Kurtosis is a statistical measure of the “fatness” of a given probability distribution. It goes beyond the norm by looking at the spread of the tails of the likelihood density function. Generally, kurtosis can either be ‘normal’ (mesokurtic), ‘less than normal’ (platykurtic) or ‘more than normal’ (leptokurtic).

The most well-known example of a normal, mesokurtic distribution is the bell-shaped curve. It has the least amount of kurtosis risk and is the most ‘balanced’ of all the kurtosis categories with respect to the data points. Platykurtic distributions have lesser kurtosis than the aforementioned bell-shaped curve. This results in thinner tails, which increases the probability of extreme values in the distribution. Lastly, leptokurtic distributions possess higher kurtosis values than normal distributions. This implies that more data points are concentrated near the mean and fewer points are present in the tails, further increasing the probability of extreme values.

Kurtosis risk is a measure of how often an investment's price moves dramatically. It looks at the shape of a probability distribution and calculates the probability of an extreme move in the price of an investment. If a probability distribution has a Leptokurtic shape with fat tails, it is more likely to experience extreme moves in its price than one with a Mesokurtic shape. Therefore, investments with higher kurtosis risks may bring in higher profits, but they can also lead to aggressive losses should the investment not pan out.

Kurtosis is a useful indicator of risk and helps investors determine the level of risk they may face with a particular investment. Knowing the kurtosis of a probability distribution is an important tool that investors should take advantage of when making investment decisions. By taking kurtosis into account, investors can meaningfully reduce risk exposure and achieve the desired results of their investments.