Variance with Percentages

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 © 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

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.

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

You’re welcome.