Is it possible to estimate the standard deviation of an investment's return after "y" years, if you know the investment's mean annual return and standard deviation? In other words, I understand how to estimate the probability that next year's return might be n standard deviations above the mean, or between +n and -n standard devations around the mean. But what if you bought and held that investment for y years. Is there a way you could estimate the standard deviation of the investment's value then? E.g., let's say that i put $10,000 into an index fund. That fund has an average return of 8%, and a standard deviation of 16%, and I plan to hold it for 20 years. According to Excel's FV function, the portfolio's expected value will be $46,609.57 by then.

Question about semi-sophisticated statistics and financial modeling - lets say you have N asset classes - each class has a mean rate of return and a standard deviation of returns. Also, assume you hold a portfolio comprised entirely of these N asset-classes, in certain proportions. How do you determine the probability that the portfolio might produce the a certain rate of return over P periods?