Consider you have 4 assets
Astarted trading on 2 Jan 1990 (i.e. data is available since that point in time for every trading day until today)
Bstarted trading on 2 Jan 1995
Calso started trading on 2 Jan 1995
Dstarted trading on 2 Jan 2010
In the simplest method, you would just use the joint history of all assets beginning on 2 Jan 2010, maybe fill missing data due to different holidays on different exchanges and compute the sample variance-covariance (VCV) matrix.
But this way you would throw away the longer history of the assets
C resulting in a less stable VCV matrix.
Is there another way to come around the problem of estimating the VCV matrix for differing length financial time series? Can you e.g. construct the VCV matrix from pairwise covariance?