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I have done a cross-sectional regression of time-series average returns on estimated Betas (over the same time horizon) to determine average premiums. So far so good. But I was told that the standard t-statistics can be biased, due to the fact that betas are estimated.

There is a solution by:

Shanken (1992) - On the estimation of beta-pricing models [Review of Financial Studies].

It does some small adjustments to the formula of the estimated covariance matrix. However I don't understand how to implement this in R. The paper is also very mathematical, but the solutions are supposed to be easy if you look e.g. at Cochrane Asset Pricing, chap 12 or http://www.uv.es/qf/06006.pdf. I cannot find anything close to that in the original paper though. I think the notation is very different.

Does anyone know how to do it, or has done it already? I needed the adjusted formula in my context (in-sample regression), or even better the R-code.

Rian1987
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1 Answers1

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I sent a similar question to the R-help mailing list only a few days ago. Today, I believe to have found an answer. See my post on Nabble: http://r.789695.n4.nabble.com/Calculate-Adjusted-vcov-Matrix-acc-to-Shanken-1992-Generated-Regressor-Problem-td4681404.html

My problem was not to include a coefficient of the first regression but the residuals. Still, my example seems to be easily adaptable to your case.

gung - Reinstate Monica
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philipp
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  • Welcome to the site, @philipp. An answer like this is fine, but note that CV is not a discussion forum. We aim to build a permanent repository of high-quality statistical information in the form of questions & answers--they aren't supposed to be chatty. Since you're new here, you may want to read out [about page](http://stats.stackexchange.com/about), which contains info for new users. There is also some information about answering questions on CV on our [help page](http://stats.stackexchange.com/help/on-topic). – gung - Reinstate Monica Dec 04 '13 at 14:53
  • Apologies, I just wanted to make sure Rian1987 got linked to a similar problem which I hope could be solved now. I wanted to comment but was unable to do so (due to a lack of reputation/ credit points?). Nevertheless, thank you for editing my post! – philipp Dec 04 '13 at 18:10
  • No problem, @philipp. Unfortunately, you can't comment everywhere until your reputation >50. – gung - Reinstate Monica Dec 04 '13 at 18:16
  • @philipp thanks for the link, maybe someone can clarify this for us ;) – Rian1987 Dec 09 '13 at 16:27