# Tag Info

13

The PCA analysis does not really tell you what the bonds do but it tells you how the rates move together. The variations of $n$ rates (i.e. 1 y, 2y, ...) are split up in (at first) abstract factors like $$\Delta R_i = \sum_{j=1}^n e_{i,j} f_j$$ where $\Delta R_i$ is the change in the rate $i$ and $f_j$ is factor $j$ and $e_{i,j}$ is the (factor loading=) ...

8

PCA(Principal Component Analysis) is the most interesting topic in QF. PCA is at the heart of quantitative data analysis. It is used in factor analysis, factor loadings, finding principal component of interest rate term structure for derivative and option pricing, data compression, eigenfaces( find the best match from a set of pictures with a , say, fuzzy ...

6

What you basically do here is a Principal Component Analysis (PCA). A good starting point in the financial sphere is Managing Diversification by Attilio Meucci (2010) Page 3: "The most natural choice of uncorrelated risk sources is provided by the principal component decomposition of the returns covariance [...] The eigenvectors define a set of N ...

3

After writing an email to Meucci directly, I posted the question in his LinkedIn Group ARPM - Advanced Risk and Portfolio Management. Below are his answer and the answer of other group members, which echo the answer and comments already given here on SE. Attilio Meucci Suppose that you are in an ideal world where you have a perfectly balanced panel of data ...

3

You will have to add some constraints to get the weight vector of the eigen vector of the smallest eigen values, otherwise 0 is a trivial solution. Without going in the details of handling those extra constraints, the reason why the vector space associated with the smallest eigen value is relevant is because if you express variance of your portfolio in the ...

1

It appears that changing the dataframe to values sorts this problem out. df = df.values before calculating the covariance matrix gives correct eigenvalues.

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