How to calculate tracking error given mismatches in available data

Question

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the current relative weights and historical returns. However, for many of the stocks there are very few returns (<36 weeks).

What is the industry standard for dealing with mismatching data when estimating portfolio volatility or tracking error? Is it commonly accepted practice to use a shrinkage estimator (as in Ledoit and Wolf) on a covariance matrix estimated using all available data points?

I have 180 weekly returns for the vast majority of the stocks. But, the portfolio's largest relative positions are in stocks that have very little data (FB, LNKD, GRPN).

Answer 1

There are many techniques, but I would begin with Stambaugh Analyzing Investments Whose Histories Differ in Lengths. The full information maximum likelihood approach he describes basically involves regressing the short history series against the long history series to obtain the covariance with the longer history securities and adding back the covariance of the residual from the short history regression. I think there's some Matlab code that implements it in this package

Once you have the full covariance matrix, you can calculate the tracking error as normal.