Can you help understand this? I understand how to calculate standard deviation: add up all the prices and take the mean, subtract each price from the mean and the square it and add everything and then divide by the number of observations, and lastly take the square root of that number. I calculated GE’s standard deviation (as well as threw the numbers into excel) at 2.05. I thought the standard deviation that was spit out was a percent. I know the standard deviation is not 2%… Any thoughts?

What’s time frame is your data?

Just one year, 252 observations.

The standard deviation is in the same units as your observations, in this case $/share. If you wanted to know the standard deviation of the average daily percentage return you would first have to transform your observations into daily returns.

So, if the mean is $15.29 and the standard deviation is $2.05, standard deviation would be: [(15.29+2.05)/15.29]-1 = 13.4% [(15.29-2.05)/15.29]-1 = 13.4% Thank you.

I just did the daily % returns and I came up with 2.1 this time…

Line up your daily % returns, then use =stdev() in excel

Sorry, but I get the same answer, 2.1 with “=stdev()” in excel…

Ah you have to multiply by the square root of the number of days to annualize the daily standard deviations

I guess I don’t remember doing that in Level 1 when calculating the stan. dev… Wouldn’t excel already do that for you if that was correct?

No - you’re calculating the daily standard deviation, because it’s based on daily returns. In level 1 you calculated annual standard deviations based on annual returns - so you didn’t have to annualize. It’s in the level three material BTW

Excel doesn’t know what type of data you are using (quarterly, weekly, monthly etc.) so you need to annualize it as art said. On level 1 you would have only been given annual returns so you wouldn’t need to do this. If you are still getting 2 you are probably not taking the daily returns and still running the function on the prices. Run the standard deviation function on the daily returns, then multiply by the sqroot of 252 to get annual STDEV. Did you pass level 1 or what?

Thank you. Yes I did, 2 years ago. And I don’t remember there being anything about annualizing by the square root of the number of observations.

oh, yes, when you scale standard deviation, you use the “square root of time” rule. That’s because in geometric brownian motion, the return scales with T (time) and so does variance. So since standard deviation is the square root of variance, you end up with the square root of time. Example: monthly return is 0.5%, monthly standard deviation is 2%. The projected annual return based on the monthly return would be 0.5% times 12 or 6%, and the annualized standard deviation based on the observed monthly stdev would be 2% times SQRT(12)… http://www.riskglossary.com/link/volatility.htm