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Background

In Eric Zivot's analysis of factor models he uses three models

  • The sample (.sample)
  • Single index model (.si)
  • Barra factor industry model (.ind)
  • PCA model (.pca)

You can download his theory and notation macro models and theory and notation fundamental models as well as the analysis slides. I have a question on an analysis.

It's from a second year PhD course and I'm a BSc student but I have spent this week trying to understand the theory and code and I think I'm on my way.

Question

I want to interpret two things:

  1. The correlation matrix given by code plotcorr() i.e. in his slides page 7, 17, 36 for sample, .ind, .pca respectively.
  2. The portfolio weights he has calculated for min variance portfolio, given by code barplot(t(w.gmin.modelnamegoeshere)) i.e. page 7, 19, 39 for modelnames .sample, .ind, .pca respectively.

So I wonder: Given these plots 4 correlation plots and 4 portfolio weights plot, are any model preferable to another?

(Note that Zivot either forget or deliberately omit the .si models for plotcorr() and portfolio weights - it's in his code but didn't make it to the powerpoint.)

My guess

  1. For the first question, my guess is that you want to be close to the sample. Because we do cor(returns) for ".sample" ".si model" ".ind model" and ".pca model" and we wish to explain the return data with a model, so being similar to the sample is what we want. Here my eyes tell me .ind looks most like .sample and hence .ind model is better.
  2. For the second question, my first guess was that you want to be close to the sample for the same reason as above. But then I hesitaded. What we do here to find - given corr(returns) and returns - a minimum variance portfolio. So the sample is a benchmark and we wish to have better risk adjusted return. Which is better of Zivot's models? I don't know.
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