Comparing standard deviation across multiple time horizons

Question

I am working on comparing a number of investments and am attempting to do a relative risk comparison but am having troubles ensuring accuracy with the standard deviations. A number of the observations have a shorter time horizon than I would like to compare (some have only a 3,4, or 5 year time horizon). I would like to use a 10-year time horizon so 10 observations in every standard deviation calculation. I believe I can assume a normal distribution for this exercise.

Based on this problem, is there a solution and if so, do I need to adjust the shorter standard deviations to ensure accuracy using a longer timeline?

This is my first time here and from the looks of it there are some very bright people. I appreciate any help you can provide.

Answer 1

Naively speaking

Normal distribution + Time evolution = Gaussian process

Among the most popular gaussian processes you have

1) Brownian motion

Std deviation grows like the square root of the horizon, so if you divide every std deviation by the square root of the number of years it refers to you can compare the investments

2) Ornstein-Uhlenbeck

Due to mean reversion std deviation does not grow like the square root of t but with a more complex formula, see here

http://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process

I'm not sure this was the point of the question, anyway, good luck with your investments