I am trying to compute the variance-covariance matrix of my portfolio composed by some shares of different companies. I would select a time horizon of two years but for some shares of one company I don't have prices older than one year because the company was not already quoted in the market. What is the best thing to do? Am I forced to select a time horizon in which I have prices for all shares(one year)? In this case, is an historical series of only one year acceptable or is it too short?
I don't have a survey, but I think most people who look at the total returns (price and dividends) of stocks, look at 3-5 years of history. Depending on what you intend to do with your covariance matrix, 1 or 2 years of daily history may be too little.
It's quite normal that if you look at 3-5 years of history, some series will have some short gaps. There are many approaches for dealing with such gaps. (You can pretend that all the return happened at the end of the gap, or happened gradually during the gap, etc.)
But if a stock really does not have history long enough to be in your universe, then there's nothing you can do to make up the missing data. If the criterion for your portfolio is that a candidate stock must have $n$ years of history, then you just can't have a stock only with $n/2$ years.
The best way around it is not to use pairwise covariance of your stock, but to identify a few factors (such as French-Fama). Then even if you have a stock with a short history (because or recent IPO or corporate action), then you can estimate its beta's to the factors without messing up your other stocks.