standard deviations for mean vs for predictions

Question

I work in finance and wanted to ask a quick question regarding standard deviation of data sets. I have collected data sets over the last 10 years and would like to use them to make a prediction for the coming year. The question I want to answer is, what the value that has a 95% probability of not being exceeded is? As we know, this is exactly $$\overline{x}+2\sigma_{\overline{x}}.$$Each of the data has about the same standard deviation. Now we learned in university that the standard deviation of the mean is just $$\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}.$$But I then get an estimate for next year with a standard deviation that is much too low and thus a maximum value that is much too low in contrast to recent years. In my opinion, this should be the approximatly the same standard deviation. Do I simply have to take the mean value for the standard deviation for predictions? What is the difference?