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You would like to implement the Markowitz optimization for a portfolio consisting of all publicly traded U.S. stocks (approximately 20 thousand, including both exchange traded

You would like to implement the Markowitz optimization for a portfolio consisting of all publicly traded U.S. stocks (approximately 20 thousand, including both exchange traded and OTC stocks). This tasks requires obtaining approximately 200 million estimated covariances (i.e. one for each pair of stocks). What is the best course of action to obtain these inputs using statistical estimation?

a.

Increase the sample to span a decade or two and use a moderately high frequency (daily returns).

b.

Use monthly or weekly rates of return, but increase the sample to span many decades.

c.

Use a relatively short time-series (2-5 years), but dramatically increase the frequency (hourly returns or shorter).

d.

It is impossible to reliably estimate the inputs required to implement the Markowitz optimization for such a large portfolio.

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