of your information are part of the "trader's secrets" ... :). Anyhow, very interesting.

@acrary
You mentioned that you trade your private account on percentage based stops, although you prefer a different - and I assume more profitable - method when trading for your company.
Why do you make a difference there ?

I will initiate some addditonal research on the effect, since my first results gave me the impression, that I'm starting to take a more in depth look at one of those "essentials of trading".

Thanx again.
 
droth, I don't use % based stops. I use 1/2% of account for risk per-trade. Ex. If I had a 100k account, then the max. risk per-trade would be $500. If I wanted to trade 5 emini contracts I could only risk 2 pts on each contract for each trade (500/(5*50)).
I use it for my personal account because it's simple to calculate, test, and implement. My expectation is large enough that I don't worry about the drag caused by the % of account allocation.
I retired from a investment bank last year. There, the money management and risk management were decided by the company. It chose a method that doesn't have % of account in the formula to avoid the drag.

Here's something I posted elsewhere that gave a way to avoid the drag of the % of account method while being conservative to avoid the risk of ruin:

A unprofitable trading method can't be improved through any money management strategy, so you must first have a profitable method before going forward.

Once you have a profitable method, you need to know a couple of things about it's characteristics. You need to know the maximum drawdown and the % of losing trades before you can apply money management to your method. You should have a minimum of 100 trades (either real or hypothetical) to base the calculations. Why at least 100? Because we need a stable database. At 100 trades, the standard error is 10% (1/sqrt(# trades)). This is acceptable when getting started.

How often should you hit a new equity high? It can be calculated by using the % losing trades. Here's how, take the % of losing trades and multiply it by itself until the number is approx. .01 (meaning 99% chance of seeing a run of however many times you do the mutiplication). For example, if I have a method that loses 40% of the time, then the number will be (.4*.4*.4*.4*.4 = .0124). This means a method with 40% losers will have no more than 5 losers in a row 99% of the time. Next, take the number of consecutive losses and multiply by 3. In this case, the number will be 15. This is called the trading cycle. The cycle is the maximum number of trades that should happen before a new equity high is achieved. Draw a line every 15 trades on your statements and make sure a new equity high is hit within the 15 trade period.
If not, the % of losers is probably greater than the sample used to caluclate this and is a warning sign of a unstable trading method. Use a higher % of losers and re-calculate until each equity peak is within every cycle.
How many contracts should I initially trade? This is largely dependent on how much pain you can stand. If you don't mind a large % drawdown, then your number's will be higher than someone else. Take the amount of equity in your account and multiply by your maximum acceptable drawdown as a % of your equity. For ex. if you have 20k and you don't mind a 40% drawdown, then 20k * .4 = 8k. Next, divide the max. acceptable drawdown by the observed drawdown. For ex. if the method had a max. drawdown of 2k then 8k/2k = 4. This would be the initial number of contracts to trade in the market.
When do I change the size? First, if the max. drawdown as seen in the past is hit, STOP trading. Once the new drawdown has stopped and a new equity high has been achieved (paper trading), then re-calculate the money management numbers and start over.
As far as compounding goes, take the starting equity + (maximum drawdown * 3). Once the account equity goes above this number, you can safely add another contract. Ex. if I start with 20k and the max. drawdown is 2k then when the account goes above 26k, then I can add another contract. You should also do the initial calculation and make sure it's acceptable before adding to your size. In this case the 26k * .4 = 10.4k. The 10.4k / 2k = 5.1, so it's okay to increase from the 4 contracts to the 5 and stay within the acceptable drawdown.
This method does not have a negative edge (as does all % of equity methods), so it'll let your account grow as you apply your edge to the market without the drag.
 
@acrary
Interesting stuff again. Thanx. I have to think it over.

To draw a summary: Following your ideas, the effect I described in my inital post, results from the negative expectancy of percentage based stops. I have to write some tests programs ...
 
Here's a little spreadsheet that will help you understand the effect. In the A column is the size of win as % of the equity risked. You can see the size of win/loss effect. In columns B-E I put in different % risked of equity strategies and the corresponding equity portfolio values. This demonstrates what happens when you increase % risk per-trade. Notice on the bottom row where the more you risk, the lower the ending equity. At the .01 level the drag is only .0055% of the account value after 10 trades. At .03 the drag goes up to .049%.
At .06 the drag goes to .197%. And at .09 the drag goes to .444%.
 

Attachments

“where the more you risk, the lower the ending equity”

The percent of risk must be a function of win% to reduce the drag. For example, based on a 50 period sample, if you have a historical win% rate of 60%, the probability of seeing at least 9 consecutive losing trades is less than 1%. Ask yourself what is the level of drawdown you can stand for this probability?

If you risk 1% per trade you will lose with 1% of probability 9*1% = 9%.

If you risk 5% per trade you will lose with 1% of probability: 9*5% = 45%

The drag effect: it takes more time to recover from 45% than from 9%.
 
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