Statistical Evaluation of Trading Results

I've just recently started going over my Statistics 101 notes from the past and I have a few questions about which statistical averages I should use when making calculations. Specifically, I'm interested in deviation averages.

In which cases should I use average deviation (AVEDEV), variance (VARP) and standard deviation (STDEVP)? I know that standard deviation is the most popular statistical tool to calculate deviations from the mean, but there has to be some application to the other deviation averages as well and I am at a loss to find any credible answers. My textbook has no answers, neither was I able to find any good answers online. Help?

standard deviation is the square root of variance. Why people use standard deviation instead of variance is because the values of standard deviations are more usable in real life. It gives the value of dispersion in the same units present in the sample you are studying. For example if your are observing weekly returns in % the std dev will be in % unlike the variance that will be in %squared which is not really usefull. the standard deviation can be directly compared to the actual result. That is what the sharp ratio is, a measure of your performance related to your risk. the formula for that is actual returns minus risk free rate divided by the standard deviation of your returns. You cannot do that with variance because you would be divided by % squared and the results would not be as easily interpreted compared to using standard deviation.

It possible also to use standard deviation in actual trading also. You can say that the average distance of price in pips from a certain SMA is 0 and the standard deviation is 50 pips, and it can be somekind of usefull because you are comparing apples with apples (0 pips with 50 pips). In this case when price is further away then 50 pips from the SMA you may say that price possibly have ventured too far and might revert to the mean (the SMA in this case). If you replace the standard deviation value by the variance's than you are comparing oranges with apples (pips with pips squarred) and you can't do much with that info.

If I remember well (i dont quite remember to be honest) variance is needed to find other information that may be useful like, for example, covariance which might be more important for portfolio management then for trading per se.

As for average deviation it pretty much gives the same info (more or less) as the standard deviation but the latter is often preferred because you can use it with the normal distribution curve, ie the bell curve, the stuff that says that the data observed is 68% contained in one standard deviation, 95% in two standard deviation etc etc. Average deviation is used for an other type of distribution, I dont remember which all I know is that I never had to use it... So in the end it really depends on the set of data you are observing. By default the financial industry usually goes with standard deviation for sizing risk and evaluate results even if we know that returns of investment vehicules usually do not follow a normal curve because of fat tails, the reason being that correction in prices usually are far more quick and brutal than rises in prices (it takes far less time for the market to collapse than for it to go up). For evaluating one's trading performance it might be a different story though i'm not sure, it depends a lot on your MM I would say, if you average down to try to stay in the trade the distribution of your results will probably have fatter tails than someone who tries to go for a 1:1 RR ratio but i am no statistician and I will shut up before misleading people. Hope it helped.