Standard deviation for non-normal distribution

[gtamfreak]

I was wondering why standard deviation is not a proper risk measure if the distribution is NOT normal. Either I didn’ t think this through earlier or I forgot the answer. Please help!

 

[S2000magician]

As long as the distribution can be characterized fully by giving only its mean and standard deviation, then the standard deviation is a perfectly proper measure of risk. A normal distribution would obviously qualify, as would a uniform distribution.
This is an example where the CFA Institute curriculum has tried to simplify things, and in doing so has ended up making a mistake.

 

[gtamfreak]

Thanks magician. I still don’t get a complete picture. What do you mean by ‘characterized fully’? When is a distribution not characterized fully by giving only its mean and variance? I’ve skimmed through the entire level1 and level2 materials but do not seem to find the answer. Any external links discussing this topic will also help me understand it.

 

[S2000magician]

For example, if you have a skewed distribution, you might have to specify its skewness as well as its mean and standard deviation; giving only the mean and standard deviation wouldn’t be sufficient.