Question

Given the shortcomings of the normal distribution in modeling some financial variables, why do you think the normal distribution is still used? What are the advantages of its continued use in financial modeling? Are fund managers and others who use risk values based on the normal distribution acting responsibly? Why or why not?

Answer 1

Why normal distribution is used?

The normal distribution is most common distribution used in stock market & also in other statistical analyses.

Any investment has two aspects, risk & return. Investors tend to look highest possible returns with lower risk. Normal distribution helps in quantifying these two aspects by mean for returns & standard deviation for risks. The graphical representation of normal distribution through mean & standard deviation that enable representation of both risk & return with a clearly defined range.

Advantages of using normal distribution in financial modeling:

1. It is a continuous distribution defined for infinite values. This is crucial because the number of returns that can occur is also infinite.
2. It is symmetrical about the mean, as a balance exists between probability of returns above & below the mean.
3. The probability of extreme outcomes is quite low for financial returns. But extreme outcomes occur less frequently.

Managers who use normal distribution acting responsibly?

The managers can be considered responsible. The risk associated with particular investment using normal distribution. The managers read various market hazards that can keep the risk under a particular level such as 3 or 5 or 10%. Such claims are based on the assumption that price changes do follow a normal distribution. Which usually not the case when it comes to stock market.

The managers think that if lot of investment of capital is made in a particular trade based on the calculations made by them the risk is low assuming that the normal distribution of returns that one is likely to expose to the risk that is significantly higher than the normal distribution actually suggests.

However the breach of assumption of normal distribution by the fund managers is not one that important when stocks are compared with one another.