[S#2] C) Losing Streak Probabilities (Part 1)
Index:
Series#2: Understanding Losing Streaks 101
C) Losing Streak Probabilities (Part 1)
Key Takeaways:
The reality is that the lower your win rate, the higher the probability is of experiencing a longer and longer losing streak throughout your trading career
Knowing the win rate range of your trading system will allow you to determine the probability of consecutive losses you could face
Understanding that you will be faced with these types of losing streaks, will at least give a reality check that this is a normal part of trading a low win rate system
To expand on my earlier post in the series relating to the expected losing streaks, I think I should talk about losing streak probabilities. Again all of this, as in, understanding losing streaks and these clusters of good and bad luck, helps to tamper expectations and ultimately improve your ability to make decisions.
Let’s have a look at the chart below.
Based on one’s win rate, you are able to see the probability of consecutive losses. I boxed off each column for when a 1% probability is reached for reference.
This was done by using the formula below:
Probability of Lossing “c” times in a row = (1-P)^c
Where:
P = Win percentage
(1-P) = Loss percentage
c = Number of consecutive losses
50% Win Rate
With a 50% win rate, which I would say for a trend-following trader, is relatively high, the probability that you can experience 2 losses in a row is 25% (=1-0.5^2). The probability of 5 losses is 3.13% (=1-0.5^5) and with 10 in a row, you can expect that to happen 0.10% (=0.5^10) of the time. One thing to note, I am using 2 decimal places to simplify things, however, if we allow for more decimals, there is a chance of further losses occurring but at an exceedingly improbable rate.
25% Win Rate
The chance of hitting larger losing streaks changes drastically the lower one’s win rate gets. So now…
The probability of 5 losses with a 25% win rate = 23.73%
The probability of 10 losses with a 25% = 5.63%
Comparing this to our 50% win rate:
23.73% (25% Win Rate) VS 3.13% (50% Win rate)
5.63% (25% Win Rate) VS 0.10% (50% Win rate)
As a trend-following home run style trader you need to be comfortable with these numbers. This is a reality that you will likely face. You will have to be okay with 10 losses in a row! And again, this is why every single article or course on trading will tell you, risk management is important…
Other Caveats:
Firstly, all the previous caveats will apply to this type of calculation but something I forgot to mention in my last post with regards to losing streaks and probabilities is this…
the notion of the “Gambler’s Fallacy”
I think this type of cognitive bias needs to be stated whenever we talk about probabilities. Gambler’s Fallacy is the “incorrect belief that, if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past”. For example, let’s say we flip a coin 10 times and all 10 times it lands on heads. The probability of the next coin flip being heads or tails is still 50% even though we have had 10 consecutive heads in a row. Just like coin flips, your win rate doesn’t adjust based on how many times you have lost. And again your win rate isn’t stagnant it fluctuates over months and years but over time using the same methodology/system your win rate should converge to a tighter and tighter range.
Rounding to 2 decimal places
As mentioned previously, I round to 2 decimal places for simplicity but there is a chance of a longer losing streak but at an exceedingly improbable rate. With this type of calculation, the value will never be absolute zero but just like winning the lottery multiple times in a row, those odds aren’t realistic.
Conclusion:
Post 2023, before taking a brief hiatus from trading I had two losing streaks consisting of 8 losses in a row. And the winning trades I did make were not high-risk to-reward (RR) trades. It left a bad taste in my mouth. After coming back to trading and hitting multiple big winning RR trades I know that this style of trading (low win rate, large winners) is possible which allowed me to not feel jaded (or at least less jaded) when I am in these bouts of “bad luck”. I am currently on an 11-loss streak and yes it doesn’t feel the best but at least going through past loss streaks has helped me to follow my methodology and know that this is just part of the course.
I think most momentum traders don’t emphasize enough the effects of losing streaks. With a normal trend-following system you will most likely have a win rate of anything from 20% to 50%. Traders will express that losing streaks will happen and that you need to “manage risk” and control emotions but really you can’t experience the effect of an extended losing streak until you are in it.
No one ever tells you what it feels like because you can’t know until you experience it. But I hope, at least knowing that this is a reality one must face will give you realistic expectations.
References:
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.
Gambler’s Fallacy - I recommend you learn more about not just this type of cognitive bias but the entirety of the subject.