Level 1 Question on Volatility and Annualized STD

Question

Hey Guys - I'm working on a Level 1 question regarding volatility. Given is the 3-month annual spot rate for periods Jan-08 through Jan-10. The third column below is the percentage change from one period to the next that I've calculated. From this third column, I've calculated the standard deviation to be 30.38%. However, I need to annualize this value. I've done so by multiplying 30.38% by the square root of 4 since the spot rates are on a 3-month basis arriving at an annualized STD of 2.53%?

Is my methodology correct on this?

3-month annual spot rate (%)
Jan-08    3%
Apr-08    2.5%          -16.67%
Jul-08    2%               -20.00%
Oct-08    3%               50.00%
Jan-09   4%               33.33%
Apr-09   5%               25.00%
Jul-09   4%                -20.00%
Oct-09   4.5%            12.50%
Jan-10   3%                -33.33%

STD =       30.38%
Annualized STD =        2.53%

Thank you for your help!

Zee Tan · Answer

I'm not sure if I follow how you get 2.53% by multiplying 30.38% by √4.

30.38% × √4 = 30.38% × 2 = 60.76%