[S#2] B) Calculating Your Expected Losing Streak
Index:
Series#2: Understanding Losing Streaks 101
B) Calculating Your Expected Losing Streak
Key Takeaways:
When trading you will inevitably face clusters of good and bad luck
Using your win rate and number of trades, you can calculate the estimated longest losing streak you can expect to have. Understanding the statistics behind these bad luck clusters will equip you with, at least, the knowledge that you are not alone and that this is a part of the ride!
As a trader, you will inevitably face streaks of good luck and streaks of bad luck. This is a mathematical fact that must be accepted. When researching losses, I found a very useful term known as “Expected Loss Sequence” or E.L.S for short. This term is defined as the longest expected losing streak a person is likely to experience, given the sample size and probability of winning. This value is also, not absolutely accurate nor guaranteed. There is no way to know how long a losing run will last but this gives you at least some perspective on the topic.
There doesn’t seem to be a mention of this in most trading articles or literature. This could be for many reasons (expressed in the caveats section) but while researching, it has come up many times within sports betting and gambling articles. Now, I think most people will say, that you can only truly experience a long loss streak once you are in it but I think understanding this concept from a trader’s perspective can be beneficial with respect to knowing that clusters of “bad luck” or consecutive losses are just part of the ride. At least knowing that you are not alone or that, it is part of the game can help to resolve some of the psychological hurdles one may face when trading a low win rate, large winner system.
Going to refer to this type of system as a “home run system or strategy” from now on.
Expected Losing Sequence:
I think we can assume that an average home run system will have a win rate of 20%-50%. For me personally, my average total win rate for this year is 16% (I am still learning and trying to get this up). Using the formula below we can create a table showing the Expected Loss Sequence and Expected Win Sequence for a variety of situations.
Expected Loss Sequence = | ln (n) / ln (1-P) |
Where:
n = Number of trades
P = Win percentage
(1-P) = Loss percentage
| … | = Absolute value
Depending on methodology, I think a 25% win rate on a home run system is reasonable and fair. Let’s have a look at the 25% Win Rate row.
With a 25% win rate on a sample size of 100 trades, you should be comfortable with a loss streak of 16. This means with a stagnant win rate of 25% there is a possibility of losing 16 times in a row without making a profitable trade. Now the higher the sample size (ie. 250, 500, 1000) is, the higher the E.L.S will be, which I think is pretty self-explanatory. But as a home run style trader, this should be a reality for you, as well for me! You have to think though, imagine not hitting a big winning trade before, and because of your inexperience as well as the win rate of your system you go 16 straight trades without a win. Many would quit right there and then. It really then comes down to confidence in your system and knowing that your trading strategy works in the long term. And the key to this level of confidence comes down to a factor I wrote about here.
After this realization, we should probably look at drawdowns. With a consistent risk per trade of 1% of your account size, using the 25% win rate at 100 trades metrics, you would have had a drawdown of 16%. This means that you should be comfortable with this high of a drawdown or you use a flexible / ranging risk per trade (which I think is a more versatile and widely used approach to risk management). Where your risk per trade is not fixed but is constrained to a range where it can fluctuate based on market conditions, your past trades, and other factors. A few caveats below with regards to the E.L.S formula.
Caveats:
Expected Loss Sequence will not be completely accurate
Because your win rate changes over time, the E.L.S will not be accurate however, with a large enough sample and a system where your win rate has remained consistent over a period of time, E.L.S will give you a good ballpark estimate of what to expect.
Expected Loss Sequence is not a guaranteed value
Even if your win rate was static for the entirety of the sample, it does not mean that you are guaranteed to have a losing streak of the E.L.S value. It is the “expected” value so there is a possibility that the losing streak is longer than the value stated.
Statistics are different in the real world
The real world of trading adds levels of complexity that will of course alter E.L.S. For example, if you have 5 losing trades in a row, a trader may take a step back and evaluate if the market environment conditions still align with the strategy one is using. In this case, reducing the amount of trading or altering your strategy slightly to capture other variations of a setup could be an option.
Conclusion:
Traders will express that losing streaks will happen and you need to “manage risk” and control emotions but you can’t experience the effect of an extended losing streak until you are in it. That said, however, at least understanding the statistics behind it and having the realization that these large clusters of bad luck will inevitably occur will at least give you some comfort that you are not alone.
The next installment of this series will focus on losing streak probabilities. It expands on an article by
, a swing trader and author of “The Trading Resource Hub”.-F4VS
References:
How to Estimate Your Longest Losing Sequence - Great article on the subject of consecutive losses with respect to sports betting
Why Trading Forex is so Difficult - Randomness in the Markets: Clusters of Bad and Good Luck - This is an interview with Dr. David Paul where he talks about good and bad luck when it comes to trading. And the mental attitude that is needed when clusters of bad luck inevitably occur. This is the reason why I wanted to start and dig further into this topic so I hope you enjoy the video as much as I did.
Tools:
Expected Loss Sequence Calculator - Shows you, based on your win rate, what your E.L.S is depending on the number of samples.