Estimating Portfolio Covariance with Assets of Unequal History Length
Summary
The document considers estimating a portfolio’s variance-covariance matrix when one holding has less price history, such as a recently listed stock. It cautions that a short sample may be inadequate for some intended uses, while noting that practitioners often examine several years of total-return history. The appropriate lookback depends on what the covariance estimate will support; the response gives no universal minimum sample length.
For occasional gaps in otherwise available return series, it mentions approaches that assign the gap’s return at its end or spread it across the gap. A genuinely unavailable pre-listing history cannot be reconstructed from the observed series. One alternative is a factor model: estimate the newer stock’s exposure to common factors, such as Fama-French factors, rather than relying only on pairwise historical covariance. This can incorporate a shorter-history stock, though the response does not provide a specific estimation procedure or assess model risk.
Key ideas
- The history length needed for covariance estimation depends on the portfolio decision it will inform.
- Longer return histories can still contain gaps that require an explicit treatment choice.
- A stock's pre-listing return history cannot be recovered from data that do not exist.
- Factor exposures can offer an alternative way to model a newer stock with limited history.
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# Covariance matrix for historical series w/ different start and end dates # Covariance matrix for historical series w/ different start and end dates 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? ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/59250 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.
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