Given a set of returns, say 500 days, and a fixed portfolio construction, you can derive the 500 daily portfolio valuation changes.
You can easily measure the mean and variance of these valuation changes. Since this is a sample you are interested in the confidence of your estimators (i.e. the mean and variance).
One method that is often used is a resampling procedure called bootstrap sampling. Perform 1000 simulations by selecting 500 datapoinst from the original 500 datapoints (WITH replacement).
Each of the 1000 simulations will yield a different mean and different variance. You can estimate the variance of the means and the variance of the variances from this data.
You can read a little more about pros and cons of bootstrap sampling over at wikipedia.
A coin toss
Personally I think bootstrap sampling is an underappreciated/underused area of statistics. Let me give highlight a simple example.
Suppose you toss a coin 20 times and receive the result:
1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1
What does that tell us? It tells us the mean is 0.55 and the variance is 0.26.
But could my mean be wrong and how wrong could it be?
In this scenario we know the true probability of a coin toss is 50% and the distribution is binomial. But consider plotting the real and parametric distributions of outcomes compared with 200 bootstrap samples of 20 datapoints with replacement:
I think that's a powerful result from such a simple technique.