Kurtosis is the last characteristic of distribution we will discuss for this course. To start, kurtosis is very similar to volatility, in that time is a major component in using it.

If you remember back to our lesson on skew, one of the things we talked about was how, if you use a take profit and stop loss to create a binary payoff structure, you are completely eliminating any influence volatility or kurtosis can have on your results.

This is because, volatility and kurtosis are a factor of time, so if you eliminate reduce the impact of time on your payoff, you eliminate these variables from your exposure.

The flip side is also true in that, if you don’t trade with a stop loss and/or take profit, you are emphasizing the impact these variables have on your exposure. This is why volatility and kurtosis are very similar in how they can be used but beyond this, they are very different.

Volatility is simply a measure of how wide a distribution is, and it’s unique in that it’s value does not change the shape of the distributions curve. It only changes its size.

A normal distribution with twice the volatility of a different normal distribution, will both have the exact same shape, only the first distribution will be “wider” in that it spans more values on the left and right tails.

Kurtosis is different in that, it actually measures the shape of the distributions curve, not it’s size. Specifically, what it measures is, how likely are extreme and moderate values to occur.

If a distribution has a kurtosis of 3, than both extreme and moderate values occur at the same frequency of a normal distribution. If a distribution has a kurtosis value that is larger than 3, that means both extreme and moderate values occur much more frequently than they would in a normal distribution.

A distribution with a kurtosis that is twice the size of the a normal distribution, will have a dramatically different shape than the normal one, additionally, it will also span more values than the normal distribution, even if it’s volatility is smaller than the normal one.

Now think back to lesson 1 and remember, the only way to build a profitable strategy is find a part of the distribution that is not normal, and take advantage of those deviations from normal in order to turn a profit.

And thankfully in trading, kurtosis is almost always higher than that would be expected in a normal distribution, making it a perfect variable to build a trading strategy around…