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Quantitative Methods #3: Volatility Measures

[1]You might have heard about variance, standard deviation and other measures of risk. What are they and how should they be used? To put things in a very simple form, they are measures that help determine how volatile a return is. How is it used? In general, an investor will demand a higher expected return if an asset is more volatile. That is key and is true both for individual assets or for an entire portfolio.

First off, when determining a variance, you must know if you have data for the entire population or simply a sample.

Population variance=

[2]

Sample variance=

[3]

These formulas are not the type of formula that you would try to understand, they are simply formulas that you must know. And don’t worry, you will use them often, you will not need to study them very much.

Since standard deviation is usually the data that you will use, you can easily convert from variance to standard deviation:

[4]

You must know the difference between the two and be very careful in the exam as the exam will often try to mix you up with one or the other.

One thing that you will find however is that comparing these is not easy if the data sets are very different. One way that you could do it is by using the coefficient of variation:

CV = standard deviation / mean