I need to compute a covariance matrix using three years of stock returns from a portfolio which has a couple of stocks with only one or two years of history (being relatively new stocks).

Should I replace the missing data with zeroes, or should I omit the offending stocks from my VaR calc?

edit: I'm interested in knowing how other quants deal with this common occurrence. To put it in context, I'm the sole quant at an old-school, long-only stock-picking firm. I like to keep risk metrics like VaR simple enough to explain to my bosses, but they still need to be correct.

  • $\begingroup$ Theoretically in a Missing Data problem you are supposed to fill in the missing data not with zeros (yuck!) but with an 'optimal prediction' of the missing data. This could be done by measuring the Beta and Residual Risk of the new stock w.r.t the S&P, and assuming that when the stock did not exist it would have had the same $\beta$ and $\sigma_{\epsilon}$ $\endgroup$ – noob2 Mar 30 '17 at 13:19
  • $\begingroup$ Another approach is to calculate each element of the covariance matrix over the period when both stocks involved exist. The drawback is each element is then calculated over a different period of time so there is no guarantee that the resulting matrix is positive definite like a good covar matrix should be. People then use special methods to massage the matrix until it is positive definite again. $\endgroup$ – noob2 Mar 30 '17 at 13:26
  • $\begingroup$ I am sure this question has been asked before many times. $\endgroup$ – noob2 Mar 30 '17 at 13:40

There are several ways, but to keep things simple: use a factor model like single index model and you will reduce a lot this problem. If you have no data (very iliquid stock), consider using a proxy from average beta and residual risk for stocks in similar industry.


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