# The Black Swan

By Lawrence

The Black Swan: The Impact of the Highly Improbable written by Nassim Nicholas Taleb is an interesting book. One of the claims in the book talks about the return of the Dow Jones Industrial Average will be cut by half if a limited number of days (the ones with biggest gain) are removed from the data series. I have created an interesting chart with variations of the idea for your enjoyment.

Best Day and Worst Day of Each Year

As oppose to removing the days with biggest gain from the DJIA, I decided to study the accumulated value of the best performing day of each year. As a trader, I am also interested in studying the accumulated value of the worst performing day of each year.

Then, I further expanded the concept to study the best/worst 2-day and 3-day runs from each year.

Here is the chart plotting all the combinations.

Best 1D is the accumulation of the best 1-day gain from each year.

Worst 1D is the accumulation of the worst 1-day loss from each year.

Combined 1D is the accumulation of both best 1-day gain and the worst 1-day loss from each year.

The 2D and 3D versions work in a similar way.

Observations

If you have the ability to foresee exactly which day in each year to go long the market for 1-day biggest gain, and also go short the market for 1-day biggest drop. You would be doing quite well as you can see from the chart’s Combined 1D line.

Don’t forget that is less than 1% exposure in the market each year. i.e. 2 days out of 260 trading days a year

If you can get both the best 3-day run and the worst 3-day drop of each year, you can solidly outperform DJIA.

And that is just 6 days out of 260 trading days a year, or 2.3%

Interesting Questions

The obvious question, How do we capture these trading days?

The less obvious question, What is the stock market doing during that other 97% of the time?

Formulas Used in the Chart

In case you are interested in conducting a similar study, here are the formulas I used to create the chart.

For the Best 1D indicator, it is just fml indicator linked to the data series with the following formula,

For the Worst 1D indicator, it is fml indicator linked to the data series with the following formula,

For the Combined 1D indicator, it is the fml3 indicator linked to the data series, Best 1D and Worst 1D indicators. The formula is as follows,

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