I have to work out a case study about principal component analysis of a interest rate portfolio.
I did nearly all the necessary steps, calculate covariance matrix, calculate eigenvalues and eigenvectors and so on.
Then I must hedge the portfolio and this is where Im stuck:
I) I selected 3 components to hedge, lets say i choose the 3M, 6M and 5Y swap as hedge. I formed the submatrix of eigenvectors calculated the inverse and the swap sensitvities.
II) To judge the efficiency of the hedge I shall calculate the variance of the unhedged and hedged portfolio. The unhedged is easy, I know it is just the Sum of the Eigenvalues multiplied by the square of the component sensitivities.
But how do I calculate the variance of the hedged portfolio?
Do i have to subtract the sensitivities from the hedge (from step I) from the sensitvities from the unhedged portfolio or just calculate the variance from the unhedged portfolio and the "sub"portfolio of the hedge and subtract this values.
Can you help me? thx