Apologies if this question doesn't belong here.
When performing mean-variance optimization on a portfolio of stocks, assuming the optimization and/or investment horizon is 30 days, should I compute the covariance matrix on rolling 30 day historical returns or on 30 day historical returns from non-overlapping periods? And what is the justification for whatever the answer is?
Using the former method (i.e. rolling), I'd have a lot more returns data points for the covariance matrix, whereas using the latter method (i.e. non-overlapping e.g. just month ends), I'd have far fewer data points for the covariance matrix.