Variance with Percentages

[Tartaglia]

Hello everyone,
I have some trouble understanding the solution to this exercide (provided by investopedia.com):
A sample of 50 stocks is drawn from a particular market in order to estimate its dividend yield. If the average dividend yield of the sample is 7.2% and its variance is 11.56%, what will be the estimated standard error of the probability distribution of the sample mean?
(a) 0.23
(b) 0.48
(c) 0.47


The solution is b), we simply divide the variance (11.56) by the number of observations (50) and then take the square root of that result.

Now, my question is this: given that the variance is provided in percent, I could have also divided (0.1156) through 50 and then take the square root, which yields 0.048. Typically, whenever you do this with other non-variance questions, you just have to multiply by 100 again to get the correct result. But here this does not work. Do I need to instead multiply by sqrt(100), since we are dealing with the variance here. I do vaguely remember some related rule from statistics, but google could not help me on this one (or I searched for the wrong terms). Can anyone help?

Thanks
Niccola

 

[S2000magician]

Nobody can help, unfortunately.
This is a problem with finance people in general: they do not know how to handle squares of percentages.
Often, for example, you’ll see a standard deviation of 9%, and a corresponding variance of 81. Stupid! It should be 0.0081 (= 0.09²). It’s off by a factor of 10,000.
You example is even worse: it’s off by a factor of 100, which makes no sense.
On the real exam you won’t see a situation like the one you describe – a variance being wrong by a factor of 100 – but you may well see one such as I described: a variance being off by a factor of 10,000.
There’s nothing you or I can do about it. Just beware.

 

[Tartaglia]

Thank you for your response S2000. I see your point and I will have to be particularly careful with these type of questions.

 

[S2000magician]

You’re welcome.