Standard Deviation - Daily vs Monthly

#1
Hi community, I was wondering if you might help me with some Standard Deviation calcs. Apologies in advance if the questions are very basic. I'm slightly overwhelmed though very very interested by the subject. I am preparing a presentation where I'd like to incorporate some stats concepts.

OK, so, let's say I have 2 versions of price movements of the same security. The first one is daily view and the second one is a monthly view. For the sake of this exercise, we will say the security increases in value by 1% everyday for 360 days straight,starting with 1% on day 1. That means, on day 1, the security is up by 1%, on day 2 it is now up by 2% (for a total of 3%), on day 3 it increases by 3% (for a total of 6%).... on day 360, it increases 360% (for a total of 64980%)

Assume also, every 30 days is a month. The monthly version therefore has 12 data points. That means, on period 1/end of month 1/day 30, the security is up by 1365%, on period 2, it increases by 1365% (for a total of 1830%)... on period 12, it increases 10365% (for a total of 64980%, same as daily). I lay all this out in Excel.

Ok, so now I calculate the standard deviation for both sets. I use the STDEV function which from numerous testing, it seems to work well. The first set of data yield me a standard deviation of approx 104% and the second set gives me approx 3245%.

The difference seems quite big. Am I missing something?

Next, I try to annualize the Std Devs calculated. I may be completely off the mark here, but the formula that I find generally is Monthly Std Dec times the square root of 12.

I fill that in with the calculated monthly std dev and I get approx 112.4 for Annualized Std Dev.

I then take the same formula but instead of square root of 12 (for 12 periods), I substituted for 360 in hopes of annualized the Daily Std Dev I had calculated. Here, I come up with approx 187.32 Annualized Std Dev. I'm not sure if this is an OK conversion of the formula... yet the point that bothers me still is that both Annualized Std Dev I've calculated are quite different.

I know this is a lot to ask, but if you wouldn't mind, can you pls tell me
- whether my methods of calculating the Daily, Monthly and the 2 Annualized Std Devs are all correct? If not, pls correct me
- If my calcs are correct, how exactly should I be interpreting the results as they seem to paint different stories regarding the volatility of the security.

Pls feel free to PM me if you'd like. I'd be happy to get on the phone to understand all this if there's too much to write. Thanks all in advance for your help.
 
#2
Yes, what I am doing is changing the absolute % everyday by increasing it 1%. All the numbers I have provided are correct. Thanks.