What method should we use to determine stop losses ?




As we have seen in our previous article, over the last 90 years, the S&P 500 ended up with a positive daily return a little bit more than 50% of the times. Over the last 5 years, the average was about 53%.

If every day you were long, you would have been right 53% of the time, and therefore you would have made money on these days. On the other hand, on the days you would have been wrong, you could have lost as much as 3, 4 even 6-7% (March 2020). It is therefore very important to use stop losses to minimize losses when days are not going our way.




Every trader has to ask the question : What would be the right number for a stop-loss? This article proposes an approach based on historical data and statistics. 


Step 1 : Use Open-Low difference historical data as reference


As a theoretical exercise, we looked at 5 years of ES data (S&P 500 futures), from October 2015 to October 2020. Futures are traded 23 hours a day, so we restricted the time frame to 9:30 to 17:00 Eastern time to represent the S&P 500 US trading session. 



We used "Open-Low difference" as a method to determine the ideal stop-loss. Open-Low difference is calculated by the following equation : 

                                    
   Low Value -  Open value 


For instance, if the price opened at 100, the lowest value for the day was 90, and then closed at 120, the "Open-Low difference" was calculated by doing 90-100 = -10. 

Example:
  • Open :100
  • Low :90
  • Close : 120
  • Open-Low difference : 100 - 90 = -10


Since the S&P has a slight tendency to be more positive than negative, for the purpose of the simulation we assumed that we were always long. Winning days have a tendency to have higher lows than losing days, so we used only data for winning days. We want the stop-loss to be low enough to prevent being stopped on winning days, but high enough to cut our losses on losing days while maintaining a good risk-reward ratio.  

Below are three charts showing the Open-Low difference of winning candles. The charts are identical, except for the red vertical line representing quantiles 25%, 50% and 75%. These 3 reference points looked like good starting points to try to find the optimal stop loss value. 

Here is an extract from wikipedia :

"In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way."


  • Q1 : -0.057% -> 25 % of records Open-Low difference are below -0.057%
  • Q2 : -0.135% -> 50 % of records Open-Low difference are below -0.135%
  • Q3 : -0.270% -> 75 % of records Open-Low difference are below -0.270%






Step 2  Run simulations 


The method used was very simple. 

(Note: please skip this description and go directly to Step 3 if you are only interested in the final conclusions).

a) Losing (Stopped) days:

For every day, calculate the Open-Low difference, and if it was equal or below the stop value, assume that the trade was stopped and the day ended with a loss equal to the stop value.

Example: 
Open  = 15
Low = 10
Close = 18
Stop_value = -3
Low - Open Difference: 15- 10 = -5

Final profit = -3 (stop value)

The Low-Open Difference is below the stop value, therefore this was a losing day, even though the market went up to 18 which is higher than the open at 15.

This would end with a profit of -3.


b) Other days

For days where the Low-Open difference is greater than the stop value, calculate the difference between Close and Open values. Note that this can still be a negative value, but this value would be higher than the stop value.

Example A: 

Open  = 15
Low = 10
Close = 13
Stop_value = -10

Low - Open Difference: 15- 10 = -5

Final profit : Close - Open = 12-15 = -2

Example B: 

Open  = 15
Low = 10
Close = 25
Stop_value = -10

Low - Open Difference: 15- 10 = -5

Final profit : Close - Open = 25-15 = 10


The simulation results are below. Q2 stop loss showed to be more profitable than Q1 and Q3. After a bit of fiddling with the data, a stop-loss of 0,16% proved to be optimal.




Step 3: Calculate profit in USD


For the purpose of calculating the profitability of the optimalstop loss of -0,16%, we assumed a S&P value 4000. The contract is the MES (not the ES), which has a value of 5$ per point. For those interested in the ES, simply multiply the USD figures by 10.

5 years ago, the S&P was around 2500-3000, so what would be profitable at 4000 (April 2021) might not have been back then or in the future. 

Assuming 10 tries, the average earning per try for one contract, including commissions, is 1,65 USD$. Some brokers require margins of only 50$ to buy a MES contract, which means using this method, one could hope to make a daily return of 3.3% on the money invested ! 






Conclusion


I was quite surprised to find that using this simple method, it is possible to build a system that seems profitable. The basic idea is trying to cut losses and preventing big downswings, and letting the market trend until the closing.

Of course, there are tons of optimization possible, for instance how to sell the position closer to the top of the day, trying to identify days that are more likely to be winning in order to increase our winning chances. And more importantly, try to identify when is a good time to short to try to benefit on big swings on both sides. We will try to explore these ideas in future articles. 














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