The normal distribution is the most extensively used probability distribution in investment analysis. It plays a key role in the modern portfolio theory.
It is a continuous bell-shaped probability distribution. It has the following key properties:
- It is completely described by two parameters - its mean, µ, and variance, σ2. It is defined as X~N(µ, σ2) and read as a normal distribution with a mean µ and variance σ2.
- It has a skewness of zero i.e. it is symmetric about the mean. It has a kurtosis of three. Therefore, its mean, median and mode are all equal.
- A linear combination of two or more normal distribution variables is also normally distributed.
- It has long tails that extend to infinity, and the area of the tails gets smaller and smaller as we move away from the mean in either direction.
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