I have some data which, essentially, gives the change in value of a particular stock option according to 1 movement in price of the underlying stock value.
For example, say stock 'ABC' has 4 different stock options (don't worry about the details), 1, 2, 3, and 4.
When ABC moves in value by $1, then stock options 1-4 change by a certain amount. What I have is a list of data indexed by date, that tells me how much options 1-4 changed that day compared to the change in the value of ABC. Not every day has data, so some days have null values
The source data looks something like this:
1. 2. 3. 4 --------------------------- 1-1-20. NONE .5 1 .9 1-2-20. .3 NONE 1 .8 1-3-20. NONE .3 1 .8
I averaged all of this data and get a table like:
1-avg. 1-std. 1-count. 2-avg. 2-std. 2-count... etc... .3 0 1 .3 .2 2
Where avg is the average, std is the standard deviation, and count is the number of samples with real (non-null) values.
My question is, how can I weight the averages according to std and count so that, for instance, if I'm trying to find the HIGHEST average, I can make a determination where, if I have two choices: an average of 10, with a standard dev of 10, and a count of 3....versus an average of 8 with a standard dev of 2 and a count of 100....that I can quantify that the average of 8 is probably a better value because it has a higher count and a lower std.
Is there maybe a quick and dirty calculation I can do?