4% vs 2% Standard Deviation = Twice as volatile?

Question

Q. If Stock A has a standard deviation of 4% and stock B has a standard deviation of 2% does that mean stock A is twice as volatile?

I understand the math behind it but as there are so many steps involved I struggle to interpretate how the volatility is reflected within the standard deviation percentage.

Answer 1

Examples: Judge according to your definition of 'volatility'. In addition to standard deviations, perhaps look at maximum and minimum values, at first and third quartiles, or at histograms.

(1) Here are 24 fake prices with mean about 100 and standard deviation about .02.

x
 [1] 100.03  99.98 100.01 100.02 100.01  99.99 100.02  99.98
 [9] 100.00 100.05  99.97 100.00 100.02  99.99 100.00  99.97
[17] 100.03 100.02 100.00 100.03 100.02 100.01  99.98  99.99
mean(x); sd(x)
## 100.005
## 0.02105892
summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  99.97   99.99  100.00  100.00  100.02  100.05 

(1) Here are 24 fake prices with mean about 100 and standard deviation about .04.

y
 [1] 100.02 100.09 100.00 100.00  99.99  99.96  99.96 100.07
 [9] 100.07 100.06 100.04  99.97  99.95  99.98 100.02 100.03
[17] 100.02 100.01  99.96  99.99 100.05 100.04  99.99  99.98
mean(y); sd(y)
## 100.0104
## 0.03961545
summary(y)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  99.95   99.98  100.00  100.01  100.04  100.09