## Geometric Mean and SD into Normal Curve

Hi

I'm working with a data set of historical return on a particular investment. I have 556 consecutive monthly price values, and i used those to calculate both the Arithmetic and Geometric Means and Standard Deviations of growth in the investment month by month. I want to use these values to forecast possible future growths. I have 3 questions:

Question #1. I calculated geometric values of

Geometric Mean: 1.007321359
Geometric SD: 1.059142531

To get this values i had to add 1 to each monthly growth values (1 + gr) then use that because its what made the math work (can't take a ln of a negative number i guess). Now that i want to go back and plug these values into a normal distribution, should i subtract 1 from each value then make my normal curve? Does it even matter? I know geomtric mean and standard deviation are log-normal distributed, but i think i'm better to use a normal distribution instead in this case....is that a bad idea?

Question #2 Can a geometric SD of 1.059142531 be approximated to an arithmetic SD of 0.059142531

Question #3 How do i convert monthly Geometric Mean and Standard Deviation to Yearly? I know how many months there were to compute the Monthly Mean and SD (556). I think converting the mean is simple, just take 1.007321359^12. What do i do about the standard deviation though?

Thanks