PC: Forbes.com

Want to manage risk? – Ask the Kurtosis!

Kurtosis: Peakedness of a normal probability distribution.

(Usually, what is seen is ‘excess’ kurtosis as for normal distribution, it is 3.

So, Kurtosis > 3 -> Leptokurtic i.e. More Peaked
So, Kurtosis < 3 -> Platykurtic i.e. Less Peaked.

In risk management, Kurtosis plays a huge role in determining the risks involved with that process/return from an investment etc. Distributions which are leptokurtic in nature have the data points more than 75% of the time within +/- 1 standard deviation as compared to 68% of normal distribution.

But, the irony is even after having most data points around the mean within a narrow band of standard deviation. It has a greater probability of large unexpected deviations as compared to Normal and Mesokurtic (excess kurtosis < 3). So, Fat tails exist for Leptokurtic Distributions

When a security has to be selected for investment, the returns are expected to be more of Platykurtic for those who are risk averse.In platykurtic, though the deviation from the mean is more than other distributions between a range of sigma (standard deviation). But the chances of getting surprising unexpected return (on either side i.e. profit or loss) is very less.UntitledChart 1: Risk Management: Kurtosis Analysis. (Please excuse the Axis titles of X and Y)

This chart shows the different kurtosis levels of a probability distributions i. e Lepto, Meso and Platy.

You can also think it like follows:

  1. Green line shows probability of returns from a portfolio of bonds (T-Bonds)
  2. Red line shows probability of returns of a very diversified portfolio of large cap equity, T-bonds and high quality Corporate Bonds.
  3. Blue line shows probability of returns from risky positions in equities and large proportion of non-linear derivatives position (with a focus on speculation).
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