Writer:Neko Trader
Debuted in FX in 2012. Since then, performance has followed a gradual downward trend... and in 2015, somehow my lifetime profit turned positive! A short-term technical trader who dreams of becoming a full-time trader
Blog:Come to the Neko Trader’s Grove

Bollinger Bands 3σ — Probability of Being Abducted by an Alien

Hello everyone, this is Neko Trader. (´・ω・｀) Hello

Last time I talked about how stupid I am...No, I explained what kind of trader I am and gave a rough explanation of Bollinger Bands.

I will link to past articles on my blog, so please feel free to stop by.

Now, this time I will go one step further,

The most notable feature of Bollinger Bands is the σ-lines above and below the centerline, which I wrote about last time as having these properties.

Properties of Bollinger Bands

• Center line ± σ linecontains the rate with about 68.2% probability
• Center line ± 2σ linecontains the rate with about 95.4% probability
• Center line ± 3σ linecontains the rate with about 99.7% probability

As soon as you see those numbers, it gets a bit complicated, doesn’t it.(；・∀・) Taraa

However, the numbers themselves aren’t what’s important.

To put it simply for clarity,

• ±σ line→ breaks about 1/3 of the time, so it will enter and exit quite often.
• Breaking the ±2σ line, →“Oh, that’s a bit rare, isn’t it?”to some extent, thisis almost the same probability as winning the lottery. However,
• Breaking the ±3σ line, → “This is serious! This is serious!”causes a big stir, and thisis about the same as someone who has been abducted by aliens... apparently.Σ(゜Д゜； No way!?

Is mean-reversion effective from ±2σ, ±3σ?

Here, a famous trading method comes to mind.

If the rarely breached ±2σ or ±3σ lines are breached even once, a mean-reversion contrarian approach is imagined, assuming a reversion to the mean from this quite abnormal state,

“If the rate crosses +2σ or +3σ, enter short with take-profit at the center line or -σ and a stop when the entry candle’s high is exceeded (or low is broken)”

This is it. (Longs from -2σ, -3σ as well)

  Now, let’s look at the USD/JPY one-hour chart I showed recently.

USD/JPY one-hour chart

And now, we will test whether contrarian trading is actually effective. 


Trading method

• Entry on ±2σ (±3σ) cross with candle closure
• Take profit at the center line, stop loss beyond the candle’s high (low)

Potential take-profit points on ±2σ cross are□in the three circled places.

□Other cross points exist, but would have continued with the trend and hit the stop.

The ±3σ crosses are○in the three circled places, but soon after the recent high/low was exceeded, so all would have resulted in a loss.

It seems there isn’t much edge…(´・ω・) Shobon

And another important thing I want to stress is that there are3 occurrences of ±3σ crosses…

…how many people have been abducted by aliens!

It’s hard not to chuckle at that realization.

Even in a quick-reading chart, you can frequently see crosses with ±2σ and even ±3σ.

Why does 0.3% occur frequently?

Surpassing 99.7% means there is a 0.3% probability, so why does this occur so often?

There is a pitfall in Bollinger Bands related to this.

Now, the question remains whether the popular Bollinger Band contrarian approach actually has edge, and whether 99.7% of rates really stay within ±3σ, which leaves some doubt.

Next time, I would like to discuss what seems to influence this with

• the pitfall of Bollinger Bands and
• another property

Think about these.

Well then everyone, may you have explosive profits today as well! (σ・∀・)σ Gotts!!